MANIPULATION AND ANALYSIS OF INTACT PROTEIN IONS …

MANIPULATION AND ANALYSIS OF INTACT PROTEIN IONS USING A PURELY

DUTY CYCLE – BASED, DIGITALLY OPERATED QUADRUPOLE MASS

FILTER (DQMF) AND ACCELERATION QUADRUPOLE

TIME-OF-FLIGHT (Q-TOF) MASS

SPECTROMETER

By

BOJANA OPACIC

A dissertation submitted in partial fulfillment of

the requirements for the degree of

DOCTOR OF PHILOSOPHY

WASHINGTON STATE UNIVERSITY

Department of Chemistry

MAY 2019

© Copyright by BOJANA OPACIC, 2019

All Rights Reserved

ii

To the Faculty of Washington State University:

The members of the Committee appointed to examine the dissertation of BOJANA

OPACIC find it satisfactory and recommend that it be accepted.

Peter T. A. Reilly, Ph.D., Chair

Brian H. Clowers, Ph.D.

Rock J. Mancini, Ph.D.

James A. Brozik, Ph.D.

iii

ACKNOWLEDGMENT

I would like to express my deepest gratitude to my advisor and mentor, Dr. Reilly, for

always encouraging me and believing in me. Thank you for the endless support and praise over

the past four years. Your passion for science and digital waveform technology has inspired me to

keep going, despite every obstacle that came my way. My success in graduate school is greatly

influenced by you, so thank you from the bottom of my heart! Thanks to all the group members

who helped me learn and who supported my efforts in the completion of this degree, especially

Dr. Nathan M. Hoffman and Adam P. Huntley.

Thanks to my committee members, Drs. Brian Clowers, Rock Mancini, and James Brozik.

I also want to thank the various administrative, facilities, and custodial staff without whom my

work wouldn’t be possible. Special thanks to Dave Savage from the machine shop.

I’m sincerely honored to have been selected as a recipient of Research Assistantship for

Diverse Scholars (RADS) by WSU graduate school and for Fowler Fellowship, Shelton, and Legg

scholarships by the Chemistry Department. Thank you for your generosity, which has undoubtedly

allowed me to successfully finish my graduate studies. Special thanks to Stacie Olsen for always

being ready and happy to answer any questions. Thanks to all the chemistry faculty that I had the

pleasure of knowing. I’d also like to acknowledge and thank Drs. Ken Nash and Kirk Peterson for

being one of the nicest and kindest chemistry professors.

I would also like to acknowledge faculty and staff at the St. Louis Community College. It

was thanks to them that I realized chemistry is the field I want to pursue. Back in 2006 I took Chem

101 class at Forest Park. I forgot the name of the instructor, but she was the one who started

everything. She was detailed, patient, tough but fair, and explained basic concepts so well, that I

had no choice but to love chemistry. Thank you and know that I remember you. Dr. Donna

iv

Friedman, Dr. Sue Clark, Dr. Tremont, and Adrienne Mazdra from Florissant Valley have all

played a part in my success and deserve gratitude. Thanks to Dr. Bethany Zolman from University

of Missouri St. Louis for giving me an opportunity to be a part of her lab and Dr. Marc Spingola

for being a fantastic teacher.

Thanks to Ernesto Martinez and Dan Pope for the help with the computer programing and

other school related assignments. You guys rock!

Finally, I would like to thank my family. My parents’ support knows no bounds and I would

like to thank them for that. I would have not made it without their love, encouragement and support.

Similarly, thanks to my friends in Pullman and St. Louis who had to listen to my struggles and

always encouraged me to move forward, especially Deni Romaniuk and Lelee Ounkham. Andrew,

Lelee and Dan, thank you for all the adventures we’ve had in the Pacific Northwest and here’s to

many more!

v

MANIPULATION AND ANALYSIS OF INTACT PROTEIN IONS USING A PURELY

DUTY CYCLE – BASED, DIGITALLY OPERATED QUADRUPOLE MASS

FILTER (DQMF) AND ACCELERATION QUADRUPOLE

TIME-OF-FLIGHT (Q-TOF) MASS

SPECTROMETER

Abstract

by Bojana Opacic, Ph.D.

Washington State University

May 2019

Chair: Peter T. A. Reilly

Mass spectrometry is one of the most widely used analytical tools for analysis of proteins

and other biological molecules. It provides information like mass, quantity and structure and it

can readily be coupled with other analytical methods. However, the traditional mass

spectrometry systems do have limitations regarding handling, resolving, and accurately

determining the mass of large, intact, low charge biomolecules. Digital quadrupole mass

spectrometers have demonstrated the ability of improved resolving power at high mass.

Additionally, digital waveform generation technology has advanced enough to provide first

comparator-based, duty-cycle controlled quadrupole mass filter. This instrument relays on

precise control of frequency and duty cycle instead of voltage, which means there is no

vi

theoretical upper mass limit that can be measured. It provides new methods of mass analysis,

which are inherently challenging for sinusoidally driven systems.

Chapter one introduces the concept and the abilities of the digital waveform technology.

It provides a background on the digital mass filter and compares it to the traditional operating

modes.

Chapter two discusses new approaches that maximize ion transport efficiency while

minimizing solvent clustering at the same time. It examines the conditions and methods for

optimal digital waveform operation of a mass filter to minimize solvent clustering.

Chapter three continues to explore capabilities of a digitally operated mass filter. The

measured response of the ion distribution as a function of axial ejection conditions is a focus of

this chapter. The energy imparted to the ion by the duty cycle-based ejection, is essentially

equivalent going to and out of the axial potential well.

Chapter four further explores digital waveform abilities. It is presented as a tutorial on

digital waveforms, stability diagrams and pseudopotential well plots. The experimental results in

stability zones A and B are presented along with advantages of mass filter operation without any

DC potential between the electrodes.

The final chapter experimentally demonstrates collision-induced dissociation of ions in a

digital linear ion trap. The isolation of a target ion is achieved in two steps followed by radial

excitation of ions by changing the duty cycle and/or frequency of the trap.

vii

TABLE OF CONTENTS

Page

ACKNOWLEDGMENT................................................................................................................ iii

ABSTRACT ................................................................................................................................... iv

LIST OF FIGURES ....................................................................................................................... ix

CHAPTER

CHAPTER ONE: INTRODUCTION TO QUADRUPOLE MASS FILTER AND

DIGITAL WAVEFORM TECHNOLOGY .........................................................................1

1.1 History and fundamentals of quadrupole mass filters ..............................................1

1.2 Digital waveforms ....................................................................................................5

1.3 Conclusion .............................................................................................................11

1.4 References ..............................................................................................................13

CHAPTER TWO: USING DIGITAL WAVEFORMS TO MITIGATE SOLVENT

CLUSTERING DURING MASS FILTER ANALYSIS OF PROTEINS .........................15

2.1 Attribution ..............................................................................................................15

2.2 Abstract ..................................................................................................................15

2.3 Introduction ............................................................................................................15

2.4 Experimental ..........................................................................................................19

2.5 Results and Discussion ..........................................................................................21

2.6 Conclusion .............................................................................................................26

2.7 Acknowledgements ................................................................................................26

2.8 References ..............................................................................................................27

CHAPTER THREE: IMPACT OF INJECTION POTENTIAL ON MEASURED ION

RESPONSE FOR DIGITALLY DRIVEN MASS FILTERS ...........................................29

viii

3.1 Attribution ..............................................................................................................29

3.2 Abstract ..................................................................................................................29

3.3 Introduction ............................................................................................................30

3.4 Experimental ..........................................................................................................32


3.6 Conclusion .............................................................................................................43

3.7 Acknowledgement .................................................................................................44

3.8 References ..............................................................................................................45

CHAPTER FOUR: DIGITAL MASS FILTER ANALYSIS IN STABILITY ZONES A

AND B ...............................................................................................................................47

4.1 Attribution ..............................................................................................................47

4.2 Abstract ..................................................................................................................47

4.3 Introduction ............................................................................................................47

4.4 Experimental ..........................................................................................................51

4.5 Axial trapping and ejection ....................................................................................53

4.6 Stability diagrams and radial well depth ................................................................57

4.7 Application of stability diagrams for mass filtering in stability zone A at a=0 .....65

4.8 Zone B evaluation ..................................................................................................68

4.9 Mass analysis in zone B .........................................................................................72

a) Results ................................................................................................................72

b) Discussion ..........................................................................................................76

1) Sensitivity ....................................................................................................76

2) Resolving power ..........................................................................................82

ix

4.10 Conclusions ..........................................................................................................83

4.11 Acknowledgement ...............................................................................................84

4.12 References ............................................................................................................85

CHAPTER FIVE: INTERFACING DIGITAL WAVEFORMS WITH ACCELERATION

QUADRUPOLE TIME-OF-FLIGHT (Q-TOF) MASS SPECTROMETER FOR

COLLISION-INDUCED DISSOCIATION (CID) OF BOVINE INSULIN ....................88

5.1 Attribution ..............................................................................................................88

5.2 Introduction ............................................................................................................88

5.3 Experimental ..........................................................................................................90


a) First isolation .....................................................................................................96

b) Second isolation .................................................................................................97

c) Excitation ...........................................................................................................98

5.5 Conclusion ...........................................................................................................101

5.6 References ............................................................................................................102

x

LIST OF FIGURES

Page

Figure 1.1: The arrangement of four electrodes of hyperboloidal shape .........................................1

Figure 1.2: Schematic of a modern-day quadrupole ........................................................................1

Figure 1.3: a) stability diagram in q,q space ....................................................................................4

b) Zoomed-in stability region A ..................................................................................4

Figure 1.4: Stability diagrams as a function of duty cycle ..............................................................4

Figure 1.5: Stability diagram in m/z vs frequency space .................................................................5

Figure 1.6: A timing diagram showing the generation of a waveform pair at 40% duty cycle .......7

Figure 1.7: The block diagram of a comparison unit with major functional blocks and

interconnecting signals labeled ......................................................................................8

Figure 1.8: 47/53 waveform duty cycle ...........................................................................................9

Figure 1.9: 40/40 waveform duty cycle .........................................................................................10

Figure 1.10: 60/60 waveform duty cycle .......................................................................................10

Figure 1.11: An example of a 32/32 comparator generated waveform .........................................11

Figure 2.1: Instrumental layout ......................................................................................................19

Figure 2.2: An example of a 32/32 comparator-generated waveform ...........................................20

Figure 2.3: A plot of the axis potentials for trapping and ejection ................................................22

Figure 2.4: Lysozyme spectra with 1V ejection beam energy .......................................................23

Figure 2.5: Lysozyme digital mass filter spectrum with -54V trapping and 1V ejection potential

........................................................................................................................................................25

Figure 3.1: Illustration of voltage comparator-based rectangular waveform generation ...............31

Figure 3.2: Dual quadrupole instrument illustration ......................................................................32

Figure 3.3: An example of a generic ejection waveform ...............................................................34

xi

Figure 3.4: DMF spectra of lysozyme trapped at -145V ...............................................................36

Figure 3.5: A series of lysozyme DMF spectra as a function of ejection time ..............................38

Figure 3.6: DMF spectra of lysozyme trapped at -160V ...............................................................42

Figure 4.1: Schematic diagram of the experimental apparatus ......................................................52

Figure 4.2: 13/13 duty cycle waveforms........................................................................................55

Figure 4.3: 57/57 duty cycle waveforms........................................................................................56

Figure 4.4: Mathieu stability diagrams of zone A in q,a space ......................................................62

Figure 4.5: a) The stability diagram in Mathieu space showing the A, B, C and D stable region

for a 50/50 (square) waveform ................................................................................64

b) The pseudopotential well depth for 100 V operation .............................................64

c) The m/z vs F stability diagram for 50/50 waveform ..............................................64

Figure 4.6: a) The stability diagram in Mathieu space showing the A and B stable regions for a

61.124/38.876 duty cycle waveform .......................................................................65

b) The 100 V operation pseudopotential well depth plot .............................................65

c) The m/z vs F stability diagram for 61.124/38.876 waveform .................................65

Figure 4.7: The DMF spectrum of TXA salts ................................................................................68

Figure 4.8: a) The stability diagram in Mathieu space showing the A and B stable regions for

75/25 duty cycle waveform .....................................................................................69


c) The m/z vs F stability diagram for 75/25 waveform ...............................................69

Figure 4.9: a) The stability diagram in Mathieu space showing the A and B stable regions for

73.06/26.94 duty cycle waveform ...........................................................................71


c) The m/z vs F stability diagram for 73.06/26.94 waveform .....................................71

Figure 4.10: a) The stability diagram in Mathieu space showing the A and B stable regions for a

76.50/23.50 duty cycle waveform ............................................................................72


c) The m/z vs F stability diagram for 76.50/23.50 waveform .....................................72

Figure 4.11: a) A close up of a 75/25 pseudopotential well ..........................................................73

b) DMF spectrum of lysozyme (zone B) at 75/25 waveform ....................................73

Figure 4.12: a) A close up of a 73.05/26.95 pseudopotential well ................................................74

xii

b) DMF spectrum of lysozyme (zone B) at 73.05/26.95 waveform ..........................74

Figure 4.13: a) A close up of a 76.6/23.4 pseudopotential well ....................................................75

b) DMF spectrum of lysozyme (zone B) at 76.6/23.4 waveform ..............................75

Figure 4.14: ESI DMF spectrum of asparagine in zone B .............................................................76

Figure 4.15: a) The equipotential contour plots of the end of a quadrupole ..................................78

b) Black arrows delineate the ion path through zone A .............................................78

Figure 4.16: The stability diagram depicting the A, B and C stability zones ................................80

Figure 5.1: Instrument schematic ...................................................................................................91

Figure 5.2: Stability diagram for 38/38 duty cycle. Broadband trapping ......................................94

Figure 5.3: Insulin trapping and excitation spectra ........................................................................95

Figure 5.4: Stability diagram for 38/38 duty cycle. First isolation ................................................96

Figure 5.5: Stability diagram for 42/36 duty cycle. Second isolation ...........................................97

Figure 5.6: Stability diagram for 42/36 duty cycle. Excitation......................................................98

xiii

Dedication

To my parents, Sretko and Milica Opačić.

1

CHAPTER ONE: INTRODUCTION TO QUADRUPOLE MASS FILTER AND DIGITAL

WAVEFORM TECHNOLOGY

1.1 History and fundamentals of quadrupole mass filters

The first appearance of a quadrupole mass filter happened in 1953 when Paul and

Steinwedel filed a patent for the arrangement of four electrodes at the University of Bonn [1-2].

Figure 1.1 shows the geometry of this device [1]. Four hyperbolic electrodes are arranged

symmetrically around a central axis

with 2r0 spacing between them. The

electric field within the mass filter is

created by connecting two opposite

rods together and applying an

alternating or RF potential of the

opposite phase to each pair, along

with direct current or DC potential of opposite polarity between the rod sets.

Modern-day mass filters are usually composed of four cylindrical metal rods as shown in

Figure 1.2 [3]. As with the original

mass filter created by Paul, the

opposing rods are connected

electrically with the two orthogonal

pairs receiving RF and DC potentials

that are of opposite phases and

opposite polarity from each other.

Figure 1.1: The arrangement of 4 electrodes of

hyperboloidal shape at a distance of r0 from the x

axis [1-2]

Figure1.2: Schematic of a modern-day quadrupole

[3].

2

Quadrupoles are routinely used as mass spectrometers, as a part of tandem mass spectrometry,

and as ion guides or collisional cells.

The fields created by the potentials applied to the electrodes of a quadrupole mass filter

(QMF) affect the trajectories of the ions introduced into the instrument. Some ions have unstable

trajectories and are lost by the collision with the rods. Other ions that are recorded on a detection

system are said to have stable trajectories. The stable path of an ion with a certain mass to charge

ratio (m/z), depends on the RF potential (V), its frequency (Ω), and the ratio of the amplitudes

between the RF and DC (U) potentials [4]. When U=0, a wide band of m/z values is transmitted

but by increasing the ratio of DC to RF potentials, the resolution can be increased until only

single values of m/z have stable trajectories. A spectrum of different m/z ions can be generated

by scanning the RF and DC voltages while keeping their ratio fixed with a constant drive

frequency.

The ion trajectories in a sinusoidally oscillating quadrupolar field can be solved by the

Mathieu equation. The more general, Hill equation, can be used to solve the ion motion in any

periodically oscillating quadrupolar field. One of the methods used to solve these equations is the

matrix method, first developed by Pipes [5] and later by Richards et. al [6] and Sudakov et. al

[7].

All the equations for the ion motion are examples of Mathieu equation which has a

general form characterized by parameters a and q. The parameters a and q are functions of U and

V, respectively,

𝑎 =8𝑧𝑒𝑈

𝑚𝑟ₒ²Ω² (1)

3

𝑞 = −4𝑧𝑒𝑉

𝑚𝑟ₒ²Ω² (2)

where z is the number of elementary charges on the ion, e is the elementary charge, m is the mass

of the ion, ro is the quadrupole radius, Ω is the angular frequency of the quadrupolar field, V is

the zero to peak RF voltage, and U is the DC potential between the electrodes.

The parameters a and q determine whether the solutions to the ion motion equations are

stable or not along each axis independently. In other words, they determine whether the

displacement along each axis passes periodically through zero, in which case the solution or ion

motion is stable, or whether the displacement increases to infinity, giving an unstable ion motion

that can no longer be confined by the device. Stability diagrams are defined in a, q space, and the

ion motion is depicted as stable only when the ions are stable in the x and y directions

simultaneously for the 2D ion traps. The x and y stability diagrams must overlap. Figure 1.3 [3]

shows the a,q space stability diagram. It depicts regions where there is stable overlap and labels

them as A, B, C, and D. Most mass analyzers in use today operate in the stability zone A (Figure

1.3 (b)) [3].

4

Standard sinusoidal instruments operate on resonantly tuned circuits, so the angular

frequency (Ω) is fixed. This results in universal stability diagrams. However, the stability

diagrams for digitally operated devices change when the duty cycle changes. Manipulation of

duty cycle is necessary for ion isolation, axial trapping and ejection, and excitation. Our group

created spreadsheets

for easy calculation

of stability diagrams

for digital ion traps

and guides [8].

Examples of duty

cycle based stability

diagrams can be seen

in Figure 1.4 [8].

Figure 1.3: (a) Stability diagram in a, q space. Overlap of the shapes represents stable

regions. (b) Zoomed-in stability region A [3]

Figure 1.4. Stability diagrams as a function of duty cycle (a) 50%

duty cycle, (b) 60% duty cycle and (c) 40% duty cycle

5

From an analytical point of view,

stability diagrams in a, q space are not

practical. For this reason, our group

developed a more user friendly, m/z vs

Frequency diagram (Figure 1.5), where

the operating conditions can be changed

and the corresponding change in the

stability diagram can be observed [8].

