1. Biomolecular Modelling: Goals, Problems, Perspectives 1. Goal simulate/predict processes such as 1.polypeptide foldingthermodynamic 2.biomolecular associationequilibria governed 3.partitioning between solventsby weak (nonbonded) 4.membrane/micelle formationforces common characteristics: -degrees of freedom: atomic (solute + solvent)hamiltonian or -equations of motion:classical dynamicsforce field -governing theory:statistical mechanicsentropy

2. Processes: Thermodynamic Equilibria Folding Micelle Formation Complexation Partitioning folded/nativedenaturedmicellemixture boundunbound in membrane in waterin mixtures

3. Definition of a model for molecular simulation MOLECULAR MODEL Degrees of freedom: atoms are the elementary particles Forces or interactions between atoms Boundary conditions Methods to generate configurations of atoms: Newton system temperature pressure Every molecule consists of atoms that are very strongly bound to each other Force Field = physico-chemical knowledge

4. Biomolecular Modelling: Goals, Problems, Perspectives Four Problems 1.the force field problem A very small (free) energy differences B entropic effects C size problem 2.the search problem A the search problem alleviated B the search problem aggravated Perspectives 3.the ensemble problem 4.the experimental problem A averaging B insufficient accuracy

5. Four Problems 1.The Force Field Problem A very small (free) energy differences (k B T = 2.5 kJ/mol) resulting from summation over very many contributions (atoms)  10 6 – 10 8 must be very accurate B accounting for entropic effects not only energy minima are of importance but whole range of x -valueswith energies ~ k B T must be included in the force field parameter calibration may have higher energy but lower free energy than energy E(x) coordinate x

6. Four Problems C size problem the larger the system, the more accurate the individual energy contributions (from atoms) must be to reach the same overall accuracy Fazit calibrate force field using thermodynamic data for small molecules in the condensed phase keep force field physical + simpletransferable computable Example GROMOS biomolecular force field

7. Choice of Model, Force Field, Sampling 3. Scoring Function, Energy Function, Force Field -continuous lattice -basis for force field or scoring function: 1. structural data - large molecules: crystal structures solution structures of proteins 2. thermodynamic data - small molecules:heat of vaporization, density in condensed phase partition coefficients , D, etc. 3. theoretical data - small molecules:electrostatic potential and gradient in gas phase torsional–angle rotation profiles

8. Determination of Force Field Parameters 2. Polar Molecules Chris Oostenbrink ethers, alcohols, esters, ketones, acids, amines, amides, aromatics, sulfides, thiols methanol ethanol 2-propanol butanol Calibration sets of small molecules 1. Non-polar molecules2. Polar molecules 3. Ionic molecules Calibration set: 28 compounds diethylether

9. Determination of Force Field Parameters Calibration set: 28 compounds ethylamine 1-butylamine ethyldiamine diethylamine n-methylacetamide acetone 2-butanone 3-pentanone acetic acid

10. Determination of Force Field Parameters Calibration set: 28 compounds methyl acetate ethyl acetate ethyl propanoate ethyl butanoate propyl acetate butyl acetate ethyl glycol dipropanoate glycerol tripropanoate

11. Determination of Force Field Parameters Calibration set: 28 compounds benzene toluene dimethylsulfide ethanethiol ethylmethylsulfide dimethylsulfide

12. Determination of Force Field Parameters force field parameter set: 17 parameters quantities to reproduce: for all 28 compounds -heat of vaporisation -density (liquid) for analogues of polar amino acid sidechains (14): -free enthalpy of solvation: in cyclohexane in water

13. Heat of Vaporization for Pure Liquids ethyldiamine 1-butylamine ethylamine average absolute deviation: 1.9 kJ/mol

14. Density for Pure Liquids ethanethiol dimethylsulfide 2-propanol acetone average absolute deviation: 4.0%

15. Free Energy of Solvation in Cyclohexane amino acid analogues (polar) Trp His Tyr Arg Phe Glu Lys Met Gln CysThr Ser Asp average absolute deviation: 2.2 kJ/mol (53A5) Asn

