Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Biomolecular Modelling: Goals, Problems, Perspectives 1. Goal simulate/predict processes such as 1. 2. 3. 4. polypeptide folding biomolecular association partitioning between solvents membrane/micelle formation common characteristics: - degrees of freedom: - equations of motion: - governing theory: thermodynamic equilibria governed by weak (nonbonded) forces atomic (solute + solvent) classical dynamics statistical mechanics hamiltonian or force field entropy Processes: Thermodynamic Equilibria Folding folded/native Micelle Formation denatured Complexation bound unbound micelle mixture Partitioning in membrane in water in mixtures Definition of a model for molecular simulation Every molecule consists of atoms that are very strongly bound to each other Degrees of freedom: atoms are the elementary particles Forces or interactions between atoms Boundary conditions MOLECULAR MODEL Force Field = physico-chemical knowledge Methods to generate configurations of atoms: Newton system temperature pressure Biomolecular Modelling: Goals, Problems, Perspectives Four Problems 1. the force field problem 3. the ensemble 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 4. the experimental problem A averaging B insufficient accuracy Four Problems 1. The Force Field Problem A very small (free) energy differences (kBT = 2.5 kJ/mol) resulting from summation over very many contributions (atoms) i 106 – 108 B accounting for entropic effects not only energy minima are of importance but whole range of i must be very accurate energy E(x) x-values with energies ~kBT must be included in the force field parameter calibration may have higher energy but lower free energy than coordinate x 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 + simple transferable computable Example GROMOS biomolecular force field Choice of Model, Force Field, Sampling 3. Scoring Function, Energy Function, Force Field - continuous n 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 e, D, h, etc. 3. theoretical data - small molecules: in gas phase electrostatic potential and gradient torsional–angle rotation profiles Determination of Force Field Parameters Calibration sets of small molecules 1. Non-polar molecules 2. Polar molecules 2. Polar Molecules 3. Ionic molecules Calibration set: 28 compounds Chris Oostenbrink methanol ethers, alcohols, esters, ketones, ethanol acids, amines, amides, aromatics, sulfides, thiols diethylether 2-propanol butanol Determination of Force Field Parameters Calibration set: 28 compounds ethylamine acetone 1-butylamine 2-butanone ethyldiamine 3-pentanone acetic acid diethylamine n-methylacetamide Determination of Force Field Parameters Calibration set: 28 compounds O methyl acetate O C O H3C butyl acetate CH3 H3C C O O ethyl acetate H3C H3C CH3 O ethyl glycol dipropanoate O ethyl propanoate H3C H2 C C C H2 H3C CH3 O H2 C C C H2 H3C H2 C CH3 O glycerol tripropanoate H3C O propyl acetate H2 C C H3C H2 C C C H2 O O C C H2 O CH2 O O ethyl butanoate H3C CH3 C H2 O H2 C C H2 C H2 C O C H2 CH3 H3C H2 C C C O H2 O C C O H2 CH O C C H2 O CH2 Determination of Force Field Parameters Calibration set: 28 compounds dimethylsulfide benzene ethanethiol ethylmethylsulfide toluene dimethylsulfide 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 Heat of Vaporization for Pure Liquids ethyldiamine 1-butylamine ethylamine average absolute deviation: 1.9 kJ/mol Density for Pure Liquids dimethylsulfide ethanethiol 2-propanol acetone average absolute deviation: 4.0% Free Energy of Solvation in Cyclohexane amino acid analogues (polar) Ser Cys Thr Lys Met Asn His Glu Arg Trp Asp Gln Phe Tyr average absolute deviation: 2.2 kJ/mol (53A5) Free Energy of Solvation in Water amino acid analogues (polar) calibrated to p, DHvap liquids Met Cys calibrated to DGhydration Lys Glu Gln Asn Phe Asp Ser Thr His Trp Arg Tyr CHARMM: 4.4 kJ/mol AMBER: 5.1 kJ/mol OPLS: 3.1 kJ/mol average absolute deviation: 10.3 kJ/mol (53A5) average absolute deviation: 0.9 kJ/mol (53A6) Stability of a 314 helix for a dodeca-beta-peptide in methanol H N O S + HO NH + NH3 + NH3 NH3 O HO A H3N B + N H N H O O O O O N H N H C HO N H N H N H D N H N H N H E O O O O O O O N H OH F Backbone RMSD from a helical NMR model structure determined for the beta-peptide in methanol methanol water 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 … 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 O O O O O O under OH N N investigation H N of peptides N N N E types H H H H