Revised Model, With Experimental Verification, For Motor Densities In Gliding Assays

Gliding assays are used to investigate cytoskeletal polymers and motor proteins in vitro, including measurements of cytoskeletal polymer stiffness and the cooperative effects of motors. A theoretical model (Duke et al., 1995) developed to extract the biophysical quantities of interest from gliding assays has been used extensively, yet the model remains incompletely validated. In gliding assay experiments using kinesin and microtubules, we found inconsistencies in model-dependent measurements of average kinesin spacing along microtubules, a key parameter for motor cooperativity and bending stiffness interpretations. We traced these inconsistencies to an implicit approximation, an infinite processivity for kinesin. We report an updated theoretical model for gliding assays incorporating the finite processivity of kinesin, and report experimental verification of the active motor density. Deviations between densities inferred from the original model and updated model range from under 25% for short microtubules (0.5 micrometers long) to greater than four-fold for long microtubules (more than 2 micrometers long). We use these revised motor densities to measure the length-dependence of microtubule bending stiffness (persistence length).