NMR structure calculation 1 Solving structures by NMR

NMR structure calculation 1

Solving structures by NMR Sample Preparation Structural restraints • Cloning, expression, purification • Isotope labelling [15 N], [13 C/15 N], [ 2 H/13 C/15 N] • NOE, H-bonds • J-couplings • Residual dipolar couplings, T 1/T 2 Resonance Assignments • Chemical shifts • Backbone • Side chains Secondary Structure Calculation • Distance geometry • Restrained molecular dynamics • Simulated annealing Chemical shift Ensemble of 3 D structures 3

Overview • Structure representation • Types of NMR data conversion into restraints • Structure calculation methods • Structure validation 4

Structure calculation Conformation 8

NMR experimental observables providing structural information • Backbone conformation from chemical shifts (Chemical Shift Index - CSI): , • Distance restraints from NOEs • Hydrogen bond restraints • Backbone and side chain dihedral angle restraints from scalar couplings • Orientation restraints from residual dipolar couplings 10

NMR data 1: NOE • For short mixing times NOE cross peak intensity is proportional to 1/r 6 of two protons. • NOE ~ 1/r 6 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) 14

Approaches to identifying NOEs • 1 H-1 H NOESY 2 D 3 D • 15 N- 1 H 1 H 1 H or 13 C-dispersed 1 H-1 H NOESY 1 1 1 H H 3 D 15 13 N 1 H 4 D 15 N 1 1 H 13 C 1 H H C 1 1 H 13 C H 15 N 15

Special NOESY experiments • Filtered, edited NOE: based on selection of NOEs from two molecules with unique labeling patterns. 1 Unlabeled peptide 1 H H 13 C Labeled protein Only NOEs at the interface • Transferred 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 H kon H H koff H Only NOEs from bound state 16

1 H-1 H distances from NOEs Long-range (tertiary structure) Sequential Intra-residue A B C D • • Z Medium-range (helices) Challenge is to assign all peaks in NOESY spectra 17

NMR data 1: NOE • Conversion of NOE into distances – Strong: 1. 8 - 2. 7 Å – Medium: 1. 8 - 3. 3 Å – Weak: 1. 8 - 5 Å Lower bound because of vdw radii of atoms 18

NOE 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 potential KNOE(rij-riju)2 if rij>riju VNOE = 0 if rijl<rij < riju KNOE(rij-rij 1)2 if rij<rijl where 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-2 So it’s somewhat permissible to violate restraints but it raises V 19

NOE pseudo-energy potential VNOE Potential rises steeply with degree of violation 0 rijl riju 20

Number of NOEs are more important than accuracy of individual NOEs Structure calculation of protein G (56 aa) with increasing numbers of NOES 21

Restraints and uncertainty ØLarge # of restraints = low values of RMSD ØLarge # of restraints for key hydrophobic side chains 22

Dealing 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. 23

Example of resolving an ambiguity during structure calculation 9. 52 ppm range of inter-atomic distances observed in trial ensemble 9 -11 Å A B 4. 34 ppm 3 -4 Å C 4. 34 ppm Due 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 never close to B, then the restraint must be A to C. 24

Practical improvements in structure calculation • Conventional approach relies on interactive assignment of NOEs: very laborious • ARIA: ambiguous restraints – use all NOEs in a spectrum even when unassigned and allow automatic assignment during successive structure calculation rounds i. e. discarding NOEs that are inconsistent with emerging structure • Combine with fully automated assignment procedures to arrive at fully automated structure calculation 26

Iterative structure calculation with assignment of ambiguous restraints start with some set of unambiguous NOEs and calculate an ensemble there 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: http: //www. pasteur. fr/recherche/unites/Binfs/aria/ 27

How 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 involved • good NMR structures usually have ≥ ~3. 5 long-range distance restraints per residue in the structured regions • to get a very good quality structure, it is usually also necessary to have some stereospecific assignments. 28

NMR data 2: H-bonds • Usually inferred from H 2 O/D 2 O 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 29

