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Computersimulation of reality real world experiment experimental data classification abstraction simplification approximation generalisation model of the world comparing is testing computational methods Three important turns in science: Thales 600 B.C. Galileo 1500 A.D. model design experiment mimic reality Rahman 1980 A.D. model on a computer predictions observe observe model model observe model Computersimulation of biomolecular systems 1) Why 2) How do we simulate ? 3) What 4) And the future … Computersimulation of biomolecular systems 1) Why do we simulate ? 2) How 3) What 4) And the future … For which problems are simulations useful ? Simulation can replace or complement the experiment: 1. Experiment is impossible Inside of stars Weather forecast 2. Experiment is too dangerous Flight simulation Explosion simulation 3. Experiment is expensive High pressure simulation Windchannel simulation 4. Experiment is blind Some properties cannot be observed on very short timescales and very small spacescales For which problems are simulations useful ? Simulations can complement the experiment: Simulation explains experiments Properties of water Folding of protein molecules knowledge new ideas Simulation suggests new experiments less experiments better chance of success Design of drugs enzymes The world of molecular simulation and experiment experiment Resolution* simulation (restricted) (unrestricted) size : 1023 molecules 1 time : 1 10-15 seconds second molecule *: Single molecules / 10-15 seconds possible (but not both in the liquid phase) Typical space / time scales size : 10-3 meter 10-9 meter time : 103 seconds 10-6 seconds Simulation and experiment are complementing methods to study different aspects of nature Computersimulation of biomolecular systems 1) Why 2) How do we simulate ? 3) What 4) And the future … 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 Choose relevant degrees of freedom: elementary particles ... ... = Particles: atomic nuclei + electrons all atoms all atoms (excluding solvent) monomers classical mechanics classical mechanics classical mechanics Force Field (atomistic) Force Field (including solvent) Force Field (statistic) Description: quantummechanics Interactions: electrostatics Broader applicability Less model parameters Physical parameters More expensive Restricted applicability More model parameters Empirical parameters Less expensive Definition of a model for molecular simulation Every molecule consists of atoms that are very strongly attached 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 Interactions in atomic simulaties : Force Field physico-chemical knowledge non-bonded interactions bonded interactions Bond stretching Angle bending Rotation around bond Planar atomgroups + - - Electrostatic interactions van der Waals interactions Definition of a model for molecular simulation Every molecule consists of atoms that are very strongly attached 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 Classical dynamics Situation at time t Force is determined by relative positions acceleration = force / mass velocity = acceleration × t position = velocity × t position velocity force Situation at time t+t Sir Isaac Newton 1642 -1727 Determinism … Generating configurations in atomic simulations: molecular dynamics ... comparable to shooting a movie of a molecular system... Time t velocities positions forces Time (t+t) new velocities new positions t 10-15 seconds Definition of a model for molecular simulation Every molecule consists of atoms that are very strongly attached 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 Boundary conditions in atomic simulations Vacuum • Surface effects (surface tension) • No dielectric screening Droplets • Still surface effects • Only partial dielectric screening • Evaporation of the solvent Periodic: rectangular system is surrounded by copies of itself Advantage: • No surface effects Disadvantage: • Artificial periodicity • High effective concentration Probably still the best approach… Computersimulation of biomolecular systems 1) Why 2) How 3) What in my research group Methods Applications do we simulate ? 4) And the future… What do biochemists or molecular biologists want to know of molecules? 1. stable structures energetically favourable structures binding equilibrium between two small organic molecules 2. Relation between structure and function water transport in the enzymes binding cavity of a protein (FABP) 3. Motions en mechanisms prediction of the three protein folding dimensional structure or the folding of proteins (polypeptides) 4. Design of new compounds binding strength of design of drugs hormone replacing molecules to the estrogenreceptor Applications of molecular dynamics simulation: Example 1 Structural interpretation of thermodynamic properties: Binding equilibrium between two small organic molecules Binding equilibrium Hydrogen bonds Complex : Cyclohexanediamine NH2 NH2 ? Cyclopentanediol H H N - HO H + O H HO N H H + Many different bindingmodes O - Average binding strength (free enthalpy) : Experimental Benzene CCl4 Gb [kJ/mol] -9.3 -11.5 MD simulation -10.4 Diol + Diamine + 252 CCl4 Molecules 2.1 – 2.2.10-9 seconds Complex formed Formation of the complex (camera focuses on the diamine) Diol + Diamine + 252 CCl4 Molecules 3.2 – 4.0.10-9 seconds Hydrogen bonds ON NO …molecules and a nanosecond later … the are free again… Results of the simulation (over 10-7 sec) : Experimentally hardly (or not) possible ! Occurrence of different binding modes : NH2 HO NH2 HO NH2 HO NH2 HO NH2 HO NH2 HO 54% 21% 7% 4% NH2 HO NH2 HO NH2 HO NH2 HO NH2 8% HO NH2 3% HO Life time : • Average life time of the complex: 2.10-10 sec (max. 3.10-9 sec) • Average life time of a hydrogen bond: 5 .10-12 sec What do biochemists or molecular biologists want to know of molecules? 