Exclusion and Hierarchy of Time Scales Lead to Spatial Segregation of Molecular Motors in Cellular Protrusions

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.

Coordination, cooperation, competition, crowding and congestion of molecular motors: Theoretical models and computer simulations

Cytoskeletal motor proteins are biological nanomachines that convert chemical energy into mechanical work to carry out various functions such as cell division, cell motility, cargo transport, muscle contraction, beating of cilia and flagella, and ciliogenesis. Most of these processes are driven by the collective operation of several motors in the crowded viscous intracellular environment. Imaging and manipulation of the motors with powerful experimental probes have been complemented by mathematical analysis and computer simulations of the corresponding theoretical models. In this article, we illustrate some of the key theoretical approaches used to understand how coordination, cooperation and competition of multiple motors in the crowded intra-cellular environment drive the processes that are essential for biological function of a cell. In spite of the focus on theory, experimentalists will also find this article as an useful summary of the progress made so far in understanding multiple motor systems.

Self-Organized Lane Formation in Bidirectional Transport by Molecular Motors

Within cells, vesicles and proteins are actively transported several micrometers along the cytoskeletal filaments. The transport along microtubules is propelled by dynein and kinesin motors, which carry the cargo in opposite directions. Bidirectional intracellular transport is performed with great efficiency, even under strong confinement, as for example in the axon. For this kind of transport system, one would expect generically cluster formation. In this Letter, we discuss the effect of the recently observed self-enhanced binding affinity along the kinesin trajectories on the microtubule. We introduce a stochastic lattice-gas model, where the enhanced binding affinity is realized via a floor field. From Monte Carlo simulations and a mean-field analysis we show that this mechanism can lead to self-organized symmetry breaking and lane formation that indeed leads to efficient bidirectional transport in narrow environments.

Length regulation of multiple flagella that self-assemble from a shared pool of components

The single-celled green algae Chlamydomonas reinhardtii with its two flagella-microtubule-based structures of equal and constant lengths-is the canonical model organism for studying size control of organelles. Experiments have identified motor-driven transport of tubulin to the flagella tips as a key component of their length control. Here we consider a class of models whose key assumption is that proteins responsible for the intraflagellar transport (IFT) of tubulin are present in limiting amounts. We show that the limiting-pool assumption is insufficient to describe the results of severing experiments, in which a flagellum is regenerated after it has been severed. Next, we consider an extension of the limiting-pool model that incorporates proteins that depolymerize microtubules. We show that this 'active disassembly' model of flagellar length control explains in quantitative detail the results of severing experiments and use it to make predictions that can be tested in experiments.

Self-organization principles of intracellular pattern formation

Dynamic patterning of specific proteins is essential for the spatio-temporal regulation of many important intracellular processes in prokaryotes, eukaryotes and multicellular organisms. The emergence of patterns generated by interactions of diffusing proteins is a paradigmatic example for self-organization. In this article, we review quantitative models for intracellular Min protein patterns in Escherichia coli, Cdc42 polarization in Saccharomyces cerevisiae and the bipolar PAR protein patterns found in Caenorhabditis elegans. By analysing the molecular processes driving these systems we derive a theoretical perspective on general principles underlying self-organized pattern formation. We argue that intracellular pattern formation is not captured by concepts such as ‘activators’, ‘inhibitors’ or ‘substrate depletion’. Instead, intracellular pattern formation is based on the redistribution of proteins by cytosolic diffusion, and the cycling of proteins between distinct conformational states. Therefore, mass-conserving reaction–diffusion equations provide the most appropriate framework to study intracellular pattern formation. We conclude that directed transport, e.g. cytosolic diffusion along an actively maintained cytosolic gradient, is the key process underlying pattern formation. Thus the basic principle of self-organization is the establishment and maintenance of directed transport by intracellular protein dynamics.

This article is part of the theme issue ‘Self-organization in cell biology’.

Multispecies exclusion process with fusion and fission of rods: A model inspired by intraflagellar transport

We introduce a multispecies exclusion model where length-conserving probabilistic fusion and fission of the hard rods are allowed. Although all rods enter the system with the same initial length ℓ=1, their length can keep changing, because of fusion and fission, as they move in a step-by-step manner towards the exit. Two neighboring hard rods of lengths ℓ_{1} and ℓ_{2} can fuse into a single rod of longer length ℓ=ℓ_{1}+ℓ_{2} provided ℓ≤N. Similarly, length-conserving fission of a rod of length ℓ^{'}≤N results in two shorter daughter rods. Based on the extremum current hypothesis, we plot the phase diagram of the model under open boundary conditions utilizing the results derived for the same model under periodic boundary condition using mean-field approximation. The density profile and the flux profile of rods are in excellent agreement with computer simulations. Although the fusion and fission of the rods are motivated by similar phenomena observed in intraflagellar transport (IFT) in eukaryotic flagella, this exclusion model is too simple to account for the quantitative experimental data for any specific organism. Nevertheless, the concepts of "flux profile" and "transition zone" that emerge from the interplay of fusion and fission in this model are likely to have important implications for IFT and for other similar transport phenomena in long cell protrusions.