On the Significance of Microtubule Flexural Behavior in Cytoskeletal Mechanics

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.