Driven Adaptive-Bias Scheme: A Hybrid Free Energy Method for Biomolecular Systems with Complex Energy Landscapes

Abstract

We present a hybrid free energy calculation method that integrates two distinct classes of nonequilibrium sampling techniques, namely, driven and adaptive-bias molecular dynamics (MD) methods. We design a biasing protocol with an explicitly time- and history-dependent bias that uses on-the-fly work measurements to gradually flatten the free-energy surface. The scheme is general in that any variation of driven MD, e.g., steered MD (SMD) or targeted MD (TMD), can be integrated into any variation of adaptive-bias MD, e.g., metadynamics (MetaD) or adaptive biasing force (ABF). Two variations will be discussed in particular: (i) driven metadynamics (D-MetaD) and (ii) driven ABF (D-ABF) that use history-dependent biasing potential and force, respectively, in order to adaptively bias the system towards a flattened free energy landscape. The asymptotic convergence of both D-MetaD and D-ABF methods is discussed in the context of nonequilibrium work relations such as Jarzynski and Hummer-Szabo relations. We show that the adaptive term of the bias in both D-MetaD and D-ABF methods converges to the same stationary state as in their non-driven counterparts, if the convergence is reached. Employing nonequilibrium work relations, a method is proposed for accurate free energy reconstruction and error estimation. Several prototypical examples including polyalanine and polyproline peptides are used to numerically illustrate the superior efficiency and faster convergence of the method compared with its adaptive-bias and driven components in isolation. We show that driven adaptive-bias scheme is particularly useful to study systems with complex free energy landscapes such as those with multiple high free energy barriers in which non-driven adaptive-bias methods fail to converge in an achievable timescale. A publication introducing D-MetaD method recently appeared in J. Phys. Chem. Lett. (JPCL 4:1882, 2013).