1 Computational aspects of structure determination by NMR

[Faculty of Science 

Chemistry] 


Chemistry] 

Outline 

Computational aspects of 

structure determination by NMR 

• Introduction 

• Structural data from NMR 

• NOE analysis 

• Aspects of structure calculations by NMR 

• Structure analysis and validation 

• NMR & biomolecular complexes 

Structural Biology - NMR 

Alexandre Bonvin 

Utrecht University 

a.m.j.j.bonvin@uu.nl 

AB 

AB 

The ABC of NMR structure 

determination 


Chemistry] 

NMR structure determination steps 


Chemistry] 

• NMR experiment 

• Resonance assignment 

• Structural restraints 

• distances 

• NOE assignment 

• torsion angles, orientation restraints, … 

• Structure calculations 

• Structure validation 

AB 

AB


Chemistry] 


Chemistry] 

Outline 

NMR experimental observables providing 

structural information 







• Backbone conformation from secondary chemical 

shifts (Chemical Shift Index- CSI) 

• Distance restraints from NOEs 

• Backbone and side chain dihedral angle 

restraints from scalar couplings 

• Orientation restraints from residual dipolar 

couplings 

AB 

AB 


Chemistry] 


Chemistry] 

Secondary chemical shifts 

Secondary chemical shifts 

• Chemical shifts deviations from random coil values contain 

information on secondary structure 

• Chemical shift index (CSI) based on H α 

, C α 

, C β 

and C’ 

secondary chemical shift (Wishart et al. J Biomol NMR 4, 171, 1994) 

H α 

C α 

C β 

C’ 

AB 

AB


Chemistry] 


Chemistry] 

Chemical shifts analysis with TALOS 

Chemical shifts analysis with TALOS 

• Torsion Angle Likelihood Obtained from Shift and sequence 

similarity (Cornilescu et al. J. Biomol. NMR 13, 289, 1999) 

• Analysis of secondary chemical shift patterns in tripeptides by 

comparison with a chemical shift database with known 3D 

structures (Xray, resolution < 2.2 Å, ~3000 triplets) 

AB 

AB 


Chemistry] 


Chemistry] 

Scalar (J) couplings 

Distance information from NOEs 

• NOEs are the result of through space dipolar interactions, 

~ 1/r 6 --> max ~ 5Å 

• Derived from 

• 1H-1H (homonuclear) spectra 

2D 

3D 

1 

H 1 

H 

1 

H 1 

H 1 

H 

• 15 N- or 13 C-dispersed (heteronuclear) spectra 

3D 

1 H 

1 

H 

1 H 

1 

H 

• Can be used directly or indirectly as derived dihedral 

angle restraints using the Karplus relationship 

4D 

15 

N 

1 H 

1 

H 

13 

C 

1 

H 

1 

H 

1 

H 

1 

H 

• Problem of conformational averaging! 

15 

N 

13 

C 

13 

C 

13 

C 

15 

N 

15 

N 

AB 

AB

13C 


Chemistry] 


Chemistry] 

Orientational restraints from dipolar (D) 

couplings 

RDC restraints 

Reports angle of internuclear 

vector relative to 

magnetic field H o 

F2 

F1 

15 

N 

• Must accommodate multiple solutions→ multiple orientations 

F3 

1 

H 

15 

N 

Ho 

1 

H 

1 

H 

1 

H 

1 H 

• The RDCs are defined by their 

orientation with respect to the 

alignment tensor 

• Energy term in the structure 

calculation E RDC 

= Σ k RDC 

(D exp 

-D calc 

) 2 

AB 

AB 


Chemistry] 


Chemistry] 

Outline 

NOE assignment 







Resonance assignment 

NOE peak list 

Chemical shift table 

Assignment of NOE peaks 

AB 

AB


Chemistry] 


Chemistry] 

Structural restraints from NOEs 

• Selection of peaks 

• Assignment to proton 

pair 

• Calibration to 

distance 

From NOEs to distances 

NOE intensity A ij 

given by: 

with 

⎡⎡ 

ρ 1 

σ 12 

... σ 

⎤⎤ 

⎢⎢ 

1N 

⎥⎥ 

σ 

R = 

⎢⎢ 21 

ρ 2 

... σ 2N ⎥⎥ 

⎢⎢ ... ... ... € ... ⎥⎥ 

⎢⎢ 

⎥⎥ 

⎣⎣ ⎢⎢ σ N 1 

σ N 2 

... ρ N ⎦⎦ ⎥⎥ 

A ij 

= [ exp( −τ m 

R )] ij 

and 

σ ij ≈ 1 

Series expansion: 

