What is the dynamical regime of cerebral cortex?

Stabilized Supralinear Network Model of Responses to Surround Stimuli in Primary Visual Cortex

In the mammalian primary visual cortex (V1), there are complex interactions between responses to stimuli present in the cell's classical receptive field (CRF) or "center" and in the surrounding region or "surround." The circuit mechanisms underlying these behaviors are likely to represent more general cortical mechanisms for integrating information. Here, we develop a circuit model that accounts for three important features of surround suppression (suppression of response to a center stimulus by addition of a surround stimulus): (1) The surround stimulus suppresses the inhibitory and excitatory currents that the cell receives; (2) The strongest suppression arises when the surround orientation matches that of the center stimulus, even when the center stimulus orientation differs from the cell's preferred orientation; and (3) A surround stimulus of a given orientation most strongly suppresses that orientation's component of the response to a plaid center stimulus ("feature-specific suppression"). We show that a stabilized supralinear network (SSN) with biologically plausible connectivity and synaptic efficacies that depend on cortical distance and orientation difference between units can consistently reproduce phenomena (1) and (3), and, qualitatively, phenomenon (2). We explain the mechanism behind each result. We argue that phenomena (2) and (3) are independent: the model with some aspects of connectivity removed still produces phenomenon (3) but not (2). The model reproduces the rapid time scale of activity decay observed in mouse V1 when thalamic input to V1 is silenced. Finally, we show that these results hold both in networks with rate-based and conductance-based spiking units.

Decoding Alzheimer's Disease: Single-Cell Sequencing Uncovers Brain Cell Heterogeneity and Pathogenesis

Alzheimer's disease (AD) is a complex neurodegenerative disorder marked by progressive cognitive decline and diverse neuropathological features. Recent advances in single-cell sequencing technologies have provided unprecedented insights into the cellular and molecular heterogeneity of the AD brain. This review systematically summarizes the applications of single-cell transcriptomic and epigenomic approaches in AD research, with a focus on the characterization of cell type- and subtype-specific transcriptomic alterations. This review highlights key discoveries related to selectively vulnerable neuronal and glial subpopulations, as well as transcriptional dysregulation associated with genetic risk loci such as APOE and TREM2. This review also discusses how the integration of single-cell RNA sequencing (scRNA-seq), assays for transposase-accessible chromatin using sequencing (ATAC-seq), and spatial transcriptomics elucidates disease trajectories and cellular communication networks across pathological stages. These insights not only enhance the understanding of the pathogenesis of AD but also pave the way for precision medicine through the identification of novel therapeutic targets and biomarkers.

Computational functions of precisely balanced neuronal microcircuits in an olfactory memory network

Models of balanced autoassociative memory networks predict that specific inhibition is critical to store information in connectivity. To explore these predictions, we characterized and manipulated different subtypes of fast-spiking interneurons in the posterior telencephalic area Dp (pDp) of adult zebrafish, the homolog of the piriform cortex. Modeling of recurrent networks with assemblies showed that a precise balance of excitation and inhibition is important to prevent not only excessive firing rates ("runaway activity") but also the stochastic occurrence of high pattern correlations ("runaway correlations"). Consistent with model predictions, runaway correlations emerged in pDp when synaptic balance was perturbed by optogenetic manipulations of feedback inhibition but not feedforward inhibition. Runaway correlations were driven by sparse subsets of strongly active neurons rather than by a general broadening of tuning curves. These results are consistent with balanced neuronal assemblies in pDp and reveal novel computational functions of inhibitory microcircuits in an autoassociative network.

Interleaving asynchronous and synchronous activity in balanced cortical networks with short-term synaptic depression

Cortical populations are in a broadly asynchronous state that is sporadically interrupted by brief epochs of coordinated population activity. Cortical models are at a loss to explain this combination of states. At one extreme are network models where recurrent inhibition dynamically stabilizes an asynchronous low activity state. While these networks are widely used, they cannot produce the coherent population-wide activity that is reported in a variety of datasets. At the other extreme are models in which strong recurrent excitation that is quickly tamed by short term synaptic depression between excitatory neurons leads to short epochs of population-wide activity. However, in these networks, inhibition plays only a perfunctory role in network stability, which is at odds with many reports across cortex. In this study we analyze spontaneously active in vitro preparations of primary auditory cortex that show dynamics that are emblematic of this mixture of states. To capture this complex population activity we use firing rate-based networks as well as biologically realistic networks of spiking neuron models where large excitation is balanced by recurrent inhibition, yet we include short-term synaptic depression dynamics of the excitatory connections. These models give very rich nonlinear behavior that mimics the core features of the in vitro data, including the possibility of low frequency (2-12 Hz) rhythmic dynamics within population events. In these networks, synaptic depression enables activity fluctuations to induce a weakening of inhibitory recruitment, which in turn triggers population events. In sum, our study extends balanced network models to account for nonlinear, population-wide correlated activity, thereby providing a critical step in a mechanistic theory of realistic cortical activity.

Identifying the impact of local connectivity patterns on dynamics in excitatory-inhibitory networks

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.

Efficient coding in biophysically realistic excitatory-inhibitory spiking networks

The principle of efficient coding posits that sensory cortical networks are designed to encode maximal sensory information with minimal metabolic cost. Despite the major influence of efficient coding in neuroscience, it has remained unclear whether fundamental empirical properties of neural network activity can be explained solely based on this normative principle. Here, we derive the structural, coding, and biophysical properties of excitatory-inhibitory recurrent networks of spiking neurons that emerge directly from imposing that the network minimizes an instantaneous loss function and a time-averaged performance measure enacting efficient coding. We assumed that the network encodes a number of independent stimulus features varying with a time scale equal to the membrane time constant of excitatory and inhibitory neurons. The optimal network has biologically plausible biophysical features, including realistic integrate-and-fire spiking dynamics, spike-triggered adaptation, and a non-specific excitatory external input. The excitatory-inhibitory recurrent connectivity between neurons with similar stimulus tuning implements feature-specific competition, similar to that recently found in visual cortex. Networks with unstructured connectivity cannot reach comparable levels of coding efficiency. The optimal ratio of excitatory vs inhibitory neurons and the ratio of mean inhibitory-to-inhibitory vs excitatory-to-inhibitory connectivity are comparable to those of cortical sensory networks. The efficient network solution exhibits an instantaneous balance between excitation and inhibition. The network can perform efficient coding even when external stimuli vary over multiple time scales. Together, these results suggest that key properties of biological neural networks may be accounted for by efficient coding.

Hierarchy between forelimb premotor and primary motor cortices and its manifestation in their firing patterns

Though hierarchy is commonly invoked in descriptions of motor cortical function, its presence and manifestation in firing patterns remain poorly resolved. Here we use optogenetic inactivation to demonstrate that short-latency influence between forelimb premotor and primary motor cortices is asymmetric during reaching in mice, demonstrating a partial hierarchy between the endogenous activity in each region. Multi-region recordings revealed that some activity is captured by similar but delayed patterns where the activity of either region leads, with premotor activity leading more. Yet firing in each region is dominated by patterns shared between regions and is equally predictive of firing in the other region at the single-neuron level. In dual-region network models fit to data, regions differed in their dependence on across-region input, rather than the amount of such input they received. Our results indicate that motor cortical hierarchy, while present, may not be exposed when inferring interactions between populations from firing patterns alone.

