Abstract
We introduce the UWHAM (binless weighted histogram analysis method) and SWHAM (stochastic UWHAM) software package that can be used to estimate the density of states and free energy differences based on the data generated by multi-state simulations. The programs used to solve the UWHAM equations are written in the C++ language and operated via the command line interface. In this paper, first we review the theoretical bases of UWHAM, its stochastic solver RE-SWHAM (replica exchange-like SWHAM)and ST-SWHAM (serial tempering-like SWHAM). Then we provide a tutorial with examples that explains how to apply the UWHAM program package to analyze the data generated by different types of multi-state simulations: umbrella sampling, replica exchange, free energy perturbation simulations, etc. The tutorial examples also show that the UWHAM equations can be solved stochastically by applying the RE-SWHAM and ST-SWHAM programs when the data ensemble is large. If the simulations at some states are far from equilibrium, the Stratified RE-SWHAM program can be applied to obtain the equilibrium distribution of the state of interest. All the source codes and the tutorial examples are available from our group’s web page: https://ronlevygroup.cst.temple.edu/software/UWHAM_and_SWHAM_webpage/index.html.
Highlights
The weighted histogram analysis method (WHAM) algorithm[1,2] is widely applied to estimate the density of states and free energy differences based on the data generated by multi-state simulations
To further remove the computational bottleneck in scaling up UWHAM, we developed methods called stochastic UWHAM (SWHAM) which solve the UWHAM equations stochastically by using generalized ensemble algorithms to resample the data collected at multiple states[21,22]
When the data ensemble is large, we show that the multi-state free energies can be obtained directly by running serial tempering-like SWHAM (ST-SWHAM), which resamples the raw data by applying the serial tempering (ST) protocol; the multi-state distributions can be obtained directly by running replica exchange-like SWHAM (RE-SWHAM), which resamples the raw data by applying the replica exchange (RE) protocol
Summary
We introduce the UWHAM (binless weighted histogram analysis method) and SWHAM (stochastic UWHAM) software package that can be used to estimate the density of states and free energy differences based on the data generated by multi-state simulations. We provide a tutorial with examples that explains how to apply the UWHAM program package to analyze the data generated by different types of multi-state simulations: umbrella sampling, replica exchange, free energy perturbation simulations, etc. The weighted histogram analysis method (WHAM) algorithm[1,2] is widely applied to estimate the density of states and free energy differences based on the data generated by multi-state simulations. To further remove the computational bottleneck in scaling up UWHAM, we developed methods called stochastic UWHAM (SWHAM) which solve the UWHAM equations stochastically by using generalized ensemble algorithms to resample the data collected at multiple states[21,22]. We introduce the tutorial examples on the web page of the UWHAM and SWHAM software package
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