Post on 05-Jan-2016
description
transcript
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
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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