Assuming that actin filaments have an effective radius of 2.8nm, a Young’s modulus of 1.8 GPa, and break at an average force of approximately 400pN. use these alues to estimate the strain at which the actin filament will break.

The relationship in between the incremental modulus, \(E_0\) , of a six-strut tensegrity model of the cell and the resting force in the actin filaments, \(F_0\) , the resting length of the actin filaments, \(l_0\) , and the resting strain of the cell, \(\epsilon_0\) , is given by:

\(E_0= 5.85*(F_0/(L_0)^2}*(1+4epsilon_0/1+12\epsilon_0)\)

Recalling that the length of the actin filaments is related to the length of the microtubules, \(L_0\) , by \(L_0=\sqrt{3/8L_{0}}\) , we can express \(E_{0}\) in terms of \(L_{0}\) as:

\(E_0= 15.6(F_0/(L_0)^2}*(1+4epsilon_0/1+12\epsilon_0)\)

In this question, you will use this equation to estimate the upper and lower bounds of \(E_{0}\) as predcted by the tensegrity model. The upper bound of the prediction can be determined by assuming the actin filaments are on the verge of breaking in the resting position. Assuming that actin filaments have an effective radius of 2.8nm, a Young’s modulus of 1.8 GPa, and break at an average force of approximately 400pN. use these alues to estimate the strain at which the actin filament will break.