1. Relative Binding Free Energies for Protein-Inhibitor Complexes CATFEE: Critical Assessment of Techniques for Free Energy Evaluation Blind test of 10 compounds. Determine relative affinities to Factor Xa, Thrombin and Trypsin. Our Interest: Test protocols and convergence Journal of Computer-Aided Molecular Design 17: 673–686, 2003. Alessandra Villa, Ronen Zangi, Gilles Pieffet

3. 1345 6 Inhibitor 2 7 8 9 10 Inhibitors

4. Trypsin Template PDB entry 1QB1 Acta Cryst. D (1999) D55 1395-1404 2,6-diphenoxypyridine ligand

5. Factor Xa Template Removed from simulations 2,6-diphenoxypyridine ligand PDB entry 1FJS Biochemistry (2000) 39, 12534-42

6. Integration Formula (work along reversible path) Methods to Compute Free Energies Simulate at fixed and integrate numerically 1 4 3 2 Requirements (at each ) Equilibrium. Ensemble average must converge. F( ) must be a smooth function.

7. Soft core potential: Addition of distance to shift the potential Alessandra Villa, Ronen Zangi, Gilles Pieffet

9. In principle each point is independent I3 to I6 I3 to I4 Alessandra Villa, Ronen Zangi, Gilles Pieffet

10. O O OH - Cl O O O O OCH 3 CH 3 O - CH 3 CH 2 3 O O CH 3 CH 3 2 4 6 1 CH 3 CH 2 2 N N CH 3 7 H H NH H N H N + N H 9 N H 10 8 N N CH 3 N N H N H N N H Cl Cycle Closure: water (kJ/mol) -277.8 9.7 52.6 268.4 -321.5 83.0 238.8 -141.8 -97.9 -28.6 2.8 61.0 -65.9 cycles -0.5 -3.4 -0.9 3.4 -2.1 Alessandra Villa, Ronen Zangi, Gilles Pieffet

11. O O OH - Cl O O O O OCH 3 CH 3 O - CH 3 CH 2 3 O O CH 3 CH 3 2 4 6 1 CH 3 CH 2 2 N N CH 3 7 H H NH H N H N + N H 9 N H 10 8 N N CH 3 N N H N H N N H Cl Cycle Closure: Factor Xa (kJ/mol) -281.9 17.4 57.9 252.4 -304.3 74.2 245.7 -127.2 -97.9 -36.5 2.1 72.3 -71.2 cycles 6.0 12.1 5.3 -5.5 3.2

12. 6, 6* 5, 5* 4, 4* 1, 1* Asymmetric Ligands hindered rotation in protein Treat rotational isomers as independent compounds + - + +

14. 3 6 4 1 1* 27 3* 6* 55* 9 8 10 74.2 Asymmetric Ligands: Factor Xa -56.9 -307.3 -304.357.9 252.4 269.5 ? Preferred conformers in factor Xa Alessandra Villa, Ronen Zangi, Gilles Pieffet

15.  G =  G factor Xa -  G water Ranking 1 >> 4 ~ 2 > 6 ~ 8 > 15 > 9 > 10 >> 7 Experimental data on the compounds investigated not yet released!. Comparison to Experiment Summary Converged and reproducible results for mutations > 10 atoms (soft core potentials). Large numbers of mutations possible (cluster computing). Initial screening? (extrapolation approaches)

16. Estimating changes in the monomer-dimer equilibrium of SUC1 upon mutation Dissociation free-energy calculated using thermodynamic integration Gilles Pieffet

17. SUC1: Structure Protein of 113 residues  and  fold –4 stranded  sheets –3 short  helices Domain swapping of the dimer: C-terminal  strand Crystallographic structure of the monomer Crystallographic structure of the dimer Gilles Pieffet

18. Experiment DM + M Kd  G diss = - RT ln Kd Kd  G DM = - RT ln ( ) Kd mutant WT =  G diss (M) -  G diss (WT) Look at difference in disassociation constant upon mutation (experimental data not without question) Gilles Pieffet

19. Thermodynamic cycle D (WT)M (WT) + M (WT) D (M)M (M) + M (M)  G diss (WT)  G diss (M)  G WT M (mono)  G WT M (dimer)  G DM =  G diss (M) -  G diss (WT) = -  G WT M (dimer) + 2  G WT M (mono) Gilles Pieffet

20. Simulation parameters Gromos96 forcefield time step of 2 fs T = 323 K T and P coupling Twin range cut-off of 0.9 and 1.4 nm Reaction-Field  78) Equilibration: 100 ps with position restraint 10 ns without position restraint Free-energy calculation: –relaxation:100 ps for each lambda point –data collection: 400 ps for the monomer 200 ps for the dimer 18  points are used for the integration Gilles Pieffet

