Motor-mediated bidirectional transport along an antipolar microtubule bundle: A mathematical model

Abstract

Long-distance bidirectional transport of organelles depends on the coordinated motion of various motor proteins on the cytoskeleton. Recent quantitative live cell imaging in the elongated hyphal cells of Ustilago maydis has demonstrated that long-range motility of motors and their endosomal cargo occurs on unipolar microtubules (MTs) near the extremities of the cell. These MTs are bundled into antipolar bundles within the central part of the cell. Dynein and kinesin-3 motors coordinate their activity to move early endosomes (EEs) in a bidirectional fashion where dynein drives motility towards MT minus ends and kinesin towards MT plus ends. Although this means that one can easily assign the drivers of bidirectional motion in the unipolar section, the bipolar orientations in the bundle mean that it is possible for either motor to drive motion in either direction. In this paper we use a multilane asymmetric simple exclusion process modeling approach to simulate and investigate phases of bidirectional motility in a minimal model of an antipolar MT bundle. In our model, EE cargos (particles) change direction on each MT with a turning rate and there is switching between MTs in the bundle at the minus ends. At these ends, particles can hop between MTs with rate q 1 on passing from a unipolar to a bipolar section (the obstacle-induced switching rate) or q 2 on passing in the other direction (the end-induced switching rate). By a combination of numerical simulations and mean-field approximations, we investigate the distribution of particles along the MTs for different values of these parameters and of , the overall density of particles within this closed system. We find that even if is low, the system can exhibit a variety of phases with shocks in the density profiles near plus and minus ends caused by queuing of particles. We discuss how the parameters influence the type of particle that dominates active transport in the bundle.

Real-time visualization of clustering and intracellular transport of gold nanoparticles by correlative imaging

“…Studies of these processes provide not only knowledge on how cells communicate with the outside world and receive nutrients and signals, but also insights about the invasion mechanism of viruses or artificial micro-/nano- agents 5 6 7 8 9 10 . Because of their significance in both fundamental cell biology and potential applications in pathology (for example, neurodegenerative or infectious diseases) 11 and theranostics (for example, drug delivery) 12 13 , extensive theoretical and experimental studies have been carried out 14 15 16 17 . The importance of nanoparticle characteristics such as size, shape and surface chemistry in their cellular interactions have been reported 18 .…”

Spatial organization of organelles in fungi: Insights from mathematical modelling

“…Recent work in the corm smut fungus U. maydis uses such theoretical approach to complement and inform live cell imaging experiments. Modelling helps to elucidate the mechanism of dynein accumulation at the plus ends of MTs ( Schuster et al, 2011a ), bidirectional EE transport ( Schuster et al, 2011c , Lin et al, 2013 , Gou et al, 2014 ) and the distribution and mobility of ribosomes and POs in hyphal cells ( Higuchi et al, 2014 , Lin et al, 2016 ). In these studies, modelling not only described dynamic processes; it also informs experimental strategies.…”

“…Hyphal cells carry an anti-polar MT array, with uni-polar MTs at both cell poles ( Schuster et al, 2011b ). To mimic EE transport in an entire cell, Lin et al considers a lattice model composed of two MTs partially bundled in an anti-polar manner with unipolar MTs at two ends ( Lin et al, 2013 ). The model allows EEs “hopping” from one MT to another, which enables EEs to travel the entire length of the cell.…”

“…EEs are evenly distributed along this MT array ( Schuster et al, 2011b ). In contrast to the lattice model in Lin et al (2013) ), Gou et al ignore the hard-core interaction between EEs, and develop a theoretical model ( Gou et al, 2014 ) based on a system of ordinary differential equations (ODEs), to describe the way in which motors and the bi-polar MT array organize spatially the EE compartment in U. maydis . This ODE model takes account of (1) average MT bundle polarity resulting from a number of MTs that are modelled by polymerization and depolymerisation processes with published rates ( Steinberg et al, 2001 ) and the assumption that isotropic MT nucleation was inhibited at cell ends, and (2) four different populations of EEs and transitions among the four populations ( Gou et al, 2014 , Dauvergne and Edelstein-Keshet, 2015 ).…”

Modelling the motion of organelles in an elongated cell via the coordination of heterogeneous drift–diffusion and long-range transport

“…Mathematical modelling has already elucidated many basic aspects of cargo transport and motor behaviour [2,27,28,29,30]. For the long-range directed transport, interactions between particles are often modelled using an exclusion process on a lattice and analysis is usually based on mean field approximations [27,31,32,33]. Diffusion of particles through a homogeneous medium can be modelled as an unbiased random walk on a discrete lattice or a Brownian motion formulated as a stochastic differential equation (SDE) on a continuous space with spatially homogeneous diffusivity [25].…”