Protein Structure Determination Part 2 Xray Crystallography The

Protein Structure Determination Part 2 -X-ray Crystallography

The method FT-1 FT Crystals X-rays Atoms

EM versus x-ray • electron microcope • resolution ≈ 1 nm • de Broglie wavelength of e- ≈ size of atom • transmitted light • lensing possible, 106 x mag. • 2 D image w/tilt • measures density. • sample is thin section • diffractometer • resolution up to 0. 1 nm = 1Å • wavelength ≈ size of atom • scattered light • no lens possible • 3 D reconstruction • measures relative edensity • sample is single crystal

X-ray diffractometer

Experimental setup X-ray source X-ray detector beam stop

Dimensions X-ray detector ay b ea m Beam width: ~0. 20 mm Crystal thickness: 0. 10 -1. 00 mm

Unit cell: ~100Å = 0. 00001 mm

Typical protein molecule: ~30Å = 0. 000003 mm

Dimensions C-C bond distance: 1. 52Å N Cα CH 3 O C Wavelength of Cu Kα X-rays: 1. 5418Å

Dimensions Angle of incidence=θ : 0 -90° N Cα CH 3 O C Bragg plane separation distance (resolution): 0. 7 -50Å

N Dimensions Carbon atom C amount an electron moves in one xray cycle X-rays see e- as if they were standing still.

Electromagnetic spectrum Wavelength of X-rays used in crystallography: 1Å - 3Å (Å = 10 -10 m) most commonly 1. 54Å (Cu ) Frequency = c/λ =(3 x 108 m/s) /(1. 54 x 10 -10 m) ≈ 2 x 1018 s-1

oscillating e- scatter X-rays …in all direction. oscillation eemission

Reflection planes • The “amplitude” of scattering is measured. • The amplitude is proportional to the differences of edensity in the direction of “reflection planes” • The orientation and separation of reflection planes is determined by the directions of the incoming and scattered rays.

10 K+ 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 Euler's theorem Bragg's law Reciprocol space Symmetry Fourier transform Inverse Fourier transform

How to know that you know • all terms defined • physical/geometric interpretation

Supplementary reading Matrix algebra “An Introduction to Matrices, Sets and Groups for Science Students” by G. Stephenson ($7. 95) Wave physics “Physics for Scientists and Engineers” by Paul A. Tipler Protein structure “Introduction to Protein Structure”-- by Carl-Ivar Branden and John Tooze “Introduction to Protein Architecture : The Structural Biology of Proteins” -- by Arthur M. Lesk

Materials Gale Rhodes “Crystallography Made Crystal Clear” 3 rd Ed. Academic Press graph paper straight edge protractor compass calculator w/trig functions http: //www. bioinfo. rpi. edu/bystrc/courses/bcbp 4870. html