The contribution of spike threshold to the dichotomy of cortical simple and complex cells

Convolutional neural network models applied to neuronal responses in macaque V1 reveal limited nonlinear processing

Computational models of the primary visual cortex (V1) have suggested that V1 neurons behave like Gabor filters followed by simple nonlinearities. However, recent work employing convolutional neural network (CNN) models has suggested that V1 relies on far more nonlinear computations than previously thought. Specifically, unit responses in an intermediate layer of VGG-19 were found to best predict macaque V1 responses to thousands of natural and synthetic images. Here, we evaluated the hypothesis that the poor performance of lower layer units in VGG-19 might be attributable to their small receptive field size rather than to their lack of complexity per se. We compared VGG-19 with AlexNet, which has much larger receptive fields in its lower layers. Whereas the best-performing layer of VGG-19 occurred after seven nonlinear steps, the first convolutional layer of AlexNet best predicted V1 responses. Although the predictive accuracy of VGG-19 was somewhat better than that of standard AlexNet, we found that a modified version of AlexNet could match the performance of VGG-19 after only a few nonlinear computations. Control analyses revealed that decreasing the size of the input images caused the best-performing layer of VGG-19 to shift to a lower layer, consistent with the hypothesis that the relationship between image size and receptive field size can strongly affect model performance. We conducted additional analyses using a Gabor pyramid model to test for nonlinear contributions of normalization and contrast saturation. Overall, our findings suggest that the feedforward responses of V1 neurons can be well explained by assuming only a few nonlinear processing stages.

Single-cell optogenetics reveals attenuation-by-suppression in visual cortical neurons

The relationship between neurons' input and spiking output is central to brain computation. Studies in vitro and in anesthetized animals suggest nonlinearities emerge in cells' input-output (activation) functions as network activity increases, yet how neurons transform inputs in vivo has been unclear. Here, we characterize cortical principal neurons' activation functions in awake mice using two-photon optogenetics. We deliver fixed inputs at the soma while neurons' activity varies with sensory stimuli. We find responses to fixed optogenetic input are nearly unchanged as neurons are excited, reflecting a linear response regime above neurons' resting point. In contrast, responses are dramatically attenuated by suppression. This attenuation is a powerful means to filter inputs arriving to suppressed cells, privileging other inputs arriving to excited neurons. These results have two major implications. First, somatic neural activation functions in vivo accord with the activation functions used in recent machine learning systems. Second, neurons' IO functions can filter sensory inputs - not only do sensory stimuli change neurons' spiking outputs, but these changes also affect responses to input, attenuating responses to some inputs while leaving others unchanged.

Foundations of visual form selectivity for neurons in macaque V1 and V2

We have measured the visually evoked activity of single neurons recorded in areas V1 and V2 of awake, fixating macaque monkeys, and captured their responses with a common computational model. We used a stimulus set composed of "droplets" of localized contrast, band-limited in orientation and spatial frequency; each brief stimulus contained a random superposition of droplets presented in and near the mapped receptive field. We accounted for neuronal responses with a 2-layer linear-nonlinear model, representing each receptive field by a combination of orientation- and scale-selective filters. We fit the data by jointly optimizing the model parameters to enforce sparsity and to prevent overfitting. We visualized and interpreted the fits in terms of an "afferent field" of nonlinearly combined inputs, dispersed in the 4 dimensions of space and spatial frequency. The resulting fits generally give a good account of the responses of neurons in both V1 and V2, capturing an average of 40% of the explainable variance in neuronal firing. Moreover, the resulting models predict neuronal responses to image families outside the test set, such as gratings of different orientations and spatial frequencies. Our results offer a common framework for understanding processing in the early visual cortex, and also demonstrate the ways in which the distributions of neuronal responses in V1 and V2 are similar but not identical.