€ 

A = exp(−τ m 

R ) = 1 − τ m 

R + τ 2 

m 

2 R 2 − ... 

r 6 f (motion) 

AB 

AB 

€ 


Chemistry] 


Chemistry] 

Two-spin approximation 

(ISPA isolated spin-pair approximation) 

• From the series expansion and assuming: 

• no internal dynamics 

• no spin diffusion 

• short mixing times 

• Get calibration factor C cal from 

• reference distances 

• averages over all distances 

⎛⎛ ⎞⎞ 

1 

d ij ≈ c 

⎜⎜ ⎟⎟ 

cal ⎜⎜ 

⎝⎝ A 

⎟⎟ 

ij ⎠⎠ 

⎛⎛ ⎞⎞ 

A 

d ij ≈ d 

⎜⎜ ref ⎟⎟ 

ref ⎜⎜ 

⎝⎝ A 

⎟⎟ 

ij ⎠⎠ 

• Problems: approximate, introduces systematic errors 

1 

6 

1 

6 

Spin diffusion 

• Spin diffusion is major source 

of error in NOE derived 

distances (in particular for long 

mixing times and large molecules) 

• Indirect paths (---) are more 

efficient than direct path 

(1/r 6 ), --> underestimation of 

distance --> wide error 

bounds necessary 

AB 

AB


Chemistry] 


Chemistry] 

Standard treatment of errors: 

upper and lower bounds 

• Loose upper and lower bounds are typically defined to 

account for errors such as peak integration, spin 

diffusion, internal dynamics, e.g. 

• distance ± 10,20% 

• Strong-medium-weak classification: 

Strong 1.8-2.8 Å 

Medium 1.8-3.5 Å 

Weak 1.8-4.5 Å 

(Very weak 1.8-5.5 Å) 

Distance restraints 

• Soft-square potential (Nilges) used to avoid large 

forces 

Force becomes constant 

>2Å violation 

AB 

AB 


Chemistry] 


Chemistry] 

Consequence of bounds 

• Bounds have to be large 

enough for cumulative error 

• Precise value not (too) 

important: even loose bounds 

restrict conformational space 

• May affect 

• precision of structure 

• validation 

Outline 







AB 

AB


Chemistry] 


Chemistry] 

Structure calculations 

• 3D structure has to satisfy: 

• experimental restraints 

• chemical knowledge 

• --> find the minimum of a target 

function that combines empirical 

force field with experimental 

restraints 

Outline 





• Empirical force field 



AB 

AB 


Chemistry] 


Chemistry] 

Empirical force fields 

Bond stretching 

l 

• Rather simple description of the forces in the system 

• Energetic penalties associated with deviation from 

“reference” or “equilibrium” values 

• V potential = V bonds 

+ V angles 

+ V torsion 

+ V non-bonded 

• Various forms possible, e.g.: 

• Morse potential 

V(l) = D c 

{1 − e [− a (l − l 0 )] } 2 

 

 

Allows dissociation 

Computationally more expensive 

V(l) 

• Harmonic potential 

V(l) = k 2 (l − l 0) 2 l 0 

l 

+ V exp 

Van der Waals electrostatic 

 

Most commonly used 

AB 

AB


Chemistry] 


Chemistry] 

Angle bending 

ϑ 

Torsional terms 

ω 

• Usually harmonic potential as for the bond stretching 

term 

V(θ) = k 2 (θ − θ 0) 2 

V(ϑ) 

• Describe rotation around bonds 

• The torsion angle ω around the B-C bond 

is defined as the angle 

between the ABC and 

BCD planes 

• V torsion should allow 

for multiple minima 

(rotameric states) 

ϑ 

AB 

AB 


Chemistry] 


Chemistry] 

Torsional terms 

ω 

Improper torsions and out-of plane bending 

motions 

• Usually expressed as a cosine series expansion: 

[ ] 

N 

V 

• V(ω) = n 

where V n is the “barrier height” 

2 1 + cos(nω − γ ) 

∑ 

n= 0 

O-CH 2 -CH 2 -O 

• Defined to maintain planarity of aromatic rings or 

chirality of atoms, e.g.: 

