A multi-layer mean-field model of the cerebellum embedding microstructure and population-specific dynamics.

Mean-field (MF) models are computational formalism used to summarize in a few statistical parameters the salient biophysical properties of an inter-wired neuronal network. Their formalism normally incorporates different types of neurons and synapses along with their topological organization. MFs are crucial to efficiently implement the computational modules of large-scale models of brain function, maintaining the specificity of local cortical microcircuits. While MFs have been generated for the isocortex, they are still missing for other parts of the brain. Here we have designed and simulated a multi-layer MF of the cerebellar microcircuit (including Granule Cells, Golgi Cells, Molecular Layer Interneurons, and Purkinje Cells) and validated it against experimental data and the corresponding spiking neural network (SNN) microcircuit model. The cerebellar MF was built using a system of equations, where properties of neuronal populations and topological parameters are embedded in inter-dependent transfer functions. The model time constant was optimised using local field potentials recorded experimentally from acute mouse cerebellar slices as a template. The MF reproduced the average dynamics of different neuronal populations in response to various input patterns and predicted the modulation of the Purkinje Cells firing depending on cortical plasticity, which drives learning in associative tasks, and the level of feedforward inhibition. The cerebellar MF provides a computationally efficient tool for future investigations of the causal relationship between microscopic neuronal properties and ensemble brain activity in virtual brain models addressing both physiological and pathological conditions.

Suppressive Traveling Waves Shape Representations of Illusory Motion in Primary Visual Cortex of Awake Primate.

How does the brain link visual stimuli across space and time? Visual illusions provide an experimental paradigm to study these processes. When two stationary dots are flashed in close spatial and temporal succession, human observers experience a percept of apparent motion. Large spatiotemporal separation challenges the visual system to keep track of object identity along the apparent motion path, the so-called "correspondence problem." Here, we use voltage-sensitive dye imaging in primary visual cortex (V1) of awake monkeys to show that intracortical connections within V1 can solve this issue by shaping cortical dynamics to represent the illusory motion. We find that the appearance of the second stimulus in V1 creates a systematic suppressive wave traveling toward the retinotopic representation of the first. Using a computational model, we show that the suppressive wave is the emergent property of a recurrent gain control fed by the intracortical network. This suppressive wave acts to explain away ambiguous correspondence problems and contributes to precisely encode the expected motion velocity at the surface of V1. Together, these results demonstrate that the nonlinear dynamics within retinotopic maps can shape cortical representations of illusory motion. Understanding these dynamics will shed light on how the brain links sensory stimuli across space and time, by preformatting population responses for a straightforward read-out by downstream areas.SIGNIFICANCE STATEMENT Traveling waves have recently been observed in different animal species, brain areas, and behavioral states. However, it is still unclear what are their functional roles. In the case of cortical visual processing, waves propagate across retinotopic maps and can hereby generate interactions between spatially and temporally separated instances of feedforward driven activity. Such interactions could participate in processing long-range apparent motion stimuli, an illusion for which no clear neuronal mechanisms have yet been proposed. Using this paradigm in awake monkeys, we show that suppressive traveling waves produce a spatiotemporal normalization of apparent motion stimuli. Our study suggests that cortical waves shape the representation of illusory moving stimulus within retinotopic maps for a straightforward read-out by downstream areas.

Modeling mesoscopic cortical dynamics using a mean-field model of conductance-based networks of adaptive exponential integrate-and-fire neurons.

Voltage-sensitive dye imaging (VSDi) has revealed fundamental properties of neocortical processing at macroscopic scales. Since for each pixel VSDi signals report the average membrane potential over hundreds of neurons, it seems natural to use a mean-field formalism to model such signals. Here, we present a mean-field model of networks of Adaptive Exponential (AdEx) integrate-and-fire neurons, with conductance-based synaptic interactions. We study a network of regular-spiking (RS) excitatory neurons and fast-spiking (FS) inhibitory neurons. We use a Master Equation formalism, together with a semi-analytic approach to the transfer function of AdEx neurons to describe the average dynamics of the coupled populations. We compare the predictions of this mean-field model to simulated networks of RS-FS cells, first at the level of the spontaneous activity of the network, which is well predicted by the analytical description. Second, we investigate the response of the network to time-varying external input, and show that the mean-field model predicts the response time course of the population. Finally, to model VSDi signals, we consider a one-dimensional ring model made of interconnected RS-FS mean-field units. We found that this model can reproduce the spatio-temporal patterns seen in VSDi of awake monkey visual cortex as a response to local and transient visual stimuli. Conversely, we show that the model allows one to infer physiological parameters from the experimentally-recorded spatio-temporal patterns.

