Biomolecular motor-driven microtubule translocation in the presence of shear flow: modeling microtubule deflection due to shear

We have previously demonstrated that shear flow aligns microtubules moving on kinesin-coated microchannels with the flow direction, and statistically analyzed the rate of microtubule alignment under different concentrations of kinesin as well as strengths of shear flow. These data qualitatively support the hypothesis that the alignment results from the leading ends of translocating microtubules bending into the direction of the flow due to viscous drag force. Here, we present a cantilever-beam model that quantitatively shows agreement between this hypothesis and observation. Specifically, the model couples the exact nonlinear solution for cantilever-beam deflection with drag coefficients determined by numerical simulations of microtubules in the presence of shear flow near a wall. Coupled with flexural rigidity results of our previous study (which used electric fields), the established model successfully predicts new experimental data for microtubule bending in response to shear flow, further supporting our hypothesis for the mechanism of microtubule alignment. We expect that the newly-calculated drag coefficients and beam-bending model may be useful for biophysical studies as well as interpretation of in vivo data and the design of kinesin/microtubule-based devices.