Convolutional neural network models of neuronal responses in macaque V1 reveal limited non-linear processing

Computational models of the primary visual cortex (V1) have suggested that V1 neurons behave like Gabor filters followed by simple non-linearities. However, recent work employing convolutional neural network (CNN) models has suggested that V1 relies on far more non-linear computations than previously thought. Specifically, unit responses in an intermediate layer of VGG-19 were found to best predict macaque V1 responses to thousands of natural and synthetic images. Here, we evaluated the hypothesis that the poor performance of lower-layer units in VGG-19 might be attributable to their small receptive field size rather than to their lack of complexity per se. We compared VGG-19 with AlexNet, which has much larger receptive fields in its lower layers. Whereas the best-performing layer of VGG-19 occurred after seven non-linear steps, the first convolutional layer of AlexNet best predicted V1 responses. Although VGG-19's predictive accuracy was somewhat better than standard AlexNet, we found that a modified version of AlexNet could match VGG-19's performance after only a few non-linear computations. Control analyses revealed that decreasing the size of the input images caused the best-performing layer of VGG-19 to shift to a lower layer, consistent with the hypothesis that the relationship between image size and receptive field size can strongly affect model performance. We conducted additional analyses using a Gabor pyramid model to test for non-linear contributions of normalization and contrast saturation. Overall, our findings suggest that the feedforward responses of V1 neurons can be well explained by assuming only a few non-linear processing stages.

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

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

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.

Functional interactions among neurons within single columns of macaque V1

Recent developments in high-density neurophysiological tools now make it possible to record from hundreds of single neurons within local, highly interconnected neural networks. Among the many advantages of such recordings is that they dramatically increase the quantity of identifiable, functional interactions between neurons thereby providing an unprecedented view of local circuits. Using high-density, Neuropixels recordings from single neocortical columns of primary visual cortex in nonhuman primates, we identified 1000s of functionally interacting neuronal pairs using established crosscorrelation approaches. Our results reveal clear and systematic variations in the synchrony and strength of functional interactions within single cortical columns. Despite neurons residing within the same column, both measures of interactions depended heavily on the vertical distance separating neuronal pairs, as well as on the similarity of stimulus tuning. In addition, we leveraged the statistical power afforded by the large numbers of functionally interacting pairs to categorize interactions between neurons based on their crosscorrelation functions. These analyses identified distinct, putative classes of functional interactions within the full population. These classes of functional interactions were corroborated by their unique distributions across defined laminar compartments and were consistent with known properties of V1 cortical circuitry, such as the lead-lag relationship between simple and complex cells. Our results provide a clear proof-of-principle for the use of high-density neurophysiological recordings to assess circuit-level interactions within local neuronal networks.

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

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

Model-based characterization of the selectivity of neurons in primary visual cortex

Statistical models are increasingly being used to understand the complexity of stimulus selectivity in primary visual cortex (V1) in the context of complex time-varying stimuli, replacing averaging responses to simple parametric stimuli. Although such models often can more accurately reflect the computations performed by V1 neurons in more natural visual environments, they do not by themselves provide insight into V1 neural selectivity to basic stimulus features such as receptive field size, spatial frequency tuning, and phase invariance. Here, we present a battery of analyses that can be directly applied to encoding models to link complex encoding models to more interpretable aspects of stimulus selectivity. We apply this battery to nonlinear models of V1 neurons recorded in awake macaque during random bar stimuli. In linking model properties to more classical measurements, we demonstrate several novel aspects of V1 selectivity not available to simpler experimental measurements. For example, this approach reveals that individual spatiotemporal elements of the V1 models often have a smaller spatial scale than the neuron as a whole, resulting in nontrivial tuning to spatial frequencies. In addition, we propose measures of nonlinear integration that suggest that classical classifications of V1 neurons into simple versus complex cells will be spatial-frequency dependent. In total, rather than obfuscate classical characterizations of V1 neurons, model-based characterizations offer a means to more fully understand their selectivity, and link their classical tuning properties to their roles in more complex, natural, visual processing.NEW & NOTEWORTHY Visual neurons are increasingly being studied with more complex, natural visual stimuli, and increasingly complex models are necessary to characterize their response properties. Here, we describe a battery of analyses that relate these more complex models to classical characterizations. Using such model-based characterizations of V1 neurons furthermore yields several new insights into V1 processing not possible to capture in more classical means to measure their visual selectivity.

Feedforward mechanisms of cross-orientation interactions in mouse V1

Sensory neurons are modulated by context. For example, in mouse primary visual cortex (V1), neuronal responses to the preferred orientation are modulated by the presence of superimposed orientations ("plaids"). The effects of this modulation are diverse; some neurons are suppressed, while others have larger responses to a plaid than its components. We investigated whether this diversity could be explained by a unified circuit mechanism. We report that this masking is maintained during suppression of cortical activity, arguing against cortical mechanisms. Instead, the heterogeneity of plaid responses is explained by an interaction between stimulus geometry and orientation tuning. Highly selective neurons are uniformly suppressed by plaids, whereas the effects in weakly selective neurons depend on the spatial configuration of the stimulus, transitioning systematically between suppression and facilitation. Thus, the diverse responses emerge as a consequence of the spatial structure of feedforward inputs, with no need to invoke cortical interactions.

