Physical techniques

to study molecular structure

DetectionSample

Radiation

X-rayne-RF

Example:

How many protein molecules are there in the solution

sample (volume, 100 l) at the concentration of 0.1 mM?

About samples of biomolecules

1 m particles

Brownian motion

1785: Jan Ingenhousz observed irregular motion of coal dust particles in

alcohol.

1827: Robert Brown watched pollen particles performing irregular motion in

water using a microscope. He repeated his experiments with dust to rule out

that the particles were alive.

1905: Einstein provided the first physical theory to explain Brownian motion.

1908: Jean Perrin did experiments to verify Einstein’s predictions. The

measurements allowed Perrin to give the first estimate of the dimensions of

water molecules. Jean Perrin won the Nobel Prize of Physics in 1926 for this

work.

History of Brownian motion

0R that require walk werandomFor

rsunit vecto are where...321

iN eeqeqeqeqR

)ee(MNq

e...eeeq1

R1

R

sexperiment Mover Average

jji

i

2M

1k

2N321

2

1

2k

2

MMM

m

k

2x

2y

2x

22x

2x

2222 q2qqq where

2τ

q

4τ

2q

4τ

qD where4Dt,q

τ

tNqR may write We

tN then t,is time total theand τ timea takesand random is stepeach that assume weIf

Each step in the x and y directions are random, but otherwise equal, such that qx

2=qy2

y

x 12

212

212

21

22

2221

2 ee22qee211qee2eeqeqeqR

steps) only two (assume Example

1eq 2eq

Random walk

2τ

qD where4Dt,RMSDDeviation SquareMean

2x2

t

MSD y

x

1D: MSD=2Dt

2D: MSD=4Dt try to show this yourself!

3D: MSD=6Dt

Random walk

Fick’s law of diffusion

dx

dCDJ

Adolf Fick (1855):

J= flux of particles (number of particles per area and time incident on a cross-section) [m-2s-1]

D= diffusion coefficient [m2s-1]

C=concentration of particles [m-3]

(sometimes n is used instead of C to represent concentration )

J

A

Random walk is due to thermal fluctuations!

1905) ip,relationsh(Einstein f

TkD B

molecules with watercollision todue force random a is R(t)

particles of radiusr whereparticle spherical afor r6f R(t)fv0ma

fv

v

R(t)

State of matter D [m2/s]

Solid 10-13

Liquid 10-9

Gas 10-5

Diffusion coefficients in different materials

1905) ip,relationsh(Einstein f

TkD B

Radiation

X-ray ne-RF

Photons and Electromagnetic Waves

• Light has a dual nature. It exhibits both wave and

particle characteristics

– Applies to all electromagnetic radiation

Particle nature of light

• Light consists of tiny packets of energy, called photons

• The photon’s energy is:

E = h f = h c /

h = 6.626 x 10-34 J s (Planck’s constant)

Wave Properties of Particles

• In 1924, Louis de Broglie postulated that because photons have wave and particle characteristics, perhaps all forms of matter have both properties

de Broglie Wavelength and Frequency

• The de Broglie wavelength of a particle is

• The frequency of matter waves is

h hp mv

ƒEh

Dual Nature of Matter

• The de Broglie equations show the dual nature of matter

• Matter concepts– Energy and momentum

• Wave concepts– Wavelength and frequency

X-Rays

• Electromagnetic radiation with short wavelengths– Wavelengths less than for ultraviolet– Wavelengths are typically about 0.1 nm– X-rays have the ability to penetrate most materials

with relative ease

• Discovered and named by Röntgen in 1895

Production of X-rays

• X-rays are produced when high-speed electrons are suddenly slowed down

Wavelengths Produced

European synchrotron Grenoble, France

Production of X-rays in synchrotron

European synchrotron

Electron energy: 6 Gev

European synchrotron

Bending magnets Undulators

A typical beamline

The three largest and most powerful synchrotrons in the world

APS, USA ESRF, Europe-France Spring-8, Japan

ObjectImage

Scattering

Lens

Direct imaging method (optical or electronic)

Analogical synthesis

ObjectImage

Scattering

Data collection

Indirect imaging method (diffraction X-ray, neutrons, e-)

Synthesis by computation (FT)

