Methods for Structure Determination Chemistry and Chemical Biology Rutgers University

X-ray (X-ray crystallography) NMR (Nuclear Magnetic Resonance) EM (Electron Microscopy) Protein Data Bank Download How are macromolecular structures determined?

The Data Pipeline Genomic Based Target Selection Data Collection Structure Determination Isolation, Expression, Purification, Crystallization PDB Deposition & Release 3D Models Annotations Publications X-ray cryst NMR EM

Some Background Symmetry –Translation, Rotation, Reflection, Inversion Crystals –Lattice, Unit cell, Asymmetric Unit Diffraction –Light diffraction, X-ray diffraction

Translation M.C. Escher

Rotation M.C. Escher

Reflection M.C. Escher

??? M.C. Escher

Crystals Mineral Protein

.... Lattice, Crystal and Unit cell , lattice object,,,,,,,,,,,,,,,, Convolution Crystal structure,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, Unit Cell 1 Unit Cell 2

Macromolecular Crystal Lattice Alexander McPherson, Introduction to Macromolecular Crystallography Wiley-Liss, 2002

Unit Cell and Asymmetric Unit

Symmetry in Crystals 1-fold 2-fold 3-fold 4-fold 6-fold , 7-, 8- and higher fold symmetries do not pack in a crystal

Crystal Systems Jenny Pickworth Glusker, Kenneth N. Trueblood, Crystal Structure Analysis: A Primer, Oxford University Press, 1985

The International Tables

Diffraction Sunrise through a screened window

Light Diffraction Henry S. Lipson Crystals and X-rays Taylor & Francis 1970

Diffraction in Action

Principles of Microscopy

The Fourier Duck Fourier Transform Reverse Transform Reverse Transform with limited resolution data

Why Use X-rays?

X-ray Diffraction Gale Rhodes, Crystallography Made Crystal Clear: A Guide for Users of Macromolecular Models, Academic Press, 1993

Miller Indices (hkl) For any plane in the unit cell with intercepts1/h, 1/k and 1/l along the x, y, and z axes the Miller indices are h,k,l If the resulting indices are fractions, multiply all to get integer numbers Intercepts : ½ a, a, ∞ Fractional intercepts : ½, 1, ∞ Miller Indices : (210)

try the Java Applet! n = 2d sin  2  angle between incident and reflected beams d spacing between planes wavelength n order of diffraction Bragg’s Law Constructive interference occurs from successive crystallographic planes (h, k, l) in the crystalline lattice

X-ray Diffraction Pattern Diffraction pattern is in reciprocal space Size and shape of unit cell determines position of diffraction peaks. Atomic positions within unit cell determines intensity of peaks. Experimental data: h,k,l and intensities (with errors) A precession photograph

Diffraction Patterns to Structure I hkl = constant.| F hkl | 2 Structure Factor  (x,y,z) = Σ F hkl e -2 π i (hx + ky +lz) Electron Density

Phase Problem Structure factor is dependent on type and location of atoms in unit cell The complete Structure Factor F for a reflection includes the phase, which cannot be measured directly. F hkl = | F hkl | e  i ϕ hkl Amplitude: from experimental measurements Amplitude: from experimental measurements Phase: must be estimated Phase: must be estimated Structure Factor

Electron Density Can be calculated by Fourier transform of diffraction data Provides an averaged image: –over all molecules in the crystal –over the time of the diffraction experiment Trp in a 1.3 A map Trp in a 2.25 A map Trp in a 4.3 A map

Microscopy vs X-ray Crystallography

The X-ray Crystallography Pipeline Protein preparation Crystal growth Data collection Phase determination Model building and refinement

Protein Preparation Purify from natural sources: e.g. liver, muscle, leaf etc. Clone in appropriate vector Express in appropriate host – bacteria, yeast, mammalian cell lines, cell free extracts Purify target protein from cell lysate

