Essential Dynamics of Proteins using Geometrical ...

Essential Dynamics of Proteins using Geometrical Simulation

with Subspace Analysis

Presentation of Doctoral Dissertation by Charles Christian David

PREVIEW The BIG PICTURE

Why BCB Loves Proteins

•  Proteins are central to cellular function, i.e., LIFE

•  We hope to uncover the secrets of how these complex macromolecules execute their functions

•  The dream is to 'watch' proteins in action: in real time at atomic resolution

•  We approach the dream with our models.

Dynamic Trajectory of Myoglobin

DISSERTATION PROJECT Overview of the research

Three Phases I.  Benchmark the Geometrical Simulation

Model (GSM)

II.  Compare GSM results to molecular dynamics (MD) and elastic network model (ENM)

III. Apply the GSM to myosin V

INTRODUCTION Overview of Essential Dynamics & PCA

Essential Dynamics (ED)

•  The process of applying Principal Component Analysis (PCA) to a protein trajectory

PCA A General Overview

PCA I •  Identifies directions of

highest variance in data

•  A standard method of data compression and dimension reduction

•  The analysis is done on a centered C-Matrix (C): – Covariance matric (Q) – Correlation matrix (R)

PCA II •  An eigenvalue decomposition is performed on C •  The eigenvalues are plotted on a “scree plot” –  Scree Plots help identify the Essential Subspace

PCA III •  The primary limitations of PCA: – Linear Transform – Second Moment – Orthogonal – Quality of Data Sampling

•  PCA is not limited to Cartesian DOF –  Internal Distance Coordinates è dPCA

PCA IV •  Major advantage of ED is choice of subset – Examine the large-scale motions within the subset of

residues – Under the influence of the entire set of residues

contained in the protein •  Active sites •  Potential allosteric pathways

Principal Component Analysis: A Method for Determining the Essential Dynamics of Proteins. Charles C. David and Donald J. Jacobs [Submitted July, 2012]

PART I Benchmarking the GSM

GEOMETRICAL MODEL Overview of the paradigm

GSM I

•  An all atom, athermal, mechanical model

•  Geometrical Constraints used to define rigid regions of the input structure

•  Molecularly realistic perturbation of those rigid regions yields conformers (Monte Carlo)

GSM II

•  FIRST Floppy Inclusions and Rigid Substructure Topology – Covalent Bonds – Hydrogen Bonds (HB) (pseudo temp) – Hydrophobic Tethers (HP Tethers)

•  Recasts the protein into a set of rigid regions joined by hinges – Rigid Cluster Decomposition (RCD)

GSM III •  FRODA

Framework Rigidity Optimized Dynamics Algorithm – MC sampling of perturbations to the RCD

– Molecular “realism” is enforced in FRODA •  Constraint violations à Reject Conformer

– Two general modes of operation: •  Diffusion (random) •  Momentum (biased)

Methods I

•  We obtained the FIRST/FRODA implementation of the GSM from the Thorpe Group at ASU

Generating stereochemically acceptable protein pathways. Farrell, D.W., Kirill, S., Thorpe, M.F. Proteins, 78, 2908-2921. 2010

•  We designed a Java software package for the ED analysis of dynamic trajectories

Essential Dynamics of Proteins with Subspace Analysis in Java. Charles C. David and Donald J. Jacobs [In Preparation]

Methods II

•  We assessed the behavior of the model for: – Effectiveness – Efficiency – Consistency

SUBSPACE METRICS Assessing Similarity of Essential Spaces

Subspace Metrics I •  Overlap:

•  Cumulative Overlap:

•  Root Mean Square Inner Product:

•  Principal Component Projections:

ji

jiij vu

vuO

⋅=

12

2

1( )

k

ijj

CO k O=

⎛ ⎞= ⎜ ⎟⎝ ⎠∑

RMSIP(I ,J ) = 1I ui !v j( )2

j=1

J

!i=1

I

!"