Heterogeneous firing responses predict diverse couplings to presynaptic activity in mice layer V pyramidal neurons.

In this study, we present a theoretical framework combining experimental characterizations and analytical calculus to capture the firing rate input-output properties of single neurons in the fluctuation-driven regime. Our framework consists of a two-step procedure to treat independently how the dendritic input translates into somatic fluctuation variables, and how the latter determine action potential firing. We use this framework to investigate the functional impact of the heterogeneity in firing responses found experimentally in young mice layer V pyramidal cells. We first design and calibrate in vitro a simplified morphological model of layer V pyramidal neurons with a dendritic tree following Rall's branching rule. Then, we propose an analytical derivation for the membrane potential fluctuations at the soma as a function of the properties of the synaptic input in dendrites. This mathematical description allows us to easily emulate various forms of synaptic input: either balanced, unbalanced, synchronized, purely proximal or purely distal synaptic activity. We find that those different forms of dendritic input activity lead to various impact on the somatic membrane potential fluctuations properties, thus raising the possibility that individual neurons will differentially couple to specific forms of activity as a result of their different firing response. We indeed found such a heterogeneous coupling between synaptic input and firing response for all types of presynaptic activity. This heterogeneity can be explained by different levels of cellular excitability in the case of the balanced, unbalanced, synchronized and purely distal activity. A notable exception appears for proximal dendritic inputs: increasing the input level can either promote firing response in some cells, or suppress it in some other cells whatever their individual excitability. This behavior can be explained by different sensitivities to the speed of the fluctuations, which was previously associated to different levels of sodium channel inactivation and density. Because local network connectivity rather targets proximal dendrites, our results suggest that this aspect of biophysical heterogeneity might be relevant to neocortical processing by controlling how individual neurons couple to local network activity.

Gain modulation of synaptic inputs by network state in auditory cortex in vivo.

The cortical network recurrent circuitry generates spontaneous activity organized into Up (active) and Down (quiescent) states during slow-wave sleep or anesthesia. These different states of cortical activation gain modulate synaptic transmission. However, the reported modulation that Up states impose on synaptic inputs is disparate in the literature, including both increases and decreases of responsiveness. Here, we tested the hypothesis that such disparate observations may depend on the intensity of the stimulation. By means of intracellular recordings, we studied synaptic transmission during Up and Down states in rat auditory cortex in vivo. Synaptic potentials were evoked either by auditory or electrical (thalamocortical, intracortical) stimulation while randomly varying the intensity of the stimulus. Synaptic potentials evoked by the same stimulus intensity were compared in Up/Down states. Up states had a scaling effect on the stimulus-evoked synaptic responses: the amplitude of weaker responses was potentiated whereas that of larger responses was maintained or decreased with respect to the amplitude during Down states. We used a computational model to explore the potential mechanisms explaining this nontrivial stimulus-response relationship. During Up/Down states, there is different excitability in the network and the neuronal conductance varies. We demonstrate that the competition between presynaptic recruitment and the changing conductance might be the central mechanism explaining the experimentally observed stimulus-response relationships. We conclude that the effect that cortical network activation has on synaptic transmission is not constant but contingent on the strength of the stimulation, with a larger modulation for stimuli involving both thalamic and cortical networks.

Feedforward and disinhibitory circuits differentially control activity of cortical somatostatin interneurons during behavioral state transitions.

Interneurons (INs), specifically those in disinhibitory circuits like somatostatin (SST) and vasoactive intestinal peptide (VIP)-INs, are strongly modulated by the behavioral context. Yet, the mechanisms by which these INs are recruited during active states and whether their activity is consistent across sensory cortices remain unclear. We now report that in mice, locomotor activity strongly recruits SST-INs in the primary somatosensory (S1) but not the visual (V1) cortex. This diverse engagement of SST-INs cannot be explained by differences in VIP-IN function but is absent in the presence of visual input, suggesting the involvement of feedforward sensory pathways. Accordingly, inactivating the somatosensory thalamus, but not decreasing VIP-IN activity, significantly reduces the modulation of SST-INs by locomotion. Model simulations suggest that the differences in SST-INs across behavioral states can be explained by varying ratios of VIP- and thalamus-driven activity. By integrating feedforward activity with neuromodulation, SST-INs are anticipated to be crucial for adapting sensory processing to behavioral states.

Network States Classification based on Local Field Potential Recordings in the Awake Mouse Neocortex.

