Simulation and theory of self-assembly and network formation in reversibly cross-linked equilibrium polymers

Harnessing entropy to enhance toughness in reversibly crosslinked polymer networks

Reversible crosslinking is a design paradigm for polymeric materials, wherein they are microscopically reinforced with chemical species that form transient crosslinks between the polymer chains. Besides the potential for self-healing, recent experimental work suggests that freely diffusing reversible crosslinks in polymer networks, such as gels, can enhance the toughness of the material without substantial change in elasticity. This presents the opportunity for making highly elastic materials that can be strained to a large extent before rupturing. Here, we employ Gaussian chain theory, molecular simulation, and polymer self-consistent field theory for networks to construct an equilibrium picture for how reversible crosslinks can toughen a polymer network without affecting its elasticity. Maximisation of polymer entropy drives the reversible crosslinks to bind preferentially near the permanent crosslinks in the network, leading to local molecular reinforcement without significant alteration of the network topology. In equilibrium conditions, permanent crosslinks share effectively the load with neighbouring reversible crosslinks, forming multi-functional crosslink points. The network is thereby globally toughened, while the linear elasticity is left largely unaltered. Practical guidelines are proposed to optimise this design in experiment, along with a discussion of key kinetic and timescale considerations.

Bundling in semiflexible polymers: A theoretical overview

Supramolecular assemblies of polymers are key modules to sustain the structure of cells and their function. The main elements of these assemblies are charged semiflexible polymers (polyelectrolytes) generally interacting via a long(er)-range repulsion and a short(er)-range attraction. The most common supramolecular structure formed by these polymers is the bundle. In the present paper, we critically review some recent theoretical and computational advances on the problem of bundle formation, and point a few promising directions for future work.

Investigation of regulation of FtsZ assembly by SulA and development of a model for FtsZ polymerization

In Escherichia coli FtsZ organizes into a cytoskeletal ring structure, the Z ring, which effects cell division. FtsZ is a GTPase, but the free energy of GTP hydrolysis does not appear to be used for generation of the constriction force, leaving open the question of the function of the GTPase activity of FtsZ. Here we study the mechanism by which SulA, an inhibitor of FtsZ induced during the SOS response, inhibits FtsZ function. We studied the effects of SulA on the in vitro activities of FtsZ, on Z rings in vivo, and on a kinetic model for FtsZ polymerization in silico. We found that the binding of SulA to FtsZ is necessary but not sufficient for inhibition of polymerization, since the assembly of FtsZ polymers in the absence of the GTPase activity was not inhibited by SulA. We developed a new model for FtsZ polymerization that accounts for the cooperativity of FtsZ and could account for cooperativity observed in other linear polymers. When SulA was included in the kinetic scheme, simulations revealed that SulA with strong affinity for FtsZ delayed, but did not prevent, the assembly of polymers when they were not hydrolyzing GTP. Furthermore, the simulations indicated that SulA controls the assembly of FtsZ by binding to a polymerization-competent form of the FtsZ molecule and preventing it from participating in assembly. In vivo stoichiometry of the disruption of Z rings by SulA suggests that FtsZ may undergo two cooperative transitions in forming the Z ring.

Simulation and theory of flexible equilibrium polymers under poor solvent conditions

Grand canonical Monte Carlo simulation and simple statistical thermodynamic theory are used to model the aggregation and phase separation of systems of reversibly polymerizing monomers, capable of forming chains with or without the ability to cyclize into rings, with isotropic square-well attractions between nonbonded pairs of monomers. The general trend observed in simulation of chain-only systems, as predicted in a number of published theoretical works, is that the critical temperature for phase separation increases and the critical monomer density decreases with rising polymer bond strength. Introduction of the equilibrium between chains and rings into the theory lowers the predicted critical temperature and increases the predicted critical density. While the chain-only theories predict a vanishing critical density in the limit of complete polymerization, when ring formation is taken into account the predicted critical density in the same limit approaches the density of the onset of the ring-chain transition. The theoretically predicted effect of cyclization on chemical potential is in good qualitative agreement with a subset of simulation results in which chain-only systems were compared with equilibrium mixtures of rings and chains. The influence of attractions on the aggregation number and radius of gyration of chains and rings observed in simulations is also discussed.