Structural Analysis has Revolutionized Biochemistry and the Life SciencesThe X-ray MethodProtein solubility as a function of the precipitant concentrationCrystal growing formatsSome Packing ExamplesWhat are transforms?Scattering, Fourier Transform, and PhasesFourier Transform and ResolutionCrystallization and TransformsMetals are located by Difference PattersonA really simple exampleProtein Models are Built from Electron Density MapsElectron Density and ResolutionProtein Models Need to be RefinedPDB is a Structural ResourceX-Ray Crystallography“If a picture is worth a thousand words, then a macromolecular structure is priceless to a physical biochemist.” –van HoldeScience 5 January 2007:Vol. 315. no. 5808, pp. 40 - 41Chemistry Nobel Rich in Structure…In particular, there were 12 Nobel Prizes in chemistry and physiology or medicine awarded for work in this field from 1956 to 2006 (table S1) (2). Almost one in four chemistry prizes since 1956 have been for structure work, and in the last decade, fully half have dealt with work related to macromolecular structure. …From 1970 to 2006, 4% of all chemistry publications dealt with crystallography, yet this subfield captured 19% of the available Nobel Prizes (table S3) (2). During the past decade, crystallography papers represented 7% of all chemistry publications, but commanded 4 of 10 available prizes.Structural Analysis has Revolutionized Biochemistry and the Life SciencesThe X-ray Method1. Grow USEFUL crystals from purified protein2. Collect X-ray diffraction data; these are only the amplitudes of a complex number3. The PHASE problem (recover information lost in detection)4. Build the model, validate it, and interpret the results.Variables that influence crystal growth1. Nature of macromolecule – Purity and concentration of macromolecule2. Nature and concentration of precipitant3. pH / Temperature / Pressure4. Level of reducing agent or oxidant5. Substrates, coenzymes, and ligands / Metal ions6. Preparation and storage of macromolecule / Proteolysis and fragmentation7. Age of macromolecule / Degree of denaturation8. Vibration and sound9. Volume of crystallization sample10. Seeding11. Amorphous precipitate12. Buffers13. Cleanliness14. Organism or species from which the macromolecule was isolated15. Gravity, gradients and convectionProtein solubility as a function of the precipitant concentrationCrystal growing formatsCrystals can take up one of 14 lattices.There are primitive lattices, with operators at the corners, and centered lattices.Symmetry operators can be combined with the various lattices to generate SPACE GROUPS.Some Packing ExamplesDown a 3-fold axisDown a 2-fold axis of P21212(4 au/cell; 1 mol/au)4X-ray tubes: the “sealed” tubeObject Transform Image Object / Real SpaceTransform / Reciprocal SpaceModelsElectron Density MapsWhat are transforms?• Transforms convert one kind of information into another. The two forms can work “back and forth”.• A picture from your digital camera starts as a map of pixels, each of different color and intensity, but to store it on your memory stick, it is transformed into a jpg file. This is a set of compact rules that allow you to recover the pixel image by reversing the jpg operation.• An X-ray scatter pattern carries information about what scattered it. We want to measure that transform and convert it back to the image of the scatterer.Scattering, Fourier Transform, and Phases1. X-rays impinge on object from direction s02. Consider an electron at origin, O3. Like all other electrons it scatters in ALL directions, but focus on s4. All other volume elements also scatter in all directions, we show one at r1scattering in direction s.5. The path difference is segment Oa - r1b. That is ∆ = (r1·s) -(r1·s0).6. ∆ phase = 2πr1·(s-so/λ) = 2πr1· S, where S = (s-so/λ). This is shown in small drawing where s0and s are unit vectors.7. S is the "monitor" for the scattering; it is normal to the "plane" P "reflecting" s0in direction s. S is short when the scattering angle is low, and long when the scattering angle is high. This will correspond to low and high resolution diffraction data. S will be associated with the crystallographic index, hkl, in crystallographic "reciprocal space".8. Total scatter in direction s arises from scattering in ALL volume elements, call it F F(S) = ∫ρ(r)e2πirSdr9. This has the form of a Fourier transform -- the physical rule governing scattering.Fourier Transform and ResolutionCrystallization and TransformsIf you measure the amplitude, and have the phase, for Fourier terms,you can use that to construct the image of the scatterer.Representation of the electron density of a one-dimensional "crystal" by a superposition of waves. The crystal is formed by a periodic repetition of a diatomic molecule, as shown at the top of the right-hand column. The component waves, each with proper phase and amplitude, are on the left. The curves on the right show the successive superposition of the five waves on the left. (From Waser, 1968.)As you add these waves in the 1D cell, the image sharpens up.Phases here are:-, +, +, -, +Increasing Res.Phases here are:-,-, +, +, -Representation of another one-dimensional crystal, this one containing a triatomicmolecule. Note that this crystal is built up from the same waves as the crystal of (a) ; only the amplitudes and phases have been changed. (From Waser, 1968.)8Solving the Phase Problem1. MIR: Multiple Isomorphous Replacement (Heavy Atom)2. MR: Molecular Replacement3. MAD: multiwavelength anomolous dispersion1. Use of Heavy Metal Ions for Phasing by MIR MethodsPhosphorylase + Ethyl Hg thiosalicylateNative PhosphorylaseMetals are located by Difference Patterson• The Diff Patterson is a map generated as: P(u,v,w) = Σ( FD –FN )2*cos (hu+kv+lw)• Once a metal is located its Fourier transform (amp and phase) can be computed; this is a vector called fH.• The known fHcan be combined with the measured amplitudes of native protein and the derivative to estimate the protein phaseA really simple exampleSome special reflections have strong phase constraints, usually due to symmetry. For example the reflections viewed down a 2-fold axis, like the h0l reflections in space group P2, are constrained to be 0 or 180 degrees. If we know fH, then getting the protein phase is simple arithmetic. We know FD=FP+FH.. Suppose we