16. Free Energy of Solvation in Water amino acid analogues (polar) Trp His Tyr Arg Phe Glu Lys Met Gln Cys Thr Ser Asp Asn calibrated to p,  H vap liquids calibrated to  G hydration average absolute deviation: 10.3 kJ/mol (53A5) average absolute deviation: 0.9 kJ/mol (53A6) CHARMM: 4.4 kJ/mol AMBER: 5.1 kJ/mol OPLS: 3.1 kJ/mol

17. Stability of a 3 14 helix for a dodeca-beta-peptide in methanol

18. Backbone RMSD from a helical NMR model structure determined for the beta-peptide in methanol methanol water

19. Applications of Molecular Simulation in (Bio)Chemistry and Physics 1.Types of Systems -liquids -solutions -electrolytes -polymers -proteins -DNA, RNA -sugars -other polymers -membranes -crystals -glasses -zeolites -metals -… 2. Types of Processes -melting -adsorption -segregation -complex formation -protein folding -order-disorder transitions -crystallisation -reactions -protein stabilisation -membrane permeation -membrane formation -… 3. Types of Properties -structural -mechanical -dynamical -thermodynamical -electric -…

20. objectives characterisation of the populated microscopic states of peptides by molecular dynamics of spontaneous reversible folding in solution investigate the effect of  thermodynamic conditions  solvent environment  amino acid composition, chain length on the peptide folding behaviour characterisation of the unfolded state

21. types of peptides under investigation -peptides in water, DMSO or methanol -peptides in methanol and/or water aminoxy-peptides in water and chloroform carbohydrate containing peptides CC CC

22. the  -world additional backbone carbon atom  four main chain torsional angles , ,  and  non-degradable peptide mimetics (resistant to several peptidases) stable secondary structures, tunable due to side-chain composition (substitution at - and/or -carbon) –helices –-sheet-like conformations, -hairpins soluble in methanol, some also in water R.P. Cheng, S.H. Gellman, W.F. DeGrado, Chem. Rev. 2001, 101, 3219-3232 

23. method Molecular Dynamics (MD) simulation using the GROMOS biomolecular simulation program GROMOS 43A1 or 45A3 force field NPT using the weak coupling method to hold temperature & pressure constant Periodic boundary conditions explicit solvent models starting structure: fully extended (unless stated otherwise)

24. Effect of thermodynamic conditions & solvent environment (pH, viscosity) on folding equilibrium -heptapeptide 1 adopts a 3 14 -helix in methanol (and pyridine) MD simulation starting from NMR model structure (in explicit methanol) –at five different temperatures: 298 K, 320 K, 340 K, 350 K and 360 K –at three different pressures: 1 atm, 1000 atm, 2000 atm –at three different solvent viscosities –at four different charge states  How is the folding/unfolding equilibrium affected? (reference simulation at the melting temperature (340 K) 1

25. folded unfolded temperature dependence folding equilibrium depends on temperature

26. pressure dependence 2000 atm 1000 atm 1 atm folding equilibrium depends on pressure

27. effect of solvent viscosities scale masses of the solvent atoms (& adapt simulation time step accordingly) normal scaling factor: 0.1  1/3  of MeOH scaling factor: 0.01  1/10  of MeOH equilibrium must not and does not depend on solvent viscosity folding rate does depend on solvent viscosity

28. effect of charge states (pH) exp. conditions (acidic) NH 3 + ….COOH 3 14 helix dominant basic: NH 2 ….COO - 3 14 helix NOT dominant neutral: NH 2 ….COOH 3 14 helix barely present all charges set to zero 3 14 helix not present most stable fold changes with pH

29. The unfolded state of peptides: Much smaller than expected ! (?) Unfolded structures all different? how different? 3 21  10 10 possibilities!! Folded structures all the same W.F. van Gunsteren, R. Bürgi, C. Peter, X. Daura, Angew. Chem. Int. Ed. 2001, 40, 352-355 X. Daura, A.G., P. Gee, C. Peter, W.F. van Gunsteren, Adv. Prot. Chem. 2002, 62, 341-360 100 ns MD: 5x10 7 configurations 2 fs apart Alice Glättli

30. A sample of unfolded states A B D G2G3G4H E F G1 MeOH 7 21 MeOH 6 18 H 2 O10 20 DMSO 8 16 CHCl 3 3 9 residuestorsional angles

