Related papers: Free-Energy Calculations in Protein Folding by Gen…
The proposed method of the free energy calculation is based on the approximation of the energy distribution in the microcanonical ensemble by the Gaussian distribution. We hope that our approach will be effective for the systems with…
Algorithms for simulating complex physical systems or solving difficult optimization problems often resort to an annealing process. Rather than simulating the system at the temperature of interest, an annealing algorithm starts at a…
A simple, efficient, and accurate method is proposed to map multi-dimensional free energy landscapes. The method combines the temperature-accelerated molecular dynamics (TAMD) proposed in [Maragliano & Vanden-Eijnden, Chem. Phys. Lett. 426,…
In this article the configurational space of two simple protein models consisting of polymers composed of a periodic sequence of four different kinds of monomers is studied as a function of temperature. In the protein models, hydrogen bond…
The equilibrium free energy landscape of off-lattice model heteropolymers as a function of an internal coordinate, namely the end-to-end distance, is reconstructed from out-of-equilibrium steered molecular dynamics data. This task is…
Competing phases or interactions in complex many-particle systems can result in free energy barriers that strongly suppress thermal equilibration. Here we discuss how extended ensemble Monte Carlo simulations can be used to study the…
Parallel tempering, also known as replica exchange Monte Carlo, is studied in the context of two simple free energy landscapes. The first is a double well potential defined by two macrostates separated by a barrier. The second is a `golf…
We present a method for determining the free energy dependence on a selected number of collective variables using an adaptive bias. The formalism provides a unified description which has metadynamics and canonical sampling as limiting…
The importance-sampling Monte Carlo algorithm appears to be the universally optimal solution to the problem of sampling the state space of statistical mechanical systems according to the relative importance of configurations for the…
The finite element method is a well-established method for the numerical solution of partial differential equations (PDEs), both linear and nonlinear. However, the repeated reassemblage of finite element matrices for nonlinear PDEs is…
We calculate the free energy of the disordered urn model using the law of large numbers. It is revealed that the saddle point equation obtained by the usage of the law of large numbers is the same as that obtained by the replica method.…
A vast array of phenomena, ranging from chemical reactions to phase transformations, are analysed in terms of a free energy surface defined with respect to a single or multiple order parameters. Enhanced sampling methods are typically used,…
We apply a recently developed adaptive algorithm that systematically improves the efficiency of parallel tempering or replica exchange methods in the numerical simulation of small proteins. Feedback iterations allow us to identify an…
Model-based deep reinforcement learning has achieved success in various domains that require high sample efficiencies, such as Go and robotics. However, there are some remaining issues, such as planning efficient explorations to learn more…
We present a new method to compute free energies at a quantum mechanical (QM) level of theory from molecular simulations using cheap reference potential energy functions, such as force fields. To overcome the poor overlap between the…
Metropolis simulations of all-atom models of peptides (i.e. small proteins) are considered. Inspired by the funnel picture of Bryngelson and Wolyness, a transformation of the updating probabilities of the dihedral angles is defined, which…
We present an Adaptively Biased Molecular Dynamics (ABMD) method for the computation of the free energy surface of a reaction coordinate using non-equilibrium dynamics. The ABMD method belongs to the general category of umbrella sampling…
We propose a new generalized-ensemble algorithm, which we refer to as the multibaric-multithermal Monte Carlo method. The multibaric-multithermal Monte Carlo simulations perform random walks widely both in volume space and in potential…
We consider the statistical mechanics of a classical particle in a one-dimensional box subjected to a random potential which constitutes a Wiener process on the coordinate axis. The distribution of the free energy and all correlation…
Because of their multimodality, mixture posterior distributions are difficult to sample with standard Markov chain Monte Carlo (MCMC) methods. We propose a strategy to enhance the sampling of MCMC in this context, using a biasing procedure…