Molecular Modeling lecture 2

Transcription

1 Molecular Modeling lecture 2 Topics 1. Secondary structure 3. Sequence similarity and homology 2. Secondary structure prediction 4. Where do protein structures come from? X-ray crystallography Solution NMR

2 Where do protein structures come from? Condensed PSD 2

3 X-ray E + X-ray Crystallography } Diffraction pattern Electron density map

4 e - oscillation scatter X-rays e- has almost zero mass, so it oscillates at the same frequency as the X-rays Oscillating e - emit light in all directions. E e - e - e - e - e - e - e- e - e - t Wavelength: λ 1.54Å Frequency = c/λ 2x10 18 s -1

5 Parallel mirror planes separated by d scatter in phase Bragg s Law: nλ=2d sinθ d θ d is the resolution, which depends on ϴ and λ

6 The amplitude of each reflection is proportional to the variability of electron density normal to the Bragg planes Bragg planes 2ϴ Xray beam ϴ d Each spot on the film represents a set of Bragg planes.

7 The image of the molecule is reconstructed by superimposing Bragg planes, shifted by phase and scaled by amplitude Each set of parallel lines represents the Bragg planes for one reflection ( one spot on the film ).

8 From the sum of waves comes an image in 3D. Sir Lawrence Bragg

9 Fitting the model to the density 3D electron density map = electron density at every point in space. Visualized by drawing 3D contours. Since we know the amino acid sequence and we know what the amino acids should look like, we can "fit" a model to the density.

10 Coordinate refinement Each atom is moved in X,Y and Z until: (1) good stereochemistry is achieved, the R-factor (2) there is a good match between the atoms and the density. Each atom is assigned a B-factor or "temperature-factor", to better fit the density. y z 4 parameters are refined for each atom + x high B density profile + B low B density profile Refined coordinates are deposited in the Protein Data Bank:

11 Structure quality: R-factor R-factor = (Fc - F o )/ (F o ) Free R-factor = R-factor calculated on data not used for refinement. Free-R is not biased by overfitting. free R-factor quality below 20% very good 20-30% typical 30-35% barely acceptable above 35% junk! 11

12 Structure quality: resolution Resolution = d in Bragg s Law. nλ=2d sinθ. Lower d is higher resolution. Resolution = resolution limit = the lowest d observed = the highest scattering angle observed. Resolution quality > 4Å nearly worthless, shows blobs of density 3-4Å medium. Shows backbone and some sidechains. 2-3Å typical good structure, all sidechains visible 1.5-2Å high resolution. Atom positions known within 0.1Å rmsd. < 1.5Å ultra high resolution! ydrogens sometimes visible. 12

13 In class exercise 2.1 Go to Search for your favorite gene (I like DFR) Refine search Xray. Resolution 2.5Å. Select one. 3D view it. Select viewer: JSMol R-mouse style structure off R-mouse color structure bonds 0.30Å R-mouse color atoms by scheme temperature (relative) R-mouse spin on Where are the atoms well ordered? Where are they flexible? 13

14 NMR Nuclear Magnetic Resonance Isotopes that have nuclear spin = 1/2 1, 13 C, 15 N and 31 P..can adopt two orientations in a magnetic field (). At equilibrium slightly more spins are aligned with the field than against it. The difference in energy down between up and down states lies in the radio frequency range. up

15 Radio pulses perturb equilibrium, which relaxes back, emitting radio freq. Short pulses "ring" through bonds --> TOCSY A TOCSY experiment finds cross-talk between 1 in a "spin system." Characteristic sets of resonances allow the easy identification of amino acids. A COSY experiment finds cross-peaks between 1 that are separated by 2 or 3 bonds. Long pulses resonate through space --> NOESY pulse resonances receiver

16 TOCSY/COSY. Characteristic patterns allow assignment of amino acid Chemical shifts for ILE: N 8.19 α 4.23 β 1.90 γc3 0.97,0.94 γc2 1.48,1.19 δc TOCSY peaks: red diamond COSY peaks: blue circle This 1 is not part of the spin system

17 NOESY: finds short distances NOESY spectra tell us which 1 are physically close in space, causing the Nuclear Oberhauser Effect (NOE). CA C N CA NOE s occurring between sequential residues, allow assignment of a sequence position to a resonance. O The structure is solved by distance geometry calculations. Atomic positions must satisfy the constraint distances and the stereochemistry. Molecular dynamics is used to refine the solution(s).