• Torsion C α -N-C-C β to maintain 

• tetrahedral conformation of C α 

35° for L-amino acids 

C ε1 

-35° for D-amino acids 

H δ1 C δ1 

• Torsion C δ1 -C γ -C ε1 -H δ1 to keep 

• aromatic hydrogen H δ1 in the plane 

C γ 

• of the ring 

C β 

• Usually implemented 

C α 

as harmonic potentials 

N 

C 

Tyr 

Single term: all minima equal 

Two terms: minima no longer equal 

AB 

AB


Chemistry] 


Chemistry] 

Electrostatic interactions 

• Atoms carry small partial charges 

• Electrostatic interactions 

calculated as the sum of interactions 

between pairs of point 

charges using Coulomb’s law 

• Slow decay as function of distance 

between atoms (~ 1/r) 

• Long-range contributions 

V elec 

= 

N 

N 

∑ ∑ 

i= 1 j = 1 

q i 

q j 

4πε 0 

r ij 

q: partial charges 

ε: dielectric constant 

Van der Waals interactions 

• Attractive long-range forces 

• Repulsive short-range forces 

Repulsion 

between nuclei 

Attraction between 

induced dipoles from 

fluctuations in electron 

clouds (London forces) 

• Often expressed using the 

Lennard-Jones 12-6 function 

V L−J 

⎡⎡ 

⎢⎢ ⎛⎛ 

σ 

⎞⎞ 

= 4ε ⎢⎢ ⎜⎜ ⎟⎟ 

⎢⎢ 

⎜⎜ 

⎝⎝ r 

⎟⎟ 

⎣⎣ 

⎠⎠ 

12 

σ: collision diameter 

ε: well depth 

− 

σ 6⎤⎤ 

⎛⎛ ⎞⎞ ⎥⎥ 

⎜⎜ ⎟⎟ 

⎜⎜ 

⎝⎝ r 

⎟⎟ 

⎥⎥ 

⎠⎠ ⎥⎥ 

⎦⎦ 

AB 

AB 


Chemistry] 


Chemistry] 

Force field: chemical information 

• topology: 

• atom names 

• atom types 

• atom masses 

• connectivity 

• parameters: 

• energy constants 

• ideal values 

€ 

Derivatives of the energy function 

• Many molecular modelling techniques based on force fields 

require the derivative of the energy (i.e. the force) to 

be calculated with respect to the coordinates. 

• The derivative can be calculated using the chain rule: 

∂V(θ) 

∂x i 

• The force on atom i due 

to V(θ) is given by: 

= ∂V(θ) 

∂θ 

∂θ 

∂r ij 

∂r ij 

∂x i 

F i 

(θ ) = − ∂V(θ) 

∂x i 

AB 

AB


Chemistry] 


Chemistry] 

Outline 





• Empirical force field 

• Structure calculation methods 



NMR structure calculation methods 

• Energy minimization ("build-up method", DIANA) 

• Metric matrix distance geometry (DISGEO, DG2) 

• Molecular dynamics methods: 

• Simulated annealing in Cartesian space from random 

structures (X-PLOR, CNS) 

• Simulated annealing in torsion angle space from 

random structures (X-PLOR, CNS, DYANA) 

AB 

AB 


Chemistry] 


Chemistry] 

Energy minimization (EM) 

Distance Geometry 

• At the minimum of the function f(x) the following is true: 

∂f 

∂x i 

= 0; ∂ 2 f 

∂x i 

2 > 0 AB 

• EM will only locate the 

nearest minimum 

• Can not cross energy 

barriers 

• Avoids "folding problem": 

• direct conversion from distances to (approximate) 

coordinates 

AB


Chemistry] 


Chemistry] 

Sir Isaac Newton 

(1642-1727) 

Classical mechanics 

• Newton’s laws of motion: 

1. A body moves in a straight line unless a 

force acts on it 

2. Force equal mass times acceleration 

3. To every action there is an equal reaction 

Classical mechanics 

• Molecular dynamics: generates successive configurations 

of the system by integrating Newton’s second law 

d 2 

dt 2 

ri = 

 

F i 

m i 

with 

t 1 

t 2 

t 3 

€ 

 

F i 

= − ∂V 

∂ r i 

€ 

 

r (t 1 

) 

€ 

 

r (t 2 

) 

 

F (t 1 

) 

 

v (t 1 

) 

 

v (t 2 

) 

AB 

AB 

€ 

€ 


Chemistry] 


