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Research Papers

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

[+] Author and Article Information
Kathleen B. Allen, F. Mert Sasoglu

Department of Mechanical Engineering and Mechanics, Drexel University, 3141 Chestnut Street, Philadelphia, PA 19104

Bradley E. Layton

Department of Mechanical Engineering and Mechanics, Drexel University, 3141 Chestnut Street, Philadelphia, PA 19104bradley.layton@drexel.edu

J Biomech Eng 131(2), 021006 (Dec 10, 2008) (10 pages) doi:10.1115/1.3005337 History: Received March 06, 2008; Revised June 16, 2008; Published December 10, 2008

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 1525. 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.

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Copyright © 2009 by American Society of Mechanical Engineers
Topics: Force , Stress , Membranes
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References

Figures

Grahic Jump Location
Figure 3

Numerical solution for the maximum membrane strain for clamped-immovable and clamped-movable membranes with radii of 50nm and 250nm versus the number of elements used to create the membranes. The clamped-immovable membranes are represented by circles, and the clamped-movable membranes are represented by triangles.

Grahic Jump Location
Figure 4

Maximum membrane deflection in the z direction versus applied force for clamped-immovable membranes of sizes 50nm, 100nm, and 250nm in radii with Poisson’s ratio of 0.3. The analytical solution is represented by the solid line and the ANSYS solution with the open circles.

Grahic Jump Location
Figure 5

von Mises stress along δΩ versus applied force for clamped-immovable membranes of sizes 50nm, 100nm, and 250nm radii with Poisson’s ratio of 0.3. The analytical solution is represented by the solid line and the ANSYS solution with the open circles. The 50nm and 100nm stresses were nearly similar.

Grahic Jump Location
Figure 6

Maximum membrane deflection in the z-direction versus applied force for clamped-movable membranes of sizes 50nm, 100nm, and 250nm radii with Poisson’s ratios of 0.3. The analytical solution is represented by the solid line and the ANSYS solution with the open circles.

Grahic Jump Location
Figure 7

von Mises stress along δΩ versus applied force for clamped-movable membranes of sizes 50nm, 100nm, and 250nm radii with Poisson’s ratios of 0.3. The analytical solution is represented by the solid line and the ANSYS solution with the open circles. The 50nm and 100nm stresses are nearly identical.

Grahic Jump Location
Figure 8

Areal strain (εareal) /MPa versus radial distance from the center of the membrane for a clamped-immovable membrane with a radius of 250nm. Membrane rupture will occur when the tension in the membrane causes the areal strain to exceed 3%. This will occur at center of the membrane on its outer surface if the normal contact stress applied exceeds ∼2.55MPa.

Grahic Jump Location
Figure 9

Areal strain (εareal) /MPa versus radial distance from the center of the membrane for a clamped-immovable membrane with a radius of 50nm. Membrane rupture will occur at center of the stress distribution on its outer surface if the normal contact stress applied exceeds ∼3.74MPa.

Grahic Jump Location
Figure 10

Areal strain (εareal) /MPa versus radial distance from the center of the membrane for a clamped-movable membrane with a radius of 250nm. Membrane rupture will occur at the center of the normal contact stress distribution on its outer surface if the normal contact stress applied exceeds ∼2.61MPa.

Grahic Jump Location
Figure 11

Areal strain (εareal) /MPa versus radial distance from the center of the membrane for a clamped-movable membrane with a radius of 50nm. Membrane rupture will occur at the center of the normal contact stress distribution on its outer surface if the normal contact stress applied exceeds ∼4.09MPa.

Grahic Jump Location
Figure 1

Scale cartoon drawing of an actin filament with a diameter of approximately 8nm impinging upon the inner surface of a phospholipid bilayer membrane with a thickness of approximately 4.5nm.

Grahic Jump Location
Figure 2

Schematic of a circular membrane deforming under a point force acting at center of the membrane. The membrane is represented by Ω, and the edge of the membrane by δΩ. Polar coordinates, r, z, θ were used. (a) The top view and side view, respectively, of a clamped and immovable membrane along δΩ, where  ∣dw∕dq∣δΩ=0 and q=qo. (b) The top view and side view, respectively, of a membrane clamped along δΩ but free to move in q, ∣dw∕dq∣δΩ=0, but q≠qo. The dashed lines depict the deformed membrane (not to scale).

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