Abstract
It has been shown that when using a Monte Carlo algorithm to estimate the electrostatic free energy of a biomolecule in a solution, individual random walks can become entrapped in the geometry. We examine a proposed solution, using a sharp restart during the Walk-on-Subdomains step, in more detail. We show that the point at which this solution introduces significant bias is related to properties intrinsic to the molecule being examined. We also examine two potential methods of generating a sharp restart point and show that they both cause no significant bias in the examined molecules and increase the stability of the run times of the individual walks.
References
[1] M. E. Davis and J. A. McCammon, Electrostatics in biomolecular structure and dynamics, Chem. Rev. 90 (1990), no. 3, 509–521. 10.1021/cr00101a005Search in Google Scholar
[2] M. O. Fenley, M. Mascagni, J. McClain, A. R. J. Silalahi and N. A. Simonov, Using correlated Monte Carlo sampling for efficiently solving the linearized Poisson–Boltzmann equation over a broad range of salt concentration, J. Chem. Theory Comput. 6 (2009), no. 1, 300–314. 10.1021/ct9003806Search in Google Scholar
[3] C. Fleming, M. Mascagni and N. Simonov, An efficient Monte Carlo approach for solving linear problems in biomolecular electrostatics, Computational Science–ICCS 2005, Springer, Berlin (2005), 760–765. 10.1007/11428862_103Search in Google Scholar
[4] F. Fogolari, P. Zuccato, G. Esposito and P. Viglino, Biomolecular electrostatics with the linearized Poisson–Boltzmann equation, Biophys. J. 76 (1999), no. 1, 1–16. 10.1016/S0006-3495(99)77173-0Search in Google Scholar
[5] P. Hamlin, W. J. Thrasher, W. Keyrouz and M. Mascagni, Geometry entrapment in walk-on-subdomains, Monte Carlo Methods Appl. 25 (2019), no. 4, 329–340. 10.1515/mcma-2019-2052Search in Google Scholar
[6] C.-O. Hwang, M. Mascagni and N. A. Simonov, Monte Carlo methods for the linearized Poisson–Boltzmann equation, Advances in Numerical Analysis, Nova Science, Hauppauge (2004). Search in Google Scholar
[7] B. Lu, Y. Zhou, M. J. Holst and J. A. McCammon, Recent progress in numerical methods for the Poisson–Boltzmann equation in biophysical applications, Commun. Comput. Phys. 3 (2008), no. 5, 973–1009. Search in Google Scholar
[8] T. Mackoy, R. C. Harris, J. Johnson, M. Mascagni and M. O. Fenley, Numerical optimization of a walk-on-spheres solver for the linear Poisson–Boltzmann equation, Commun. Comput. Phys. 13 (2013), no. 1, 195–206. 10.4208/cicp.220711.041011sSearch in Google Scholar
[9] M. Mascagni and N. A. Simonov, Monte Carlo method for calculating the electrostatic energy of a molecule, Computational Science—ICCS 2003. Part I, Lecture Notes in Comput. Sci. 2657, Springer, Berlin (2003), 63–72. 10.1007/3-540-44860-8_7Search in Google Scholar
[10] M. Mascagni and N. A. Simonov, Monte Carlo methods for calculating some physical properties of large molecules, SIAM J. Sci. Comput. 26 (2004), no. 1, 339–357. 10.1137/S1064827503422221Search in Google Scholar
[11] A. Pal and S. Reuveni, First passage under restart, Phys. Rev. Lett. 118 (2017), no. 3, Article ID 030603. 10.1103/PhysRevLett.118.030603Search in Google Scholar PubMed
[12] E. W. Weisstein, Sphere–sphere intersection. From MathWorld—A Wolfram Web Resource, http://mathworld.wolfram.com/Sphere-SphereIntersection.html, Last visited on 9/8/2019. Search in Google Scholar
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