A mathematical analysis of an activator-inhibitor Rho GTPase model

IF 1 Q3 Engineering

Journal of Computational Dynamics Pub Date : 2021-01-01 DOI:10.3934/jcd.2021024

V. O. Juma, L. Dehmelt, Stéphanie Portet, A. Madzvamuse

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引用次数: 3

Abstract

Recent experimental observations reveal that local cellular contraction pulses emerge via a combination of fast positive and slow negative feedbacks based on a signal network composed of Rho, GEF and Myosin interactions [22]. As an examplary, we propose to study a plausible, hypothetical temporal model that mirrors general principles of fast positive and slow negative feedback, a hallmark for activator-inhibitor models. The methodology involves (ⅰ) a qualitative analysis to unravel system switching between different states (stable, excitable, oscillatory and bistable) through model parameter variations; (ⅱ) a numerical bifurcation analysis using the positive feedback mediator concentration as a bifurcation parameter, (ⅲ) a sensitivity analysis to quantify the effect of parameter uncertainty on the model output for different dynamic regimes of the model system; and (ⅳ) numerical simulations of the model system for model predictions. Our methodological approach supports the role of mathematical and computational models in unravelling mechanisms for molecular and developmental processes and provides tools for analysis of temporal models of this nature.

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活化剂-抑制剂Rho GTPase模型的数学分析

最近的实验观察表明，局部细胞收缩脉冲是通过快速正反馈和缓慢负反馈的组合出现的，这是基于Rho、GEF和Myosin相互作用组成的信号网络[22]。作为一个例子，我们建议研究一个合理的、假设的时间模型，该模型反映了快速正反馈和缓慢负反馈的一般原则，这是激活剂-抑制剂模型的一个标志。方法包括:(ⅰ)定性分析，通过模型参数变化揭示系统在不同状态(稳定、可激、振荡和双稳态)之间的切换;(ⅱ)以正反馈介质浓度为分岔参数进行数值分岔分析;(ⅲ)对模型系统不同动力状态下参数不确定性对模型输出的影响进行敏感性分析;(四)模型系统的数值模拟，用于模型预测。我们的方法支持数学和计算模型在揭示分子和发育过程机制中的作用，并为分析这种性质的时间模型提供工具。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Computational Dynamics Engineering-Computational Mechanics

CiteScore

2.30

自引率

10.00%

发文量

期刊介绍： JCD is focused on the intersection of computation with deterministic and stochastic dynamics. The mission of the journal is to publish papers that explore new computational methods for analyzing dynamic problems or use novel dynamical methods to improve computation. The subject matter of JCD includes both fundamental mathematical contributions and applications to problems from science and engineering. A non-exhaustive list of topics includes * Computation of phase-space structures and bifurcations * Multi-time-scale methods * Structure-preserving integration * Nonlinear and stochastic model reduction * Set-valued numerical techniques * Network and distributed dynamics JCD includes both original research and survey papers that give a detailed and illuminating treatment of an important area of current interest. The editorial board of JCD consists of world-leading researchers from mathematics, engineering, and science, all of whom are experts in both computational methods and the theory of dynamical systems.