29 research outputs found
Frustrated Polyelectrolyte Bundles and T=0 Josephson-Junction Arrays
We establish a one-to-one mapping between a model for hexagonal
polyelectrolyte bundles and a model for two-dimensional, frustrated
Josephson-junction arrays. We find that the T=0 insulator-to-superconductor
transition of the {\it quantum} system corresponds to a continuous
liquid-to-solid transition of the condensed charge in the finite temperature
{\it classical} system. We find that the role of the vector potential in the
quantum system is played by elastic strain in the classical system. Exploiting
this correspondence we show that the transition is accompanied by a spontaneous
breaking of chiral symmetry and that at the transition the polyelectrolyte
bundle adopts a universal response to shear.Comment: 4 pages, 2 figures, 1 table minor changes to text, reference adde
Geometric Signatures of Switching Behavior in Mechanobiology
The proteins involved in cells' mechanobiological processes have evolved
specialized and surprising responses to applied forces. Biochemical
transformations that show catch-to-slip switching and force-induced pathway
switching serve important functions in cell adhesion, mechano-sensing and
signaling, and protein folding. We show that these switching behaviors are
generated by singularities in the flow field that describes force-induced
deformation of bound and transition states. These singularities allow for a
complete characterization of switching mechanisms in 2-dimensional (2D) free
energy landscapes, and provide a path toward elucidating novel forms of
switching in higher dimensional models. Remarkably, the singularity that
generates a catch-slip switch occurs in almost every 2D free energy landscape,
implying that almost any bond admitting a 2D model will exhibit catch-slip
behavior under appropriate force. We apply our analysis to models of P-selectin
and antigen extraction to illustrate how these singularities provide an
intuitive framework for explaining known behaviors and predicting new
behaviors.Comment: 6 pages, 3 figure
Viral self-assembly as a thermodynamic process
The protein shells, or capsids, of all sphere-like viruses adopt icosahedral
symmetry. In the present paper we propose a statistical thermodynamic model for
viral self-assembly. We find that icosahedral symmetry is not expected for
viral capsids constructed from structurally identical protein subunits and that
this symmetry requires (at least) two internal "switching" configurations of
the protein. Our results indicate that icosahedral symmetry is not a generic
consequence of free energy minimization but requires optimization of internal
structural parameters of the capsid proteins.Comment: pdf file, 13 pages, three figure
Physics of viral dynamics
Viral capsids are often regarded as inert structural units, but in actuality they display fascinating dynamics during different stages of their life cycle. With the advent of single-particle approaches and high-resolution techniques, it is now possible to scrutinize viral dynamics during and after their assembly and during the subsequent development pathway into infectious viruses. In this Review, the focus is on the dynamical properties of viruses, the different physical virology techniques that are being used to study them, and the physical concepts that have been developed to describe viral dynamics
Elasticity Theory and Shape Transitions of Viral Shells
Recently, continuum elasticity theory has been applied to explain the shape
transition of icosahedral viral capsids - single-protein-thick crystalline
shells - from spherical to buckled/faceted as their radius increases through a
critical value determined by the competition between stretching and bending
energies of a closed 2D elastic network. In the present work we generalize this
approach to capsids with non-icosahedral symmetries, e.g., spherocylindrical
and conical shells. One key new physical ingredient is the role played by
nonzero spontaneous curvature. Another is associated with the special way in
which the energy of the twelve topologically-required five-fold sites depends
on the background local curvature of the shell in which they are embedded.
Systematic evaluation of these contributions leads to a shape phase diagram in
which transitions are observed from icosahedral to spherocylindrical capsids as
a function of the ratio of stretching to bending energies and of the
spontaneous curvature of the 2D protein network. We find that the transition
from icosahedral to spherocylindrical symmetry is continuous or weakly
first-order near the onset of buckling, leading to extensive shape degeneracy.
These results are discussed in the context of experimentally observed
variations in the shapes of a variety of viral capsids.Comment: 53 pages, 17 figure
Chiral symmetry breaking in Langmuir monolayers and smectic films
Langmuir monolayers and freely suspended smectic films can exhibit a spontaneous breaking of chiral symmetry. The order parameter that characterizes this symmetry breaking is coupled to variations in the direction of molecular tilt. As a result, chiral symmetry breaking leads to the spontaneous formation of complex equilibrium patterns with either 1D or 2D modifications in the direction of molecular tilt. A Landau theory for this pattern formation gives a general phase diagram, which includes a uniform nonchiral phase, a striped pattern, a square lattice, and a uniform chiral phase
Phase Diagram of Chiral Biopolymer Wigner Crystals
We study the statistical mechanics of counterion Wigner crystals associated
with hexagonal bundles of chiral biopolymers. We show that, due to spontaneous
chiral symmetry breaking induced by frustration, these Wigner crystals would be
chiral even if the biopolymers themselves were not chiral. Using a duality
transformation of the model onto a "spin-charge" Hamiltonian, we show that
melting of the Wigner crystal is due to the unbinding of screw dislocations and
that the melting temperature has a singular dependence on the intrinsic
chirality of the biopolymers. Finally, we report that, if electrostatic
interactions are strongly screened, the counterions can condense in the form of
an intermediate achiral Wigner solid phase that melts by the unbinding of
fractional topological charges.Comment: 43 pages, 13 figure