Abstract
Quantitative description of cell mechanics has challenged biological scientists for the past two decades. Various structural models have been attempted to analyze the structure of the cytoskeleton. One important aspect that has been largely ignored in all these modeling approaches is related to the flexural and buckling behavior of microtubular filaments. The objective of this paper is to explore the influence of this flexural and buckling behavior in cytoskeletal mechanics. In vitro the microtubules are observed to buckle in the first mode, reminiscent of a free, simply-supported beam. In vivo images of microtubules, however, indicate that the buckling mostly occurs in higher modes. This buckling mode switch takes place mostly because of the lateral support of microtubules via their connections to actin and intermediate filaments. These lateral loads are exerted throughout the microtubule length and yield a considerable bending behavior that, unless properly accounted for, would produce erroneous results in the modeling and analysis of the cytoskeletal mechanics.One of the promising attempts towards mechanical modeling of the cytoskeleton is the tensegrity model, which simplifies the complex network of cytoskeletal filaments into a combination merely of tension-bearing actin filaments and compression-bearing microtubules. Interestingly, this discrete model can qualitatively explain many experimental observations in cell mechanics. However, evidence suggests that the simplicity of this model may undermine the accuracy of its predictions, given the model's underlying assumption that “every single member bears solely either tensile or compressive behavior,” i.e. neglecting the flexural behavior of the microtubule filaments. We invoke an anisotropic continuum model for microtubules and compare the bending energy stored in a single microtubule with its axial strain energy at the verge of buckling. Our results suggest that the bending energy can exceed the axial energy of microtubules by 40 folds. A modification to tensegrity model is, therefore, proved necessary in order to take into account the flexural response of microtubules. The concept of “bendo-tensegrity” is proposed as a modification to contemporary cytoskeletal tensegrity models.
Highlights
Living cells actively respond to their mechanical environment, altering their proliferation rate, cytoskeletal configuration, and gene expression pattern when exposed to a mechanical perturbation
To incorporate mechanical effects of other cytoskeletal filaments on microtubules, most researchers have simulated a microtubule filament as a beam surrounded by an elastic continuum [14,22,23,31]
A semi-discrete method is adopted and it is assumed that loads on the microtubule filament are applied at alternating continuous intervals, whereas load distribution pattern for each interval will be derived in the following
Summary
Living cells actively respond to their mechanical environment, altering their proliferation rate, cytoskeletal configuration, and gene expression pattern when exposed to a mechanical perturbation. The details of how cells sense mechanical signals and how mechanical signals are transduced and transmitted from the extracellular matrix (ECM) throughout the cell have remained ambiguous [1,2] This has motivated quantitative models for the cytoskeleton [1], as a mechanical structure hosting and participating in signaling pathways of the cell [1,2,3]. The tensegrity structure should be free from any shearintroducing structural behavior (i.e. bending and torsion) [8] Such a condition would imply that all members must be straight, all joints must be moment-free (or hinge), and loads should be applied exclusively to joints [9]. A tensegrity structure owes its stability to the pre-existing tensile stress (pre-stress) in its members, since its slender members could transfer the load only when they are under tension [5]
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