10NMR experimental observables providing structural information Backbone conformation from chemical shifts (Chemical Shift Index - CSI): , Distance restraints from NOEsHydrogen bond restraintsBackbone and side chain dihedral angle restraints from scalar couplingsOrientation restraints from residual dipolar couplings
13约束生成 NOE 指认 转化为距离 Unique：只有一种可能 Ambiguous：有多种可能 实验通常可检测 <5Å 距离是不精确的：距离范围距离是大量的精确结构其中一种可能是正确的多种可能都是正确的（谱峰重叠）
14NMR data 1: NOEFor short mixing times NOE cross peak intensity is proportional to 1/r6 of two protons.NOE ~ 1/r6 f(tc)For well structured areas of a macromolecule f(tc) can be considered to be constant. (in practice this is assumed to be true for all parts of the molecule)Calibration of cross peaks by using a proton pair of known local geometry (distance)Because of multiple simplifying assumptions of the relationship between NOE and distance it is usually used only qualitatively (class NOEs in three bins: strong, medium and weak)
15Approaches to identifying NOEs 1H-1H NOESY15N- or 13C-dispersed 1H-1H NOESY3D1H13C15NWhat do these mean?1H15N13C4D
16Special NOESY experiments Filtered, edited NOE: based on selection of NOEs from two molecules with unique labeling patterns.1H13CUnlabeledpeptideLabeledproteinOnly NOEs at the interfaceOnly NOEs from bound stateHkonkoffTransferred NOE: based on 1) faster build-up of NOEs in large versus small molecules; 2) Fast exchange 3) NOEs of bound state detected at resonance frequencies of free state
171H-1H distances from NOEs Long-range(tertiary structure)SequentialIntra-residueABCDZ• • • •Medium-range(helices)Challenge is to assign all peaks in NOESY spectra
18NMR data 1: NOE Conversion of NOE into distances Strong: 1.8 - 2.7 Å Medium: ÅWeak: ÅLower bound because of vdw radii of atoms
19NOE pseudo-energy potential Generate “fake” energy potentials representing the cost of violating the distance or angle restraints. Here’s an example of a distance restraint potentialKNOE(rij-riju)2 if rij>rijuVNOE =if rijl<rij < rijuKNOE(rij-rij1)2 if rij<rijlwhere rijl and riju are the lower and upper bounds of our distance restraint, and KNOE is some chosen force constant, typically ~ 250 kcal mol-1 nm-2So it’s somewhat permissible to violate restraints but it raises V
20NOE pseudo-energy potential VNOEPotential rises steeply with degree of violationrijl riju
21Number of NOEs are more important than accuracy of individual NOEs Structure calculation of protein G (56 aa) with increasing numbers of NOES
22Restraints and uncertainty Large # of restraints = low values of RMSDLarge # of restraints for key hydrophobic side chains
23Dealing 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 calculation. This is often done for restraints that involve more complicated ambiguities, e.g. 3 HA-->10 HN, 43 HN, or 57 HN, where three amides all have the same shift.can also make stereospecific assignments iteratively using what are called floating chirality methods.
24Example of resolving an ambiguity during structure calculation 9-11 Å9.52 ppmB4.34 ppmrange of inter-atomic distances observed in trial ensemble3-4 ÅC4.34 ppmDue to resonance overlap between atoms B and C, an NOE crosspeak between 9.52 ppm and 4.34 ppm could be A to C or A to B - this restraint is ambiguous.But if an ensemble generated with this ambiguous restraint shows that A is neverclose to B, then the restraint must be A to C.
