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

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 $∼15–25$⁠. 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 $50nm$ radius membrane can withstand $∼4MPa$ of normal contact stress before membrane rupture whereas a $250nm$ radius membrane can withstand $∼2.5MPa$⁠. 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.