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

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 γ representing the flexibility of singlet microtubules was estimated to γ = (6.8 ± 0.8) · 10^?3μm^?1. From the value of γ, the elastic modulus for bending, ε, and Young's modulus, Y, of singlet microtubules were computed to be ε = ～ 10^?16 dyne·cm² and Y = ～ 10⁹ 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 = ～ 10² 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.