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# Long-distance propagation of forces in a cell

What might be the differences, if there is any, between mechanical signaling and chemical signaling in a living cell?

Some argue that since a local applied force decays rapidly at the cell surface, it causes only local deformation that, in turn, can activate only local biochemical activities (e.g., protein phosphorylation), followed by diffusion and/or tranlocation based signaling, similar to soluble ligand induced chemical signaling. However, recent experiments have shown that a force of a physiological magnitude, applied via a focal adhesion, can propagate a long distance into the cell to deform cytoplasmic structures and nuclear structures at remote sites.

These observations disagree with existing cell models and prevailing views on mechanical signaling. We show that this "action at a distance" results from the inhomogeneity in the cell: a prestressed and stiff actin bundle *guides* the propagation of forces over long distances.

Our models highlight the enormous ratios of the prestress and the modulus of the actin bundle to the modulus of the cytoskeletal network. For a normal cell, the models predict that forces propagate over characteristic lengths comparable to the size of the cell. The characteristic lengths can be altered, however, by treatments of the cell. Our models provide a possible mechanism for the long-distance force propagation in a living cell, a potential major difference between mechanical signaling and chemical signaling.

Ning Wang and Zhigang Suo, Long-distance propagation of forces in a cell, Biochemical and Biophysical Research Communications 328, 1133-1138 (2005)

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## Comments

## prestress in actin bundle

An error, the solution for equation (1) is v(x)=A*exp(-x/L1)+B*exp(x/L1)

Question: In the

Modelssection, how is the statement that “the prestress exerts a force hb^2*sigma_b*d^2/dx^2*dx” derived? thanks.## Force due to prestress in actin fiber

Thank you for pointing out a typo of sign in the paper. I looked at the paper again. The typo should not affect the rest of the paper, because we interpreted the result as exponential decay, and discussed the length scale L1.

I have just replaced the reprint with a preprint to avoid possible copyright issues. (Incidentally, I just notice that in the preprint the sign is correct.)

The prestress in the actin fiber gives an axial force T = sigma_b*hb^2. Let the slope of the actin fiber be q = dv/dx. The vertical force due to the tension on an element dx is

Tq(x+dx)-Tq(x) = T*d^2v/dx^2

To reach equation (1), we also need to estimate the effect of the cytoskeleton network on an actin fiber. This effect is estimated by thinking the network as an array of springs.