Chemistry] 

Molecular dynamics 

Simulated annealing 

• Direction of motion 

depends on 

• forces (derived from force 

field and experimental 

restraints) 

• momentum 

• Temperature control and variation 

• Molecular dynamics can 

overcome local energy 

barriers 

AB 

AB


Chemistry] 


Chemistry] 

Simulated annealing with energy scaling 

Example of a NMR simulated annealing 

scheme 

• More flexible annealing schemes 

• Different variation of 

different energy terms 

• E.g.: 

• E chem / E exp 

• E covalent / E exp / E nonbond 

AB 

AB 


Chemistry] 


Chemistry] 

SA example 

SA example: IL8 dimer 

AB 

AB


Chemistry] 


Chemistry] 

SA example: BPTI 

Torsion angle dynamics 

• dynamics time step dictated 

by bond stretching: waste of 

CPU time 

• important motions are around 

torsions 

• ~ 3 degrees of freedom per 

AA (vs 3N atom 

for Cartesian 

dynamics) 

• Available in DYANA, X-PLOR, 

CNS, X-PLOR-NIH 

AB 

AB 


Chemistry] 


Chemistry] 

Calculation of structure ensembles 

Outline 

• Repeat calculation (20-200-xxx 

times) 

• Random variation of initial 

conditions (starting structure/ 

velocities) 

• Obtain information on 

• uniqueness / different folds 

• "dynamics” 







• Structure selection problem! 

AB 

AB


Chemistry] 


Chemistry] 

Validation of structures: Why? 

• Structures should be reliable: 

• Satisfy experimental data 

• Good local and overall quality 

• Protein structures are a valuable source for 

understanding biology 

• Structure based drug design 

• Homology modeling 

• --> Only “good” structures are typically used 

Structure analysis and validation 

• Geometry (rmsd from idealized bonds, angles…) 

• Energetics (non-bonded, restraint energies…) 

• Violations analysis 

• Rmsd: pairwise (useful e.g. for clustering), 

from average, per residue rmsds 

• Stereochemical quality 

AB 

AB 


Chemistry] 


Chemistry] 

Validation of structures 


Bonded geometry 

Rotamers 

Electrostatics and hydrogen bonding 

AB 

Inter-atomic bumps 

AB


Chemistry] 


Chemistry] 


Improving protein NMR structures 

• Refinements in explicit or implicit water for final 

optimization 

• Better packing (van der Waals, electrostatic) 

• Better “outside” of proteins 

Backbone conformation 

• Refinement in explicit water: 

• Solvate the protein in water 

• Run restrained Molecular Dynamics simulation, including full 

electrostatics and van der Waals 

• Minimize the structures 

Ramachandran plot 

AB 

AB 


Chemistry] 


Chemistry] 

Outline 

Protein-protein complexes 







AB 

AB 

Understanding protein function 

requires to take the step from 

structure to interactions, the latter 

being much more numerous 

PNAS 100, 12123 (2003) 

Science 302, 1727 (2003)


Chemistry] 


Chemistry] 

NMR-based protein complexes 

Application example: lactose repressor 

• Typically based on intermolecular NOEs and residual 

dipolar couplings 

• Collection of restraints is a difficult and rather lengthy 

process 

• Requires rather complete assignments (side-chains) at the 

interface 

Headpiece 

Core 

domain 

Folding of a 

fourth helix 

upon binding 

To DNA 

• For efficient structure determination and large complexes, 

isotope labeling is a requisite 

Lewis et al. (1996). Science 271,1247. 

AB 

AB 

Solution structures of the 

free and (SymL)DNA-bound lac 

headpiece solved by NMR 

Spronk et al. (1999) Structure 7, 1483 


Chemistry] 


Chemistry] 

Isotope labeling helps a lot! 