Since there is no DC potential between

the waveforms, the parameter a is equal

to zero.

As previously mentioned, a mass spectrum from a mass filter is traditionally generated by

scanning the RF amplitude and DC voltage while keeping their ratio fixed. This configuration

limits the m/z values that can be measured due to the maximum RF amplitude that can be applied

before electrical breakdown occurs [9]. Consequently, the majority of the commercial

quadrupole mass filters can measure ions only up to m/z of 2000 [9]. If the higher masses are to

be measured, the RF frequency has to be lowered, which would require the construction of a new

resonant circuit. By lowering the frequency at the same ion beam energy, the ions would

experience lower number of RF cycles as they move through the QMF, which in turn decreases

the resolving power [10]. In addition to decreasing resolving power, lowering the RF frequency

also lowers the signal intensity by decreasing the acceptance area at the entrance of the QMF

[10].

Figure 1.5. Stability diagram in m/z vs

frequency space. Black dot represents an ion of

a certain m/z at the edge of the stability region.

6

Most amplitude scans on QMFs are done where the potential varies sinusoidally over

time. However, they can also be done with any non-sinusoidal, periodic, waveform. Richards,

Huey, and Hiller were the first to use square waves in 1973 (Richards). Their aim was to

introduce constant time ratios instead of constant voltage ratios normally used [11]. The

technology went virtually unnoticed until 2001 when Li Ding presented the operation of digital

ion traps with variable frequency at the 49th conference on mass spectrometry in Chicago [12].

Ding’s further work showed the potential to extend the working mass range with use of digital

waveform technology [13]. Soon after, his work along with Brancia’s showed electron capture

dissociation and ion isolation by manipulating digital waveforms [14,15]. Work in our group

demonstrated various ion manipulation and fragmentation capabilities using digital waveform

technology including development of novel ion fragmentation techniques [16] and

preconcentration of ions in a digital linear ion trap [17].

Low voltage waveforms used to drive digitally operated ion traps and guides have been

generated by counting edges of a fast master clock. The examples on how low voltage

waveforms are produced can be found in literature [18]. Duty cycle control, based on clock edge

counting, is limited by the integer number of clock cycle counts that create a rectangular wave

[19]. Due to this limitation, the development of a purely duty cycle-based mass filter was

hindered until our group developed a comparator-based waveform generation system [20]. The

work in this dissertation demonstrates performance and capabilities of a purely duty cycle-

controlled, digital mass filter, a first of its kind.

1.2 Digital waveforms

7

Our lab introduced a new method of waveform comparison to produce low voltage digital

waveforms to operate the digital quadrupole mass filter [20]. This method works by comparing a

static DC level to a periodic waveform to produce an output waveform as seen in Figure 1.6. The

block diagram describing major functional blocks in waveform generation can be seen in Figure

1.7.

Figure1.6: A timing diagram showing the generation of a waveform pair at

40% duty cycle. A comparison of the sine wave with the superimposed blue

and red DC references produces output waveforms A and B. The centerline

denotes the center of the sinusoid oscillation [20].

8

Direct

digital synthesis

(DDS) is used to

generate

rectangular waves

with variable

frequency and duty

cycle [20]. This

type of technology

is a frequency synthesizer where waveforms can be generated from a single based frequency and

they are widely used in digital ion traps [13]. In our group, low voltage waveform generation was

accomplished by comparing the DDS generated sine wave to the digital-to-analog converter

voltages, or DAC generated DC level (see Figure 1.6). This method of waveform generation

provides duty cycle resolution previously unavailable by traditional methods like clock edge

counting [20]. The duty cycle of each output waveform is independently controlled by the DAC

output DC comparison level. For example, waveform A is produced by comparison of the blue

DC level to the SINE wave and it produces a high-level output when SINE is of greater

amplitude than the DC level (t0 to t1). In the similar way, waveform B is produced by comparison

of the red DC level to the SINE wave and generates high level output when SINE is of lower

amplitude than the DC level (t2 to t3). Equations 3 and 4 determine the DC comparison levels for

waveforms A and B, respectively [20].

𝑉𝑟𝑒𝑓𝑎 = cos(𝜋𝛿) 𝐶𝑎𝑚𝑝 + 𝐶𝑜𝑓𝑓𝑠𝑒𝑡 (3)

Figure 1.7: The block diagram of a comparison unit with major

functional blocks and interconnecting signals labeled [20].

9

𝑉𝑟𝑒𝑓𝑏 = cos (𝜋(1 − 𝛿)𝐶𝑎𝑚𝑝 + 𝐶𝑜𝑓𝑓𝑠𝑒𝑡 (4)

Where δ is the duty cycle, Camp is the sine amplitude and Coffset is the correction for sine

offset.

The two waveforms in Figure 1.6 produce quadrupolar field from t0 to t1 and t2 to t3 since

one waveform is high and the other one is low. Time periods from t1 to t2 and t3 to t4 produce non

quadrupolar fields since both waveforms are at the same potential. A more detailed explanation

follows below.

In the following figures, only the output waveforms generated by the comparator unit are

shown and they are overlaid. Let’s say a user demands a duty cycle of 47/53 (Figure 1.8). This

means that 47% of the time

the output waveform A is

high and for 53% of the

time, it’s low. The same is

true for the waveform B but

in the opposite phase – it’s

high for 53% of the time and

low for 47% of the time. The

applied field is purely

quadrupolar since the sum of the duty cycles is equal to 1, which means there is no overlap

where the two waveforms are of equal amplitude. In terms of ion stability, this field confines

Figure 1.8: 47/53 waveform duty cycle. Both are equal

amplitude but opposite phases.

10

ions radially (x and y directions) and there is no axial potential (in the z direction), provided the

applied voltages are of the equal amplitude.

Waveform duty cycle

can also be changed to affect

the ion stability along the z

axis. Figure 1.9 shows the

40/40 duty cycle waveforms.

For 40% of the time the two

waveforms are high and for

60% of the time they are low.

This means that there is a time

period during which both of the waveforms are low, creating a negative potential between the

rods and the end caps that traps the ions. This is called axial trapping and it occurs when the sum

of the duty cycles is less than

one and the applied waveforms

are of equal but opposite

amplitudes. Alternatively,

when the sum of the duty cycles

is greater than one, 60/60 duty

cycle, a net positive axial

potential is created (Figure

1.10) that ejects the ions. In

both instances, the duty cycles

Figure 1.9: 40/40 waveform duty cycle. Trapping

waveform. Both waves are low for 20% of the time.

Figure 1.10: 60/60 waveform duty cycle. Ejecting

waveform. Both waveforms are high for 20% of the time.

11

of the waves are the same and there is no high mass boundary created that narrows the range of

stability. Therefore, the ions are axially confined or ejected on-demand without greatly changing

the radial stability. The switching of the applied waveforms is instantaneous, and this speed

cannot be matched by sinusoidal waveform technology. Ion handling demonstrated by DWT

takes advantage of the ability to change these parameters rapidly at will [19].

The time-weighted average of the DC axis potential, caused by the duty cycle, can be

calculated by:

𝑉𝑎𝑥𝑖𝑠 = 𝛴ₙ𝑡ₙ (𝑉₁,ₙ+𝑉₂,ₙ

2) (5)

Where V1,n is the voltage of the first

rod pair during the nth constant

voltage segment of the rectangular

pair of waveforms. V2,n is the

second rod pairs’ voltage during the

nth constant voltage segment of the

two waveforms. Figure 1.7 shows

the definition of the constant

voltage time segments. This

equation for calculating DC axis potential is only applicable when Mathieu parameter a is equal

to zero.

1.3 Conclusion

Figure 1.11. An example of a 32/32 comparator-

generated waveform that defines the constant voltage

segments of the waveform, t1, t2, t3, and t4. V+ and V-

are the power supply voltages [19].

12

Digital waveform technology is arguably the most important driver of the ability to

analyze high mass ions. All other commercial mass spectrometer technology uses sinusoidally

driven traps, guides, and filters and therefore have a limited mass range. Only DWT has the

ability to vary the frequency so that it can be used to analyze the entire range of protein masses

while reducing the complexity and the cost of the hardware. Some examples of work already

accomplished by DWT include: increased mass range [21]; enabling the small and large ions to

be analyzed on the same instrument [22],; analysis of singly charged, intact protein markers with

high signal-to noise ratio [22]); it provides the ability to trap millions of ions at any value of m/z

[23]); and preconcentration and charge state isolation of large ions [17]. Work in this disertation

aims to expand utilization and capabilities of digital wavefrom technology on a purely duty

cycle-controlled digital mass filter.

13

1.4 References

1. Paul W. and Raether M.,“Daselektrischemassenfilter,” Z.Phys.140, 262– 273 (1955).

2. Paul W., Reinhard H. P., and U. von Zahn, “Das elektrische massenfilter als

massenspektrometer und isotopentrenner,” Z. Phys. 152, 143–182 (1958).

3. March, R., & Todd, John F. J. (2005). Quadrupole ion trap mass spectrometry (2nd ed.,

Chemical analysis; v. 165). Hoboken, N.J.: J. Wiley.

4. Douglas D. J., “Linear quadrupoles in mass spectrometry,” Mass Spectrom. Rev. 28,

937–960 (2009).

5. Pipes L. A., “Matrix solution of equations of the Mathieu-Hill type” Journal of Applied

Physics 24 (1953) 902-910

6. Richards J. A., Huey R. M., and Hiller J., “Waveform parameter tolerances for the

quadrupole mass filter with rectangular excitation,” Int. J. Mass Spectrom. Ion Phys. 15,

417–428 (1974).

7. Konenkov, N.V., Sudakov, M., Douglas, D.J.: “Matrix methods for the calculation of

stability diagrams in quadrupole mass spectrometry.” J. Am. Soc. Mass Spectrom. 13,

597-613 (2002).

8. Brabeck, G. F., Reilly, P. T. A., “Mapping ion stability in digitally driven ion traps and

guides,” Int. J. Mass Spectrom. 364, 1-8 (2014)

9. Shinholt, D. L., Anthony S. N., Alexander A. W., Draper B. E., Jarrold M. F.:“A

frequency and amplitude scanned quadrupole mass filter for the analysis of high m / z

ions. Review of Scientific Instruments, 85(11), 113109/1-113109/9 (2014)

10. Dawson P. H., Quadrupole Mass Spectrometry and Its Applications (Elsevier,

Amsterdam, 1976).

11. Richards J. A., Huey R. M., and Hiller J., “A new operating mode for the quadrupole

mass filter,” Int. J. Mass Spectrom. Ion Phys. 12, 317–339 (1973).

12. Ding L., Gelsthrope A., Nutal J., Kumashiro S.: “Rectangular Wave Quadrupole Field

and Digital QMS Technology”. 49th American Society for Mass Spectrometry Conference

on Mass Spectrometry and Applied Topics. Chicago, Illinois. 2001

13. Ding L., Sudakov M., Brancia F. L., Giles R., and Kumashiro S., “A digital ion trap mass

spectrometer coupled with atmospheric pressure ion sources,” J. Mass Spectrom. 39,

471–484 (2004).

14

14. Ding L., and Brancia F. L.: "Electron Capture Dissociation in a Digital Ion Trap Mass

Spectrometer." Analytical Chemistry 78.6 (2006): 1995-2000 Web (2006).

15. Brancia F. L., McCullough B., Entwistle A., Grossmann J. G., and Ding L., “Digital

asymmetric waveform isolation (DAWI) in a digital linear ion trap,” J. Am. Soc. Mass

Spectrom. 21, 1530–1533 (2010).

16. Brabeck G. F., Chen H., Hoffman N. M., Wang L., and Reilly P. T. A., “Development of

MS^n in Digitally Operated Linear Ion Guides,” Analytical Chemistry, vol. 86, pp. 7757-

7763, Aug. 2014.

17. Gotlib, Z.P., Brabeck, G.F., Reilly, P.T.: “Methodology and characterization of isolation

and preconcentration in a gas-filled digital linear ion guide”. Anal. Chem. 89, 4287–

4293 (2017)

18. Koizumi H., Jatko B., Andrews W. H. Jr., Whitten W. B., and Reilly P. T. A.:“A novel

phase coherent programmable clock for high precision arbitrary waveform generation

applied to digital ion trap mass spectrometry,” Int. J. Mass Spectrom. 292, 23–31 (2010).

19. Brabeck G. F., Koizumi H., Koizumi E., and Reilly P. T. A.: “Characterization of

quadrupole mass filters operated with frequency-asymmetric and amplitude-asymmetric

waveforms,” International Journal of Mass Spectrometry, vol. 404, 8-13, (2016)

20. Hoffman N. M., Gotlib Z. P., Opacic B., Clowers B. H., and Reilly P. T. A.: “A

Comparison Based Digital Waveform Generator for High Resolution Duty Cycle”

Review of Scientific Instruments 89, 084101 (2018).

21. Chen, H., Lee, J., Reilly, P.T.A.: “High-resolution ultra-high mass spectrometry:

increasing the m/z range of protein analysis”. Proteomics. 12, 3020–3029 (2012)

22. Lee, J., Chen, H., Liu, T., Berkman, C.E., Reilly, P.T.A.: “High resolution time-of-flight

mass analysis of the entire range of intact singly-charged proteins”. Anal. Chem. 83,

9406–9412 (2011)

23. Wang, X., Chen, H., Lee, J., Reilly, P.T.A.: “Increasing the trapping mass range

to m/z = 10(9)- a major step toward high resolution mass analysis of intact RNA, DNA,

and viruses”. Int. J. Mass Spectrom. 328, 28–35 (2012)

15

CHAPTER TWO: USING DIGITAL WAVEFORMS TO MITIGATE SOLVENT

CLUSTERING DURING MASS FILTER ANALYSIS OF PROTEINS

Bojana Opačić, Nathan M. Hoffman, Zachary P. Gotlib,

Brian H. Clowers and Peter T. A. Reilly*

Department of Chemistry, Washington State University

February 17, 2018

2.1 Attribution

This chapter was adapted with permission from: Bojana Opačić, Nathan M. Hoffman,

Zachary P. Gotlib, Brian H. Clowers, and Peter T. A. Reilly. “Using Digital Waveforms to

Mitigate Solvent Clustering During Mass Filter Analysis of Proteins.” Journal of the American

Society for Mass Spectrometry. (2018) 29:2081-2085 Copyright 2018, American Society for

Mass Spectrometry. BO was first author for this manuscript. NMH developed comparator-based

waveform generator. ZPG wrote the front-end computational tools. BO performed the

experiments. BO and PTAR wrote the manuscript. BO, NMH, BHC, and PTAR edited and

revised the manuscript.

2.2 Abstract

With advances in the precision of digital electronics, waveform generation technology

has progressed to a state that enables the creation of m/z filters that are purely digitally-driven.

These advances present new methods of performing mass analyses that provide information from

a chemical system that are inherently difficult to achieve by other means. One notable

characteristic of digitally-driven mass filters is the capacity to transmit ions at m/z ratios that

16

vastly exceed the capabilities of traditional resonant systems. However, the capacity to probe ion

m/z ratios that span multiple orders of magnitudes across multiple orders of magnitude presents a

new set of issues requiring a solution. In the present work, when probing multiply charged

protein species beyond m/z 2000 using a gentle atmospheric pressure interface, the presence of

solvent adducts and poorly resolved multimers can severely degrade spectral fidelity. Increasing

energy imparted into a target ion population is one approach minimizing these clusters, however,

the use of digital waveform technology provides an alternative that maximizes ion transport

efficiency and simultaneously minimizes solvent clustering. In addition to the frequency of the

applied waveform, digital manipulation also provides control over the duty cycle of the target

waveform. This work examines the conditions and approach leading to optimal digital

waveform operation to minimize solvent clustering.

2.3 Introduction

The idea of using digital waveforms for mass filter analysis is attributed to Richards ca

1973.[1] Unfortunately, the technology at the time to support digital waveform based mass filter

analysis could not really compete and overtake the already established sinusoidal technology.

With the advent of direct digital synthesis (DDS), high voltage field effect transistors (HV-FET)

and field programmable gate arrays (FPGA) in the 1990’s, the technology to enable digital

waveform based mass analysis became available. Digital waveform technology (DWT) was first

used to create a square wave driven 3D ion trap by Shimadzu and introduced in 2001.[2] Over

the next five years Shimadzu developed digital ion trap technology [3-6]; however, a commercial

product was never produced. Though digital in nature, the approach and specific technology

employed did not allow the square wave driven ion trap to outperform its sinusoidal waveform

17

technology (SWT) driven counterpart. Presumably, SWT traps were too entrenched in the

market and the technology was too established for the square wave trap venture to be profitable.

Nonetheless, DWT had three notable theoretical advantages compared to SWT that remained

unexplored. The first is the high frequency resolution over an extremely wide band that is

available through DDS that enables a broad range of m/z to be probed with a single system.[7]

Next is the ability to change the radial [8-10] and axial [11] stability of the ions on demand by

changing the waveform duty cycle. The third, and perhaps most subtle capability enabled by

DWT, is the agility of the waveform generation system. Waveforms can be changed

instantaneously and then changed again with the only limitation being the speed at which the

waveform parameters may be transferred and registered on the DDS hardware. To be clear, the

speed of the second change is what we refer to as agility.[12] The agility of the current

waveform technology used in this work allows changes to be accomplished within one waveform

cycle and allows the user to probe the impact of differing rates of excitation of the ions. This

provides noticeable advantages with respect to ion excitation [8], isolation [13] and even mass

analysis.[14]

To ease the implementation and adoption of DWT, careful control of the duty cycle (i.e.

the ratio of the high and low states of the waveform) supported the development of a digitally

controlled mass filter. [15, 16] Historically, the method for generating rectangular waves was

based on using DDS to create a frequency variable clock to operate digital counters. Using this

approach, the duty cycle resolution was inherently limited by the integer number of clock cycle

counts that created the rectangular wave. Despite the limitation of this generation method, the

concept of using the duty cycle to create a narrowed mass window was first demonstrated by

18

creating a crude mass filter to analyze IgG [17] and later, that same year, the duty cycle was used

by Shimadzu to isolate charge states of cytochrome c.[18] Counter based rectangular WFG was

also used in combination with frequency hopping to produce a narrow window of masses

isolated within a linear ion guide.[13] This process was good enough to produce a credible, albeit

slow, mass filter.

More recently, our group reported a comparator based method of rectangular waveform

generation that provides superior duty cycle resolution compared to the initial reports limited by

integer multiples of the waveform clock.[15, 16] Presently, the rectangular wave is created by

comparing the highly accurate DDS sine wave output with a potential provided by an 18-bit

digital to analog converter (DAC). The waveform duty cycle changes precisely with the change

in the DAC output. This method provides sufficient duty cycle resolution to create purely digital

mass filters and provides new methods of trapping and mass analysis.

