Of fishes and birthdays: Efficient estimation of polymer configurational entropies

TL;DR

This paper introduces an efficient algorithm for estimating the configurational entropy of polymers using coincidence statistics, reducing the sample size needed compared to traditional methods, thus enabling more accurate protein free energy calculations.

Contribution

The paper presents a novel entropy estimation algorithm based on coincidence counting and energy partitioning, significantly reducing sample requirements for accurate results.

Findings

Requires approximately the square root of 2^S samples, unlike traditional methods needing 2^S.

Reduces bias in entropy estimation through energy-based grouping.

Applicable to protein free energy estimation with improved efficiency.

Abstract

We present an algorithm to estimate the configurational entropy $S$ of a polymer. The algorithm uses the statistics of coincidences among random samples of configurations and is related to the catch-tag-release method for estimation of population sizes, and to the classic "birthday paradox". Bias in the entropy estimation is decreased by grouping configurations in nearly equiprobable partitions based on their energies, and estimating entropies separately within each partition. Whereas most entropy estimation algorithms require $N\sim 2^{S}$ samples to achieve small bias, our approach typically needs only $N\sim \sqrt{2^{S}}$. Thus the algorithm can be applied to estimate protein free energies with increased accuracy and decreased computational cost.