Orientation selectivity in inhibition-dominated networks of spiking neurons: effect of single neuron properties and network dynamics

Adaptation-induced sharpening of orientation tuning curves in the mouse visual cortex

OBJECTIVE

Orientation selectivity is an emergent property of visual neurons across species with columnar and noncolumnar organization of the visual cortex. The emergence of orientation selectivity is more established in columnar cortical areas than in noncolumnar ones. Thus, how does orientation selectivity emerge in noncolumnar cortical areas after an adaptation protocol? Adaptation refers to the constant presentation of a nonoptimal stimulus (adapter) to a neuron under observation for a specific time. Previously, it had been shown that adaptation has varying effects on the tuning properties of neurons, such as orientation, spatial frequency, motion and so on.

BASIC METHODS

We recorded the mouse primary visual neurons (V1) at different orientations in the control (preadaptation) condition. This was followed by adapting neurons uninterruptedly for 12 min and then recording the same neurons postadaptation. An orientation selectivity index (OSI) for neurons was computed to compare them pre- and post-adaptation.

MAIN RESULTS

We show that 12-min adaptation increases the OSI of visual neurons ( n  = 113), that is, sharpens their tuning. Moreover, the OSI postadaptation increases linearly as a function of the OSI preadaptation.

CONCLUSION

The increased OSI postadaptation may result from a specific dendritic neural mechanism, potentially facilitating the rapid learning of novel features.

Effects of Light Isoflurane Anesthesia on Organization of Direction and Orientation Selectivity in the Superficial Layer of the Mouse Superior Colliculus

The superior colliculus (SC) is the midbrain center for integrating visual and multimodal sensory information. Neurons in the SC exhibit direction and orientation selectivity. Recent studies reported that neurons with similar preferences formed clusters in the mouse SC (Ahmadlou and Heimel, 2015; Feinberg and Meister, 2015; de Malmazet et al., 2018; Li et al., 2020). However, it remains controversial as to how these clusters are organized within the SC (Inayat et al., 2015; Chen et al., 2021). Here, we found that different brain states (i.e., awake or anesthetized with isoflurane) changed the selectivity of individual SC neurons and organizations of the neuronal population in both male and female mice. Using two-photon Ca2+ imaging, we examined both individual neuronal responses and the spatial patterns of their population responses. Under isoflurane anesthesia, orientation selectivity increased and a larger number of orientation-selective cells were observed when compared with the awake condition, whereas the proportions of direction-selective cells were similar in both conditions. Furthermore, direction- and orientation-selective cells located at closer positions showed more similar preferences, and cluster-like spatial patterns were enhanced. Inhibitory responses of direction-selective neurons were also reduced under isoflurane anesthesia. Thus, the changes in the spatial organization of response patterns were considered to be because of changes in the balance of excitation and inhibition, with excitation dominance, in the local circuits. These results provide new insights into the possibility that the functional organization of feature selectivity in the brain is affected by brain state.SIGNIFICANCE STATEMENT Recent large-scale recording studies are changing our view of visual maps in the superior colliculus (SC), including findings of cluster-like localizations of direction- and orientation-selective neurons. However, results from several laboratories are conflicting regarding the presence of cluster-like organization. Here, we demonstrated that light isoflurane anesthesia affected the direction- and orientation-tuning properties in the mouse superficial SC and that their cluster-like localization pattern was enhanced by the anesthesia. Furthermore, the effect of anesthesia on direction selectivity appeared to be different in the excitatory and inhibitory populations in the SC. Our results suggest that the functional organization of direction and orientation selectivity might be regulated by the excitation-inhibition balance that depends on the brain state.

What is the dynamical regime of cerebral cortex?

Many studies have shown that the excitation and inhibition received by cortical neurons remain roughly balanced across many conditions. A key question for understanding the dynamical regime of cortex is the nature of this balancing. Theorists have shown that network dynamics can yield systematic cancellation of most of a neuron's excitatory input by inhibition. We review a wide range of evidence pointing to this cancellation occurring in a regime in which the balance is loose, meaning that the net input remaining after cancellation of excitation and inhibition is comparable in size with the factors that cancel, rather than tight, meaning that the net input is very small relative to the canceling factors. This choice of regime has important implications for cortical functional responses, as we describe: loose balance, but not tight balance, can yield many nonlinear population behaviors seen in sensory cortical neurons, allow the presence of correlated variability, and yield decrease of that variability with increasing external stimulus drive as observed across multiple cortical areas.