Recent studies using intracellular recordings in awake behaving mice revealed that cortical network states, defined based on membrane potential features, modulate sensory responses and perceptual outcomes. Single-cell intracellular recordings are difficult and have low yield compared to extracellular recordings of population signals, such as local field potentials (LFPs). However, it is currently unclear how to identify these behaviorally-relevant network states from the LFP. We used simultaneous LFP and intracellular recordings in the somatosensory cortex of awake mice to design a network state classification from the LFP, the Network State Index (NSI). We used the NSI to analyze the relationship between single-cell (intracellular) and population (LFP) signals over different network states of wakefulness. We found that graded levels of population signal faithfully predicted the levels of single-cell depolarization in nonrhythmic regimes whereas, in δ ([2-4 Hz]) oscillatory regimes, the graded levels of rhythmicity in the LFP mapped into a stereotypical oscillatory pattern of membrane potential. Finally, we showed that the variability of network states, beyond the occurrence of slow oscillatory activity, critically shaped the average correlations between single-cell and population signals. Application of the LFP-based NSI to mouse visual cortex data showed that this index increased with pupil size and during locomotion and had a U-shaped dependence on population firing rates. NSI-based characterization provides a ready-to-use tool to understand from LFP recordings how the modulation of local network dynamics shapes the flexibility of sensory processing during behavior.

Activity-dependent modulation of NMDA receptors by endogenous zinc shapes dendritic function in cortical neurons.

NMDA receptors (NMDARs) have been proposed to control single-neuron computations in vivo. However, whether specific mechanisms regulate the function of such receptors and modulate input-output transformations performed by cortical neurons under in vivo-like conditions is understudied. Here, we report that in layer 2/3 pyramidal neurons (L2/3 PNs), repeated synaptic stimulation results in an activity-dependent decrease in NMDAR function by vesicular zinc. Such a mechanism shifts the threshold for dendritic non-linearities and strongly reduces LTP. Modulation of NMDARs is cell and pathway specific, being present selectively in L2/3-L2/3 connections but absent in inputs originating from L4 neurons. Numerical simulations highlight that activity-dependent modulation of NMDARs influences dendritic computations, endowing L2/3 PN dendrites with the ability to sustain non-linear integrations constant across different regimes of synaptic activity like those found in vivo. Our results unveil vesicular zinc as an important endogenous modulator of dendritic function in cortical PNs.

Visual-area-specific tonic modulation of GABA release by endocannabinoids sets the activity and coordination of neocortical principal neurons.

Perisomatic inhibition of pyramidal neurons (PNs) coordinates cortical network activity during sensory processing, and this role is mainly attributed to parvalbumin-expressing basket cells (BCs). However, cannabinoid receptor type 1 (CB1)-expressing interneurons are also BCs, but the connectivity and function of these elusive but prominent neocortical inhibitory neurons are unclear. We find that their connectivity pattern is visual area specific. Persistently active CB1 signaling suppresses GABA release from CB1 BCs in the medial secondary visual cortex (V2M), but not in the primary visual cortex (V1). Accordingly, in vivo, tonic CB1 signaling is responsible for higher but less coordinated PN activity in the V2M than in the V1. These differential firing dynamics in the V1 and V2M can be captured by a computational network model that incorporates visual-area-specific properties. Our results indicate a differential CB1-mediated mechanism controlling PN activity, suggesting an alternative connectivity scheme of a specific GABAergic circuit in different cortical areas.

The Spectrum of Asynchronous Dynamics in Spiking Networks as a Model for the Diversity of Non-rhythmic Waking States in the Neocortex.

The awake cortex exhibits diverse non-rhythmic network states. However, how these states emerge and how each state impacts network function is unclear. Here, we demonstrate that model networks of spiking neurons with moderate recurrent interactions display a spectrum of non-rhythmic asynchronous dynamics based on the level of afferent excitation, from afferent input-dominated (AD) regimes, characterized by unbalanced synaptic currents and sparse firing, to recurrent input-dominated (RD) regimes, characterized by balanced synaptic currents and dense firing. The model predicted regime-specific relationships between different neural biophysical properties, which were all experimentally validated in the somatosensory cortex (S1) of awake mice. Moreover, AD regimes more precisely encoded spatiotemporal patterns of presynaptic activity, while RD regimes better encoded the strength of afferent inputs. These results provide a theoretical foundation for how recurrent neocortical circuits generate non-rhythmic waking states and how these different states modulate the processing of incoming information.

Enhanced Responsiveness and Low-Level Awareness in Stochastic Network States.

Desynchronized brain states are known to be associated with arousal and increased awareness, but the exact mechanisms are unknown. Here, we show that neuronal networks displaying asynchronous irregular (AI) activity can implement a low-level form of awareness, due to their specific responsiveness properties. We emphasize the importance of the conductance state and stochasticity to explain these properties. We suggest that the purpose of cortical structures is to generate AI states with optimal responsiveness, to be globally aware of external stimuli.