H 2 O • • H2N O O N H F N H O N H H2N SYINSDGTWT O N H G B N H N H OH C O H N O O O N H O O N H H N N H O O N H N H O O O H N N H N H O C H N O OH O aminoxy-peptides in water and chloroform O H • O -peptides in water, DMSO or methanol -peptides in methanol and/or water A • O O N H O O N H O O N H O carbohydrate containing peptides O N H O O the -world O • O O O O H N N N N N H H H H additional backbone carbon atom four main chain torsional angles , , and 2 O N H OH A O H2N O N H O N H O NH O N H O N H OH B • • • 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 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) Effect of thermodynamic conditions & solvent environment (pH, viscosity) on folding equilibrium • -heptapeptide 1 adopts a 314-helix in methanol (and pyridine) • MD simulation starting from NMR model structure (in explicit methanol) – – – – at at at at five different temperatures: 298 K, 320 K, 340 K, 350 K and 360 K three different pressures: 1 atm, 1000 atm, 2000 atm three different solvent viscosities four different charge states How is the folding/unfolding equilibrium affected? (reference simulation at the melting temperature (340 K) O A H2N O N H OH N H N H N H N H N H O O O O O 1 O B H N O N N N O O O O N N OH temperature dependence unfolded folded folding equilibrium depends on temperature pressure dependence 2000 atm 1000 atm 1 atm folding equilibrium depends on pressure effect of solvent viscosities scale masses of the solvent atoms (& adapt simulation time step accordingly) normal scaling factor: 0.1 1/3 h of MeOH scaling factor: 0.01 1/10 h of MeOH equilibrium must not and does not depend on solvent viscosity folding rate does depend on solvent viscosity effect of charge states (pH) exp. conditions (acidic) NH3+….COOH 314 helix dominant basic: NH2….COO314 helix NOT dominant neutral: NH2….COOH 314 helix barely present all charges set to zero 314 helix not present most stable fold changes with pH The unfolded state of peptides: Much smaller than expected ! (?) all different? how different? RMSD [nm] Unfolded structures 321 1010 possibilities!! 0.4 0.3 0.2 0.1 0 0 50 100 150 200 t [ns] 100 ns MD: 5x107 configurations 2 fs apart Folded structures Alice Glättli 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 A sample of unfolded states residues O A H2N O N H O B H2N O N H O C H2N N H OH N H N H N H N H O O O O O OH N H N H N H O O O O N H OH N H N H N H N H N H O O O O O torsional angles MeOH 7 21 MeOH 6 18 MeOH 6 18 MeOH 6 18 MeOH 6 18 H2O 10 20 DMSO 8 16 CHCl3 3 9 A B E F D NH2 D O H2N N H N H O E H2N O N H F G SYINSDGTWT H N O O O H N N H O N H O N H O H N N H O O O O H N N H O O H OH N H N H N H N H O O O O OH N H N H N H O O O O O O O N H O O O N H O G1 O G2 G3 G4 H System A B Exp. conformer 314-helix 314-helix Exp. temperature 298 298 298 298 298 278 340 298 Sim. temperature 340 298 340 340 340 353 340 340 Sim. length 200 102 101 100 50 60 150 73 RMSD similarity cut-off [nm] 0.1 0.08 0.08 0.08 0.08 0.12 0.1 0.07 Sampling of EC Ranking of EC in cluster analysis yes C D unknown yes E hairpin yes F G -hairpin 3:5 12/10helix yes yes H , 310 helices yes 1.88 helix yes 1 2 2 1 21 13 1 30 15 10 16 1 2 19 2 4 6 5 15 11 4 Life time of EC [ps] 463 750 90 205 113 116 74 # events of folding to EC 129 21 105 38 3 25 209 1723 4133 616 694 7509 4000 220 # conformers visited during folding to EC 19 22 9 9 23 17 6 Weight of MPC [%] 30 18 26 19 16 32 19 19 2 4 3 4 5 2 4 4 Life time of MPC [ps] 463 278 230 157 205 2079 367 74 # events of folding to MPC 129 68 123 131 38 9 81 209 1723 1245 204 473 694 2409 1465 220 19 10 3 7 9 13 9 6 Total number of conformers 360 200 76 286 129 111 179 148 # unfolded conformers (to 99% weight) 234 131 39 208 88 78 108 100 # unfolded conformers (to 75% weight) 28 19 7 36 13 14 23 15 # unfolded conformers (to 50% weight) 6 6 3 9 5 5 9 6 Weight of EC [%] Estimated free energy of folding [kJ mol -1] Time of folding to EC [ps] Estimated free energy of folding [kJ mol -1] Time of folding to MPC [ps] # conformers visited during folding to MPC 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) 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 probability P(Q) (linear) average <Q> quantity Q Example: circular dichroism(CD)-spectra -peptides NOE’s + J-values of peptides in crystal solution Four Problems NOE’s: J-values: X-ray: are notoriously insensitive to the (atom-atom-distance) distribution provided a small part satisfies the NOE bounds may be sensitive to dihedral angle distribution crystal contains