Dynamics of a Large-Scale Spiking Neural Network with Quadratic Integrate-and-Fire Neurons

Since the high dimension and complexity of the large-scale spiking neural network, it is difficult to research the network dynamics. In recent decades, the mean-field approximation has been a useful method to reduce the dimension of the network. In this study, we construct a large-scale spiking neural network with quadratic integrate-and-fire neurons and reduce it to a mean-field model to research the network dynamics. We find that the activity of the mean-field model is consistent with the network activity. Based on this agreement, a two-parameter bifurcation analysis is performed on the mean-field model to understand the network dynamics. The bifurcation scenario indicates that the network model has the quiescence state, the steady state with a relatively high firing rate, and the synchronization state which correspond to the stable node, stable focus, and stable limit cycle of the system, respectively. There exist several stable limit cycles with different periods, so we can observe the synchronization states with different periods. Additionally, the model shows bistability in some regions of the bifurcation diagram which suggests that two different activities coexist in the network. The mechanisms that how these states switch are also indicated by the bifurcation curves.

Spatial clustering of orientation preference in primary visual cortex of the large rodent agouti

All rodents investigated so far possess orientation-selective neurons in the primary visual cortex (V1) but – in contrast to carnivores and primates – no evidence of periodic maps with pinwheel-like structures. Theoretical studies debating whether phylogeny or universal principles determine development of pinwheels point to V1 size as a critical constraint. Thus, we set out to study maps of agouti, a big diurnal rodent with a V1 size comparable to cats'. In electrophysiology, we detected interspersed orientation and direction-selective neurons with a bias for horizontal contours, corroborated by homogeneous activation in optical imaging. Compatible with spatial clustering at short distance, nearby neurons tended to exhibit similar orientation preference. Our results argue against V1 size as a key parameter in determining the presence of periodic orientation maps. They are consistent with a phylogenetic influence on the map layout and development, potentially reflecting distinct retinal traits or interspecies differences in cortical circuitry.

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Agouti V1 neurons are among the highest orientation- and direction-selective neurons in rodents

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They respond best to low spatial frequencies and with a bias for horizontal orientations

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There is no evidence of systematic periodic maps of orientation columns for agouti

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Neurons along the vertical cortical axis tend to have similar orientation preferences

Theory of neuronal perturbome in cortical networks

Brains are composed of networks of neurons that are highly interconnected. A central question in neuroscience is how such neuronal networks operate in tandem to make a functioning brain. To understand this, we need to study how neurons interact with each other in action, such as when viewing a visual scene or performing a motor task. One way to approach this question is by perturbing the activity of functioning neurons and measuring the resulting influence on other neurons. By using computational models of neuronal networks, we studied how this influence in visual networks depends on connectivity. Our results help to interpret contradictory results from previous experimental studies and explain how different connectivity patterns can enhance information processing during natural vision.

To unravel the functional properties of the brain, we need to untangle how neurons interact with each other and coordinate in large-scale recurrent networks. One way to address this question is to measure the functional influence of individual neurons on each other by perturbing them in vivo. Application of such single-neuron perturbations in mouse visual cortex has recently revealed feature-specific suppression between excitatory neurons, despite the presence of highly specific excitatory connectivity, which was deemed to underlie feature-specific amplification. Here, we studied which connectivity profiles are consistent with these seemingly contradictory observations, by modeling the effect of single-neuron perturbations in large-scale neuronal networks. Our numerical simulations and mathematical analysis revealed that, contrary to the prima facie assumption, neither inhibition dominance nor broad inhibition alone were sufficient to explain the experimental findings; instead, strong and functionally specific excitatory–inhibitory connectivity was necessary, consistent with recent findings in the primary visual cortex of rodents. Such networks had a higher capacity to encode and decode natural images, and this was accompanied by the emergence of response gain nonlinearities at the population level. Our study provides a general computational framework to investigate how single-neuron perturbations are linked to cortical connectivity and sensory coding and paves the road to map the perturbome of neuronal networks in future studies.

