Solving NMR Structures II: Calculation and evaluationNMR data do not uniquely define a 3D protein structure (single set of coordinates)The NMR EnsembleSlide 4NMR structures include hydrogen coordinatesMethods for structure calculationStarting points for calculationsDG--Distance geometryrMD--Restrained molecular dynamicsPseudo-energy potentials for rMDExample of nOe pseudopotentialSA-Simulated annealingDealing with ambiguous restraintsExample of resolving an ambiguity during structure calculationIterative structure calculation with assignment of ambiguous restraintsAcceptance criteria: choosing structures for an ensemblePrecision of NMR Structures (Resolution)Reporting ensemble RMSD“Minimized average” structureHow many restraints do we need to get a high-resolution NMR structure?Assessing Structure QualityStructural Statistics TablesSolving NMR Structures II:Calculation and evaluationWhat NMR-based (solution) structures look likethe NMR ensembleinclusion of hydrogen coordinatesMethods for calculating structuresdistance geometry, restrained molecular dynamics, simulated annealingEvaluating the quality of NMR structuresresolution, stereochemical quality, restraint violations, etcNMR data do not uniquely define a 3D protein structure (single set of coordinates)•Restraints are ranges of allowed distances, angles etc. rather than single values, reflecting the fact that the experimental data contain uncertainties both in measurement and interpretation.•Only a limited number of the possible restraints are observable experimentallydue to peak overlap/chemical shift degeneracy, lack of stereospecific assignments, etc.•View of protein structure as a single set of atomic coordinates may itself be physically unrealistic!proteins are dynamic moleculesThe NMR Ensemble•NMR methods not calculate a single structure, but rather repeat a structure calculation many times to generate an ensemble of structures•The structure calculations are designed to thoroughly explore all regions of conformational space that satisfy the experimentally derived restraints•At the same time, they often impose some physical reasonableness on the system, such as bond angles, distances and proper stereochemistry.•The ideal result is an ensemble which A. satisfies all the experimental restraints (minimizes violations)B. at the same time accurately represents the full permissible conformational space under the restraints (maximizes RMSD between ensemble members)C. looks like a real proteinThe NMR EnsembleAt right, an ensemble of 25 structures for Syrian hamster prion protein(only the backbone is shown)Liu et al. Biochemistry (1999) 38, 5362.The fact that NMR structures are reported as ensembles gives them a “fuzzy” appearance which is both informative and sometimes annoyingNMR structures include hydrogen coordinates• X-ray structures do not generally include hydrogen atoms in atomic coordinate files, because the heavy atoms dominate the diffraction pattern and the hydrogen atoms are not explicitly seen.• By contrast, NMR restraints such as NOE distance restraints and hydrogen bond restraints often explicitly include the positions of hydrogen atoms. Therefore, these positions are reported in the PDB coordinate files.Methods for structure calculation•distance geometry (DG)•restrained molecular dynamics (rMD)•simulated annealing (SA)•hybrid methodsStarting points for calculations•to get the most unbiased, representative ensemble, it is wise to start the calculations from a set of randomly generated starting structures.•Alternatively, in some methods the same initial structure is used for each trial structure calculation, but the calculation trajectory is pushed in a different initial direction each time using a random-number generator.DG--Distance geometry•In distance geometry, one uses the nOe-derived distance restraints to generate a distance matrix, which one then uses as a guide in calculating a structure•Structures calculated from distance geometry will produce the correct overall fold but usually have poor local geometry (e.g. improper bond angles, distances)•hence distance geometry must be combined with some extensive energy minimization method to generate physically reasonable structuresrMD--Restrained molecular dynamics•Molecular dynamics involves computing the potential energy V with respect to the atomic coordinates. Usually this is defined as the sum of a number of terms:Vtotal= Vbond+ Vangle+ Vdihedr+ VvdW+ Vcoulomb+ VNMR•the first five terms here are “real” energy terms corresponding to such forces as van der Waals and electrostatic repulsions and attractions, cost of deforming bond lengths and angles...these come from some standard molecular force field like CHARMM or AMBER •the NMR restraints are incorporated into the VNMR term, which is a “pseudoenergy” or “pseudopotential” term included to represent the cost of violating the restraintsPseudo-energy potentials for rMD•Generate “fake” energy potentials representing the cost of violating the distance or angle restraints. Here’s an example of a distance restraint potentialKNOE(rij-rij1)2 if rij<rijlKNOE(rij-riju)2 if rij>riju0 if rijl<rij < riju VNOE =where rijl and riju are the lower and upper boundsof our distance restraint, and KNOE is somechosen force constant, typically ~ 250 kcal mol-1 nm-2So it’s somewhat permissible to violate restraints but it raises VExample of nOe pseudopotentialrijl riju0VNOEpotentialrises steeply with degreeof violationSA-Simulated annealing•SA is essentially a special implementation of rMD and uses similar potentials but employs raising the temperature of the system and then slow cooling in order not to get trapped in local energy minima•SA is very efficient at locating the global minimum of the target functionDealing with ambiguous restraints•often not possible to tell which atoms are involved in a NOESY crosspeak, either because of a lack of stereospecific assignments or because multiple protons have the same chemical shift•sometimes an ambiguous restraint is included but is expressed ambiguously in the restraint file, e.g. 3 HA --> 6 HB#, where the # wildcard indicates that the beta protons of residue 6 are not stereospecifically assigned. This is quite commonly done for stereochemical ambiguities.•it is also possible to leave ambiguous restraints out and then try to resolve them iteratively using multiple cycles of