Cytoskeleton-Membrane Interactions in Neuronal Growth Cones: A Finite Analysis Study

Abstract

Revealing the molecular events of neuronal growth is critical to obtaining a deeper understanding of nervous system development, neural injury response, and neural tissue engineering. Central to this is the need to understand the mechanical interactions between the cytoskeleton and the cell membrane, and how these interactions affect the overall growth mechanics of neurons. Using finite element analysis, the stress in the membrane produced by an actin filament or a microtubule acting against a deformable membrane was modeled, and the deformation, stress, and strain were computed for the membrane. Parameters to represent the flexural rigidities of the well-studied actin and tubulin cytoskeletal proteins, as well as the mechanical properties of cell membranes, were used in the simulations. Our model predicts that a single actin filament is able to produce a normal contact stress on the cell membrane that is sufficient to cause membrane deformation but not growth. Our model also predicts that under clamped boundary conditions a filament with a buckling strength equal to or smaller than an actin filament would not cause the areal strain in the membrane to exceed 3%, and therefore the filament is incapable of causing membrane rupture or puncture to a safety factor of approximately 15-25. Decreasing the radius of the membrane upon which the normal contact stress is acting allows an increase in the amount of normal contact stress that the membrane can withstand before rupture. The model predicts that a 50 nm radius membrane can withstand approximately 4 MPa of normal contact stress before membrane rupture whereas a 250 nm radius membrane can withstand approximately 2.5 MPa. Understanding how the mechanical properties of cytoskeletal elements have coevolved with their respective cell membranes may yield insights into the events that gave rise to the sequences and superquaternary structures of the major cytoskeletal proteins. Additionally, numerical modeling of membranes can be used to analyze the forces and stresses generated by nanoscale biological probes during cellular injection.

Molecular Modeling of the Axial and Circumferential Elastic Moduli of Tubulin

“…Of particular interest may be the investigation of evolutionary trends that drove tubulin to its current state as it evolved to support its myriad of mechanical roles (59,60). Future work will include using values obtained for the elastic moduli and incorporating them into a finite element model to perform bending and buckling tests (e.g., (61)). We will assume the microtubule to be a fully stable polymerized chain.…”

WallGen, Software to Construct Layered Cellulose-Hemicellulose Networks and Predict Their Small Deformation Mechanics

“…Examples include predicting cell response to microindentation (Bolduc et al, 2006) or compression between flat plates (Smith et al, 1998) and predicting the mechanics of pulped fiber networks in paper (Hansson and Rasmuson, 2004). These applications have not involved mechanical representation of individual wall polymers, but FEA has been used at this scale to model individual microtubules and F-actin polymers pulling on membranes (Allen et al, 2009) and at even finer scales to model tubulin lattice deformation within single microtubules (Schaap et al, 2006). Modern FEA programs have features of potential value for developing more sophisticated models of wall mechanics: components can have nonlinear force-extension properties and viscoelastic properties, and conditions can be specified to break links between components of the microstructure.…”

Three-dimensional transverse vibration of microtubules

“…Thus the mechanics of MTs has excited extensive studies in the last two decades [10][11][12][13][14]. Specifically, the vibration of MTs has drawn considerable attention from the communities of nano and biomechanics [10][11][12][13][14][15][16][17] as it has the potential to impact on the intracellular physiological processes [18][19][20][21], provides a physical mechanism for the novel noninvasive biosensors [22] and facilitates the development of advanced biomimetic nanomaterials, e.g., MT-graphene nanotubes, whose applications rely heavily on MT vibration [23,24].…”