Population codes enable learning from few examples by shaping inductive bias

Learning from a limited number of experiences requires suitable inductive biases. To identify how inductive biases are implemented in and shaped by neural codes, we analyze sample-efficient learning of arbitrary stimulus-response maps from arbitrary neural codes with biologically-plausible readouts. We develop an analytical theory that predicts the generalization error of the readout as a function of the number of observed examples. Our theory illustrates in a mathematically precise way how the structure of population codes shapes inductive bias, and how a match between the code and the task is crucial for sample-efficient learning. It elucidates a bias to explain observed data with simple stimulus-response maps. Using recordings from the mouse primary visual cortex, we demonstrate the existence of an efficiency bias towards low-frequency orientation discrimination tasks for grating stimuli and low spatial frequency reconstruction tasks for natural images. We reproduce the discrimination bias in a simple model of primary visual cortex, and further show how invariances in the code to certain stimulus variations alter learning performance. We extend our methods to time-dependent neural codes and predict the sample efficiency of readouts from recurrent networks. We observe that many different codes can support the same inductive bias. By analyzing recordings from the mouse primary visual cortex, we demonstrate that biological codes have lower total activity than other codes with identical bias. Finally, we discuss implications of our theory in the context of recent developments in neuroscience and artificial intelligence. Overall, our study provides a concrete method for elucidating inductive biases of the brain and promotes sample-efficient learning as a general normative coding principle.

Nonlinear transient amplification in recurrent neural networks with short-term plasticity

To rapidly process information, neural circuits have to amplify specific activity patterns transiently. How the brain performs this nonlinear operation remains elusive. Hebbian assemblies are one possibility whereby strong recurrent excitatory connections boost neuronal activity. However, such Hebbian amplification is often associated with dynamical slowing of network dynamics, non-transient attractor states, and pathological run-away activity. Feedback inhibition can alleviate these effects but typically linearizes responses and reduces amplification gain. Here, we study nonlinear transient amplification (NTA), a plausible alternative mechanism that reconciles strong recurrent excitation with rapid amplification while avoiding the above issues. NTA has two distinct temporal phases. Initially, positive feedback excitation selectively amplifies inputs that exceed a critical threshold. Subsequently, short-term plasticity quenches the run-away dynamics into an inhibition-stabilized network state. By characterizing NTA in supralinear network models, we establish that the resulting onset transients are stimulus selective and well-suited for speedy information processing. Further, we find that excitatory-inhibitory co-tuning widens the parameter regime in which NTA is possible in the absence of persistent activity. In summary, NTA provides a parsimonious explanation for how excitatory-inhibitory co-tuning and short-term plasticity collaborate in recurrent networks to achieve transient amplification.

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.

Optogenetic Activation of Interneuron Subtypes Modulates Visual Contrast Responses of Mouse V1 Neurons

Interneurons are critical for information processing in the cortex. In vitro optogenetic studies in mouse primary visual cortex (V1) have sketched the connectivity of a local neural circuit comprising excitatory pyramidal neurons and distinct interneuron subtypes that express parvalbumin (Pvalb+), somatostatin (SOM+), or vasoactive intestinal peptide (VIP+). However, in vivo studies focusing on V1 orientation tuning have ascribed discrepant computational roles to specific interneuron subtypes. Here, we sought to clarify the differences between interneuron subtypes by examining the effects of optogenetic activation of Pvalb+, SOM+, or VIP+ interneurons on contrast tuning of V1 neurons while also accounting for cortical depth and photostimulation intensity. We found that illumination of the cortical surface produced a similar spectrum of saturating additive photostimulation effects in all 3 interneuron subtypes, which varied with cortical depth rather than light intensity in Pvalb+ and SOM+ cells. Pyramidal cell modulation was well explained by a conductance-based model that incorporated these interneuron photostimulation effects.

