平衡态与非平衡态分子溶剂化自由能的计算效率比较
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摘要
着眼于13个中性氨基酸侧链类似物在水中的溶剂化自由能的计算,来比较两种计算自由能的平衡态动力学模拟和非平衡态动力学模拟方法在高性能计算机上的表现.研究发现,利用非平衡态动力学模拟来计算自由能除了在准确度上和平衡态动力学模拟的计算一致之外,在计算效率和实际所需时间上,非平衡方法计算效率更高,实际所需时间更少.
In this study, we used calculations to determine the solvation free energies of 13 side chain analogs of neutral amino acids in water to compare the performance of equilibrium and nonequilibrium molecular dynamic simulations on high-performance computers. We found that nonequilibrium molecular dynamic simulations have the same accuracy as equilibrium molecular dynamic simulations in calculations for solvation free energies. From the perspective of efficiency and computational cost, the nonequilibrium method is more efficient and requires less computational time.
In this study, we used calculations to determine the solvation free energies of 13 side chain analogs of neutral amino acids in water to compare the performance of equilibrium and nonequilibrium molecular dynamic simulations on high-performance computers. We found that nonequilibrium molecular dynamic simulations have the same accuracy as equilibrium molecular dynamic simulations in calculations for solvation free energies. From the perspective of efficiency and computational cost, the nonequilibrium method is more efficient and requires less computational time.
引文
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[2] HANSEN N, VAN GUNSTEREN W F. Practical aspects of free-energy calculations:A review[J]. J Chem Theory Comput, 2014, 10(7):2632-2647.
[3] WOLFENDEN R, ANDERSSON L, CULLIS P M, et al. Affinities of amino acid side chains for solvent water[J]. Biochemistry, 1981, 20(4):849-855.
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[9] WANG J M, WOLF R M, CALDWELL J W, et al. Development and testing of a general amber force field[J].J Comput Chem, 2004, 25:1157-1174.
[10] CASE D A, BERRYMAN J T, BETZ R M, et al. AMBER 2014[Z]. San Francisco:University of California,2014.
[11] ZWANZIG R W. High-temperature equation of state by a perturbation method. I. nonpolar gases[J]. J Chem Phys, 1954, 22(8):1420-1426.
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[13] BENNETT C H. Efficient estimation of free energy differences from monte carlo data[J]. J Comput Phys, 1976,22(2):245-268.
[14] SHIRTS M R, CHODREA J D. Statistically optimal analysis of samples from multiple equilibrium states[J]. J Chem Phys, 2008, 129(12):124105.
[15] PALIWAL H, SHIRTS M R. A benchmark test set for alchemical free energy transformations and its use to quantify error in common free energy methods[J]. J Chem Theory Comput, 2011, 7(12):4115-4134.
[16] BRUCKNER S, BORESCH S. Efficiency of alchemical free energy simulations. I. A practical comparison of the exponential formula, thermodynamic integration, and bennett's acceptance ratio method[J]. J Comput Chem,2011, 32(7):1303-1319.
[17] RUITER A, BORESCH S, OOSTENBRINK C. Comparison of thermodynamic integration and bennett acceptance ratio for calculating relative protein-ligand binding free energies[J]. J Comput Chem, 2013, 34(12):1024-1034.
[18] JARZYNSKI C. Nonequilibrium equality for free energy differences[J]. Phys Rev Lett, 1997, 78:2690-2693.
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[23] SHIRTS M R, BAIR E, HOOKER G, et al. Equilibrium free energies from nonequilibrium measurements using maximum-likelihood methods[J]. Phys Rev Lett, 2003, 91:140601.
[24] COSSINS B P, FOUCHER S, EDGE C M, et al. Assessment of nonequilibrium free energy methods[J]. J Phys Chem B, 2009, 113:5508-5519.
[25] GOETTE M, GRUBMULLER H. Accuracy and convergence of free energy differences calculated from nonequilibrium switching processes[J]. J Comput Chem, 2009, 30:447-456.
[26] JARZYNSKI C. Equilibrium free-energy differences from nonequilibrium measurements:A master-equation approach[J]. Phys Rev E, 1997, 56:5018-5035.
[27] HENDRIX D A, JARZYNSKI C. A fast growth method of computing free energy differences[J]. J Chem Phys,2001, 114:5974-5981.
[28] HUMMER G. Fast-growth thermodynamic integration:Error and efficiency analysis[J]. J Chem Phys, 2001,114:7330-7337.
