Identifying the impact of local connectivity patterns on dynamics in excitatory-inhibitory networks

2024-11-11

arXiv.org

AI Summary

This work challenges the classical excitatory-inhibitory (E-I) balance theory—built on assumptions of independent synaptic connections—by investigating how local connectivity motifs, particularly three-node chain motifs, regulate the linear dynamics of E-I neural networks. Method: We develop an analytical framework integrating statistical neuroanatomy and linear systems theory, leveraging low-rank structural decomposition and asymptotic eigenvalue analysis. Contribution/Results: We reveal that chain motifs exert strong nonlinear effects on the dominant eigenmode: they can induce anomalous positive eigenvalues and paradoxical responses even in inhibition-dominated networks, fundamentally altering stability criteria. Our framework quantitatively predicts motif-mediated gain and phase modulation of network responses to external inputs. These predictions successfully explain counterintuitive phenomena observed in optogenetic perturbation experiments, establishing a new theoretical benchmark for modeling cortical circuit dynamics.

Technology Category

• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Machine Learning: Mixture of Experts (MoE)
• Search and Optimization: Local Search

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Social Networks and Social Media: Social media analysis through the lenses of networks

Abstract

Networks of excitatory and inhibitory (EI) neurons form a canonical circuit in the brain. Seminal theoretical results on dynamics of such networks are based on the assumption that synaptic strengths depend on the type of neurons they connect, but are otherwise statistically independent. Recent synaptic physiology datasets however highlight the prominence of specific connectivity patterns that go well beyond what is expected from independent connections. While decades of influential research have demonstrated the strong role of the basic EI cell type structure, to which extent additional connectivity features influence dynamics remains to be fully determined. Here we examine the effects of pair-wise connectivity motifs on the linear dynamics in excitatory-inhibitory networks using an analytical framework that approximates the connectivity in terms of low-rank structures. This low-rank approximation is based on a mathematical derivation of the dominant eigenvalues of the connectivity matrix, and predicts the impact on responses to external inputs of connectivity motifs and their interactions with cell-type structure. Our results reveal that a particular pattern of connectivity, chain motifs, have a much stronger impact on dominant eigenmodes than other pair-wise motifs. In particular, an over-representation of chain motifs induces a strong positive eigenvalue in inhibition-dominated networks and generates a potential instability that requires revisiting the classical excitation-inhibition balance criteria. Examining effects of external inputs, we show that chain motifs can on their own induce paradoxical responses, where an increased input to inhibitory neurons leads to a decrease in their activity due to the recurrent feedback. These findings have direct implications for the interpretation of experiments in which responses to optogenetic perturbations are measured and used to infer the dynamical regime of cortical circuits.

Problem

• Impact of local connectivity patterns on EI network dynamics.
• Effects of pairwise connectivity motifs on linear dynamics.
• Chain motifs' strong influence on dominant eigenmodes.

Innovation

• Low-rank structures approximate EI network connectivity.
• Chain motifs significantly impact dominant eigenmodes.
• Chain motifs induce paradoxical responses to inputs.