Digitally driven mass filters extend the mass range beyond the currently available

technology. With this increase in range, lower charge states of proteins and multimers are easily

observed. These species tend to bind solvent better than higher charge state ions presumably

because they are less denatured by greater charge-charge interactions. In this manuscript, we

demonstrate a combination of digital ion trapping and mass filter methods that can be used to

greatly minimize the presence of solvent adducts during the mass filter analysis of intact proteins

using standard quadrupole rods.

19

2.4 Experimental

In this work lysozyme

was used to demonstrate

mass filter analysis of

intact proteins. It was

purchased from Sigma

Aldrich company (St.

Louis, MO) and used

without further

purification. 50% methanol/ 50% water (both HPLC grade and both from Fisher Chemical,

Waltham MA) was used dissolve to dissolve the lysozyme and produce a 6 µM solution. No

acid was added to the solution in order to shift the mass distribution to lower charge states. The

instrument used in this effort is depicted in Figure 1. The sample was introduced by electrospray

ionization using the commercial fused silica capillary 30 ± 2 µm tip (New Objective Co.) with an

applied potential of +2600 V relative to the pinhole inlet. Sample solutions were pneumatically

pushed through the capillary at 1 psig. Ions enter the instrument through a 300 µm diameter thin

plate orifice and expand within a digitally-operated ion funnel operated at 500 kHz and 48Vp-p

with a -50 VDC potential across the funnel in a differentially pumped chamber at approximately

1.3 Torr.[19] The AC and DC fields of the funnel collimate and push the ions toward the exit

orifice and into a digitally-operated ion guide at 10 mTorr.

Figure 2.1: Instrumental layout detailing a stacked ring ion

funnel which transitions into a ion guide which itself is digitally

driven. The first ion guide can also serve as an ion trapping

device prior to mass filtering in the second quadrupole.

20

The guide is driven by a pair of

high voltage waveforms created by two

separate pulsers, one for each electrode

pair. The pulsers are essentially high

voltage switches that toggle the output

from high voltage DC power supplies.

The power supplies were maintained at

a constant difference of 300V. The duty

cycle of a waveform is defined by the percentage of the cycle that the waveform is in the high

state. To achieve trapping and m/z filtering, the waveforms applied to each pair of electrodes of a

quadrupole guide or filter are defined by a pair of duty cycles, the percentages of time the

waveforms are in the high states. For axial trapping waveforms, the duty cycle values add to less

than 100 %, whereas duty cycle values for ejection add to greater than 100 %. In these

experiments, the trapping duty cycle was set to 32/32 and the trapping time was held constant at

68 ms. The 32/32 axial trapping waveforms are depicted in Figure 2 to illustrate the waveform

nomenclature used. The values tn define the four period fractions of constant potential during the

waveform. The ejection duty cycles were changed from 50/50 to 80/80 in increments of 10,

while maintaining a constant ejection axis potential of 1 V. To maintain the constant ejection

axis potential with the changing duty cycle, the pulser power supply voltages where changed to

compensate for the duty cycle induced axis potential shift. The trapping axis potential changes

while at a constant trapping duty cycle because of the change in the pulser power supply

potential. The time weighted average of the DC axis potential for trapping or ejection is given

by:

Figure 2.2: Depicts an example of a 32/32

comparator generated waveform that defines the

constant voltage segments of the waveform, t1, t2,

t3 and t4. V+ and V- are the power supply voltages.

21

𝑉𝑎𝑥𝑖𝑠 = ∑ 𝑡𝑛 (𝑉1,𝑛+𝑉2,𝑛

2)𝑛 , (1)

where V1,n is the voltage of electrode pair 1 during the nth constant voltage segment of the

rectangular waveform pair. V2,n is the voltage on electrode pair 2 during the nth constant voltage

segment of the waveforms (see Figure 2 for the definition of the constant voltage time segments).

This equation defines the DC axis potential for any rectangular waveform pair when the Mathieu

parameter a = 0. The digital mass filter (DMF) had zero axis potential and the duty cycle applied

to it was 61.1/38.9. The ions exiting the DMF impacted into the conversion dynode at

approximately –7000 V. The converted charges were detected with an electron multiplier. The

amplifier gain was set to 1x108.

2.5 Results and Discussion

There is a limited mass range for SWT driven analyzers that is defined by the frequency of

the resonantly tuned rf driving circuit. For commercial triple quadrupole mass spectrometers,

2000 to 3000 mass units is the general upper mass limit because they scan the voltage at fixed

frequency. To broaden the mass range of SWT driven instruments, multiple resonantly tuned rf

driving circuits (i.e., multiple WFGs) would be required to increase the range by an order of

magnitude. Implementation of multiple driving circuits is difficult to orchestrate and more

expensive. On the other hand, because DWT scans the frequency while fixing the voltage, the

m/z that can be observed is limited only by the ionization source and transfer optics. In fact,

digital mass filter analysis (albeit poorly resolved because of the limitation of the WFG at the

time) has been demonstrated to m/z 1 x 106 and the range was only limited by the detector

sensitivity.[17]

22

In this work, we present the digital

mass filter spectra of lysozyme taken as a

function of duty cycle trapping axis potential

and the same ejection axis potential Vaxis or

beam voltage into an awaiting digital mass

filter. The ions were axially collected and

trapped in the first quadrupole for 68 ms

with a broadband 32/32 trapping duty cycle

waveform and subsequently axially ejected

into the mass filter with varying ejection duty cycles. For reference, Figure 2 illustrates a

comparator generated 32/32 waveform. The axial beam energy at ejection was maintained at 1 V

by adjusting the DC power supplies (V+ and V-) that drive the high voltage pulsers. Because the

axis potential of the mass filter was maintained at 0V, the beam energy (voltage) at ejection is

defined by the time weighted average of the DC axis potential calculated in equation (1). Figure

3 presents the axis potentials during axial trapping of the ions in the first quadrupole and

subsequent ejection of the trapped ions into the digital mass filter. Because the axis potential at

ejection is maintained at 1V the power supply potentials, V+ and V-, have to be adjusted to offset

the change made by changing the ejection duty cycle. These power supply voltage changes also

change the axis potential during trapping in the manner described by the above equation. The

axis potentials and corresponding power supply voltages are shown in Figure 3. Figure 2 shows

an example of comparator generated waveforms to define the constant voltage segments of the

waveforms. The t1 and t3 segments V1n and V3n are V+ and V- and vice versa, while during t2 and

Figure 2.3: A plot of the axis potentials for

trapping and ejection for 50/50, 60/60, 70/70

and 80/80 duty cycle ejection. A 32/32

trapping duty cycle was used yielding a -53, -

83, -113 and -143V axis potentials during

collection, respectively.

23

t4 they are at V- to create axial trapping waveform conditions (They would be at V+ during axial

ejection).

Figure 4 presents the spectra of lysozyme injected into the digital mass filter with (a) 50/50, (b)

60/60, (c) 70/70 and (d) 80/80 duty cycle and 1 V beam energy. The axis potentials during the

68 ms trapping period are (a) -53V, (b) -83V, (c) -113V and (d) -143 V. The processes of

trapping and ejection represent two relatively large changes in the axis potential for each

presented spectrum. The 50/50 duty cycle ejection spectrum shown in Figure 4 (a) presents clear

formation of solvent adducts with the intact protein ions as evidenced by the broadening of the

Figure 2.4: Lysozyme spectra at (a) 50/50, (b) 60/60, (c) 70/70 and (d) 80/80 duty cycle eject

waveform with 1V beam energy. Changing the trapping well depth with increasing ejection

duty cycle decreases solvent adducts.

24

mass peaks. Solvent adduction is clearly charge state dependent because the lower m/z (higher

charge) ions demonstrate much narrower peak widths.

The electrosprayed solution was 6 µM in a denaturing 50% water 50% ethanol solution

with no acid added. These ESI conditions were selected to yield lower charge state (higher m/z)

distributions. The increased concentration of the working solution was chosen to promote the

formation of multimeric species. The charge states have been labeled for each peak as were the

positions of the multimer ions up trimer ions. Although there is evidence of higher order

multimers as revealed by the unlabeled peaks in the spectra. Only the dimer and trimer ion

positions were labeled with ‘D’ and ‘T’, respectively. Multimeric species are prominently

observed in the spectra displayed in Figures 4 and 5 presumably because no acid was added to

the electrosprayed solution. A 6 µM solution of lysozyme does not normally yield such large

concentrations of multimers when acid is added.

It is also worth noting that the presence and distribution of such multimers and charge

states were manipulated using DWT technology in a fashion unique to this mode of mass

filtering. As the duty cycle of the ejection and the depth of the axial trapping well increases in

the spectral series, the presence of solvent adducts decreases as does the larger charge state

multimers. Moreover, there appears to be a shift to lower charge state multimers as evidenced by

the emergence of the band of peaks above m/z 5,000 for the 80/80 duty cycle spectrum. The

unlabeled peaks in the 80/80 ejection spectrum do not fit within the trimer, dimer or monomer

ion series. Currently, we suspect that these peaks arise from higher order multimers including

tetramers and even possibly pentamers. All four spectra in Figure 4 are on the same scale and

the collection time was 68 ms for each. Therefore, the results above m/z 5000 suggest charge

25

stripping of higher order multimer ions while multimer ion cleavage is most likely creating the

changes in the ion distributions.

Clearly the trapping and ejection

processes are heating the ions, the deeper

axial trapping wells yielding greater

thermal excitation. Large changes in axis

potential in moving into or out of a gas-

filled quadrupole induces collisional

heating. This trapping well induced

heating can easily be prevented merely by

changing the trapping duty cycle. For

example, the trapping duty cycle during

the 80/80 ejection scan can be changed to

61.8/61.8 to yield the same -53 V axial potential observed in the 50/50 ejection scan in Figure 4.

Consequently, even though these power supply potentials and trapping and ejection duty cycles

are very different, the spectra should be identical because they both have a -53 V axis potential

during trapping and a 1 V axis potential during ejection. This hypothesis was tested with the

lysozyme spectra presented in Figure 5. The spectra were taken in tandem, (a) presents a

61.8/61.8 trapping and 80/80 ejection duty cycle and (b) presents a 32/32 trapping and 50/50

ejection duty cycle. Both feature an approximately -53V trapping and a 1V ejection potential.

Given the positive comparison, our supposition that the change in the axis potentials drive the

thermal excitation that yield the redistribution of the ions appears to be correct.

Figure 2.5: Lysozyme digital mass filter

spectrum with (a) 61.8/61.8 trapping and 80/80

ejection duty cycle and (b) 32/32 trapping and

50/50 ejection duty cycle. Both feature a -54V

trapping and a 1V ejection potential and are

essentially identical

26

This work highlights the capacity of DWT to manipulated large ions and control the

degree of multimer formation. Specifically, our data show that the excitation of non-covalently

bound multimeric protein ions can be tightly controlled to strip the ions of solvent adducts while

maintaining the noncovalent binding of the proteins. While it is certainly true that the SWT axis

potential can be shifted to cause thermal heating of the ions, it is the ability to perform this

operation with the agility and precision of DWT trapping followed by controlled rapid ejection

that sets it apart. DWT provides more options as well as speed and precision for manipulating

the ions while vastly increasing the mass range. Moreover, we have previously shown that there

are other options for exciting ions trapped in a linear quadrupole.[8] It has again been

demonstrated that menu of options for DWT manipulation of ions exceeds that offered by SWT.

2.6 Conclusion

The work shown here demonstrates the capabilities of DWT to manipulate and analyze

intact proteins and their noncovalent multimeric ions. DWT was precisely used to excite the

protein and cluster ions to remove solvent adducts while maintaining the integrity of the

multimeric ions. Consequently, intact proteins and noncovalent clusters can be mass analyzed

with a DWT based mass filter. Though the DWT based spectra observed here double the range

of commercial triple quadrupole mass spectrometers, the real mass range of this analyzer has yet

to be demonstrated. According to theory, the range should be limited by ion source conditions

and the range of the detector which presently approaches 1 MDa.[17]

2.7 Acknowledgement

This work was supported by the National Science Foundation Award No. 1352780.

27

2.8 References

1. Richards, J.A., Huey, R.M., Hiller, J.: A new operating mode for the quadrupole mass

filter International Journal of Mass Spectrometry and Ion Physics. 12, 317-339 (1973)

2. Ding, L., Gelsthrope, A, Nutall, J, Kumashiro, S: Rectangular Wave Quadrupole Field

and Digital Q(IT)MS Technology. in 49th American Society for Mass Spectrometry

Conference on Mass Spectrometry and Applied Topics. 2001. Chicago, Illinois.

3. Ding, L., Brancia, F.L.: Electron capture dissociation in a digital ion trap mass

spectrometer. Analytical Chemistry. 78, 1995-2000 (2006)

4. Ding, L., Kumashiro, S.: Ion motion in the rectangular wave quadrupole field and digital

operation mode of a quadrupole ion trap mass spectrometer. Rapid Commun. Mass

Spectrom. 20, 3-8 (2006)

5. Ding, L., Sudakov, M., Brancia, F.L., Giles, R., Kumashiro, S.: A digital ion trap mass

spectrometer coupled with atmospheric pressure ion sources. Journal of Mass

Spectrometry. 39, 471-484 (2004)

6. Ding, L., Sudakov, M., Kumashiro, S.: A simulation study of the digital ion trap mass

spectrometer. International Journal of Mass Spectrometry. 221, 117-138 (2002)

7. Brandon, D. Direct Digital Synthesizers in Clocking Applications Time Jitter in Direct

Digital Synthesizer-Based Clocking Systems. Analog Devices Applications Notes, 2006.

1-8.

8. Brabeck, G.F., Chen, H., Hoffman, N.M., Wang, L., Reilly, P.T.A.: Development of MSn

in Digitally Operated Linear Ion Guides. Analytical Chemistry. 86, 7757-7763 (2014)

9. Brabeck, G.F., Reilly, P.T.A.: Mapping ion stability in digitally driven ion traps and

guides. International Journal of Mass Spectrometry. 364, 1-8 (2014)

10. Brabeck, G.F., Reilly, P.T.A.: Computational analysis of non-traditional waveform

quadrupole mass filters Journal of The American Society for Mass Spectrometry. 27,

1122-1127 (2016)

11. Lee, J., Marino, M.A., Koizumi, H., Reilly, P.T.A.: Simulation of duty cycle-based

trapping and ejection of massive ions using linear digital quadrupoles: The enabling

technology for high resolution time-of-flight mass spectrometry in the ultra high mass

range. International Journal of Mass Spectrometry 304, 36-40 (2011)

12. Hoffman, N.M., Gotlib, Z.P., Opačić, B., Huntley, A.P., Moon, A.M., Donahoe, K.E.G.,

Brabeck, G.F., Reilly, P.T.A.: Digital Waveform Technology and the Next Generation of

Mass Spectrometers. Journal of The American Society for Mass Spectrometry. 29, 331-

341 (2018)

28

13. Gotlib, Z.P., Brabeck, G.F., Reilly, P.T.: Methodology and Characterization of Isolation

and Preconcentration in a Gas-Filled Digital Linear Ion Guide. Anal Chem. 89, 4287-

4293 (2017)

14. Donahoe, K.E.G., Moon, A. M., Gotlib, Z. P., Hoffman, N. M., Reilly, P. T. A.: Digital

Mass Scanning Techniques without Dipolar Auxiliary Waveforms. in 65th American

Society for Mass Spectrometry Conference. 2017. Indianapolis, IN.

15. Hoffman, N.M., Gotlib, Z.P., Opačić, B., Clowers, B.H., Reilly, P.T.A.: A Comparison

Based Digital Waveform Generator for High Resolution Duty Cycle. Review of Scientific

Instruments. Under Review, (2017)

16. Hoffman, N.M., Gotlib, Z. P., Opačić, B., Clowers, B.H., Reilly, P.T.A.: Generation of

Digital Waveforms with High Resolution Duty Cycle in 65th American Society for Mass

Spectrometry Conference on Mass Spectrometry and Allied Topics. 2017. Indianapolis,

IN.

17. Koizumi, H., Whitten, W.B., Reilly, P.T.A.: Controlling the Expansion into Vacuum—the

Enabling Technology for Trapping Atmosphere-Sampled Particulate Ions Journal of the

American Society for Mass Spectrometry. 21, 242-248 (2010)

18. Brancia, F.L., McCullough, B., Entwistle, A., Grossmann, J.G., Ding, L.: Digital

Asymmetric Waveform Isolation (DAWI) in a Digital Linear Ion Trap. Journal of the

American Society for Mass Spectrometry. 21, 1530-1533 (2010)

19. Hoffman, N.M., Opačić, B., Reilly, P.T.A.: Note: An inexpensive square waveform ion

funnel driver. Review of Scientific Instruments. 88, 3 (2017)

29

CHAPTER THREE: IMPACT OF INJECTION POTENTIAL ON MEASURED ION

RESPONSE FOR DIGITALLY DRIVEN MASS FILTERS

Bojana Opačić, Nathan M. Hoffman, Brian H. Clowers and Peter T. A. Reilly*

Department of Chemistry, Washington State University

June 19, 2018

3.1 Attribution

This chapter adapted with permission from: Bojana Opačić, Nathan M. Hoffman, Brian

H. Clowers and Peter T. A. Reilly. “Impact of Injection Potential on Measured Ion Response for

Digitally Driven Mass Filters.” International Journal of Mass Spectrometry, 434 (2018) 1-6

Copyright 2018, Elsevier. BO was the first author for this manuscript. NMH created comparator-

based waveform generator system. BO performed experiments. BO and PTAR wrote the

manuscript. BO, NMH, BHC and PTAR edited and revised the manuscript.

3.2 Abstract

Digital Waveform Technology (DWT) has recently evolved to provide sufficient duty

cycle resolution necessary to create a purely digital waveform-based mass filter. Digital

operation provides a number of options that remain extremely challenging for sinusoidal

waveform technology (SWT) driven systems. One of those options is collecting ions in a gas-

filled digital ion guide/trap and subsequently axially injecting the collected ions in a temporally-

short and spatially-focused packet into the digital mass filter (DMF). This work explores the

effects of trapping ions before mass analysis. In particular, it focusses on the measured response

30

of the ion distribution as a function of axial ejection conditions while maintaining identical

trapping conditions.

3.3 Introduction

The concept of using rectangular waveforms to operate an ion guide or mass filter

originated with Richards in 1973.[1] Unfortunately, it was another good idea that had to wait for

the technology to catch up. It was not until a quarter of a century later in the late 1990s that the

development of direct digital synthesis (DDS), high voltage field effect transistors (HV-FET)

and field programmable gate arrays (FPGA) provided the necessary foundations for digital

waveform technologies applied to mass analysis. DDS served to generate accurate and precise

low voltage square waveforms while FPGAs functioned to rapidly alter these waveforms on time

scales compatible with m/z manipulation. HV-FETs were required to amplify the waveforms to

the high voltages needed to operate these digital devices. Finally, in 2001, Shimadzu introduced

the first square waveform driven 3D ion trap at the ASMS meeting in Chicago.[2] They

developed this technology over the next 5 years [3-6] without producing a commercial product.