a much narrower distribution than a (aqueous) solution Fazit Experimental 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 Fazit Experimental data may converge over time towards simulation results Calculation of CD-spectra from molecular dynamics trajectories Calculation of circular dichroism (CD) spectra O H2N O N H O O N H O N H positive Cotton effect at ~200 nm O N H N H OH zero crossing between 205 and 210 nm A Peptide A: DM-BHP • geminal dimethylation inhibits the formation of a 314 helix O H2N O N H O O N H O N H N H O N H OH B • no NMR data available • CD spectrum shows a pattern, which is “typical” for a 314 helix O H2N O N H O N H O N H O N H O N H OH A O H2N O N H O N H O N H O N H O N H OH B Peptide B: BHP • can adopt a 314 helix, confirmed by NMR experiments, CD spectrum similar negative Cotton effect between 215 and 220 nm A. Glättli, X. Daura, D. Seebach and W.F. van Gunsteren J. Am. Chem. Soc. 2002, 124, 12972 – 12978 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 spectra Same structure ? CD spectra per cluster Similarity criterion: backbone RMSD 0.09nm 10000 structures, 10psec apart A B helical cluster 2 cluster 1 helical structure 74.6 % 20.5 % 18.1 % 14.5 % 12.9 % 4.5 % 2.6 % 1.9 % 6.8 % 1.7 % 4.6 % 1.6 % Non-helical conformers exhibit the CD pattern assigned to the 314 helix, the “helical” conformer doesn’t. CD spectra of single structures A a b c a, b, c d e f B a, b, c A certain CD pattern originates from spatially very different structures. a d b e c f Cluster analysis of the combined (100nsec) trajectories DM-BHP & BHP at 298K conformers present in both ensembles cluster = conformation virtually NO OVERLAP between the conformational ensembles of both molecules, which have similar CD spectra !! A β-hexapeptide O O O N H OH O O N H OH N H OH O O N H OH N H OH O N H O Ph OH • β-hexapeptide with hydroxyl groups attached to the α-carbons • NMR model structure suggests the formation of a 28-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 Bundle of 20 NMR model structures (protection groups not shown) Gademann et al., Angew. Chem. Int. Ed., 42 (2003), p. 1534 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 Occurrence of Hydrogen Bonds [%] MD simulation refinement Donor-Acceptor 298 K 340 K X-PLOR NH(i)-O(i-2) [HB8] MD simulation refinement Donor-Acceptor 298 K 340 K X-PLOR OH(i)-O(i-1) [HB7] NH(3)-O(1) 0 1 20 OH(6)-O(5) NH(4)-O(2) 0 1 25 OH(i)-O(i-2) [HB11] NH(5)-O(3) 2 4 10 NH(i)-O(i-3) [HB12] 0 14 0 OH(4)-O(2) 0 8 10 OH(5)-O(3) 1 22 0 1 10 0 NH(3)-O(0) 0 30 0 OH(6)-O(4) NH(4)-O(1) 0 26 0 OH(i)-O(i-3) [HB15] NH(5)-O(2) 0 35 0 OH(4)-O(1) 1 26 0 NH(6)-O(3) 1 18 0 OH(5)-O(2) 0 10 0 38 0 0 NH(i)-O(i+1) [HB10] OH(i)-O(i+2) [HB13] NH(2)-O(3) 11 0 0 NH(5)-O(6) 11 1 0 OH(3)-O(5) None of the H-bond patterns supporting the formation of a 28-P-helix were detected in the simulations. Conformational Analysis of the combined MD & NMR “ensembles” MD at 298 K + NMR bundle MD at 340 K + NMR bundle Another possible secondary structure element: 2.512-P-helix • 2.512-P-helix is for ~ 35 % populated at 340 K • stability 298 is to be confirmed (by simulation at 298 K starting from helix) 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, 3J-values) when comparing models with experimental data (aspect: experimental problem) 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 Acknowledgements Gruppe informatikgestützte Chemie (igc) http://www.igc.ethz.ch Dirk Bakowies (Germany) Alice Glättli (Switzerland) Riccardo Baron (Italy) David Kony (France) Indira Chandrasekhar (India) Chris Oostenbrink (Holland) Markus Christen (Switzerland) Merijn Schenk (Holland) Peter Gee (England) Daniel Trzesniak (Brasil) Daan Geerke (Holland) Haibo Yu (China) Daniela Kalbermatter (Switzerland) Bojan Zagrovic (Croatia) Conformational Distribution in Crystal versus Solution Solute Molecule polypeptide: (Aib)6 – Leu – Aib h h achiral L-amino-acid NMR: NOE’s suggest helical structure in solution 3J-values (H -H ) = 6.9 Hz N C X-ray: R-helix is found R- or L-helix? ? crystal structure: satisfies NOE’s but 3J-value = 4.2 Hz MD Simulations DMSO solution: NOE’s satisfied 3J = 6.8 Hz L- and R-helical fragments are present crystal: R-helix agrees with X-ray only one NOE’s satisfied 3J = 4.0 Hz conformation present R-helix Conformational Distribution in Crystal versus Solution Conformational Distribution in Solution and in Crystal is different NOE’s: 3J’s: not sensitive are sensitive probability P(x) <NOE> same <3J> different crystal solution conformation x