Motor Protein Accumulation on Antiparallel Microtubule Overlaps

Modelling intracellular transport in crowded environments: effects of motor association to cargos

In intracellular transports, motor proteins transport macromolecules as cargos to desired locations by moving on biopolymers such as microtubules. Recent experiments suggest that, while moving in crowded environments, cargos that can associate motor proteins during their translocation have larger run-length and association time compared to free motors. Here, we model the dynamics of a cargo that can associate at the most m free motors present on the microtubule track as obstacles to its motion. The proposed models display competing effects of association and crowding, leading to a peak in the run-length with the free-motor density. For m = 2 and 3, we show that this feature is governed by the largest eigenvalue of the transition matrix describing the cargo dynamics. In all the above cases, free motors are assumed to be present on the microtubule as stalled obstacles. We finally compare simulation results for the run-length for general scenarios where the free motors undergo processive motion in addition to binding and unbinding to or from the microtubule.

Computational Studies Reveal How Passive Cross-Linkers Regulate Anaphase Spindle Elongation

In eukaryotic cell division, a series of events are organized to produce two daughter cells. The spindle elongation in anaphase B is essential for providing enough space to maintain cell size and distribute sister chromatids properly, which is associated with microtubules and microtubule-associated proteins such as kinesin-5 Eg5 and the Ase1-related protein, PRC1. The available experimental data indicated that after the start of anaphase B more PRC1 proteins can bind to the antiparallel microtubule pairs in the spindle but the excess amount of PRC1 proteins can lead to the failure of cell division, indicating that PRC1 proteins can regulate the spindle elongation in a concentration-dependent manner. However, the underlying mechanism of the PRC1 proteins regulating the spindle elongation has not been explained up to now. Here, we use a simplified model, where only the two important participants (kinesin-5 Eg5 motors and PRC1 proteins) are considered, to study the spindle elongation during anaphase B. We first show that only in the appropriate range of the PRC1 concentration can the spindle elongation complete properly. Furthermore, we explore the underlying mechanism of PRC1 as a regulator for spindle elongation.

Totally asymmetric simple exclusion process with local resetting in a resource-constrained environment

Inspired by the process of mRNA translation, in which the stochastic degradation of mRNA-ribosome machinery is modeled by the resetting dynamics, we study an open totally asymmetric simple exclusion process with local resetting at the entry site in a resource-constrained environment. The effect of constrained resources on the stationary properties of the system has been comprehended in the form of the filling factor. The mean-field approximations are utilized to obtain stationary state features, such as density profiles and phase diagrams. The phase diagram possesses pure phases as well as coexisting phases, including a low-density-high-density phase separation, which did not manifest under periodic boundary conditions despite the system being closed there as well. The role of the resetting rate has been investigated on the stationary properties of the system, depending on how the filling factor scales with the system size. In contrast to the resetting model for infinite resources, two distinct phase transitions are observed for the smaller values of the filling factor leading to a change in the topology of the phase diagram. The impact of the resetting rate along with the finite-size effect has also been examined on the shock dynamics. All the mean-field results are found in remarkable agreement with the Monte Carlo simulations.

Multiple reentrance transitions in exclusion process with finite reservoir

The proposed study is motivated by the scenario of two-way vehicular traffic. We consider a totally asymmetric simple exclusion process in the presence of a finite reservoir along with the particle attachment, detachment, and lane-switching phenomena. The various system properties in terms of phase diagrams, density profiles, phase transitions, finite size effect, and shock position are analyzed, considering the available number of particles in the system and different values of coupling rate, by employing the generalized mean-field theory and the obtained results are detected to be a good match with the Monte Carlo simulation outcomes. It is discovered that the finite resources significantly affect the phase diagram for different coupling rate values, which leads to nonmonotonic changes in the number of phases in the phase plane for comparatively minor lane-changing rates and produces various exciting features. We calculate the critical value of the total number of particles in the system at which the multiple phases in the phase diagram appear or disappear. The competition between the limited particles, bidirectional motion, Langmuir kinetics, and particle lane-shifting behavior yields unanticipated and unique mixed phases, including the double shock phase, multiple reentrance and bulk-induced phase transitions, and phase segregation of the single shock phase.