Neural circuit mechanisms to transform cerebellar population dynamics for motor control in monkeys

We exploit identification of neuron types during extracellular recording to demonstrate how the cerebellar cortex's well-established architecture transforms inputs into outputs. During smooth pursuit eye movements, the floccular complex performs distinct input-output transformations of temporal dynamics and directional response properties. The responses of different interneuron types localize the circuit mechanisms of each transformation. Mossy fibers and unipolar brush cells emphasize eye position dynamics uniformly across the cardinal axes; Purkinje cells and molecular layer interneurons code eye velocity along directionally biased axes; Golgi cells show unmodulated firing. Differential directional response properties of different neuron types localize the directional input-output transformation to the last-order inputs to Purkinje cells. Differential temporal dynamics pinpoint the site of the temporal input-output transformation to granule cells. Specific granule cell population dynamics allow the temporal transformations required in the area we study and generalize to many temporal transformations, providing a complete framework to understand cerebellar circuit computation.

Impact statement

We dissect the circuit computations performed by the floccular complex of the cerebellum during an exemplar sensory-motor behavior, taking advantage of knowledge of the circuit architecture, existence of discrete neuron types, and a newfound ability to identify neuron types from extracellular recordings. Our results describe the contributions of the major neuron types to the cerebellar input-output computations, identify the population dynamics needed in granule cells to support those computations, and to create a basis set to enable temporally-specific motor behavior and motor learning.

Excitation-Inhibition Balance, Neural Criticality, and Activities in Neuronal Circuits

Neural activities in local circuits exhibit complex and multilevel dynamic features. Individual neurons spike irregularly, which is believed to originate from receiving balanced amounts of excitatory and inhibitory inputs, known as the excitation-inhibition balance. The spatial-temporal cascades of clustered neuronal spikes occur in variable sizes and durations, manifested as neural avalanches with scale-free features. These may be explained by the neural criticality hypothesis, which posits that neural systems operate around the transition between distinct dynamic states. Here, we summarize the experimental evidence for and the underlying theory of excitation-inhibition balance and neural criticality. Furthermore, we review recent studies of excitatory-inhibitory networks with synaptic kinetics as a simple solution to reconcile these two apparently distinct theories in a single circuit model. This provides a more unified understanding of multilevel neural activities in local circuits, from spontaneous to stimulus-response dynamics.

Contextual modulation emerges by integrating feedforward and feedback processing in mouse visual cortex

Sensory systems use context to infer meaning. Accordingly, context profoundly influences neural responses to sensory stimuli. However, a cohesive understanding of the circuit mechanisms governing contextual effects across different stimulus conditions is still lacking. Here we present a unified circuit model of mouse visual cortex that accounts for the main standard forms of contextual modulation. This data-driven and biologically realistic circuit, including three primary inhibitory cell types, sheds light on how bottom-up, top-down, and recurrent inputs are integrated across retinotopic space to generate contextual effects in layer 2/3. We establish causal relationships between neural responses, geometrical features of the inputs, and the connectivity patterns. The model not only reveals how a single canonical cortical circuit differently modulates sensory response depending on context but also generates multiple testable predictions, offering insights that apply to broader neural circuitry.

Exact linear theory of perturbation response in a space- and feature-dependent cortical circuit model

What are the principles that govern the responses of cortical networks to their inputs and the emergence of these responses from recurrent connectivity? Recent experiments have probed these questions by measuring cortical responses to two-photon optogenetic perturbations of single cells in the mouse primary visual cortex. A robust theoretical framework is needed to determine the implications of these responses for cortical recurrence. Here we propose a novel analytical approach: a formulation of the dependence of cell-type-specific connectivity on spatial distance that yields an exact solution for the linear perturbation response of a model with multiple cell types and space- and feature-dependent connectivity. Importantly and unlike previous approaches, the solution is valid in regimes of strong as well as weak intra-cortical coupling. Analysis reveals the structure of connectivity implied by various features of single-cell perturbation responses, such as the surprisingly narrow spatial radius of nearby excitation beyond which inhibition dominates, the number of transitions between mean excitation and inhibition thereafter, and the dependence of these responses on feature preferences. Comparison of these results to existing optogenetic perturbation data yields constraints on cell-type-specific connection strengths and their tuning dependence. Finally, we provide experimental predictions regarding the response of inhibitory neurons to single-cell perturbations and the modulation of perturbation response by neuronal gain; the latter can explain observed differences in the feature-tuning of perturbation responses in the presence vs. absence of visual stimuli.

Efficient coding in biophysically realistic excitatory-inhibitory spiking networks

The principle of efficient coding posits that sensory cortical networks are designed to encode maximal sensory information with minimal metabolic cost. Despite the major influence of efficient coding in neuroscience, it has remained unclear whether fundamental empirical properties of neural network activity can be explained solely based on this normative principle. Here, we derive the structural, coding, and biophysical properties of excitatory-inhibitory recurrent networks of spiking neurons that emerge directly from imposing that the network minimizes an instantaneous loss function and a time-averaged performance measure enacting efficient coding. We assumed that the network encodes a number of independent stimulus features varying with a time scale equal to the membrane time constant of excitatory and inhibitory neurons. The optimal network has biologically-plausible biophysical features, including realistic integrate-and-fire spiking dynamics, spike-triggered adaptation, and a non-specific excitatory external input. The excitatory-inhibitory recurrent connectivity between neurons with similar stimulus tuning implements feature-specific competition, similar to that recently found in visual cortex. Networks with unstructured connectivity cannot reach comparable levels of coding efficiency. The optimal ratio of excitatory vs inhibitory neurons and the ratio of mean inhibitory-to-inhibitory vs excitatory-to-inhibitory connectivity are comparable to those of cortical sensory networks. The efficient network solution exhibits an instantaneous balance between excitation and inhibition. The network can perform efficient coding even when external stimuli vary over multiple time scales. Together, these results suggest that key properties of biological neural networks may be accounted for by efficient coding.

Critical Avalanches in Excitation-Inhibition Balanced Networks Reconcile Response Reliability with Sensitivity for Optimal Neural Representation

Neural criticality has emerged as a unified framework that reconciles diverse multiscale neuronal dynamics such as the irregular firing of individual neurons, sparse synchrony in neuronal populations, and the emergence of scale-free avalanches. However, the functional role of neuronal criticality remains ambiguous. Here, we investigate the neural dynamics and representations in response to external signals in excitation-inhibition balanced networks. We reveal that, in contrast with the case for the traditional critical branching model, the critical state of the balanced network simultaneously achieves maximal response sensitivity, maximal response reliability, and the optimal representation of external signals due to the presence of reliable avalanches induced by external signals. We further demonstrate that heterogeneity in inhibitory connections is a mechanism underlying the reliable critical avalanches and optimal representation. Our study addresses a longstanding challenge concerning the functional significance of neuronal criticality, namely the intricate coexistence of reliability and sensitivity.

