Protein Structure Determination

Part 2 --

X-ray Crystallography

Para ver esta película, debedisponer de QuickTime™ y deun descompresor TIFF (LZW).

Para ver esta película, debedisponer de QuickTime™ y deun descompresor TIFF (LZW).

The method

Crystals X-rays Atoms

FT FT-1

EM versus x-ray

• electron microcope

• resolution ≈ 1nm

• de Broglie wavelength of e- ≈ size of atom

• transmitted light

• lensing possible, 106x mag.

• 2D image w/tilt

• measures density.

• sample is thin section

• diffractometer• resolution up to 0.1nm

= 1Å• wavelength ≈ size of

atom• scattered light• no lens possible• 3D reconstruction• measures relative e-

density• sample is single crystal

X-ray diffractometer

Experimental setupX-ray source X-ray detector

beam stop

Dimensions

X-ray beam

X-ray detector

Beam width: ~0.20 mm

Crystal thickness: 0.10-1.00 mm

Unit cell: ~100Å = 0.00001mm

Typical protein molecule: ~30Å = 0.000003 mm

N

O

CH3CαC

C-C bond distance: 1.52Å

Wavelength of Cu Kα X-rays: 1.5418Å

Dimensions

N

O

CH3CαC

Angle of incidence=θ: 0-90°

Bragg plane separation distance (resolution): 0.7-50Å

Dimensions

C

N

C

Dimensions

X-rays see e- as if they were standing still.

Carbon atom

amount an electron moves in one xray cycle

Electromagnetic spectrum

Wavelength of X-rays used in crystallography: 1Å - 3Å (Å = 10-10m) most commonly 1.54Å (Cu )

Frequency = c/λ=(3x108m/s)/(1.54x10-10m) ≈ 2x1018 s-1

oscillating e- scatter X-rays

…in all direction.

e-

oscillation

emission

Reflection planes

•The “amplitude” of scattering is measured.

•The amplitude is proportional to the differences of e- density in the direction of “reflection planes”

•The orientation and separation of reflection planes is determined by the directions of the incoming and scattered rays.

10K+ reflections

•Moving the X-rays and the detector gives a new set of planes.

•Changing the angle of reflection changes the spacing (resolution).

Reconstruction of e- density

The density at every point in the crystal is calculated by summing over all of the density waves.

Topics covering in this course

• Crystal growth• Diffraction theory• Symmetry• Experimental methods • Interpretation of data• Software

Equations you will need to know

€

e iα = cosα + isinα

€

nλ = 2d sinθ

€

vS =

v s o −

v s

λ

€

vx sym = M

v x +

v v

€

F hkl( ) = ρ xyz( )xyz

∑ e2πi hx+ky +lz( )

€

ρ xyz( ) = F hkl( )hkl

∑ e−2πi hx+ky+lz( )

Bragg's law

Euler's theorem

Reciprocol space

Symmetry

Fourier transform

Inverse Fourier transform

How to know that you know

• all terms defined• physical/geometric interpretation

Supplementary reading

“An Introduction to Matrices, Sets and Groups for Science Students”by G. Stephenson ($7.95)

“Physics for Scientists and Engineers” by Paul A. Tipler

Matrix algebra

Wave physics

“Introduction to Protein Structure”-- by Carl-Ivar Branden and John Tooze

“Introduction to Protein Architecture : The Structural Biology of Proteins” -- by Arthur M. Lesk

Protein structure

Materials

Gale Rhodes “Crystallography Made Crystal Clear”

3rd Ed. Academic Press

graph paper

straight edge

protractor

compass

calculator w/trig functions

http://www.bioinfo.rpi.edu/bystrc/courses/bcbp4870/bcbp4870.html