Periodic clustering of simple and complex cells in visual cortex

Neurons in the primary visual cortex (V1) are often classified as simple or complex cells, but it is debated whether they are discrete hierarchical classes of neurons or if they represent a continuum of variation within a single class of cells. Herein, we show that simple and complex cells may arise commonly from the feedforward projections from the retina. From analysis of the cortical receptive fields in cats, we show evidence that simple and complex cells originate from the periodic variation of ON-OFF segregation in the feedforward projection of retinal mosaics, by which they organize into periodic clusters in V1. From data in cats, we observed that clusters of simple and complex receptive fields correlate topographically with orientation maps, which supports our model prediction. Our results suggest that simple and complex cells are not two distinct neural populations but arise from common retinal afferents, simultaneous with orientation tuning.

Contrast adaptation and interocular transfer in cortical cells: A re-analysis & a two-stage gain-control model of binocular combination

How do V1 cells respond to, adapt to, and combine signals from the two eyes? We tested a simple functional model that has monocular and binocular stages of divisive contrast gain control (CGC) that sit before, and after, binocular summation respectively. Interocular suppression (IOS) was another potential influence on contrast gain. Howarth, Vorobyov & Sengpiel (2009, Cerebral Cortex, 19, 1835-1843) studied contrast adaptation and interocular transfer in cat V1 cells. In our re-analysis we found that ocular dominance (OD) and contrast adaptation at a fixed test contrast were well described by a re-scaling of the unadapted orientation tuning curve - a simple change in response gain. We compared six variants of the basic model, and one model fitted the gain data notably better than the others did. When the dominant eye was tested, adaptation reduced cell response gain more when that eye was adapted than when the other eye was adapted. But when the non-dominant eye was tested, adapting either eye gave about the same reduction in overall gain, and there was an interaction between OD and adapting eye that was well described by the best-fitting model. Two key features of this model are that signals driving IOS arise 'early', before attenuation due to OD, while suppressive CGC signals are 'late' and so affected by OD. We show that late CGC confers a functional advantage: it yields partial compensation for OD, which should reduce ocular imbalance at the input to binocular summation, and improve the cell's sensitivity to variation in stereo disparity.

A Disinhibitory Circuit for Contextual Modulation in Primary Visual Cortex

Context guides perception by influencing stimulus saliency. Accordingly, in visual cortex, responses to a stimulus are modulated by context, the visual scene surrounding the stimulus. Responses are suppressed when stimulus and surround are similar but not when they differ. The underlying mechanisms remain unclear. Here, we use optical recordings, manipulations, and computational modeling to show that disinhibitory circuits consisting of vasoactive intestinal peptide (VIP)-expressing and somatostatin (SOM)-expressing inhibitory neurons modulate responses in mouse visual cortex depending on similarity between stimulus and surround, primarily by modulating recurrent excitation. When stimulus and surround are similar, VIP neurons are inactive, and activity of SOM neurons leads to suppression of excitatory neurons. However, when stimulus and surround differ, VIP neurons are active, inhibiting SOM neurons, which leads to relief of excitatory neurons from suppression. We have identified a canonical cortical disinhibitory circuit that contributes to contextual modulation and may regulate perceptual saliency.

Central Vestibular Tuning Arises from Patterned Convergence of Otolith Afferents

As sensory information moves through the brain, higher-order areas exhibit more complex tuning than lower areas. Though models predict that complexity arises via convergent inputs from neurons with diverse response properties, in most vertebrate systems, convergence has only been inferred rather than tested directly. Here, we measure sensory computations in zebrafish vestibular neurons across multiple axes in vivo. We establish that whole-cell physiological recordings reveal tuning of individual vestibular afferent inputs and their postsynaptic targets. Strong, sparse synaptic inputs can be distinguished by their amplitudes, permitting analysis of afferent convergence in vivo. An independent approach, serial-section electron microscopy, supports the inferred connectivity. We find that afferents with similar or differing preferred directions converge on central vestibular neurons, conferring more simple or complex tuning, respectively. Together, these results provide a direct, quantifiable demonstration of feedforward input convergence in vivo.

Synaptic and intrinsic mechanisms underlying development of cortical direction selectivity

Modifications of synaptic inputs and cell-intrinsic properties both contribute to neuronal plasticity and development. To better understand these mechanisms, we undertook an intracellular analysis of the development of direction selectivity in the ferret visual cortex, which occurs rapidly over a few days after eye opening. We found strong evidence of developmental changes in linear spatiotemporal receptive fields of simple cells, implying alterations in circuit inputs. Further, this receptive field plasticity was accompanied by increases in near-spike-threshold excitability and input-output gain that resulted in dramatically increased spiking responses in the experienced state. Increases in subthreshold membrane responses induced by the receptive field plasticity and the increased input-output spiking gain were both necessary to explain the elevated firing rates in experienced ferrets. These results demonstrate that cortical direction selectivity develops through a combination of plasticity in inputs and in cell-intrinsic properties.

