In vivo extracellular recordings of thalamic and cortical visual responses reveal V1 connectivity rules.

The brain's connectome provides the scaffold for canonical neural computations. However, a comparison of connectivity studies in the mouse primary visual cortex (V1) reveals that the average number and strength of connections between specific neuron types can vary. Can variability in V1 connectivity measurements coexist with canonical neural computations? We developed a theory-driven approach to deduce V1 network connectivity from visual responses in mouse V1 and visual thalamus (dLGN). Our method revealed that the same recorded visual responses were captured by multiple connectivity configurations. Remarkably, the magnitude and selectivity of connectivity weights followed a specific order across most of the inferred connectivity configurations. We argue that this order stems from the specific shapes of the recorded contrast response functions and contrast invariance of orientation tuning. Remarkably, despite variability across connectivity studies, connectivity weights computed from individual published connectivity reports followed the order we identified with our method, suggesting that the relations between the weights, rather than their magnitudes, represent a connectivity motif supporting canonical V1 computations.

Targeting operational regimes of interest in recurrent neural networks.

Neural computations emerge from local recurrent neural circuits or computational units such as cortical columns that comprise hundreds to a few thousand neurons. Continuous progress in connectomics, electrophysiology, and calcium imaging require tractable spiking network models that can consistently incorporate new information about the network structure and reproduce the recorded neural activity features. However, for spiking networks, it is challenging to predict which connectivity configurations and neural properties can generate fundamental operational states and specific experimentally reported nonlinear cortical computations. Theoretical descriptions for the computational state of cortical spiking circuits are diverse, including the balanced state where excitatory and inhibitory inputs balance almost perfectly or the inhibition stabilized state (ISN) where the excitatory part of the circuit is unstable. It remains an open question whether these states can co-exist with experimentally reported nonlinear computations and whether they can be recovered in biologically realistic implementations of spiking networks. Here, we show how to identify spiking network connectivity patterns underlying diverse nonlinear computations such as XOR, bistability, inhibitory stabilization, supersaturation, and persistent activity. We establish a mapping between the stabilized supralinear network (SSN) and spiking activity which allows us to pinpoint the location in parameter space where these activity regimes occur. Notably, we find that biologically-sized spiking networks can have irregular asynchronous activity that does not require strong excitation-inhibition balance or large feedforward input and we show that the dynamic firing rate trajectories in spiking networks can be precisely targeted without error-driven training algorithms.

Computational insights into mRNA and protein dynamics underlying synaptic plasticity rules.

Recent advances in experimental techniques provide an unprecedented peek into the intricate molecular dynamics inside synapses and dendrites. The experimental insights into the molecular turnover revealed that such processes as diffusion, active transport, spine uptake, and local protein synthesis could dynamically modulate the copy numbers of plasticity-related molecules in synapses. Subsequently, theoretical models were designed to understand the interaction of these processes better and to explain how local synaptic plasticity cues can up or down-regulate the molecular copy numbers across synapses. In this review, we discuss the recent advances in experimental techniques and computational models to highlight how these complementary approaches can provide insight into molecular cross-talk across synapses, ultimately allowing us to develop biologically-inspired neural network models to understand brain function.

How to incorporate biological insights into network models and why it matters.

Due to the staggering complexity of the brain and its neural circuitry, neuroscientists rely on the analysis of mathematical models to elucidate its function. From Hodgkin and Huxley's detailed description of the action potential in 1952 to today, new theories and increasing computational power have opened up novel avenues to study how neural circuits implement the computations that underlie behaviour. Computational neuroscientists have developed many models of neural circuits that differ in complexity, biological realism or emergent network properties. With recent advances in experimental techniques for detailed anatomical reconstructions or large-scale activity recordings, rich biological data have become more available. The challenge when building network models is to reflect experimental results, either through a high level of detail or by finding an appropriate level of abstraction. Meanwhile, machine learning has facilitated the development of artificial neural networks, which are trained to perform specific tasks. While they have proven successful at achieving task-oriented behaviour, they are often abstract constructs that differ in many features from the physiology of brain circuits. Thus, it is unclear whether the mechanisms underlying computation in biological circuits can be investigated by analysing artificial networks that accomplish the same function but differ in their mechanisms. Here, we argue that building biologically realistic network models is crucial to establishing causal relationships between neurons, synapses, circuits and behaviour. More specifically, we advocate for network models that consider the connectivity structure and the recorded activity dynamics while evaluating task performance.

Stabilized supralinear network can give rise to bistable, oscillatory, and persistent activity.

A hallmark of cortical circuits is their versatility. They can perform multiple fundamental computations such as normalization, memory storage, and rhythm generation. Yet it is far from clear how such versatility can be achieved in a single circuit, given that specialized models are often needed to replicate each computation. Here, we show that the stabilized supralinear network (SSN) model, which was originally proposed for sensory integration phenomena such as contrast invariance, normalization, and surround suppression, can give rise to dynamic cortical features of working memory, persistent activity, and rhythm generation. We study the SSN model analytically and uncover regimes where it can provide a substrate for working memory by supporting two stable steady states. Furthermore, we prove that the SSN model can sustain finite firing rates following input withdrawal and present an exact connectivity condition for such persistent activity. In addition, we show that the SSN model can undergo a supercritical Hopf bifurcation and generate global oscillations. Based on the SSN model, we outline the synaptic and neuronal mechanisms underlying computational versatility of cortical circuits. Our work shows that the SSN is an exactly solvable nonlinear recurrent neural network model that could pave the way for a unified theory of cortical function.

How mRNA Localization and Protein Synthesis Sites Influence Dendritic Protein Distribution and Dynamics.

Proteins drive the function of neuronal synapses. The synapses are distributed throughout the dendritic arbor, often hundreds of micrometers away from the soma. It is still unclear how somatic and dendritic sources of proteins shape protein distribution and respectively contribute to local protein changes during synaptic plasticity. Here, we present a unique computational framework describing for a given protein species the dendritic distribution of the mRNA and the corresponding protein in a dendrite. Using CaMKIIα as a test case, our model reveals the key role active transport plays in the maintenance of dendritic mRNA and protein levels and predicts the short and long timescales of protein dynamics. Our model reveals the fundamental role of mRNA localization and dendritic mRNA translation in synaptic maintenance and plasticity in distal compartments. We developed a web application for neuroscientists to explore the dynamics of the mRNA or protein of interest.