P189 Elementary Dynamics of Neural Microcircuits

Stefano Masserini*1,2,3, Richard Kempter1,2,3

1 Institute for Theoretical Biology, Humboldt-Universität zu Berlin, Berlin, Germany
2Bernstein Center for Computational Neuroscience, Berlin, Germany
3Charité-Universitätsmedizin Berlin, Einstein Center for Neurosciences, Berlin, Germany

*Email: stefanomasse@gmail.com

Introduction

Cell type diversity is a major direction in which systems neuroscience has expanded in the last decade, as networks of excitatory (E) and inhibitory (I) neurons enriched with specific neuronal populations with their own distinct role in the network dynamics. These advances have mostly been driven by new experimental techniques, often inspiring circuit-specific modeling, even when stark similarities across cortical areas would have allowed describing the dynamics of these microcircuits with a more general mathematical language. Steps toward a general description have been taken by using linear approximations to understand how connectivity shapes responses to perturbations from within or outside the network [1,2].

Methods
In this work, we expand on these findings by studying microcircuit dynamics in the simplest nonlinear model, the threshold-linear network (TLN), and generalize insights originally obtained for all-inhibitory TLNs [3]. This model greatly extends the dynamical repertoire of purely linear networks, by allowing for oscillations and multistability. On the other hand, it retains the simplicity of linear models, since the conditions for each nonlinear regime can be computed in closed form and intuitively interpreted in terms of input and connectivity requirements. With this tool, we not only map previously unrelated systems neuroscience hypotheses to a common reference space, but also gain new insights into specific circuits across the brain.
Results
Namely, we compare balancing strategies in inhibition-stabilized E-I networks and discuss different types of bistability in hippocampal E-I-I networks. We then examine the conditions for gamma oscillations in the canonical circuit (Fig. 1A), providing a mechanistic explanation for the opposing effects of PV and SOM interneurons [4]. In E-E-I circuits, we show that connectivity determines three fundamentally different types of assembly interactions, while in E-E-I-I circuits we find that balanced clustering prevents coordinated inputs to one E-I unit from exerting lateral inhibition (Fig. 1B), while opponent clustering can induce competition even between strongly coupled E assemblies, resulting in different bistable configurations (Fig. 1C).
Discussion
While TLNs have so far not been regarded as a standard rate model for neural populations, these applications show that they can provide interpretable conditions even for the emergence of complex dynamical landscapes. These conditions should be taken into account by future modeling work on neural microcircuits, at least as a benchmark to determine whether additional complexity is necessary to explain their dynamics of interest. The simple structure of this model is also amenable to the addition of variables representing synaptic plasticity or slow adaptive currents. TLNs can also be directly compared to spiking networks, for example because they are the first-order mean-field limit for networks of Poisson neurons [5].




Figure 1. (A) Canonical circuit. (Aii-iii) Oscillation coherence. (Aiv) Effects of impairing SOM or PV (matching shading). (B-C) EEII network. (Bii-iii) Firing modulation wrt bottom left point. (Biv) Modulation example (shaded area). (Cii) Dynamical landscape, smaller regions are EII or EEI bistability. (Ciii) Lateral inhibition by either inputs to E1 or I1. (Civ) EI bistability. Input to I1 induces switch.
Acknowledgements
The authors thank Gaspar Cano, Carina Curto, Atilla Kelemen, John Rinzel, Archili Sakevarashvili, and Tilo Schwalger for insightful discussions about this study. Founding source: German Research Foundation, project 327654276--SFB 1315.
References
[1]https://doi.org/10.1101/2020.10.13.336727
[2] https://doi.org/10.1073/pnas.231104012
[3] https://doi.org/10.48550/arXiv.1804.00794
[4]https://doi.org/10.1038/nn.4562
[5] https://doi.org/10.48550/arXiv.2412.16111