Locally weighted histogram analysis and stochastic solution for large-scale multi-state free energy estimation

Area of Science:

• Computational Chemistry
• Statistical Mechanics
• Biophysics

Background:

• The weighted histogram analysis method (WHAM) is crucial for calculating free energies and expectations from multiple ensembles in chemistry and physics.
• Standard WHAM becomes computationally infeasible with hundreds of distributions due to its high cost.

Purpose of the Study:

• To develop a computationally efficient alternative to standard WHAM for large datasets.
• To introduce local WHAM and an adaptive stochastic procedure for faster and accurate free energy estimation.

Main Methods:

• Developed local WHAM from a simulations of simulations (SOS) perspective using generalized serial tempering (GST).
• Implemented an adaptive SOS procedure for stochastic solution of local WHAM equations with multiple jump attempts.
• Applied methods to estimate binding free energies and distributions using replica exchange molecular dynamics simulations.

Main Results:

• Local WHAM, with one jump attempt per GST cycle, solves equations orders of magnitude faster than global WHAM with similar accuracy.
• The adaptive SOS procedure yields more accurate equilibrium distributions than local WHAM with a single jump attempt.
• Accurate results were obtained even from limited, non-fully equilibrated simulations, demonstrating broad applicability.

Conclusions:

• Local WHAM offers a significant computational advantage for handling large datasets in free energy calculations.
• The proposed methods are broadly applicable to data from various sampling algorithms, including tempering methods.
• Accurate free energy estimates are achievable even with limited simulation sampling.