Thermal Fluctuations of Anisotropic Semiflexible Polymers

TL;DR

This paper introduces a finite element modeling framework to simulate the thermal fluctuations of anisotropic semiflexible polymers like microtubules, providing insights into their mechanical properties and challenging previous experimental interpretations.

Contribution

The study develops a finite element approach for anisotropic polymers, validating it against analytical models and applying it to microtubules to analyze their persistence length and anisotropic effects.

Findings

Finite element framework accurately matches analytical MSD predictions.

Anisotropic properties do not explain the length-dependent persistence length of microtubules.

The model provides a tool for interpreting experimental data on anisotropic biopolymers.

Abstract

Thermal fluctuations of microtubules (MTs) and other cytoskeletal filaments govern to a great extent the complex rheological properties of the cytoskeleton in eukaryotic cells. In recent years, much effort has been put into capturing the dynamics of these fluctuations by means of analytical and numerical models. These attempts have been very successful for, but also remain limited to, isotropic polymers. To correctly interpret experimental work on (strongly) anisotropic semiflexible polymers, there is a need for a numerical modelling tool that accurately captures the dynamics of polymers with anisotropic material properties. In the current study, we present a finite element (FE) framework for simulating the thermal dynamics of a single anisotropic semiflexible polymer. First, we demonstrate the accuracy of our framework by comparison of the simulated mean square displacement (MSD) of the end-to-end distance with analytical predictions based on the worm-like chain model. Then, we implement a transversely isotropic material model, characteristic for biopolymers such as MTs, and study the persistence length for various ratios between the longitudinal shear modulus and corresponding Young's modulus. Finally, we put our findings in context by addressing a recent experimental work on grafted transversely isotropic MTs. In that research, a simplified static mechanical model was used to deduce a very high level of MT anisotropy to explain the observation that the persistence length of grafted MTs increases as contour length increases. We show, by means of our FE framework, that the anisotropic properties cannot account for the reported length-dependent persistence length.