Microtubule Motional Diffusion Coefficient in Motility Assays is Determined by Heterogeneity in Motor Stiffness

In the past twenty years, our ability to manipulate and engineer devices at the nano-scale has grown exponentially. As the fabrication of autonomous systems at these scales becomes a reality, the observation of biological structures can help us understand general design principles at the nano-scale. The gliding motility assay is an excellent model system for the observation of collective behavior of coupled motors. Indeed, hundreds of surface-adhered kinesin motors propel one microtubule filament. Filament motion has been observed using fluorescence microscopy, revealing fluctuations in gliding velocity. We here theoretically characterize the motional diffusion coefficients through the heterogeneity factor proposed by Sekimoto and Tawada, and use a Brownian dynamics simulation of kinesin head diffusion under an anharmonic potential to determine a theoretical value of 0.3 for this heterogeneity factor.