31. SystemABCDEFGH Exp. conformer3 14 -helix unknownhairpin12/10- helix -hairpin 3:5 , 3 10 helices 1.8 8 helix Exp. temperature298 278340298 Sim. temperature340298340 353340 Sim. length200102101100506015073 RMSD similarity cut-off [nm]0.10.08 0.120.10.07 Sampling of ECyes Ranking of EC in cluster analysis122121131 Weight of EC [%]301510161219 Estimated free energy of folding [kJ mol -1 ]246515114 Life time of EC [ps]4637509020511311674 # events of folding to EC1292110538325209 Time of folding to EC [ps]1723413361669475094000220 # conformers visited during folding to EC19229923176 Weight of MPC [%]30182619163219 Estimated free energy of folding [kJ mol -1 ]24345244 Life time of MPC [ps]463278230157205207936774 # events of folding to MPC1296812313138981209 Time of folding to MPC [ps]1723124520447369424091465220 # conformers visited during folding to MPC19103791396 Total number of conformers36020076286129111179148 # unfolded conformers (to 99% weight)234131392088878108100 # unfolded conformers (to 75% weight)281973613142315 # unfolded conformers (to 50% weight)66395596

32. conclusion unfolded state of peptides The accessible conformational space seems to be much smaller than the theoretical conformational space (even at high temperature)  key factor for the observed fast folding of these peptides The correlation analysis suggests that as the chain length of the peptide increases the gain in kinetic stability overcasts the loss in folding speed.  folding – a more efficient process for longer chains  more systematic investigation needed (larger sample of peptides with increasing chain length)

33. Four Problems 4. The Experimental Problem A Any experiment involves averaging over time and space (molecules) So it determines the average of a distribution, not the distribution itself However: Very different distributions may yield same average Example: circular dichroism(CD)-spectra -peptides NOE’s + J-values of peptides incrystal solution probability P(Q) quantity Q (linear) average

34. Four Problems NOE’s:are notoriously insensitive to the (atom-atom-distance) distribution provided a small part satisfies the NOE bounds J-values:may be sensitive to dihedral angle distribution X-ray:crystal contains a much narrower distribution than a (aqueous) solution FazitExperimental data cannot define a conformational ensemble B Experimental data have insufficient accuracy for force field calibration and testing accuracy of NOE’s, J-values, structure factors, etc. is limited but may improve with methodological and technical progress Example: NMR data on beta-hexapeptide, alpha-octapeptide FazitExperimental data may converge over time towards simulation results

35. Calculation of CD-spectra from molecular dynamics trajectories

36. Peptide A: DM-BHP geminal dimethylation inhibits the formation of a 3 14 helix no NMR data available CD spectrum shows a pattern, which is “typical” for a 3 14 helix Calculation of circular dichroism (CD) spectra Peptide B: BHP can adopt a 3 14 helix, confirmed by NMR experiments, CD spectrum similar negative Cotton effect between 215 and 220 nm positive Cotton effect at ~200 nm zero crossing between 205 and 210 nm A. Glättli, X. Daura, D. Seebach and W.F. van Gunsteren J. Am. Chem. Soc. 2002, 124, 12972 – 12978

37. Mean CD spectra MD at T = 298 K, 1 atm in 1462/1463 methanol, starting from extended structure DM-BHP:  peak at 197 nm  weak negative Cotton effect at 223 nm  zero crossing at 213 nm BHP:  peak at 197 nm  negative Cotton effect at 221 nm  zero crossing at 215 nm Same structure ?Same spectra

38. CD spectra per cluster Non-helical conformers exhibit the CD pattern assigned to the 3 14 helix, the “helical” conformer doesn’t. helical structure cluster 2 cluster 1 Similarity criterion: backbone RMSD  0.09nm 10000 structures, 10psec apart 2.6 % 74.6 % 12.9 % A 20.5 % 18.1 % 14.5 % 6.8 % 4.6 % 4.5 % 1.9 % 1.7 % 1.6 % B helical

39. CD spectra of single structures abc def A abc def B A certain CD pattern originates from spatially very different structures. a, b, c

40. cluster = conformation conformers present in both ensembles DM-BHP & BHP at 298K Cluster analysis of the combined (100nsec) trajectories  virtually NO OVERLAP between the conformational ensembles of both molecules, which have similar CD spectra !!

