Solvent Hydrodynamics Enhances the Collective Diffusion of Membrane Lipids

Short Peptide Self-Assembly in the Martini Coarse-Grain Force Field Family

ConspectusPivotal to the success of any computational experiment is the ability to make reliable predictions about the system under study and the time required to yield these results. Biomolecular interactions is one area of research that sits in every camp of resolution vs the time required, from the quantum mechanical level to in vivo studies. At an approximate midpoint, there is coarse-grained molecular dynamics, for which the Martini force fields have become the most widely used, fast enough to simulate the entire membrane of a mitochondrion though lacking atom-specific precision. While many force fields have been parametrized to account for a specific system under study, the Martini force field has aimed at casting a wider net with more generalized bead types that have demonstrated suitability for broad use and reuse in applications from protein-graphene oxide coassembly to polysaccharides interactions.In this Account, the progressive (Martini versions 1 through 3) and peripheral (Sour Martini, constant pH, Martini Straight, Dry Martini, etc.) developmental trajectory of the Martini force field will be analyzed in terms of self-assembling systems with a focus on short (two to three amino acids) peptide self-assembly in aqueous environments. In particular, this will focus on the effects of the Martini solvent model and compare how changes in bead definitions and mapping have effects on different systems. Considerable effort in the development of Martini has been expended to reduce the "stickiness" of amino acids to better simulate proteins in bilayers. We have included in this Account a short study of dipeptide self-assembly in water, using all mainstream Martini force fields, to examine their ability to reproduce this behavior. The three most recently released versions of Martini and variations in their solvents are used to simulate in triplicate all 400 dipeptides of the 20 gene-encoded amino acids. The ability of the force fields to model the self-assembly of the dipeptides in aqueoues environments is determined by the measurement of the aggregation propensity, and additional descriptors are used to gain further insight into the dipeptide aggregates.

Hydrodynamics induce superdiffusive jumps of passive tracers along critical paths of random networks and colloidal gels

We present a numerical study on the effect of hydrodynamic interactions (HI) on the diffusion of inert point tracer particles in several fixed random structures. As expected, the diffusion is hampered by the extra hydrodynamic friction introduced by the obstacle network. However, a non-trivial effect due to HI appears in the analysis of the van-Hove displacement probability close to the percolation threshold, where tracers diffuse through critical fractal paths. We show that the tracer dynamics can be split up into short and long jumps, the latter being ruled by either exponential or Gaussian van Hove distribution tails. While at short time HI slow down the tracer diffusion, at long times, hydrodynamic interactions with the obstacles increase the probability of longer jumps, which circumvent the traps of the labyrinth more easily. Notably, the relation between the anomalous diffusion exponent and the fractal dimension of the critical (intricate) paths is greater than one, which implies that the long-time (long-jump) diffusion is mildly superdiffuse. A possible reason for such a hastening of the diffusion along the network corridors is the hydrodynamically induced mobility anisotropy, which favours displacements parallel to the walls, an effect which has already been experimentally observed in collagen gels.

Hydrodynamic coupling for particle-based solvent-free membrane models

The great challenge with biological membrane systems is the wide range of scales involved, from nanometers and picoseconds for individual lipids to the micrometers and beyond millisecond for cellular signaling processes. While solvent-free coarse-grained membrane models are convenient for large-scale simulations and promising to provide insight into slow processes involving membranes, these models usually have unrealistic kinetics. One major obstacle is the lack of an equally convenient way of introducing hydrodynamic coupling without significantly increasing the computational cost of the model. To address this, we introduce a framework based on anisotropic Langevin dynamics, for which major in-plane and out-of-plane hydrodynamic effects are modeled via friction and diffusion tensors from analytical or semi-analytical solutions to Stokes hydrodynamic equations. Using this framework, in conjunction with our recently developed membrane model, we obtain accurate dispersion relations for planar membrane patches, both free-standing and in the vicinity of a wall. We briefly discuss how non-equilibrium dynamics is affected by hydrodynamic interactions. We also measure the surface viscosity of the model membrane and discuss the affecting dissipative mechanisms.

Hydrodynamics of immiscible binary fluids with viscosity contrast: a multiparticle collision dynamics approach

We present a multiparticle collision dynamics (MPC) implementation of layered immiscible fluids A and B of different shear viscosities separated by planar interfaces. The simulated flow profile for imposed steady shear motion and the time-dependent shear stress functions are in excellent agreement with our continuum hydrodynamics results for the composite fluid. The wave-vector dependent transverse velocity auto-correlation functions (TVAF) in the bulk-fluid regions of the layers decay exponentially, and agree with those of single-phase isotropic MPC fluids. In addition, we determine the hydrodynamic mobilities of an embedded colloidal sphere moving steadily parallel or transverse to a fluid-fluid interface, as functions of the distance from the interface. The obtained mobilities are in good agreement with hydrodynamic force multipoles calculations, for a no-slip sphere moving under creeping flow conditions near a clean, ideally flat interface. The proposed MPC fluid-layer model can be straightforwardly implemented, and it is computationally very efficient. Yet, owing to the spatial discretization inherent to the MPC method, the model can not reproduce all hydrodynamic features of an ideally flat interface between immiscible fluids.

Large-scale simulation of biomembranes incorporating realistic kinetics into coarse-grained models

Biomembranes are two-dimensional assemblies of phospholipids that are only a few nanometres thick, but form micrometre-sized structures vital to cellular function. Explicit molecular modelling of biologically relevant membrane systems is computationally expensive due to the large number of solvent particles and slow membrane kinetics. Coarse-grained solvent-free membrane models offer efficient sampling but sacrifice realistic kinetics, thereby limiting the ability to predict pathways and mechanisms of membrane processes. Here, we present a framework for integrating coarse-grained membrane models with continuum-based hydrodynamics. This framework facilitates efficient simulation of large biomembrane systems with large timesteps, while achieving realistic equilibrium and non-equilibrium kinetics. It helps to bridge between the nanometer/nanosecond spatiotemporal resolutions of coarse-grained models and biologically relevant time- and lengthscales. As a demonstration, we investigate fluctuations of red blood cells, with varying cytoplasmic viscosities, in 150-milliseconds-long trajectories, and compare kinetic properties against single-cell experimental observations.