18 Steps in Protein NMR Overview 1. Grow protein in 13 C and/or 15 N enriched media. 2. Purify and concentrate protein. 3. Collect NMR spectra (2,3 or 4-dimensions). 4. Assign the peaks (TOCSY/COSY). 5. Assign distance constraints (NOESY) 6. Solve the distance geometry problem.

19 NMR result: an ensemble of structures Ensemble = the set of structures that satisfy distance geometry and stereochemistry. Shows flexible and poorly modeled regions.

20 In class exercise 2.2 Go to Search for your favorite gene (I like DFR) Refine search Solution NMR and molecular weight between and Select one. 3D view it. Select View: JSMol. R-mouse Style Structure backbone R-mouse color structure backbone by scheme group R-mouse animation animation mode loop R-mouse animation play Try other renderings. Where is the structure well determined? Where is there uncertainty? 20

21 Other NMR experiments Additional information about the conformation may be gained by /D-exchange Deuterium ( 2 ) is invisible to NMR. Disappearing 1 's tell us which ones are exposed to solvent. Especially amide N's. Temperature sensitivity of resonances. Chemical shift oh 1 changes with T less if -bonded. SQC Direct coupling of 15 N to 1 through a single bond.

22 MOE This week Run first part of MoeTour (elp/tutorials/getting Started) Open File/Protein database. Retrieve any protein. Explore renderings (Atom/, Ribbon/ )

23 Review questions What specific interaction defines an alpha helix? What defines a beta sheet? ow is a beta strand not a beta sheet? What does the Chou-Fasman method do? Is secondary structure conserved across distantly related proteins? Is tertiary structure conserved across distantly related proteins? What is a sequence profile? What does PSI-Pred do? ow do we measure the accuracy of secondary structure prediction? What are the results of Xray crystallography? ow is NMR different than Xray? What does resolution mean in Xray crystallography? What is an ensemble in NMR? 23

24 Supplementary slides 24

25 2.3 Coordinate systems Cartesian versus Internal 25

26 Two ways to express structure: Cartesian coordinates X Y Z ATOM 1 N VAL DFR 152 ATOM 2 CA VAL DFR 153 ATOM 3 C VAL DFR 154 ATOM 4 O VAL DFR 155 ATOM 5 CB VAL DFR 156 ATOM 6 CG1 VAL DFR 157 ATOM 7 CG2 VAL DFR 158 Biologists use angstroms, physicists use nanometers. Å = angstroms = m 1Å = 0.1 nm Z Y X Cartesian coordinates have a reference frame

27 Internal coordinates are independent of reference frame Internal coordinates model the covalent structure of the molecule. Components: bond lengths C 1.54Å C bond angles torsion (dihedral) angles C C planar groups pairwise distances 109 C C=O NMR structures are solved in Internal coordinates. X-ray structures are solved in Cartesian coordinates. C=O

28 Short peptides can be expressed as a set of torsion angles N φ ψ ω χ 1 χ 2 ALA 1~~~ VAL 2~~~ GLY 3~~~ IS 4~~~ TR 5~~~ O N O φ χ1 χ ψ 2 ω N O internal coordinates of a 5-residue peptide N 3 Cartesian coordinates If there are sufficient constraints, then internals coordinates may be converted to Cartesian coordinates.

29 Internal coordinates versus global coordinates Internal coordinates to my house: From the walking bridge, take a right, go five blocks, then a left and a right, then bear left and go half a block. It s on the left. Global coordinates to my house: N W What kind of coordinates system is this, global or internal? 110 8th St, Troy NY What kind of coordinates do you get from a GPS?

30 Before Cartesian cartography Internal coordinates versus global coordinates A. Vespucci s map of the world, made before J. arrison s clock (1735),...and after, using global coordinates. using internal coordinates.

31 If Amerigo Vespucci had mapped a protein... These two molecules have identical torsion angles, and only slight differences in backbone bond lengths and bond angles. Protein structure if it were solved by John arrison Protein structure if it were solved by Amerigo Vespucci. Note local similarity, global distorions.