NMR structure calculation

1. NMR structure calculation

2. NMR结构解析流程 生物信息学和生物化学分析 样品制备（蛋白质表达纯化，标记） 核磁共振数据收集 化学位移指认 NOE指认 结构计算 核磁共振初步鉴定 二级结构分析

3. Solving structures by NMR • Structural restraints • NOE, H-bonds • J-couplings • Residual dipolar couplings, T1/T2 • Chemical shifts • Sample Preparation • Cloning, expression, purification • Isotope labelling • [15N], [13C/15N],[ 2H/13C/15N] • Resonance Assignments • Backbone • Side chains • Structure Calculation • Distance geometry • Restrained molecular dynamics • Simulated annealing Secondary Structure Chemical shift Ensemble of 3D structures

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

5. 蛋白质结构层次 • 氨基酸通过肽键形成的生物高分子 • 一级结构、二级结构、三级结构、四级结构 • 肽键具有双键性质而不能任意旋转 • 主链可旋转的二面角，

6. 20种常见的氨基酸残基 通常NMR中一个自旋系统是指一个氨基酸残基上的所有原子

7. NMR解析蛋白质溶液结构 • 测定原子（氢原子）之间的距离信息和其他约束信息，得到空间结构模型 • 化学结构（氨基酸序列，即一级结构）已知，测定空间结构（三级结构，四级结构）

8. Structure calculation Conformation

9. 结构计算 • 基本方法 • 由实验得到各种构象约束信息：距离，二面角 • 约束信息是不完备的 • 约束信息是不精确的 • 计算满足这些约束条件的构象 • 距离几何（Distance Geometry） • 约束条件下的分子动力学模拟（Restrained Molecular Dynamics Simulation） • 模拟退火（Simulated Annealing）

10. 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

11. 由化学位移得到二级结构的信息 • 二级结构 • CSI：化学位移与无规卷曲的多肽化学位移之差 • TALOS：基于数据库比对预测二面角 • 可用于结构计算和分析

12. 约束信息 • 距离约束 • 1H-1H NOE • 氢键 • 二面角约束 • 主链 • 侧链 • 肽键：反式－顺式 • 其他 • 手性 L-氨基酸

13. 约束生成 • NOE • 指认 • Unique：只有一种可能 • Ambiguous：有多种可能 • 转化为距离 • 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）

14. NMR data 1: NOE • For 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)

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

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

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

18. 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

19. 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-rij1)2 if rij<rijl where rijlandrijuare 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

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

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

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

23. 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 toresolve 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.

24. Example of resolving an ambiguityduring structure calculation A 9-11 Å 9.52 ppm B 4.34 ppm range of inter-atomic distances observed in trial ensemble 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.

25. 自动化结构计算 • NOE自动指认 • CANDID/CYANA • 只需提供指认的化学位移列表和NOE谱峰列表 • 自动进行NOE指认 • 自动通过7个结构计算循环（100个结构取二十个），逐步优化指认结果 • 自动计算结果正确性依赖于原子化学位移指认的比例和正确性 （至少>90%） • SANE • 依赖初始结构的自动NOE指认

26. Practical improvements instructure 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

27. 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/

28. 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.

29. NMR data 2: H-bonds • Usually 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

30. C=O H-N Backbone Hydrogen Bonds • 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) • When H-bonding atoms are known  can impose a series of distance/angle constraints to enforce standard H-bond geometries

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

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

33. 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

34. F3 F2 F1 Orientational constraints from residual dipolar couplings (RDC) Ho 1H 1H Reports angle of inter-nuclear vector relative to magnetic field Ho 13C 15N 1H 1H 15N 1H • Requires medium to partially align molecules • Must accommodate multiple solutions multiple orientations

36. Alignment tensor and RDC: DAB DAB(q,f) = DaAB{ (3cos2q-1) + R(sin2qcos2f)3/2}

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

38. Structure refinement with NOEs NOEs & RDC (A) NOEs & RDC (A) + (B) 7.3 ± 3.1Å 4.5 ± 2.1Å 3.4 ± 1.5Å

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

40. 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.

41. 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

42. KNOE(rij-riju)2 if rij>riju 0 if rijl<rij <riju VNOE = KNOE(rij-rij1)2 if rij<rijl 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 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)

43. Restrained molecular dynamics • Molecular dynamics involves computing the potential energy Vwith 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 restraints

44. SA-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 function

45. 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

46. 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 • Some programs try to do both at once • Need a reasonable starting structure • NMR data is not perfect: noise, incomplete data  multiple solutions (conformational ensemble)

47. 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

48. 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 • More dynamics at loops/surface • Constraints in all directions in the interior

49. 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)

50. 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.