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arXiv · 2109.14095

Neuron Growth Control by PDE Backstepping: Axon Length Regulation by Tubulin Flux Actuation in Soma

Cenk Demir·Shumon Koga·Miroslav Krstic
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Abstract

In this work, stabilization of an axonal growth in a neuron associated with the dynamics of tubulin concentration is proposed by designing a boundary control. The dynamics are given by a parabolic Partial Differential Equation (PDE) of the tubulin concentration, with a spatial domain of the axon's length governed by an Ordinary Differential Equation (ODE) coupled with the tubulin concentration in the growth cone. We propose a novel backstepping method for the coupled PDE-ODE dynamics with a moving boundary, and design a control law for the tubulin concentration flux in the soma. Through employing the Lyapunov analysis to a nonlinear target system, we prove a local exponential stability of the closed-loop system under the proposed control law in the spatial $H_1$-norm.

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Cenk Demir, Shumon Koga, Miroslav Krstic. 2021-09-28. Neuron Growth Control by PDE Backstepping: Axon Length Regulation by Tubulin Flux Actuation in Soma. https://arxiv.org/abs/2109.14095

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