21. Mutations studied All mutations correspond to the transformation of a residue into an alanine.  G DM < 0Dimer of WT is more stable than dimer in mutant  G DM > 0 Dimer of WT is less stable than dimer in mutant Gilles Pieffet

22. Monomer:  G = 11.6 kJ/molSim:  G = -2.2 kJ/mol dimer:  G = 25.4 kJ/molExp:  G = -2.4 kJ/mol Gilles Pieffet

23. Monomer:  G = 4.6 kJ/molSim:  G = -18.9 kJ/mol dimer:  G = 28.1 kJ/molExp:  G = -0.4 kJ/mol Gilles Pieffet

24. Monomer:  G = 1.5 kJ/molSim:  G = -5.1 kJ/mol dimer:  G = 8.1 kJ/molExp:  G = -2.7 kJ/mol Gilles Pieffet

25. Monomer:  G = -5.2 kJ/molSim:  G = -27.5 kJ/mol dimer:  G = 17.1 kJ/molExp:  G = -2.3 kJ/mol Gilles Pieffet

26. Results Gilles Pieffet

27. Relative stability of the wild type dimer with respect to some mutants (kJ/mol).

28. Case of the LA95 mutation Monomer Gilles Pieffet

29. Case of the LA95 mutation Dimer

30. Results Gilles Pieffet

31. Monomer:  G = 4.6 kJ/molSim:  G = -18.9 kJ/mol dimer:  G = 28.1 kJ/molExp:  G = -0.4 kJ/mol Gilles Pieffet

32. Monomer:  G = 0.4 kJ/molSim:  G = -4.2 kJ/mol dimer:  G = 3.4 kJ/molExp:  G = 0.4 kJ/mol Gilles Pieffet

33. Monomer:  G = -3.5 kJ/molSim:  G = -31.2 kJ/mol dimer:  G = 24.2 kJ/molExp:  G = 0.4 kJ/mol Gilles Pieffet

34. Divergence for specific values:  = 0.40, 0.45, 0.50, 0.55 for the monomer  = 0.30, 0.40, 0.45, 0.50 for the dimer Gilles Pieffet

36. Results Gilles Pieffet

37. Conclusions no simple mutations when it comes to proteins sampling on a multi ns timescale needed to get convergence due to protein fluctuations. Not possible to tell if sampling/force field/structural problems. Gilles Pieffet

38. Incorporating the effect of ionic strength in free-energy calculations using explicit ions Serena Donnini and Alessandra Villa Different protocols: ignore ions (ions independent, water high dielectric) neutralize the system (neutral system is more natural) add lots of ions Also:physiological ionic strength 0.1-0.2 molar. different claims concerning the creation of a net charge (create counter charge?) Generally ambiguous. Why worry?

39. Incorporation of explicit ions in free energy calculations Serena Donnini and Alessandra Villa Cancellation of effects within a thermodynamic cycle? Protein charge = +2 Ligand charge = -2 Should one incorporate ions in the unlighted state? Will effects cancel?

40. Consider a very simple mutation: 1.Only a change in dipole. 2.No change in number or atoms or net charge 3.Atoms partly buried. Serena Donnini and Alessandra Villa Incorporation of explicit ions in free energy calculations Consider the same mutation in: 1. a charged molecule. 2. a neutral molecule Ionic environment 1.no ions 2.just enough to neutralize charged system 3.0.04M ionic strength 4.0.1M ionic strength 5.0.2 M ionic strength Thermodynamic integration 18 values simulate at fixed integrate numerically

41. Serena Donnini and Alessandra Villa Mutation of 2-phosphoglycolic acid (PGA) to 3-phosphonopropanoic acid (3PP) (triosephosphate isomerase inhibitors) pH ~7.0 pH ~2.0

42. Bonded parameters Mutation 2-phosphoglycolic acid (PGA) to 3-phosphonopropanoic acid (3PP)

43. Serena Donnini and Alessandra Villa charged form 2 - some difference to neutral neutral form not much effect What did I expect? + 2 Na + similar to neutral form more ions less effect + +

44. Internal terms irrelevant Reaction field of the solvent

45. Free energies are in kJ mol -1. Ionic strengths are in M. Uncharged SpeciesCharged Species Ionic Strength Serena Donnini and Alessandra Villa Incorporation of explicit ions in free energy calculations Slight trend

46. Charged Species Uncharged Species Serena Donnini and Alessandra Villa 200 ps sampling at each value 200 ps sampling at each value

47. Serena Donnini and Alessandra Villa Incorporation of explicit ions in free energy calculations No. of ions > 1 in close proximity negligible effect.