Propagation of orientation selectivity in a spiking network model of layered primary visual cortex

Neurons in different layers of sensory cortex generally have different functional properties. But what determines firing rates and tuning properties of neurons in different layers? Orientation selectivity in primary visual cortex (V1) is an interesting case to study these questions. Thalamic projections essentially determine the preferred orientation of neurons that receive direct input. But how is this tuning propagated though layers, and how can selective responses emerge in layers that do not have direct access to the thalamus? Here we combine numerical simulations with mathematical analyses to address this problem. We find that a large-scale network, which just accounts for experimentally measured layer and cell-type specific connection probabilities, yields firing rates and orientation selectivities matching electrophysiological recordings in rodent V1 surprisingly well. Further analysis, however, is complicated by the fact that neuronal responses emerge in a dynamic fashion and cannot be directly inferred from static neuroanatomy, as some connections tend to have unintuitive effects due to recurrent interactions and strong feedback loops. These emergent phenomena can be understood by linearizing and coarse-graining. In fact, we were able to derive a low-dimensional linear dynamical system effectively describing stimulus-driven activity layer by layer. This low-dimensional system explains layer-specific firing rates and orientation tuning by accounting for the different gain factors of the aggregate system. Our theory can also be used to design novel optogenetic stimulation experiments, thus facilitating further exploration of the interplay between connectivity and function.

Understanding the precise roles of neuronal sub-populations in shaping the activity of networks is a fundamental objective of neuroscience research. In complex neuronal network structures like the neocortex, the relation between the connectome and the algorithm implemented in it is often not self-explaining. To this end, our work makes three important contributions. First, we show that the connectivity extracted by anatomical and physiological experiments in visual cortex suffices to explain important properties of the various sub-populations, including their selectivity to visual stimulation. Second, we introduce a novel system-level approach for the analysis of input-output relations of recurrent networks, which leads to the observed activity patterns. Third, we present a method for the design of future optogenetic experiments that can be used to devise specific stimuli resulting in a predictable change of neuronal activity. In summary, we introduce a novel framework to determine the relevant features of neuronal microcircuit function that can be applied to a wide range of neuronal systems.

Mechanisms underlying contrast-dependent orientation selectivity in mouse V1

Recently, sophisticated optogenetic tools for mouse have enabled many detailed studies of the neuronal circuits of its primary visual cortex (V1), providing much more specific information than is available for cat or monkey. Among various other differences, they show a striking contrast dependency in orientation selectivity in mouse V1 rather than the well-known contrast invariance for cat and monkey. Constrained by the existing experiment data, we develop a comprehensive large-scale model of an effective input layer of mouse V1 that successfully reproduces the contrast-dependent phenomena and many other response properties. The model helps to probe different mechanisms based on excitation–inhibition balance that underlie both contrast dependencies and invariance, and it provides implications for future studies on these circuits.

Recent experiments have shown that mouse primary visual cortex (V1) is very different from that of cat or monkey, including response properties—one of which is that contrast invariance in the orientation selectivity (OS) of the neurons’ firing rates is replaced in mouse with contrast-dependent sharpening (broadening) of OS in excitatory (inhibitory) neurons. These differences indicate a different circuit design for mouse V1 than that of cat or monkey. Here we develop a large-scale computational model of an effective input layer of mouse V1. Constrained by experiment data, the model successfully reproduces experimentally observed response properties—for example, distributions of firing rates, orientation tuning widths, and response modulations of simple and complex neurons, including the contrast dependence of orientation tuning curves. Analysis of the model shows that strong feedback inhibition and strong orientation-preferential cortical excitation to the excitatory population are the predominant mechanisms underlying the contrast-sharpening of OS in excitatory neurons, while the contrast-broadening of OS in inhibitory neurons results from a strong but nonpreferential cortical excitation to these inhibitory neurons, with the resulting contrast-broadened inhibition producing a secondary enhancement on the contrast-sharpened OS of excitatory neurons. Finally, based on these mechanisms, we show that adjusting the detailed balances between the predominant mechanisms can lead to contrast invariance—providing insights for future studies on contrast dependence (invariance).

