Multi-Platform Compatible Software for Analysis of Polymer Bending Mechanics

John S Graham,Brannon R Mccullough,W Austin Elam,Hyeran Kang,Wenxiang Cao,Enrique M De La Cruz,Monica Soncini

doi:10.1371/journal.pone.0094766

Abstract

Cytoskeletal polymers play a fundamental role in the responses of cells to both external and internal stresses. Quantitative knowledge of the mechanical properties of those polymers is essential for developing predictive models of cell mechanics and mechano-sensing. Linear cytoskeletal polymers, such as actin filaments and microtubules, can grow to cellular length scales at which they behave as semiflexible polymers that undergo thermally-driven shape deformations. Bending deformations are often modeled using the wormlike chain model. A quantitative metric of a polymer's resistance to bending is the persistence length, the fundamental parameter of that model. A polymer's bending persistence length is extracted from its shape as visualized using various imaging techniques. However, the analysis methodologies required for determining the persistence length are often not readily within reach of most biological researchers or educators. Motivated by that limitation, we developed user-friendly, multi-platform compatible software to determine the bending persistence length from images of surface-adsorbed or freely fluctuating polymers. Three different types of analysis are available (cosine correlation, end-to-end and bending-mode analyses), allowing for rigorous cross-checking of analysis results. The software is freely available and we provide sample data of adsorbed and fluctuating filaments and expected analysis results for educational and tutorial purposes.

Highlights

Biological systems must respond to mechanical stresses and strains in a manner that does not compromise their function
The ‘‘wormlike chain’’ model is commonly used to describe semiflexible polymer mechanics and considers the end-to-end distance of a linear, unbranched polymer as a sum of unit vectors tangent to the polymer chain [4]. This model is characterized by a fundamental parameter [5], the bending persistence length (Lp), that is extracted from analysis of the polymer’s bending energy and the directional correlation of the unit tangent vectors
Our discussion is limited to protein biopolymers, the software can be used to analyze any polymer chain visualized either when adsorbed to a substrate or while fluctuating freely in solution

Summary

Introduction

Biological systems must respond to mechanical stresses and strains in a manner that does not compromise their function. In some cases those responses regulate cellular processes. The ‘‘wormlike chain’’ model is commonly used to describe semiflexible polymer mechanics and considers the end-to-end distance of a linear, unbranched polymer as a sum of unit vectors tangent to the polymer chain [4] This model is characterized by a fundamental parameter [5], the bending persistence length (Lp), that is extracted from analysis of the polymer’s bending energy and the directional correlation of the unit tangent vectors

Methods

Conclusion