791_ak_lecture4

# 791_ak_lecture4 - 7.91 Amy Keating Solving structures using...

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Solving structures using X-ray crystallography & NMR spectroscopy 7.91 Amy Keating

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How are X-ray crystal structures determined? 1. Grow crystals - structure determination by X-ray crystallography relies on the repeating structure of a crystalline lattice. 2. Collect a diffraction pattern - periodically spaced atoms in the crystal give specific “spots” where X-rays interfere constructively. 3. Carry out a Fourier transform to get from “reciprocal space” to a real space description of the electron density. 4. THIS STEP REQUIRES KNOWLEDGE OF THE PHASES OF THE INTERFERING WAVES, WHICH CAN’T BE DIRECTLY MEASURED THE PHASE PROBLEM 4. Build a preliminary model of the protein into the envelope of electron density that results from the experiment. 5. Refine the structure through an iterative process of changing the model and comparing how it fits the data.
The Phase Problem: we don’t know what phases to use to add up all of the contributing waves. BIG PROBLEM. | F hkl |exp( i α hkl ) = observable amplitude atomic scattering factor - related the phase of F is determined by the to electron density around atom j x, y and z coordinates of the atoms What we observe is I hkl α |F khl | 2 we can’t measure the phases directly Get phases from molecular replacement, or heavy atom methods

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X-Ray Crystal Structure Refinement The model: Computed The data: Actual intensities of spots intensities of spots F obs ( h , k , l ) F calc ( h , k , l ) ] 2 U X -ray expt = ∑[ Summation h , k , l Actual intensity of spot Intensity of spot calculated runs over spots observed in expt from trial structure U hybrid = U Model Molec + sU expt ray - X Simulated annealing on hybrid potential rapidly improves correspondence between structure and X-ray observations while maintaining reasonable chemistry (large radius of convergence) Previous method effectively used local minimization which became trapped in local minima (small radius of convergence)
The Free R factor current model 90% of X-ray amplitudes R = Σ ||F obs calc ||/ Σ |F obs | model-derived amplitudes change model 10% of X-ray amplitudes R free = Σ ||F obs calc ||/ Σ |F obs | assess model | - |F | - |F

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What parameters do you refine? • Atomic coordinates X, Y, Z • The temperature factor of each atom, B • Can also refine the occupancy u B = 8 π 2 x u 2 2 = mean square atomic displacement B results from atomic vibrations and disorder units = Å 2 Example: B = 20 --> 0.5Å displacement B = 80 --> 1Å displacement
Atomic coordinates in the PDB file X Y Z occ B ATOM 1 N GLU 4 28.492 3.212 23.465 1.00 70.88 ATOM 2 CA GLU 4 27.552 4.354 23.629 1.00 69.99 ATOM 3 C GLU 4 26.545 4.432 22.489 0.00 67.56 ATOM 4 O GLU 4 26.915 4.250 21.328 0.00 68.09 ATOM 5 CB GLU 4 28.326 5.683 23.680 0.00 72.34 ATOM 6 CG GLU 4 27.447 6.910 23.973 0.00 75.98 ATOM 7 CD GLU 4 28.123 8.247 23.659 0.00 78.43 ATOM 8 OE1 GLU 4 29.375 8.299 23.604 0.00 79.32 ATOM 9 OE2 GLU 4 27.393 9.251 23.468 0.00 79.58 ATOM 10 N ARG 5 25.274 4.610 22.852 1.00 63.77 ATOM 11 CA ARG 5 24.179 4.807 21.907 1.00 59.83 ATOM 12 C ARG 5 23.411 3.698 21.219 1.00 56.20 ATOM 13 O ARG 5 23.987 2.808 20.596 1.00 57.33 ATOM 14 CB ARG 5 24.604 5.784 20.812 1.00 60.86 ATOM 15 CG ARG 5 23.926 7.127 20.866 1.00 61.89 ATOM 16 CD ARG 5 24.295 7.944 19.647 1.00 62.21

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791_ak_lecture4 - 7.91 Amy Keating Solving structures using...

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