Constitutive-Law Estimation of Bio-Filaments from their MD Simulations

Abstract

Continuum-mechanics based models have recently evolved as viable tools to efficiently simulate large deformations of bio-filaments. However, the deformations predicted from these models are highly sensitive to their underlying constitutive-law model. Unfortunately, lack of rigorous methods for identification of constitutive-law models leaves no option but to make ad hoc assumptions and crude approximations in constitutive-law models. We recently developed a novel system identification technique together with an inverse rod model that can systematically estimate the constitutive laws of bio-filaments from their discrete structure (MD) simulations; refer to [J. Appl. Mech., 79(5), p. 051005] and [Automatica 47(6), p. 1175-1182]. An attempt to apply this technique to microtubules suggests that traditionally assumed linearly elastic constitutive laws are inaccurate, and backs the claim of existence of twist-tension coupling in the microtubules. Furthermore, microtubules exhibit kinking with hysteresis supporting the hypothesis of a non-convex constitutive law.