Small-sample limit of the Bennett acceptance ratio method and the variationally derived intermediates

Area of Science:

• Biophysics
• Condensed Matter Physics
• Computational Chemistry

Background:

• Free energy calculations offer microscopic insights into thermodynamic driving forces.
• Methods like Bennett acceptance ratio (BAR) and variationally derived intermediates (VI) are optimal for minimizing mean-squared error in free energy calculations.
• These optimal methods rely on approximations that fail with limited sample points.

Purpose of the Study:

• To analyze the performance of BAR and VI methods under conditions with very few sample points.
• To determine the conditions under which BAR and VI become suboptimal.
• To provide guidance on selecting appropriate estimators for free energy calculations.

Main Methods:

• Analysis of one-dimensional test systems.
• Evaluation of the Bennett acceptance ratio (BAR) and variationally derived intermediates (VI) methods.
• Investigation of the relationship between sample size, configuration space overlap, and method accuracy.

Main Results:

• Both BAR and VI methods are suboptimal when applied to very few sample points.
• Established uncertainty estimates for these methods are inaccurate in low-sample regimes.
• Variationally derived intermediates (VI) requires fewer than seven samples per state to become optimal.
• Bennett acceptance ratio (BAR) requires an increasing number of samples as the overlap between end states decreases, following an inverse power law.

Conclusions:

• The optimality of BAR and VI methods is contingent on sufficient sample size and system overlap.
• The number of samples required for BAR optimality is inversely proportional to the overlap of configuration space densities.
• These findings offer crucial guidance for selecting appropriate free energy calculation estimators based on system properties and available data.