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.

翻译：兴奋与抑制（EI）神经元网络构成了大脑中的典型环路。关于此类网络动力学的开创性理论结果基于以下假设：突触强度取决于所连接神经元的类型，但在其他方面具有统计独立性。然而，最近的突触生理学数据集凸显了特定连接模式的突出性，这些模式远远超出了独立连接所能预期的范围。尽管数十年的重要研究已证明了基本EI细胞类型结构的强大作用，但额外连接特征在多大程度上影响动力学仍有待全面阐明。本文通过将连接性近似为低秩结构的分析框架，研究了成对连接模体对EI网络线性动力学的影响。该低秩近似基于对连接矩阵主导特征值的数学推导，并预测了连接模体及其与细胞类型结构相互作用对外部输入响应的影响。我们的结果表明，一种特定的连接模式——链式模体——对其他成对模体在主导特征模态上具有更强的影响。链式模体的过度表达会在抑制主导的网络中诱发强烈的正特征值，并产生潜在的不稳定性，这需要重新审视经典的兴奋-抑制平衡准则。通过考察外部输入的影响，我们发现链式模体可单独诱发悖论性响应：由于循环反馈作用，对抑制神经元输入的增加反而导致其活动降低。这些发现对解释光遗传学扰动响应实验具有直接意义，此类实验常被用于推断皮层环路的动力学状态。