Finite-strain elasticity theory and liquid-liquid phase separation in compressible gels.

The theory of finite-strain elasticity is applied to the phenomenon of cavitation observed in polymer gels following liquid-liquid phase separation of the solvent, which opens a fascinating window on the role of finite-strain elasticity theory in soft materials in general. We show that compressibility effects strongly enhance cavitation in simple materials that obey neo-Hookean elasticity. On the other hand, cavitation phenomena in gels of flexible polymers in a binary solvent that phase separates are surprisingly similar to those of incompressible materials. We find that, as a function of the interfacial energy between the two solvent components, there is a sharp transition between cavitation and classical nucleation and growth. Next, biopolymer gels are characterized by strain hardening and even very low levels of strain hardening turn out to suppress cavitation in polymer gels that obey Flory-Huggins theory in the absence of strain hardening. Our results indicate that cavitation is, in essence, not possible for polymer networks that show strain hardening.

Sensing the shape of a cell with reaction diffusion and energy minimization.

Some dividing cells sense their shape by becoming polarized along their long axis. Cell polarity is controlled in part by polarity proteins, like Rho GTPases, cycling between active membrane-bound forms and inactive cytosolic forms, modeled as a "wave-pinning" reaction-diffusion process. Does shape sensing emerge from wave pinning? We show that wave pinning senses the cell's long axis. Simulating wave pinning on a curved surface, we find that high-activity domains migrate to peaks and troughs of the surface. For smooth surfaces, a simple rule of minimizing the domain perimeter while keeping its area fixed predicts the final position of the domain and its shape. However, when we introduce roughness to our surfaces, shape sensing can be disrupted, and high-activity domains can become localized to locations other than the global peaks and valleys of the surface. On rough surfaces, the domains of the wave-pinning model are more robust in finding the peaks and troughs than the minimization rule, although both can become trapped in steady states away from the peaks and valleys. We can control the robustness of shape sensing by altering the Rho GTPase diffusivity and the domain size. We also find that the shape-sensing properties of cell polarity models can explain how domains localize to curved regions of deformed cells. Our results help to understand the factors that allow cells to sense their shape-and the limits that membrane roughness can place on this process.

Finite Temperature Phase Behavior of Viral Capsids as Oriented Particle Shells.

A general phase plot is proposed for discrete particle shells that allows for thermal fluctuations of the shell geometry and of the inter-particle connectivities. The phase plot contains a first-order melting transition, a buckling transition, and a collapse transition and is used to interpret the thermodynamics of microbiological shells.

Ground state instabilities of protein shells are eliminated by buckling.

We propose a hybrid discrete-continuum model to study the ground state of protein shells. The model allows for shape transformation of the shell and buckling transitions as well as the competition between states with different symmetries that characterize discrete particle models with radial pair potentials. Our main results are as follows. For large Föppl-von Kármán (FvK) numbers the shells have stable isometric ground states. As the FvK number is reduced, shells undergo a buckling transition resembling that of thin-shell elasticity theory. When the width of the pair potential is reduced below a critical value, then buckling coincides with the onset of structural instability triggered by over-stretched pair potentials. Chiral shells are found to be more prone to structural instability than achiral shells. It is argued that the well-width appropriate for protein shells lies below the structural instability threshold. This means that the self-assembly of protein shells with a well-defined, stable structure is possible only if the bending energy of the shell is sufficiently low so that the FvK number of the assembled shell is above the buckling threshold.