In spite of the years of development, three core aspects of DWT were not fully explored

even though they are, in our opinion, game changing. These features are: first, phenomenal

frequency resolution,[7] second, the ability to rapidly change the axial [8] and radial [9-11]

stability of the ions and third, is the agility of the waveform generator.[11, 12] Agility, in this

case, is defined by the number of waveforms that can be applied before switching to another set

of waveform conditions. Digital waveform generators (DWFG) can often do this after only one

period of the waveform. These features allow new methods of axially and radially trapping,

31

ejecting, isolating, exciting and shuttling ions around that greatly expand the capabilities of ion

traps and guides in comparison to sinusoidal waveform technology (SWT).

More recently, our group

invented another method of

producing rectangular waveforms

using a comparator and an 18-bit

digital to analog converter

(DAC).[13] The idea was to

compare the amplitude of the sine

wave output of the DDS with a

fixed potential output of the

DAC. The comparator output

provides the low voltage

rectangular waveforms. Figure 1

illustrates the waveform

generation process. The sine wave is depicted in blue and the DAC created voltage for

comparison with the sine voltage is depicted in orange. In this case, when the sine wave

amplitude is greater than the DAC input voltage, the comparator outputs a high and a low

voltage when the sine amplitude is less, thereby yielding the rectangular wave output (red trace).

The precision of the DAC and the threshold level of the comparator define the duty cycle

resolution to roughly 10 ppm and makes a purely digital mass filter feasible. The duty cycle and

the frequency of the waveforms can be changed essentially instantaneously with the minimum

Figure 3.1: Illustration of voltage comparator-based

rectangular waveform generation is high resolution duty

cycle control.

32

application time of the new waveform defined by the speed with which the new waveform

information can be down loaded to the DAC and the DDS, respectively.

This DWFG provides unprecedented control of the duty cycle not only for the DMF but

also for the gas-filled ion guide that precedes it. Exact duty cycle control of the guide allows the

ions to be precisely manipulated while they are axially trapped and ejected. In a previous

publication, we examined the effect of axial trapping potential on DMF generated spectra while

using the duty cycle to keep the DMF injection beam energy constant.[14] This work continues

the systematic investigation of the effect of the duty cycle based ion manipulation by varying the

injection energy into the DMF on the mass spectra to determine the response of the measured ion

populations.

3.4 Experimental

In this work lysozyme was used

to demonstrate DWT-based ion

trapping followed by mass filter

analysis of intact proteins. It was

purchased from Sigma Aldrich

Company (St. Louis, MO) and used without further purification. 50% methanol/ 50% water

(both HPLC grade and both from Fisher Chemical, Waltham MA) was used to dissolve the

lysozyme and produce a 6 µM solution. No acid was added to the solution in order to maintain

the mass distribution in lower charge states.

The instrument used in this effort is depicted in Figure 2. The sample was introduced by

electrospray ionization using the commercial fused silica capillary 30 ± 2 µm tip (New Objective

Figure 3.2: Dual quadrupole instrument illustration.

33

Co.) with an applied potential of +2600V relative to the pinhole inlet. Sample solutions were

pneumatically pushed through the capillary at 1 psig. Ions enter the instrument through a 300

µm diameter thin plate orifice and expand within a digitally-operated ion funnel operated at 500

kHz and 48 Vp-p with a -50V DC potential across the funnel in a differentially pumped chamber

at approximately 1.3 Torr.[15] The AC and DC fields of the funnel collimate and push the ions

toward the exit orifice and into a digitally-operated ion guide at ~10 mTorr.

The guide is driven by a pair of high voltage waveforms, one for each electrode pair. The

duty cycle of each waveform is defined by the percentage of the cycle that the waveform is in the

high state. The waveforms applied to each pair of electrodes of a quadrupole guide or filter are

defined by a pair of duty cycles. For axial trapping waveforms, the duty cycle values add to less

than 100 %, whereas duty cycle values for ejection add to greater than 100 %. In these

experiments, the trapping duty cycle and the trapping time were held constant so that the trapped

ion population was always consistent for each set of spectra. In some cases, the trapping time

was adjusted to avoid detector saturation. The ejection axis potentials were varied at 1, 10 and

20 V at a constant 80/80 ejection duty cycle to demonstrate their effect on measured ion

distribution.

The duty cycle derived axis potential is defined as a time-weighted average of the DC

axis potentials during a waveform cycle. In the case of our waveform generator, there are four

34

waveform fractions of constant potential

along the central axis of the quadrupoles, t1

through t4, as shown in Figure 3. t1 and t3

are defined by the fractions of the period

where the electrodes are at V+ and V- and

vice versa, where V+ and V- are the positive

and negative potentials supplied to the high

voltage pulsers. t1 and t3 form the

quadrupolar portion of the waveform period. t2 and t4 define the fractions of the waveform

period when both electrode pairs are at the same potential, either V+ and V-. The time weighted

average of the DC axis potential for trapping or ejection is given by:

𝑉𝑎𝑥𝑖𝑠 = ∑ 𝑡𝑛 (𝑉1,𝑛+𝑉2,𝑛

2)𝑛 , (1)

where V1,n and V2,n are either V+ or V- as defined by the applied waveform for each waveform

segment. The digital mass filter (DMF) was maintained at zero axis potential and the duty cycle

applied to it was 61.1/38.9. The ions exiting the DMF impacted into the conversion dynode at

approximately –7000 V. The converted charges were detected with an electron multiplier. The

amplifier gain was set to 1x108.

3.5 Results and Discussion

In a previous paper,[14] DWT was shown to be able to manipulate the trapping axis

potential to reduce the severity of solvent adduction onto intact lysozyme while maintaining

multimer association. Injection into and ejection out of the gas filled quadrupole produced

Figure 3.3: An example of a generic ejection

waveform that defines the waveform fractions,

tn, of constant potential along the central axis.

35

thermal activation of the protein and multimer ions. Here our goal is to determine the effect of

increasing the ejection potential out of the linear trap and into the DMF. Specifically, we were

interested in observing more thermal effects as well as sampling effects into the DMF.

The effects of the ejection potential were demonstrated by maintaining a constant

trapping potential and ejection duty cycle (80/80) while varying the ejection potential from 1 to

20 V. Using the previous trapping time of 68 ms caused detector saturation to occur because ion

sampling efficiency into the DMF is generally better at higher ejection potential.[14] Trapping

time was reduced to 10 ms to prevent this issue. Figure 4 depicts the ESI spectra of lysozyme as

a function of ejection potential into the DMF. The ions were trapped with a -145 V axis

potential to minimize solvent adduction and ejected with an 80/80 duty cycle. Figure 4 (a)

depicts the spectra at a 1 V, (b) 10 V and (c) 20 V ejection potential. All the spectra were taken

consecutively from the same sample and spray conditions.

The first thing noted was the change in scale in moving to higher ejection energy. The

peak intensity of the 20 V ejection potential was about an order of magnitude greater than the 1

V ejection potential. This means that the efficiency of transmission through the DMF can be

36

increased by an order of magnitude with

minor reduction in resolution merely by

modestly increasing the ejection potential.

The second observation was the

change in the relative ion population

distributions. Increasing the ejection

voltage skewed the distribution toward

higher m/z. The increasing intensity with

increasing ejection voltage can be

rationalized by recognizing that higher

ejection potentials yield better field

penetration into the quadrupole which

yields better sampling of the ions inside

the quadrupole. The trapped ions form a

cigar-shaped ion cloud with roughly

uniform density that tapers off in the

vicinity of the end cap electrodes.[16] The

axial ejection process samples the cloud

from the tapered end. Only a small

fraction of the trapped ions are actually

sampled into the mass filter during the 400

s ejection time. This ejection time can

easily be extended without affecting the

Figure 3.4: DMF spectrum of lysozyme trapped

at -145V and ejected into the mass filter with (a)

1V, (b) 10V and (c) 20V. Spectra reveal the

effect of ejection energy on the ion distribution.

37

scan time too significantly; however, increasing it from the current value of 400 s will not

greatly increase the number of ions sampled into the DMF. If the ejection waveform application

time is infinitely extended, the temporal ion profile yields an initial surge that quickly tapers off

into a slow trickle. The surge results from extraction field penetration into the quadrupole

sampling ions from the end of the ion cloud. Beyond the extraction field created by the duty

cycle change, there is essentially no axial field. To escape the quadrupole, the ions have to

diffuse into the extraction field to be ejected. The process of completely emptying the

quadrupole of axially trapped intact proteins by diffusion at 10 mTorr is a frightfully slow

process that can take minutes or even hours depending on the ion size.[17] Realistically, only

the ions in the vicinity of the exit end cap are sampled into the DMF. Increasing the amplitude

of the extraction field increases the intensity and width of the ejection ion surge; hence, the

increase in sensitivity.

To further illustrate sampling issues, ions were trapped for 68 ms at the same -145V

trapping potential and 1 V ejection into the DMF while the ejection duration was varied from 50

to 140 s. This data is shown in Figure 5. At 50 s ejection time, the distribution is skewed

toward the high charge state (low m/z) side of the spectrum. Increasing the ejection time to 140

s gradually and significantly increases the number of ions sampled and the intensity of the low

charge states at higher m/z. A similar change in the ion sampling is occurring in Figure 4 in

changing the ejection potential from 1 to 10V.

Can the sensitivity of the trapping method of mass filter analysis be further improved?

Certainly. Sampling of the trapped ion cloud from the guide into the DMF depends on the

penetration of the extraction field into the ion cloud. This is dependent on the shape and position

38

of the ion cloud within the trapping guide. That can be changed. For example, the exit end cap

between the guide and the DMF can be biased to move the border of the cloud closer to the end

cap electrode and further into the extraction field. This effect of the cloud penetration into the

extraction field has already been demonstrated by the need to reduce the extraction time in

Figure 4 to 10 ms. Decreasing the trapping time reduces the trapped ion population and shrinks

the cloud size primarily along the z-axis thereby reducing the number of ions sampled by the

extraction field. Ideally, it would be preferred to sample the majority of the trapped ion cloud

into the DMF to obtain the highest sensitivity. It has been shown that the extraction field can be

Figure 3.5: A series of lysozyme DMF spectra as a function ejection time from 50 to 140 s.

Ions were trapped for 68 ms with a -145 V axis potential to provide the same trapped ion

population. The series reveals a low m/z bias can occur during axial ejection into a DMF if

the sampling time is too short.

39

extended by increasing the ejection voltage to significant effect (see Figure 4); however, that still

presents only a minor increase in the fraction sampled into the DMF.

More of the trapped ions can be sampled merely by changing the shape of the ion cloud.

This can be done by creating a field along the z-axis of the quadrupole and thereby causing the

ions to collect and concentrate in the vicinity of the exit end cap where the extraction field easily

penetrates. Methods of creation of z-axis fields in multipole guides are well-known and have

been reviewed.[18] Simulations of ion collection near the exit end cap using z fields followed by

duty cycle based ejection have also been performed.[8] Our current dual quadrupole DMF

system is not equipped with the ability to apply z-axis fields; however, they should enhance the

sensitivity of the instrument considerably.

The third observation of the series presented in Figure 4 was the inconsistent changing of

the ion distribution. Normally, if a sampling issue changed the measured ion distribution, you

would expect the higher charge states to exit the quadrupole first because the ions experience an

extraction energy that is proportional to their charge, higher charge states yield higher kinetic

energies. Increasing the energy should then increase the lower charge state populations.

Eventually the distribution would be expected to level out and remain consistent as it did in

Figure 5 because a statistical representation of the ion population was reached when increasing

the ejection potential. However, in this case, it did the opposite. The distribution skewed back

to favoring the high charge state ions (see Figure 4). The ion distributions of the trapped ions are

identical because the same sample and procedures were used to trap them. The changes in the

distributions observed have to occur during the axial ejection process and they are dependent on

the ejection energy.

40

The ion population trapped is different from the one sampled into the DMF. The

inconsistent evolution of the ion distribution suggests that there was more than one phenomenon

occurring at the same time that related to the ejection voltage. In an effort to understand these

phenomena, a comparison of the DMF measured ion distribution at 1 V ejection at different

trapping times, 10 and 68 ms, is shown in Figure 4 (a) and its inset respectively. Increasing the

ion population by a factor of approximately 7 reveals a substantial change measured ion

distribution. Increasing the population expands the ion cloud along the z-axis and more ions are

sampled into the DMF per ejection cycle. Presumably, increasing the population does not

change the trapped ion distribution because it is unlikely that highly-charged ions can get close

enough to interact under normal conditions. Therefore, because the ions were trapped and

ejected with identical waveforms, the difference between the measured ion distribution in Figure

4 (a) and its inset is solely due to charge state sampling issues that may occur under low ion

population conditions and low energy ejection.

On the other hand, the change in measured ion distributions between 10 and 20 V

ejection was primarily due to the collision energy change. The internal energy imparted to the

ions during trapping was identical to moving into a collision cell and it was defined by the

potential drop into the trap. Switching the duty cycle to eject results in a similar change in

potential albeit an increase instead of a decrease. That change in potential inside a collision cell

similarly imparts internal energy into the ions in the same way that entering the cell does, but the

mechanism is very different.

Before ejection, the ions are translationally cool in the deep axial potential well. There is

no axial force on the ions while they are in the well. They diffuse freely along the z-axis. The

41

waveform is then instantaneously switched. The ions in the vicinity of the end cap electrode

now “feel” the force imposed by the potential drop along z-axis. That potential drop is between

1 and 20 V in these experiments. An axial 20 V potential drop is not enough to cause the

collisional excitation observed. That excitation is produced radially by the switching of the

waveform. Ion motion during axial trapping is defined by waveforms that have a time-averaged

negative potential and by a time-averaged positive potential during ejection. This sudden change

in the radial potential imparts radial force that quickly changes the trajectories of the ions and

imparts collisional energy. The net effect is that the change in potential in moving the ion out of

the axial well is primarily imparted radially during ejection and axially during injection.

The energy of ejection adds to the internal energy imparted to the ions during the

trapping process. This added energy was not insignificant. The proof can be seen at the base of

the high charge state (low m/z) side of the measured distribution in Figure 4. The base of the +8

charge state peak broadened as the ejection energy increased. This broadening was asymmetrical

and occurred on the low mass side of the peaks. It represents small fragment loss from the

charged proteins without any cleavage along the protein backbone.

The proof of small fragment loss was demonstrated by decreasing the trapping potential

from -145 to -160 V and performing the mass measurements again. These results are shown in

Figure 6. The same trend in change of the ion distribution with increasing ejection potential was

seen and thereby revealed the reproducibility of the observation. Also revealed was an increase

in small fragment loss for the high charge state ions with increasing ejection voltage. Increasing

the axial trapping well depth increased the amount of energy deposited into the ion during

42

trapping. It also increased the amount of

energy imparted into the ions upon

ejection. T effects of this increase are

shown in Figure 6.

Comparison of the ion

distributions at 1V ejection at -145 and -

160V trapping axis potential showed a

decrease in overall ion intensity, more

small fragment loss from the high charge

states and higher relative intensity for the

high m/z and multimeric ions. A similar

trend was seen in the 10 V ejection

spectra with a greater degree of small

fragment loss and higher intensity

multimeric ions. The 20 V ejection

spectrum in Figure 6 (c) revealed a much

greater increase in small fragment loss

along with an increase in the intensity of

the high charge states with a

corresponding decrease in multimeric ions

thereby suggesting multimeric

dissociation was yielding the corresponding increase in intensity of the high charge state

43

monomer ions. It seems logical that multimer fragmentation can occur along with small

fragment loss.

3.6 Conclusion

The idea of trapping the ions and concentrating them before mass analysis is a well-

established and long-standing approach in mass analysis. Trapping ions in linear traps is

especially advantageous because the capture efficiency is high compared to their 3D

counterparts.[16] Additionally, the ions can be ejected in a temporally short and spatially-

focused packets.[19] Unfortunately, only a small portion of the trapped ions are sampled into the

DMF. Variation of the ejection potential was used to demonstrate the effect of sampling issues

in the presented spectra. Those results show that the ion intensity can be significantly increased

merely by increasing the ejection energy in order to sample a larger fraction of the trapped ions.

It is our assertion that the sensitivity of the trapping technique can be greatly enhanced by the

application of a field along the z-axis of the linear trap so that the ions collect and concentrate in

front of the exit end cap where the field from the ejection waveform can easily eject them in a

short and concentrated plug. The addition of a z-axis field will reduce the observed sampling

issue so that the measured distributions are representative of the trapped ion population.[8]

Moreover, the imposed z-field will greatly enhance the efficiency of the ejection process making

trapping DMF mass analysis more sensitive.

Next, the ejection process was revealed to be equivalent to the trapping process in terms

of ion excitation by demonstrating the measured ion distribution changed as a function of

ejection potential while the trapped ion distribution remained constant. A radial mechanism for

imparting collision energy to the ions during duty cycle based ejection was discussed. This work

44

showed that it is possible to quickly increase the internal energy of a small protein enough to

cause small fragment loss and break apart non-covalently bound protein complexes.

The changes in the ion distributions shown here were observed because of the control of

the ions that DWT provides. Electrosprayed multimeric ions of intact proteins adduct large

amounts of solvent. DWT permits energetic trapping and ejection of the ions. It can be

controlled to first reduce solvent adduction and then used to dissociate multimer ions and yield

small fragment loss. It is the control of the ions provided by DWT that make it a new and

powerful

3.7 Acknowledgement


45

3.8 References

1. Richards, J.A., R.M. Huey, and J. Hiller, A new operating mode for the quadrupole mass

filter International Journal of Mass Spectrometry and Ion Physics, 1973. 12: p. 317-339.

2. Ding, L., et al. Rectangular Wave Quadrupole Field and Digital Q(IT)MS Technology. in

49th American Society for Mass Spectrometry Conference on Mass Spectrometry and

Applied Topics. 2001. Chicago, Illinois.

3. Ding, L. and F.L. Brancia, Electron capture dissociation in a digital ion trap mass

spectrometer. Analytical Chemistry, 2006. 78(6): p. 1995-2000.

4. Ding, L. and S. Kumashiro, Ion motion in the rectangular wave quadrupole field and

digital operation mode of a quadrupole ion trap mass spectrometer. Rapid

Communications Mass Spectrometry, 2006. 20(1): p. 3-8.

5. Ding, L., et al., A digital ion trap mass spectrometer coupled with atmospheric pressure

ion sources. Journal of Mass Spectrometry, 2004. 39(5): p. 471-484.