Mechanisms of Feature Selectivity and Invariance in Primary Visual Cortex

Visual object identification requires both selectivity for specific visual features that are important to the object's identity and invariance to feature manipulations. For example, a hand can be shifted in position, rotated, or contracted but still be recognized as a hand. How are the competing requirements of selectivity and invariance built into the early stages of visual processing? Typically, cells in the primary visual cortex are classified as either simple or complex. They both show selectivity for edge-orientation but complex cells develop invariance to edge position within the receptive field (spatial phase). Using a data-driven model that extracts the spatial structures and nonlinearities associated with neuronal computation, we quantitatively describe the balance between selectivity and invariance in complex cells. Phase invariance is frequently partial, while invariance to orientation and spatial frequency are more extensive than expected. The invariance arises due to two independent factors: (1) the structure and number of filters and (2) the form of nonlinearities that act upon the filter outputs. Both vary more than previously considered, so primary visual cortex forms an elaborate set of generic feature sensitivities, providing the foundation for more sophisticated object processing.

Emergence of spatially periodic diffusive waves in small-world neuronal networks

It has been observed in experiment that the anatomical structure of neuronal networks in the brain possesses the feature of small-world networks. Yet how the small-world structure affects network dynamics remains to be fully clarified. Here we study the dynamics of a class of small-world networks consisting of pulse-coupled integrate-and-fire (I&F) neurons. Under stochastic Poisson drive, we find that the activity of the entire network resembles diffusive waves. To understand its underlying mechanism, we analyze the simplified regular-lattice network consisting of firing-rate-based neurons as an approximation to the original I&F small-world network. We demonstrate both analytically and numerically that, with strongly coupled connections, in the absence of noise, the activity of the firing-rate-based regular-lattice network spatially forms a static grating pattern that corresponds to the spatial distribution of the firing rate observed in the I&F small-world neuronal network. We further show that the spatial grating pattern with different phases comprise the continuous attractor of both the I&F small-world and firing-rate-based regular-lattice network dynamics. In the presence of input noise, the activity of both networks is perturbed along the continuous attractor, which gives rise to the diffusive waves. Our numerical simulations and theoretical analysis may potentially provide insights into the understanding of the generation of wave patterns observed in cortical networks.

Functional Logic of Layer 2/3 Inhibitory Connectivity in the Ferret Visual Cortex

Understanding how cortical inhibition shapes circuit function requires identifying the connectivity rules relating the response properties of inhibitory interneurons and their postsynaptic targets. Here we explore the orientation tuning of layer 2/3 inhibitory inputs in the ferret visual cortex using a combination of in vivo axon imaging, functional input mapping, and physiology. Inhibitory boutons exhibit robust orientation-tuned responses with preferences that can differ significantly from the cortical column in which they reside. Inhibitory input fields measured with patterned optogenetic stimulation and intracellular recordings revealed that these inputs originate from a wide range of orientation domains, inconsistent with a model of co-tuned inhibition and excitation. Intracellular synaptic conductance measurements confirm that individual neurons can depart from a co-tuned regime. Our results argue against a simple rule for the arrangement of inhibitory inputs supplied by layer 2/3 circuits and suggest that heterogeneity in presynaptic inhibitory networks contributes to neural response properties.

Synaptic Basis for Contrast-Dependent Shifts in Functional Identity in Mouse V1

A central transformation that occurs within mammalian visual cortex is the change from linear, polarity-sensitive responses to nonlinear, polarity-insensitive responses. These neurons are classically labelled as either simple or complex, respectively, on the basis of their response linearity (Skottun et al., 1991). While the difference between cell classes is clear when the stimulus strength is high, reducing stimulus strength diminishes the differences between the cell types and causes some complex cells to respond as simple cells (Crowder et al., 2007; van Kleef et al., 2010; Hietanen et al., 2013). To understand the synaptic basis for this shift in behavior, we used in vivo whole-cell recordings while systematically shifting stimulus contrast. We find systematic shifts in the degree of complex cell responses in mouse primary visual cortex (V1) at the subthreshold level, demonstrating that synaptic inputs change in concert with the shifts in response linearity and that the change in response linearity is not simply due to the threshold nonlinearity. These shifts are consistent with a visual cortex model in which the recurrent amplification acts as a critical component in the generation of complex cell responses (Chance et al., 1999).