Geometry and dynamics of representations in a precisely balanced memory network related to olfactory cortex

Biological memory networks are thought to store information by experience-dependent changes in the synaptic connectivity between assemblies of neurons. Recent models suggest that these assemblies contain both excitatory and inhibitory neurons (E/I assemblies), resulting in co-tuning and precise balance of excitation and inhibition. To understand computational consequences of E/I assemblies under biologically realistic constraints we built a spiking network model based on experimental data from telencephalic area Dp of adult zebrafish, a precisely balanced recurrent network homologous to piriform cortex. We found that E/I assemblies stabilized firing rate distributions compared to networks with excitatory assemblies and global inhibition. Unlike classical memory models, networks with E/I assemblies did not show discrete attractor dynamics. Rather, responses to learned inputs were locally constrained onto manifolds that 'focused' activity into neuronal subspaces. The covariance structure of these manifolds supported pattern classification when information was retrieved from selected neuronal subsets. Networks with E/I assemblies therefore transformed the geometry of neuronal coding space, resulting in continuous representations that reflected both relatedness of inputs and an individual's experience. Such continuous representations enable fast pattern classification, can support continual learning, and may provide a basis for higher-order learning and cognitive computations.

Sub-threshold neuronal activity and the dynamical regime of cerebral cortex

Cortical neurons exhibit temporally irregular spiking patterns and heterogeneous firing rates. These features arise in model circuits operating in a 'fluctuation-driven regime', in which fluctuations in membrane potentials emerge from the network dynamics. However, it is still debated whether the cortex operates in such a regime. We evaluated the fluctuation-driven hypothesis by analyzing spiking and sub-threshold membrane potentials of neurons in the frontal cortex of mice performing a decision-making task. We showed that while standard fluctuation-driven models successfully account for spiking statistics, they fall short in capturing the heterogeneity in sub-threshold activity. This limitation is an inevitable outcome of bombarding single-compartment neurons with a large number of pre-synaptic inputs, thereby clamping the voltage of all neurons to more or less the same average voltage. To address this, we effectively incorporated dendritic morphology into the standard models. Inclusion of dendritic morphology in the neuronal models increased neuronal selectivity and reduced error trials, suggesting a functional role for dendrites during decision-making. Our work suggests that, during decision-making, cortical neurons in high-order cortical areas operate in a fluctuation-driven regime.

Desegregation of neuronal predictive processing

Neural circuits construct internal 'world-models' to guide behavior. The predictive processing framework posits that neural activity signaling sensory predictions and concurrently computing prediction-errors is a signature of those internal models. Here, to understand how the brain generates predictions for complex sensorimotor signals, we investigate the emergence of high-dimensional, multi-modal predictive representations in recurrent networks. We find that robust predictive processing arises in a network with loose excitatory/inhibitory balance. Contrary to previous proposals of functionally specialized cell-types, the network exhibits desegregation of stimulus and prediction-error representations. We confirmed these model predictions by experimentally probing predictive-coding circuits using a rich stimulus-set to violate learned expectations. When constrained by data, our model further reveals and makes concrete testable experimental predictions for the distinct functional roles of excitatory and inhibitory neurons, and of neurons in different layers along a laminar hierarchy, in computing multi-modal predictions. These results together imply that in natural conditions, neural representations of internal models are highly distributed, yet structured to allow flexible readout of behaviorally-relevant information. The generality of our model advances the understanding of computation of internal models across species, by incorporating different types of predictive computations into a unified framework.

The mechanics of correlated variability in segregated cortical excitatory subnetworks

Understanding the genesis of shared trial-to-trial variability in neuronal population activity within the sensory cortex is critical to uncovering the biological basis of information processing in the brain. Shared variability is often a reflection of the structure of cortical connectivity since it likely arises, in part, from local circuit inputs. A series of experiments from segregated networks of (excitatory) pyramidal neurons in the mouse primary visual cortex challenge this view. Specifically, the across-network correlations were found to be larger than predicted given the known weak cross-network connectivity. We aim to uncover the circuit mechanisms responsible for these enhanced correlations through biologically motivated cortical circuit models. Our central finding is that coupling each excitatory subpopulation with a specific inhibitory subpopulation provides the most robust network-intrinsic solution in shaping these enhanced correlations. This result argues for the existence of excitatory-inhibitory functional assemblies in early sensory areas which mirror not just response properties but also connectivity between pyramidal cells. Furthermore, our findings provide theoretical support for recent experimental observations showing that cortical inhibition forms structural and functional subnetworks with excitatory cells, in contrast to the classical view that inhibition is a nonspecific blanket suppression of local excitation.

Mean-field solution of the neural dynamics in a Greenberg-Hastings model with excitatory and inhibitory units

We present a mean-field solution of the dynamics of a Greenberg-Hastings neural network with both excitatory and inhibitory units. We analyze the dynamical phase transitions that appear in the stationary state as the model parameters are varied. Analytical solutions are compared with numerical simulations of the microscopic model defined on a fully connected network. We found that the stationary state of this system exhibits a first-order dynamical phase transition (with the associated hysteresis) when the fraction of inhibitory units f is smaller than some critical value f_{t}≲1/2, even for a finite system. Moreover, any solution for f<1/2 can be mapped to a solution for purely excitatory systems (f=0). In finite systems, when the system is dominated by inhibition (f>f_{t}), the first-order transition is replaced by a pseudocritical one, namely a continuous crossover between regions of low and high activity that resembles the finite size behavior of a continuous phase transition order parameter. However, in the thermodynamic limit (i.e., infinite-system-size limit), we found that f_{t}→1/2 and the activity for the inhibition dominated case (f≥f_{t}) becomes negligible for any value of the parameters, while the first-order transition between low- and high-activity phases for f Collapse

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Affiliation(s)