Filter out all but protein-DNA NOEs 

13 

C, 15 N 13 

C, 15 N 

12 

C, 14 N 

12 

C, 14 N 

protein 

1 H 

12 

C, 14 N 12 

C, 14 N 

13 

C, 15 N 

13 

C, 15 N 

AB 

AB 

1 H 

DNA


Chemistry] 


Chemistry] 

Lac hp62VC-DNA(O1) restraints statistics 

Lac hp62VC-DNA(O1) docking 

protocol 

Protein (dimer) 

Intraresidue NOEs 514 

Sequential NOEs(|i-j| = 1) 419 

Medium range NOEs(1


Chemistry] 


Chemistry] 

Experimental sources: mutagenesis 

Experimental sources: H/D exchange 

Advantages/disadvantages 

Detection 


Detection 

+ Residue level information 

- Loss of native structure 

should be checked 

- Binding assays 

- Surface plasmon resonance 

- Mass spectrometry 

- Yeast two hybrid 

- Phage display libraries, … 

+ Residue information 

- Direct vs indirect effects 

- Labeling needed for NMR 

- Mass spectrometry 

- NMR 15 N HSQC 

AB 

AB 


Chemistry] 


Chemistry] 

Experimental sources: 

NMR chemical shift perturbations 


NMR orientational data (RDCs, relaxation) 


+ Residue/atomic level 

+ No need for assignment if 

combined with a.a. selective labeling 

- Direct vs indirect effects 

- Labeling needed 

Detection 

- NMR 15 N or 13 C HSQC 


+ Atomic level 

- Labeling needed 

Detection 

- NMR 

AB 

AB


NMR saturation transfer 


Chemistry] 

HADDOCK: High Ambiguity Driven DOCKing 

NMR titrations 

NMR crosssaturation 

mutagenesis 

Amide protons at interface 

are saturated 

==> intensity decrease 

Cross-linking 

HADDOCK 

High Ambiguity Driven DOCKing 

H/D exchange 

A 

j 

i 

eff 

k d iAB 

x y 

z 

B 


+ Residue/atomic level 

+ No need for assignment if 

combined with a.a. selective labeling 

- Labeling (including deuteration) needed 

Bioinformatic predictions 

EFRGSFSHL 

EFKGAFQHV 

EFKVSWNHM 

LFRLTWHHV 

IYANKWAHV 

EFEPSYPHI 

NMR anisotropy data 

RDCs, para-restraints, diffusion anisotropy 

Other sources 

e.g. SAXS, cryoEM 

AB 

Dominguez, Boelens & Bonvin (2003). JACS 125, 1731 http://www.nmr.chem.uu.nl/haddock 


Chemistry] 

HADDOCK docking protocol 

AB

Protein biosynthesis and export 

Signal sequences control the entry of proteins to export pathways 

SecA - signal sequence recognition 

The 204-kDa SecA is the central player of the secretion machinery 

Crystal structure known, but no structural information 

for the the complex 

MMITLRKRRKLPLAVAVAAGVMSAQAMA 

Use the power of NMR to study this very large complex 

⎡⎡ 

K 

r 

= 

⎢⎢ 

⎢⎢⎣⎣ 

R 

c 

2 , 

para 

1 

1 1 

6 6 

⎛⎛ 

3 

τ 

⎞⎞⎤⎤ 

c 

⎞⎞⎤⎤ 

c 

⎜⎜ 

⎜⎜ 

2 2 ⎟⎟ 

⎟⎟ 

4τ 

+ 

2 2 ⎥⎥⎥⎥ 

hτ 

⎟⎟ 

⎟⎟ 

⎝⎝ + ωhτ 

c c⎠⎠⎥⎥⎦⎦ 

⎠⎠⎥⎥⎦⎦ 



Use relaxation paramagnetic enhancement (RPE) 

to obtain inter-molecular distances 

Use relaxation paramagnetic enhancement (RPE) 

to obtain inter-molecular distances 

MMITLRKRRKLPLAVAVAAGVMSAQAMA 

C 

C 

Measure distances between ~ 10-28 Å 

Battiste & Wagner, Biochemistry 2000, 39, 5355. 

SecA perdeutarated, only methyl groups of Val, Ile and Leu protonated



We obtained 160 SecA-signal peptide distance restraints! 

Structure of the complex calculated with HADDOCK 

based on 160 SecA-signal peptide distance restraints! 



Chemistry] 

The End. 

hydrophobic 

acidic 

Arg8 

Arg6 

Lys10 

Lys7 

Ala19 

Val15 

Ala16 

Ala14 Val17 

Leu13 

Leu11 

Met22 

Structural basis for the promiscuous 

recognition 

… dual binding mode! 

Thank you for your attention! 

Gelis et al., Cell 2007 

AB

Rigid body energy minimization 


Chemistry] 

Semi-flexible SA refinement in 

torsion angle space 


Chemistry] 

AB 

AB 


Chemistry] 

Refinement in explicit water 

AB

1 Computational aspects of structure determination by NMR

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?