Backbone Hydrogen Bonds C=O H-N • NH chemical shift at low field (high ppm) • Slow rate of NH exchange with solvent • Characteristic pattern of NOEs • (Scalar couplings across the H-bond) Ø When H-bonding atoms are known can impose a series of distance/angle constraints to enforce standard H-bond geometries 30

NMR data 3: J couplings 3 J(H N, Ha) H N Ca H b a, 310 HN q = -60º Ha N 31

Dihedral angles from scalar couplings • • 6 Hz Ø Must accommodate multiple solutions multiple J values ØBut database shows few occupy higher energy conformations 32

Dihedral angle potential • Convert J data into allowed dihedral angles and introduce a restraining potential to maintain the allowed angles • Directly restrain against J-couplings • V=kj (Jobs-Jcalc)2 33

Orientational constraints from residual dipolar couplings (RDC) Ho F 2 F 1 F 3 13 C Reports angle of inter-nuclear vector relative to magnetic field Ho 1 H 1 H 15 N 1 H ØRequires medium to partially align molecules ØMust accommodate multiple solutions multiple orientations 34

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Alignment tensor and RDC: DAB(q, f) = Da. AB{ (3 cos 2 q-1) + R(sin 2 qcos 2 f)3/2} 36

15 N-1 H dipolar couplings A 5% (w/v) DTDPC: DHPC (3: 1) neutral (a) + 3% CTAB positive 0 20 40 60 residue 80 100 37

Structure refinement with NOEs & RDC (A) + (B) 7. 3 ± 3. 1Å 4. 5 ± 2. 1Å 3. 4 ± 1. 5Å 38

Methods for structure calculation • distance geometry (DG) • restrained molecular dynamics (r. MD) • simulated annealing (SA) • hybrid methods 39

Starting 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. 40

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 structures 41

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+ Vvd. W+ 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 restraints 43

SA-Simulated annealing • SA is essentially a special implementation of r. MD 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 function 44

Further refinements • Refinement of structure including full force field and e. g. explicit water molecules – May improve structural quality but may also increase experimental violations 45

NMR structure calculations • Objective is to determine all conformations consistent with the experimental data • Programs that only do conformational search lead to bad chemistry use molecular force fields improve molecular properties Ø Some programs try to do both at once Ø Need a reasonable starting structure • NMR data is not perfect: noise, incomplete data multiple solutions (conformational ensemble) 46

NMR ensemble • NMR methods do not calculate a single structure, but rather repeat structure calculations many times to generate an ensemble of structures • 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 C. looks like a real protein 47

NMR ensemble The fact that NMR structures are reported as ensembles gives them a “fuzzy” appearance which is both informative and sometimes annoying • Secondary structures well defined, loops variable • Interiors well defined, surfaces more variable • Trends the same for backbone and side chains Ø More dynamics at loops/surface Ø Constraints in all directions in the interior 48

Minimized 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 mean • this 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 ensemble • for highly disordered regions a minimized average will not be informative and may even be misleading--such regions are sometimes left out of the minimized average • sometimes 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) 49

NMR 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. 50

Assessing the quality of NMR structures • Number of experimental constraints • RMSD of structural ensemble (subjective!) • Violation of constraints- number, magnitude • Molecular energies • Comparison to known structures: PROCHECK • Back-calculation of experimental parameters 51

Acceptance 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 Å – no dihedral angle restraint violations greater than 5 – no gross violations of reasonable molecular geometry • sometimes structures are rejected on other grounds as well: – too many residues with backbone angles in disfavored regions of Ramachandran space – too high a final potential energy in the r. MD calculation 52

Precision of NMR Structures (Resolution) • judged by RMSD of superimposed ensemble of accepted structures • RMSDs for both backbone (Ca, N, CC=O) and all heavy atoms (i. e. everything except hydrogen) are typically reported, e. g. bb 0. 6 Å heavy 1. 4 Å • sometimes only the more ordered regions are included in the reported RMSD, e. g. for a 58 residue protein you will see RMSD (residues 558) if residues 1 -4 are completely disordered. 53

