Chirality Effects in Molecular Chainmail

Abstract

Motivated by the observation of positive Gaussian curvature in kinetoplast DNA networks, we consider the effect of linking chirality in square lattice molecular chainmail networks using Langevin dynamics simulations and constrained gradient optimization. Linking chirality here refers to ordering of over-under versus under-over linkages between a loop and its neighbors. We consider fully alternating linking, maximally non-alternating, and partially non-alternating linking chiralities. We find that in simulations of polymer chainmail networks, the linking chirality dictates the sign of the Gaussian curvature of the final state of the chainmail membranes. Alternating networks have positive Gaussian curvature, similar to what is observed in kinetoplast DNA networks. Maximally non-alternating networks form isotropic membranes with negative Gaussian curvature. Partially non-alternating networks form flat diamond-shaped sheets which undergo a thermal folding transition when sufficiently large, similar to the crumpling transition in tethered membranes. We further investigate this topology-curvature relationship on geometric grounds by considering the tightest possible configurations and the constraints that must be satisfied to achieve them.

18 pages, 12 figures

References in corpus (11)

• Electric Field Effect in Atomically Thin Carbon Films
• Disclinations, dislocations and continuous defects: a reappraisal
• On the Minimum Ropelength of Knots and Links
• Equilibrium mechanisms of self-limiting assembly
• Knot Tightening By Constrained Gradient Descent
• Geometry of Calugareanu's theorem
• Hidden symmetries generate rigid folding mechanisms in periodic origami
• Ring-o-rings: a new category of supramolecular structures with topologically tunable properties
• Buckling and metastability in membranes with dilation arrays
• Dynamical Scaling of Polymerized Membranes
• Electronic structure of negatively curved graphene