http://www.mmtsb.org/workshops/mmtsb-ctbp_workshop_2009/ReadingMaterials/chem_phys_lett_remd_paper.pdf

Replica-exchange molecular dynamics method for protein folding

https://arxiv.org/pdf/physics/9710041.pdf

Parallel tempering algorithm for conformational studies of biological molecules

http://www.cs.hunter.cuny.edu/~felisav/StochasticProcesses/Course_Material_files/BBG_jedc96.pdf

Monte Carlo methods for security pricing

We have developed a new simulation algorithm for free-energy calculations. The method is a multidimensional extension of the replica-exchange method. While pairs of replicas with different temperatures are exchanged during the simulation in the original replica-exchange method, pairs of replicas with different temperatures and/or different parameters of the potential energy are exchanged in the new algorithm. This greatly enhances the sampling of the conformational space and allows accurate calculations of free energy in a wide temperature range from a single simulation run, using the weighted histogram analysis method.

Multidimensional replica-exchange method for free-energy calculations

In complex systems with many degrees of freedom such as peptides and proteins, there exists a huge number of local-minimum-energy states. Conventional simulations in the canonical ensemble are of little use, because they tend to get trapped in states of these energy local minima. A simulation in generalized ensemble performs a random walk in potential energy space and can overcome this difficulty. From only one simulation run, one can obtain canonical-ensemble averages of physical quantities as functions of temperature by the single-histogram and/or multiple-histogram reweighting techniques. In this article we review uses of the generalized-ensemble algorithms in biomolecular systems. Three well-known methods, namely, multicanonical algorithm, simulated tempering, and replica-exchange method, are described first. Both Monte Carlo and molecular dynamics versions of the algorithms are given. We then present three new generalized-ensemble algorithms that combine the merits of the above methods. The effectiveness of the methods for molecular simulations in the protein folding problem is tested with short peptide systems. © 2001 John Wiley & Sons, Inc. Biopolymers (Pept Sci) 60: 96–123, 2001

https://www.tb.phys.nagoya-u.ac.jp/~okamoto/review/bp_review-01.pdf

Generalized-ensemble algorithms for molecular simulations of biopolymers.

We consider self-avoiding walks on the simple cubic lattice in which neighboring pairs of vertices of the walk (not connected by an edge) have an associated pair-wise additive energy. If the associated force is attractive, then the walk can collapse from a coil to a compact ball. We describe two Monte Carlo algorithms which we used to investigate this collapse process, and the properties of the walk as a function of the energy or temperature. We report results about the thermodynamic and configurational properties of the walks and estimate the location of the collapse transition.

Monte carlo study of the interacting self-avoiding walk model in three dimensions

1. Lattice models of linear and ring polymers 2. Lattice models of branched polymers 3. Interacting lattice clusters 4. Scaling, criticality and tricriticality 5. Directed lattice paths 6. Convex lattice vesicles and directed animals 7. Self-avoiding walks and polygons 8. Self-avoiding walks in slabs and wedges 9. Interaction models of self-avoiding walks 10. Adsorbing walks in the hexagonal lattice 11. Interacting models of animals, trees and networks 12. Interacting models of vesicles and surfaces 13. Monte Carlo methods for the self-avoiding walk

/pdf/the-statistical-mechanics-of-interacting-walks-polygons-b0xcalbdxj.pdf

The statistical mechanics of interacting walks, polygons, animals and vesicles

The sixth, seventh and eighth virial coefficients of hard discs and hard spheres are evaluated numerically (Monte Carlo integration) I improve on the best previous estimates for the seventh virial coefficients, and the integration of the eighth virial coefficient is new The best estimates for these coefficients for hard discs are B7 /b6 = 0114 86(7) and B8/b7 = 0065 14(8); and for hard spheres B7/b6 = 001307(7) and B8/b7 = 000432(10) b is the second virial coefficient in each case Pade approximations to the excess pressure and the excess free energy are computed from these results and compared to data otherwise obtained

https://iopscience.iop.org/article/10.1088/0305-4470/26/19/014/pdf

Virial coefficients for hard discs and hard spheres

We use Monte Carlo methods to investigate the asymptotic behaviour of the number and mean-square radius of gyration of polygons in the simple cubic lattice with fixed knot type. Let be the number of n-edge polygons of a fixed knot type in the cubic lattice, and let be the mean square radius of gyration of all the polygons counted by . If we assume that , where is the growth constant of polygons of knot type , and is the entropic exponent of polygons of knot type , then our numerical data are consistent with the relation , where is the unknot and is the number of prime factors of the knot . If we assume that , then our data are consistent with both and being independent of . These results support the claims made in Janse van Rensburg and Whittington (1991a 24 3935) and Orlandini et al (1996 29 L299, 1998 Topology and Geometry in Polymer Science (IMA Volumes in Mathematics and its Applications) (Berlin: Springer)).

Asymptotics of knotted lattice polygons

Self-avoiding walks on three-dimensional lattices are flexible linear objects which can be self-entangled. The authors discuss several ways to measure entanglement complexity for n-step walks, and prove that these complexity measures tend to infinity with n. For small n, they use Monte Carlo methods to estimate and compare the n-dependence of two of these complexity measures.

https://iopscience.iop.org/article/10.1088/0305-4470/25/24/010/pdf

E J Janse van Rensburg

Papers

Monte carlo study of the interacting self-avoiding walk model in three dimensions

The statistical mechanics of interacting walks, polygons, animals and vesicles

Virial coefficients for hard discs and hard spheres

Asymptotics of knotted lattice polygons

Entanglement complexity of self-avoiding walks