#$%

&'

12

PCi = XT !vi

Subspace Metrics II •  Principal Angles – An optimization that gives the best alignment

between the two subspaces – Reveals timescales of dynamic congruency

VS DIM = 3 SS DIM = 2 2 PAs

Results I

•  FRODA yields trajectories very quickly

•  The trajectories equilibrate rapidly when using the momentum perturbation (MP)

Conformation RMSD

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

1

10

1

20

1

30

1

40

1

50

1

60

1

70

1

80

1

90

1

10

01

11

01

12

01

13

01

14

01

15

01

16

01

17

01

18

01

19

01

20

01

RM

SD

[Å

]

Conformation Number

Ecutoff=0

Ecutoff=-1.0

Ecutoff=-3.0

Ecutoff=-5.0

MD

A

REFc

Residue RMSD

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

9.0

1

11

21

31

41

51

61

71

81

91

10

1

11

1

12

1

13

1

14

1

15

1

RM

SD

[Å

]

Residue Number

Ecutoff=0

Ecutoff=-1.0

Ecutoff=-3.0

Ecutoff=-5.0

MD

B

REFc

RMSD Distributions

0

0.5

1

1.5

2

2.5

1 1.2 1.4 1.6 1.8 2 2.2 2.4

De

nsit

y

RMSD [Å]

FRODA MD

C

Results II •  Momentum bias is very effective

Figure 2.1 Conformation RMSD using FRODA Diffusion mode.!Running FRODA in diffusion mode yields trajectories that do not equilibrate rapidly due to low efficiency in how configuration space is sampled. These results are for MV in rigor state, which contains 946 residues.!

Results III •  Output frequency can be optimized –  For most proteins: 10 ≤ FREQ ≤ 50

!"

!#$"

%"

%#$"

&"

&#$"

'"

%"

%!%"

&!%"

'!%"

(!%"

$!%"

)!%"

*!%"

+!%"

,!%"

%-!!%"

%-%!%"

%-&!%"

%-'!%"

%-(!%"

%-$!%"

%-)!%"

%-*!%"

%-+!%"

%-,!%"

./01

"

23456%" 23456%!"

Figure 2.2 The dependency of equilibration rate on output frequency.!There is a trade-off between sampling every conformation and sampling every 100th conformation. Here, the conformational RMSD is plotted as a function of FRODA output, with the abscissa showing conformations from 1 to 2,000. Using an output frequency of 25 to 50 balances the time needed to sample more of the configuration space with the requirement to achieve sufficient statistical sampling. These results are for myoglobin, which contains 151 residues.!

Results IV •  Constraint violations are minimized by: – Step Size ≤ 0.01Å when using MP

Results V •  Configuration space is well sampled based on

the projections onto the top two PC modes

Results VI •  Dependency on model parameters

PDB ID 2nwd: Structure of chemically synthesized human lysozyme at 1 Angstrom resolution

Results VII •  There is a great degree of similarity in the essential

spaces over a wide range of parameter choices –  This suggests a Range of Physicality

•  Amplitude vs. correlation in the motion

Conclusions •  The GSM is very fast and yields trajectories that equilibrate

rapidly when using the MP •  The simulations did not become irrevocably jammed nor

did they yield structures containing large constraint violations

•  Sampling of the native basin is efficient as assessed by

projecting the DVs on the top few PCA modes •  The Essential Mode Spaces are highly conserved over a

wide range of constraint assignment parameters as measured by RMSIP and PA –  A Range of Physicality was observed

•  The GSM well characterizes the native basin defined by the

input structure

PART II Model-to-Model Comparisons of the GSM, ANM, and MD

THE MODELS A Brief Introduction

Models: ENM I •  A single point (Cα) represents each residue

•  Each point forms a node on a graph while edges represent the interactions, within a cutoff distance –  Typically a single value is used for all interactions

•  Anisotropic Network Model (ANM)

Models: ENM II •  The key simplifying assumption made in

all ENMs is the harmonic approximation

!

!"#$%&'()*'+,&%#-'.%/0"1&'/0'23&',42"5&'6242&'7/8&1&8'42'8"00&%&,2'%&6/1

"! #$%&'$(! ')$! %*'+,$! ('*'$-!.&#$/$#! *'! *! 01! (2*/$! *(! *! (+%3/$! $%$435!.+%+.6.7! 8! #$'*+/$#

('462'64$!*%#!$%$43$'+2(!.*5!4$,$*/!.6/'+9/$!(6:('*'$(!;<=-!<>-!$'27?-!@)+2)!+%!'64%!2&%'*+%!.6/'+9

.>-! $'27?7! <'462'64*/! .&#$/(! 2&44$(9&%#+%3! '&! #+AA$4$%'! )+$4*42)+2*/! /$,$/(! &A! 4$(&/6'+&%! *4$! ()&@%B! *%! $/*('+2!