[29] YTREBERG F M, ZUCKERMAN D M. Single-ensemble nonequilibrium path-sampling estimates of free energy differences[J]. J Chem Phys, 2004, 120:10876-10879.
[30] LECHNER W, OBERHOFER H, DELLAGO C, et al. Equilibrium free energies from fast-switching trajectories with large time steps[J]. J Chem Phys, 2006, 124:044113.
[31] BAYLY C I, CIEPLAK P, CORNELL W, et al. A well-behaved electrostatic potential based method using charge restraints for deriving atomic charges:The RESP model[J]. J Phys Chem, 1993, 97(40):10269-10280.
[32] FRISCH M J, TRUCKS G W, SCHLEGEL H B, et al. Gaussian 09, Revision B.01.[Z], Wallingford:Ganussian Inc, 2010.
[33] STEINBRECHER T, MOBLEY D L, CASE D A. Nonlinear scaling schemes for lennard-jones interactions in free energy calculations[J]. J Chem Phys, 2007, 127:214108.
[34] DARDEN T, YORK D, PEDERSEN L. Particle mesh ewald:An nlog(N)method for ewald sums in large systems[J]. J Chem Phys, 1993, 98:10089-10092.
[35] WENNMOHS F, SCHINDLER M. Development of a multipoint model for sulfur in proteins:A new parametrization scheme to reproduce high-level ab initio interaction energies[J]. J Comput Chem, 2005, 26(3):283-293.
[36] OLIVET A, VEGA L F. Optimized molecular force field for sulfur hexafluoride simulations[J]. J Chem Phys,2007, 126(14):144502.
[37] ZHANG X J, GONG Z, LI J, et al. Intermolecular sulfur... oxygen interactions:Theoretical and statistical investigations[J]. J Chem Inf Model, 2015, 55:2138-2153.
[38] WANG M T, LI P F, JIA X Y, et al. An efficient strategy for the calculations of solvation free energies in water and chloroform at quantum mechanical/molecular mechanical level[J]. J Chem Inf Model, 2017, 57:2476-2489.
[2] HANSEN N, VAN GUNSTEREN W F. Practical aspects of free-energy calculations:A review[J]. J Chem Theory Comput, 2014, 10(7):2632-2647.
[3] WOLFENDEN R, ANDERSSON L, CULLIS P M, et al. Affinities of amino acid side chains for solvent water[J]. Biochemistry, 1981, 20(4):849-855.
[4] RADZICKA A, WOLFENDEN R. Comparing the polarities of the amino acids:Side-chain distribution coefficients between the vapor phase, cyclohexane, 1-octanol and neutral aqueous solution[J]. Biochemistry, 1988,27(5):1664-1670.
[5]SHIRTS M R, PITERA J W, SWOPE W C, et al. extremely precise free energy calculations of amino acid side chain analogs:Comparison of common molecular mechanics force fields for proteins[J]. J Chem Phys, 2003,119(11):5740-5761.
[6] HESS B, NICO F A. Hydration thermodynamic properties of amino acid analogues:A systematic comparison of biomolecular force fields and water models[J]. J Phys Chem B, 2006, 110(35):17616-17626.
[7] VILLA A, MARK A E. Calculation of the free energy of solvation for neutral analogs of amino acid side chains[J]. J Comput Chem, 2002, 23(5):548-553.
[8] MACCALLUM J L, TIELEMAN D P. Calculation of the water-cyclohexane transfer free energies of neutral amino acid side-chain analogs using the all-atom force field[J]. J Comput Chem, 2003, 24(15):1930-1935.
[9] WANG J M, WOLF R M, CALDWELL J W, et al. Development and testing of a general amber force field[J].J Comput Chem, 2004, 25:1157-1174.
[10] CASE D A, BERRYMAN J T, BETZ R M, et al. AMBER 2014[Z]. San Francisco:University of California,2014.
[11] ZWANZIG R W. High-temperature equation of state by a perturbation method. I. nonpolar gases[J]. J Chem Phys, 1954, 22(8):1420-1426.
[12] KIRKWOOD J G. Statistical mechanics of fluid mixtures[J]. J Chem Phys, 1935, 3(5):300-313.
[13] BENNETT C H. Efficient estimation of free energy differences from monte carlo data[J]. J Comput Phys, 1976,22(2):245-268.
[14] SHIRTS M R, CHODREA J D. Statistically optimal analysis of samples from multiple equilibrium states[J]. J Chem Phys, 2008, 129(12):124105.
