Theory of active transport in filopodia and stereocilia

Abstract

The biological processes in elongated organelles of living cells are often regulated by molecular motor transport. We determined spatial distributions of motors in such organelles, corresponding to a basic scenario when motors only walk along the substrate, bind, unbind, and diffuse. We developed a mean-field model, which quantitatively reproduces elaborate stochastic simulation results as well as provides a physical interpretation of experimentally observed distributions of Myosin IIIa in stereocilia and filopodia. The mean-field model showed that the jamming of the walking motors is conspicuous, and therefore damps the active motor flux. However, when the motor distributions are coupled to the delivery of actin monomers toward the tip, even the concentration bump of G actin that they create before they jam is enough to speed up the diffusion to allow for severalfold longer filopodia. We found that the concentration profile of G actin along the filopodium is rather nontrivial, containing a narrow minimum near the base followed by a broad maximum. For efficient enough actin transport, this nonmonotonous shape is expected to occur under a broad set of conditions. We also find that the stationary motor distribution is universal for the given set of model parameters regardless of the organelle length, which follows from the form of the kinetic equations and the boundary conditions. M olecular motor transport in a living cell is one of the most fascinating processes in cellular biophysics. Molecular motors play crucial roles in many elongated organelles, such as neuronal axons (1), flagella (2), filopodia (3), stereocilia (4, 5), and microvilli (4). A naive view of cellular motor transport is that of motor molecules orderly following each other on the substrate and carrying cargo, which they unload at a destination point. However, in reality, motors not only walk, but also diffuse around the cell, randomly binding and unbinding to their substrate filaments and/or cargo. To a large extent these processes are governed by molecular noise. To understand how the motors perform their functions-be it cargo delivery to the growing end of an organelle or creating stresses in a flagellum, or even in artificial systems (6, 7)-it is necessary to know their spatial distribution in these systems.The spatial distribution of the motors could influence the delivery of building material toward the growing end of a dynamic elongated organelle, such as a filopodium or a stereocilium. In the absence of motors, the length of such organelle is expected to be limited by the slow diffusional delivery of the material to the tip (8). Furthermore, prior computational modeling of simple, conveyor-belt-like transport of monomeric species by molecular motors indicated that specially designed cooperative mechanisms are needed to achieve any appreciable active transport flux (9). Two main reasons for the transport inefficiency are sequestration of cargo by motors and diminution of motor speeds due to clogging of the filamentous bundle by walking mo...

Modelling the effect of myosin X motors on filopodia growth

“…There must therefore be another mechanism that allows the filopodia to reach lengths as large as 40 µm [11]. One possibility, that we explore in this section, is that larger lengths are made possible via the directed transport of actin monomers by myosin motors [16,17]. which have been associated with filopodia growth for a long time [35][36][37].…”

“…We note that similar equations have appeared in Refs. [11,16,17], although the coupling between ratchet dynamics and simultaneous advection and diffusion of G-actin is new to our approach. The first equation, Eq.…”

“…While the lamellipodium is arguably the best documented structure in crawling cells, there are a number of other important actin-driven protrusions, such as actin ruffles, pseudopodia, podosomes and filopodia [9][10][11][12][13][14][15][16][17][18][19]. We will be in particular concerned with the latter in the current work.…”

“…There have been a number of studies on the physics of filopodia in recent years [11,[14][15][16][17][18][19]. Mogilner and Rubinstein proposed a mean-field theory to study filopodia dynamics in a seminal paper [11], and Monte Carlo simulations of varying levels of complexity have been implemented [16,19] to assess the role of fluctuations and of actin-binding proteins.…”

Traffic jams and shocks of molecular motors inside cellular protrusions

“…Several works have dealt with this boundary condition (b.c.) together with attachment/detachment kinetics of the motors to the tracks [8][9][10]. These models find that at steady-state the tubes are practically all jammed, and * Corresponding author: nir.gov@weizmann.ac.il longer tubes have longer jammed (accumulation of motors) regions, in contrast with the observations for cellular protrusions.…”