2. Computersimulation of reality real world experiment experimental data predictions computational methods model of the world classification abstraction simplification approximation generalisation comparing is testing Three important turns in science: Thales 600 B.C. design experiment observemodel Galileo 1500 A.D. Rahman1980 A.D. mimic reality on a computer observe

3. Computersimulation of biomolecular systems 1) Why 2) How 3) What 4) And the future … do we simulate ?

4. 1) Why 2) How 3) What 4) And the future … do we simulate ? Computersimulation of biomolecular systems

5. For which problems are simulations useful ? Simulation can replace or complement the experiment: 1.Experiment is impossibleInside of stars Weather forecast 2.Experiment is too dangerousFlight simulation Explosion simulation 3.Experiment is expensiveHigh pressure simulation Windchannel simulation 4.Experiment is blindSome properties cannot be observed on very short time- scales and very small space- scales

6. Simulations can complement the experiment:  Simulation explains experimentsProperties of water Folding of protein molecules  Simulation suggests Design of drugs new experiments enzymes less experiments better chance of success knowledge new ideas For which problems are simulations useful ?

7. The world of molecular simulation and experiment Simulation and experiment are complementing methods to study different aspects of nature experimentsimulation Typical space / time scales size : 10 -3 meter10 -9 meter time : 10 3 seconds10 -6 seconds Resolution* size : 10 23 molecules1 molecule time :1 second 10 -15 seconds *: Single molecules / 10 -15 seconds possible (but not both in the liquid phase) (restricted)(unrestricted)

8. 1) Why 2) How 3) What 4) And the future … do we simulate ? Computersimulation of biomolecular systems

9. 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

10. Choose relevant degrees of freedom: elementary particles... atomic nuclei + electrons quantummechanics electrostatics all atoms (excluding solvent) classical mechanics Force Field (including solvent) monomers classical mechanics Force Field (statistic) Particles: Description: all atoms classical mechanics Force Field (atomistic) Interactions: Broader applicability Less model parameters Physical parameters More expensive Restricted applicability More model parameters Empirical parameters Less expensive =

11. 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 Force Field = physico-chemical knowledge Every molecule consists of atoms that are very strongly attached

12. Interactions in atomic simulaties : Force Field physico-chemical knowledge Rotation around bond Planar atomgroups van der Waals interactions Electrostatic interactions - + - - Bond stretching non-bonded interactions bonded interactions Angle bending

13. 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 Force Field = physico-chemical knowledge Every molecule consists of atoms that are very strongly attached

14. Situation at time t+  t Classical dynamics Situation at time t Force is determined by relative positions acceleration = force / mass  velocity = acceleration ×  t  position = velocity ×  t force velocity positionDeterminism … Sir Isaac Newton 1642 -1727

15. Generating configurations in atomic simulations: molecular dynamics new positions Time t Time (t+  t) positions velocities forces new velocities... comparable to shooting a movie of a molecular system...  t  10 -15 seconds

16. 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 Force Field = physico-chemical knowledge Every molecule consists of atoms that are very strongly attached

17. Boundary conditions in atomic simulations Vacuum Droplets Periodic: rectangular system is surrounded by copies of itself Surface effects (surface tension) No dielectric screening Still surface effects Only partial dielectric screening Evaporation of the solvent Advantage: No surface effects Disadvantage: Artificial periodicity High effective concentration Probably still the best approach…

18. 1) Why 2) How 3) What 4) And the future… do we simulate ? Methods Applications in my research group Computersimulation of biomolecular systems

19. 1.stable structuresbinding equilibrium  energetically favourable structuresbetween two small organic molecules 2.Relation between structure and functionwater transport in the  enzymesbinding cavity of a protein (FABP) 3.Motions en mechanismsprediction of the three-  protein foldingdimensional structure or the folding of proteins (polypeptides) 4.Design of new compoundsbinding strength of  design of drugshormone replacing molecules to the estrogenreceptor What do biochemists or molecular biologists want to know of molecules?

20. Example 1 Structural interpretation of thermodynamic properties: Binding equilibrium between two small organic molecules Applications of molecular dynamics simulation:

21. Binding equilibrium Hydrogen bonds NH 2 HO H H O H N H H H O N ? Cyclohexane- diamine Cyclopentane- diol  + +  - -  - -  + + Complex : ExperimentalMD simulation Benzene CCl 4  G b [kJ/mol] -9.3-11.5 -10.4 Average binding strength (free enthalpy) : Many different bindingmodes

22. Formation of the complex (camera focuses on the diamine) Diol + Diamine + 252 CCl 4 Molecules 2.1 – 2.2. 10 -9 seconds Complex formed

23. Diol + Diamine + 252 CCl 4 Molecules 3.2 – 4.0. 10 -9 seconds … and a nanosecond later … the molecules are free again… Hydrogen bonds O  N N  O

24. NH 2 HO NH 2 HO NH 2 HO NH 2 HO NH 2 HO NH 2 HO 54% 21% 8% 7% 4% 3% Occurrence of different binding modes : 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 Results of the simulation (over 10 -7 sec) :  Experimentally hardly (or not) possible !

