1. Computer Simulation of Biomolecules and the Interpretation of NMR Measurements generates ensemble of molecular configurations all atomic quantities Problems 1.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

2. Computer Simulation of Biomolecules and the Interpretation of NMR Measurements Simulation structure, dynamics, energetics can be analyzed in detail ensemble of conformations Experiment structure and dynamics are convoluted average over an ensemble of conformations

3. 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?

4. If 1. and exact problem solved 2. infinite sampling The Molecular Modelling Approach Choose: 1.(essential) degrees of freedom for electronic atomic solvent 2.interaction function between degrees of freedom (force field, e.g. GROMOS) 3.equations of motion or sampling method to generate a Boltzmann-weighted ensemble of conformers: probability ~ 4.function How to Calculate a Quantity ? to be compared to Otherwise make other choices and repeat

5. Effects of Motional (Ensemble) Averaging 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?

6. Test of Force Field and NMR Data for Hen Egg White Lysozyme 3.5 ns Simulations Set-Up (NPT ensemble) Parameter set 43A1 (1996)45A3 (2001) Solute atoms1321 Water molecules8357 Counter ions (Cl - )88 Total atoms26392 Box length (nm) (truncated octahedron) ; 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 permittivity66

7. 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 3 J HN -coupling constants 100 3 J  -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)

8. 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

9. 3 J-values: differences between MD or NMR structures and experiment Number of differences between experimental 3 J-coupling constants and simulated 3 J-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) 1.61.6 2.0 2.0 R-Value 15% 22% rmsd (Hz) 1.4 1.8 exp. J-values not used exp. J-values are used structures

10. 3 J-values: differences between MD or NMR structures and experiment Number of 3 J-values that differ from the experimental values is comparable 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)

11. 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