Preserving the Boltzmann ensemble in replica-exchange molecular dynamics

Area of Science:

• Computational chemistry
• Statistical mechanics
• Biophysics

Background:

• Molecular dynamics (MD) simulations are crucial for studying biomolecular systems.
• Replica-exchange molecular dynamics (REMD) enhances sampling by running multiple simulations at different temperatures.
• The ergodicity of underlying MD integrators is critical for REMD accuracy.

Purpose of the Study:

• To analyze the convergence behavior of REMD simulations.
• To identify limitations of commonly used deterministic MD integrators within REMD.
• To propose a method for ensuring REMD ergodicity and accurate ensemble generation.

Main Methods:

• Analysis of numerical integrators for isothermal MD simulations.
• Assessment of ergodicity properties (measure invariance, irreducibility) of deterministic algorithms.
• Testing REMD performance on model systems: Gaussian distribution, bimodal distribution, and alanine dipeptide.

Main Results:

• Common deterministic MD algorithms used in constant-temperature simulations are not measure invariant or irreducible, thus not ergodic.
• REMD simulations employing these non-ergodic algorithms also fail to be ergodic.
• Significant errors in ensemble generation were observed for REMD simulations with these algorithms.
• Initial configurations with unfavorable energy may prevent systems from reaching the minimum energy configuration.

Conclusions:

• Standard deterministic integrators compromise the ergodicity of REMD, hindering accurate simulation of biomolecules.
• REMD simulations may fail to explore the entire configuration space or converge to the correct equilibrium Boltzmann ensemble.
• A stochastic hybrid Monte Carlo correction can be integrated to ensure REMD ergodicity and accurate sampling.