Interpretation of correlated neural variability from models of feed-forward and recurrent circuits

Neural populations respond to the repeated presentations of a sensory stimulus with correlated variability. These correlations have been studied in detail, with respect to their mechanistic origin, as well as their influence on stimulus discrimination and on the performance of population codes. A number of theoretical studies have endeavored to link network architecture to the nature of the correlations in neural activity. Here, we contribute to this effort: in models of circuits of stochastic neurons, we elucidate the implications of various network architectures—recurrent connections, shared feed-forward projections, and shared gain fluctuations—on the stimulus dependence in correlations. Specifically, we derive mathematical relations that specify the dependence of population-averaged covariances on firing rates, for different network architectures. In turn, these relations can be used to analyze data on population activity. We examine recordings from neural populations in mouse auditory cortex. We find that a recurrent network model with random effective connections captures the observed statistics. Furthermore, using our circuit model, we investigate the relation between network parameters, correlations, and how well different stimuli can be discriminated from one another based on the population activity. As such, our approach allows us to relate properties of the neural circuit to information processing.

The response of neurons to a stimulus is variable across trials. A natural solution for reliable coding in the face of noise is the averaging across a neural population. The nature of this averaging depends on the structure of noise correlations in the neural population. In turn, the correlation structure depends on the way noise and correlations are generated in neural circuits. It is in general difficult to identify the origin of correlations from the observed population activity alone. In this article, we explore different theoretical scenarios of the way in which correlations can be generated, and we relate these to the architecture of feed-forward and recurrent neural circuits. Analyzing population recordings of the activity in mouse auditory cortex in response to sound stimuli, we find that population statistics are consistent with those generated in a recurrent network model. Using this model, we can then quantify the effects of network properties on average population responses, noise correlations, and the representation of sensory information.

Integration of Continuous-Time Dynamics in a Spiking Neural Network Simulator

Contemporary modeling approaches to the dynamics of neural networks include two important classes of models: biologically grounded spiking neuron models and functionally inspired rate-based units. We present a unified simulation framework that supports the combination of the two for multi-scale modeling, enables the quantitative validation of mean-field approaches by spiking network simulations, and provides an increase in reliability by usage of the same simulation code and the same network model specifications for both model classes. While most spiking simulations rely on the communication of discrete events, rate models require time-continuous interactions between neurons. Exploiting the conceptual similarity to the inclusion of gap junctions in spiking network simulations, we arrive at a reference implementation of instantaneous and delayed interactions between rate-based models in a spiking network simulator. The separation of rate dynamics from the general connection and communication infrastructure ensures flexibility of the framework. In addition to the standard implementation we present an iterative approach based on waveform-relaxation techniques to reduce communication and increase performance for large-scale simulations of rate-based models with instantaneous interactions. Finally we demonstrate the broad applicability of the framework by considering various examples from the literature, ranging from random networks to neural-field models. The study provides the prerequisite for interactions between rate-based and spiking models in a joint simulation.

Fundamental Activity Constraints Lead to Specific Interpretations of the Connectome

The continuous integration of experimental data into coherent models of the brain is an increasing challenge of modern neuroscience. Such models provide a bridge between structure and activity, and identify the mechanisms giving rise to experimental observations. Nevertheless, structurally realistic network models of spiking neurons are necessarily underconstrained even if experimental data on brain connectivity are incorporated to the best of our knowledge. Guided by physiological observations, any model must therefore explore the parameter ranges within the uncertainty of the data. Based on simulation results alone, however, the mechanisms underlying stable and physiologically realistic activity often remain obscure. We here employ a mean-field reduction of the dynamics, which allows us to include activity constraints into the process of model construction. We shape the phase space of a multi-scale network model of the vision-related areas of macaque cortex by systematically refining its connectivity. Fundamental constraints on the activity, i.e., prohibiting quiescence and requiring global stability, prove sufficient to obtain realistic layer- and area-specific activity. Only small adaptations of the structure are required, showing that the network operates close to an instability. The procedure identifies components of the network critical to its collective dynamics and creates hypotheses for structural data and future experiments. The method can be applied to networks involving any neuron model with a known gain function.

