Flatness and Intrinsic Curvature of Linked-Ring Membranes

TL;DR

This study uses Monte Carlo simulations to explore the shape, flatness, and intrinsic curvature of linked-ring membranes, revealing unique concave structures influenced by ring thickness and linking patterns, with implications for biological kinetoplasts.

Contribution

It introduces a novel simulation approach to analyze linked-ring membrane properties, highlighting intrinsic curvature and shape behaviors not seen in covalent membranes.

Findings

Linked-ring membranes exhibit intrinsic concavity due to entropic effects.

Increasing ring thickness enhances membrane swelling and concavity.

The linking network influences the degree of membrane curvature.

Abstract

Recent experiments have elucidated the physical properties of kinetoplasts, which are chain-mail-like structures found in the mitochondria of trypanosome parasites formed from catenated DNA rings. Inspired by these studies, we use Monte Carlo simulations to examine the behavior of two-dimensional networks ("membranes") of linked rings. For simplicity, we consider only identical rings that are circular and rigid and that form networks with a regular linking structure. We find that the scaling of the eigenvalues of the shape tensor with membrane size are consistent with the behavior of the flat phase observed in self-avoiding covalent membranes. Increasing ring thickness tends to swell the membrane. Remarkably, unlike covalent membranes, the linked-ring membranes tend to form concave structures with an intrinsic curvature of entropic origin associated with local excluded-volume interactions. The degree of concavity increases with increasing ring thickness and is also affected by the type of linking network. The relevance of the properties of linked-ring model membranes to those observed in kinetoplasts is discussed.