TaBoo SeArch Algorithm with a Modified Inverse Histogram for Reproducing Biologically Relevant Rare Events of Proteins

Ligand Binding Path Sampling Based on Parallel Cascade Selection Molecular Dynamics: LB-PaCS-MD

Parallel cascade selection molecular dynamics (PaCS-MD) is a rare-event sampling method that generates transition pathways between a reactant and product. To sample the transition pathways, PaCS-MD repeats short-time MD simulations from important configurations as conformational resampling cycles. In this study, PaCS-MD was extended to sample ligand binding pathways toward a target protein, which is referred to as LB-PaCS-MD. In a ligand-concentrated environment, where multiple ligand copies are randomly arranged around the target protein, LB-PaCS-MD allows for the frequent sampling of ligand binding pathways. To select the important configurations, we specified the center of mass (COM) distance between each ligand and the relevant binding site of the target protein, where snapshots generated by the short-time MD simulations were ranked by their COM distance values. From each cycle, snapshots with smaller COM distance values were selected as the important configurations to be resampled using the short-time MD simulations. By repeating conformational resampling cycles, the COM distance values gradually decreased and converged to constants, meaning that a set of ligand binding pathways toward the target protein was sampled by LB-PaCS-MD. To demonstrate relative efficiency, LB-PaCS-MD was applied to several proteins, and their ligand binding pathways were sampled more frequently than conventional MD simulations.

Strengthening the PSO algorithm with a new technique inspired by the golf game and solving the complex engineering problem

This study has been inspired by golf ball movements during the game to improve particle swarm optimization. Because, all movements from the first to the last move of the golf ball are the moves made by the player to win the game. Winning this game is also a result of successful implementation of the desired moves. Therefore, the movements of the golf ball are also an optimization, and this has a meaning in the scientific world. In this sense, the movements of the particles in the PSO algorithm have been associated with the movements of the golf ball in the game. Thus, the velocities of the particles have converted to parabolically descending structure as they approach the target. Based on this feature, this meta-heuristic technique is called RDV (random descending velocity) IW PSO. In this way, the result obtained is improved thousands of times with very small movements. For the application of the proposed new technique, the inverse kinematics calculation of the 7-joint robot arm has been performed and the obtained results have been compared with the traditional PSO, some IW techniques, artificial bee colony, firefly algorithm and quantum PSO.

A Two-Ended Data-Driven Accelerated Sampling Method for Exploring the Transition Pathways between Two Known States of Protein

Conformational transitions of protein between different states are often associated with their biological functions. These dynamic processes, however, are usually not easy to be well characterized by experimental measurements, mainly because of inadequate temporal and spatial resolution. Meantime, sampling of configuration space with molecular dynamics (MD) simulations is still a challenge. Here we proposed a robust two-ended data-driven accelerated (teDA2) conformational sampling method, which drives the structural change in an adaptively updated feature space without introducing a bias potential. teDA2 was applied to explore adenylate kinase (ADK), a model with well characterized "open" and "closed" states. A single conformational transition event of ADK could be achieved within only a few or tens of nanoseconds sampled with teDA2. By analyzing hundreds of transition events, we reproduced different mechanisms and the associated pathways for domain motion of ADK reported in the literature. The multiroute characteristic of ADK was confirmed by the fact that some metastable states identified with teDA2 resemble available crystal structures determined at different conditions. This feature was further validated with Markov state modeling with independent MD simulations. Therefore, our work provides strong evidence for the conformational plasticity of protein, which is mainly due to the inherent degree of flexibility. As a reliable and efficient enhanced sampling protocol, teDA2 could be used to study the dynamics between functional states of various biomolecular machines.

Selection rules on initial structures in parallel cascade selection molecular dynamics affect conformational sampling efficiency

Parallel cascade selection molecular dynamics (PaCS-MD) is a conformational sampling method for generating transition pathways from a given reactant to a product. In PaCS-MD, initial structures relevant to conformational transitions of proteins are selected and resampled by short-time MD simulations. As a general reaction coordinate, a root-mean-square deviation measured from the product (RMSD) is employed to rank the resampled configurations. Quantitatively, n initial structures are randomly selected from among the top X % of highly ranked configurations and resampled again. In PaCS-MD, the selection of initial structures and their conformational resampling are repeated as a cycle to promote the essential conformational transitions. Therefore, rules for selecting the initial structures might affect the conformational sampling efficiency. In the present study, to address the conformational sampling efficiency depending on the selection rule, the open-closed transition of di-ubiquitin was reproduced by PaCS-MD based on the resampling from the top X = 0.1, 1.0, 2.0, 5.0, 10.0, 25.0, 30.0, 40.0, and 50.0% of highly ranked configurations. Judging from broadness of sampled conformational area and required cycles, we conclude that the resampling from the top ∼2.0% of highly ranked configurations might be the most efficient for generating a set of transition pathways in PaCS-MD.

Self-Avoiding Conformational Sampling Based on Histories of Past Conformational Searches

Self-avoiding conformational sampling (SACS) is proposed as an enhanced conformational sampling method for proteins. In SACS, the following conformational resampling is repeated for a given protein: (1) identification of newly visited states in a subspace and (2) conformational resampling by restarting short-time molecular dynamics (MD) simulations from the newly visited states. To identify the newly visited states, a set of history-dependent histograms projected onto the subspace is used. One is constructed from the trajectories sampled at the current (ith) cycle, and the other is constructed from all of the trajectories accumulated up through the previous ((i - 1)th) cycle. By reference to the history-dependent histograms, the newly visited states appearing at the current (ith) cycle are defined as a difference set between them. By repeating the cycle of conformational resampling, SACS prevents the system from revisiting states that have already been visited for previous cycles, promoting structural transitions via resampling from the newly visited states. To verify the conformational sampling efficiency of SACS, the present method was applied to reveal underlying mechanisms of biologically important domain motions of maltodextrin binding protein in explicit water and successfully reproduced the open-closed transition with a reasonable (nanosecond-order) computational cost.