Incident wave

Scattered wave

Scattering of a plane monochrome wave

Janin & Delepierre

A molecule represented by electron density

Scattering by an object of finite volume

Scattered beam

Incident beam

Janin & Delepierre

Schematic for X-ray Diffraction

• The diffracted radiation is very intense in certain directions

– These directions correspond to constructive interference from waves reflected from the layers of the crystal

Diffraction Grating

• The condition for maxima is

d sin θbright = m λ• m = 0, 1, 2, …

http://en.wikipedia.org/wiki/Image:Photo_51.jpg

Photo 51

X-ray Diffraction of DNA

Planes in crystal lattice

Bragg’s Law

• The beam reflected from the lower surface travels farther than the one reflected from the upper surface

• Bragg’s Law gives the conditions for constructive interference2 d sinθ = mλ; m = 1, 2, 3…

A protein crystal

X-ray diffraction pattern of a protein crystal

http://en.wikipedia.org/wiki/X-ray_crystallography

Electron density of a protein

Scattering and diffraction of neutrons

Institut Laue-Langevin, Grenoble, France

Electrically Neutral

Microscopically Magnetic

Ångstrom wavelengths

Energies of millielectronvolts

Why use neutrons?

The Electron Microscope

• The electron microscope depends on the wave characteristics of electrons

• Microscopes can only resolve details that are slightly smaller than the wavelength of the radiation used to illuminate the object

• The electrons can be accelerated to high energies and have small wavelengths

Nuclear Magnetic Resonance (NMR) spectroscopy

http://en.wikipedia.org/wiki/Nuclear_magnetic_resonance

Superconducting magnets 21.5 T Earth’s magnetic field 5 x 10-5 T

• Nuclei can have integral spins (e.g. I = 1, 2, 3 ....): 2H, 6Li, 14N fractional spins (e.g. I = 1/2, 3/2, 5/2 ....): 1H, 15Nor no spin (I = 0): 12C, 16O

• Isotopes of particular interest for biomolecular research are 1H, 13C, 15N and 31P, which have I = 1/2.

• Spins are associated with magnetic moments by:

Spin and magnetic moment

m = ħ I

A Spinning Gyroscopein a Gravity Field

A Spinning Chargein a Magnetic Field

http://www.cem.msu.edu/~reusch/VirtualText/Spectrpy/nmr/nmr2.htm#pulse

Larmor frequency

= B0

Continuous wave (CW) NMR

http://www.cem.msu.edu/~reusch/VirtualText/Spectrpy/nmr/nmr1.htm

Chemical shift

http://www.cem.msu.edu/~reusch/VirtualText/Spectrpy/nmr/nmr1.htm

Chemical shift

http://www.cem.msu.edu/~reusch/VirtualText/Spectrpy/nmr/nmr1.htm

Chemical shift

http://www.cem.msu.edu/~reusch/VirtualText/Spectrpy/nmr/nmr1.htm

Chemical shift

= (f - fref)/fref

Pulsed Fourier Transform (FT) NMR

RF

http://www.cem.msu.edu/~reusch/VirtualText/Spectrpy/nmr/nmr1.htm

Fourier transform (FT) NMR

http://www.cem.msu.edu/~reusch/VirtualText/Spectrpy/nmr/nmr1.htm

Fourier transform (FT) NMR

http://www.cem.msu.edu/~reusch/VirtualText/Spectrpy/nmr/nmr1.htm

http://www.cryst.bbk.ac.uk/PPS2/projects/schirra/html/2dnmr.htm#noesy

Proton 1D NMR spectrum of a protein

Proton 1D NMR spectrum of a DNA fragment

http://www.bruker-nmr.de/guide/

A 2D NMR spectrum

Nuclear Overhauser Effect Spectroscopy (NOESY)

provides information on proton-proton distances

http://www.cryst.bbk.ac.uk/PPS2/projects/schirra/images/2dnosy_1.gif

NOE ~ 1/r6

• Distances between nuclei

• Angles between bonds

• Motions in solution

Information obtained by NMR

Today’s lesson:

1) Molecules in solution; Brownian motion

2) X-ray

3) Scattering and diffraction

4) Neutron scattering

5) Electron Microscopy (EM)

6) Nuclear Magnetic Resonance (NMR) spectroscopy