Joaquin Almeira Instituto de Física Enrique Gaviola (IFEG-CONICET), Facultad de Matemática Astronomía Física y Computación, Universidad Nacional de Córdoba, 5000 Córdoba, Argentina Consejo Nacional de Investigaciones Científcas y Tecnológicas (CONICET), 1425 Buenos Aires, Argentina Facultad de Matemática Astronomía Física y Computación, Universidad Nacional de Córdoba, 5000 Córdoba, Argentina
Tomas S Grigera Consejo Nacional de Investigaciones Científcas y Tecnológicas (CONICET), 1425 Buenos Aires, Argentina Instituto de Física de Líquidos y Sistemas Biológicos (IFLYSIB), CONICET and Universidad Nacional de La Plata, 1900 La Plata, Argentina Departamento de Física, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, 1900 La Plata, Argentina Istituto dei Sistemi Complessi, Consiglio Nazionale delle Ricerche, 00185 Rome, Italy
Daniel A Martin Consejo Nacional de Investigaciones Científcas y Tecnológicas (CONICET), 1425 Buenos Aires, Argentina Instituto de Ciencias Físicas (ICIFI-CONICET), Center for Complex Systems and Brain Sciences (CEMSC3), Escuela de Ciencia y Tecnología, Universidad Nacional de Gral. San Martín, Campus Miguelete, San Martín, 1650 Buenos Aires, Argentina
Dante R Chialvo Consejo Nacional de Investigaciones Científcas y Tecnológicas (CONICET), 1425 Buenos Aires, Argentina Instituto de Ciencias Físicas (ICIFI-CONICET), Center for Complex Systems and Brain Sciences (CEMSC3), Escuela de Ciencia y Tecnología, Universidad Nacional de Gral. San Martín, Campus Miguelete, San Martín, 1650 Buenos Aires, Argentina
Sergio A Cannas Instituto de Física Enrique Gaviola (IFEG-CONICET), Facultad de Matemática Astronomía Física y Computación, Universidad Nacional de Córdoba, 5000 Córdoba, Argentina Consejo Nacional de Investigaciones Científcas y Tecnológicas (CONICET), 1425 Buenos Aires, Argentina Facultad de Matemática Astronomía Física y Computación, Universidad Nacional de Córdoba, 5000 Córdoba, Argentina

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Synapse-type-specific competitive Hebbian learning forms functional recurrent networks

Cortical networks exhibit complex stimulus-response patterns that are based on specific recurrent interactions between neurons. For example, the balance between excitatory and inhibitory currents has been identified as a central component of cortical computations. However, it remains unclear how the required synaptic connectivity can emerge in developing circuits where synapses between excitatory and inhibitory neurons are simultaneously plastic. Using theory and modeling, we propose that a wide range of cortical response properties can arise from a single plasticity paradigm that acts simultaneously at all excitatory and inhibitory connections-Hebbian learning that is stabilized by the synapse-type-specific competition for a limited supply of synaptic resources. In plastic recurrent circuits, this competition enables the formation and decorrelation of inhibition-balanced receptive fields. Networks develop an assembly structure with stronger synaptic connections between similarly tuned excitatory and inhibitory neurons and exhibit response normalization and orientation-specific center-surround suppression, reflecting the stimulus statistics during training. These results demonstrate how neurons can self-organize into functional networks and suggest an essential role for synapse-type-specific competitive learning in the development of cortical circuits.

The stabilized supralinear network accounts for the contrast dependence of visual cortical gamma oscillations

When stimulated, neural populations in the visual cortex exhibit fast rhythmic activity with frequencies in the gamma band (30-80 Hz). The gamma rhythm manifests as a broad resonance peak in the power-spectrum of recorded local field potentials, which exhibits various stimulus dependencies. In particular, in macaque primary visual cortex (V1), the gamma peak frequency increases with increasing stimulus contrast. Moreover, this contrast dependence is local: when contrast varies smoothly over visual space, the gamma peak frequency in each cortical column is controlled by the local contrast in that column's receptive field. No parsimonious mechanistic explanation for these contrast dependencies of V1 gamma oscillations has been proposed. The stabilized supralinear network (SSN) is a mechanistic model of cortical circuits that has accounted for a range of visual cortical response nonlinearities and contextual modulations, as well as their contrast dependence. Here, we begin by showing that a reduced SSN model without retinotopy robustly captures the contrast dependence of gamma peak frequency, and provides a mechanistic explanation for this effect based on the observed non-saturating and supralinear input-output function of V1 neurons. Given this result, the local dependence on contrast can trivially be captured in a retinotopic SSN which however lacks horizontal synaptic connections between its cortical columns. However, long-range horizontal connections in V1 are in fact strong, and underlie contextual modulation effects such as surround suppression. We thus explored whether a retinotopically organized SSN model of V1 with strong excitatory horizontal connections can exhibit both surround suppression and the local contrast dependence of gamma peak frequency. We found that retinotopic SSNs can account for both effects, but only when the horizontal excitatory projections are composed of two components with different patterns of spatial fall-off with distance: a short-range component that only targets the source column, combined with a long-range component that targets columns neighboring the source column. We thus make a specific qualitative prediction for the spatial structure of horizontal connections in macaque V1, consistent with the columnar structure of cortex.

Approximating Nonlinear Functions With Latent Boundaries in Low-Rank Excitatory-Inhibitory Spiking Networks

Deep feedforward and recurrent neural networks have become successful functional models of the brain, but they neglect obvious biological details such as spikes and Dale's law. Here we argue that these details are crucial in order to understand how real neural circuits operate. Towards this aim, we put forth a new framework for spike-based computation in low-rank excitatory-inhibitory spiking networks. By considering populations with rank-1 connectivity, we cast each neuron's spiking threshold as a boundary in a low-dimensional input-output space. We then show how the combined thresholds of a population of inhibitory neurons form a stable boundary in this space, and those of a population of excitatory neurons form an unstable boundary. Combining the two boundaries results in a rank-2 excitatory-inhibitory (EI) network with inhibition-stabilized dynamics at the intersection of the two boundaries. The computation of the resulting networks can be understood as the difference of two convex functions and is thereby capable of approximating arbitrary non-linear input-output mappings. We demonstrate several properties of these networks, including noise suppression and amplification, irregular activity and synaptic balance, as well as how they relate to rate network dynamics in the limit that the boundary becomes soft. Finally, while our work focuses on small networks (5-50 neurons), we discuss potential avenues for scaling up to much larger networks. Overall, our work proposes a new perspective on spiking networks that may serve as a starting point for a mechanistic understanding of biological spike-based computation.

Top-down modulation in canonical cortical circuits with short-term plasticity

Cortical dynamics and computations are strongly influenced by diverse GABAergic interneurons, including those expressing parvalbumin (PV), somatostatin (SST), and vasoactive intestinal peptide (VIP). Together with excitatory (E) neurons, they form a canonical microcircuit and exhibit counterintuitive nonlinear phenomena. One instance of such phenomena is response reversal, whereby SST neurons show opposite responses to top-down modulation via VIP depending on the presence of bottom-up sensory input, indicating that the network may function in different regimes under different stimulation conditions. Combining analytical and computational approaches, we demonstrate that model networks with multiple interneuron subtypes and experimentally identified short-term plasticity mechanisms can implement response reversal. Surprisingly, despite not directly affecting SST and VIP activity, PV-to-E short-term depression has a decisive impact on SST response reversal. We show how response reversal relates to inhibition stabilization and the paradoxical effect in the presence of several short-term plasticity mechanisms demonstrating that response reversal coincides with a change in the indispensability of SST for network stabilization. In summary, our work suggests a role of short-term plasticity mechanisms in generating nonlinear phenomena in networks with multiple interneuron subtypes and makes several experimentally testable predictions.

