Buckling of a single microtubule by optical trapping forces: Direct measurement of microtubule rigidity

Abstract

As major determinants of cell shape and polarity, microtubules are required to have suitable rigidity. However, our knowledge of the mechanical properties of microtubules is far from satisfactory. We report here a new method of measuring the flexural rigidity of a single microtubule by direct buckling using the optical trapping technique. Microtubule buckling was induced by applying a small longitudinal compressing force through an optically trapped microsphere that was firmly attached to the microtubule. Three ways of estimating the flexural rigidity of a continuous slender rod, one from the observed critical load of buckling and two from deflected lengths and angles of bending, yielded values which agreed well when applied to the analysis of buckling microtubules. Unexpectedly, we found that the rigidity was not constant as expected but was dependent on microtubule length. This length dependency explains the discrepancies among reported values of microtubule flexural rigidity measured by different methods. Comparing microtubules of identical lengths, microtubules assembled with brain-derived associated proteins (4 × 10⁻²³ Nm² at around 10 m̈m in length) were four times more rigid than those assembled from purified tubulin and stabilized with taxol (1 × 10⁻²³ Nm²).