麻省理工大学：《Foundations of Biology》课程教学资源（英文版）Lecture 1 How are X-ray crystal structures

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

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

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 CANT 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

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 dont know what phases to use to add up all of the contributing waves, BIG PROBLEM Px2=7222 7-2r(hx+y+) atoms Fk lexp(iah )=Fnk)=>f, exp[2T.i(h u)+kyu+lx) 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 Inki a Fk l2 we cant measure the phases directly Get phases from molecular replacement, or heavy atom methods

The Phase Problem: we don’t know what phases to use to add up all of the contributing waves. BIG PROBLEM. | Fhkl | exp( i αhkl ) = 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 Ihkl α |Fkhl|2 we can’t measure the phases directly Get phases from molecular replacement, or heavy atom methods

X-Ray crystal structure Refinement The model ∴:: The data: Actual 一+:: intensities of sp0 intensities of spots ● xm=∑[k- h k/ Summation Actual intensity of spot Intensity of spot calculated runs over spots observed in expt from trial structure U Molec model SUx ay expt 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

X-Ray Crystal Structure Refinement The model: Computed The data: Actual intensities of spots intensities of spots Fobs ( h,k,l) − Fcalc ( h,k,l) ] 2 UX -ray expt = ∑ [ Summation h ,k ,l Actual intensity of spot Intensity of spot calculated runs over spots observed in expt from trial structure Uhybrid = U Molec Model + 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 90%of X-ray current 10% of X-ray amplitudes model amplitudes model-derived amplitudes R=EIlFobsl-IF alcl/>Fobsl rere=2IIFobsl-IF alcl I/>1FobsI change model assess model

The Free R factor current model 90% of X-ray amplitudes R = Σ||Fobs calc||/Σ|Fobs| model-derived amplitudes change model 10% of X-ray amplitudes Rfree = Σ||Fobs calc||/Σ|Fobs| assess model | - |F | - |F

What parameters do you refine? Atomic coordinates xy, z The temperature factor of each atom, b Can also refine the occupancy b=8T2x u 2= mean square atomic displacement b results from atomic vibrations and disorder units=82 Example: b=20->0.5a displacement B=80-->1A displ aceme ent

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 π2 x u2 2 = mean square atomic displacement B results from atomic vibrations and disorder units = Å2 Example: B = 20 --> 0.5Å displacement B = 80 --> 1Å displacement

Atomic coordinates in the pdb file OCC B ATOI 1 N GLU 28.4923.21223.4651.0070.88 ATOM 2 CA GLU 27.5524.35423.6291.0069.99 ATO 3 C GLU 26.5454.43222.4890.0067.56 ATON 40 GLU 26.9154.25021.3280.0068.09 ATOM 5 CB GLU 28.3265.68323.6800.0072.34 ATOM 6 CG GLU 27.4476.91023.9730.0075.98 ATOM 7 CD GLU 28.1238.24723.6590.0078.43 ATON 8 OE1 GLU 29.3758.29923.6040.0079.32 ATOM 9 OE2 GLU 27.3939.25123.4680.0079.58 ATOM 10 N ARG 25.2744.61022.8521.0063.77 ATOM 11 CA ARG 24.1794.80721.9071.0059.83 ATOM 12 C ARG 23.4113.69821.2191.0056.20 ATOM 13 O ARG 4444444445555555 23.9872.80820.5961.0057.33 ATOM 14 CB ARG 24.6045.78420.8121.0060.86 ATOM 15 CG ARG 23.9267.12720.8661.0061.89 ATOM 16 CD ARG 24.2957.94419.6471.0062.21

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

Is your structure correct? How unusual is the structure geometry? ·Doesⅰ t contain rare conformations? Does it make chemical sense? PDB AD ?》◆e PROTEIN DATA BANK Validation Tutorial PDB Home Contact Server The ADIT Validation Server allows the user allows the user to check the format consistency of coordinates (PRECHECk) and to create validation reports about a stucture before depositon (VALIDATION). These checks can be done independently by the user Tutorial I File Format Information I Possible Format Problems I Validation Server at osaka University, Japan I To start a new validation session, select the experimental method (x-ray or NMR) from the pull-down menus below, and press the begiN button Meo:xry÷BE http://pdb.rutgersedu/validate/

Is your structure correct? • How unusual is the structure geometry? • Does it contain rare conformations? • Does it make chemical sense? http://pdb.rutgers.edu/validate/

PROCHECK Backbone geometry Ramachandran plot new-entry R Peptide torsion angles 益 Plot basics Ably № mber d nom gi:nm同Md ber daytime Tesidues showm as1Tamgles) oia nabbed residu http://pdb.rutgersedu w tatty_oLta

Backbone geometry http://pdb.rutgers.edu/

Side chain lle chil distribution geometry x angle here might indicate error in structure 0389 150180210240270300330380 x1 lle chi2 distribution X2 isoleucine www.fCcc.edu/research/labs/dunbrack/confanalysis.html

Side chain geometry O N χ1 χ2 isoleucine χ angle here might www.fccc.edu/research/labs/dunbrack/confanalysis.html indicate error in structure