Qualitative behavior and robustness of dendritic trafficking

TL;DR

This paper models neuronal ion channel trafficking using a nonlinear closed-loop system, analyzing stability and robustness to understand how regulation interacts with cell growth and potential oscillations.

Contribution

It introduces a novel nonlinear model of ion channel trafficking and applies dominance theory and dissipativity analysis to study stability and robustness.

Findings

Steady regulation can lead to pathological oscillations.

The model predicts robustness limits under uncertainties.

Cell growth impacts ion channel regulation stability.

Abstract

The paper studies homeostatic ion channel trafficking in neurons. We derive a nonlinear closed-loop model that captures active transport with degradation, channel insertion, average membrane potential activity, and integral control. We study the model via dominance theory and differential dissipativity to show when steady regulation gives way to pathological oscillations. We provide quantitative results on the robustness of the closed loop behavior to static and dynamic uncertainties, which allows us to understand how cell growth interacts with ion channel regulation.