Canonical computations of cerebral cortex

The idea that there is a fundamental cortical circuit that performs canonical computations remains compelling though far from proven. Here we review evidence for two canonical operations within sensory cortical areas: a feedforward computation of selectivity; and a recurrent computation of gain in which, given sufficiently strong external input, perhaps from multiple sources, intracortical input largely, but not completely, cancels this external input. This operation leads to many characteristic cortical nonlinearities in integrating multiple stimuli. The cortical computation must combine such local processing with hierarchical processing across areas. We point to important changes in moving from sensory cortex to motor and frontal cortex and the possibility of substantial differences between cortex in rodents vs. species with columnar organization of selectivity.

Emergence of Functional Specificity in Balanced Networks with Synaptic Plasticity

In rodent visual cortex, synaptic connections between orientation-selective neurons are unspecific at the time of eye opening, and become to some degree functionally specific only later during development. An explanation for this two-stage process was proposed in terms of Hebbian plasticity based on visual experience that would eventually enhance connections between neurons with similar response features. For this to work, however, two conditions must be satisfied: First, orientation selective neuronal responses must exist before specific recurrent synaptic connections can be established. Second, Hebbian learning must be compatible with the recurrent network dynamics contributing to orientation selectivity, and the resulting specific connectivity must remain stable for unspecific background activity. Previous studies have mainly focused on very simple models, where the receptive fields of neurons were essentially determined by feedforward mechanisms, and where the recurrent network was small, lacking the complex recurrent dynamics of large-scale networks of excitatory and inhibitory neurons. Here we studied the emergence of functionally specific connectivity in large-scale recurrent networks with synaptic plasticity. Our results show that balanced random networks, which already exhibit highly selective responses at eye opening, can develop feature-specific connectivity if appropriate rules of synaptic plasticity are invoked within and between excitatory and inhibitory populations. If these conditions are met, the initial orientation selectivity guides the process of Hebbian learning and, as a result, functionally specific and a surplus of bidirectional connections emerge. Our results thus demonstrate the cooperation of synaptic plasticity and recurrent dynamics in large-scale functional networks with realistic receptive fields, highlight the role of inhibition as a critical element in this process, and paves the road for further computational studies of sensory processing in neocortical network models equipped with synaptic plasticity.

In primary visual cortex of mammals, neurons are selective to the orientation of contrast edges. In some species, as cats and monkeys, neurons preferring similar orientations are adjacent on the cortical surface, leading to smooth orientation maps. In rodents, in contrast, such spatial orientation maps do not exist, and neurons of different specificities are mixed in a salt-and-pepper fashion. During development, however, a “functional” map of orientation selectivity emerges, where connections between neurons of similar preferred orientations are selectively enhanced. Here we show how such feature-specific connectivity can arise in realistic neocortical networks of excitatory and inhibitory neurons. Our results demonstrate how recurrent dynamics can work in cooperation with synaptic plasticity to form networks where neurons preferring similar stimulus features connect more strongly together. Such networks, in turn, are known to enhance the specificity of neuronal responses to a stimulus. Our study thus reveals how self-organizing connectivity in neuronal networks enable them to achieve new or enhanced functions, and it underlines the essential role of recurrent inhibition and plasticity in this process.

Processing of Feature Selectivity in Cortical Networks with Specific Connectivity

Although non-specific at the onset of eye opening, networks in rodent visual cortex attain a non-random structure after eye opening, with a specific bias for connections between neurons of similar preferred orientations. As orientation selectivity is already present at eye opening, it remains unclear how this specificity in network wiring contributes to feature selectivity. Using large-scale inhibition-dominated spiking networks as a model, we show that feature-specific connectivity leads to a linear amplification of feedforward tuning, consistent with recent electrophysiological single-neuron recordings in rodent neocortex. Our results show that optimal amplification is achieved at an intermediate regime of specific connectivity. In this configuration a moderate increase of pairwise correlations is observed, consistent with recent experimental findings. Furthermore, we observed that feature-specific connectivity leads to the emergence of orientation-selective reverberating activity, and entails pattern completion in network responses. Our theoretical analysis provides a mechanistic understanding of subnetworks’ responses to visual stimuli, and casts light on the regime of operation of sensory cortices in the presence of specific connectivity.