Identifying the impact of local connectivity patterns on dynamics in excitatory-inhibitory networks (2411.06802v3)

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 pairwise connectivity motifs on the linear dynamics in EI 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 pairwise motifs. An overrepresentation 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.

• The paper introduces an analytical framework linking chain motifs with outlier eigenvalues that affect neural stability.
• Researchers apply a low-rank approximation method to reveal how even weak chain motifs can destabilize inhibition-dominated circuits.
• Findings underscore the importance of incorporating detailed synaptic connectivity for accurate modeling of neural dynamics.

An Analysis of Local Connectivity Patterns in Excitatory-Inhibitory Networks and Their Impact on Network Dynamics

The paper "Identifying the impact of local connectivity patterns on dynamics in excitatory-inhibitory networks" investigates the effects of specific local connectivity motifs on the dynamics of excitatory-inhibitory (EI) neuronal networks. This work challenges the conventional assumption that synaptic couplings are independent random variables, an assumption frequently employed in theoretical neuroscience to simplify the analysis of complex networks.

Central to this paper is the introduction of an analytical framework to understand how pair-wise connectivity motifs, particularly chain motifs, influence linear dynamics. The researchers employ a low-rank approximation method to model the connectivity matrices and paper their predominant eigenmodes. Their key finding reveals that chain motifs induce an outlier eigenvalue, significantly impacting the network's stability. Inhibition-dominated networks with chain motifs may exhibit instabilities, reversing traditional notions of excitation-inhibition balance, which the authors support through analytical and numerical analysis. Additionally, this paper provides a detailed analysis of paradoxical responses in inhibitory neurons that can arise due to these motifs.

Numerical Findings and Bold Claims

The authors present robust results showing that chain motifs have a profound influence on the resonant modes of the eigenvalue spectrum, specifically inducing a strong positive eigenvalue. This suggests that even weak representations of chain motifs can destabilize the network unless counterbalanced appropriately. The paper extends these findings to sparsely connected networks, where similar effects are observed, pointing towards broad implications for understanding the functional and dynamic characteristics of biological neuronal circuits.

Practical and Theoretical Implications

Practically, these results have implications for interpreting experimental data in systems neuroscience, particularly in studies involving optogenetic perturbations. The strong effect of local chain motifs suggests that detailed structural information at the synaptic level should be incorporated into models predicting network responses, beyond just considering mean synaptic weight and neuronal type.

Theoretically, this work opens new directions in the exploration of synaptic architecture's impact on network dynamics. It calls into question the sufficiency of models that ignore the second-order structure in synaptic connections, suggesting that other similar high-order connectivity features might have as yet undiscovered influences. The potential instability induced by chain motifs raises caution for instances where classical balance is assumed, emphasizing that network responses to external inputs are profoundly affected by these local structural patterns.

Future Directions

This research lays groundwork for further exploration into neural network stability and the effect of various local motifs. Future studies could extend this analysis to networks with more diverse neuron types and synaptic structures, utilizing advancements in connectomics. As large-scale datasets become more accessible, the development of models that integrate these complex synaptic features will be critical.

In conclusion, this paper presents comprehensive insights into how specific connectivity patterns affect the dynamics of excitatory-inhibitory networks. It demonstrates that often overlooked features such as chain motifs are pivotal in determining network behavior, providing an impetus for revisiting existing models of brain networks and integrating newfound knowledge about connectivity motifs. The paper is a notable contribution to theoretical neuroscience, emphasizing the intricacies of synaptic architecture in shaping neuronal network dynamics.