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.

Membrane invagination induced by Shiga toxin B-subunit: from molecular structure to tube formation.

The bacterial Shiga toxin is composed of an enzymatically active A-subunit, and a receptor-binding homopentameric B-subunit (STxB) that mediates intracellular toxin trafficking. Upon STxB-mediated binding to the glycolipid globotriaosylceramide (Gb3) at the plasma membrane of target cells, Shiga toxin is internalized by clathrin-dependent and independent endocytosis. The formation of tubular membrane invaginations is an essential step in the clathrin-independent STxB uptake process. However, the mechanism by which STxB induces these invaginations has remained unclear. Using a combination of all-atom molecular dynamics and Monte Carlo simulations we show that the molecular architecture of STxB enables the following sequence of events: the Gb3 binding sites on STxB are arranged such that tight avidity-based binding results in a small increment of local curvature. Membrane-mediated clustering of several toxin molecules then creates a tubular membrane invagination that drives toxin entry into the cell. This mechanism requires: (1) a precise molecular architecture of the STxB binding sites; (2) a fluid bilayer in order for the tubular invagination to form. Although, STxB binding to the membrane requires specific interactions with Gb3 lipids, our study points to a generic molecular design principle for clathrin-independent endocytosis of nanoparticles.

Two-component membrane material properties and domain formation from dissipative particle dynamics.

The material parameters (area stretch modulus and bending rigidity) of two-component amphiphilic membranes are determined from dissipative particle dynamics simulations. The preferred area per molecule for each species is varied so as to produce homogeneous mixtures or nonhomogeneous mixtures that form domains. If the latter mixtures are composed of amphiphiles with the same tail length, but different preferred areas per molecule, their material parameters increase monotonically as a function of composition. By contrast, mixtures of amphiphiles that differ in both tail length and preferred area per molecule form both homogeneous and nonhomogeneous mixtures that both exhibit smaller values of their material properties compared to the corresponding pure systems. When the same nonhomogeneous mixtures of amphiphiles are assembled into planar membrane patches and vesicles, the resulting domain shapes are different when the bending rigidities of the domains are sufficiently different. Additionally, both bilayer and monolayer domains are observed in vesicles. We conclude that the evolution of the domain shapes is influenced by the high curvature of the vesicles in the simulation, a result that may be relevant for biological vesicle membranes.

Effect of chain length and asymmetry on material properties of bilayer membranes.

Dissipative particle dynamics is used to extract the material parameters (bending and area stretch moduli) of a bilayer membrane patch. Some experiments indicate that the area stretch modulus of lipid vesicles varies little as the chain length of the lipids composing the bilayer increases. Here we show that making the interactions between the hydrophilic head groups of the model amphiphiles proportional to the hydrophobic tail length reproduces the above result for the area stretch modulus. We also show that the area stretch modulus of bilayers composed of amphiphiles with the same number of tail beads but with asymmetric chains is less than that of bilayers with symmetric chains. The effects on the bilayer density and lateral stress profiles of changes to the amphiphile architecture are also presented.

Lateral and transverse diffusion in two-component bilayer membranes.

We study the lateral and transverse diffusion of amphiphiles in two-component bilayer membranes, using a coarse-grained model for amphiphilic molecules and combined Monte Carlo-Molecular Dynamics simulations. Membrane structural properties, such as the mean thickness, are also measured. The dependence of such properties on membrane composition, inter-molecular interactions, and amphiphile stiffness is determined. In particular, we show that addition of shorter amphiphiles drives the model membrane towards a more fluid state, with increased amphiphile lateral diffusion rates. These results can be understood in the framework of a simple free-volume model. Furthermore, we observe an increase in the trans-membrane diffusion when the interaction energy of amphiphiles with their neighboring molecules is decreased.

Thermally induced proliferation of pores in a model fluid membrane.

The growth of thermally induced pores in a two-dimensional model fluid membrane is investigated by Monte Carlo simulation. Holes appear in the membrane via an activated process, and their subsequent growth is controlled by an edge energy per unit length or line tension. The barrier height and line tension, together with a lateral tension, are the independent parameters of the model. In the resulting phase diagram, a rupture transition separates an intact membrane from a disintegrated state. The approach to the ruptured state shows distinct regimes. Reducing the barrier height at large line tension produces multiple, quasi-independent, small holes whose behavior is dominated by their edge energy, whereas at lower line tensions shape fluctuations of the holes facilitate their coalescence into a single large hole. At a small value of line tension and large barrier height, a single hole spontaneously permeabilizes the membrane in an entropically driven phase transition. Entropy dominates pore growth for line tensions not far below those measured for artificial vesicles. Permeabilization of lipid bilayers by certain peptides involves perturbing lipid-lipid cohesive energies, and our simulations show that at small line tensions the entropy of hole shape fluctuations destroys the model membrane's stability.

Entropy-driven instability and rupture of fluid membranes.

A computer simulation is used to investigate hole formation in a model membrane. The model parameters are the stress applied to the membrane, and the edge energy per unit length along the hole boundary (edge tension). Even at zero stress, the membrane has an entropically driven instability against hole formation. Within the model, the minimum edge tension required for the stability of a typical biological membrane is in the region of 1 x 10(-11) J/m, which is similar to the edge tension obtained in many measurements of biomembranes. At the zero-stress instability threshold, the hole shape is the same as a self-avoiding ring, but under compression, the hole shape assumes a branched polymer form. In the presence of large holes at zero stress, the membrane itself behaves like a branched polymer. The boundaries of the phase diagram for membrane stability are obtained, and general features of the rate of membrane rupture under stress are investigated. A model in which the entropy of hole formation is proportional to the hole perimeter is used to interpret the simulation results at small stress near the instability threshold.