A Quantitative Model of Cellular Elasticity Based on Tensegrity

A tensegrity structure composed of six struts interconnected with 24 elastic cables is used as a quantitative model of the steady-state elastic response of cells, with the struts and cables representing microtubules and actin filaments, respectively. The model is stretched uniaxially and the Young’s modulus $E0$ is obtained from the initial slope of the stress versus strain curve of an equivalent continuum. It is found that $E0$ is directly proportional to the pre-existing tension in the cables (or compression in the struts) and inversely proportional to the cable (or strut) length square. This relationship is used to predict the upper and lower bounds of $E0$ of cells, assuming that the cable tension equals the yield force of actin (∼400 pN) for the upper bound, and that the strut compression equals the critical buckling force of microtubules for the lower bound. The cable (or strut) length is determined from the assumption that model dimensions match the diameter of probes used in standard mechanical tests on cells. Predicted values are compared to reported data for the Young’s modulus of various cells. If the probe diameter is greater than or equal to 3 μm, these data are closer to the lower bound than to the upper bound. This, in turn, suggests that microtubules of the CSK carry initial compression that exceeds their critical buckling force (order of $100-101 pN),$ but is much smaller than the yield force of actin. If the probe diameter is less than or equal to 2 μm, experimental data fall outside the region defined by the upper and lower bounds. [S0148-0731(00)00101-1]