Cover Slip Precipitant Solution Protein + Precipitant Crystal Growth: Vapor Diffusion Common precipitants: –Polyethylene glycol –Salts ammonium sulfate sodium chloride – Alcohols Isopropanol Methylpentanediol (MPD)

Theory/phase_methods.html Crystallization Conditions Crystallization Phase Diagram

Data Collection Rotating Anode Diffractometer Crystal mounted in nylon loop. Frozen in liquid N2 Crystal mounted in glass capillary

Synchrotron X-ray source NSLS Beamline X12C

Crystal Diffraction Low Resolution (small angle) Low Resolution (small angle) High Resolution (large angle) High Resolution (large angle) Beam Stop Shadow Water Ring ~3-5 Å Water Ring ~3-5 Å Jeff Dahl, Sars protease,

Different crystal forms of the same protein yield different diffraction patterns trp repressor, sodium phosphatetrp repressor, ammonium sulfate

Data Obtained Crystal unit cell dimensions Lattice type, possible space groups Resolution Limit Merged data set with index, intensity + error for each reflection a = Å b = Å c = Å α = 90.0° ß = 91.25° γ = 90.0° Monoclinic lattice (P2 or P2 1 ) H K L intensity error etc. a = Å b = Å c = Å α = 90.0° ß = 91.25° γ = 90.0° Monoclinic lattice (P2 or P2 1 ) H K L intensity error etc.

Direct methods –Estimate from probability relationships applied to most intense diffraction peaks Patterson methods –Multiple Isomorphous Replacement –Anomalous Dispersion Molecular replacement Density Improvement –Non-crystallographic symmetry averaging –Solvent flattening Phase Determination

Patterson Function Convolution of electron density with itself Evaluated at points u,v,w throughout unit cell Map of vectors between scattering atom in the real crystal cell (translated to Patterson origin) crystal Patterson map

Isomorphous Replacement Derivative – native crystal = heavy atom Deriv. diffn – native diffn = heavy atom diffn Patterson synthesis > peaks based on distance between heavy atoms in structure gives initial phase. Real space Reciprocal space

Anomalous Dispersion Friedel’s Law: I hkl = I -h-k-l Members of a Friedel pair have equal amplitude and opposite phase In anomalous scattering crystals Friedel’s law is not obeyed

Molecular Replacement New structure expected to resemble one previously determined Use Patterson-based methods to find the orientation of known model in new crystal lattice (i.e. find rotation R and translation T)

Density Modification Improve map by adding additional “knowledge” Typical modifications: Molecular averaging Solvent Flattening Histogram Matching Image from C. Lawson

Calculate Map Edit model Refine Initial Model Experimental Data Stereochemical Knowledge Final Model Model Building-Refinement Cycle

Crystal Structures Lysozyme Hemoglobin Ribonuclease Myoglobin: Kendrew, Bodo, Dintzis, Parrish, Wyckoff, Phillips, Nature , Hemoglobin: Perutz, Proc. R. Soc. A265, ,1962. Lysozyme: Blake, Koenig, Mair, North, Phillips, Sarma, Nature , Ribonuclease: Kartha, Bello, Harker, Nature 213, Wyckoff, Hardman, Allewell, Inagami, Johnson, Richards. J. Biol. Chem. 242, , Myoglobin

Structural Data PDB 3a6b -snip-

Types of Electron Density Maps Experimentally phased map: –F obs, Phi calc “model” map: –(2F obs – F calc ), Phi calc “difference” map –(F obs – F calc ) or (F obs – F obs ), Phi calc

R-factor Equation

R versus R free

Typical Statistical Table

Validation: Ramachandran Plot

Graphical Display and Model Fitting View maps and model together to: –Look at crystal contacts –assess map regions with unassigned density –assess model geometry problems –Build missing polymer residues –Add waters, ligands Image from C. Lawson

Some Movie Links Crystal Mounting Robot – Crystal Diffraction – Optical diffraction – dex.html Enjoy!

References IUCr Online dictionary of Crystallography – Educational web sites and resources – An interactive SF tutorial – intro.htmlhttp:// intro.html