Continuum model for tubulin-driven neurite elongation

McLean, Douglas R.

doi:10.1016/s0925-2312(04)00093-1

Cited by 7 publications

(27 citation statements)

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“…It is interesting to investigate the possible steady-state solutions of a dynamic model. If the given soma concentration c s is constant and all variables c, l, c c of the model equations (14) are assumed to be independent of time, then we denote the unknown constant axon length by l ∞ , and note that c c = c ∞ holds by the ODE for l (t). Then the model equations (14) yield the following linear boundary-value problem for the unknown function c = c(x) and the constant l ∞ > 0:…”

Section: All Steady-state Solutions and Their Propertiesmentioning

confidence: 99%

“…The biological interpretation is that when the soma concentration satisfies c s < c ∞ f (z 0 ) = 7.12 · 10 −4 mol/m 3 , it is so small that no growth can occur. If the soma concentration was larger earlier so that the axon has reached a certain length and cs drops to a value below 7.12 · 10 −4 mol/m 3 , then the dynamic equation for the axon length in (14) implies that l (t) < 0, i.e., the axon shrinks.…”

Section: All Steady-state Solutions and Their Propertiesmentioning

confidence: 99%

“…When there is no diffusion that can smooth out sharp gradients, one cannot exclude the case c − c c . Removing the continuity assumption, Equation (13) should be used for the dynamics of the cone concentration c c instead of the second equation of (14) where the assumption c − = c c have been used. Then the boundary condition at x = l(t) in (21) should be replaced by Dc − x = ac − − gl c c c .…”

Section: The Cases With D =mentioning

confidence: 99%

“…Because of the substantial length of an axon it is, however, natural to assume that the concentration of a substance varies both with time and position along the axon. Deriving a dynamic model from a physical law, such as the conservation of mass, leads then necessarily to a partial differential equation (PDE); see [5,6,12,13,14,20,22]. The multi-compartment model by Hjort et al [8], which has a system of ODEs for each axon, is essentially a spatially discretization of a PDE.…”

Section: Introductionmentioning

confidence: 99%

“…The different steady-state solutions are presented in [12]. In [6,14], numerical simulations of the model are presented. In [6], Graham et al also introduced an additional parameter, the autoregulation gain, related to the production of tubulin in the soma.…”

Section: Introductionmentioning

confidence: 99%

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A one-dimensional moving-boundary model for tubulin-driven axonal growth

Diehl

Henningsson

Heyden

et al. 2014

Journal of Theoretical Biology

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A one-dimensional continuum-mechanical model of axonal elongation due to assembly of tubulin dimers in the growth cone is presented. The conservation of mass leads to a coupled system of three differential equations. A partial differential equation models the dynamic and spatial behaviour of the concentration of tubulin that is transported along the axon from the soma to the growth cone. Two ordinary differential equations describe the time-variation of the concentration of free tubulin in the growth cone and the speed of elongation, respectively. All steady-state solutions of the model are categorized. Given a set of the biological parameter values, it is shown how one easily can infer whether there exist zero, one or two steady-state solutions and directly determine the possible steady-state lengths of the axon. Explicit expressions are given for each stationary concentration distribution. It is thereby easy to examine the influence of each biological parameter on a steady state. Numerical simulations indicate that when there exist two steady states, the one with shorter axon length is unstable and the longer is stable. Another result is that, for nominal parameter values extracted from literature, in a large portion of a fully grown axon the concentration of free tubulin is lower than both concentrations in the soma and in the growth cone.

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Section: All Steady-state Solutions and Their Propertiesmentioning

confidence: 99%

Section: All Steady-state Solutions and Their Propertiesmentioning

confidence: 99%

Section: The Cases With D =mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A one-dimensional moving-boundary model for tubulin-driven axonal growth

Diehl

Henningsson

Heyden

et al. 2014

Journal of Theoretical Biology

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Biologically plausible models of neurite outgrowth

Kiddie

2005

Progress in Brain Research

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EngineeredIn Vitro/In SilicoModels To Examine Neurite Target Preference

Voyiadjis

Buettner

Shreiber

et al. 2011

Journal of Neurotrauma

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Research on spinal cord injury (SCI) repair focuses on developing mechanisms to allow neurites to grow past an injury site. In this article, we observe that numerous divergent paths (i.e., spinal roots) are present along the spinal column, and hence guidance strategies must be devised to ensure that regrowing neurites reach viable targets. Therefore, we have engineered an in vitro micropatterned model in which cultured E7 dorsal root ganglia (DRG) explants may enter alternate pathways (?roots?) along a branching micropattern. Alongside this in vitro model, we have developed an in silico simulation that we validate by comparison with independent experiments. We find in both in silico and in vitro models that the probability of a neurite entering a given root decreases exponentially with respect to the number of roots away from the DRG; consequently, the likelihood of neurites reaching a distant root can be vanishingly small. This result represents a starting point for future strategies to optimize the likelihood that neurites will reach appropriate targets in the regenerating nervous system, and provides a new computational tool to evaluate the feasibility and expected success of neurite guidance in complex geometries.

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Continuum model for tubulin-driven neurite elongation

Cited by 7 publications

References 0 publications

A one-dimensional moving-boundary model for tubulin-driven axonal growth

A one-dimensional moving-boundary model for tubulin-driven axonal growth

Biologically plausible models of neurite outgrowth

EngineeredIn Vitro/In SilicoModels To Examine Neurite Target Preference

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