Charge block-driven liquid-liquid phase separation - mechanism and biological roles.

Liquid-liquid phase separation (LLPS) has increasingly been found to play pivotal roles in a number of intracellular events and reactions, and has introduced a new paradigm in cell biology to explain protein-protein and enzyme-ligand interactions beyond conventional molecular and biochemical theories. LLPS is driven by the cumulative effects of weak and promiscuous interactions, including electrostatic, hydrophobic and cation-π interactions, among polypeptides containing intrinsically disordered regions (IDRs) and describes the macroscopic behaviours of IDR-containing proteins in an intracellular milieu. Recent studies have revealed that interactions between 'charge blocks' - clusters of like charges along the polypeptide chain - strongly induce LLPS and play fundamental roles in its spatiotemporal regulation. Introducing a new parameter, termed 'charge blockiness', into physicochemical models of disordered polypeptides has yielded a better understanding of how the intrinsic amino acid sequence of a polypeptide determines the spatiotemporal occurrence of LLPS within a cell. Charge blockiness might also explain why some post-translational modifications segregate within IDRs and how they regulate LLPS. In this Review, we summarise recent progress towards understanding the mechanism and biological roles of charge block-driven LLPS and discuss how this new characteristic parameter of polypeptides offers new possibilities in the fields of structural biology and cell biology.

Conducting transition analysis of thin films composed of long flexible macromolecules: Percolation study.

By simulating percolation and critical phenomena of labelled species inside films composed of single-component linear homogeneous macromolecules using the molecular Monte Carlo method in 3 dimensions, we study the dependence of these conducting transition and critical phenomena upon both thermal movements, i.e. spontaneous mobility, and extra-molecular topological constraints of the molecules. Systems containing topological constraints and/or composed of immobile particles, e.g. lattice models and chemical gelation, were studied in conventional works on percolation. Coordinates of the randomly distributed particles in the conventional lattice models are limited to discrete lattice points. Moreover, each particle is spatially fixed at the distributed position, which results in a temporally unchanged network structure. Although each polymer in the chemical gels can spontaneously move in the continuous space, the network structure is fixed when cross-linking reaction ends. By contrast to these conventional systems, all the molecules in the present system freely move and spontaneously diffuse in the continuous space. The network structure of the present molecules continues changing dynamically. The percolation and critical phenomena of such dynamic network structures are examined here. We reveal that these phenomena also occur in the present system, and that both the universality class and percolation threshold are independent of the extra-molecular topological constraints.

Two-dimensional percolation phenomena of single-component linear homopolymer brushes.

Percolation phenomena of homopolymer brushes on a planar substrate are simulated using the molecular Monte Carlo method in 3 dimensions. The grafted polymers are isolated from each other at extremely low grafting density, whereas a continuous polymer layer covers the whole substrate when the density rises to extremely high values. This indicates that percolation clusters of the grafted polymers, bridging both the edges of the substrate, appear at an intermediate density. We construct phase diagrams of this percolation phenomenon. Critical phenomena at the transition are also studied.

Particle Monte Carlo simulation of string-like colloidal assembly in two and three dimensions.

We simulate structural phase behavior of polymer-grafted colloidal particles by molecular Monte Carlo technique. The interparticle potential, which has a finite repulsive square-step outside a rigid core of the colloid, was previously confirmed via numerical self-consistent field calculation. This model potential is purely repulsive. We simulate these model colloids in the canonical ensemble in two and three dimensions and find that these particles containing no interparticle attraction self-assemble and align in a string-like assembly, at low temperature and high density. This string-like colloidal assembly is related to percolation phenomena. Analyzing the cluster size distribution and the average string length, we build phase diagrams and discover that the average string length diverges around the region where the melting transition line and the percolation transition line cross. This result is similar to Ising spin systems, in which the percolation transition line and the order-disorder line meet at a critical point.

Measuring excess free energies of self-assembled membrane structures.

Using computer simulation of a solvent-free, coarse-grained model for amphiphilic membranes, we study the excess free energy of hourglass-shaped connections (i.e., stalks) between two apposed bilayer membranes. In order to calculate the free energy by simulation in the canonical ensemble, we reversibly transfer two apposed bilayers into a configuration with a stalk in three steps. First, we gradually replace the intermolecular interactions by an external, ordering field. The latter is chosen such that the structure of the non-interacting system in this field closely resembles the structure of the original, interacting system in the absence of the external field. The absence of structural changes along this path suggests that it is reversible; a fact which is confirmed by expanded-ensemble simulations. Second, the external, ordering field is changed as to transform the non-interacting system from the apposed bilayer structure to two-bilayers connected by a stalk. The final external field is chosen such that the structure of the non-interacting system resembles the structure of the stalk in the interacting system without a field. On the third branch of the transformation path, we reversibly replace the external, ordering field by non-bonded interactions. Using expanded-ensemble techniques, the free energy change along this reversible path can be obtained with an accuracy of 10(-3)k(B)T per molecule in the n VT-ensemble. Calculating the chemical potential, we obtain the free energy of a stalk in the grandcanonical ensemble, and employing semi-grandcanonical techniques, we calculate the change of the excess free energy upon altering the molecular architecture. This computational strategy can be applied to compute the free energy of self-assembled phases in lipid and copolymer systems, and the excess free energy of defects or interfaces.

Computing free energies of interfaces in self-assembling systems.

Using molecular simulation of a coarse-grained model for a symmetric diblock copolymer melt, we calculate the free energy of interfaces between lamellar morphologies with different orientations. Two examples are considered: (a) a T-junction between two lamellar structures with perpendicular orientation and (b) a surface reconstruction that arises when lamella-forming diblock copolymers assemble on a stripe-patterned surface, where the pattern period is significantly larger than the lamellar spacing in the bulk. The computational scheme relies on reversibly relating the defect structure to a reference state by an external ordering field. Free energy differences are accurately obtained by using a combination of expanded-ensemble and replica-exchange Monte Carlo techniques.