Effect of kinesin velocity distribution on slow axonal transport

Abstract

Abstract:The goal of this paper is to investigate the effect that a distribution of kinesin motor velocities could have on cytoskeletal element (CE) concentration waves in slow axonal transport. Previous models of slow axonal transport based on the stop-and-go hypothesis (P. Jung, A. Brown, Modeling the slowing of neurofilament transport along the mouse sciatic nerve, Physical Biology 6 (2009) 046002) assumed that in the anterograde running state all CEs move with one and the same velocity as they are propelled by kinesin motors. This paper extends the aforementioned theoretical approach by allowing for a distribution of kinesin motor velocities; the distribution is described by a probability density function (PDF). For a two kinetic state model (that accounts for the pausing and running populations of CEs) an analytical solution describing the propagation of the CE concentration wave is derived. Published experimental data are used to obtain an analytical expression for the PDF characterizing the kinesin velocity distribution; this analytical expression is then utilized as an input for computations. It is demonstrated that accounting for the kinesin velocity distribution increases the rate of spreading of the CE concentration waves, which is a significant improvement in the two kinetic state model.

How the formation of amyloid plaques and neurofibrillary tangles may be related: a mathematical modelling study

“…Parameters v * a and v * r should be understood as average instantaneous velocities of rapid motions of tau on MTs when tau is propelled by kinesin and dynein motors, respectively. These are effective properties because the velocity of cargo that is propelled by molecular motors may depend on the number of motors, whether there is coordination between the motors or a tug-of-war between them [35], how crowded the MT is [36,37], and many other factors [38,39]. Coordination means that while a cargo is transported by one group of motors, the opposing motors are deactivated.…”

Analytical comparison between Nixon–Logvinenko’s and Jung–Brown’s theories of slow neurofilament transport in axons

“…Analytical solutions of the two-kinetic state model of Jung and Brown were obtained in Kuznetsov [32] (assuming an infinite NF half-life) and Kuznetsov [33] (assuming a finite NF half-life). Effects of kinesin velocity distribution were considered in Kuznetsov [34]. In order to enable a comparison between Nixon-Logvinenko's and Jung-Brown's theories, here we supplemented the two-kinetic state model developed in Jung and Brown [29] with a third kinetic state that accounts for stationary NFs.…”