%$'@&4C!.&#$/!4$94$($%'*'+&%!@)$4$!')$!3/&:*/!$%$435!.+%+.6.!&%!*!01!(2*/$!;"?!+(!*994&D+.

9&'$%'+*/!*/&%3!$*2)!.&#$!#+4$2'+&%!;$737!*%+(&'4&9+2!%$'@&4C!.&#$/!;8"E??F!'@&!(6:('*

$2"/,6)'

! $D*.+%*'+&%! &A! ')$!

/$!.+24&('*'$(!;.=-!

*'$#!:5!*!)*4.&%+2!

'$(!<=!*%#!<>!(*.9/$#!:5!

3/&: /!.&'+&%(!%$*4!%*'+,$! ('*'$! 2&%#+'+&%(F! *%#!*%!$%($.:/$!&A! 2&%A&4.$4(! (*.9/$#!:5! (.*//! A/62'6*'+&%(! +%! ')$!

%$+3 :&4)&&#! &A! $*2)! (6:('*'$7! G)$! #+*34*.(! )*,$! :$$%! 2&%('462'$#! 6(+%3! ')$! A&//&@+%3! 4)&#&9(+%! ('462'64$(!

#$9&(+'$#! +%! ')$! HIJB! ! =K=L! ;"?F! =K=L! *%#! M08H! ;<=! *%#! <>?! *%#! =NOO-! =1PE-! =QPR-! =SLQ-! =K=L-! >1OT-!

>QHU-!>VMW-!>VMX-!>VMT-!>YZU-!>H[I-!M0LS-!M0LE!;.+24&('*'$(?7!N+364$!+(!*#&9'$#!A4&.!;J*)*4!$'!*/7-!>\\L?7!

!

!

*

)

! X!

Models: ENM III

•  Normal Modes characterize the correlated motions of the protein

•  Longest timescales and largest amplitude motions are obtained from the lowest frequency modes

•  A coarse-grained model that requires little computational time, even for large proteins

Models: MD I

•  A comprehensive all-atom model – Classical, not QM

•  Basic assumption of the model: – Protein behavior can be elucidated by

examining how it’s molecular structure evolves through a set of molecular steps under the influence of a specified potential or forcefield

Models: MD II

•  A typical MD potential:

Models: MD III

•  Thermal simulation: Proteins are hydrated The entire system of protein plus solvent is equilibrated at a specific temperature

•  The benefit: Trajectory represents an ensemble in the thermodynamic sense

Methods •  We selected 4 single domain proteins

(monomers)

•  Assessment of similarity was done by comparing the top 20 mode spaces from each of the models, plus an experimental set

The 4 Target Proteins •  1A6N deoxy-myoglobin:

SCOP class α, 151 residues –  The focus of these results

•  1WIT twitchin: SCOP class β, 93 residues

•  1UBQ ubiquitin:

SCOP class α+β, 76 residues •  1YPI triosephosphate isomerase:

SCOP class α/β, 247 residues

Characterizing Protein Motions from Structure, Charles C. David, Donald J. Jacobs, Journal of Molecular Graphics and Modelling 31 (2011) 41–56

Results I: PC Projections

•  PCs for the top 5 modes indicate degree of equilibration and mode space similarity – Fluctuations from FRODA and MD contrast a

thermal and mechanical simulation

PCs Using FRODA Modes


PCs Using MD Modes


PCs Using ANM Modes


ANM Consistency

0

10

20

30

40

50

60

70

80

90

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

De

gre

es

Principal Angle

ANM_0_1 (.89) ANM_0_2 (92) ANM_0_3 (.90) ANM_0_4 (.90) ANM_0_5 (.95) ANM_0_6 (.93) ANM_0_7 (.89) ANM_0_8 (.92) ANM_0_9 (.89) ANM_0_10 (.92) ANM_0_11 (.91) ANM_0_12 (.92) ANM_0_13 (.92) ANM_0_14 (.91) ANM_0_15 (.89) ANM_0_16 (.90) ANM_0_17 (.92) ANM_0_18 (.94) ANM_0_19 (.89) ANM_0_20 (.89)