Tune it in: mechanisms and computational significance of neuron-autonomous plasticity

The activity of a neural network is a result of synaptic signals that convey the communication between neurons and neuron-based intrinsic currents that determine the neuron’s input-output transfer function. Ample studies have demonstrated that cell-based excitability, and in particular intrinsic excitability, is modulated by learning and that these modifications play a key role in learning-related behavioral changes. The field of cell-based plasticity is largely growing, and it entails numerous experimental findings that demonstrate a large diversity of currents that are affected by learning. The diverse effect of learning on the neuron’s excitability emphasizes the need for a framework under which cell-based plasticity can be categorized to enable the assessment of the computational roles of the intrinsic modifications. We divide the domain of cell-based plasticity into three main categories, where the first category entails the currents that mediate the passive properties and single-spike generation, the second category entails the currents that mediate spike frequency adaptation, and the third category entails a novel learning-induced mechanism where all excitatory and inhibitory synapses double their strength. Curiously, this elementary division enables a natural categorization of the computational roles of these learning-induced plasticities. The computational roles are diverse and include modification of the neuronal mode of action, such as bursting, prolonged, and fast responsive; attention-like effect where the signal detection is improved; transfer of the network into an active state; biasing the competition for memory allocation; and transforming an environmental cue into a dominant cue and enabling a quicker formation of new memories.

Transformation of Feature Selectivity From Membrane Potential to Spikes in the Mouse Superior Colliculus

Neurons in the visual system display varying degrees of selectivity for stimulus features such as orientation and direction. Such feature selectivity is generated and processed by intricate circuit and synaptic mechanisms. A key factor in this process is the input-output transformation from membrane potential (V_m) to spikes in individual neurons. Here, we use in vivo whole-cell recording to study V_m-to-spike transformation of visual feature selectivity in the superficial neurons of the mouse superior colliculus (SC). As expected from the spike threshold effect, direction and orientation selectivity increase from V_m to spike responses. The degree of this increase is highly variable, and interestingly, it is correlated with the receptive field size of the recorded neurons. We find that the relationships between V_m and spike rate and between V_m dynamics and spike initiation are also correlated with receptive field size, which likely contribute to the observed input-output transformation of feature selectivity. Together, our findings provide useful information for understanding information processing and visual transformation in the mouse SC.

E-I balance emerges naturally from continuous Hebbian learning in autonomous neural networks

Spontaneous brain activity is characterized in part by a balanced asynchronous chaotic state. Cortical recordings show that excitatory (E) and inhibitory (I) drivings in the E-I balanced state are substantially larger than the overall input. We show that such a state arises naturally in fully adapting networks which are deterministic, autonomously active and not subject to stochastic external or internal drivings. Temporary imbalances between excitatory and inhibitory inputs lead to large but short-lived activity bursts that stabilize irregular dynamics. We simulate autonomous networks of rate-encoding neurons for which all synaptic weights are plastic and subject to a Hebbian plasticity rule, the flux rule, that can be derived from the stationarity principle of statistical learning. Moreover, the average firing rate is regulated individually via a standard homeostatic adaption of the bias of each neuron's input-output non-linear function. Additionally, networks with and without short-term plasticity are considered. E-I balance may arise only when the mean excitatory and inhibitory weights are themselves balanced, modulo the overall activity level. We show that synaptic weight balance, which has been considered hitherto as given, naturally arises in autonomous neural networks when the here considered self-limiting Hebbian synaptic plasticity rule is continuously active.

Mechanisms of Orientation Selectivity in the Primary Visual Cortex

The mechanisms underlying the emergence of orientation selectivity in the visual cortex have been, and continue to be, the subjects of intense scrutiny. Orientation selectivity reflects a dramatic change in the representation of the visual world: Whereas afferent thalamic neurons are generally orientation insensitive, neurons in the primary visual cortex (V1) are extremely sensitive to stimulus orientation. This profound change in the receptive field structure along the visual pathway has positioned V1 as a model system for studying the circuitry that underlies neural computations across the neocortex. The neocortex is characterized anatomically by the relative uniformity of its circuitry despite its role in processing distinct signals from region to region. A combination of physiological, anatomical, and theoretical studies has shed some light on the circuitry components necessary for generating orientation selectivity in V1. This targeted effort has led to critical insights, as well as controversies, concerning how neural circuits in the neocortex perform computations.

