Dynamics of outgrowth in a continuum model of neurite elongation

Abstract

Neurite outgrowth (dendrites and axons) should be a stable, but easily regulated process to enable a neuron to make its appropriate network connections during development. We explore the dynamics of outgrowth in a mathematical continuum model of neurite elongation. The model describes the construction of the internal microtubule cytoskeleton, which results from the production and transport of tubulin dimers and their assembly into microtubules at the growing neurite tip. Tubulin is assumed to be largely synthesised in the cell body from where it is transported by active mechanisms and by diffusion along the neurite. It is argued that this construction process is a fundamental limiting factor in neurite elongation. In the model, elongation is highly stable when tubulin transport is dominated by either active transport or diffusion, but oscillations in length may occur when both active transport and diffusion contribute. Autoregulation of tubulin production can eliminate these oscillations. In all cases a stable steady-state length is reached, provided there is intrinsic decay of tubulin. Small changes in growth parameters, such as the tubulin production rate, can lead to large changes in length. Thus cytoskeleton construction can be both stable and easily regulated, as seems necessary for neurite outgrowth during nervous system development.

Stochastic models of intracellular transport

“…Numerical simulations of the full time-dependent model show that these steadystates are stable and in both regimes the approach to steady-state is overdamped. On the other hand, for intermediate values of L damped oscillations occur resulting in overshoot (Graham et al, 2006).…”

“…Axon elongation is a consequence of the interplay between force generation at the growth cone that pulls the axon forward, pushing forces due to microtubule and actin polymerization and depolymerization, the rate of protein synthesis at the cell body, and the action of cytoskeletal motors (Baas and Ahmad, 2001;Goldberg, 2003;Lamoureux et al, 1989;Mitchison and Kirschner, 1988;O'Toole et al, 2008;Suter and Miller, 2011). Several models of axonal elongation have focused on the sequence of processes based on the production of tubulin dimers at the cell body, the active transport of these proteins to the the tip of the growing axon, and microtubule extension at the growth cone (Graham et al, 2006;Kiddie et al, 2005;McLean and Graham, 2004;Miller and Samulels, 1997;van Veen and van Pelt, 1994). One motivation for identifying the polymerization of microtubules as a rate limiting step is that axonal growth occurs at a similar rate to the slow axonal transport of tubulin, namely, around 1mm per day.…”

“…(It is possible that short, freshly nucleated microtubles are also actively transported into axons (Baas and Buster, 2004)). For the sake of illustration, consider a continuum model of the active transport of tubulin (Graham et al, 2006;McLean and Graham, 2004). Let c(x, t) denote the concentration of tubulin at position x along the axon at time t. Suppose that at time t the axon has length l(t) so that x ∈ [0, l(t)].…”

“…One clear example is given by the actin and microtubular cytoskeletons, which not only provide tracks for intracellular transport, but also determine cell shape and polarity (Lacayo et al, 2007), drive cell motility (Mogilner and Edelstein-Keshet, 2002;Rafelski and Theriot, 2004), and form the spindle apparatus during cell division (Eggert et al, 2006;Glotzer, 2009). Self-organization of the cytoskeleton and its regulation by cell signaling also plays a crucial role in axonal growth and guidance during neurogenesis and cortical development (Goldberg, 2003;Graham et al, 2006;Suter and Miller, 2011).…”

Analytical solution of equations describing slow axonal transport based on the stop-and-go hypothesis

“…In particular, defects in slow axonal transport of NFs may lead to aggregation of NFs in certain regions in an axon [14]; such aggregation has been linked to human motor neuron diseases [15,16]. The study of NF transport is also important for understanding the dynamics of axon elongation for growing axons [17,18].…”