Flexural rigidity of singlet microtubules estimated from statistical analysis of their contour lengths and end-to-end distances

Abstract

Microtubules in solutions, observed under a dark-field microscope, show incessant Brownian movement such as translational, rotational and flexing motion. A large number of microtubules, spontaneously stuck to the under surface of a coverslip, were photographed and the contour lengths and end-to-end distances of their images were measured. From the statistical analysis of the contour lengths and end-to-end distances, a value for the parameter lambda representing the flexibility of singlet microtubules was estimated to be lambda = (6.8 +/- 0.8) . 10(-3) micrometers-1. From the value of lambda, the elastic modulus for bending, epsilon, and Young's modulus, Y, of singlet microtubules were computed to be epsilon = approximately 10(-16) and Y = approximately 10(9) dyne . cm-2, respectively. The microscopic elastic constant, k, of bonding between two tubulin monomers neighboring along the singlet microtubule was computed to be k = congruent to 10(2) dyne . cm-1. A singlet microtubule is an order of magnitude as strong against bending and as weak against stretching as an F-actin filament.