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.

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The primary goal of this work is to establish a robust, repeatable method for growing forebrain nerve cells in a parallel manner by stretching them using a microfabricated PDMS beam array and printing arrays of neurons. The highly compliant, transparent, biocompatible PDMS micro beam array may offer a method for more rapid throughput in cell and protein mechanics force measurement experiments with sensitivities necessary for highly compliant structures such as axons. This work has two endpoints. One is to use a neural array as an experimental testbed for investigating neuronal cell growth hypotheses. The other endpoint is to build a neuronal-based, biosensor device capable of acting as a cell-based sensor. We present preliminary results for microbeams attaching to nerve cells. The attachment ratio the life-length and the axon lengths of the chick forebrain cells on microprinted spots will also be compared with an equivalent protein coated area of cells.

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