Theory of strength and stability of kinetochore-microtubule attachments: collective effects of dynamic load-sharing

Measurement of the life time of attachments formed by a single microtubule (MT) with a single kinetochore (kt) {\it in-vitro} under force-clamp conditions revealed a catch-bond-like behavior. In the past the physical origin of this apparently counter-intuitive phenomenon was traced to the nature of the force-dependence of the (de-)polymerization kinetics of the microtubules. Here first the same model kt-MT attachment is subjected to external tension that is ramped up till the attachment gets ruptured; the trend of variation of the rupture force distribution with increasing loading rate is consistent with that displayed by the catch bonds formed in some other ligand-receptor systems. We then extend the formalism to model an attachment of a bundle of multiple parallel microtubules with a single kt under force-clamp and force-ramp conditions. From numerical studies of the model we predict the trends of variation of the mean life time and mean rupture force with the increasing number of MTs in the bundle. Both the mean life time and the mean rupture force display nontrivial nonlinear dependence on the maximum number of MTs that can attach simultaneously to the same kt.