A robust balancing mechanism for spiking neural networks

Dynamical balance of excitation and inhibition is usually invoked to explain the irregular low firing activity observed in the cortex. We propose a robust nonlinear balancing mechanism for a random network of spiking neurons, which works also in the absence of strong external currents. Biologically, the mechanism exploits the plasticity of excitatory-excitatory synapses induced by short-term depression. Mathematically, the nonlinear response of the synaptic activity is the key ingredient responsible for the emergence of a stable balanced regime. Our claim is supported by a simple self-consistent analysis accompanied by extensive simulations performed for increasing network sizes. The observed regime is essentially fluctuation driven and characterized by highly irregular spiking dynamics of all neurons.

Response sub-additivity and variability quenching in visual cortex

Sub-additivity and variability are ubiquitous response motifs in the primary visual cortex (V1). Response sub-additivity enables the construction of useful interpretations of the visual environment, whereas response variability indicates the factors that limit the precision with which the brain can do this. There is increasing evidence that experimental manipulations that elicit response sub-additivity often also quench response variability. Here, we provide an overview of these phenomena and suggest that they may have common origins. We discuss empirical findings and recent model-based insights into the functional operations, computational objectives and circuit mechanisms underlying V1 activity. These different modelling approaches all predict that response sub-additivity and variability quenching often co-occur. The phenomenology of these two response motifs, as well as many of the insights obtained about them in V1, generalize to other cortical areas. Thus, the connection between response sub-additivity and variability quenching may be a canonical motif across the cortex.

How does the primate brain combine generative and discriminative computations in vision?

Vision is widely understood as an inference problem. However, two contrasting conceptions of the inference process have each been influential in research on biological vision as well as the engineering of machine vision. The first emphasizes bottom-up signal flow, describing vision as a largely feedforward, discriminative inference process that filters and transforms the visual information to remove irrelevant variation and represent behaviorally relevant information in a format suitable for downstream functions of cognition and behavioral control. In this conception, vision is driven by the sensory data, and perception is direct because the processing proceeds from the data to the latent variables of interest. The notion of "inference" in this conception is that of the engineering literature on neural networks, where feedforward convolutional neural networks processing images are said to perform inference. The alternative conception is that of vision as an inference process in Helmholtz's sense, where the sensory evidence is evaluated in the context of a generative model of the causal processes that give rise to it. In this conception, vision inverts a generative model through an interrogation of the sensory evidence in a process often thought to involve top-down predictions of sensory data to evaluate the likelihood of alternative hypotheses. The authors include scientists rooted in roughly equal numbers in each of the conceptions and motivated to overcome what might be a false dichotomy between them and engage the other perspective in the realm of theory and experiment. The primate brain employs an unknown algorithm that may combine the advantages of both conceptions. We explain and clarify the terminology, review the key empirical evidence, and propose an empirical research program that transcends the dichotomy and sets the stage for revealing the mysterious hybrid algorithm of primate vision.

Exact Analysis of the Subthreshold Variability for Conductance-Based Neuronal Models with Synchronous Synaptic Inputs

The spiking activity of neocortical neurons exhibits a striking level of variability, even when these networks are driven by identical stimuli. The approximately Poisson firing of neurons has led to the hypothesis that these neural networks operate in the asynchronous state. In the asynchronous state, neurons fire independently from one another, so that the probability that a neuron experience synchronous synaptic inputs is exceedingly low. While the models of asynchronous neurons lead to observed spiking variability, it is not clear whether the asynchronous state can also account for the level of subthreshold membrane potential variability. We propose a new analytical framework to rigorously quantify the subthreshold variability of a single conductance-based neuron in response to synaptic inputs with prescribed degrees of synchrony. Technically, we leverage the theory of exchangeability to model input synchrony via jump-process-based synaptic drives; we then perform a moment analysis of the stationary response of a neuronal model with all-or-none conductances that neglects postspiking reset. As a result, we produce exact, interpretable closed forms for the first two stationary moments of the membrane voltage, with explicit dependence on the input synaptic numbers, strengths, and synchrony. For biophysically relevant parameters, we find that the asynchronous regime yields realistic subthreshold variability (voltage variance ≃4-9 mV2) only when driven by a restricted number of large synapses, compatible with strong thalamic drive. By contrast, we find that achieving realistic subthreshold variability with dense cortico-cortical inputs requires including weak but nonzero input synchrony, consistent with measured pairwise spiking correlations. We also show that, without synchrony, the neural variability averages out to zero for all scaling limits with vanishing synaptic weights, independent of any balanced state hypothesis. This result challenges the theoretical basis for mean-field theories of the asynchronous state.

Exact analysis of the subthreshold variability for conductance-based neuronal models with synchronous synaptic inputs

The spiking activity of neocortical neurons exhibits a striking level of variability, even when these networks are driven by identical stimuli. The approximately Poisson firing of neurons has led to the hypothesis that these neural networks operate in the asynchronous state. In the asynchronous state neurons fire independently from one another, so that the probability that a neuron experience synchronous synaptic inputs is exceedingly low. While the models of asynchronous neurons lead to observed spiking variability, it is not clear whether the asynchronous state can also account for the level of subthreshold membrane potential variability. We propose a new analytical framework to rigorously quantify the subthreshold variability of a single conductance-based neuron in response to synaptic inputs with prescribed degrees of synchrony. Technically we leverage the theory of exchangeability to model input synchrony via jump-process-based synaptic drives; we then perform a moment analysis of the stationary response of a neuronal model with all-or-none conductances that neglects post-spiking reset. As a result, we produce exact, interpretable closed forms for the first two stationary moments of the membrane voltage, with explicit dependence on the input synaptic numbers, strengths, and synchrony. For biophysically relevant parameters, we find that the asynchronous regime only yields realistic subthreshold variability (voltage variance ≃ 4 - 9 m V 2 ) when driven by a restricted number of large synapses, compatible with strong thalamic drive. By contrast, we find that achieving realistic subthreshold variability with dense cortico-cortical inputs requires including weak but nonzero input synchrony, consistent with measured pairwise spiking correlations. We also show that without synchrony, the neural variability averages out to zero for all scaling limits with vanishing synaptic weights, independent of any balanced state hypothesis. This result challenges the theoretical basis for mean-field theories of the asynchronous state.

Excitation creates a distributed pattern of cortical suppression due to varied recurrent input

Dense local, recurrent connections are a major feature of cortical circuits, yet how they affect neurons' responses has been unclear, with some studies reporting weak recurrent effects, some reporting amplification, and others indicating local suppression. Here, we show that optogenetic input to mouse V1 excitatory neurons generates salt-and-pepper patterns of both excitation and suppression. Responses in individual neurons are not strongly predicted by that neuron's direct input. A balanced-state network model reconciles a set of diverse observations: the observed dynamics, suppressed responses, decoupling of input and output, and long tail of excited responses. The model shows recurrent excitatory-excitatory connections are strong and also variable across neurons. Together, these results demonstrate that excitatory recurrent connections can have major effects on cortical computations by shaping and changing neurons' responses to input.

