Abstract
Shadow Hybrid Monte Carlo (SHMC) is a new method for sampling the phase space of large biological molecules. It improves sampling by allowing larger time steps and system sizes in the molecular dynamics (MD) step of Hybrid Monte Carlo (HMC). This is achieved by sampling from high order approximations to the modified Hamiltonian, which is exactly integrated by a symplectic MD integrator. SHMC requires extra storage, modest computational overhead, and a reweighting step to obtain averages from the canonical ensemble. Numerical experiments are performed on biological molecules, ranging from a small peptide with 66 atoms to a large solvated protein with 14281 atoms. Experimentally, SHMC achieves an order magnitude speedup in sampling efficiency for medium sized proteins.
Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
References
Berne, B.J., Straub, J.E.: Novel methods of sampling phase space in the simulation of biological systems. Curr. Topics in Struct. Biol. 7, 181–189 (1997)
Leach, A.R.: Molecular Modelling: Principles and Applications. Addison-Wesley, Reading (1996)
Schlick, T.: Molecular Modeling and Simulation - An Interdisciplinary Guide. Springer, New York (2002)
Brass, A., Pendleton, B.J., Chen, Y., Robson, B.: Hybrid Monte Carlo simulations theory and initial comparison with molecular dynamics. Biopolymers 33, 1307–1315 (1993)
Sanz-Serna, J.M., Calvo, M.P.: Numerical Hamiltonian Problems. Chapman and Hall, London (1994)
Hockney, R.W., Eastwood, J.W.: Computer Simulation Using Particles. McGraw-Hill, New York (1981)
Duane, S., Kennedy, A.D., Pendleton, B.J., Roweth, D.: Hybrid Monte Carlo. Phys. Lett. B 195, 216–222 (1987)
Creutz, M.: Global Monte Carlo algorithms for many-fermion systems. Phys. Rev. D 38, 1228–1238 (1988)
Mehlig, B., Heermann, D.W., Forrest, B.M.: Hybrid Monte Carlo method for condensed-matter systems. Phys. Rev. B 45, 679–685 (1992)
Creutz, M., Gocksch, A.: Higher-order hybrid monte carlo algorithms. Phys. Rev. Lett. 63, 9–12 (1989)
Skeel, R.D., Hardy, D.J.: Practical construction of modified Hamiltonians. SIAM J. Sci. Comput. 23, 1172–1188 (2001)
Hairer, E., Lubich, C.: Asymptotic expansions and backward analysis for numerical integrators. In: Dynamics of Algorithms, New York. IMA Vol. Math. Appl., vol. 118, pp. 91–106. Springer, Heidelberg (2000)
Matthey, T., Cickovski, T., Hampton, S., Ko, A., Ma, Q., Slabach, T., Izaguirre, J.A.: ProtoMol: an object-oriented framework for prototyping novel algorithms for molecular dynamics. Submitted to ACM Trans. Math. Softw. (2003)
Kirchhoff, P.D., Bass, M.B., Hanks, B.A., Briggs, J., Collet, A., McCammon, J.A.: Structural fluctuations of a cryptophane host: A molecular dynamics simulation. J. Am. Chem. Soc. 118, 3237–3246 (1996)
Hampton, S.: Improved sampling of configuration space of biomolecules using shadow hybrid monte carlo. Master’s thesis, University of Notre Dame, Notre Dame, Indiana, USA (2004)
Neal, R.M.: An improved acceptance procedure for the hybrid Monte Carlo algorithm. J. Comput. Phys. 111, 194–203 (1994)
Lavenberg, S.S., Welch, P.D.: A perspective on the use of control variables to increase the efficiency of monte carlo simulations. Management Science 27, 322–335 (1981)
Schüette, C., Fischer, A., Huisinga, W., Deuflhard, P.: A direct approach to conformational dynamics based on hybrid Monte Carlo. J. Comput. Phys. 151, 146–168 (1999)
Schüette, C.: Conformational dynamics: Modelling, theory, algorithm, and application to biomolecules. Technical report, Konrad-Zuse-Zentrum für Informationstechnik Berlin, SC 99-18 (1999)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Hampton, S.S., Izaguirre, J.A. (2004). Improved Sampling for Biological Molecules Using Shadow Hybrid Monte Carlo. In: Bubak, M., van Albada, G.D., Sloot, P.M.A., Dongarra, J. (eds) Computational Science - ICCS 2004. ICCS 2004. Lecture Notes in Computer Science, vol 3037. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24687-9_34
Download citation
DOI: https://doi.org/10.1007/978-3-540-24687-9_34
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-22115-9
Online ISBN: 978-3-540-24687-9
eBook Packages: Springer Book Archive