6. Ding, L., M. Sudakov, and S. Kumashiro, A simulation study of the digital ion trap mass

spectrometer. International Journal of Mass Spectrometry, 2002. 221(2): p. 117-138.



1-8.

8. Lee, J., et al., Simulation of duty cycle-based trapping and ejection of massive ions using

linear digital quadrupoles: The enabling technology for high resolution time-of-flight

mass spectrometry in the ultra high mass range. International Journal of Mass

Spectrometry 2011. 304(1): p. 36-40.

9. Brabeck, G.F., et al., Development of MSn in Digitally Operated Linear Ion Guides.

Analytical Chemistry, 2014. 86(15): p. 7757-7763.

10. Brabeck, G.F. and P.T.A. Reilly, Mapping ion stability in digitally driven ion traps and

guides. International Journal of Mass Spectrometry, 2014. 364: p. 1-8.

11. Gotlib, Z.P., G.F. Brabeck, and P.T. Reilly, Methodology and Characterization of

Isolation and Preconcentration in a Gas-Filled Digital Linear Ion Guide. Anal Chem,

2017. 89(7): p. 4287-4293.

12. Hoffman, N.M., et al., Digital Waveform Technology and the Next Generation of Mass

Spectrometers. Journal of The American Society for Mass Spectrometry, 2018. 29: p.

331-341.

46

13. Hoffman, N.M., et al., A Comparison Based Digital Waveform Generator for High

Resolution Duty Cycle. Review of Scientific Instruments, 2017. Accepted 7/8/2018.

14. Opacic, B., et al., Using Digital Waveforms to Mitigate Solvent Clustering During Mass

Filter Analysis of Proteins. Journal of The American Society for Mass Spectrometry,

2018.

15. Hoffman, N.M., B. Opačić, and P.T.A. Reilly, Note: An inexpensive square waveform ion

funnel driver. Review of Scientific Instruments, 2017. 88(1): p. 3.

16. Schwartz, J.C., M.W. Senko, and J.E.P. Syka, A two-dimensional quadrupole ion trap

mass spectrometer. Journal of the American Society for Mass Spectrometry, 2002. 13(6):

p. 659-669.

17. Chernushevich, I.V. and B.A. Thomson, Collisional Cooling of Large Ions in

Electrospray Mass Spectrometry. Analytical Chemistry, 2004. 76(6): p. 1754-1760.

18. Wilcox, B.E., C.L. Hendrickson, and A.G. Marshall, Improved ion extraction from a

linear octopole ion trap: SIMION analysis and experimental demonstration. Journal of

the American Society for Mass Spectrometry, 2002. 13(11): p. 1304-1312.

19. Wang, X., et al., Increasing the trapping mass range to m/z=10(9)-A major step toward

high resolution mass analysis of intact RNA, DNA and viruses. International Journal of

Mass Spectrometry, 2012. 328: p. 28-35.

47

CHAPTER FOUR: DIGITAL MASS FILTER ANALYSIS IN STABILITY ZONES A AND B

Bojana Opačić, Adam P. Huntley, Brian H. Clowers and Peter T. A. Reilly*

Washington State University, Department of Chemistry, Pullman, WA 99164

*Corresponding Author: [email protected]

4.1 Attribution

This chapter was adapted with permission from: Bojana Opačić, Adam P. Huntley, Brian

H. Clowers and Peter T. A. Reilly. “Digital Mass Filter Analysis in Stability Zones A and B.”

Journal of Mass Spectrometry, 2018;53:1155-1168 Copyright 2018 John Wiley & Sons, Ltd. BO

was the first author for this manuscript. BO performed the experiments. BO and PTAR wrote the

manuscript. BO, APH, BHC, and PTAR edited and revised the manuscript. Figures were

submitted to the publisher at the end of the manuscript.

4.2 Abstract:

Digitally driven mass filter analysis is an advancing field. This work presents a tutorial

of digital waveforms, stability diagrams and pseudopotential well plots. Experimental results on

digitally-driven mass filter analysis in stability zones A and B are also shown. This work

explains duty cycle manipulation of the waveforms to axially trap and eject ions from linear

quadrupoles, how to change and distort the stability diagrams to create mass filters and their

effects on the pseudopotential well depth. It discusses the sensitivity and resolution that can be

obtained and what limits these benchmarks. It reveals the advantages of mass filter operation

without any added DC potential between the quadrupole electrodes (a = 0).

4.3 Introduction:

Beyond its unlimited mass range, digital waveform technology (DWT) provides quick

and easy ways of manipulating ions that cannot be easily reproduced with the current sinusoidal

48

waveform technology (SWT). DWT enables a simple ion guide to become a sophisticated ion

trap that can be filled with a large number of ions. Those ions can then be axially ejected in a

temporally narrow packet containing millions of ions. The duty cycle axial ejection process was

first modeled by our group using an ion trajectory program (SIMION, www.sisweb.com) [1].

The axil trapping and ejection process was also experimentally demonstrated by capturing

millions of singly-charged aerodynamically-sized urea particles that ranged in size up to 200 nm

(~3 x 109 Da) [2]. Our group demonstrated the agility of DWT by isolating large protein ions in

narrow mass windows without significant ion loss [3]. This same methodology was used to

preconcentrate specific low abundance ions to saturation for subsequent analysis in the same

study [3]. We also used the agility of DWT to create a new method of excitation that jumps the

selected ions into the unstable region by changing the duty cycle or the frequency for a few

cycles and then jumping back into the stable regions before the excited ions can escape, the

isolated excited ions then undergo collision activated dissociation in the same ion guide [4].

Our work demonstrated that the energy and motion of the ions can be precisely controlled

merely by changing the duty cycle and frequency of the trap. It is the duty cycle that

manipulates the stability diagrams of the ions in both the axial and radial directions. The

frequency moves the ions within the stability diagram set by the waveform duty cycle.

Direct digital synthesis (DDS) is the standard method of creating low voltage waveforms

digitally and provides magnificent frequency resolution [5]. Comprehensive understanding of

the DDS methodology can be found in reference [5]. A 32-bit DDS permits 0.02 Hz resolution

at every frequency available. To provide a measure of this ability, the frequencies of m/z 1000

and 1001 were shown through the use of the m/z versus frequency stability diagram to be

separated by roughly 140 Hz [6]. This provides ~7000 frequency steps or ~3500 mass steps

49

between the two masses. If greater mass step resolution is needed a commercial 48-bit DDS is

also available. This would provide 229 million mass steps in between the two masses. Since the

frequency defines the mass, the achievable mass accuracy should be excellent. Also, the ability

to manipulate the ions within any stability diagram will be better.

Ions can also be manipulated axially with the duty cycle. The energy range that they can

be ejected axially with is defined by the waveform voltage, V0-p [1]. How finely the ejected ion

beam voltage can be defined depends on the resolution of the waveform duty cycle. Until

recently, the low voltage waveforms were created using counters that were operated with a

frequency-variable clock [7]. The resolution of the duty cycle was dependent on the resolution

of the counters that was generally around 1% or greater (8-bit). This produces a beam voltage

resolution of about 2 V that does not permit resolved control of the axial beam energy.

The waveform duty cycle can also be used to manipulate the radial stability of the ions.

A counter-type waveform generator (WFG) was used by our group to make a crude mass filter

with a resolving power of R = 10 = m/m to demonstrate that digitally-driven mass filter

analysis could be achieved up to m/z = 1,000,000 [8]. Unfortunately, the counter-based WFG

duty cycle resolution was not sufficient to create a very effective mass filter. In a previous

publication [9], our group used matrix solutions to the Hill equation to analyze of methods of

mass filtering with non-traditional waveforms. This study revealed that duty cycle resolution in

the 10 ppm range would be required to create an effective mass filter using the duty cycle alone

to create the mass window. Counter-based waveform generation could not meet this requirement

because the high frequency range of DDS cannot supply sufficient duty cycle resolution. A new

method of waveform generation was required to produce the needed duty cycle resolution.

50

Our group developed a new method of waveform generation that met that need [7]. A

prototype digital mass filter was created and its capabilities of manipulating and filtering ions

were demonstrated [10]. The new WFG is based on analog comparators. DDS sine wave and

18-bit DAC outputs are fed into a comparator. When the sine output voltage exceeds the voltage

supplied by the DAC, the comparator outputs a waveform high and when it does not it outputs a

low to create the rectangular waveform. The duty cycle resolution of the waveform is then

defined by the resolution of the DAC and the threshold of the comparator [7]. Our WFG permits

duty cycle resolution out to the 5th decimal place (10 ppm). This is sufficient to create a mass

filter with ample resolution [9]. The 5th decimal place allows the creation of a mass window

with a q/q resolution of 8,700 (see equation 6 of reference [9]). This number is smaller than the

measured resolution (R = m/m) because m in this case defines the full width at half maximum

of the distribution of ions that pass through the mass filter, whereas q defines the width of the

mass window at the baseline. In other words, the complete range of masses that are stable within

the mass filter regardless of well depth. This result suggests that the DMF can obtain the same

resolution benchmarks as exhibited by their sinusoidally-driven counterparts.

Recent publications have focused on demonstrating the capabilities of this new digital

mass filter by using DWT to change the trapping and ejection conditions of ions in a collection

quadrupole to prepare them for digital mass filter (DMF) analysis [10, 11]. That work

demonstrated DWT control of the ions by desolvating them while maintaining non-covalent

association of multimeric ions. The study presented here continues our work with DMF analysis

by examining low mass range limitations and their causes and provides a tutorial of the use of

the stability diagrams and well depth plots. These are used to show how changing the duty cycle

affects radial and axial stability and creates and manipulates mass windows. These concepts

51

were used to examine mass analysis in the zone B stability region. Mass analyses were used to

demonstrate these concepts.

4.4 Experimental:

A 6 µM solution of lysozyme was prepared in 50:50 methanol water solution without the

addition of acid. Lysozyme was purchased from Sigma Aldrich (St. Louis, MO) while HPLC

grade methanol and water were purchased from Fisher Chemical (Waltham, MA). TXA salts

and asparagine were also purchased from Sigma Aldrich and used without further purification.

A schematic of the instrument is shown in Figure 1. Ions were created by electrospray

and introduced into the instrument via a commercial fused silica capillary that has 30 ± 2 µm

internal diameter tip (New Objective Inc.: www.newobjective.com) at a potential of +2400 V.

The solution was pneumatically pushed through the capillary at 1 psig. Ions entered the

instrument through a 300 µm thin plate orifice where they expand within an ion funnel. The ion

funnel is approximately 10 cm long consisting of a stack of 50 ring electrodes with an operating

pressure of approximately 1.1 Torr. The ion funnel was digitally operated at 500 kHz and 48 Vp-

p waveform amplitude [12]. The digital RF on the ring electrodes guides the ions toward the

central axis while a 30 V DC potential applied across the ion funnel guides them toward and

through the exit orifice (see Figure 1). A jet disrupter was placed along the central path through

the ion funnel that blocks the large droplets from entering the instrument while permitting ions to

flow around [13]. The ions exit the funnel orifice into a digitally-operated quadrupole ion guide.

52

The quadrupole ion guide is located in the second differentially-pumped chamber with an

operating pressure of approximately 11 mTorr. The ion guide, composed of 9.5 mm diameter

rods (r0 = 4.16 mm), was driven by a pair of high voltage digitally-generated waveforms, one for

each electrode pair. Each electrode pair oscillates between a positive voltage (V+) and a negative

voltage (V-). The waveform defines the times in which the electrodes are in the V+ and V- states.

The duty cycle of an individual waveform is defined as the percentage of the period that the

waveform is in high or positive voltage state, V+. The waveforms are applied out of phase so

that the potentials of the electrode pairs are in opposing states to create a quadrupolar field. The

end cap electrodes were maintained at ground potential. Adapting the waveforms to manipulate

the ions will be discussed below.

Once the ions are ejected, they enter the digitally-operated mass filter (DMF), composed

of 9.5 mm diameter rods (r0 = 4.16 mm), that has an operating pressure of 2.9 x10-7 Torr. The

ions exiting the DMF are focused by Einzel lenses into the conversion dynode with an applied

potential of approximately -7000 V. The gain on the signal amplifier was set to 1x108 V/A. This

work primarily addresses the use of digital waveforms to perform trap and eject mass filter

Figure 4.1: Schematic diagram of the experimental apparatus.

53

analysis using two quadrupoles. The process starts with trapping the ions in the first quadrupole

and is followed by subsequent ejection into the mass filter.

The mass filter spectrum is created by setting the mass window width as defined by q

with the duty cycle. The spectrum is then scanned by stepping the frequency of the quadrupole

in linear mass steps. The duration of each mass step can be set from microseconds to constant

frequency. With our 32-bit WFG, the mass can be stepped at ~1 mDa at 1000 Da or any greater

value. The resolving power of the mass spectrum, defined by q/q, remains constant over the

entire spectrum. The value of the Mathieu parameter q also does not change during the scan.

The value of q of the trapping quadrupole is also set to a constant during the scan; therefore, the

frequency of the trapping quadrupole is also stepped during the mass scan to maintain consistent

ion sampling. The ion collection times in the spectra were optimized to maintain the signal level

above 1 V. Stability diagrams (m/z versus frequency) directly define the mass scan line as well

as the mass window width. A direct comparison of the scanning methods of DWT and SWT

driven mass filters may be found in reference [9].

4.5 Axial trapping and ejection:

To axially trap positive ions in a linear quadrupole, the duty cycles of the waveforms

must have a sum of less than 100%. This criterion guarantees that there are intervals during the

waveform period when both electrode pairs are in the V- state at the same time. This creates a

time averaged negative potential between both rod pairs and the end cap electrodes, thereby

creating an axial trapping potential at both ends that allow the ions to collect in the guide.

Whereas to eject the ions, the duty cycle values of the waveforms must sum to greater than 100

%. This creates a time averaged positive potential between the rods and the end caps that pushes

the ions out of the quadrupole when they are near the ends [1]. The ability to instantaneously

54

change the waveforms allows the ions to be collected in the guide and subsequently be ejected

into a mass analyzer on demand. This method of trapping and ejecting ions into a mass analyzer

has a lot of advantages that have been previously discussed [1, 11, 14-16]. The manipulation of

duty cycles to change and manipulate the DC axis potential in the ion guide and its effects are

described in detail in our recent publications [11, 16].

An example of a 13/13 axial trapping waveform used in this work is shown in Figure 2.

The temporal arrangement of high voltage pulses arises because of the method of waveform

generation. In this example the waveforms were generated by the comparator method [7]. This

generation method requires that the high voltage pulses of each rod pair center on the low

voltage pulses of the other rod pair. For more information about this generation method see

reference [7]. The 13/13 nomenclature defines the duty cycles of the waveforms applied. Each

waveform is in the high state or V+ state for 13% of the period and for 87% of the period they are

in the low state at V-. Because the two duty cycles add to less than 100%, there is a time

weighted averaged negative potential between the rods and the end cap electrodes. The axial

potential is calculated as a sum of time weighted potentials of one waveform cycle by the

following formula:

𝑉𝑎𝑥𝑖𝑠 = ∑ 𝑡𝑛𝑛 ((𝑉𝑛,1 + 𝑉𝑛,2)/2) (1)

55

Where tn defines the constant potential fractions of the waveform period (Figure 2) and requires

that ∑ 𝑡𝑛𝑛 = 1. 𝑉𝑛,1 defines the voltage of rod pair 1 during the nth interval and 𝑉𝑛,2 defines the

voltage of rod pair 2 during that same period. In the above example, voltages (or the waveform

amplitudes) applied by the pair of pulsers are +120V and -120V. During time intervals t1 and t3,

one of the waveforms is high while the other is low. Intervals where the potentials are opposed

create the oscillating quadrupolar field that radially traps the ions. The time average of the

potentials is zero during these quadrupolar field intervals so t1 and t3 do not contribute to the

axial potential sum in equation (1). Consequently, the intervals t2 and t4 define the axial potential

in this example. Both rod pairs are at -120V during these intervals, so the average potential

during that time is -120V. Since the axis potential is a time weighted average, the -120 V

potential is multiplied by the fractions t2 (0.37) and t4 (0.37) and summed yielding -88.8V for the

axial trapping potential. The ability to change the duty cycle within the 5th decimal place means

that the time averaged DC axis potential can be changed by millivolts if required. The axis

Figure 4.2: 13/13 duty cycle waveforms. Time intervals t1 and t3 of the two waveforms are in

the opposite phase, so the average potential at this time is zero since the waveform

amplitudes are ±120V. Time intervals t2 and t4 are equal and in the low state, trapping the

ions. The average amplitude at each time point is -120V.

56

potential can also be increased or decreased merely by changing the pulser power supply

voltages by a fixed amount relative to ground potential, 0 V.

Operating the first quadrupole with the waveform illustrated in Figure 2 means that if the

ions exit the ion funnel at ground potential, they undergo a -88.8 V drop into the gas-filled

quadrupole. The first quadrupole is then operating as a collision cell (~11 mTorr). The ions are

thereby internally heated through collisions as they are trapped in the first quadrupole. The

waveform duty cycles can be controlled to 5th decimal place (0.001%) using the comparator-

based waveform generation method. This provides very precise control of the collision energy

over the entire range of available collisions energies [16].

After the ions are collected and translationally cooled through collisions in the first

quadrupole, the waveform is switched to eject the ions into the DMF on demand. In this

example, ejection is performed by switching the duty cycle to 57/57. This waveform is

presented in Figure 3. The potential is calculated in the same way as above.

Figure 4.3: 57/57 duty cycle waveforms applied to a digital ion guide during ejection. Time

intervals t1 and t3 of the two waveforms are in the opposite phase, so the average potential at

this time is zero since the waveform amplitudes are ±120V. Time intervals t2 and t4 are

equal and in the high state, ejecting the ions. The average amplitude at each time point is

+120V.

57

As before, the two waveforms are in the opposite phase during t1 and t3. The average

potential during this interval is zero because the power supplies were set to ± 120V. Time

intervals t2 and t4, where both waveforms are high, yields an average amplitude of +120V. Both

intervals last for 7% of the time, yielding a summed axial ejection potential of + 16.8 V (0.07 ×

120 + 0.07 × 120 = 16.8 V). In this case, if the axis potential of the digitally-operated mass filter

is 0 V, the ions enter with 16.8 V of energy. Changing the axis potential while the ions are

inside the first quadrupole affects them energetically in the same manner that occurs when the

ions are injected into the guide. In other words, the ions are kinetically excited as they enter and

as they leave the gas-filled quadrupole [11]. The ion ejection energy can be just as precisely

controlled by changing the duty cycle.

4.6 Stability diagrams and radial well depth

Any discussion of ion isolation and mass filtering should begin with stability diagrams.

Either isolation or mass filtering of ions require that the operator keeps the ions of interest stable

while making all of others unstable. These objectives can be accomplished in stepwise

procedures as is often used for mass isolation or all at once in the case of filtering.