D


ANM essential subspaces are highly conserved when using multiple structures from a dynamic trajectory

FRODA Consistency

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

1

E 0, C

0

E 0, C

.5

E -.5, C

.5

E -1, C

0

E -1, C

.1

E -1, C

.2

E -1, C

.3

E -1, C

.4

E -1, C

.5

E -1.5,

C 0

E -1.5,

C .1

E -1.5,

C .2

E -1.5,

C .3

E -1.5,

C .4

E -1.5,

C .5

E -2, C

0

E -2, C

.1

E -2, C

.2

E -2, C

.3

E -2, C

.4

E -2, C

.5

E -3, C

0

E -3, C

.1

E -3, C

.5

E -4, C

0

E -4, C

.1

E -4, C

.5

E -5, C

0

E -5, C

.5

E -10,

C 0

E -10,

C .5

RM

SIP

FRODA Values for Ecutoff (E) and HP-tether cutoff (C)

FRODA-8 FRODA-20 ANM MD

A


FRODA is consistent across a range of parameter choices that control rigidity/flexibility

FRODA & MD Internal Consistency

0

10

20

30

40

50

60

70

80

90

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

De

gre

es

Principal Angle

FRODA_I-II (.94) FRODA_I-ALL (.95)

FRODA_II-ALL (.97) MD_I-II (.81)

MD_I-ALL (.91) MD_II-ALL (.90)

C


FRODA and MD trajectories show internal consistency

Model Similarity

0

10

20

30

40

50

60

70

80

90

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

De

gre

es

Principal Angle

ANM_MD (.53) ANM_FRODA_8 (.78) ANM_FRODA_20 (.74)

MD_FRODA_8 (.57) MD_FRODA_20 (.58) FRODA-8_FRODA-20 (.93) A


All three models share much in common FRODA and ANM are much more alike than FRODA and MD or ANM and MD

Results IV •  FRODA captures a set of 100

experimental structures as well as ANM, and significantly better than MD


Please cite this article in press as: C.C. David, D.J. Jacobs, Characterizing protein motions from structure. J. Mol. Graph. Model. (2011),doi:10.1016/j.jmgm.2011.08.004