[15] PALIWAL H, SHIRTS M R. A benchmark test set for alchemical free energy transformations and its use to quantify error in common free energy methods[J]. J Chem Theory Comput, 2011, 7(12):4115-4134.
[16] BRUCKNER S, BORESCH S. Efficiency of alchemical free energy simulations. I. A practical comparison of the exponential formula, thermodynamic integration, and bennett's acceptance ratio method[J]. J Comput Chem,2011, 32(7):1303-1319.
[17] RUITER A, BORESCH S, OOSTENBRINK C. Comparison of thermodynamic integration and bennett acceptance ratio for calculating relative protein-ligand binding free energies[J]. J Comput Chem, 2013, 34(12):1024-1034.
[18] JARZYNSKI C. Nonequilibrium equality for free energy differences[J]. Phys Rev Lett, 1997, 78:2690-2693.
[19] CROOKS G. Nonequilibrium measurements of free energy differences for microscopically reversible markovian systems[J]. J Statis Phys, 1998, 90:1481-1487.
[20] CROOKS G. Entropy production fluctuation theorem and the nonequilibrium work relation for free energy differences[J]. Phys Rev E, 1999, 60:2721-2726.
[21] CROOKS G. Path-ensemble averages in systems driven far from equilibrium[J]. Phys Rev E, 1999, 61:2361-2726.
[22] JARZYNSKI C. Rare events and the convergence of exponentially averaged work values[J]. Phys Rev E, 2006,73:046105.
[23] SHIRTS M R, BAIR E, HOOKER G, et al. Equilibrium free energies from nonequilibrium measurements using maximum-likelihood methods[J]. Phys Rev Lett, 2003, 91:140601.
[24] COSSINS B P, FOUCHER S, EDGE C M, et al. Assessment of nonequilibrium free energy methods[J]. J Phys Chem B, 2009, 113:5508-5519.
[25] GOETTE M, GRUBMULLER H. Accuracy and convergence of free energy differences calculated from nonequilibrium switching processes[J]. J Comput Chem, 2009, 30:447-456.
[26] JARZYNSKI C. Equilibrium free-energy differences from nonequilibrium measurements:A master-equation approach[J]. Phys Rev E, 1997, 56:5018-5035.
[27] HENDRIX D A, JARZYNSKI C. A fast growth method of computing free energy differences[J]. J Chem Phys,2001, 114:5974-5981.
[28] HUMMER G. Fast-growth thermodynamic integration:Error and efficiency analysis[J]. J Chem Phys, 2001,114:7330-7337.
[29] YTREBERG F M, ZUCKERMAN D M. Single-ensemble nonequilibrium path-sampling estimates of free energy differences[J]. J Chem Phys, 2004, 120:10876-10879.
[30] LECHNER W, OBERHOFER H, DELLAGO C, et al. Equilibrium free energies from fast-switching trajectories with large time steps[J]. J Chem Phys, 2006, 124:044113.
[31] BAYLY C I, CIEPLAK P, CORNELL W, et al. A well-behaved electrostatic potential based method using charge restraints for deriving atomic charges:The RESP model[J]. J Phys Chem, 1993, 97(40):10269-10280.
[32] FRISCH M J, TRUCKS G W, SCHLEGEL H B, et al. Gaussian 09, Revision B.01.[Z], Wallingford:Ganussian Inc, 2010.
[33] STEINBRECHER T, MOBLEY D L, CASE D A. Nonlinear scaling schemes for lennard-jones interactions in free energy calculations[J]. J Chem Phys, 2007, 127:214108.
[34] DARDEN T, YORK D, PEDERSEN L. Particle mesh ewald:An nlog(N)method for ewald sums in large systems[J]. J Chem Phys, 1993, 98:10089-10092.
[35] WENNMOHS F, SCHINDLER M. Development of a multipoint model for sulfur in proteins:A new parametrization scheme to reproduce high-level ab initio interaction energies[J]. J Comput Chem, 2005, 26(3):283-293.
[36] OLIVET A, VEGA L F. Optimized molecular force field for sulfur hexafluoride simulations[J]. J Chem Phys,2007, 126(14):144502.
[37] ZHANG X J, GONG Z, LI J, et al. Intermolecular sulfur... oxygen interactions:Theoretical and statistical investigations[J]. J Chem Inf Model, 2015, 55:2138-2153.
[38] WANG M T, LI P F, JIA X Y, et al. An efficient strategy for the calculations of solvation free energies in water and chloroform at quantum mechanical/molecular mechanical level[J]. J Chem Inf Model, 2017, 57:2476-2489.