26Practical improvements in structure calculation Conventional approach relies on interactive assignment of NOEs: very laboriousARIA: ambiguous restraintsuse all NOEs in a spectrum even when unassigned and allow automatic assignment during successive structure calculation roundsi.e. discarding NOEs that are inconsistent with emerging structureCombine with fully automated assignment procedures to arrive at fully automated structure calculation
27Iterative structure calculation with assignment of ambiguous restraints start with some set of unambiguous NOEs and calculate an ensemblethere are programs such as ARIA, with automatic routines for iterative assignment of ambiguous restraints. The key to success is to make absolutely sure the restraints you start with are right!source:
28How many restraints to get a high-resolution NMR structure? usually ~15-20 NOE distance restraints per residue, but the total # is not as important as how many long-range restraints you have, meaning long-range in the sequence: |i-j|> 5, where i and j are the two residues involvedgood NMR structures usually have ≥ ~3.5 long-range distance restraints per residue in the structured regionsto get a very good quality structure, it is usually also necessary to have some stereospecific assignments.
29NMR data 2: H-bondsUsually inferred from H2O/D2O exchange protection; Hence a priory not known which groups form the H-bond. Hence only used during structure refinement to improve convergence, and precision of the family of structure.significant impact on structure quality measures
30Backbone Hydrogen Bonds C=OH-NNH chemical shift at low field (high ppm)Slow rate of NH exchange with solventCharacteristic pattern of NOEs(Scalar couplings across the H-bond)When H-bonding atoms are known can impose a series of distance/angle constraints to enforce standard H-bond geometries
31NMR data 3: J couplingsN CaHf3J(HN,Ha)bHNa,310q = f-60ºNHa
32Dihedral angles from scalar couplings •6 HzMust accommodate multiple solutions multiple J valuesBut database shows few occupy higher energy conformations
33Dihedral angle potential Convert J data into allowed dihedral angles and introduce a restraining potential to maintain the allowed anglesDirectly restrain against J-couplingsV=kj (Jobs-Jcalc)2
34Orientational constraints from residual dipolar couplings (RDC) Ho1H1HReports angle of inter-nuclear vector relative to magnetic field Ho13C15N1H1HF1F2F315N1HRequires medium to partially align moleculesMust accommodate multiple solutions multiple orientations
40Starting 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.
41DG--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 structureStructures 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 structures
42分子动力学模拟 模拟分子随机运动，使其达到能量的最小值 约束条件转化为MD中的能量项 模拟退火：克服局部的能量最小点 KNOE(rij-rij1) if rij<rijlKNOE(rij-riju) if rij>rijuif rijl<rij < rijuVNOE =模拟分子随机运动，使其达到能量的最小值约束条件转化为MD中的能量项Vtotal= Vbond+ Vangle+ Vdihedr+ Vvdw+ Vcoulomb+ VNMR模拟退火：克服局部的能量最小点计算多个结构，取能量较低的若干结构作为结果Ensemble (NMR信息的不完备和不精确)
43Restrained 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+ VNMRthe 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 AMBERthe NMR restraints are incorporated into the VNMR term, which is a “pseudoenergy” or “pseudopotential” term included to represent the cost of violating the restraints
44SA-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 minimaSA is very efficient at locating the global minimum of the target function
45Further refinementsRefinement of structure including full force field and e.g. explicit water moleculesMay improve structural quality but may also increase experimental violations
46NMR structure calculations Objective is to determine all conformations consistent with the experimental dataPrograms that only do conformational search lead to bad chemistry use molecular force fields improve molecular propertiesSome programs try to do both at onceNeed a reasonable starting structureNMR data is not perfect: noise, incomplete data multiple solutions (conformational ensemble)
47NMR ensembleNMR methods do not calculate a single structure, but rather repeat structure calculations many times to generate an ensemble of structuresStructure calculations are designed to thoroughly explore all regions of conformational space that satisfy the experimentally derived restraintsAt 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 whichA. satisfies all the experimental restraints (minimizes violations)B. at the same time accurately represents the full permissible conformational space under the restraintsC. looks like a real protein
48NMR ensembleThe fact that NMR structures are reported as ensembles gives them a “fuzzy” appearance which is both informative and sometimes annoyingSecondary structures well defined, loops variableInteriors well defined, surfaces more variableTrends the same for backbone and side chainsMore dynamics at loops/surfaceConstraints in all directions in the interior
49Minimized average structure a minimized average is just that: a mean structure is calculated from the ensemble and then subjected to energy minimization to restore reasonable geometry, which is often lost in the calculation of a meanthis is NMR’s way of generating a single representative structure from the data. It is much easier to visualize structural features from a minimized average than from the ensemblefor highly disordered regions a minimized average will not be informative and may even be misleading--such regions are sometimes left out of the minimized averagesometimes when an NMR structure is deposited in the PDB, there will be separate entries for both the ensemble and the minimized average. It is nice when people do this. Alternatively, a member of the ensemble may be identified which is considered the most representative (often the one closest to the mean)
50NMR 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.