25. What do biochemists or molecular biologists want to know of molecules? 1.stable structuresbinding equilibrium  energetically favourable structuresbetween two small organic molecules 2.Relation between structure and functionwater transport in the  enzymesbinding cavity of a protein (FABP) 3.Motions en mechanismsprediction of the three-  protein foldingdimensional structure or the folding of proteins (polypeptides) 4.Design of new compoundsbinding strength of  design of drugshormone replacing molecules to the estrogenreceptor

26. Boundaries: membranes consist of lipids with pores of proteins Hereditary information in the nucleus: DNA Proteins: e.g. haemoglobin for oxygen transport Carbohydrates: storage of energy and molecular stamps Biomolecules

27. Important to understand enzymatic reactions: the dynamics of the binding cavity Simulation allows one to follow the movements of individual molecules Example 2 The watertransport in the binding cavity of a protein (FABP) Applications of molecular dynamics simulation:

28. What do biochemists or molecular biologists want to know of molecules? 1.stable structuresbinding equilibrium  energetically favourable structuresbetween two small organic molecules 2.Relation between structure and functionwater transport in the  enzymesbinding cavity of a protein (FABP) 3.Motions en mechanismsprediction of the three-  protein foldingdimensional structure or the folding of proteins (polypeptides) 4.Design of new compoundsbinding strength of  design of drugshormone replacing molecules to the estrogenreceptor

29. Example 3 Protein folding the challenge Proteins consist of chains of amino acids (primary structure) In an organism proteins only function if they have been correctly folded three- dimensionally. (secondary and tertiary structure) What is the relation between amino acid sequence and folded spatial structure? How does the folding process take place? 20 kinds Applications of molecular dynamics simulation:

30. 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 Foldingsimulation

31. Unfolded structures all different? how different? 3 21  10 10 possibilities!! Folded structures all the same

32. Surprising result after simulations of many polypeptides number of amino acids in the protein 10 100 Folding time (exp/sim) in seconds 10 -8 10 -2 possible structures 3 20  10 9 3 200  10 90 relevant (observed) structures 10 3 10 9 number of peptide protein The number of relevant unfolded structures is much and much smaller than the number of possible unfolded structures Assuming that the number of relevant unfolded structures is proportional to the folding time, only 10 9 protein structures need to be simulated instead of 10 90 structures.  Folding mechanism is simpler than generally expected: searching through only 10 9 structures  Protein folding on a computer is possible before 2010

33. Simulations can complement the experiment:  Simulation explains experimentsProperties of water Folding of protein molecules  Simulation suggests Design of drugs new experiments enzymes less experiments better chance of success knowledge new ideas For which problems are simulations useful ?

34. What do biochemists or molecular biologists want to know of molecules? 1.stable structuresbinding equilibrium  energetically favourable structuresbetween two small organic molecules 2.Relation between structure and functionwater transport in the  enzymesbinding cavity of a protein (FABP) 3.Motions en mechanismsprediction of the three-  protein foldingdimensional structure or the folding of proteins (polypeptides) 4.Design of new compoundsbinding strength of  design of drugshormone replacing molecules to the estrogenreceptor

35. Example 4 Design of drugs testing compounds with the computer Enzymes work according to the “lock and key”-principle Applications of molecular dynamics simulations: 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

36. 16 hydroxylated PCB’s Unphysical reference state Polychlorinated biphenyls

37. Binding to the estrogen receptor 16 hydroxylated PCB’s: 10 < k B T  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

38. 1) Why 2) How 3) What 4) And the future … Computersimulation of biomolecular systems

39. Yearmolecular system: type, sizelength of the simulation in seconds 1957 first molecular dynamics simulation (hard discs, two dimensions) 1964 atomic liquid (argon) 10 -11 1971 molecular liquid (water) 5. 10 -12 1976 protein (no solvent) 2. 10 -11 1983 protein in water 2. 10 -11 1989protein-DNA complex in water 10 -10 1997 polypeptide folding in solvent 10 -7 2001micelle formation 10 -7 200xfolding of a small protein 10 -3 History: classical molecular dynamics simulations of biomolecular systems

40. And the future... 2001Biomolecules in water (~10 4 atomen) 10 -8 sec 2029Biomolecules in water 10 -3 sec 2034E-coli bacteria (~10 11 atoms) 10 -9 sec 2056Mammalian cell (~10 15 atoms) 10 -9 sec 2080Biomolecules in water 10 6 sec 2172Human body (~10 27 atoms) 1 sec As fast as nature ! Protein folding sooner? Standard classical simulations : Computer speed increases with a factor 10 about every 5½ year! Upper limit to computer speed ? Accuracy of classical models and force fields ? Better approximations and simplifications But :

41. Computersimulation of reality real world experiment experimental data predictions computational methods model of the world classification abstraction simplification approximation generalisation comparing is testing

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