Particle-based membrane model for mesoscopic simulation of cellular dynamics

Abstract

We present a simple and computationally efficient coarse-grained and solvent-free model for simulating lipid bilayer membranes. In order to be used in concert with particle-based reaction-diffusion simulations, the model is purely based on interacting and reacting particles, each representing a coarse patch of a lipid monolayer. Particle interactions include nearest-neighbor bond-stretching and angle-bending, and are parameterized so as to reproduce the local membrane mechanics given by the Helfrich energy density over a range of relevant curvatures. In-plane fluidity is implemented with Monte Carlo bond-flipping moves. The physical accuracy of the model is verified by five tests: (i) Power spectrum analysis of equilibrium thermal undulations is used to verify that the particle-based representation correctly captures the dynamics predicted by the continuum model of fluid membranes. (ii) It is verified that the input bending stiffness, against which the potential parameters are optimized, is accurately recovered. (iii) Isothermal area compressibility modulus of the membrane is calculated and is shown to be tunable to reproduce available values for different lipid bilayers, independent of the bending rigidity. (iv) Simulation of two-dimensional shear flow under a gravity force is employed to measure the effective in-plane viscosity of the membrane model, and show the possibility of modeling membranes with specified viscosities. (v) Interaction of the bilayer membrane with a spherical nanoparticle is modeled as a test case for large membrane deformations and budding involved in cellular processes such as endocytosis. The results are shown to coincide well with the predicted behavior of continuum models, and the membrane model successfully mimics the expected budding behavior. We expect our model to be of high practical usability for ultra coarse-grained molecular dynamics or particle-based reaction-diffusion simulations of biological systems.

ReaDDy 2: Fast and flexible software framework for interacting-particle reaction dynamics

“…Planned extensions include simulation kernels for specialized hardware platforms, such as graphics processors and highly parallel HPC environments. Also planned is a MD-GFRD integrator [38] to speed up computations in dilute systems, and a particle-based membrane model as described in [36] that reproduces mechanical properties of cellular membranes.…”

“…On mesoscopic length scales these interactions can be used to induce structure, e.g., volume-exclusion in crowded systems [25, 42], clustering of weakly interacting macromolecules [49], restriction of diffusing particles to arbitrarily-shaped membranes [42, 23, 43]. Furthermore it allows to study the large-scale structure of polymers and membranes [36]. When not only considering interactions but also reactions, a wide range of reactive biochemical systems are in the scope of the model.…”

Grand canonical diffusion-influenced reactions: A stochastic theory with applications to multiscale reaction-diffusion simulations

“…Simulations in this region could also include more detailed dynamics via MSM/RD [58], where Markov state models (MSMs) [59][60][61][62] extracted from detailed molecular dynamics simulations are coupled to particle-based reaction diffusion (RD) simulations. A more realistic simulation of the membrane could also be implemented with the novel particlebased membrane model from [63]. We should also note it is theoretically possible to do a particle-based simulation or even a molecular dynamics simulation on the whole region.…”

High-throughput of measure-preserving integrators for constant temperature molecular dynamics simulations on GPUs

“…MTK algorithms are already applicable to a wide range of scientific problems and have been expanding their applications in several areas, such as: Physical Chemistry [27], Theoretical and Computational Chemistry [28], Materials Engineering [29], Macromolecular and Materials Chemistry [30], Biochemistry [31], Cellular and Cell Biology science [32], and so on. The implementation of the MTK algorithms is not trivial and its evaluation is computationally expensive.…”