Avoiding non-equilibrium effects in adaptive biasing force calculations

ABSTRACT

When using the adaptive biasing force (ABF) algorithm in free-energy calculations, unbiased sampling is performed across the transition coordinate to estimate the biasing force (F_bias). In practice, however, setting the number of molecular dynamics steps (N_samples) that precede the application of the time-dependent bias is arbitrary. In this paper, we find that N_samples has a significant effect on the outcome of the free-energy calculation. When N_samples is too small, marked non-equilibrium effects may occur, conducive to slow convergence, or possibly erroneous results. This phenomenon is observed in a variety of prototypical cases. Conversely, setting arbitrarily N_samples to an exaggeratedly large value implies extra computational efforts. To avoid possible non-equilibrium artifacts while maintaining computational effectiveness, we propose a reliable scheme to make an appropriate choice of N_samples in ABF-based free-energy calculations, resting on the evolution F_bias as a function of N_samples. Monitoring the latter, a value of N_samples that minimises the computational cost while guaranteeing convergence of F_bias can be determined. This method offers a safeguard for reliable free-energy calculations using ABF-based algorithms.

KEYWORDS:

• Free-energy calculations
• time-dependent bias
• non- equilibrium effects

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant number 21773125], the Natural Science Foundation of Tianjin, China [grant number 18JCYBJC20500], the Fundamental Research Funds for the Central Universities, Nankai University [grant number 63191743], the China Postdoctoral Science Foundation [grant number bs6619012], the Agence Nationale de la Recherche [grant ProteaseInAction].