Atomistic-based continuum constitutive relation for microtubules: elastic modulus prediction

Mechanical behavior of cells is primarily governed by the cytoskeleton (CSK), a remarkable system of filaments consisting of microtubules, actin filaments and intermediate filaments. This system defines the shape and bulk mechanical properties of the cell. In order to understand how the CSK network influences the mechanical behavior of living cells from a theoretical perspective, the mechanical properties of an individual CSK filament must first be properly described. Existing atomistic simulation methods have computational size limitations; conversely, conventional continuum mechanics lack fundamental nanoscale information. Here a new simulation method is developed that bridges the gap between these two simulation regimes using an atomistic-based continuum constitutive relation for microtubules based on the interatomic potential for proteins and specific atomic structures. This theory is used to predict the elastic modulus of microtubules, which agrees with the range of experimentally measured values without any parameter fitting. The proposed method is applicable to other biopolymers if the subunits are bonded through noncovalent bonds.