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40212-GB6
Entropy-Enthalpy Contributions to Solvation Using Parallel Tempering Monte Carlo Methods
Free energy calculations using free energy perturbation or thermodynamic integration is a very powerful tool for a wide variety of applications. Much of the work in our group concerns calculating free energies for a range of temperatures from which we can determine entropy, enthalpy, and heat capacity changes. Calculating free energies are more computationally demanding than typical computer simulations, requiring fairly extensive sampling.(1) The requirements of extensive sampling and sampling over a range of temperatures make free energy calculations an ideal application for replica exchange, or parallel tempering.(2, 3) Replica exchange molecular dynamics (REMD) improves sampling efficiency by running several identical replicas of the system at different temperatures. Each replica is simulated with conventional molecular dynamics or Monte Carlo, and in addition to the local sampling of phase space, global moves are attempted which involve exchanges between replicas. The inclusion of configurations from the high temperature replicas allows the system to cross over energy barriers that would be too high for the system at the lower temperature. The combination of free energy calculations with REMD would increase sampling efficiency while simultaneously finding the free energy values at all temperatures. Additionally, averages at a particular temperature can be enhanced by using data from other temperatures using the weighted histogram analysis method (WHAM).(4, 5)
We modified our computer programs to include REMD and performed some calculations to test the method. Initial calculations were then performed for two prototype systems, the solvation free energies of methane and of butane in water.(6) These initial calculations were done using REMD with three system replicas at different temperatures (283, 298, and 313 K). This temperature range is often used in standard free energy calculations in order to find the entropy change from the temperature dependence of ?G. The initial results found that the REMD method led to free energies with smaller error bars. The following figures compare the error estimates for ?G at 298 K using the REMD method with the standard method, both with and without using WHAM to combine data at different temperatures. REMD consistently gives smaller error bars for a method that, if the additional temperatures would have been simulated anyway, is no more computationally expensive than running three independent simulations. To get comparably small error bars with conventional methods would require simulations roughly twice as long as using REMD.(6)
A focus of the research in our group involves free energy calculations for proteins, similar in method to those presented in Figure 1, but much larger in size.(7) The efficiency of RE drops significantly as the system size grows and the size of the systems we want to study are beyond what can be done in conventional RE. To surmount this problem, we developed a new RE method.(8) This method is about a factor of ten times more efficient than conventional RE. During the final year of the grant period (2006-2007), the grant was used to support two students. One student, Hongtao Yu, in his first year of the PhD program at UNO, began to study the free energy of water in polar and nonpolar environments, using our new RE method. A second student was supported for a summer prior to beginning her graduate work at UNO. This student, Alexis Lee, worked to add the new RE method to the commonly used program Amber in order to study conformational changes in polypeptides. This work all grew out of this PRF grant, which spurred the group's first work in RE making us aware of first the great utility of the method but also its limitations, which in turn inspired us to improve the method.
1. Shirts, M. R., Pitera, J. W., Swope, W. C., and Pande, V. S. (2003) J. Chem. Phys. 119, 5740-5761.
2. Geyer, C. J. (1991) in Computing Science and Statistics: Proceedings of the 23rd Symposium on the Interface pp p. 156, American Statistical Association, New York.
3. Marinari, E., and Parisi, G. (1992) Europhys. Lett. 19, 451.
4. Ferrenberg, A. M., and Swendsen, R. H. (1989) Physical Review Letters 63, 1195-1198.
5. Kumar, S., Bouzida, D., Swendsen, R. H., Kollman, P. A., and Rosenberg, J. M. (1992) J. Comp. Chem. 13, 1011-1021.
6. Rick, S. W. (2006) J. Chem. Theory Comp. 2, 939-946.
7. Olano, L. R., and Rick, S. W. (2004) J. Am. Chem. Soc. 126, 7991-8000.
8. Rick, S. W. (2007) J. Chem. Phys. 126, 054102.
