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

Abstract

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.

Heterogeneous force network in 3D cellularized collagen networks

“…In addition, the transport properties (e.g., macromolecule diffusivity) [32,[37][38][39][40][41][42][43][44][45][46] and mechanical properties (e.g., elastic moduli, bulk rheology, stress distribution, etc.) [14,16,18,35,[47][48][49][50][51][52][53] of biopolymer network, which are respectively crucial to the chemical and mechanical signalling between the cells, strongly depend on the network microstructure.…”

Mechanical properties and characteristics of microtubules: A review

“…GPa [147], which shows that the longitudinal elastic modulus is two orders of magnitude higher than the circumferential modulus. It can be evaluated that the elastic moduli predicted by atomistic-continuum modeling fall in the reasonable range and matches well with recently reported theoretical and experimental values.…”

“…In order to study the subtle mechanical behavior of biopolymers, a series of works based on an atomistic-based model has been reported, in which real geometric and characteristics were not considered in the simulation of guanosine (GDP/GTP) molecules and longitudinal biopolymers were modeled using simplified infinite bodies [147]. Hence, the length dependent mechanical properties such as the flexural rigidities and detailed interaction are not reflected, which play essential roles in vibration analysis.…”

Normal Calculus on Moving Surfaces

“…Methods to model this motion have yielded some, but still quite few analytical results -the bulk of which have been obtained over the past four decades [1,2]. Most advances in this field of modelling have arose by modelling investigations which approximated Constitutive Equations of the Membrane and various Cytoskeletal components, and then proceeded apply various facets of Continuum Mechanics to the surface in an attempt to understand the effects of Microtubule Dynamics on the membrane [2,3] and the effects of local Actin Concentrations to the surface [4].…”