Motor guidance by long-range communication on the microtubule highway

Coupling of motor proteins within arrays drives muscle contraction, flagellar beating, chromosome segregation, and other biological processes. Current models of motor coupling invoke either direct mechanical linkage or protein crowding, which rely on short-range motor-motor interactions. In contrast, coupling mechanisms that act at longer length scales remain largely unexplored. Here we report that microtubules can physically couple motor movement in the absence of detectable short-range interactions. The human kinesin-4 Kif4A changes the run length and velocity of other motors on the same microtubule in the dilute binding limit, when approximately 10-nm-sized motors are much farther apart than the motor size. This effect does not depend on specific motor-motor interactions because similar changes in Kif4A motility are induced by kinesin-1 motors. A micrometer-scale attractive interaction potential between motors is sufficient to recreate the experimental results in a biophysical model. Unexpectedly, our theory suggests that long-range microtubule-mediated coupling affects not only binding kinetics but also motor mechanochemistry. Therefore, the model predicts that motors can sense and respond to motors bound several micrometers away on a microtubule. Our results are consistent with a paradigm in which long-range motor interactions along the microtubule enable additional forms of collective motor behavior, possibly due to changes in the microtubule lattice.

Modeling spatiotemporally varying protein-protein interactions in CyLaKS, the Cytoskeleton Lattice-based Kinetic Simulator

Interaction of cytoskeletal filaments, motor proteins, and crosslinking proteins drives important cellular processes such as cell division and cell movement. Cytoskeletal networks also exhibit nonequilibrium self-assembly in reconstituted systems. An emerging problem in cytoskeletal modeling and simulation is spatiotemporal alteration of the dynamics of filaments, motors, and associated proteins. This can occur due to motor crowding, obstacles along the filament, motor interactions and direction switching, and changes, defects, or heterogeneity in the filament binding lattice. How such spatiotemporally varying cytoskeletal filaments and motor interactions affect their collective properties is not fully understood. We developed the Cytoskeleton Lattice-based Kinetic Simulator (CyLaKS) to investigate such problems. The simulation model builds on previous work by incorporating motor mechanochemistry into a simulation with many interacting motors and/or associated proteins on a discretized lattice. CyLaKS also includes detailed balance in binding kinetics, movement, and lattice heterogeneity. The simulation framework is flexible and extensible for future modeling work and is available on GitHub for others to freely use or build upon. Here we illustrate the use of CyLaKS to study long-range motor interactions, microtubule lattice heterogeneity, motion of a heterodimeric motor, and how changing crosslinker number affects filament separation.

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.

Biologically motivated three-species exclusion model: Effects of leaky scanning and overlapping genes on initiation of protein synthesis

The totally asymmetric simple exclusion process was originally introduced as a model for the trafficlike collective movement of ribosomes on a messenger RNA (mRNA) that serves as the track for the motorlike forward stepping of individual ribosomes. In each step, a ribosome elongates a protein by a single unit using the track also as a template for protein synthesis. But, prefabricated functionally competent ribosomes are not available to begin synthesis of protein; a subunit directionally scans the mRNA in search of the predesignated site where it is supposed to bind with the other subunit and begin the synthesis of the corresponding protein. However, because of "leaky" scanning, a fraction of the scanning subunits miss the target site and continue their search beyond the first target. Sometimes such scanners successfully identify the site that marks the site for initiation of the synthesis of a different protein. In this paper, we develop an exclusion model with three interconvertible species of hard rods to capture some of the key features of these biological phenomena and study the effects of the interference of the flow of the different species of rods on the same lattice. More specifically, we identify the mean time for the initiation of protein synthesis as appropriate mean first-passage time that we calculate analytically using the formalism of backward master equations. Despite the approximations made, our analytical predictions are in reasonably good agreement with the numerical data that we obtain by performing Monte Carlo simulations.

