Brownian dynamics simulations of attractive polymers in solution

Phase behaviour and structure of a model biomolecular condensate

Phase separation of immiscible fluids is a common phenomenon in polymer chemistry, and is recognized as an important mechanism by which cells compartmentalize their biochemical reactions. Biomolecular condensates are condensed fluid droplets in cells that form by liquid-liquid phase separation of intrinsically-disordered proteins. They have a wide range of functions and are associated with chronic neurodegenerative diseases in which they become pathologically rigid. However, it remains unclear how their material properties depend on the molecular structure of the proteins. Here we explore the phase behaviour and structure of a model biomolecular condensate composed of semi-flexible polymers with attractive end-caps using coarse-grained simulations. The model contains the minimal molecular features that are sufficient to observe liquid-liquid phase separation of soluble polymers into a porous, three-dimensional network in which their end-caps reversibly bind at junctions. The distance between connected junctions scales with the polymer length as a self-avoiding random walk over a wide range of concentration with a weak affinity-dependent prefactor. By contrast, the average number of polymers that meet at the junctions depends on the end-cap affinity but only weakly on the polymer length. The structured porosity of the condensed phase suggests a mechanism for cells to regulate biomolecular condensates. Protein interaction sites may be turned on or off to modulate the condensate's porosity and therefore the diffusion and interaction of additional proteins.

Brownian dynamics simulations of associating diblock copolymers

A novel coarse-grained computational model for associating polymers is proposed that is based on a Gaussian "blob" representation of the polymer chains. The model allows a large number of model polymers to be simulated at moderate computational cost over a wide packing fraction range using the Brownian dynamics, BD, technique. The attraction of the hydrophobic part of the polymer to those on other molecules can lead to strong aggregation of the polymer molecules in real systems, and this is included in the model by an attractive potential felt by the Gaussian blobs to a common "nodal" point that represents the center of the micelle. Attention here is confined to model AB diblock copolymers in which the hydrophilic block, A, has a much higher mass than the hydrophobic moiety, B, which leads to relatively small aggregation numbers, Nagg, of approximately 8. The aggregation number at low packing fractions is found to increase with packing fraction, as observed in experiments, with a functional form that closely follows a simple theory derived here that is based on entropy-derived mean-field terms for the free-energy change associated with the incorporation of the polymer molecule into the micelle. The computational model exhibits an extremely low critical micelle concentration (cmc), and micelles with Nagg approximately 5 are observed at the lowest packing fractions, phi, simulated ( approximately 10-4), which is consistent with experiment. The long-time self-diffusion coefficient of the polymers (and hence micelles) decreases logarithmically with packing fraction, and the viscosity increased with concentration according to the Huggins equation. The spherical blob coarse graining results in the simulable time scales being longer than the Rouse time of the chain, and hence for the nonassociating polymers the intrinsic viscosity is an input parameter in the model. The introduction of association leads to the partial inclusion of the intrinsic viscosity in the simulation and has an effect on the computed Huggins coefficient, kH, which is found to be approximately 6 in those cases.

Nonequilibrium Monte Carlo simulation of lattice block copolymer chains subject to oscillatory shear flow

This paper has extended nonequilibrium Monte Carlo (MC) approach to simulate oscillatory shear flow in a lattice block copolymer system. Phase transition and associated rheological behaviors of multiple self-avoiding chains have been investigated. Stress tensor has been obtained based upon sampled configuration distribution functions. At low temperatures, micellar structures have been observed and the underlying frequency-dependent rheological properties exhibit different initial slopes. The simulation outputs are consistent with the experimental observations in literature. Chain deformation during oscillatory shear flow has also been revealed. Although MC simulation cannot account for hydrodynamic interaction, the highlight of our simulation approach is that it can, at small computing cost, investigate polymer chains simultaneously at different spatial scales, i.e., macroscopic rheological behaviors, mesoscopic self-assembled structures, and microscopic chain configurations.