The motion of ions in purely quadrupolar fields in each orthogonal direction (x and y in

the case of a linear quadrupole) are independent of each other [17]. The imposition of higher

order fields (which exist in any geometry to some extent) can cause some coupling between the

axial motions of the ions. However, these effects are generally not noticeable. Therefore, the

calculation of ion stability is made with the assumption that the fields are purely quadrupolar.

This assumption does not seem to greatly reduce the predictive capability of the stability

calculations.

58

The motion of the ions is determined using a second order linear differential equation. In

its generalized form, it can be applied to ion motion in all periodic electric fields and is known as

the Hill equation [18]. The Mathieu equation that is normally used to calculate stability

diagrams is a special case of the Hill equation and is only applicable to sinusoidally driven traps

and guides. Consequently, the Hill equation has to be used for the rectangular waveforms that

are used by digitally-driven ion traps [18].

The Hill equation can be solved using matrix methods [19]. Because waveforms are

periodic, it need only be solved over one RF period (T) to fully define ion motion over time [18,

19]. The full waveform period is divided up into n temporal elements of duration tn wherein the

trapping voltages are constant. Since the voltage is constant during each time segment tn, the

position and velocity of the ion can be analytically defined for any point in that time segment.

The position and velocity of the ion can be calculated at the end of a constant voltage time

segment in a quadrupolar field provided these quantities are known at the beginning.

Propagating the ions through each constant voltage time segment calculations permits the ion

motion to be known over the entire waveform cycle. Each constant voltage time segment

element tn will then have its own 2x2 matrix to define the motion during that interval. These

matrices are then multiplied together over the entire waveform period to yield the 2x2 transfer

matrix M [6, 18]. The transfer matrix can then be used to calculate the ion position and velocity

after one cycle. Because the waveform is periodic, position and velocity can be determined after

m cycles of the waveform by using the transfer matrix m times. Consequently, the ion motion

can be defined at any point in time using the following equation:

(𝑥𝑚+1

𝑣𝑚+1) = M𝑚 ∙ (

𝑥0

𝑣0) (2)

59

The transfer matrix accurately describes ion motion for any periodic waveform provided that the

constant voltage elements accurately depict the waveform [9]. For waveforms such as sine

waves with continuously changing potentials, the larger the number of constant voltage steps, the

more accurately the transfer matrix defines the ion motion. In our previous study [9], we found

that 128 constant voltage steps to calculate stability diagrams for waveforms with continuously

changing potentials provided accurate reproduction of the stability boundaries without being

computationally overwhelming. On the other hand, rectangular waveforms have a finite number

of constant voltage elements, being limited to three generally for counter produced waveforms

[6] or four for comparator produced waveforms [7]. These constant voltage segments precisely

define the waveform. Consequently, the matrix solutions for rectangular waveforms are exact

[6].

The stability diagram for any periodic waveform is then generated by relating the trace of

the 2x2 transfer matrix to the stability parameter β at each point in the stability plane with the

following equation:

|𝑇𝑟(𝑀𝑢)| = 𝑚11 + 𝑚22 = 2 cos(𝛽𝑢𝜋) (3)

β ranges from 0 to 1 for stable ions; therefore, absolute values of the trace of the transfer matrix

range between 0 and 2 for stable ions. When the absolute value of the trace becomes greater

than 2, the ions are no longer stable [6].

The next concept to understand is the pseudopotential well depth. A pseudopotential,

also known as an effective potential, is an approximation that allows for a simplified description

of a complex system. In this case, the motion and stability of ions in a periodic electric field is

the complex system. When the motion of the ions is modeled by a second order differential

equation, it is difficult to define the energy of binding ions in a trap. To simplify, the system is

60

approximated as ions in a parabolic potential well. Because β defines the stability of the ions, it

can be used to calculate the pseudopotential well depth. The depth of this well along any axis u,

Du, is defined by the stability parameter βu [20]:

𝐷𝑢 = −𝛽𝑢

2𝑉

2𝑞𝑢 (4)

where V is the zero-to-peak voltage of the device and qu is the value of the Mathieu parameter

[17] at that point in the stability plane. Because β can be determined at any point in the stability

plane, the pseudopotential well depth can be determined at any point too [20].

While the pseudopotential can be used to approximate the strength of binding ions in the

trap at any point in the stability plane, it cannot be used to describe the motion of the ions over

the same range because it cannot account for the higher order oscillations imposed as the value

of q increases. The motion of the ions can be modeled by the pseudopotential if the higher order

oscillations are negligible and there is only secular oscillation of the ions. This is the essence of

the Dehmelt approximation that is applicable to values of q < 0.4 for sinusoidally-driven systems

[17] and q < 0.3 for square wave-driven systems [21].

To recap, matrix solutions of the Hill equation provide the stability of the ions as well as

a pseudopotential well depth for any point in the stability plane but only along one of the

orthogonal axes at a time. Each axis (in the x or y direction in this case) has to be generated

separately, the results are then combined to create the stability diagram. This process will be

described in more detail below. Each change in the duty cycle changes the constant voltage time

segments and thus changes the transfer matrix, ion motion and stability. Consequently, the Hill

equation has to be solved for each new waveform. Fortunately, it is not necessary for users to

learn to perform these calculations themselves. Our group has developed spreadsheet programs

that generate stability diagrams. They are available free at our website:

61

https://reilly.chem.wsu.edu/digital-waveform-stability-diagrams-2/. These programs are easy to

use and effective. All of the stability diagrams and well depth plots illustrated in this work were

generated from these spreadsheet programs.

Illustration of their use proceeds with the simplest case, square wave operation. Figure 4

(a) presents the stability diagram along the x-axis for a 2D ion guide with a 50/50 duty cycle.

The Mathieu parameters q and a that are used to define the x- and y-axes of the plot have the

same definitions used for sinusoidal waveform stability diagrams [6, 17]. The area of the plot in

blue defines the range of q and a coordinates where the ions are stable along the x-axis.

Likewise, Figure 4 (b) defines the range of q and a coordinates where the ions are stable along

the y- axis by the area in yellow. By themselves, these diagrams do not define the stability of

ions in the guide because it is possible to be stable on one axis and be unstable on another.

Consequently, to be stable in the trap or guide, the ions have to be stable along both axes

simultaneously. Therefore, a complete stability diagram is created by overlaying the diagrams in

Figure 4 (a) and (b). Where they overlap, as defined by the green region in Figure 4 (c), the ions

are stable along both axes simultaneously. If an ion is in the blue region, it is stable along the x-

axis but unstable along the y-axis, it excites along the y-axis and impacts with one of the y-

electrodes. The converse is true for ions in the yellow region and they impact on the x-

electrodes. Ions in the white region of Figure 4 (c) are not stable in any direction. They excite

and impact in all directions.

62

Sinusoidal ion trap

users may notice the

similarity between the

square wave stability

diagram in Figure 4 (c)

and the stability diagram

for sine waves [6, 17]. In

fact, if the q-axis of Figure

4 (c) is rescaled by a factor

of 4/, the two diagrams

can be overlaid. This

observation leads to the

suggestion that ion motion

in square and sine wave

operated traps are

essentially the same within

a constant.

These stability

diagrams by themselves

have limited value. They

let the user know whether

or not an ion is stable.

However, they are binary,

Figure 4.4: Mathieu stability diagrams of zone A in q, a space

of (a) the stability in the x-axis direction (blue), (b) the stability

in the y-axis direction (yellow) and (c) the overlay of the x and

y-stability diagrams to define the green region where the ions

are stable in both the x- and y- directions simultaneously. This

color coding system is consistent throughout all stability

diagrams.

63

stable or unstable. They do not describe how effectively the ions are bound in the trap. The

pseudopotential well depth is used for this purpose. Well depth is usually defined in Mathieu (q,

a) space. It may be determined at any point in that space. Three dimensional plots of well depth

have been created and can be found in reference [9]. Like stability, the well depth is determined

along each orthogonal axis independently. To define the well depth of an ion trap or guide, the

well depth plots for each axis are overlaid.

Definition of the well depth is simplified because digital trap and guides are normally

operated without imposing a DC potential between the electrodes. Consequently, the Mathieu

parameter a is always zero. Therefore, only 2D plots of the well depth as a function the Mathieu

parameter q are required for digital operation of guides and traps under normal conditions. The

variables for operation of a digitally-driven ion trap or guide are frequency and mass. Stability

diagrams made as a function of m/z and frequency are much more user friendly. These diagrams

are not universal. They require the user to specify the operational voltage and radius of the

device that they are using; however, they are useful because these parameters do not generally

change during mass analysis. A spreadsheet program that calculates (m/z, F) stability diagrams

and well depth for a = 0 can also be found on our group website.

Figure 5 illustrates the concepts discussed in this section. Figure 5 (a) shows the stability

diagram for square wave operation (50/50 duty cycle) of a 2D ion guide that covers the range of

the first four stability regions labeled A through D. This is the same labeling scheme shown in

March’s book [17]. Zones A and C lie symmetrically on the a = 0 axis. Zones B and D require

the use of a DC potential between the electrode sets (i.e., a ≠ 0) to access these stability regions

with this waveform.

64

Figure 5 (b) illustrates the pseudopotential well depth (in volts/100V0-p operation) along

the a = 0 line as a function of q on the same scale as the (q, a) stability diagram in (a). Wherever

there is a green area on the a = 0 line in 5 (a), the value of the well depth dips below zero in 5

(c). It illustrates the well depth of zones A and C as a function of q. The well depth along each

orthogonal axis is presented in Figure 5 (b); however, because the stability zones are symmetric

about the a = 0 axis (see Figure 5 (a)), the well depth plots precisely overlay each other. This

happens whenever the duty cycles of the applied waveforms are the same.

Figure 5 (c) depicts the square wave stability diagram in (F, m/z) space for a = 0. We call

this the broadband stability region due to the large range of stable ion masses at any given

Figure 4.5: (a) The stability diagram in Mathieu space showing the A, B, C and D stable

region for a 50/50 (square) waveform. (b) The pseudopotential well depth plot for 100 V0-p

operation as a function of q along the a = 0 line of the stability diagram in (a). (c) The m/z.

F stability diagram at a = 0, V = 100 V0-p and r0 = 4.15 mm for a 50/50 waveform.

65

frequency. Figure 5 (c) depicts the A and the C stability zones. The narrowness of the stability

range in zone C may suggest to some that it may be used as a mass filter. However, this is not

practical because, while transmission of ions through zone C may be mass resolved, there is also

likely to be unresolved transmission of higher mass ions through zone A simultaneously at the

same frequency.

4.7 Application of stability diagrams for mass filtering in stability zone A at a = 0

Stability and well depth plots change significantly with changes in duty cycle. With

enough control over the waveform duty cycles, a narrow mass window can be created that will

permit mass filter analysis [9].

Figure 6 (a) shows the stability diagram for a 61.124/38.876 duty cycle waveform. To

create a mass window without adding a time averaged DC potential between the quadrupole

Figure 4.6: (a) The stability diagram in Mathieu space showing the A and B stable regions

for a 61.124/38.876 duty cycle waveform. (b) The 100 V0-p operating voltage

pseudopotential well depth plot as a function of q along the a = 0 line of the stability diagram

in (a). The m/z. F stability diagram at a = 0, V = 100 V0-p and r0 = 4.15 mm for a

61.124/38.876 duty cycle waveform.

66

electrodes and the end caps, the sum of the duty cycles of the applied waveforms must add to

100% [6]. When the duty cycle of the first waveform is not equal to the second, high and low

mass cutoffs are created producing a mass window. Increasing the difference between duty

cycle 1 and 2 narrows the mass window. When the duty cycle is increased beyond

61.2099/38.7901 the mass window disappears [9]. Mass window creation occurs by distorting

the stabilities along each axis so that the intersection of the green stable region with the a = 0 line

narrows. The inset of Figure 6 (a) provides a zoomed view of the range of stable q values along

the a = 0 line for the 61.124/38.876 duty cycle waveform. The ratio of q/Δq=m/m,

approximately 100, is the resolving power [9]. Here m defines the possible range of

transmitted masses without consideration of transmission efficiency. Therefore, the measured

m at full width half maximum of the transmitted peak will be smaller than the m derived from

q. q/q provides a benchmark to compare resolving power with other methods of mass filter

analysis.

Changing the duty cycle changes the well depth plots. Figure 6 (b) shows that the wells

split and shift in depth. The 61.124/38.876 waveform creates a deeper well along the x-axis and

is shifted toward lower values of q than the 50/50 square wave well (see Figure 6 (b) and

compare with Figure 5 (b)). The y-axis well is shallower and shifted toward higher values of q.

The range of stability along the a = 0 line is defined by the overlap of the two wells. The depth

of the mass window is defined by the intersection of the two wells at a little over 0.1 V when

operating at 100 V0-p and a radius of 4.15 mm (see Figure 6 (b) and inset). As the overlap of

these wells shown in the inset of Figure 6 (b) get smaller, the mass window pseudopotential well

becomes shallower (lowering the ion transmission) and the width of the window gets smaller

67

(decreasing delta q) increasing the resolving power. Since ion transmission correlates with

window well depth, this demonstrates that better resolution requires lower ion transmission.

The (F, m/z) stability diagram shown in Figure 6 (c) defines the relationship between

mass and frequency for the mass filter. It can also be used to identify the mass limits of the

analysis. The mass is inversely proportional to the frequency squared [22]. Therefore, there is

no upper limit for mass filter analysis because there is no practical limit to the low range of the

frequency. There is, however, an upper limit to the frequency that is imposed by the available

hardware that limits the low mass cutoff of analysis. For our instrument, this limit is currently

defined by the high voltage pulsers. Normally, our lab uses Directed Energy Inc. (DEI) pulsers

to create the high voltage waveforms from the generated low voltage waveforms. The 1500 V

DEI pulser specifications set the frequency maximum at 240 kHz. This limit is set to keep the

high voltage field effect transistors (FETs) from overheating at the maximum voltage of 1500 Vp-

p. The power dissipation limit of these pulsers is 150 W. The thermal output power P of the

FETS is defined by P=CFV2, where C is the capacitance of the system, and F and V are the

frequency and peak to peak voltage. Here assuming a system capacitance of ~ 250 pF yields a

thermal output 10 % under 150 W power limit. However, if a reduced voltage is used, then the

pulsers can easily be driven to higher frequency without thermally damaging the FETs. This

higher frequency is limited by the gate circuit of the pulsers to roughly 550 kHz. That frequency

sets the lower mass limit of our DMF system when it operates with DEI pulsers. From Figure 6

(c), that lower limit would be around m/z = 300.

Credible mass spectra can be obtained at this frequency limit with DEI pulsers in the low

mass range even with the voltage at 60 V0-p with well depth limited to less than 0.1 V. This was

demonstrated by the mass spectrum of tranexamic acid (TXA) salts shown in Figure 7.

68

There are other commercial pulser options available that will provide higher frequencies and

thereby permits lower mass limits. For example, Behlke Inc. (www.behlke.com) makes high

voltage pulsers that can operate at 3 MHz at higher voltages. Consequently, mass analysis can

be performed down to less than m/z = 20, if desired or necessary with DMFs. These pulser

systems are naturally more expensive. However, there is yet another option.

4.8 Zone B evaluation

Mass analysis can also be reliably performed in stability zone B merely by further increasing

the duty cycle. Changing the duty cycle distorts the x- and y-axes stability zones. Continuing to

increase the duty cycle beyond the zone A mass filter limit at 61.2099/38.7901 moves zone A

Figure 4.7: The DMF spectrum of TXA salts near the low mass cutoff defined by the

maximum frequency (550 kHz) provided by DEI Inc. high voltage pulsers.

69

below the a = 0 line while moving zone B onto it. A 75/25 waveform centers zone B on the a =

0 line (see Figure 8 (a)). Therefore, the ions are not stable in zone A and are stable in zone B for

this waveform at a = 0 operation.

At this duty cycle, the y-axis well sits in the middle of the x-axis well (see Figure 8 (b)

and inset). The y-axis well then defines the pseudopotential well depth of the ion in the trap in

zone B because the ions are always stable in both directions when inside the y-axis well. From

the inset, it appears that roughly -6 V of well depth are available for every 100 V0-p of trapping

potential for this waveform. Figure 8 (c) maps the narrow green stability region as a function of

m/z and frequency. Comparison of Figures 6 (c) and 8(c) show the same values of m/z are stable


for a 75/25 duty cycle waveform. (b) The 100 V0-p operation pseudopotential well depth

plot as a function of q along the a = 0 line of the stability diagram in (a). The m/z. F

stability diagram at a = 0, V = 100 V0-p and r0 = 4.15 mm for a 75/25 duty cycle waveform.

70

at lower frequencies. The width of the well of q ~ 0.1 is too large to be an effective mass filter

because q/q = m/m = ~20 is an indication of the resolving power that would be attained.

With enough resolution, changing of the duty cycle can be used to further narrow the

mass window to create a credible mass filter in zone B. Changing the waveform by decreasing

the larger duty cycle value while increasing the smaller value shifts the y-axis well to the lower q

while moving the x-axis well to higher q. A 73.06/26.94 waveform m/z, F stability diagram is

shown in Figure 9 (a). The stability window where the two wells overlap has shifted toward

higher mass relative to the x-stability region shown in blue. The pseudopotential well depth as a

function of q is shown in Figure 9 (b). The inset of 9 (b) shows that this duty cycle combination

creates a narrow mass window with a q/q resolving power of ~100 and a well depth of ~-0.22

V. The same resolving power yields a deeper well for the mass window in stability zone B than

in zone A.

71

Changing the waveform by increasing the larger duty cycle while decreasing the smaller

shifts the y-axis well to the higher q while moving the x-axis well to lower q. A 76.50/23.50

waveform m/z, F stability diagram is shown in Figure 10 (a). The stability window has shifted

toward lower mass relative to the x-stability region shown in blue. The pseudopotential well

depth as a function of q is shown in Figure 10 (b). The inset of 10 (b) shows that this duty cycle

combination creates a narrow mass window with a q/q resolving power of ~100 and a well

depth of ~-0.52 V. The same resolving power yields a significantly deeper well for the mass

window in stability zone B. Increasing the well depth should increase transmission as well as

increase the attainable resolution.


for a 73.06/26.94 duty cycle waveform. (b) The 100 V pseudopotential well depth plot as a

function of q along the a = 0 line of the stability diagram in (a). The m/z. F stability diagram

at a = 0, V = 100 V0-p and r0 = 4.15 mm for a 73.06/26.94 duty cycle waveform.

72

4.9 Mass analysis in zone B

(a) Results:

Figure 11 shows the results obtained when the mass filter duty cycle was set to 75/25. The

sum of the duty cycles is 100%, so there is no axial potential created. At this duty cycle, the

well-depth diagram shows the potential of less than -7V that confines the ions in radial direction.

