NMR structure calculation

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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

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Solving structures by NMR

Sample Preparation•Cloning, expression, purification •Isotope labelling [15N], [13C/15N],[ 2H/13C/15N]

Resonance Assignments

• Backbone

• Side chains

Secondary Structure

Chemical shift

Structural restraints

•NOE, H-bonds

•J-couplings

•Residual dipolar couplings, T1/T2

•Chemical shifts

Structure Calculation•Distance geometry•Restrained molecular dynamics•Simulated annealing

Ensemble of 3D structures

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Overview

• Structure representation

• Types of NMR data conversion into restraints

• Structure calculation methods

• Structure validation

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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，

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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

20种常见的氨基酸残基

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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）

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Structure calculation

Conformation

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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 ）

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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

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

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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

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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）

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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)

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Approaches to identifying NOEs

• 15N- or 13C-dispersed 1H-1H NOESY

3D 1H

13C

1H1H

15N

1H

1H

15N

1H

13C

1H

13C

1H

13C

1H

15N

1H

15N

4D

1H 1H2D

1H 1H 1H3D

• 1H-1H NOESY

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Special NOESY experiments

• Filtered, edited NOE: based on selection of NOEs from two molecules with unique labeling patterns.

1H 1H

13CUnlabeled

peptide

Labeledprotein

Only NOEs at the interface

Only NOEs from bound state

H

H

HH

kon

koff

• 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

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1H-1H distances from NOEs

A B C D Z• • • • Intra-residue

Sequential

Medium-range(helices)

Long-range(tertiary structure)

Challenge is to assign all peaks in NOESY spectra

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

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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-rij1)2 if rij<rij

l

KNOE(rij-riju)2 if rij>rij

u

0 if rijl<rij < rij

u VNOE =

where rijl and rij

u 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 V19

NOE pseudo-energy potential

rijl rij

u

0

VNOE

Potential rises steeply with degree of violation

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Number of NOEs are more important than accuracy of individual NOEs

Structure calculation of protein G (56 aa) with increasing numbers of NOES

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Restraints and uncertainty

Large # of restraints = low values of RMSD

Large # of restraints for key hydrophobic side chains

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.

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AB

C

9.52 ppm

4.34 ppm

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 neverclose to B, then the restraint must be A to C.

Example of resolving an ambiguityduring structure calculation

9-11 Å

3-4 Årange of inter-atomic distances observed in trial ensemble

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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

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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 roundsi.e. discarding NOEs that are inconsistent with emerging structure

• Combine with fully automated assignment procedures to arrive at fully automated structure calculation

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Iterative structure calculation with assignment of ambiguous

restraints

source: http://www.pasteur.fr/recherche/unites/Binfs/aria/

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!

start with some set of unambiguous NOEs and calculate an ensemble

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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.

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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

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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

C=O H-N

NMR data 3: J couplings

0

2

4

6

8

10

-180 -120 -60 0 60 120 180

3J H

NH

H (

Hz)

3J=6.4cos 2-1.4cos+1.9

N Ca

H

H

N

HN

H

= -60º

3J(HN,H)

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• • • •6 Hz

Dihedral angles from scalar couplings

Must accommodate multiple solutions multiple J valuesBut database shows few occupy higher energy conformations

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

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Requires medium to partially align molecules Must accommodate multiple solutions multiple orientations

1H

15N

1H

15N

Ho

F1

F2F3

1H13C

1H

1H

Reports angle of inter-nuclear vector relative to magnetic field Ho

Orientational constraints from residual dipolar couplings (RDC)

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DAB(,) = DaAB{ (3cos2-1) + R(sin2cos2)3/2}

Alignment tensor and RDC: DAB

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15N-1H dipolar couplings

A5% (w/v) DTDPC:DHPC (3:1)

neutral

positive

(a) + 3% CTAB

0 20 40 60 80 100

residue37

Structure refinement

with NOEs

7.3 ± 3.1Å

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NOEs & RDC (A) + (B)

4.5 ± 2.1Å 3.4 ± 1.5Å

NOEs & RDC (A)

Methods for structure calculation

• distance geometry (DG)

• restrained molecular dynamics (rMD)

• simulated annealing (SA)

• hybrid methods

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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.

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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

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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 )

KNOE(rij-rij1)2 if rij<rij

l

KNOE(rij-riju)2 if rij>rij

u

0 if rijl<rij < rij

u VNOE =

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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 restraints 43

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

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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

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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)

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

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NMR ensemble

The fact that NMR structures are reported as ensembles gives them a “fuzzy” appearance which is both informative and sometimes annoying

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• 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

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)

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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.

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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

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 rMD calculation52

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 5-58) if residues 1-4 are completely disordered.

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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.

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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

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Structural Statistics Tables

list of restraints, # and type

precision of structure (RMSD)

agreement of ensemble structures with restraints

(RMS)

calculated energies

sometimes also see listings of Ramachandran statistics, deviations from ideal covalent geometry, etc.

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Structure validationXPLOR/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 geometrydihedral anglesnon-bonded interactionmain chain H-bondsstereochemistrychiralitydisulphide bonds 57

结构评价

• 能量• 二级结构• 拉氏图

– 尽可能少的氨基酸残基处于不允许区

• RMSD （均方根偏差）– 表明结构的收敛程度

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Example of Procheck results

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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

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Grx-C1的结构计算

• CYANA ：结构初步优化– 力场相对简单– 运行速度快– 无需初始结构– 结构相对较为粗略

• Amber ：结构精修– 具有更精细的力场参数，使用溶剂化模型（或显式加溶剂）

从而获得更加合理的局部构象– 需要整体折叠正确的初始结构– 运算量大，速度慢

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Grx-C1的结构计算

• CANDID/CYANA 得到初始结构（全自动）– 2 CPU, ~8 小时

• SANE-CYANA 循环，进行初步优化（半自动）– 手工分析违约和未指认的 NOE

– 每个循环 2CPU ～ 1 小时– ～ 20-40 个循环

• SANE-AMBER 循环，进行结构精修（半自动）– 每个循环 20 CPU ～ 15 小时– ～ 10~30 个循环

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结构计算结果• PDB 1Z7P(ensemble), 1Z7R(mean) http://www.rcsb.org/pdb

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结构计算结果

• 约束统计– NOE ： 4845– 二面角： 160– 氢键： 47– 手性： 287

• 违约状况– 距离 无 >0.2Å – 二面角 无

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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/procheck_nmr.html

• MOLMOL 结构分析与绘图http://hugin.ethz.ch/wuthrich/software/molmol/

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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– PyMol Free http://pymol.sourceforge.net/– MolScript Free http://www.avatar.se/molscript/– RasMol Free http://www.openrasmol.org/– VMD Free http://www.ks.uiuc.edu/Research/vmd/

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