Generalized ensemble simulation

Yoda T, Sugita Y, Okamoto Y (2004) Secondary-structure preferences of force fields for proteins evaluated by generalized-ensemble simulations. Chem Phys 307 269... 

Keywords alchemical free energy simulation combined quantum mechanical/ molecular mechanical potential generalized ensemble simulation conformational sampling long-range electrostatic interaction... 

Sugita, Y. (2009). Free-energy landscapes of proteins in solution by generalized-ensemble simulations. Frontiers in Bioscience, 14,1292. 

Bitetti-Putzer, R. Yang, W. Karplus, M., Generalized ensembles serve to improve the convergence of free energy simulations, Chem. Phys. Lett. 2003, 377, 633-641... 

Andricioaei, I. Straub, J.E. Karplus, M., Simulation of quantum systems using path integrals in a generalized ensemble, Chem. Phys. Lett. 2001, 346, 274—282... 

Mitsutake, A. Sugita, Y. Okamoto, Y., Generalized-ensemble algorithms for molecular simulations of biopolymers, Biopolymers 2001, 60, 96-123... 

Having specified the interactions (i.e., the model of the system), the actual simulation then constructs a sequence of states (or the system trajectory) in some statistical mechanical ensemble. Simulations can be stochastic (Monte Carlo (MC)) or deterministic (MD), or they can combine elements of both, such as force-biased MC, Brownian dynamics, or generalized Lan-gevin dynamics. It is usually assumed that the laws of classical mechanics (i.e., Newton s second law) may adequately describe the atoms and molecules in the physical system. 

The molecular simulations in this generalized ensemble perform random walks both in the potential energy space and in the volume space. 

We now present some of the simulation results by the generalized-ensemble algorithms that were described in the previous section. 

In this article, we have reviewed some of powerful generalized-ensemble algorithms for both Monte Carlo simulations and molecular dynamics simulations. A simulation in generalized ensemble realizes a random walk in potential energy space, alleviating the multiple-minima problem that is a common difficulty in simulations of complex systems with many degrees of freedom. 

An optimal choice of weights can be found by measuring the local dif-fusivity of a random walk along the reaction coordinates and applying the feedback method to shift weight towards the bottlenecks in the simulation. This generalized ensemble optimization approach has recently been illustrated for the simulation of dense Lennard-Jones fluids close to the vapor-liquid equilibrium [21]. The interaction between particles in the fluid is described by a... 

In this section we will present generalizations of extended ensemble simulations to world line quantum Monte Carlo simulations, in particular ... 

Another advantage of extended ensemble simulations is the ability to directly calculate the density of states and from it thermodynamic properties such as the entropy or the free energy that are not directly accessible in canonical simulations. In the following we will again use quantum magnets as concrete examples. A generalization to bosonic and fermionic models will always be straightforward. 

The first-order generalized ensemble-based QM/MM AFE simulations... 

Okamoto, Y. Generalized-ensemble algorithms Enhanced sampling techniques for Monte Carlo and molecular dynamics simulations. J. Mol. Graph. Model. 2004, 22, 425-39. 

Hyperparallel tempering simulations are conducted on a composite ensemble, which consists of M, noninteracting replicas of the above-mentioned generalized ensemble. Each replica can have a different set of generalized potentials. The complete state of the composite ensemble is specified through X = (xi, X2,..., XmY, where x, denotes the state of the ith replica. The partition function of the composite ensemble is given by... 

Grand-canonical simulations are somewhat more cumbersome to use than canonical or isothermal-isobaric ensemble simulations. Their implementation often requires exploratory work, because it is generally easier to anticipate or specify the density, pressure or composition of a system (one usually has some reference or an intuitive feeling about such properties), rather than its chemical potentials. 

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