Implementation of Telescoping Boxes in Adaptive Steered Molecular Dynamics

Abstract

Long-time dynamical processes, such as those involving protein unfolding and ligand interactions, can be accelerated and realized through steered molecular dynamics (SMD). The challenge has been the extraction of information from such simulations that generalize for complex nonequilibrium processes. The use of Jarzynski’s equality opened the possibility of determining the free energy along the steered coordinate, but sampling over the nonequilibrium trajectories is slow to converge. Adaptive steered molecular dynamics (ASMD) and other related techniques have been introduced to overcome this challenge through the use of stages. Here, we take advantage of these stages to address the numerical cost that arises from the required use of very large solvent boxes. We introduce telescoping box schemes within adaptive steered molecular dynamics (ASMD) in which we adjust the solvent box between stages and thereby vary (and optimize) the required number of solvent molecules. We have benchmarked the method on a relatively long α-helical peptide, Ala30, with respect to the potential of mean force and hydrogen bonds. We show that the use of telescoping boxes introduces little numerical error while significantly reducing the computational cost.

Telescoping-Solvation-Box Protocol-Based Umbrella Sampling Method for Potential Mean Force Estimation

“…The explicit water model contributes massively to the systems’ degrees of freedom. Additionally, the water box must be large enough to limit the boundary effects on the system . While the solvent-associated expensive computational cost can be somewhat mitigated through the usage of implicit and coarse-grained solvent models, it comes with a cost of reduced accuracy and loss of system details.…”

“…The primary advantage of TELUS and Block-TELUS protocols over the telescoping ASMD described in the original work is that these protocols can be applied to obtain PMF corresponding to non-distance-based collective variables like hydrophobic contacts between residues, α-helical content, and local bilayer thickness. , Although not tested here, a 2D TELUS and Block-TELUS protocol can be applied to estimate the free energy surfaces associated with the process of interest. For example, in the case of enhanced sampling of a molecule’s diffusion across a membrane, the 2D Block-TELUS protocol, with the molecule’s displacement normal to the membrane and hydrophobic contacts between molecule and lipid as collective variables, can be applied to get the translocation free energy surface, mitigating the errors associated with usage of 1D collective variable in membrane simulations. , …”

“…The primary advantage of TELUS and Block-TELUS protocols over the telescoping ASMD described in the original work 28 is that these protocols can be applied to obtain PMF corresponding to non-distance-based collective variables like hydrophobic contacts between residues, 64 α-helical content, 65 and local bilayer thickness. 66,67 Although not tested here, a 2D TELUS and Block-TELUS protocol can be applied to estimate the free energy surfaces associated with the process of interest.…”

“…This relaxation step removes extra energy added to the system during the steering process while performing no additional work. On that note, Zhuang et al 28 introduced the implementation of a telescoping solvation box along with naive ASMD. In this method, solvation box size was adjusted between the ASMD stages, hence requiring fewer solvent molecules in the initial stages of the helix−coil transition of polyalanine peptide test system, thereby reducing computational resources at the cost of little numerical errors.…”

Molecular Modelling of Ionic Liquids: Situations When Charge Scaling Seems Insufficient

“…The first one is grabbing initial configurations/seeds, and the second one is performing nonequilibrium pulling simulations initiated from these initial conditions. Although there are approximated techniques to improve the efficiency, e.g., eliminating the need for initial configurational sampling with some selection criterion [ 123 , 124 ], in order to make the current simulation protocol fully bias-free and as general as possible, we retained the ordinary fast-switching protocol. Thus, equilibrium sampling at the solute–solvent decoupled state is performed to grab initial conditions, from which the unidirectional perturbation in the solute-creation direction is spawned.…”