Dale’s Principle Is Necessary for an Optimal Neuronal Network’s Dynamics

• 作者: Eleonora Catsigeras
• 来源期刊: 应用数学(英文)
• 学科: 数学
• 关键词: Neural Networks IMPULSIVE ODE DISCONTINUOUS DYNAMICAL Systems Directed & Weighted GRAPHS Mathematical Model in BIOLOGY
• 年，卷（期）: yysxyw_2013,（10）
• 页码范围: 15-29
• 页数: 15页
• 分类号: O1

摘要

We study a mathematical model of biological neuronal networks composed by any finite number N ≥ 2 of non-necessarily identical cells. The model is a deterministic dynamical system governed by finite-dimensional impulsive differential equations. The statical structure of the network is described by a directed and weighted graph whose nodes are certain subsets of neurons, and whose edges are the groups of synaptical connections among those subsets. First, we prove that among all the possible networks such as their respective graphs are mutually isomorphic, there exists a dynamical optimum. This optimal network exhibits the richest dynamics: namely, it is capable to show the most diverse set of responses (i.e. orbits in the future) under external stimulus or signals. Second, we prove that all the neurons of a dynamically optimal neuronal network necessarily satisfy Dale’s Principle, i.e. each neuron must be either excitatory or inhibitory, but not mixed. So, Dale’s Principle is a mathematical necessary consequence of a theoretic optimization process of the dynamics of the network. Finally, we prove that Dale’s Principle is not sufficient for the dynamical optimization of the network.