Mechanisms underlying reshuffling of visual responses by optogenetic stimulation in mice and monkeys

The ability to optogenetically perturb neural circuits opens an unprecedented window into mechanisms governing circuit function. We analyzed and theoretically modeled neuronal responses to visual and optogenetic inputs in mouse and monkey V1. In both species, optogenetic stimulation of excitatory neurons strongly modulated the activity of single neurons yet had weak or no effects on the distribution of firing rates across the population. Thus, the optogenetic inputs reshuffled firing rates across the network. Key statistics of mouse and monkey responses lay on a continuum, with mice/monkeys occupying the low-/high-rate regions, respectively. We show that neuronal reshuffling emerges generically in randomly connected excitatory/inhibitory networks, provided the coupling strength (combination of recurrent coupling and external input) is sufficient that powerful inhibitory feedback cancels the mean optogenetic input. A more realistic model, distinguishing tuned visual vs. untuned optogenetic input in a structured network, reduces the coupling strength needed to explain reshuffling.

Computational role of sleep in memory reorganization

Sleep is considered to play an essential role in memory reorganization. Despite its importance, classical theoretical models did not focus on some sleep characteristics. Here, we review recent theoretical approaches investigating their roles in learning and discuss the possibility that non-rapid eye movement (NREM) sleep selectively consolidates memory, and rapid eye movement (REM) sleep reorganizes the representations of memories. We first review the possibility that slow waves during NREM sleep contribute to memory selection by using sequential firing patterns and the existence of up and down states. Second, we discuss the role of dreaming during REM sleep in developing neuronal representations. We finally discuss how to develop these points further, emphasizing the connections to experimental neuroscience and machine learning.

Early selection of task-relevant features through population gating

Brains can gracefully weed out irrelevant stimuli to guide behavior. This feat is believed to rely on a progressive selection of task-relevant stimuli across the cortical hierarchy, but the specific across-area interactions enabling stimulus selection are still unclear. Here, we propose that population gating, occurring within primary auditory cortex (A1) but controlled by top-down inputs from prelimbic region of medial prefrontal cortex (mPFC), can support across-area stimulus selection. Examining single-unit activity recorded while rats performed an auditory context-dependent task, we found that A1 encoded relevant and irrelevant stimuli along a common dimension of its neural space. Yet, the relevant stimulus encoding was enhanced along an extra dimension. In turn, mPFC encoded only the stimulus relevant to the ongoing context. To identify candidate mechanisms for stimulus selection within A1, we reverse-engineered low-rank RNNs trained on a similar task. Our analyses predicted that two context-modulated neural populations gated their preferred stimulus in opposite contexts, which we confirmed in further analyses of A1. Finally, we show in a two-region RNN how population gating within A1 could be controlled by top-down inputs from PFC, enabling flexible across-area communication despite fixed inter-areal connectivity.

Geometry of population activity in spiking networks with low-rank structure

Recurrent network models are instrumental in investigating how behaviorally-relevant computations emerge from collective neural dynamics. A recently developed class of models based on low-rank connectivity provides an analytically tractable framework for understanding of how connectivity structure determines the geometry of low-dimensional dynamics and the ensuing computations. Such models however lack some fundamental biological constraints, and in particular represent individual neurons in terms of abstract units that communicate through continuous firing rates rather than discrete action potentials. Here we examine how far the theoretical insights obtained from low-rank rate networks transfer to more biologically plausible networks of spiking neurons. Adding a low-rank structure on top of random excitatory-inhibitory connectivity, we systematically compare the geometry of activity in networks of integrate-and-fire neurons to rate networks with statistically equivalent low-rank connectivity. We show that the mean-field predictions of rate networks allow us to identify low-dimensional dynamics at constant population-average activity in spiking networks, as well as novel non-linear regimes of activity such as out-of-phase oscillations and slow manifolds. We finally exploit these results to directly build spiking networks that perform nonlinear computations.

Investigating the ability of astrocytes to drive neural network synchrony

Recent experimental works have implicated astrocytes as a significant cell type underlying several neuronal processes in the mammalian brain, from encoding sensory information to neurological disorders. Despite this progress, it is still unclear how astrocytes are communicating with and driving their neuronal neighbors. While previous computational modeling works have helped propose mechanisms responsible for driving these interactions, they have primarily focused on interactions at the synaptic level, with microscale models of calcium dynamics and neurotransmitter diffusion. Since it is computationally infeasible to include the intricate microscale details in a network-scale model, little computational work has been done to understand how astrocytes may be influencing spiking patterns and synchronization of large networks. We overcome this issue by first developing an "effective" astrocyte that can be easily implemented to already established network frameworks. We do this by showing that the astrocyte proximity to a synapse makes synaptic transmission faster, weaker, and less reliable. Thus, our "effective" astrocytes can be incorporated by considering heterogeneous synaptic time constants, which are parametrized only by the degree of astrocytic proximity at that synapse. We then apply our framework to large networks of exponential integrate-and-fire neurons with various spatial structures. Depending on key parameters, such as the number of synapses ensheathed and the strength of this ensheathment, we show that astrocytes can push the network to a synchronous state and exhibit spatially correlated patterns.

Amplified cortical neural responses as animals learn to use novel activity patterns

Cerebral cortex supports representations of the world in patterns of neural activity, used by the brain to make decisions and guide behavior. Past work has found diverse, or limited, changes in the primary sensory cortex in response to learning, suggesting that the key computations might occur in downstream regions. Alternatively, sensory cortical changes may be central to learning. We studied cortical learning by using controlled inputs we insert: we trained mice to recognize entirely novel, non-sensory patterns of cortical activity in the primary visual cortex (V1) created by optogenetic stimulation. As animals learned to use these novel patterns, we found that their detection abilities improved by an order of magnitude or more. The behavioral change was accompanied by large increases in V1 neural responses to fixed optogenetic input. Neural response amplification to novel optogenetic inputs had little effect on existing visual sensory responses. A recurrent cortical model shows that this amplification can be achieved by a small mean shift in recurrent network synaptic strength. Amplification would seem to be desirable to improve decision-making in a detection task; therefore, these results suggest that adult recurrent cortical plasticity plays a significant role in improving behavioral performance during learning.

Distributing task-related neural activity across a cortical network through task-independent connections

Task-related neural activity is widespread across populations of neurons during goal-directed behaviors. However, little is known about the synaptic reorganization and circuit mechanisms that lead to broad activity changes. Here we trained a subset of neurons in a spiking network with strong synaptic interactions to reproduce the activity of neurons in the motor cortex during a decision-making task. Task-related activity, resembling the neural data, emerged across the network, even in the untrained neurons. Analysis of trained networks showed that strong untrained synapses, which were independent of the task and determined the dynamical state of the network, mediated the spread of task-related activity. Optogenetic perturbations suggest that the motor cortex is strongly-coupled, supporting the applicability of the mechanism to cortical networks. Our results reveal a cortical mechanism that facilitates distributed representations of task-variables by spreading the activity from a subset of plastic neurons to the entire network through task-independent strong synapses.

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.

