Molecular motors of the kinesin-1 family move in a directed and processive fashion along microtubules. It is generally accepted that steric hindrance of motors leads to crowding effects; however, little is known about the specific interactions involved. We employ an agent-based lattice gas model to study the impact of interactions that enhance the detachment of motors from crowded filaments on their collective dynamics. The predictions of our model quantitatively agree with the experimentally observed concentration dependence of key motor characteristics including their run length, dwell time, velocity, and landing rate. From the anomalous stepping statistics of individual motors that exhibit relatively long pauses, we infer that kinesin-1 motors sometimes lapse into an inactive state. Hereby, the formation of traffic jams amplifies the impact of single inactive motors and leads to a crowding dependence of the frequencies and durations of the resulting periods of no or slow motion. We interpret these findings and conclude that kinesin-1 spends a significant fraction of its stepping cycle in a weakly bound state in which only one of its heads is bound to the microtubule.
Molecular spiders are synthetic molecular motors based on DNA nanotechnology. While natural molecular motors have evolved towards very high efficiency, it remains a major challenge to develop efficient designs for man-made molecular motors. Inspired by biological motor proteins such as kinesin and myosin, molecular spiders comprise a body and several legs. The legs walk on a lattice that is coated with substrate which can be cleaved catalytically. We propose a molecular spider design in which n spiders form a team. Our theoretical considerations show that coupling several spiders together alters the dynamics of the resulting team significantly. Although spiders operate at a scale where diffusion is dominant, spider teams can be tuned to behave nearly ballistic, which results in fast and predictable motion. Based on the separation of time scales of substrate and product dwell times, we develop a theory which utilizes equivalence classes to coarse-grain the microstate space. In addition, we calculate diffusion coefficients of the spider teams, employing a mapping of an n-spider team to an n-dimensional random walker on a confined lattice. We validate these results with Monte Carlo simulations and predict optimal parameters of the molecular spider team architecture which makes their motion most directed and maximally predictable.
The availability of protein is an important factor for the determination of the size of the mitotic spindle. Involved in spindle-size regulation is kinesin-8, a molecular motor and microtubule (MT) depolymerase, which is known to tightly control MT length. Here, we propose and analyze a theoretical model in which kinesin-induced MT depolymerization competes with spontaneous polymerization while supplies of both tubulin and kinesin are limited. In contrast to previous studies where resources were unconstrained, we find that, for a wide range of concentrations, MT length regulation is bistable. We test our predictions by conducting in vitro experiments and find that the bistable behavior manifests in a bimodal MT length distribution. DOI: 10.1103/PhysRevLett.120.148101 The absolute and relative abundance of particular sets of proteins is important for a wide range of processes in cells. For example, during Xenopus laevis embryogenesis, importin α becomes progressively localized to the cell membrane [1]. As a consequence of importin's depletion from the cytoplasm, the protein kif2a escapes inactivation and decreases the size of the mitotic spindle. Similarly, formation of the mitotic spindle reduces the concentration of free tubulin dimers, the building blocks of microtubules (MTs). Thus, up to 60% of all tubulin heterodimers [2,3] may be incorporated into the spindle [4]. In addition, it has been shown in vivo and in vitro that both spindle size [4,5] and the lengths of its constituent MTs [6] scale with cytoplasmic volume.Assembly and disassembly of MTs are regulated by a set of proteins that interact with the plus ends of protofilaments [7,8]. One of these factors, the molecular motor kinesin-8, acts as a depolymerase [8,9]. As a consequence, spindle size increases in its absence [10] and decreases upon overexpression of the protein [11]. Moreover, the kinesin-8 homolog Kip3 from Saccharomyces cerevisiae has been shown to depolymerize MTs in a length-dependent fashion [9,12]. This is facilitated by a density gradient on the MT, caused by the interplay between the processive motion of Kip3 along the MT and its depolymerase activity at the plus end, which effectively enables the MT to "sense" its own length [12,13]. In combination with spontaneous MT polymerization, the Kip3 gradient leads to a length regulation mechanism [14,15].Here, we explore the combined effect of limited resources and Kip3-induced depolymerization on the length regulation of MTs. As seen in theoretical studies on the collective motion of molecular motors, resource limitation affects the density profile on the MT: regions of low and high motor density separate, as a localized domain wall emerges on the MT [16][17][18][19]. This is a direct result of resource limitation and does not rely on the existence of a motor density gradient, as necessary for domain wall localization in the presence of unlimited resources [20][21][22][23]. So far, most work on the role of limited resources has focused on single components of the relevant system [17][...
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