Distribution of lifetimes of kinetochore–microtubule attachments: interplay of energy landscape, molecular motors and microtubule (de-)polymerization

Soft mechano-chemistry of molecular hubs in mitotic spindle: biomechanics and mechanical proofreading at microtubule ends

A microtubule (MT) is a long stiff tube-shaped filament formed by a hierarchical organization of a large number of tubulin protein molecules. These filaments constitute a major structural component of the scaffold of a multi-component macromolecular machine called mitotic spindle. The plus ends of the MTs are tethered to some specific binding partners by molecular tethers while those of some others are crosslinked by crosslinking molecules. Because of the non-covalent binding involved in the tethering and crosslinking, the attachments formed are intrinsically 'soft'. These attachments are transient because these can get ruptured spontaneously by thermal fluctuations. By implementing in silico the standard protocols of in vitro molecular force spectroscopy, we compute the lifetimes of simple theoretical models of these attachments. The mean lifetime is essentially a mean first-passage time. The stability of cross-linked antiparallel MTs is shown to decrease monotonically with increasing tension, a characteristic of all 'slip-bonds'. This is in sharp contrast to the nonmonotonic variation of the mean lifetime with tension, a mechanical fingerprint of 'catch-bonds', displayed by the MTs tethered to two distinct binding partners. We mention plausible functional implications of these observations in the context of mechanical proofreading.

Molecular force spectroscopy of kinetochore-microtubule attachment in silico: Mechanical signatures of an unusual catch bond and collective effects

Measurement of the lifetime of attachments formed by a single microtubule (MT) with a single kinetochore (kt) in vitro under force-clamp conditions had earlier revealed a catch-bond-like behavior. In the past, the physical origin of this apparently counterintuitive phenomenon was traced to the nature of the force dependence of the (de)polymerization kinetics of the MTs. Here, first the same model MT-kt attachment is subjected to external tension that increases linearly with time until rupture occurs. In our force-ramp experiments in silico, the model displays the well known "mechanical signatures" of a catch bond probed by molecular force spectroscopy. Exploiting this evidence, we have further strengthened the analogy between MT-kt attachments and common ligand-receptor bonds in spite of the crucial differences in their underlying physical mechanisms. We then extend the formalism to model the stochastic kinetics of an attachment formed by a bundle of multiple parallel microtubules with a single kt considering the effect of rebinding under force-clamp and force-ramp conditions. From numerical studies of the model we predict the trends of variation of the mean lifetime and mean rupture force with the increasing number of MTs in the bundle. Both the mean lifetime and the mean rupture force display nontrivial nonlinear dependence on the maximum number of MTs that can attach simultaneously to the same kt.

Phenomenological and microscopic theories for catch bonds

Lifetimes of bound states of protein complexes or biomolecule folded states typically decrease when subject to mechanical force. However, a plethora of biological systems exhibit the counter-intuitive phenomenon of catch bonding, where non-covalent bonds become stronger under externally applied forces. The quest to understand the origin of catch-bond behavior has led to the development of phenomenological and microscopic theories that can quantitatively recapitulate experimental data. Here, we assess the successes and limitations of such theories in explaining experimental data. The most widely applied approach is a phenomenological two-state model, which fits all of the available data on a variety of complexes: actomyosin, kinetochore-microtubule, selectin-ligand, and cadherin-catenin binding to filamentous actin. With a primary focus on the selectin family of cell-adhesion complexes, we discuss the positives and negatives of phenomenological models and the importance of evaluating the physical relevance of fitting parameters. We describe a microscopic theory for selectins, which provides a structural basis for catch bonds and predicts a crucial allosteric role for residues Asn82-Glu88. We emphasize the need for new theories and simulations that can mimic experimental conditions, given the complex response of cell adhesion complexes to force and their potential role in a variety of biological contexts.