The stabilized supralinear network accounts for the contrast dependence of visual cortical gamma oscillations

When stimulated, neural populations in the visual cortex exhibit fast rhythmic activity with frequencies in the gamma band (30-80 Hz). The gamma rhythm manifests as a broad resonance peak in the power-spectrum of recorded local field potentials, which exhibits various stimulus dependencies. In particular, in macaque primary visual cortex (V1), the gamma peak frequency increases with increasing stimulus contrast. Moreover, this contrast dependence is local: when contrast varies smoothly over visual space, the gamma peak frequency in each cortical column is controlled by the local contrast in that column's receptive field. No parsimonious mechanistic explanation for these contrast dependencies of V1 gamma oscillations has been proposed. The stabilized supralinear network (SSN) is a mechanistic model of cortical circuits that has accounted for a range of visual cortical response nonlinearities and contextual modulations, as well as their contrast dependence. Here, we begin by showing that a reduced SSN model without retinotopy robustly captures the contrast dependence of gamma peak frequency, and provides a mechanistic explanation for this effect based on the observed non-saturating and supralinear input-output function of V1 neurons. Given this result, the local dependence on contrast can trivially be captured in a retinotopic SSN which however lacks horizontal synaptic connections between its cortical columns. However, long-range horizontal connections in V1 are in fact strong, and underlie contextual modulation effects such as surround suppression. We thus explored whether a retinotopically organized SSN model of V1 with strong excitatory horizontal connections can exhibit both surround suppression and the local contrast dependence of gamma peak frequency. We found that retinotopic SSNs can account for both effects, but only when the horizontal excitatory projections are composed of two components with different patterns of spatial fall-off with distance: a short-range component that only targets the source column, combined with a long-range component that targets columns neighboring the source column. We thus make a specific qualitative prediction for the spatial structure of horizontal connections in macaque V1, consistent with the columnar structure of cortex.

The mechanics of correlated variability in segregated cortical excitatory subnetworks

Understanding the genesis of shared trial-to-trial variability in neural activity within sensory cortex is critical to uncovering the biological basis of information processing in the brain. Shared variability is often a reflection of the structure of cortical connectivity since this variability likely arises, in part, from local circuit inputs. A series of experiments from segregated networks of (excitatory) pyramidal neurons in mouse primary visual cortex challenge this view. Specifically, the across-network correlations were found to be larger than predicted given the known weak cross-network connectivity. We aim to uncover the circuit mechanisms responsible for these enhanced correlations through biologically motivated cortical circuit models. Our central finding is that coupling each excitatory subpopulation with a specific inhibitory subpopulation provides the most robust network-intrinsic solution in shaping these enhanced correlations. This result argues for the existence of excitatory-inhibitory functional assemblies in early sensory areas which mirror not just response properties but also connectivity between pyramidal cells.

Stability and learning in excitatory synapses by nonlinear inhibitory plasticity

Synaptic changes are hypothesized to underlie learning and memory formation in the brain. But Hebbian synaptic plasticity of excitatory synapses on its own is unstable, leading to either unlimited growth of synaptic strengths or silencing of neuronal activity without additional homeostatic mechanisms. To control excitatory synaptic strengths, we propose a novel form of synaptic plasticity at inhibitory synapses. Using computational modeling, we suggest two key features of inhibitory plasticity, dominance of inhibition over excitation and a nonlinear dependence on the firing rate of postsynaptic excitatory neurons whereby inhibitory synaptic strengths change with the same sign (potentiate or depress) as excitatory synaptic strengths. We demonstrate that the stable synaptic strengths realized by this novel inhibitory plasticity model affects excitatory/inhibitory weight ratios in agreement with experimental results. Applying a disinhibitory signal can gate plasticity and lead to the generation of receptive fields and strong bidirectional connectivity in a recurrent network. Hence, a novel form of nonlinear inhibitory plasticity can simultaneously stabilize excitatory synaptic strengths and enable learning upon disinhibition.

Input correlations impede suppression of chaos and learning in balanced firing-rate networks

Neural circuits exhibit complex activity patterns, both spontaneously and evoked by external stimuli. Information encoding and learning in neural circuits depend on how well time-varying stimuli can control spontaneous network activity. We show that in firing-rate networks in the balanced state, external control of recurrent dynamics, i.e., the suppression of internally-generated chaotic variability, strongly depends on correlations in the input. A distinctive feature of balanced networks is that, because common external input is dynamically canceled by recurrent feedback, it is far more difficult to suppress chaos with common input into each neuron than through independent input. To study this phenomenon, we develop a non-stationary dynamic mean-field theory for driven networks. The theory explains how the activity statistics and the largest Lyapunov exponent depend on the frequency and amplitude of the input, recurrent coupling strength, and network size, for both common and independent input. We further show that uncorrelated inputs facilitate learning in balanced networks.

Calibrating Vision: Concepts and Questions

The idea that visual coding and perception are shaped by experience and adjust to changes in the environment or the observer is universally recognized as a cornerstone of visual processing, yet the functions and processes mediating these calibrations remain in many ways poorly understood. In this article we review a number of facets and issues surrounding the general notion of calibration, with a focus on plasticity within the encoding and representational stages of visual processing. These include how many types of calibrations there are - and how we decide; how plasticity for encoding is intertwined with other principles of sensory coding; how it is instantiated at the level of the dynamic networks mediating vision; how it varies with development or between individuals; and the factors that may limit the form or degree of the adjustments. Our goal is to give a small glimpse of an enormous and fundamental dimension of vision, and to point to some of the unresolved questions in our understanding of how and why ongoing calibrations are a pervasive and essential element of vision.

A microcircuit model involving parvalbumin, somatostatin, and vasoactive intestinal polypeptide inhibitory interneurons for the modulation of neuronal oscillation during visual processing

Various subtypes of inhibitory interneurons contact one another to organize cortical networks. Most cortical inhibitory interneurons express 1 of 3 genes: parvalbumin (PV), somatostatin (SOM), or vasoactive intestinal polypeptide (VIP). This diversity of inhibition allows the flexible regulation of neuronal responses within and between cortical areas. However, the exact roles of these interneuron subtypes and of excitatory pyramidal (Pyr) neurons in regulating neuronal network activity and establishing perception (via interactions between feedforward sensory and feedback attentional signals) remain largely unknown. To explore the regulatory roles of distinct neuronal types in cortical computation, we developed a computational microcircuit model with biologically plausible visual cortex layers 2/3 that combined Pyr neurons and the 3 inhibitory interneuron subtypes to generate network activity. In simulations with our model, inhibitory signals from PV and SOM neurons preferentially induced neuronal firing at gamma (30-80 Hz) and beta (20-30 Hz) frequencies, respectively, in agreement with observed physiological results. Furthermore, our model indicated that rapid inhibition from VIP to SOM subtypes underlies marked attentional modulation for low-gamma frequency (30-50 Hz) in Pyr neuron responses. Our results suggest the distinct but cooperative roles of inhibitory interneuron subtypes in the establishment of visual perception.