48. Serena Donnini and Alessandra Villa Incorporation of explicit ions in free energy calculations

49. Serena Donnini and Alessandra Villa Average lifetime each ion ~ 7ns need 100’s ns at each lambda value Incorporation of explicit ions in free energy calculations no ions in close proximity minimum distance closest ion

50. Conclusions Experimentally the effect of the ionic strength on free energy differences is not expected to be very large. Close proximity of ions has major effect even for mutations that do not involve change in net charge. Inclusion of explicit ions can lead to severe sampling problems. Options: 1.No inclusion of ions and accept errors associated with an overall charged system. 2.Perform simulations at high ionic strength to ensure sampling of ionic distribution.

51. Calculating free energies from non-equilibrium work?

52. Free Energy Calculations for Dummies Two methods to estimate the difference in free energy between two states of a system A and B. free energy = work to go from A to B via a reversible path Method 1. Method 2. free energy = -kT ln [equilibrium probability (partition) function]

53. Method 1. Reversible work work = force x distance force = derivative of a potential w.r.t. coordinate average force w.r.t. arbitrary coordinate thermodynamic integration equilibrium ensemble

54. Method 2. Probability function + Relative probability of finding the system in 1 of 2 states. Perturbation Formula for an equilibrium ensemble

55. Non-Equilibrium Simulation If not in equilibrium do work against the environment -> overestimate free energy In a dissipative system w A->B   F A->B But now I am told No need to worry about intermediate states no need to worry about equilibrium Does not fit to either of the two general methods Has been described as “remarkable”, “amazing”, “unexpected”. Can I think of a trivial test case to convince myself it must be correct?

56. Grow Particle Work to slowly grow particle System in always in equilibrium

57. Particle Insertion Energy of adding a particle weighted by probability of finding an appropriate location. (in an equilibrium ensemble) works well in low density systems but.....

58. ... also works in principle for a ship in the ocean

59. Particle deletion Can not have sampled states appropriate to the ensemble were there is no particle If particle insertion is good for low density systems when does particle deletion work? NEVER for systems with excluded volume

60. ... also fails boat test. water and boat cannot occupy the same space at the same time.

61. A B  G A->B = 0 Move particle from location A to location B in box of water. Very simple test case for non-equilibrium pulling in a dissipative environment.

62. A B  G A->B = 0 Move particle from A to B Method 1. Reversible work a.Very slowly pull particle from A to B (system always in equilibrium). b.Determine average force. x trivial

63. A B  G A->B = 0 Move particle from A to B Method 2. Probability function a.Particle insertion at A and particle insertion at B b.Probability of finding particle at A or B x trivial

64. A B  G A->B = 0 Move particle from A to B Non-equilibrium pulling x many paths w > 0 some paths w = 0 must find paths for which w < 0 longer the path faster I pull more likely w > 0 must find path with w <<0

65. A B  G A->B = 0 Move particle from A to B Non-equilibrium pulling x What about instantaneous move (passing through intermediates) Doesn't work particle deletion at A particle insertion at B average never converges

66. A B  G A->B = 0 Move particle from A to B Non-equilibrium pulling x Do any paths give w = 0 Yes but rare

67. A B  G A->B = 0 Move particle from A to B Non-equilibrium pulling x Which if any paths give w < 0 Particle must be pushed from A to B by the environment

68. The boat test If I pull my boat from A to B often enough one day the ocean will feel sorry for me and push me for free. I gain energy and disprove the 2nd law of thermodynamics.

69. What to do In a dissipative system w A->B   F A->B is heavily weighted towards the lowest value of w A->B However the best estimate of  F A->B (excluding statistical fluctuations) is simply the lowest value rather than the exponential average.

71. Round Table 2: When are free energy calculations useful? 1.For academia 2. Industry (drug design, prediction of properties) I am only ever interested in things that don’t work Computational methods only have to be fast when they do not really work Fast free energy methods? Extrapolation approaches?

72. Force field Gromos 43a2 Villa et al. J.Comp.Chem. (2002) 23 p.548 For other force fields see: J.Comp.Chem. (2003) 24 p 1930 J.Chem. Phys. (2003) 119 p. 5740 Parameterization of force fields

75. Trp

76. Explaining things in detail: Binding Benzamidine inhibitors to trypsin

78. Actually we do well 1.Vijay is doing free energy calculations as I would like to do. (except for using perturbation approaches) 2. Conformational preferences of peptides. 3. Prediction of binding conformations of ligands. (first step toward predicting energies) Recurring trends