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Abstract Objective . In the presence of oscillatory electric fields, the motion of electrolyte ions in biological tissues is often limited by the confinement created by cell and organelle walls. This confinement induces the organization of the ions into dynamic double layers. This work determines the contribution of these double layers to the bulk conductivity and permittivity of tissues. Approach . Tissues are modeled as repeated units of electrolyte regions separated by dielectric walls. Within the electrolyte regions, a coarse-grained model is used to describe the associated ionic charge distribution. The model emphasizes the role of the displacement current in addition to the ionic current and enables the evaluation of macroscopic conductivities and permittivities. Main results . We obtain analytical expressions for the bulk conductivity and permittivity as a function of the frequency of the oscillatory electric field. These expressions explicitly include the geometric information of the repeated structure and the contribution of the dynamic double layers. The low-frequency limit of the conductivity expression yields a result predicted by the Debye permittivity form. The model also provides a microscopic interpretation of the Maxwell–Wagner effect. Significance . The results obtained contribute to the interpretation of the macroscopic measurements of electrical properties of tissues in terms of their microscopic structure. The model enables a critical assessment of the justification for the use of macroscopic models to analyze the transmission of electrical signals through tissues. 

Most coarse-grained models of individual capsomers associated with viruses employ rigid building blocks that do not exhibit shape adaptation during self-assembly. We develop a coarse-grained general model of viral capsomers that incorporates their stretching and bending energies while retaining many features of the rigid-body models, including an overall trapezoidal shape with attractive interaction sites embedded in the lateral walls to favor icosahedral capsid assembly. Molecular dynamics simulations of deformable capsomers reproduce the rich self-assembly behavior associated with a general T=1 icosahedral virus system in the absence of a genome. Transitions from non-assembled configurations to icosahedral capsids to kinetically-trapped malformed structures are observed as the steric attraction between capsomers is increased. An assembly diagram in the space of capsomer–capsomer steric attraction and capsomer deformability reveals that assembling capsomers of higher deformability into capsids requires increasingly large steric attraction between capsomers. Increasing capsomer deformability can reverse incorrect capsomer–capsomer binding, facilitating transitions from malformed structures to symmetric capsids; however, making capsomers too soft inhibits assembly and yields fluid-like structures. 

Abstract Classical molecular dynamics simulations are based on solving Newton’s equations of motion. Using a small timestep, numerical integrators such as Verlet generate trajectories of particles as solutions to Newton’s equations. We introduce operators derived using recurrent neural networks that accurately solve Newton’s equations utilizing sequences of past trajectory data, and produce energy-conserving dynamics of particles using timesteps up to 4000 times larger compared to the Verlet timestep. We demonstrate significant speedup in many example problems including 3D systems of up to 16 particles.