Abstract
Quasi-one-dimensional microtubules (MTs) in cells enjoy high axial rigidity but large transverse flexibility due to the inter-protofilament (PF) sliding. This study aims to explore the structure–property relation for MTs and examine the relevance of the beam theories to their unique features. A molecular structural mechanics (MSM) model was used to identify the origin of the inter-PF sliding and its role in bending and vibration of MTs. The beam models were then fitted to the MSM to reveal how they cope with the distinct mechanical responses induced by the inter-PF sliding. Clear evidence showed that the inter-PF sliding is due to the soft inter-PF bonds and leads to the length-dependent bending stiffness. The Euler beam theory is found to adequately describe MT deformation when the inter-PF sliding is largely prohibited. Nevertheless, neither shear deformation nor the nonlocal effect considered in the ‘more accurate’ beam theories can fully capture the effect of the inter-PF sliding. This reflects the distinct deformation mechanisms between an MT and its equivalent continuous body.
Highlights
Microtubules (MTs) are a structural element and primary organizer in the cytoskeleton of eukaryotic cells (Chretien and Fuller 2000)
The mechanics of MTs (Felgner et al 1996; Gao and Lei 2009; Gittes et al 1993; Kikumoto et al 2006; Li et al 2006; Takasone et al 2002; Tounsi et al 2010; Valdman et al 2012; Zhang and Wang 2017) has been studied extensively in the last two decades, where the length dependency of equivalent bending stiffness (EI)eq was captured as a unique feature of MTs and interpreted primarily via the continuum mechanics models (CMMs)
These results suggested that the upper limit of the shear modulus of MTs should be at the order of 1 MPa, which is close to the shear modulus 1.4 MPa measured in Kis et al (2002)
Summary
Microtubules (MTs) are a structural element and primary organizer in the cytoskeleton of eukaryotic cells (Chretien and Fuller 2000) They form “tracks” on which motor proteins transport organelles and construct the spindle apparatus to facilitate cell division (Howard and Hyman 2003). In 2002, using this technique Kis et al (2002) first reported the length-dependence of (EI)eq for MTs and attributed it to their low shear modulus G. This theory (Kis et al 2002) was used by Kasas et al to study the effect of anisotropy on MTs via the finite element method (Kasas et al 2004). Pampaloni et al employed the theory to understand the lengthdependent (EI)eq achieved experimentally (Pampaloni et al 2006)
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