I F -E C NTRODUCTION TO REE NERGY ALCULATIONS I NTRODUCTION TO F -E C REE NERGY ALCULATIONS Chris Chipot Laboratoire International Associé CNRS-UIUC, Unité Mixte de Recherche n° 7565, Université de Lorraine Beckman Institute for Advanced Science and Technology, Department of Physics University of Illinois at Urbana-Champaign HANDS-ON WORKSHOP ON ENHANCED SAMPLING AND FREE-ENERGY CALCULATIONS NIH CENTER FOR MACROMOLECULAR MODELING & BIOINFORMATICS, URBANA, ILLINOIS, SEPTEMBER 2017 I F -E C O NTRODUCTION TO REE NERGY ALCULATIONS UTLINE I NTRODUCTION The race for longer and larger simulations What is the best method for a given problem? A - LCHEMICAL FREE ENERGY CALCULATIONS - A tool to address host-guest chemistry questions - Good practices, guidelines and recommendations G - EOMETRICAL FREE ENERGY CALCULATIONS - Potentials of mean force and transport phenomena - Potentials of mean force and recognition and association phenomena - What about non-equilibrium work computer experiments? HANDS-ON WORKSHOP ON ENHANCED SAMPLING AND FREE-ENERGY CALCULATIONS NIH CENTER FOR MACROMOLECULAR MODELING & BIOINFORMATICS, URBANA, ILLINOIS, SEPTEMBER 2017 I F -E C O NTRODUCTION TO REE NERGY ALCULATIONS UTLINE I NTRODUCTION The race for longer and larger simulations What is the best method for a given problem? A - LCHEMICAL FREE ENERGY CALCULATIONS - A tool to address host-guest chemistry questions - Good practices, guidelines and recommendations G - EOMETRICAL FREE ENERGY CALCULATIONS - Potentials of mean force and transport phenomena - Potentials of mean force and recognition and association phenomena - What about non-equilibrium work computer experiments? HANDS-ON WORKSHOP ON ENHANCED SAMPLING AND FREE-ENERGY CALCULATIONS NIH CENTER FOR MACROMOLECULAR MODELING & BIOINFORMATICS, URBANA, ILLINOIS, SEPTEMBER 2017 I F -E C I NTRODUCTION TO REE NERGY ALCULATIONS NTRODUCTION T HE RACE FOR LONGER AND LARGER SIMULATIONS First molecular dynamics simulation. Phase transition in model liquids. 2 d x i m = F i i dt2 8 @U (x) F = > < i � @x i > : A TURNING POINT IN COMPUTATIONAL STRUCTURAL BIOLOGY First molecular dynamics simulation applied to a small protein, BPTI, over 8 ps. Alder, B. J.; Wainwright, T. E. J. Chem. Phys., 1957, 27, 1208-1209 McCammon, J. A.; Gelin, B. R.; Karplus, M. Nature, 1977, 267, 585-590 HANDS-ON WORKSHOP ON ENHANCED SAMPLING AND FREE-ENERGY CALCULATIONS NIH CENTER FOR MACROMOLECULAR MODELING & BIOINFORMATICS, URBANA, ILLINOIS, SEPTEMBER 2017 I F -E C I NTRODUCTION TO REE NERGY ALCULATIONS NTRODUCTION T HE RACE FOR LONGER AND LARGER SIMULATIONS Brute-force simulations struggling to bridge the gap between time and size scales Free-energy calculations are computational tweezers to anatomize and explore relevant degrees of freedom 10-12 ps 103 1 1 gigaflop 104 10-9 ns 10-3 105 1 teraflop 10-6 µs 106 10-6 107 ms 10-3 100 teraflops 108 1 s 10-9 109 size time time 10 petaflops HANDS-ON WORKSHOP ON ENHANCED SAMPLING AND FREE-ENERGY CALCULATIONS NIH CENTER FOR MACROMOLECULAR MODELING & BIOINFORMATICS, URBANA, ILLINOIS, SEPTEMBER 2017 I F -E C I I NTRODUCTION TO REE NERGY ALCULATIONS NTRODUCTION NTRODUCTION W - ? HAT ARE FREE ENERGY CALCULATIONS COMMONLY USED FOR - protein-ligand binding - site-directed mutagenesis - protein-protein binding - partition coefficients Transport phenomena Recognition and association phenomena - permeabilities - activation barriers -structural modifications Conformational transitions HANDS-ON WORKSHOP ON ENHANCED SAMPLING AND FREE-ENERGY CALCULATIONS NIH CENTER FOR MACROMOLECULAR MODELING & BIOINFORMATICS, URBANA, ILLINOIS, SEPTEMBER 2017 I F -E C I NTRODUCTION TO REE NERGY ALCULATIONS NTRODUCTION W ? HAT IS THE BEST METHOD FOR A GIVEN PROBLEM Free-energy differences can be estimated computationally following four possible routes 1 (1) Methods based on histograms �A(⇠) = ln P (⇠) +� A 0 � � (2) Non-equilibrium work simulations exp( ��A) = exp( �w) � h � i exp( ��A) = exp( ��U ) (3) Perturbation theory 0 � h � i z dA(⇠) @U 1 @ ln J = | | (4) Measuring the derivative and integrating it d⇠ @⇠ � � @⇠ ⌧ �⇠ Zwanzig, R. W. J. Chem. Phys. 1954, 22, 1420-1426 Torrie, G. M.; Valleau, J. P. Chem. Phys. Lett. 1974, 28, 578-581 Pohorille, A.; Jarzynski, C.; Chipot, C. J. Phys. Chem. B 2010, 114, 10235-10253 Widom, B. J. Chem. Phys. 1963, 39, 2808-2812 Kirkwood, J. G. J. Chem. Phys. 1935, 3, 300-313 Isralewitz, B.; Gao, M.; Schulten, K. Curr. Opin. Struct. Biol. 2001, 11, 224-230 Carter, E. et al. Chem. Phys. Lett. 1989, 156, 472-477 Jarzynski, C. Phys. Rev. Lett. 1997, 78, 2690-2693 HANDS-ON WORKSHOP ON ENHANCED SAMPLING AND FREE-ENERGY CALCULATIONS NIH CENTER FOR MACROMOLECULAR MODELING & BIOINFORMATICS, URBANA, ILLINOIS, SEPTEMBER 2017 I F -E C I NTRODUCTION TO REE NERGY ALCULATIONS NTRODUCTION W ? HAT IS THE BEST METHOD FOR A GIVEN PROBLEM Nascent membrane proteins typically insert into the membrane via the Sec-translocon. Membrane insertion of arginine, for instance, requires 14–17 kcal/mol according to molecular dynamics simulations, but only 2–3 kcal/mol according to experiment. How does the translocon reduce the energetic cost and gain that accompanies insertion? Arg+ Leu ∆G Becker, T. et al. Science 2009, 326, 1369-1373 Dorairaj, S.; Allen, T. W. Proc. Natl. Acad. Sci. USA 2007, 104, 4943-4948 Hessa, T. et al. Nature 2007, 450, 1026-1030 Gumbart, J. C.; Chipot, C.; Schulten, K. Proc. Natl Acad. Sci. USA 2011, 108, 3596-3601 HANDS-ON WORKSHOP ON ENHANCED SAMPLING AND FREE-ENERGY CALCULATIONS NIH CENTER FOR MACROMOLECULAR MODELING & BIOINFORMATICS, URBANA, ILLINOIS, SEPTEMBER 2017 I F -E C I NTRODUCTION TO REE NERGY ALCULATIONS NTRODUCTION eABF gABF MtD F - REE ENERGY METHODS 2016 2011 US egABF ABF 2017 2004 TI / geometric eABF transformations Colvars 2000 2010 ABF FEP / WMA 2008 Hamiltonian MW/ABF hopping / FEP scripted FEP 2014 Chipot group 2009 variables 2001 2015 Roux group TI Fiorin / Hénin constant-pH MD 2007 Others 2016 HANDS-ON WORKSHOP ON ENHANCED SAMPLING AND FREE-ENERGY CALCULATIONS NIH CENTER FOR MACROMOLECULAR MODELING & BIOINFORMATICS, URBANA, ILLINOIS, SEPTEMBER 2017 I F -E C O NTRODUCTION TO REE NERGY ALCULATIONS UTLINE I NTRODUCTION The race for longer and larger simulations What is the best method for a given problem? A - LCHEMICAL FREE ENERGY CALCULATIONS - A tool to address host-guest chemistry questions - Good practices, guidelines and recommendations G - EOMETRICAL FREE ENERGY CALCULATIONS - Potentials of mean force and transport phenomena - Potentials of mean force and recognition and association phenomena - What about non-equilibrium work computer experiments? HANDS-ON WORKSHOP ON ENHANCED SAMPLING AND FREE-ENERGY CALCULATIONS NIH CENTER FOR MACROMOLECULAR MODELING & BIOINFORMATICS, URBANA, ILLINOIS, SEPTEMBER 2017