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.

We develop a stochastic kinetic model of a pre-formed attachment of a mictrotuble (MT) with a cell cortex, in which the MT is tethered to the cell by a group of active motor proteins. Such an attachment is a particularly unique case of ligand-receptor bonds: The MT ligand changes its length (and thus binding sites) with time by polymerization-depolymerization kinetics, while multiple motor receptors tend to walk actively along the MT length. These processes, combined with force-mediated unbinding of the motors, result in an elaborate behavior of the MT connection to the cell cortex. We present results for the strength and lifetime of the system through the well-established force-clamp and force-ramp protocols when external tension is applied to the MT. The simulation results reveal that the MT-cell attachment behaves as a catch-bond or slip-bond depending on system parameters. We provide analytical approximations of the lifetime and discuss implications of our results on in-vitro experiments.Chromosome segregation is the most important process during the mitosis phase of cell cycle [1]. In eukaryotic cells, sister chromatids, that result from chromosome replication, are segregated by a complex multi-component machine called mitotic spindle [2][3][4]. Microtubule (MT) [5], a stiff tubular filament, whose typical diameter is about 25 nm, forms a major component of the scaffolding of the spindle. A MT is a polar filament in the sense that its two ends are dissimilar; the plus end is more dynamic than the minus end. During the morphogenesis of the spindle [6,7], MTs form transient molecular joints (non-covant bonds) with specific partners. The attachments of the MTs with the chromosomes, mediated by a proteineous complex called kinetochore [8,9], has been under intense investigation in recent years. The forces exerted by these MTs on the kinetochores eventually pull the two sister chromatids apart in the late stages of mitosis thereby driving their journeys to the opposite poles of the spindle [10,11]. In contrast, another set of MTs, called astral MT, diverge from the spindle poles and their distal ends (the so-called plus ends) form contacts with the cell cortex. The kinetochore-MT attachment has been under intense investigation in recent years for the obviously important role it plays in timely and accurate segregation of the chromosomes. However, in this paper we focus exclusively on the MT-cortex attachment.Understanding the physics of the attachment formed by a single MT with the cortex is the first step in ultimately understanding how forces generated by all such attachments collectively determine the position and orientation of the spindle [12][13][14][15][16]. The studies reported in this paper are important also from the perspective of research on MTs and cytoskeletal motor proteins that use MT as the 'track' [17,18], particularly those which play crucial force-coupling roles by residing at the plus end [19][20][21]. Moreover, in spite of the simplicity of the system of our study where only a single MT is a...

We introduce exclusion models of two distinguishable species of hard rods with their distinct sites of entry and exit under open boundary conditions. In the first model both species of rods move in the same direction whereas in the other two models they move in the opposite direction. These models are motivated by the biological phenomenon known as Transcriptional Interference. Therefore, the rules for the kinetics of the models, particularly the rules for the outcome of the encounter of the rods, are also formulated to mimic those observed in Transcriptional Interference. By a combination of mean-field theory and computer simulation of these models we demonstrate how the flux of one species of rods is completely switched off by the other. Exploring the parameter space of the model we also establish the conditions under which switch-like regulation of two fluxes is possible; from the extensive analysis we discover more than one possible mechanism of this phenomenon.

A microtubule (MT) is a hollow tube of approximately 25 nm diameter. The two ends of the tube are dissimilar and are designated as 'plus' and 'minus' ends. Motivated by the collective push and pull exerted by a bundle of MTs during chromosome segregation in a living cell, we have developed here a much simplified theoretical model of a bundle of parallel dynamic MTs. The plusend of all the MTs in the bundle are permanently attached to a movable 'wall' by a device whose detailed structure is not treated explicitly in our model. The only requirement is that the device allows polymerization and depolymerization of each MT at the plus-end. In spite of the absence of external force and direct lateral interactions between the MTs, the group of polymerizing MTs attached to the wall create a load force against the group of depolymerizing MTs and vice-versa; the load against a group is shared equally by the members of that group. Such indirect interactions among the MTs gives rise to the rich variety of possible states of collective dynamics that we have identified by computer simulations of the model in different parameter regimes. The bi-directional motion of the cargo, caused by the load-dependence of the polymerization kinetics, is a "proof-ofprinciple" that the bi-directional motion of chromosomes before cell division does not necessarily need active participation of motor proteins.

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.