Reporting 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 RMSDs – from mean: calculate a mean structure from the ensemble and measure RMSD of each ensemble structure from it, then calculate the mean of these RMSDs – pairwise 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. 54

Assessing structure quality • run the ensemble through the program PROCHECK-NMR to assess its quality • high-resolution structure will have backbone RMSD ≤ ~0. 8 Å, heavy atom RMSD ≤ ~1. 5 Å • low RMS deviation from restraints (good agreement w/restraints) • will have good stereochemical quality: – ideally >90% of residues in core (most favorable) regions of Ramachandran plot – very few “unusual” side chain angles and rotamers (as judged by those commonly found in crystal structures) – low deviations from idealized covalent geometry 55

Structural Statistics Tables list of restraints, # and type calculated energies agreement of ensemble structures with restraints (RMS) precision of structure (RMSD) sometimes also see listings of Ramachandran statistics, deviations from ideal covalent geometry, etc. 56

Structure 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 structures i. e. is the structure consistent with what we know about structure ? residue by residue output covalent geometry dihedral angles non-bonded interaction main chain H-bonds stereochemistry chirality disulphide bonds 57

Example of Procheck results 59

Cross validation • Leaving out a percentage of experimental constraints. Recalculating structures and checking for consistency with unused data – Can be done with “same type of data” eg NOE – More often used with NOE’s and RDCs 60

结构计算结果 • PDB 1 Z 7 P(ensemble), 1 Z 7 R(mean) http: //www. rcsb. org/pdb 63

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结构评价 Most favored regions (%) 88. 8 Additionally allowed regions (%) 10. 7 Generously allowed regions (%) 0. 5 Disallowed regions (%) 0. 0 RMSD All residues Regular secondary structure Backbone heavy atoms 0. 88 0. 32 All heavy atoms 1. 13 0. 68 66

使用的软件 • NMRPipe 数据处理 http: //spin. niddk. nih. gov/bax/software/NMRPipe/ • NMRView 指认分析 http: //www. onemoonscientific. com/nmrview/ • CYANA结构计算 500 Euro http: //www. las. jp/prod/cyana/eg/ • TALOS基于化学位移预测主链二面角 (NMRPipe的一部分) http: //spin. niddk. nih. gov/NMRPipe/talos/ • SANE基于结构的NOE自动指认 J Biomol NMR, 2001 19(4) 321 -9 • Amber 分子动力学模拟。用于结构优化 $400 http: //amber. scripps. edu/ • PROCHECK-NMR 结构分析与评价 http: //www. biochem. ucl. ac. uk/~roman/procheck_nmr. html • MOLMOL 结构分析与绘图 http: //hugin. ethz. ch/wuthrich/software/molmol/ 67

其他软件 • 数据处理 – Felix $? ? http: //www. accelrys. com/products/felix/index. html – AZARA Free http: //www. bio. cam. ac. uk/azara/ – PROSA (Free? ) http: //guentert. gsc. riken. go. jp/Software/Prosa. html • 指认分析 – – Felix $? ? http: //www. accelrys. com/products/felix/index. html XEASY $ 200 http: //hugin. ethz. ch/wuthrich/software/xeasy/index. html Sparky Free http: //www. cgl. ucsf. edu/home/sparky/ CARA Free http: //www. nmr. ch • 结构计算 – CNS Free http: //cns. csb. yale. edu/ – XPLOR Free http: //xplor. csb. yale. edu/xplor/ – XPLOR-NIH Free http: //nmr. cit. nih. gov/xplor-nih/ • 分子绘图 – – Py. Mol Free http: //pymol. sourceforge. net/ Mol. Script Free http: //www. avatar. se/molscript/ Ras. Mol Free http: //www. openrasmol. org/ VMD Free http: //www. ks. uiuc. edu/Research/vmd/ 68