ARTICLE IN PRESSG ModelJMG 6108 1–16

14 C.C. David, D.J. Jacobs / Journal of Molecular Graphics and Modelling xxx (2011) xxx–xxx

examining the entire set of 20 PAs and the average COs. PA val-774

ues of less than 23◦ are considered to be within the small angle775

approximation and suggest excellent similarity. Fig. 8 shows the776

comparison of the model mode subspaces using the metric of777

PA, with RMSIP values shown parenthetically in the legend. From778

Fig. 8A, it is clear that the most similar mode subspaces are those779

from FRODA-8 and FRODA-20 with an RMSIP score of 0.93 and780

PAs less than 23◦ for the top fifteen modes. The next most simi-781

lar mode subspaces are from FRODA and ANM. These comparisons782

yield a RMSIP value near 0.75 and have PAs within the small783

angle approximation for six modes. The mode subspace compar-784

isons between ANM and MD and MD and FRODA are very similar,785

each having an RMSIP value between 0.5 and 0.6 and PA values786

less than 45◦ for the top five modes. While these angle values787

are not within the small angle approximation, they do indicate a788

good amount of similarity, commensurate with the good RMSIP789

score.790

The RMSIP scores between the model mode subspaces are791

shown for the four proteins investigated in Fig. 9 (left column).792

The average cumulative overlaps (for the entire set of 20 modes)793

between the model mode subspaces are shown in Fig. 9 (mid-794

dle column), and the first PA results are likewise shown in Fig. 9795

(right column). Again, it is clear that the ANM and FRODA mode796

subspaces are best able to capture each other’s essential motions.797

This was especially evident when looking at the top ten modes798

where the average CO remains greater than 0.70 (not shown).799

Additionally, ANM to MD as well as MD to FRODA maintain an800

average CO greater than 0.50 for the top 12 modes (not shown).801

While not excellent, these values parallel the results seen in Fig. 8802

and indicate a substantial amount of compatibility between the803

essential motions contained in these subspaces. Similar results804

were found for the other three SCOP classes of protein as shown805

in Fig. 9, with the RMSIP between FRODA and MD within the806

range of 0.51–0.63, and the RMSIP between ANM and FRODA807

within the range of 0.69–0.78 for all four SCOP classes. To put808

these values in perspective, the RMSIP between the FRODA-8809

and FRODA-20 modes spanned the range of 0.64–0.93 over the810

four studied proteins, indicating that the inter-model compar-811

isons were on par with the intra-model comparisons. For all four812

classes of proteins investigated, the ANM to MD RMSIP values813

were the lowest, spanning the range of (0.45–0.57). This result814

shows that ANM and MD are the most divergent of the three815

models investigated here. As Fig. 9 shows, there are no significant816

differences between the four proteins based on SCOP classifica-817

tion.818

3.7. Projection of experimental structures on the model modes819

An important consideration beyond the model-to-model com-820

parisons that have been performed is how well are actual821

experimental structures accommodated by the three different822

models. To address this question, a 20-dimensional subspace was823

derived from the experimental dataset of myoglobins, and com-824

pared to those obtained from each model. We are specifically825

assessing how well the 3 models under investigation were able826

to access the set of experimental structures given only the initial827

structure. Fig. 10A and B show the projection of the experimen-828

tal displacement vectors onto the model modes. In both panels,829

it is evident that the ANM mode space captures the experimen-830

tal displacements best, with FRODA doing almost as well in terms831

of both the size of conformational space defined by the top three832

modes and the significance of the overlaps generated therein. The833

MD based PCA mode space does significantly worse in terms of the834

amount of conformational space covered and fails to yield any sig-835

nificant overlap to the experimental displacements. These results836

are echoed in Fig. 10C showing the RMSIP values of ANM and FRODA837

Fig. 10. Experimental and model subspace comparisons. Projection of the experi-mental displacement vectors on model modes 1, 2 (Top A) and on modes 2, 3 (middleB). The PA results from comparing the experimentally derived mode space to themodel mode spaces, with the RMSIP values shown parenthetically in the legend(bottom C). The level line is drawn for PA value 23◦ in C.

mode subspaces to the experimental mode subspace are about 0.60 838

while the RMSIP value of the MD mode subspace to the experi- 839

mental mode subspace is only 0.44, a significantly lower result. 840

Taken together, these results indicate that both ANM and FRODA 841

are able to capture the majority of the displacements seen in the 842

experimental structures, while MD captures significantly less of the 843

displacements. 844

Conclusions •  The simulated structures project differentially

into the model mode spaces, but reveal significant overlap in the Essential Subspaces

•  The models show solid intra-consistency

•  There is substantial inter-consistency – MD is unique in its ability to sample outside the

native basin defined by the input structure •  MD thus yields distinctive results

•  The FRODA and ANM Essential Subspaces capture the experimental set of structures best

PART III Application of the GSM to myosin V

Introduction I •  Myosins are molecular motors capable of

converting chemical energy into mechanical work through a cyclic interaction with actin filaments. Myosin V (MV) below:

Myosin V Dynamics

Introduction II •  We collaborated with experimentalists who study

myosins using FRET

•  FRET allows us to determine the distance between a donor and acceptor probe

PROJECT I Applying the GSM to myosin V

Introduction

•  We selected a subset of 106 residues that defined the nucleotide-binding pocket (NBP)

•  We investigated how conformational changes in the NBP are communicated to the lever arm and actin-binding cleft (ABC)

Myosin V showing NBP

Methods •  We explore ED of MV using the GSM starting

with three different X-ray crystal structures (1OE9, 1W7J, 1W7I)

•  Our results are based on dPCA, compatible with our focus on three residues (171, 294, 525)

Myosin V Showing NBP, ATP, and residues 171, 294, 525

Results •  We obtained distinct distributions for the 171-294 distance in

the MV.ATP structure and the MV.ADP structure –  Thus, the MV.ADP structure is not capable of converting to the closed

pocket conformation without significant constraint breaking

•  For the MV.ADP state, very few modes of pocket opening/closing agree with experiment –  The crystal structure represents the weak, open pocket MV.ADP state

•  We saw more evidence for a novel post-power-stroke MV.ADP state –  NBP and ABC are both closed –  This is the strong closed pocket MV.ADP state –  This state has not yet been crystalized

Jacobs, D.J., et al., Kinetics and thermodynamics of the rate-limiting conformational change in the actomyosin V mechanochemical cycle. J Mol Biol. 407(5): p. 716-30. Sun, M., et al., Characterization of the pre-force-generation state in the actomyosin cross-bridge cycle. Proc Natl Acad Sci U S A, 2008. 105(25): p. 8631-6.

