Free energy calculations with alchemlyb

Transcription

1 Free energy calculations with alchemlyb Oliver Beckstein Arizona State University SPIDAL Teleconference

2 Binding free energy measure of how strong a protein P and a ligand X stick together key quantity in quantitative mechanistic explanations of biological processes and in drug discovery free energy (i.e., averaged over all other degrees of freedom (such as solvent, protein motions, )) free energy difference exp[ A(T, V, N)/kT ] = dp 3N dx 3N e H(p,x)/kT ΔA = A bound A unbound ΔA = ln P + X ΔF PX dx3n exp[ U(x)/kT ] χ bound (x) dx 3N exp[ U(x)/kT ] χ unbound (x) H(p, x) = N i=1 p 2 i 2m i + U(x)

3 Alchemical free energy calculations force fields for H, molecular dynamics (MD) simulations for sampling free energy is a state function: generate non-physical paths between physical end states (bound/unbound) use stratification ( windows ) of path with parameter λ H(λ) = (1 λ)h bound + λh unbound, 0 λ 1 U Coulomb (x 1, x 2 ; λ) = 1 (1 λ)q 1 q 2 4πϵ 0 x 1 x 2 λ 3 λ 4 λ 2 λ 5 λ 6 λ 1 = 0 λ n = 1

4 Methods Free Energy Perturbation (FEP): Zwanzig FEP, BAR, MBAR (overlaps of distributions) ΔA = kt ln exp[ ΔU(x)/kT] 1, Thermodynamic Integration (TI): TI ΔA = 1 0 dλ H(λ) λ with ΔU(x) = U 1 (x) U 0 (x) exp( ΔA/kT ) = 1 + exp[(δu C)/kT ] exp[(δu C)/kT ] 1 1 exp( C/kT ) ΔA/kT = C/kT ln n 1 n 2 (MBAR is more complicated: uses overlaps between all windows) ΔU(x) = U λn+1 (x) U λn (x) λ FEP BAR TI C. Chipot and A. Pohorille, editors. Free energy calculations. Number 86 in Springer Series in Chemical Physics. Springer, Berlin, 2007.

5 Thermodynamic cycle for absolute binding free energy calculations appearance in solvent (no protein) decoupling from protein P + X ΔF PX MD simulations with multiple λ 5 50 λ-windows per free energy component 10 ns 250 ns per window D. L. Mobley, J. D. Chodera, and K. A. Dill. On the use of orientational restraints and symmetry corrections in alchemical free energy calculations. 125:084902, 2006.

6 Simulation output Per timestep FEP: ΔU ΔU λi,λ j j for window i TI: U/ λ But: different file formats for different codes (Gromacs, Amber, NAMD, ) solution: common interface via alchemlyb U(x; λ) λ λ i

7 alchemlyb O Beckstein (ASU), D Mobley (UC Irvine), M Shirts (U Colorado, Boulder) David Dotson (ASU), Dominik Wille (Freie Univ. Berlin) Silicon Therapeutics (STX) (Bryce Allen, Shuai Liu)

8 alchemlyb: basic idea data data data parse standard form (pandas DataFrame) preprocess standard form (pandas DataFrame) estimate ΔA ΔU λi,λ j j U(x; λ) λ λ i preprocessors slicing statistical inefficiency equilibrium detection estimators TI BAR MBAR

9 TI example

10

11

12 NapA elevator mechanism K305 D156 TM 5 T126:O TM 4 D157 Nature Struct. Mol. Biol., 23 (2016): ion binding in different states? dimer domain e. TM 5 D156 Inward-facing S4 A153:O [ need coordination image ] T126:O K305 TM 4 D157 Nature, 501 (2013): Na+ ion core domain

13 Absolute binding free energies: alchemistry Ion-in-solvent i. j. + alchemical binding pathway h. g. (analytic) f. equivalent e a. b. c. d. NapA complex Windowed alchemical free energy calculations (TI or MBAR) 150 ns 250 ns per lambda window (Coulomb/vdW decoupling) for windows ~8 µs (!) Position restraints (and analytical removal) Additional repulsive ion-ion potential to enforce one-ion occupancy (rigorously removed in calculation)

14 Amount of raw free energy data NapA FEP simulations (one free energy) windows time µs size GB total time µs total size (GB) VDW Coulomb repulsion restraint conformations: IF and OF (2) protonation states: 3 repeats: x2 (some) ~12 sets of simulations: ~2 TB (in ~130,000 files)

15 <latexit sha1_base64="0i1nre9o2xwd6b+g814wnznx2wk=">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</latexit> Absolute binding free energies: alchemistry DG 0 i = DG 0 protein+ion,i DG 0 hydration NapA IF D156 D157 K305 ΔG 0 (kj/mol) 103±1 H 44.6±0.9 H H 24.2±13.0 (not binding ignore state) Δ G (kj/mol) Convergence of ion hydration calculation coulomb vdw repulsion simulation time used (ns) Δ G (kj/mol) simulation time used (ns) Δ G (kj/mol) ion-ion simulation time used (ns) Na + ion in CHARMM TIP3P water ΔGhydration (kj/mol) Coulomb 382.7±0.2 VdW 8.81±0.05 repulsion 0.258±0.005 restraint total 392.0±0.2

16 Convergence of protein ion calculations ion-ion Coulomb H χ 180º χ 90º all kj/mol restraint kj/mol D156 D157 K305 repulsion Very slow convergence of Coulomb Slow degrees of freedom (e.g., D157 χ1 dihedral) Time (ns) χ1 Time (ns) Na+ D157

17 Challenge data analysis is cumbersome and slow(ish), even with dask on a 6 core workstation (hours) on-demand analysis with all current data/while new data is coming in? run on HPC system (e.g. XSEDE PSC Bridges)?