1. stable structures energetically favourable structures binding equilibrium between two small organic molecules 2. Relation between structure and function water transport in the enzymes binding cavity of a protein (FABP) 3. Motions en mechanisms prediction of the three protein folding dimensional structure or the folding of proteins (polypeptides) 4. Design of new compounds binding strength of design of drugs hormone replacing molecules to the estrogenreceptor Biomolecules Boundaries: membranes consist of lipids with pores of proteins Hereditary information in the nucleus: DNA Carbohydrates: storage of energy and molecular stamps Proteins: e.g. haemoglobin for oxygen transport Applications of molecular dynamics simulation: Example 2 The watertransport in the binding cavity of a protein (FABP) • Important to understand enzymatic reactions: the dynamics of the binding cavity • Simulation allows one to follow the movements of individual molecules What do biochemists or molecular biologists want to know of molecules? 1. stable structures energetically favourable structures binding equilibrium between two small organic molecules 2. Relation between structure and function water transport in the enzymes binding cavity of a protein (FABP) 3. Motions en mechanisms prediction of the three protein folding dimensional structure or the folding of proteins (polypeptides) 4. Design of new compounds binding strength of design of drugs hormone replacing molecules to the estrogenreceptor Applications of molecular dynamics simulation: Example 3 Protein folding the challenge Proteins consist of chains of amino acids (primary structure) 20 kinds In an organism proteins only function if they have been correctly folded threedimensionally. (secondary and tertiary structure) • What is the relation between amino acid sequence and folded spatial structure? • How does the folding process take place? Foldingsimulation • Proteins are too large systems to simulate the slow folding process. • Smaller model compounds can be correctly folded on the computer. Information about folding mechanisms and the unfolded state: surprise all different? how different? 321 1010 possibilities!! RMSD [nm] Unfolded structures 0.4 0.3 0.2 0.1 0 0 50 100 t [ns] Folded structures all the same 150 200 Surprising result after simulations of many polypeptides The number of relevant unfolded structures is much and much smaller than the number of possible unfolded structures number of possible relevant (observed) structures structures number of amino acids in the protein Folding time (exp/sim) in seconds peptide 10 10-8 320 109 103 protein 100 10-2 3200 1090 109 Assuming that the number of relevant unfolded structures is proportional to the folding time, only 109 protein structures need to be simulated instead of 1090 structures. Folding mechanism is simpler than generally expected: searching through only 109 structures Protein folding on a computer is possible before 2010 For which problems are simulations useful ? Simulations can complement the experiment: Simulation explains experiments Properties of water Folding of protein molecules knowledge new ideas Simulation suggests new experiments less experiments better chance of success Design of drugs enzymes What do biochemists or molecular biologists want to know of molecules? 1. stable structures energetically favourable structures binding equilibrium between two small organic molecules 2. Relation between structure and function water transport in the enzymes binding cavity of a protein (FABP) 3. Motions en mechanisms prediction of the three protein folding dimensional structure or the folding of proteins (polypeptides) 4. Design of new compounds binding strength of design of drugs hormone replacing molecules to the estrogenreceptor Applications of molecular dynamics simulations: Example 4 Design of drugs testing compounds with the computer Enzymes work according to the “lock and key”-principle the “key hole”: the active site in the protein containing a “fitting key”: the active site with an active molecule the active and a new molecule (to be tested) superimposed a “new key”?: The active site with the molecule to be tested Polychlorinated biphenyls Unphysical reference state 16 hydroxylated PCB’s Cl HO Cl HO HO Cl HO Cl Cl Cl Cl HO HO Cl Cl Cl Cl HO Cl Cl Cl HO Cl Cl Cl Cl Cl Cl Cl Cl Cl Cl Cl Cl Cl Cl Cl Cl HO Cl Cl Cl Cl Cl HO Cl HO Cl HO Cl Cl Cl HO Cl Cl HO Cl Cl HO Cl Cl Cl Cl Cl Cl Cl Cl HO Cl Cl Cl Binding to the estrogen receptor 16 hydroxylated PCB’s: 10 < kBT 2.5 kJ mol-1 13 < 1 kcal mol-1 Average deviation: 2.5 kJ mol-1 Variation exp. values: 4.2 kJ mol-1 Computersimulation of biomolecular systems 1) Why 2) How 3) What 4) And the future … History: classical molecular dynamics simulations of biomolecular systems Year molecular system: type, size length of the simulation in seconds 1957 first molecular dynamics simulation (hard discs, two dimensions) 1964 atomic liquid (argon) 1971 molecular liquid (water) 5 .10-12 1976 protein (no solvent) 2 .10-11 1983 protein in water 2 .10-11 1989 protein-DNA complex in water 10-10 1997 polypeptide folding in solvent 10-7 2001 micelle formation 10-7 200x folding of a small protein 10-3 10-11 And the future ... Computer speed increases with a factor 10 about every 5½ year! Standard classical simulations : 2001 Biomolecules in water (~104 atomen) 10-8 sec 2029 Biomolecules in water 10-3 sec 2034 E-coli bacteria (~1011 atoms) 10-9 sec 2056 Mammalian cell (~1015 atoms) 10-9 sec 2080 Biomolecules in water 106 sec 2172 Human body (~1027 atoms) But : Protein folding sooner? 1 sec • Upper limit to computer speed ? • Accuracy of classical models and force fields ? • Better approximations and simplifications As fast as nature ! Computersimulation of reality real world experiment classification abstraction simplification approximation generalisation model of the world experimental data comparing is testing computational methods predictions 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) Daniel Trzesniak (Brasil) Peter Gee (England) Alex de Vries (Holland) Daan Geerke (Holland) Haibo Yu (China) Daniela Kalbermatter (Switzerland)