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