Geometry of antiparallel microtubule bundles regulates relative sliding and stalling by PRC1 and Kif4A

Motor and non-motor crosslinking proteins play critical roles in determining the size and stability of microtubule-based architectures. Currently, we have a limited understanding of how geometrical properties of microtubule arrays, in turn, regulate the output of crosslinking proteins. Here we investigate this problem in the context of microtubule sliding by two interacting proteins: the non-motor crosslinker PRC1 and the kinesin Kif4A. The collective activity of PRC1 and Kif4A also results in their accumulation at microtubule plus-ends (‘end-tag’). Sliding stalls when the end-tags on antiparallel microtubules collide, forming a stable overlap. Interestingly, we find that structural properties of the initial array regulate microtubule organization by PRC1-Kif4A. First, sliding velocity scales with initial microtubule-overlap length. Second, the width of the final overlap scales with microtubule lengths. Our analyses reveal how micron-scale geometrical features of antiparallel microtubules can regulate the activity of nanometer-sized proteins to define the structure and mechanics of microtubule-based architectures.

Enhanced Dynamics of Confined Cytoskeletal Filaments Driven by Asymmetric Motors

Cytoskeletal filaments and molecular motors facilitate the micron-scale force generation necessary for the distribution of organelles and the restructuring of the cytoskeleton within eukaryotic cells. Although the mesoscopic structure and the dynamics of such filaments have been studied in vitro and in vivo, their connection with filament polarity-dependent motor-mediated force generation is not well understood. Using 2D Brownian dynamics simulations, we study a dense, confined mixture of rigid microtubules (MTs) and active springs that have arms that cross-link neighboring MT pairs and move unidirectionally on the attached MT. We simulate depletion interactions between MTs using an attractive potential. We show that dimeric motors, with a motile arm on only one of the two MTs, produce large polarity-sorted MT clusters, whereas tetrameric motors, with motile arms on both microtubules, produce bundles. Furthermore, dimeric motors induce, on average, higher velocities between antialigned MTs than tetrameric motors. Our results, where MTs move faster near the confining wall, are consistent with experimental observations in Drosophila oocytes where enhanced microtubule activity is found close to the confining plasma membrane.

Interference of two codirectional exclusion processes in the presence of a static bottleneck: A biologically motivated model

We develop a two-species exclusion process with a distinct pair of entry and exit sites for each species of rigid rods. The relatively slower forward stepping of the rods in an extended bottleneck region, located in between the two entry sites, controls the extent of interference of the codirectional flow of the two species of rods. The relative positions of the sites of entry of the two species of rods with respect to the location of the bottleneck are motivated by a biological phenomenon. However, the primary focus of the study here is to explore the effects of the interference of the flow of the two species of rods on their spatiotemporal organization and the regulations of this interference by the extended bottleneck. By a combination of mean-field theory and computer simulation, we calculate the flux of both species of rods and their density profiles as well as the composite phase diagrams of the system. If the bottleneck is sufficiently stringent, then some of the phases become practically unrealizable, although not ruled out on the basis of any fundamental physical principle. Moreover, the extent of suppression of flow of the downstream entrants by the flow of the upstream entrants can also be regulated by the strength of the bottleneck. We speculate on the possible implications of the results in the context of the biological phenomenon that motivated the formulation of the theoretical model.

Phase-plane analysis of the totally asymmetric simple exclusion process with binding kinetics and switching between antiparallel lanes

Motor protein motion on biopolymers can be described by models related to the totally asymmetric simple exclusion process (TASEP). Inspired by experiments on the motion of kinesin-4 motors on antiparallel microtubule overlaps, we analyze a model incorporating the TASEP on two antiparallel lanes with binding kinetics and lane switching. We determine the steady-state motor density profiles using phase-plane analysis of the steady-state mean field equations and kinetic Monte Carlo simulations. We focus on the density-density phase plane, where we find an analytic solution to the mean field model. By studying the phase-space flows, we determine the model's fixed points and their changes with parameters. Phases previously identified for the single-lane model occur for low switching rate between lanes. We predict a multiple coexistence phase due to additional fixed points that appear as the switching rate increases: switching moves motors from the higher-density to the lower-density lane, causing local jamming and creating multiple domain walls. We determine the phase diagram of the model for both symmetric and general boundary conditions.