Extended Adaptive Biasing Force Algorithm. An On-the-Fly Implementation for Accurate Free-Energy Calculations

Proper use of the adaptive biasing
force (ABF) algorithm in free-energy
calculations needs certain prerequisites to be met, namely, that the
Jacobian for the metric transformation and its first derivative be
available and the coarse variables be independent and fully decoupled
from any holonomic constraint or geometric restraint, thereby limiting
singularly the field of application of the approach. The extended
ABF (eABF) algorithm circumvents these intrinsic limitations by applying
the time-dependent bias onto a fictitious particle coupled to the
coarse variable of interest by means of a stiff spring. However, with
the current implementation of eABF in the popular molecular dynamics
engine NAMD, a trajectory-based post-treatment is necessary to derive
the underlying free-energy change. Usually, such a posthoc analysis
leads to a decrease in the reliability of the free-energy estimates
due to the inevitable loss of information, as well as to a drop in
efficiency, which stems from substantial read-write accesses to file
systems. We have developed a user-friendly, on-the-fly code for performing
eABF simulations within NAMD. In the present contribution, this code
is probed in eight illustrative examples. The performance of the algorithm
is compared with traditional ABF, on the one hand, and the original
eABF implementation combined with a posthoc analysis, on the other
hand. Our results indicate that the on-the-fly eABF algorithm (i)
supplies the correct free-energy landscape in those critical cases
where the coarse variables at play are coupled to either each other
or to geometric restraints or holonomic constraints, (ii) greatly
improves the reliability of the free-energy change, compared to the
outcome of a posthoc analysis, and (iii) represents a negligible additional
computational effort compared to regular ABF. Moreover, in the proposed
implementation, guidelines for choosing two parameters of the eABF
algorithm, namely the stiffness of the spring and the mass of the
fictitious particles, are proposed. The present on-the-fly eABF implementation
can be viewed as the second generation of the ABF algorithm, expected
to be widely utilized in the theoretical investigation of recognition
and association phenomena relevant to physics, chemistry, and biology.