Multiplicative Shot-Noise: A New Route to Stability of Plastic Networks

Fluctuations of synaptic weights, among many other physical, biological, and ecological quantities, are driven by coincident events of two "parent" processes. We propose a multiplicative shot-noise model that can capture the behaviors of a broad range of such natural phenomena, and analytically derive an approximation that accurately predicts its statistics. We apply our results to study the effects of a multiplicative synaptic plasticity rule that was recently extracted from measurements in physiological conditions. Using mean-field theory analysis and network simulations, we investigate how this rule shapes the connectivity and dynamics of recurrent spiking neural networks. The multiplicative plasticity rule is shown to support efficient learning of input stimuli, and it gives a stable, unimodal synaptic-weight distribution with a large fraction of strong synapses. The strong synapses remain stable over long times but do not "run away." Our results suggest that the multiplicative shot-noise offers a new route to understand the tradeoff between flexibility and stability in neural circuits and other dynamic networks.

Different Excitation-Inhibition Correlations Between Spontaneous and Tone-evoked Activity in Primary Auditory Cortex Neurons

Tone-evoked synaptic excitation and inhibition are highly correlated in many neurons with V-shaped tuning curves in the primary auditory cortex of pentobarbital-anesthetized rats. In contrast, there is less correlation between spontaneous excitation and inhibition in visual cortex neurons under the same anesthetic conditions. However, it was not known whether the primary auditory cortex resembles visual cortex in having spontaneous excitation and inhibition that is less correlated than tone-evoked excitation and inhibition. Here we report whole-cell voltage-clamp measurements of spontaneous excitation and inhibition in primary auditory cortex neurons of pentobarbital-anesthetized rats. Spontaneous excitatory and inhibitory currents appeared to mainly consist of distinct events, with the inhibitory event rate typically lower than the excitatory event rate. We use the ratio of the excitatory event rate to the inhibitory event rate, and the assumption that the excitatory and inhibitory synaptic currents can each be reasonably described as a filtered Poisson process, to estimate the maximum spontaneous excitatory-inhibitory correlation for each neuron. In a subset of neurons, we also measured tone-evoked excitation and inhibition. In neurons with V-shaped tuning curves, although tone-evoked excitation and inhibition were highly correlated, the spontaneous inhibitory event rate was typically sufficiently lower than the spontaneous excitatory event rate to indicate a lower excitatory-inhibitory correlation for spontaneous activity than for tone-evoked responses.

Evaluating the extent to which homeostatic plasticity learns to compute prediction errors in unstructured neuronal networks

The brain is believed to operate in part by making predictions about sensory stimuli and encoding deviations from these predictions in the activity of "prediction error neurons." This principle defines the widely influential theory of predictive coding. The precise circuitry and plasticity mechanisms through which animals learn to compute and update their predictions are unknown. Homeostatic inhibitory synaptic plasticity is a promising mechanism for training neuronal networks to perform predictive coding. Homeostatic plasticity causes neurons to maintain a steady, baseline firing rate in response to inputs that closely match the inputs on which a network was trained, but firing rates can deviate away from this baseline in response to stimuli that are mismatched from training. We combine computer simulations and mathematical analysis systematically to test the extent to which randomly connected, unstructured networks compute prediction errors after training with homeostatic inhibitory synaptic plasticity. We find that homeostatic plasticity alone is sufficient for computing prediction errors for trivial time-constant stimuli, but not for more realistic time-varying stimuli. We use a mean-field theory of plastic networks to explain our findings and characterize the assumptions under which they apply.

NNMT: Mean-Field Based Analysis Tools for Neuronal Network Models

Mean-field theory of neuronal networks has led to numerous advances in our analytical and intuitive understanding of their dynamics during the past decades. In order to make mean-field based analysis tools more accessible, we implemented an extensible, easy-to-use open-source Python toolbox that collects a variety of mean-field methods for the leaky integrate-and-fire neuron model. The Neuronal Network Mean-field Toolbox (NNMT) in its current state allows for estimating properties of large neuronal networks, such as firing rates, power spectra, and dynamical stability in mean-field and linear response approximation, without running simulations. In this article, we describe how the toolbox is implemented, show how it is used to reproduce results of previous studies, and discuss different use-cases, such as parameter space explorations, or mapping different network models. Although the initial version of the toolbox focuses on methods for leaky integrate-and-fire neurons, its structure is designed to be open and extensible. It aims to provide a platform for collecting analytical methods for neuronal network model analysis, such that the neuroscientific community can take maximal advantage of them.

Theory of Gating in Recurrent Neural Networks

Recurrent neural networks (RNNs) are powerful dynamical models, widely used in machine learning (ML) and neuroscience. Prior theoretical work has focused on RNNs with additive interactions. However gating i.e., multiplicative interactions are ubiquitous in real neurons and also the central feature of the best-performing RNNs in ML. Here, we show that gating offers flexible control of two salient features of the collective dynamics: (i) timescales and (ii) dimensionality. The gate controlling timescales leads to a novel marginally stable state, where the network functions as a flexible integrator. Unlike previous approaches, gating permits this important function without parameter fine-tuning or special symmetries. Gates also provide a flexible, context-dependent mechanism to reset the memory trace, thus complementing the memory function. The gate modulating the dimensionality can induce a novel, discontinuous chaotic transition, where inputs push a stable system to strong chaotic activity, in contrast to the typically stabilizing effect of inputs. At this transition, unlike additive RNNs, the proliferation of critical points (topological complexity) is decoupled from the appearance of chaotic dynamics (dynamical complexity). The rich dynamics are summarized in phase diagrams, thus providing a map for principled parameter initialization choices to ML practitioners.

Stoney vs. Histed: Quantifying the spatial effects of intracortical microstimulation

BACKGROUND

Intracortical microstimulation (ICMS) is used to map neural circuits and restore lost sensory modalities such as vision, hearing, and somatosensation. The spatial effects of ICMS remain controversial: Stoney and colleagues proposed that the volume of somatic activation increased with stimulation intensity, while Histed et al., suggested activation density, but not somatic activation volume, increases with stimulation intensity.

OBJECTIVE

We used computational modeling to quantify the spatial effects of ICMS intensity and unify the apparently paradoxical findings of Histed and Stoney.

METHODS

We implemented a biophysically-based computational model of a cortical column comprising neurons with realistic morphology and representative synapses. We quantified the spatial effects of single pulses and short trains of ICMS, including the volume of activated neurons and the density of activated neurons as a function of stimulation intensity.

RESULTS

At all amplitudes, the dominant mode of somatic activation was by antidromic propagation to the soma following axonal activation, rather than via transsynaptic activation. There were no occurrences of direct activation of somata or dendrites. The volume over which antidromic action potentials were initiated grew with stimulation amplitude, while the volume of somatic activation increased marginally. However, the density of somatic activation within the activated volume increased with stimulation amplitude.

CONCLUSIONS

The results resolve the apparent paradox between Stoney and Histed's results by demonstrating that the volume over which action potentials are initiated grows with ICMS amplitude, consistent with Stoney. However, the volume occupied by the activated somata remains approximately constant, while the density of activated neurons within that volume increase, consistent with Histed.