Hybrid molecular dynamics simulations of living filaments

Adaptive partitioning molecular dynamics using an extended Hamiltonian approach

A recently proposed extended Hamiltonian approach to switching interaction potentials is generalized to enable adaptive partitioning molecular dynamics simulations. Switching is performed along a fictitious classical degree of freedom whose value determines the mixing ratio of the two potentials on a time scale determined by its associated mass. We propose to choose this associated fictitious mass adaptively so as to ensure a constant time scale for all switching processes. For different model systems, including a harmonic oscillator and a Lennard-Jones fluid, we investigate the window of switching time scales that guarantees the conservation of the extended Hamiltonian for a large number of switching events. The methodology is first applied in the microcanonical ensemble and then generalized to the canonical ensemble using a Nosé-Hoover chain thermostat. It is shown that the method is stable for thousands of consecutive switching events during a single simulation, with constant temperature and a conserved extended Hamiltonian. A slight modification of the original Hamiltonian is introduced to avoid accumulation of small numerical errors incurred after each switching process.

Connecting the quantum and classical mechanics simulation world: Applications of reactive step molecular dynamics simulations

This article presents the application of the reactive step molecular dynamics simulation method [M. Biedermann, D. Diddens, and A. Heuer, J. Chem. Theory Comput. 17, 1074 (2021)] toward two different atomistic, chemically reactive systems. During reactive steps, transitions from reactant to product molecules are modeled according to physically correct transition probabilities based on quantum chemical information about the reactions such as molecular reaction rates via instant exchange of the employed force field and a subsequent, short relaxation of the structure. In the first application, we study the follow-up reactions of singly reduced ethylene carbonate (EC) radicals in EC solution, first, via extensive ab initio molecular dynamics simulations and, second, with the reactive step algorithm. A direct comparison of both simulation methods shows excellent agreement. Then, we employ the reactive step algorithm to simulate the enolate formation of 2-methylcyclopropanone with the base lithium diisopropylamine. Thereby, we can demonstrate that the reactive step algorithm is also capable of capturing effects from kinetic vs thermodynamic control of chemical reactions during simulation.

Multiscale simulation of actin filaments and actin-associated proteins

Actin is an important cytoskeletal protein that serves as a building block to form filament networks that span across the cell. These networks are orchestrated by a myriad of other cytoskeletal entities including the unbranched filament-forming protein formin and branched network-forming protein complex Arp2/3. Computational models have been able to provide insights into many important structural transitions that are involved in forming these networks, and into the nature of interactions essential for actin filament formation and for regulating the behavior of actin-associated proteins. In this review, we summarize a subset of such models that focus on the atomistic features and those that can integrate atomistic features into a larger picture in a multiscale fashion.

Particle-Based Modeling of Living Actin Filaments in an Optical Trap

We report a coarse-grained molecular dynamics simulation study of a bundle of parallel actin filaments under supercritical conditions pressing against a loaded mobile wall using a particle-based approach where each particle represents an actin unit. The filaments are grafted to a fixed wall at one end and are reactive at the other end, where they can perform single monomer (de)polymerization steps and push on a mobile obstacle. We simulate a reactive grand canonical ensemble in a box of fixed transverse area A, with a fixed number of grafted filaments Nf, at temperature T and monomer chemical potential μ1. For a single filament case (Nf=1) and for a bundle of Nf=8 filaments, we analyze the structural and dynamical properties at equilibrium where the external load compensates the average force exerted by the bundle. The dynamics of the bundle-moving-wall unit are characteristic of an over-damped Brownian oscillator in agreement with recent in vitro experiments by an optical trap setup. We analyze the influence of the pressing wall on the kinetic rates of (de)polymerization events for the filaments. Both static and dynamic results compare reasonably well with recent theoretical treatments of the same system. Thus, we consider the proposed model as a good tool to investigate the properties of a bundle of living filaments.

Compressive force generation by a bundle of living biofilaments

To study the compressional forces exerted by a bundle of living stiff filaments pressing on a surface, akin to the case of an actin bundle in filopodia structures, we have performed particulate molecular dynamics simulations of a grafted bundle of parallel living (self-assembling) filaments, in chemical equilibrium with a solution of their constitutive monomers. Equilibrium is established as these filaments, grafted at one end to a wall of the simulation box, grow at their chemically active free end, and encounter the opposite confining wall of the simulation box. Further growth of filaments requires bending and thus energy, which automatically limit the populations of longer filaments. The resulting filament sizes distribution and the force exerted by the bundle on the obstacle are analyzed for different grafting densities and different sub- or supercritical conditions, these properties being compared with the predictions of the corresponding ideal confined bundle model. In this analysis, non-ideal effects due to interactions between filaments and confinement effects are singled out. For all state points considered at the same temperature and at the same gap width between the two surfaces, the force per filament exerted on the opposite wall appears to be a function of a rescaled free monomer density ρ1(eff). This quantity can be estimated directly from the characteristic length of the exponential filament size distribution P observed in the size domain where these grafted filaments are not in direct contact with the wall. We also analyze the dynamics of the filament contour length fluctuations in terms of effective polymerization (U) and depolymerization (W) rates, where again it is possible to disentangle non-ideal and confinement effects.