Computer Simulation of Biomolecules and the Interpretation of NMR Measurements

generates ensemble of molecular configurations all atomic quantities

Problems1. ensemble incomplete

- time scale too short- sampling limited

2. quality of model or force field

correct prediction?

yields average observable (not all) quantities over ensemble

1. ensemble not known only average over time/space

2. insufficient data or observables to determine an atomic model

correct interpretation?

Relation Simulation versus Experiment

Computer Simulation of Biomolecules and the Interpretation of NMR Measurements

Simulation

structure, dynamics, energeticscan be analyzed in detail

ensemble of conformations

Experiment

structure and dynamics areconvoluted

average over an ensemble ofconformations

Computer Simulation of Biomolecules and the Interpretation of NMR Measurements

Five Questions

1. Is the ensemble generated by MD simulation realistic?2. Are the approximations used to derive structure and dynamics from

experiment adequate?NMR: - flexible model

- rigid model- naïve model- spin diffusion

CD: - negative cotton effect helix

3. Can the composition of the ensemble be derived from ensemble averages?

4. How sensitive is the ensemble average to the composition of the ensemble?

5. Can (unrestrained) MD simulation help to interpret NMR- or CD-spectra?

If

1. and exact problem solved

2. infinite sampling

The Molecular Modelling Approach

Choose:

1. (essential) degrees of freedom for electronic

atomicsolvent

2. interaction function between degrees of freedom (force field, e.g. GROMOS)

3. equations of motion or sampling methodto generate a Boltzmann-weighted ensemble of conformers:probability ~

4. function

r

( )q r

How to Calculate a Quantity ?

to be compared to

( )q r

( )physV r

exp( ( ) / )physBV r k T

( )q r

r

q r

EXPq

( )physV r ( )q r

Otherwise

make other choices and

repeat

Effects of Motional (Ensemble) Averaging

( )r

r rq q

r

q r

averaged q single structure q

mean structure q

CD- if a structure reproduces parameters is this structure “the NMR solution structure?

or CD

- what is the sensitivity of parameters to the composition of NMR

the ensemble?or

CD- can the composition of the ensemble be derived from NMR

parameters?

Test of Force Field and NMR Data for Hen Egg White Lysozyme

3.5 ns SimulationsSet-Up (NPT ensemble)

Parameter set43A1 (1996) 45A3 (2001)

Solute atoms 1321 1321

Water molecules 8357 8357

Counter ions (Cl-) 8 8

Total atoms 26392 26392

Box length (nm)(truncated octahedron)

8.18 8.18

Pair-list cut-off radius (nm) 0.8

NB interaction cut-off (nm) 1.4

PB Reaction field cut-off (nm) 1.4

Dielectric permittivity 66

Test of Force Field and NMR Data for Hen Egg White Lysozyme

Experimental Data(Smith et. al., 1991, 1993; Buck et. al., 1995; Schwalbe et. al., 2001)

1158 NOE derived inter-proton distances (set1 1993)

1525 NOE derived inter-proton distances (set2 2001)

95 3JHN-coupling constants

100 3J-coupling constants

124 backbone and 28 side-chain order parameters

X-ray coordinates (PDB 1aki, 1.5 A )

NMR coordinates (PDB 1e8l, ensemble of 50 structures)

NOE bound violations in HEW

out of 1158 NOE’s

out of 1525 NOE’s (30% more)

NOE bound violations computed from MD trajectories (43A1(1996)/45A3(2001)) against two sets of experimental NOE distance bounds from

Smith et. al. (set1, 1993) and from Schwalbe et. al. (set2, 2001)

Over time (1993 2001) the experimental data converged towards simulated ones

3J-values: differences between MD or NMR structures and experiment

Number of differences between experimental 3J-coupling constants and simulated 3J-coupling constants averaged (time window of 0.0–3.5 ns) over the MD trajectories generated using the force field parameter sets 43A1 (1996) and 45A3 (2001) and over the set of 50 NMR model structures (PDB code: 1E8L).

R-Value 19% 18% 24% 23%rmsd (Hz) 1.6 1.6 2.0 2.0

R-Value 15% 22%

rmsd (Hz) 1.4 1.8

exp. J-values not used

exp. J-valuesare used

structures structures

3J-values: differences between MD or NMR structures and experiment

Number of 3J-values that differ from the experimental values iscomparable for- MD ensembles- set of NMR model structures

Remarkable, since the experimental J-values were not used to generate MD ensembles were used to generate set of 50 NMR model structures (2001)

NOE bound violations in HEW Lysozyme

parameter set 43A1 (1996)experimental NOE set01 (1993)

parameter set 45A3 (2001)experimental NOE set01 (1993)

parameter set 43A1 (1996)experimental NOE set02 (2001)

parameter set 45A3 (2001)experimental NOE set02 (2001)

violations