Results of dPCA analysis based on the relative motions of three residue pairs: 294-171, 171-525, and 294-525, in all three crystal structures. (ADP.BeFX is an ATP mimic)

!!""

"""""""""""""""""""""""""""""""""""""""""""""

!"#$

%!%$

&'&$

!"#$ !$#% $ $#% "#$ "#% &#$

"'"!&()

"'"!%&%

&()!%&% *+,

*-+#./01

*-+

234/5"5-6789:;/5<=>

(

)$

*+,-./$0$

Kinetics and Thermodynamics of the Rate Limiting Conformational Change in the myosin V Mechanochemical Cycle. (2011). Donald J. Jacobs, Darshan Trivedi, Charles C. David, and Christopher M. Yengo, Journal of Molecular Biology, Apr 15;407(5):716-30

Mode 1 from dPCA MV.ATP

PROJECT II Applying the GSM to myosin V

Introduction I

•  Understanding the mechanism of force generation in MV requires elucidating allosteric communication pathways critical to motor function

•  Three well conserved regions involved: – The P-loop – Switch I – Switch II

Switch II Mutants Reveal Coupling Between the Nucleotide- and Actin-Binding Regions in Myosin V Darshan V. Trivedi, Charles C. David, Donald J. Jacobs, and Christopher M. Yengo, Biophysical Journal Volume 102 Issue 11 pp.2545-2555. doi:10.1016/j.bpj.2012.04.025

Introduction II •  Switch I is chiefly involved in the communication

pathways between the active site and the ABC

•  Switch II mediates the communication to the converter-lever arm domain

•  To understand how Switch II affects the conformational dynamics of the NBP and ABC, we introduced two single site mutations

– G440A: Eliminates a highly conserved hydrogen bond to the gamma phosphate of ATP

– E442A: Eliminates a highly conserved salt bridge between Switch I and Switch II

Methods

•  We defined three subsets: – NBP [106] – Actin Binding Region (ABR) [455] – A proposed Communication Pathway (CP) [89]

•  Conformational changes in these subsets were investigated using GSM with ED

Myosin V showing ABR

Results I •  Switch I-Switch II interactions stabilize the closed nucleotide

binding pocket conformation in the absence of actin

•  The NBP in the ATP state had reduced dynamics of Switch I in the G440A mutant –  This hinders Switch I-Switch II interactions –  Reduces the stability of the closed NBP conformation

•  The mobility of the P loop is increased by both Switch II mutants


The first PC mode of the NBP of mutant and wild-type myosin V

Results II •  The G440A mutation alters ABR dynamics

–  In the rigor state, the G440A mutant increases dynamics of a region of the U50 domain: •  The cardiomyopathy loop •  The C-terminus of the HO-helix

–  There is a dramatic increase in the mobility of helix-loop-helix region of the L50 domain

•  The G440A mutation makes F441 highly dynamic in the ATP state –  Disruption of Switch II rotation by G440A alters the mobility of F441 –  This hinders F441 interaction with the surrounding hydrophobic

environment

•  These two alterations result in disruption of the communication pathways between the active site and the U50 and L50 regions

The first PC mode of the ABR of mutant and wild-type myosin V


CONCLUSION Summary of the Work

Summary •  We have established the GSM as a viable alternative and/or

co-model to either an ENM or MD

•  The GSM is both efficient and effective at determining the native state dynamics of a protein –  The GSM is qualitatively and quantitatively similar to MD and ANM

•  The GSM is scalable –  Applied to a wide range of proteins with success including small, single

domain proteins and large multi-domain, multi-state proteins like MV

•  ED of GSM trajectories is an effective method to tease out the biological motions of a subset of residues in a protein

Thank You! •  Mentors, Colleagues, Friends, & Family •  UNCC for my financial aid •  NIH for supporting my research

Essential Dynamics of Proteins using Geometrical ...

Documents

Transcript of Essential Dynamics of Proteins using Geometrical ...