51Assessing the quality of NMR structures Number of experimental constraintsRMSD of structural ensemble (subjective!)Violation of constraints- number, magnitudeMolecular energiesComparison to known structures: PROCHECKBack-calculation of experimental parameters
52Acceptance criteria: choosing structures for an ensemble typical to generate 50 or more trial structures, but not all will converge to a final structure that is physically reasonable or consistent with the experimentally derived NMR restraints. We want to throw such structures away rather than include them in our reported ensemble.these are typical acceptance criteria for including calculated structures in the ensemble:no more than 1 NOE distance restraint violation greater than 0.4 Åno dihedral angle restraint violations greater than 5no gross violations of reasonable molecular geometrysometimes structures are rejected on other grounds as well:too many residues with backbone angles in disfavored regions of Ramachandran spacetoo high a final potential energy in the rMD calculation
53Precision of NMR Structures (Resolution) judged by RMSD of superimposed ensemble of accepted structuresRMSDs for both backbone (Ca, N, CC=O) and all heavy atoms (i.e. everything except hydrogen) are typically reported, e.g.bb 0.6 Åheavy 1.4 Åsometimes only the more ordered regions are included in the reported RMSD, e.g. for a 58 residue protein you will see RMSD (residues 5-58) if residues 1-4 are completely disordered.
54Reporting ensemble RMSD Two major ways of calculating RMSD of the ensemble:pairwise: compute RMSDs for all possible pairs of structures in the ensemble, and calculate the mean of these RMSDsfrom mean: calculate a mean structure from the ensemble and measure RMSD of each ensemble structure from it, then calculate the mean of these RMSDspairwise will generally give a slightly higher number, so be aware that these two ways of reporting RMSD are not completely equal. Usually the Materials and Methods, or a footnote somewhere in the paper, will indicate which is being used.
55Assessing structure quality run the ensemble through the program PROCHECK-NMR to assess its qualityhigh-resolution structure will have backbone RMSD ≤ ~0.8 Å, heavy atom RMSD ≤ ~1.5 Ålow RMS deviation from restraints (good agreement w/restraints)will have good stereochemical quality:ideally >90% of residues in core (most favorable) regions of Ramachandran plotvery few “unusual” side chain angles and rotamers (as judged by those commonly found in crystal structures)low deviations from idealized covalent geometry
56Structural Statistics Tables list of restraints, # and typecalculated energiesagreement of ensemble structures with restraints (RMS)precision of structure (RMSD)sometimes also see listings of Ramachandran statistics, deviations from ideal covalent geometry, etc.
57Structure validation XPLOR/CNS: Consistency with data? convergence of structure calculation (eg rmsd over all atoms)restraint violations?Procheck: programme that analyses and evaluates a family of structuresi.e. is the structure consistent with what we know about structure ?residue by residue outputcovalent geometrydihedral anglesnon-bonded interactionmain chain H-bondsstereochemistrychiralitydisulphide bonds
60Cross validationLeaving out a percentage of experimental constraints. Recalculating structures and checking for consistency with unused dataCan be done with “same type of data” eg NOEMore often used with NOE’s and RDCs
66Regular secondary structure 结构评价Most favored regions (%)88.8Additionally allowed regions (%)10.7Generously allowed regions (%)0.5Disallowed regions (%)0.0RMSDAll residuesRegular secondary structureBackbone heavy atoms0.880.32All heavy atoms1.130.68