41. A β-hexapeptide Bundle of 20 NMR model structures (protection groups not shown) β-hexapeptide with hydroxyl groups attached to the α-carbons NMR model structure suggests the formation of a 2 8 -P-helix MD simulation from totally extended conformation at two different temperatures (298 K & 340K) using the GROMOS 45A3 force field no NOE-distance or J-value restraining Gademann et al., Angew. Chem. Int. Ed., 42 (2003), p. 1534

42. NOE distance violations & backbone J-values at 298 K 2 violations (~0.05 nm) average deviation from exp. J-values: 0.44 Hz at 340 K 1 violation ( ~ 0.03 nm) average deviation from exp. J-values: 0.91 Hz NMR bundle no violation average deviation from exp. J-values: 0.57 Hz

43. Occurrence of Hydrogen Bonds [%] None of the H-bond patterns supporting the formation of a 2 8 -P-helix were detected in the simulations. MD simulation refinement MD simulation refinement

44. Conformational Analysis of the combined MD & NMR “ensembles” MD at 298 K + NMR bundle MD at 340 K + NMR bundle

45. Another possible secondary structure element: 2.5 12 -P-helix 2.5 12 -P-helix is for ~ 35 % populated at 340 K stability 298 is to be confirmed (by simulation at 298 K starting from helix)

46. Conclusions 1.MD simulation using a “thermodynamic” force field (GROMOS) (without NMR restraints) reproduces experimental NOE/J-value data equally good or better than a set of 20 NMR model structures derived by classical single structure refinement techniques (XPLOR) (aspect: force field problem) 2.Single structures may not be representative for the (Boltzmann) ensemble of structures in solution (aspect: ensemble problem) 3.Standard (NMR) structure refinement procedures should be revised in order to avoid the deposition of non-representative model structures in structure data banks (aspect: search problem) 4.Don’t compare secondary (derived) data (structures, angles) but primary (measured) data (NOE’s, 3 J-values) when comparing models with experimental data (aspect: experimental problem)

47. Computer-aided Chemistry: ETH Zuerich Molecular Simulation Package GROMOS = Groningen Molecular Simulation + GROMOS Force Field Generally available: http://www.igc.ethz.ch/gromos Research Topics searching conformational space force field development –atomic –polarization –long range Coulomb techniques to compute free energy 3D structure determination –NMR data –X-ray data quantum MD: reactions solvent mixtures, partitioning interpretation exp. data applications –proteins, sugar, DNA, RNA, lipids, membranes, polymers –protein folding, stability –ligand binding –enzyme reactions

48. Alice Glättli (Switzerland) David Kony (France) Chris Oostenbrink (Holland) Merijn Schenk (Holland) Daniel Trzesniak (Brasil) Haibo Yu (China) Bojan Zagrovic (Croatia) Acknowledgements Dirk Bakowies (Germany) Riccardo Baron (Italy) Indira Chandrasekhar (India) Markus Christen (Switzerland) Peter Gee (England) Daan Geerke (Holland) Daniela Kalbermatter (Switzerland) Gruppe informatikgestützte Chemie (igc) http://www.igc.ethz.ch

51. Conformational Distribution in Crystal versus Solution Solute Molecule polypeptide:(Aib) 6 – Leu – Aib  achiral L-amino-acid NMR:NOE’s suggest helical structure in solution R- or L-helix? 3 J-values (H N -H C ) = 6.9 Hz X-ray:R-helix is found ? crystal structure: satisfies NOE’s but 3 J-value = 4.2 Hz MD Simulations DMSO solution:NOE’s satisfiedL- and R-helical 3 J = 6.8 Hzfragments are present crystal:R-helix agrees with X-rayonly one NOE’s satisfiedconformation present 3 J = 4.0 HzR-helix

52. Conformational Distribution in Crystal versus Solution Conformational Distribution in Solution and in Crystal is different NOE’s:not sensitive 3 J’s:are sensitive conformation x probability P(x) crystalsolution same different