Simple Growth Models of Rigid Multifilament Biopolymers

TL;DR

This paper develops simple theoretical models to analyze the growth dynamics of rigid biopolymers with multiple protofilaments, providing explicit formulas for growth velocity and dispersion, and validating them against detailed models and experimental data.

Contribution

It introduces an approximate analytical framework that accounts for protofilament interactions and end structures, enabling exact growth predictions for any number of protofilaments.

Findings

Exact growth velocity and dispersion formulas derived for any protofilament number.

Approximate models closely match detailed dynamics for large lateral interactions.

The theory successfully explains experimental microtubule growth data.

Abstract

The growth dynamics of rigid biopolymers, consisting of $N$ parallel protofilaments, is investigated theoretically using simple approximate models. In our approach, the structure of a polymer's growing end and lateral interactions between protofilaments are explicitly taken into account, and it is argued that only few conformations are important for biopolymer's growth. As a result, exact analytic expressions for growth velocity and dispersion are obtained for {\it any} number of protofilaments and arbitrary geometry of the growing end of the biopolymer. Our theoretical predictions are compared with a full description of biopolymer growth dynamics for the simplest N=2 model. It is found that the results from the approximate theory are approaching the exact ones for large lateral interactions between the protofilaments. Our theory is also applied to analyze the experimental data on the growth of microtubules.