The red trace that depicts the potential well in the y-axis direction is nested inside of the blue

trace (x-axis potential well) indicating that the y-axis potential well defines the ion stability in

the zone B. The q value corresponding to the deepest part of the y-axis well is 2.0 and it was

used to obtain this spectrum. The pulser power supplies were set to ± 120V. The ions are

trapped in the first quadrupole with a 13/13 waveform. This corresponds to -88.8V of axial

trapping potential. The ions were then ejected with a 51/51 waveform, which creates a 2.4 V


for a 76.50/23.50 duty cycle waveform. (b) The 100 V pseudopotential well depth plot as a

function of q along the a = 0 line of the stability diagram in (a). The m/z. F stability diagram

at a = 0, V = 100 V0-p and r0 = 4.15 mm for a 76.50/23.50 duty cycle waveform.

73

axial potential in the first quadrupole while the digital mass filter operating with a 75/25

waveform has a 0 V axis potential. The first quad was operated in the stability zone A while the

mass filter was operated in the stability zone B with 75/25 waveform at q = 2.0. Ions are trapped

in the first quadrupole for 20 ms and ejection duration was set to 2 ms. The trapping time had to

be decreased to 20 ms to avoid saturating the detector. The resolving power of the +8 charge

state was found to be 92. Here m is defined by the FWHM of the peak as opposed to the range

of masses that the filter can theoretically pass. In this case m is smaller and the observed

resolving power was better than the value of 20 that was projected from the stability diagram.

In Figure 12 the mass filter waveform was changed to 73.05/26.95. This moved the y-

axis potential well toward lower q values and the x-axis toward higher. The small overlap of red

and blue traces resulted in the less than -0.2 V radial stability well with a q of 1.77 (see inset

Figure 12 (a)). The conditions on the first quadrupole were 13/13 for axial trapping (-88.8V),

and 57/57 for axial ejection (16.8V), q was 0.6 and the trapping duration was set to 100 ms. The

Figure 4.11: (a) A close up of a 75/25 pseudopotential well for operation at 120 V0-p. (b)

DMF spectrum of lysozyme (zone B) with a 75/25 waveform revealing a resolving power

of R = m/m = 92.

74

resolving power of the +8 charge state was calculated in the same manner as above and was

found to be 166. The increase in the resolving power was due to narrowing the mass window

while maintaining ion throughput.

Figure 13 shows the pseudopotential well-depth of the 76.6/23.4 mass filter waveform. In

this case the y-axis potential-well shifted toward higher q and the x-axis well shifted toward

lower q resulting in a small overlap between red and blue traces. The overlap gives ions less than

-0.27 V of radial well depth and sets q at 2.25 (see the inset of Figure 13 (a)). The first

quadrupole was operated with identical trapping and ejection conditions as the previous example

with the exception of trapping duration, which was in this case 80ms. The resolving power for +8

charge state was 293.

Figure 4.12: (a) A close up of a 73.05/26.95 pseudopotential well for operation at 120 V0-

p. (b) DMF spectrum of lysozyme (zone B) with a 73.05/26.95 waveform revealing a

resolving power of R = m/m = 166.

75

The low mass limit of our system is not defined by the DMF operating in zone B, rather it is

determined by the low mass cutoff of the first quadrupole ion guide used to capture the ions

before analysis. Low mass analysis in zone B is shown in Figure 14. For this work, recently

developed in house high voltage pulsers with a high frequency limit of 700 kHz were used to

mass analyze asparagine at 132 Da. Here the first quadrupole was operated at 60 V0-p to capture

the ions with a well depth of -15V before injecting them into the DMF operating in zone B. The

low mass cutoff for ion capture in the 1st quadrupole ion guide was ~ m/z = 120. As shown in

Figure 14, operating in zone B handles mass analysis in this range well.

Figure 4.13: a) A close up of a 76.6/23.4 waveform pseudopotential well for operation at

120 V0-p. (b) DMF spectrum of lysozyme (zone B) with a 76.6/23.4 waveform revealing a

resolving power of R = m/m = 293.

76

(b) Discussion:

1. Sensitivity

Quadrupole mass filters (QMFs) and their hybrids, triple quadrupoles and QTOFs are known

for their sensitivity [23]. QMFs obtain that sensitivity by monitoring a single mass for a

prolonged period of time and integrating the detector response. This monitoring is often

performed by ion counting to obtain the best sensitivity, which is limited by the efficiency of ion

injection into the filter. Generally, pushing ions into and through a mass filter is an inefficient

Figure 4.14: ESI DMF spectrum of asparagine operating in zone B. The low mass limit

was defined at 700 kHz by trapping in zone A in the first quadrupole.

77

process and is affected by the width of the mass window. The narrower the mass window, the

lower the transmission efficiency. There is always a tradeoff between resolution and sensitivity

in mass filter analysis.

The connection between resolution and sensitivity is the pseudopotential well depth. As we

have shown above with the use of stability diagrams and well depth plots, the well depth shrinks

as the mass window narrows. For a given mass window width, the deeper the well the better the

transmission/sensitivity. The best results are then defined by the slopes of the walls of the

pseudopotential well. Steeper slopes produce deeper wells for a given window width and better

sensitivity. Duty cycle-induced zone B yields steeper slopes than zone A (See Figures 6 (b), 11

(b), 12 (b) and 13 (b)). Zone B for sinusoidal operation yields a steep slope pseudopotential well

also. However, transfer of ions into zone B under sinusoidal conditions is problematic because

the filter has to operate at a Mathieu parameter near a = 2.5 and requires substantially higher

operating voltages. This issue has been seen as a disadvantage [24]. The loss of sensitivity for

zone B analysis will now be discussed using stability diagrams.

Operating a mass filter at nonzero values of the Mathieu parameter a requires a DC field

between the electrodes. This field develops over the path from the end cap to a distance of

approximately 1.5 times the quadruple radius along the central axis of the device where the

quadrupolar fields grow to full strength. This is known as the fringe field region [25] and it is

depicted in the equipotential contour plot in Figure 15 (a) as the curved equipotential lines shown

at the ends of the quadrupole. The equipotential lines straighten out after approximately 1.5 r0.

These fringe fields can be defocusing [26].

78

An example of this defocusing issue can be seen from zone A mass filter analysis during

sinusoidal operation using stability diagrams. In Figure 15 (b) the a, q stability diagram of zone

A is depicted. The ions enter the quadrupole through the end cap electrode where the AC and

DC potentials are zero. Because the values of q and a are directly proportional to these

respective potentials, they are also zero at the end cap electrode. Mass filter analysis is

performed at the apex of the zone A stability region [17]. If the ions move directly from the end

cap electrode into a quadrupole operating as a mass filter, they are believed to take the straight-

line path through the stability diagram to the apex depicted with a black arrow. The straight-line

Figure 4.15: (a) shows the equipotential contour plot of the ends of a quadrupole showing

the fringe fields. (b) The black arrows delineate the ion path through zone A stability

diagram when the ions move from the end cap electrode into the mass filter. The horizontal

red arrow marks the ion path through the stability diagram when the ion moves from the

end cap electrode into the RF-only short quadrupoles. The vertical red arrow indicates the

path when the ions transition from the short quadrupole into the mass analyzer. The short

RF-only quadrupole ensures the ions remain stable during injection into mass filter.

79

path assumes that the fields are developing linearly. This path shows that the ions are passing

through the unstable blue region and presents an opportunity for ion loss.

To overcome the loss of ions, short RF-only quadrupole stub electrodes can be placed

between the end cap and the mass filter [27]. These electrodes operate at the same RF voltage as

the mass filter and eliminate the defocusing effect by delaying the DC ramp until the quadrupole

potential is fully developed. This can be seen from the red arrowed path in the stability diagram

shown in Figure 15 (b). Because the stub electrodes are RF only, the path through them

represents a ramp of q along the a = 0 line as depicted by the horizontal red arrow. As the ions

transition from the stub electrodes into the mass filter, the DC potential develops, and the ions

follow the vertical arrow up to the apex where the ions are filtered. With the stub electrodes, the

ion path into the mass filter operating in zone A is completely stable (always in the green stable

region). They enhance the sensitivity of mass filter analysis.

The reason for the loss of sensitivity for zone B analysis during sinusoidal operation is

shown in the stability diagram in Figure 16. Unlike zone A analysis, the short RF-only

quadrupole is not effective in zone B. The horizontal red arrow shows the path through the

stability diagram when the ions traverse the RF-only quadrupole. They pass through the stable

zone A and become unstable as the quadrupole fields fully develop when the ions are directly

below the zone B analysis point. When the ions pass out of the RF-only quadrupole and into the

zone B analyzer, the DC potential quickly ramps up and they vertically traverse the stability

diagram to zone B. All of that white region the ions travel through is not stable in the horizontal

or the vertical direction. Consequently, adding the RF-only quadrupole stubs before the filter

just provides more opportunity for the ions to defocus and be lost. Therefore, it is better to forgo

the RF-only stubs and allow the ions to move directly from the end cap into the zone B analyzer.

80

The ions would then traverse the path defined by the black arrow through the stability diagram.

This path is defocusing too because it passes through the white region; however, it minimizes ion

loss by getting the ions into the analyzer as quickly as possible to minimize the defocusing

effect. It is the instability of the ion path into the sinusoidally-operated zone B analyzer that

causes the loss of transmission and sensitivity.

Figure 4.16: The stability diagram depicting the A, B and C stability zones. The Black

arrow depicts the ion path through the diagram when the ions move from the end cap

directly into the zone B mass analyzer. The horizontal red arrow depicts the path from the

end cap through RF-only short quadrupole. The vertical red arrow shows the transition

from into the zone B mass analyzer. Both paths are unstable.

81

For sinusoidal operation without the use of the RF-only electrodes, ion losses entering the

zone B analyzer are much greater than the losses entering the zone A analyzer. The AC and DC

operation voltages are much higher for zone B analysis at any given value of m/z and thereby

yield greater defocusing forces on the ions as they move into the analyzer. Oddly, the opposite is

true for DMF analysis at a = 0. In fact, we have experimentally observed an increase in

sensitivity in moving from zone A to zone B analysis.

It is really the DC potential that creates the defocusing effect as the ions transition into

the mass filter. For DMF analysis in zone A and B, there is no direct DC potential applied

between the quadrupole electrodes. This is the condition for a = 0. Zone A and B analyses

occur at the same AC potential. However, there is a time-averaged DC potential imposed by the

duty cycle of the waveform. The time averaged voltage for DMF operation in zone A with a

~61/39 is approximately 22 V DC/100 V AC operation. This is about the same as for sinusoidal

operation at 100 V AC. The time averaged DC potential at 100 V AC zone B operation with a

75/25 waveform is about 50 V DC. This difference is not as large as the change in DC potential

that occurs when transitioning between zones A and B for sinusoidal analysis which is

approximately a factor of 10 (a = ~0.25 → a = ~2.5). Moreover, the defocusing force increases

with increasing m/z for sinusoidally-driven mass filter analysis because the AC and DC voltages

increase linearly with mass and become much larger during the scan. On the other hand, the AC

voltage remains constant for a = 0 DMF analysis.

For DMF zone A and B analyses, the ions move directly into the analyzer over the same

distance through the same fringe fields. The change in the time-averaged DC potential in

moving from zone A to zone B is a little more than a factor of 2. While this is a significant

change, we have observed an increase as opposed to a decrease in transmission/sensitivity at

82

constant AC voltage for DMF analysis. We have correlated that to the increase in well depth of

the window. However, we also point out that we were able to use higher ion beam energies into

the quadrupole while maintaining resolution. This same observation was made for sinusoidal

zone B analysis [26]. Unlike sinusoidal zone B analysis, it appears that increasing the well depth

and increasing the beam energy has a larger effect on increasing the transmission than the change

in time averaged DC potential has on reducing it while using the DMF in zone B.

2. Resolving power

The resolution of our mass filter system is not limited by our waveforms. Rather, it is

limited by the construction of our quadrupoles. Our mass filter is constructed of 3/8 inch

diameter cold-rolled stainless steel rods that are held in place by peek holders. The rod

electrodes are not precision ground and the holders do not permit the spacing to be engineered to

the nearest micrometer. Our quadrupoles were only meant to be ion guides, not analyzing

quadrupoles. Because they are used to analyze intact proteins, the rods are removed from their

holders to clean them when they become contaminated. Consequently, the variation of the radius

along the quadrupole is at best ± 20 m routinely after each cleaning. The variation in radius can

be related to the resolving power by q/q = r/2r. The radius of our quadrupoles is 4.15 mm.

This suggests the resolving power should be limited to about 104. This is essentially what we

are achieving from zone A and zone B analyses. We have achieved approximately R = m/m =

300 in zone B and in zone A previously. The resolving power often varies after cleaning

(sometimes R = 400-500 have been achieved) and thereby suggests that it is limited by geometric

factors, namely variation in the radius along the length of the quadrupole.

There is no reason that DWT cannot achieve the same resolving power currently enjoyed

by commercial sinusoidally-driven systems. Our theoretical analysis of mass filters shows that

83

q asymptotically approaches zero as the waveform duty cycle approaches 61.2099/38.7901 [9].

The changes to the duty cycle that have been made to create filtering waveforms in this study

have occurred in the first and second places after the decimal place of the percent duty cycle.

We can make changes in the duty cycle in the 3rd place after the decimal and observe a response.

Control of the duty cycle to the 3rd place after the decimal suggests that there is already sufficient

control of q to reproduce the resolution of commercial instruments according to our empirical

fit of the resolving power from reference [9]:

𝑞

∆𝑞= (

𝛿

11.5∙𝛿0∙|𝛿0−𝛿|) (5)

Where δ is the fraction of the period when the waveform is in the high state or fractional duty

cycle and δ0 is the fractional duty cycle at the asymptote where q becomes zero. At the point

where δ0- δ= 0.00001, q/q = ~8700. To put this into context, this is on par with the

capabilities of the best commercial triple quadrupole instrument. Our digital waveform

generation method allows very good control of the mass window. Consequently, if our

waveform generation (WFG) system were used with engineered analyzing quadrupoles, better

resolving power and sensitivity should be obtained.

4.10 Conclusions:

This work describes mass filter analysis using digital waveforms in stability zones A and B.

It is meant to be a tutorial of the use of the duty cycle, stability diagrams and pseudopotential

well plots to aid the reader in the operation of DMFs, reveal the differences between SWT and

DWT based instruments, discuss limitations and suggest possible futures. It showed the facility

with which zone B analysis could be used to enhance the measurements in the low mass range

and improve sensitivity and resolution. Zone B analysis showed an increase in sensitivity and

84

resolution over zone A analysis. These results and the analysis presented in this work suggest a

bright future for DMF analysis.

4.11 Acknowledgement:


85

4.12 References

1. Lee, J., et al., Simulation of duty cycle-based trapping and ejection of massive ions using

linear digital quadrupoles: The enabling technology for high resolution time-of-flight

mass spectrometry in the ultra high mass range. International Journal of Mass

Spectrometry 2011. 304(1): p. 36-40.

2. Wang, X., et al., Increasing the trapping mass range to m/z=10(9)-A major step toward

high resolution mass analysis of intact RNA, DNA and viruses. International Journal of

Mass Spectrometry, 2012. 328: p. 28-35.

3. Gotlib, Z.P., G.F. Brabeck, and P.T. Reilly, Methodology and Characterization of

Isolation and Preconcentration in a Gas-Filled Digital Linear Ion Guide. Anal Chem,

2017. 89(7): p. 4287-4293.

4. Brabeck, G.F., et al., Development of MSn in Digitally Operated Linear Ion Guides.

Analytical Chemistry, 2014. 86(15): p. 7757-7763.



1-8.

6. Brabeck, G.F. and P.T.A. Reilly, Mapping ion stability in digitally driven ion traps and

guides. International Journal of Mass Spectrometry, 2014. 364: p. 1-8.

7. Hoffman, N.M., et al., A Comparison Based Digital Waveform Generator for High

Resolution Duty Cycle. Review of Scientific Instruments, 2017. Accepted 7/8/2018.

8. Koizumi, H., W.B. Whitten, and P.T.A. Reilly, Controlling the Expansion into Vacuum—

the Enabling Technology for Trapping Atmosphere-Sampled Particulate Ions Journal of

the American Society for Mass Spectrometry, 2010. 21(1): p. 242-248.

9. Brabeck, G.F. and P.T.A. Reilly, Computational analysis of non-traditional waveform

quadrupole mass filters Journal of The American Society for Mass Spectrometry, 2016.

27(6): p. 1122-1127.

10. Opacic, B., et al., Using Digital Waveforms to Mitigate Solvent Clustering During Mass


2018.

11. Opačić, B., et al., Impact of Injection Potential on Measured Ion Response for Digitally

Driven Mass Filters. International Journal of Mass Spectrometry, 2018. Accepted

August 30, 2018.

12. Hoffman, N.M., B. Opačić, and P.T.A. Reilly, Note: An inexpensive square waveform ion

funnel driver. Review of Scientific Instruments, 2017. 88(1): p. 3.

86

13. Kim, T., et al., A Multicapillary Inlet Jet Disruption Electrodynamic Ion Funnel Interface

for Improved Sensitivity Using Atmospheric Pressure Ion Sources. Analytical Chemistry,

2001. 73(17): p. 4162-4170.

14. Lee, J., et al., High Resolution Time-of-Flight Mass Analysis of the Entire Range of Intact

Singly-Charged Proteins. Analytical Chemistry, 2011. 83: p. 9406-9412.

15. Chen, H., J. Lee, and P.T.A. Reilly, High-resolution ultra-high mass spectrometry:

Increasing the m/z range of protein analysis. Proteomics, 2012. 12(19-20): p. 3020-3029.

16. Opačić, B., et al., Using Digital Waveforms to Mitigate Solvent Clustering During Mass


2018.

17. March, R.E. and J.F.J. Todd, Quadrupole ion trap mass spectrometry. 2005, Hoboken,

N.J.: J. Wiley.

18. Konenkov, N.V., M. Sudakov, and D.J. Douglas, Matrix methods for the calculation of

stability diagrams in quadrupole mass spectrometry. Journal of the American Society for

Mass Spectrometry, 2002. 13(6): p. 597-613.

19. Pipes, L.A., Matrix Solution of Equations of the Mathieu-Hill Type. Journal of Applied

Physics, 1953. 24(7): p. 902-910.

20. Reilly, P.T.A. and G.F. Brabeck, Mapping the pseudopotential well for all values of the

Mathieu parameter q in digital and sinusoidal ion traps. International Journal of Mass

Spectrometry, 2015. 392: p. 86-90.

21. Ding, L., M. Sudakov, and S. Kumashiro, A simulation study of the digital ion trap mass

spectrometer. International Journal of Mass Spectrometry, 2002. 221(2): p. 117-138

.

