The Extended Generalized Adaptive Biasing Force Algorithm for Multidimensional Free-Energy Calculations

Free-energy calculations in multiple
dimensions constitute a challenging
problem, owing to the significant computational cost incurred to achieve
ergodic sampling. The generalized adaptive biasing force (gABF) algorithm
calculates n one-dimensional lists of biasing forces
to approximate the n-dimensional matrix by ignoring
the coupling terms ordinarily taken into account in classical ABF
simulations, thereby greatly accelerating sampling in the multidimensional
space. This approximation may however occasionally lead to poor, incomplete
exploration of the conformational space compared to classical ABF,
especially when the selected coarse variables are strongly coupled.
It has been found that introducing extended potentials coupled to
the coarse variables of interest can virtually eliminate this shortcoming,
and, thus, improve the efficiency of gABF simulations. In the present
contribution, we propose a new free-energy method, coined extended
generalized ABF (egABF), combining gABF with an extended Lagrangian
strategy. The results for three illustrative examples indicate that
(i) egABF can explore the transition coordinate much more efficiently
compared with classical ABF, eABF, and gABF, in both simple and complex
cases and (ii) egABF can achieve a higher accuracy than gABF, with
a root mean-squared deviation between egABF and eABF free-energy profiles
on the order of kBT.
Furthermore, the new egABF algorithm outruns the previous ABF-based
algorithms in high-dimensional free-energy calculations and, hence,
represents a powerful importance-sampling alternative for the investigation
of complex chemical and biological processes.