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1. The role of extended range of interactions in the dynamics of interacting molecular motors

   https://doi.org/10.1088/1751-8121/ac7092  

   Spaulding, Cade; Teimouri, Hamid; Narasimhan, S L; Kolomeisky, Anatoly B (June 2022, Journal of Physics A: Mathematical and Theoretical)

   Abstract Motor proteins, also known as biological molecular motors, play important roles in various intracellular processes. Experimental investigations suggest that molecular motors interact with each other during the cellular transport, but the nature of such interactions remains not well understood. Stimulated by these observations, we present a theoretical study aimed to understand the effect of the range of interactions on dynamics of interacting molecular motors. For this purpose, we develop a new version of the totally asymmetric simple exclusion processes in which nearest-neighbor as well as the next nearest-neighbor interactions are taken into account in a thermodynamically consistent way. A theoretical framework based on a cluster mean-field approximation, which partially takes correlations into account, is developed to evaluate the stationary properties of the system. It is found that fundamental current–density relations in the system strongly depend on the strength and the sign of interactions, as well as on the range of interactions. For repulsive interactions stronger than some critical value, a mean-field theoretical approach predicts that increasing the range of interactions might lead to a change from unimodal to trimodal dependence in the flux-density fundamental diagram. However, it is not fully supported by extensive Monte Carlo computer simulations that test theoretical predictions. Although in most ranges of parameters a reasonable agreement between theoretical calculations and computer simulations is observed, there are situations when the cluster mean-field approach fails to describe properly the dynamics in the system. Theoretical arguments to explain these observations are presented. Our theoretical analysis clarifies the microscopic picture of how the range of interactions influences the dynamics of interacting molecular motors. 

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2. Molecular dynamics simulations of anisotropic particles accelerated by neural-net predicted interactions

   https://doi.org/10.1063/5.0206636  

   Argun, B Ruşen; Fu, Yu; Statt, Antonia (June 2024, The Journal of Chemical Physics)

   Rigid bodies, made of smaller composite beads, are commonly used to simulate anisotropic particles with molecular dynamics or Monte Carlo methods. To accurately represent the particle shape and to obtain smooth and realistic effective pair interactions between two rigid bodies, each body may need to contain hundreds of spherical beads. Given an interacting pair of particles, traditional molecular dynamics methods calculate all the inter-body distances between the beads of the rigid bodies within a certain distance. For a system containing many anisotropic particles, these distance calculations are computationally costly and limit the attainable system size and simulation time. However, the effective interaction between two rigid particles should only depend on the distance between their center of masses and their relative orientation. Therefore, a function capable of directly mapping the center of mass distance and orientation to the interaction energy between the two rigid bodies would completely bypass inter-bead distance calculations. It is challenging to derive such a general function analytically for almost any non-spherical rigid body. In this study, we have trained neural nets, powerful tools to fit nonlinear functions to complex datasets, to achieve this task. The pair configuration (center of mass distance and relative orientation) is taken as an input, and the energy, forces, and torques between two rigid particles are predicted directly. We show that molecular dynamics simulations of cubes and cylinders performed with forces and torques obtained from the gradients of the energy neural-nets quantitatively match traditional simulations that use composite rigid bodies. Both structural quantities and dynamic measures are in agreement, while achieving up to 23 times speedup over traditional molecular dynamics, depending on hardware and system size. The method presented here can, in principle, be applied to any irregular concave or convex shape with any pair interaction, provided that sufficient training data can be obtained. 

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3. Molecular search with conformational change: One-dimensional discrete-state stochastic model

   https://doi.org/https://doi.org/10.1063/1.5051035  

   Shin, Jaeoh; Kolomeisky, Anatoly B (November 2018, Journal of chemical physics)

   Molecular search phenomena are observed in a variety of chemical and biological systems. During the search, the participating particles frequently move in complex inhomogeneous environments with random transitions between different dynamic modes. To understand the mechanisms of molecular search with alternating dynamics, we investigate the search dynamics with stochastic transitions between two conformations in a one-dimensional discrete-state stochastic model. It is explicitly analyzed using the first-passage time probability method to obtain a full dynamic description of the search process. A general dynamic phase diagram is developed. It is found that there are several dynamic regimes in the molecular search with conformational transitions, and they are determined by the relative values of the relevant length scales in the system. Theoretical predictions are fully supported by Monte Carlo computer simulations. 

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4. Facilitation of DNA loop formation by protein–DNA non-specific interactions

   https://doi.org/10.1039/c9sm00671k  

   Shin, Jaeoh; Kolomeisky, Anatoly B. (July 2019, Soft Matter)

   Complex DNA topological structures, including polymer loops, are frequently observed in biological processes when protein molecules simultaneously bind to several distant sites on DNA. However, the molecular mechanisms of formation of these systems remain not well understood. Existing theoretical studies focus only on specific interactions between protein and DNA molecules at target sequences. However, the electrostatic origin of primary protein–DNA interactions suggests that interactions of proteins with all DNA segments should be considered. Here we theoretically investigate the role of non-specific interactions between protein and DNA molecules on the dynamics of loop formation. Our approach is based on analyzing a discrete-state stochastic model via a method of first-passage probabilities supplemented by Monte Carlo computer simulations. It is found that depending on a protein sliding length during the non-specific binding event three different dynamic regimes of the DNA loop formation might be observed. In addition, the loop formation time might be optimized by varying the protein sliding length, the size of the DNA molecule, and the position of the specific target sequences on DNA. Our results demonstrate the importance of non-specific protein–DNA interactions in the dynamics of DNA loop formations. 

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5. Development of a PointNet for Detecting Morphologies of Self-Assembled Block Oligomers in Atomistic Simulations

   Shen, Z.; Sun, Y.; Lodge, T.P.; Siepmann, J.I. (May 2021, The journal of physical chemistry)

   ABSTRACT: Molecular simulations with atomistic or coarse- 6 grained force fields are a powerful approach for understanding and 7 predicting the self-assembly phase behavior of complex molecules. 8 Amphiphiles, block oligomers, and block polymers can form 9 mesophases with different ordered morphologies describing the 10 spatial distribution of the blocks, but entirely amorphous nature for 11 local packing and chain conformation. Screening block oligomer 12 chemistry and architecture through molecular simulations to find 13 promising candidates for functional materials is aided by effective 14 and straightforward morphology identification techniques. Captur- 15 ing 3-dimensional periodic structures, such as ordered network 16 morphologies, is hampered by the requirement that the number of 17 molecules in the simulated system and the shape of the periodic simulation box need to be commensurate with those of the resulting 18 network phase. Common strategies for structure identification include structure factors and order parameters, but these fail to 19 identify imperfect structures in simulations with incorrect system sizes. Building upon pioneering work by DeFever et al. [Chem. Sci. 20 2019, 10, 7503−7515] who implemented a PointNet (i.e., a neural network designed for computer vision applications using point 21 clouds) to detect local structure in simulations of single-bead particles and water molecules, we present a PointNet for detection of 22 nonlocal ordered morphologies of complex block oligomers. Our PointNet was trained using atomic coordinates from molecular 23 dynamics simulation trajectories and synthetic point clouds for ordered network morphologies that were absent from previous 24 simulations. In contrast to prior work on simple molecules, we observe that large point clouds with 1000 or more points are needed 25 for the more complex block oligomers. The trained PointNet model achieves an accuracy as high as 0.99 for globally ordered 26 morphologies formed by linear diblock, linear triblock, and 3-arm and 4-arm star-block oligomers, and it also allows for the discovery 27 of emerging ordered patterns from nonequilibrium systems. 

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