Population receptive field (pRF) measurements of chromatic responses in human visual cortex using fMRI

The spatial sensitivity of the human visual system depends on stimulus color: achromatic gratings can be resolved at relatively high spatial frequencies while sensitivity to isoluminant color contrast tends to be more low-pass. Models of early spatial vision often assume that the receptive field size of pattern-sensitive neurons is correlated with their spatial frequency sensitivity - larger receptive fields are typically associated with lower optimal spatial frequency. A strong prediction of this model is that neurons coding isoluminant chromatic patterns should have, on average, a larger receptive field size than neurons sensitive to achromatic patterns. Here, we test this assumption using functional magnetic resonance imaging (fMRI). We show that while spatial frequency sensitivity depends on chromaticity in the manner predicted by behavioral measurements, population receptive field (pRF) size measurements show no such dependency. At any given eccentricity, the mean pRF size for neuronal populations driven by luminance, opponent red/green and S-cone isolating contrast, are identical. Changes in pRF size (for example, an increase with eccentricity and visual area hierarchy) are also identical across the three chromatic conditions. These results suggest that fMRI measurements of receptive field size and spatial resolution can be decoupled under some circumstances - potentially reflecting a fundamental dissociation between these parameters at the level of neuronal populations.

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Novel use of fMRI population receptive field (pRF) mapping, using chromatic stimuli.

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Spatial frequency sensitivity in early visual areas measured with fMRI.

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Differences in spatial sensitivity found between S-cone and luminance conditions.

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No significant differences in pRF sizes between S-cone and luminance conditions.

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Suggests that pRF sizes and spatial resolution are not coupled.

The divisive normalization model of V1 neurons: a comprehensive comparison of physiological data and model predictions

The physiological responses of simple and complex cells in the primary visual cortex (V1) have been studied extensively and modeled at different levels. At the functional level, the divisive normalization model (DNM; Heeger DJ. Vis Neurosci 9: 181-197, 1992) has accounted for a wide range of single-cell recordings in terms of a combination of linear filtering, nonlinear rectification, and divisive normalization. We propose standardizing the formulation of the DNM and implementing it in software that takes static grayscale images as inputs and produces firing rate responses as outputs. We also review a comprehensive suite of 30 empirical phenomena and report a series of simulation experiments that qualitatively replicate dozens of key experiments with a standard parameter set consistent with physiological measurements. This systematic approach identifies novel falsifiable predictions of the DNM. We show how the model simultaneously satisfies the conflicting desiderata of flexibility and falsifiability. Our key idea is that, while adjustable parameters are needed to accommodate the diversity across neurons, they must be fixed for a given individual neuron. This requirement introduces falsifiable constraints when this single neuron is probed with multiple stimuli. We also present mathematical analyses and simulation experiments that explicate some of these constraints.

Linking structure and activity in nonlinear spiking networks

Recent experimental advances are producing an avalanche of data on both neural connectivity and neural activity. To take full advantage of these two emerging datasets we need a framework that links them, revealing how collective neural activity arises from the structure of neural connectivity and intrinsic neural dynamics. This problem of structure-driven activity has drawn major interest in computational neuroscience. Existing methods for relating activity and architecture in spiking networks rely on linearizing activity around a central operating point and thus fail to capture the nonlinear responses of individual neurons that are the hallmark of neural information processing. Here, we overcome this limitation and present a new relationship between connectivity and activity in networks of nonlinear spiking neurons by developing a diagrammatic fluctuation expansion based on statistical field theory. We explicitly show how recurrent network structure produces pairwise and higher-order correlated activity, and how nonlinearities impact the networks’ spiking activity. Our findings open new avenues to investigating how single-neuron nonlinearities—including those of different cell types—combine with connectivity to shape population activity and function.

