Abstract
We investigated the dissociation process of tri-N-acetyl-d-glucosamine from hen egg white lysozyme using parallel cascade selection molecular dynamics (PaCS-MD), which comprises cycles of multiple unbiased MD simulations using a selection of MD snapshots as the initial structures for the next cycle. Dissociation was significantly accelerated by PaCS-MD, in which the probability of rare event occurrence toward dissociation was enhanced by the selection and rerandomization of the initial velocities. Although this complex was stable during 1 μs of conventional MD, PaCS-MD easily induced dissociation within 100-101 ns. We found that velocity rerandomization enhances the dissociation of triNAG from the bound state, whereas diffusion plays a more important role in the unbound state. We calculated the dissociation free energy by analyzing all PaCS-MD trajectories using the Markov state model (MSM), compared the results to those obtained by combinations of PaCS-MD and umbrella sampling (US), steered MD (SMD) and US, and SMD and the Jarzynski equality, and experimentally determined binding free energy. PaCS-MD/MSM yielded results most comparable to the experimentally determined binding free energy, independent of simulation parameter variations, and also gave the lowest standard errors.
Highlights
Calculation of free energy differences between distinct molecular states has a long history and remains an active research theme in computational chemistry, physics, and biophysics
The negatively charged residues in the cleft are surrounded by the positively charged and hydrophobic residues. triNAG formed long-lasting hydrogen bonds with ASN59, TRP62, TRP63, ASP101, ASN103, and ALA107 of LYZ during the 1 μs conventional Molecular dynamics (MD) run, identical to those found in the crystal structure (PDB ID: 1HEW)[31] and by other computational studies.[32−34] Of the above-listed residues, ASP52 is known to play several key roles in catalysis.[66]
Using multicanonical MD, Kamiya et al showed that ASP101 and TRP62 are important amino acids for the interaction of triNAG and LYZ during the association process.[69]
Summary
Calculation of free energy differences between distinct molecular states has a long history and remains an active research theme in computational chemistry, physics, and biophysics. Computational methods for determining free energy can be categorized into four major groups: thermodynamic integration (TI), sampling-based methods, nonequilibrium dynamics, and adaptive biasing techniques.[1] Kirkwood[2] first introduced TI, which is widely used. Zwanzig proposed alchemical free energy perturbation, which decomposes a free energy change into multiple intermediate steps.[3]. The free energy perturbation approach was extended to methods based on reaction coordinates, including umbrella sampling (US).[4,5] Of the nonequilibrium dynamics methods, the Jarzynski equality[6] is the most widely used to determine the relation between free energy change and nonequilibrium trajectories. E.g., metadynamics[7,8] and Wang−Landau methods,[9] monitor the reaction coordinates and penalize the visited region by using adaptive forces.[1]
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