Question

1. We previously found a relationship between the incremental modulus, E₀, of a six-strut tensegrity model of the cell and the resting force in the actin filaments, F₀, the resting length of the actin filaments, l_o, and the resting strain of the cell ε₀:. Recalling that the length of the actin filaments is related to the length of the microtubules, L₀, by  we can express E₀in terms of L₀as  In this question you will use this equation to estimate the upper and lower E₀as predicted by the tensegrity model.
   1. The upper bound of the prediction can be determined by assuming that the actin filaments are on the verge of breaking in the resting position. Assuming that the actin filaments have an effective radius of 2.8 nm, a Young’s modulus of 1.8 GPa, and break at an average force of approximately 400 pN. Use these values to estimate the strain at which an actin filament will break.
   2. Plot E₀versus L₀for L₀ranging from 1 to 6 um, taking into account the estimate for resting strain you calculated in (a). You will find it clearer to use a log axis for the modulus. This curve represents the upper bound of the tensegrity model.
   3. Based on force balances on the struts, it can be shown that the force in a strut in the resting position, P₀, is related to the resting force in the actin filament by  The lower bound can be determined by assuming that the microtubules are on the verge of buckling in the resting position. Express E₀in terms of the microtubule flexural rigidity, initial actin filament strain, and L₀assuming the microtubules are on the verge of buckling in the resting position.

Answer 1