Structured Excitatory-Inhibitory Networks: a low-rank approach
Networks of excitatory and inhibitory (EI) neurons form a canonical circuit in the brain. Classical theoretical analyses of dynamics in EI networks have revealed key principles such as EI balance or paradoxical responses to external inputs. These seminal results assume that synaptic strengths depend on the type of neurons they connect but are otherwise statistically independent. However, recent synaptic physiology datasets have uncovered connectivity patterns that deviate significantly from independent connection models. Simultaneously, studies of task-trained recurrent networks have emphasized the role of connectivity structure in implementing neural computations. Despite these findings, integrating detailed connectivity structures into mean-field theories of EI networks remains a substantial challenge. In this talk, I will outline a theoretical approach to understanding dynamics in structured EI networks by employing a low-rank approximation based on an analytical computation of the dominant eigenvalues of the full connectivity matrix. I will illustrate this approach by investigating the effects of pair-wise connectivity motifs on linear dynamics in EI networks. Specifically, I will present recent results demonstrating that an over-representation of chain motifs induces a strong positive eigenvalue in inhibition-dominated networks, generating a potential instability that challenges classical EI balance criteria. Furthermore, by examining the effects of external input, we found that chain motifs can, on their own, induce paradoxical responses, wherein an increased input to inhibitory neurons leads to a counterintuitive decrease in their activity through recurrent feedback mechanisms. Altogether, our theoretical approach opens new avenues for relating recorded connectivity structures with dynamics and computations in biological networks. Presented in the van Vreeswijk Theoretical Neuroscience Seminar series (formerly WWTNS) on 2025-01-22. Recording duration: 00:47:27.
How do Astrocytes Sculpt Synaptic Circuits?
How does a neuron decide when and where to make a synapse?
Precise synaptic connectivity is a prerequisite for the function of neural circuits, yet individual neurons, taken out of their developmental context, readily form unspecific synapses. How does genetically encoded brain wiring deal with this apparent contradiction? Brain wiring is a developmental growth process that is not only characterized by precision, but also flexibility and robustness. As in any other growth process, cellular interactions are restricted in space and time. Correspondingly, molecular and cellular interactions are restricted to those that 'get to see' each other during development. This seminar will explore the question how neurons decide when and where to make synapses using the Drosophila visual system as a model. New findings reveal that pattern formation during growth and the kinetics of live neuronal interactions restrict synapse formation and partner choice for neurons that are not otherwise prevented from making incorrect synapses in this system. For example, cell biological mechanisms like autophagy as well as developmental temperature restrict inappropriate partner choice through a process of kinetic exclusion that critically contributes to wiring specificity. The seminar will explore these and other neuronal strategies when and where to make synapses during developmental growth that contribute to precise, flexible and robust outcomes in brain wiring.
Microglia, memories, and the extracellular space
Microglia are the immune cells of the brain, and play increasingly appreciated roles in synapse formation, brain plasticity, and cognition. A growing appreciation that the immune system involved in diseases like schizophrenia, epilepsy, and neurodegenerative diseases has led to renewed interest in how microglia regulate synaptic connectivity. Our group previously identified the IL-1 family cytokine Interleukin-33 (IL-33) as a novel regulator of microglial activation and function. I will discuss a mechanism by which microglia regulate synaptic plasticity and long-term memories by engulfing brain extracellular matrix (ECM) proteins. These studies raise the question of how these pathways may be altered or could be modified in the context of disease.
Glassy phase in dynamically balanced networks
We study the dynamics of (inhibitory) balanced networks at varying (i) the level of symmetry in the synaptic connectivity; and (ii) the ariance of the synaptic efficacies (synaptic gain). We find three regimes of activity. For suitably low synaptic gain, regardless of the level of symmetry, there exists a unique stable fixed point. Using a cavity-like approach, we develop a quantitative theory that describes the statistics of the activity in this unique fixed point, and the conditions for its stability. Increasing the synaptic gain, the unique fixed point destabilizes, and the network exhibits chaotic activity for zero or negative levels of symmetry (i.e., random or antisymmetric). Instead, for positive levels of symmetry, there is multi-stability among a large number of marginally stable fixed points. In this regime, ergodicity is broken and the network exhibits non-exponential relaxational dynamics. We discuss the potential relevance of such a “glassy” phase to explain some features of cortical activity.
A geometric framework to predict structure from function in neural networks
The structural connectivity matrix of synaptic weights between neurons is a critical determinant of overall network function. However, quantitative links between neural network structure and function are complex and subtle. For example, many networks can give rise to similar functional responses, and the same network can function differently depending on context. Whether certain patterns of synaptic connectivity are required to generate specific network-level computations is largely unknown. Here we introduce a geometric framework for identifying synaptic connections required by steady-state responses in recurrent networks of rectified-linear neurons. Assuming that the number of specified response patterns does not exceed the number of input synapses, we analytically calculate all feedforward and recurrent connectivity matrices that can generate the specified responses from the network inputs. We then use this analytical characterization to rigorously analyze the solution space geometry and derive certainty conditions guaranteeing a non-zero synapse between neurons.