Protein Structure Determination Using NMR Restraints

BCMB/CHEM 819004/06/05

Programs for NMR Based Structure Determination

• CNS - Brunger, A. T.; Adams, P. D.; Clore, G. M.; DeLano, W. L.; Gros, P.; Grosse-Kunstleve, R. W.; Jiang, J. S.; Kuszewski, J.; Nilges, M.; Pannu, N. S.; Read, R. J.; Rice, L. M.; Simonson, T.; Warren, G. L. Acta Cryst. D 1998, 54, 905.

• XPLOR-NIH - Schwieters, C. D.; Kuszewski, J. J.; Tjandra, N.;Clore, G. M. J. Magn. Reson. 2003, 160, 65.

• DYANA - Guntert, P.; Mumenthaler, C.; Wuthrich, K. J. Mol. Biol. 1997, 273, 283.

• ARIA - Linge JP, Habeck M, Rieping W, et al. Bioinformatics2003, 19, 315-316 JAN 22 2003

NOE data from 2D and 3D experiments are a primary source of information

Icp = C{exp(-ρT) • (1 – exp(-2σT)}

ρ = 2W1 + W2 + W0 , σ = (W2 - W0)

T

dIcp/dT ∝ 1/r6

Icp

NOESY Spectrum of ACP

Potential NOE Interactions

In an Idealized α-Helix

Some can be used as a distance calibration

Long range NOEs (sidechain to sidechain) are among the most important in structure determination

Getting an Initial Structure - Embedding

• Metric Matrix – producing an approximate fold from an extended chain

• View as a set of products of vectors in N dimensional hyperspace

• W. Braun, Quart. Rev. Biophys. 19, 115-157 (1987)

M =

ri• rjrj

ri

Dij0

ri• rj can be written in terms of distancesD2

ij = ri2 + rj

2 - 2ri• rj

Solving for positions in Cartesian space

• Fill in matrix with inter-atom distances – some from NOEs – a lot from covalent geometry -

• Diagonalize M; | λ | = | A | | M | | A-1 |; | M | = | A-1 | | λ | | A | • A diagonal matrix corresponds to vectors in real space• Only 3 λ should be finite and equal (ri• ri finite only for x•x, etc)• ri• ri = Σk λk Aik

-1 Ajk = Aj1-1Ai1+Aj2

-1Ai2+Aj3-1Ai3 = xixi + yiyi + zizi

• Hence, elements of A are x,y,z coordinates of atoms• In practice often use upper and lower bounds and fill in matrix by

random number selection within bounds• Solution is only approximate

Structures Using Error Functions and Simulated Annealing

E = Ebond + Evdw + Eangle + ….. + ENMR

ENMR = ΣI (robs – rtrial)I 2 … (or use rmin,max for robs)

xnew = xold + t • vx = xold + t • ∫ axdt, ynew = …

ax = Fx/m= - (1/m) • dE/dx + arand(T), ay = …

T

t

20 NMR Structures of DnaJ

Validation of Structures

• R factor for NOEs: n ~ 1/6R = ΣNOEs[(Iobs)n – (Icalc)n] / ΣNOEs (Iobs)n

• Other statistics: rmsd of backbone and all atoms.

• NOE violations• Molecular energy• Procheck output

Structure Refinement Using RDCs

Write RDCs in principal alignment frame:D = (Da/r3){(3cos2θ – 1)/r3 + (3/2)Rsin2θcos(2φ)}

Write error function in terms of Dmeas and DcalcERDC = (Dmeas – Dcalc)2

Seek minimum in ERDC to refine structure –Need to float alignment axes during search

REsidual Dipolar Coupling Analysis Tool(REDCAT)

Valafar, H., & J.H. Prestegard (2004), J. Mag. Res. 167: 228-241Dosset, Hus, Marion & Blackledge (2001), JBNMR, 20: 223-231

• Given a proposed structure and RDCs, calculates order tensor solutions.

• Finds best order tensor solution.• Gives principal elements and Euler angles.• Back-calculates RDCs.• Estimates errors and helps identify

problematic data.

Access “Prepare Input” From File menu

Input from file menu is pdb file and rdc list

# Pf-Fe-Rubredoxin residues 2-54# H-N RDCs from field induced orientation-0.27-0.259999990.31999

HEADER METAL BINDING PROTEIN 1BQ8.pdbATOM 1 N MET A 1 24.235 -3.831 5.464 ATOM 2 CA MET A 1 22.963 -4.052 4.750 ATOM 3 C MET A 1 22.621 -2.823 3.939 ATOM 4 O MET A 1 23.394 -1.866 3.931

Loaded Coordinates and Couplings

A List of Possible Solutions is Generated by Monte Carlo Sampling

Problematic Data Identification by Numbers of Rejections Caused

Error Analysis with Error < 1.0

Green: Acceptable error, Red: Small indicated error, Gray: Excluded from analysis.

Best Solution After the Adjustment of Errors