22. March, R.E. and J.F.J. Todd, eds. Practical Aspects of Ion Trap Mass Spectrometry:

Chemical, Biomedical, and Environmental Applications. Modern Mass Spectrometry

Series. Vol. 3. 1995, CRC Press: Boca Raton, FL. 544.

23. Harris, D.C., Quantitative Chemical Analysis. Ninth ed. 2016, New York, NY: W. H.

Freeman and Company. 792.

24. Syed, S.U.A.H., et al., Quadrupole Mass Filter: Design and Performance for Operation

in Stability Zone 3. Journal of The American Society for Mass Spectrometry, 2013.

24(10): p. 1493-1500.

25. Schwartz, J.C., M.W. Senko, and J.E.P. Syka, A two-dimensional quadrupole ion trap

mass spectrometer. Journal of the American Society for Mass Spectrometry, 2002. 13(6):

p. 659-669.

87

26. Du, Z., D. J. Douglas, and N. Konenkov, Elemental analysis with quadrupole mass filters

operated in higher stability regions. Journal of Analytical Atomic Spectrometry, 1999.

14(8): p. 1111-1119.

27. Douglas, D.J., Linear Quadrupoles in Mass Spectrometry. Mass Spectrometry Reviews,

2009. 28(6): p. 937-960.

88

CHAPTER FIVE: INTERFACING DIGITAL WAVEFORMS WITH ACCELERATION

QUADRUPOLE TIME-OF-FLIGHT (Q-TOF) MASS SPECTROMETER FOR

COLLISION-INDUCED DISSOCIATION (CID)

OF BOVINE INSULIN

5.1 Attribution

The instrument program and the user interface (UI) for the following studies were

created/edited by Adam P. Huntley.

5.2 Introduction

The digital quadrupole mass filter (DQMF) that was the focus of the previous chapters,

lets only one m/z reach the detector at each step. The ions were generated using an unenclosed

electrospray source and so the distribution of charges in a population of ions entering the

instrument is constant. The entering ions are stored in the digital linear ion trap. The stored

population of ions is generally different from the population entering the trap but usually

contains several charge states. However, since the frequencies of the trap and mass filter are

consistently stepped together, the measured population directly correlates with the population

entering the instrument. In general, the spectral quality is improved because only one m/z hits the

detector per step. Although the digital mass filter has good resolving power due to its mass

selectivity, it does present a barrier for some type of analyses. One analysis that this particular

instrument cannot perform in a timely manner, is collision-induced dissociation (CID).

CID is the process of collisional activation followed by fragmentation of the ion. Since it

is not known what the fragments of the ion dissociation will be, mass filtering is not the

89

appropriate technique to use because it only allows for one m/z to reach the detector. Therefore,

interrogating the products of the CID process one mass step at a time would be very time

consuming. Time of flight analysis after ion fragmentation is not only possible but also very

efficient because unlike in the mass filter analysis, all the product ions after CID are passed to

the detector. All ions in the population are measured simultaneously, and their intensities are

proportional to the number of ions in distribution. The fragmentation process with the use of

digital waveforms, involves a collection then storage of a population of ions in a linear trap,

followed by isolation of a target ion population for CID. The isolated ion population is stored

while their isolation induced motion slows down by colliding with inert gas molecules. They are

then excited by making them unstable for a short duration of time, or by changing their natural

motion in the trap by changing the duty cycle repeatedly. This excitation and collisional cooling

process can be repeated. There is no limitation to how often they can be excited. This provides a

great amount of control of the excitation process. The internal energy of the isolated ions can be

slowly raised until they fragment. All product ions are then ejected into the Q-TOF to be mass

analyzed.

To perform Q-TOF CID, the instrument program and user interface (UI) were modified.

The former mass filter program determined and scanned through the stable frequencies

automatically based on q, Δ m/z, and the start and end m/z. In the Q-TOF MS CID program, this

automation was removed because the conditions of the linear trap need to be stable for ions with

largely different m/z values and because it is not known what the fragment ions will be. The trap

stability was determined by the operator by choosing the duty cycle and frequency combination

that trapped and stored largely different m/z ions. There was also the addition of multiple

excitation blocks. Each block was programmatically the same. They changed duty cycle, or

90

frequency, or both for a duration of time. After this change, the trap returned to broadband

trapping stability for a second duration. The number, duration and intensity of times of excitation

are adjustable and limitless. To understand the spectra that result from the fragmentation, the

initial m/z needs to be known. Each excitation function can also be used to isolate ions by

momentarily changing conditions of the trap so only one value of m/z is stable. An initial

problem with isolation was that ions were still entering the trap. This was solved by lowering the

frequency of the digital ion funnel and keeping it low until isolation and excitation are complete

and the trap ejected the product ions. Substantially lowering the funnel frequency caused the

incoming ions to be unstable, so that they didn’t pass through the funnel and into the trap. At the

lowered frequency, only very large m/z ions were stable in the funnel. The low mass cut off was

much higher than the largest ions in the electrosprayed population; therefore, the funnel operated

as an effective ion gate.

5.3 Experimental

For the last chapter of this dissertation, insulin was used to demonstrate the CID

experiment. It was purchased from Sigma Aldrich Company (St. Louis, MO) and used without

further purification. The solution was made in 50% methanol/ 50% water (HPLC grade, Fisher

Chemical, Waltham, MA). Glacial acetic acid (Fisher Scientific, Hampton, NH) was added to the

insulin solution to help dissolve it and the final concentration obtained was 40 µM. The graphical

representation of the instrument used can be seen in Figure 5.1.

91

The sample was introduced by electrospray ionization using the commercial fused silica

capillary with

a 30 ± 2 µm

tip (New

Objective

Co.) with an

applied

potential of

+2600 V

relative to the

heated

capillary inlet.

The capillary

inlet was heated to 100 °C. Sample solution was pneumatically pushed through the ESI capillary

at 1 psig. Ions entered the instrument through a 0.015 cm diameter inlet heated capillary and

expanded within a digitally operated ion funnel operated at 170 kHz and 48 volts peak to peak

(rectangular waves). There was -10V of DC potential across the ion funnel. The pressure in the

differentially pumped ion funnel chamber was 1.25 Torr. The AC potential applied to the ion

funnel collimated ions and the DC potential helped move them toward the exit orifice (4 mm)

and into the digitally operated ion guide at 5.2 mTorr.

The guide was driven by a pair of high voltage waveforms created by two separate

pulsers, one for each electrode pair. The power supplies were maintained at + and -100V. The

duty cycle of the waveforms and the calculations for axial trapping and ejection of ions were

Figure 5.1. Instrument schematic.

92

explained in chapter one and will not be discussed here. The trapping duty cycle for the insulin

analysis was set to 38/38 for 2 seconds at 375 kHz. The ejection duty cycle was 53/53 with 8 ms

duration. The second quadrupole was used as an ion guide. The pressure in this chamber was

5.5x10-6 Torr. The duty cycle was set to 50/50 and pulser voltages to ±100V.

The isolation of the +4 charge state was accomplished in two steps. First by changing the

frequency to 235 kHz to eliminate the higher charge state ions. In the second step, the duty cycle

was changed to 42/36 and the frequency to 430 kHz to eliminate the lower charge state peak. The

isolated +4 charge states insulin ions were then excited by changing the frequency to 435 kHz,

which caused them to radially heat up and eventually fragment by going from trapping to

excitation conditions (more detailed explanation in the discussion part). After the excitation step,

the ions were translationally cooled through collisions with gas molecules in the first quadrupole

during the switch back to the trapping conditions, and then ejected into the second quadrupole by

changing the duty cycle. The axis potential in the second quadrupole was 0V, so the ions entered

with the same energy as they were ejected with. They passed through the second quadrupole with

the same beam energy they had when they entered, and then they exited into the TOF region.

The ions exiting the second quadrupole passed through the exit orifice (4 mm) and

focusing lenses, entering the orthogonal TOF at 3.5x10-7 Torr. After 600 µs delay, the ions were

being pushed by +210V towards the accelerating region. The puller aids in that by applying -

240V. Accelerating region had -575V of potential after which ions entered a field free region at -

4600V. Reflectron was set to -1175V and +1000V. Ions hit the MCP detector at -5000V, V2 =

1180V, V3 = 2600V, PMT = -660V. The signal was recorded by a digitizer to be stored on the

computer.

93

5.4 Results and discussion

In CID, or tandem MS, the ions collide with inert gas and fragment in patterns that

depend on many parameters such as composition, size, charge state, excitation method and

instrument type [1]. All currently available methods of CID are limited to ions below roughly

m/z 8600 [2-3]. Clearly, better methods of CID are needed.

Digital waveform technology gives more control for ion fragmentation due to its ability

to manipulate the ion stability by using a duty cycle and frequency methods. The energy can be

applied into ions in new ways that are not possible in sinusoidally driven devices. This

technology will increase the mass range of the CID process. In addition, fragmentation with duty

cycle manipulation allows for the simplification of instrumentation and provides a new way for

the control of the energy of excitation and the duration of fragmentation of high mass ions.

The advantage of DWT is that it can be used to excite a very broad range of secular

frequencies and it can be performed in an extremely controlled manner to minimize ion loss and

control the rate and duration of excitation [4]. While the rate and duration of resonant excitation

(CID) in an ion trap can be controlled, the bandwidth of excitation is fixed [5]. Unfortunately,

the secular frequency bandwidth of ions increases with increasing mass and that bandwidth

becomes much broader than the excitation bandwidth and thereby provides more paths for

relaxation. A mass limit is reached where the rate of relaxation far exceeds the rate of excitation

so that sufficient levels of internal energy cannot be achieved for fragmentation [3]. The ability

to excite an extremely broad range of secular frequencies with digital waveform technology will

overcome this issue.

94

Insulin ions were used to demonstrate the isolation and excitation capability of the DWT

on intact proteins. The ions were axially collected and trapped in the first quadrupole for 2

seconds with a broadband 38/38 trapping duty cycle waveform. Figure 5.2 shows the stability

diagram for the trapping duty cycle and the illustrates the relative positions of the three charge

states within the stable region (green area). The axial trapping potential was calculated using the

time weighted average of the DC axis potential (Equation 1.) and was found to be -24V.

𝑉ₐₓₛ = 𝛴ₙ𝑡ₙ (𝑉₁,ₙ+𝑉₂,ₙ

2) (1)

Figure 5.2. 0.38/0.38 stability diagram. Broadband trapping. Approximate ion

positions indicated as black dots on the green area at 375 kHz. All three ions were

in the stable region.

95

The ions were ejected with 53/53 duty cycle, which was calculated to be +6V using the above

equation. Because the axis potential of the second quadrupole was set to zero (50/50 duty cycle),

the ions were introduced into the TOF region with +6V of energy.

Due to the low ion transmission as evidenced by the spectra in Figure 5.3, +4 charge state

was picked as the ion of interest being the most intense peak. The discussion on the isolation

process follows.

Figure 5.3. Insulin trapping and excitation spectra. +4 charge state was isolated in a two-

step procedure and then excited causing fragmentation.

50 60 70 80 90 100 110

-0.050

-0.045

-0.040

-0.035

-0.030

-0.025

-0.020

-0.015

-0.010

-0.005

0.000

0.005

Off

set

Y v

alu

es

Time (s)

Excitation

Second isolation

First isolation

Trapping

+5 +3

+3

+4

Fragment

+4

+4

+4

96

a) First isolation:

Figure 5.4 graphically explains the loss of low mass ions or +5 charge state of insulin. The duty

cycle was kept the same as it was for the trapping, but the frequency was changed to 235 kHz so

that the +5 peak was outside of the stable region. This assured loss of all the masses below

approximately 1200 m/z.

Figure 5.4. Stability diagram for 38/38 duty cycle. First isolation. 235 kHz frequency

creates a low mass cutoff. +5 charge state is outside of the stable region as are all the

lower masses.

97

b) Second isolation

To remove the high mass ions, on the right side of the +4 charge state, the duty cycle was

changed to 42/36 to create a smaller mass window. The frequency was moved to 430 kHz which

consequently made the +3 ions outside of the stability region causing them to be lost. Figure 5.5

shows this graphically. Since the ion flow during the entire isolation time was prevented by the

ion funnel, what remains in the trap after the second isolation step are only +4 charge state ions.

Figure 5.5. Stability diagram for 42/36 duty cycle. Second isolation. Frequency

of 430 kHz creates high mass cutoff. +3 charge state is in the unstable (blue)

region and is lost. +5 charge state was eliminated during the first isolation step.

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c) Excitation

Now that the only ions present in the first quadrupole were the +4 insulin charge states,

the excitation was applied in an effort to fragment them. This was done in the following way:

the ions go from the excitation conditions to the trapping conditions for as many cycles as

entered by the user. In this case, the ions cycled back and forth for 30,000 times. Again, during

that time the ion funnel was preventing the influx of new ions. The ions were radially excited in

two different ways. The excitation duty cycle was 42/36 and the frequency was 435 kHz. By

Figure 5.6. Stability diagram for 42/36 duty cycle. Excitation. Frequency of 435

kHz brings the +4 charge state closer to the stability boundary where it spends some

time heating up and eventually fragmenting.

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moving to the higher frequency and changing the duty cycle, the ions were forced to the edge of

the stable region (see Figure 5.6) where they spent 100 µs. Being so close to the boundary caused

them to get radially excited, but not so much so that they leave the trap. During the time near the

edge of the stability, the ions experienced an increase in translational kinetic energy that yielded

energetic collisions with the background gas and their internal energy slowly increased until they

fragmented. Any resulting charged fragments that were created during the excitation procedure,

were stabilized away from the boundary.

Another mechanism that radially excited ions was the switching of well depth that the

ions experience when going from trapping to excitation conditions. Well depth refers to the

energy that the ions are bound with in the trap or radial energy. At the trapping conditions, 38/38

duty cycle and 375 kHz, for +4 charge state ions, the value of q is 0.288, which corresponds to -

9V of well depth energy. The value of q for excitation conditions, 42/36 duty cycle at 435kHz, is

0.210 yielding a 0.8V of well depth energy. By switching from trapping to excitation conditions,

the ions experienced the change in radial energy that went back and forth from -9V to -0.8V.

This cycle of radial energy change was repeated for 30,000 times causing the ions to slowly heat

up and fragment. As evidenced from the spectrum, this excitation method was very gentle

resulting in only one detected fragment along with the parent ion.

The beauty of this excitation method is in the ability to increase or decrease the change in

energy that the ions are experiencing, the duration of the excitation, and the number of

excitations. The bigger the change in frequency is (or duty cycle), the more energy per jump (or

the cycle) the ions would experience and therefore, more energy would be deposited into the

ions, resulting in more fragmentation. By having more fragments that occur with more energy

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deposition, a protein signature could be generated making the DWT a useful technique in

identification of proteins.

The advantage of DWT is the ability to apply selected excitation for long periods of time

or for as many cycles as necessary, as evidenced in the example above. The traditional CID

techniques cannot do that due to the rates of ion relaxation. They heat their ions a lot in short

energy bursts and get many more fragments, which can be problematic.

+4 charge state had an approximate mass of 1435 m/z. The fragment that resulted from

the excitation procedure had a mass of approximately 1509 m/z. This indicated that the fragment

had less charges than the parent peak. Bovine insulin consists of A and B chains that are

connected with 2 disulfide bridges and has a mass of 5733.55 Da [6]. The third disulfide bridge

interconnects the A chain. B chain is longer with 11 amino acid residues that are hanging from

the back side of one of the disulfide bridges in the primary structure. These 11 amino acids have

a mass of 1212 Da without C or N terminus and the calculations suggested their loss from the

parent ion. This fragment took one charge with it leaving the parent ion with 3 charges. The

detected fragment is a +3 insulin without the 11 amino acids on the B chain. Based on this

conclusion, the breakage occurred between cysteine and glycine residues (C-N bond), right

before the disulfide bond, where 11 amino acids are connected to the rest of the B chain. We

believe that those 11 amino acids were hanging from the rest of the more tightly held structure of

insulin and broke off during the excitation process. In the work done by Fierens and others,

human insulin was fragmented with different collision activation energies [7]. Under the low

CID energy, they also observed one major fragment from a selected charge state. This confirms

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our conclusion that the duty cycle-based fragmentation is a gentle process and shows another

useful aspect of DWT.

5.5 Conclusion

These new methods of fragmentation can be applied to ultra-high mass proteins to break

their internal bonds and allow for their identification. By slowly adding the energy to the proteins

it is expected that fragmentation will occur as a function of bond energy – the weaker bonds will

break first such as dipole-dipole interactions. This will be followed by the breakage of disulfide

bonds which would allow for the identification of proteins based on the mass of the amino acid

chains. Further fragmentation is also expected, but it is not clear how specifically the cleavage

will occur. It is hoped that it will be specific enough to provide further identification.

Digital waveform technology gives more control for ion fragmentation due to its ability

to manipulate the ion stability by using a duty cycle and frequency methods [4]. The energy can

be applied into ions in new ways that are not possible in sinusoidally driven devices. This

technology will increase the mass range of the CID process. In addition, fragmentation with duty

cycle manipulation allows for the simplification of instrumentation and provides a new way for

the control of the energy of excitation and the duration of fragmentation of high mass ions.

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5.6 References

1. Paizs, B., & Suhai, S. (2005). Fragmentation pathways of protonated peptides. Mass

Spectrometry Reviews, 24(4), 508-548.

2. Reid, G., Wu, J., Chrisman, P., Wells, J., & Mcluckey, S. (2001). Charge-state-dependent

sequence analysis of protonated ubiquitin ions via ion trap tandem mass spectrometry.

Analytical Chemistry, 73(14), 3274-81.

3. Wells, M.J. and S.A. McLuckey, Collision‐Induced Dissociation (CID) of Peptides and

Proteins. Methods in Enzymology, 2005. 402: p. 148-185.]

4. G. F. Brabeck, H. Chen, N. M. Hoffman, L. Wang, and P. T. A. Reilly, “Development of

MS^n in Digitally Operated Linear Ion Guides,” Analytical Chemistry, vol. 86, pp. 7757-

7763, Aug. 2014.

5. Goeringer, D.E., et al., Theory Of High-Resolution Mass-Spectrometry Achieved Via

Resonance Ejection In The Quadrupole Ion Trap. Analytical Chemistry, 1992. 64(13): p.

1434-1439.

6. Holleman, Frits, Gale, E.A.M.. Animal insulins [internet]. 2014 Aug 13; Diapedia

8104090217 rev. no. 11. Available from: https://doi.org/10.14496/dia.8104090217.11

7. Fierens, Colette, et al. “Strategies for Determination of Insulin with Tandem Electrospray

Mass Spectrometry: Implications for Other Analyte Proteins?” Rapid Communications in

Mass Spectrometry, vol. 15, no. 16, 2001, pp. 1433–1441.

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