Neuronal networks, like many biological systems, exhibit variable activity. This activity is shaped by both the underlying biology of the component neurons and the structure of their interactions. How can we combine knowledge of these two things—that is, models of individual neurons and of their interactions—to predict the statistics of single- and multi-neuron activity? Current approaches rely on linearizing neural activity around a stationary state. In the face of neural nonlinearities, however, these linear methods can fail to predict spiking statistics and even fail to correctly predict whether activity is stable or pathological. Here, we show how to calculate any spike train cumulant in a broad class of models, while systematically accounting for nonlinear effects. We then study a fundamental effect of nonlinear input-rate transfer–coupling between different orders of spiking statistic–and how this depends on single-neuron and network properties.

Fractional-order leaky integrate-and-fire model with long-term memory and power law dynamics

Pyramidal neurons produce different spiking patterns to process information, communicate with each other and transform information. These spiking patterns have complex and multiple time scale dynamics that have been described with the fractional-order leaky integrate-and-Fire (FLIF) model. Models with fractional (non-integer) order differentiation that generalize power law dynamics can be used to describe complex temporal voltage dynamics. The main characteristic of FLIF model is that it depends on all past values of the voltage that causes long-term memory. The model produces spikes with high interspike interval variability and displays several spiking properties such as upward spike-frequency adaptation and long spike latency in response to a constant stimulus. We show that the subthreshold voltage and the firing rate of the fractional-order model make transitions from exponential to power law dynamics when the fractional order α decreases from 1 to smaller values. The firing rate displays different types of spike timing adaptation caused by changes on initial values. We also show that the voltage-memory trace and fractional coefficient are the causes of these different types of spiking properties. The voltage-memory trace that represents the long-term memory has a feedback regulatory mechanism and affects spiking activity. The results suggest that fractional-order models might be appropriate for understanding multiple time scale neuronal dynamics. Overall, a neuron with fractional dynamics displays history dependent activities that might be very useful and powerful for effective information processing.

Cortical amplification models of experience-dependent development of selective columns and response sparsification

The development of direction-selective cortical columns requires visual experience, but the neural circuits and plasticity mechanisms that are responsible for this developmental transition are unknown. To gain insight into the mechanisms that could underlie experience-dependent increases in selectivity, we explored families of cortical amplifier models that enhance weakly biased feedforward signals. Here we focused exclusively on possible contributions of cortico-cortical connections and took feedforward input to be constant. We modeled pairs of interconnected columns that received equal and oppositely biased inputs. In a single-element model of cortical columns, we found two ways that cortical columns could receive biased feedforward input and exhibit strong but unselective responses to stimuli: 1) within-column recurrent excitatory connections could be strong enough to amplify both strong and weak feedforward input, or 2) columns that received differently biased inputs could have strong excitatory cross-connections that destroy selectivity. A Hebbian plasticity rule combined with simulated experience with stimuli weakened these strong cross-connections across cortical columns, allowing the individual columns to respond selectively to their biased inputs. In a model that included both excitatory and inhibitory neurons in each column, an additional means of obtaining selectivity through the cortical circuit was uncovered: cross-column suppression of inhibition-stabilized networks. When each column operated as an inhibition-stabilized network, cross-column excitation onto inhibitory neurons forced competition between the columns but in a manner that did not involve strong null-direction inhibition, consistent with experimental measurements of direction selectivity in visual cortex. Experimental predictions of these possible contributions of cortical circuits are discussed.NEW & NOTEWORTHY Sensory circuits are initially constructed via mechanisms that are independent of sensory experience, but later refinement requires experience. We constructed models of how circuits that receive biased feedforward inputs can be initially unselective and then be modified by experience and plasticity so that the resulting circuit exhibits increased selectivity. We propose that neighboring cortical columns may initially exhibit coupling that is too strong for selectivity. Experience-dependent mechanisms decrease this coupling so individual columns can exhibit selectivity.

Predicting epileptic seizures from scalp EEG based on attractor state analysis

BACKGROUND AND OBJECTIVE

Epilepsy is the second most common disease of the brain. Epilepsy makes it difficult for patients to live a normal life because it is difficult to predict when seizures will occur. In this regard, if seizures could be predicted a reasonable period of time before their occurrence, epilepsy patients could take precautions against them and improve their safety and quality of life. In this paper, we investigate a novel seizure precursor based on attractor state analysis for seizure prediction.

METHODS

We analyze the transition process from normal to seizure attractor state and investigate a precursor phenomenon seen before reaching the seizure attractor state. From the result of an analysis, we define a quantified spectral measure in scalp EEG for seizure prediction. From scalp EEG recordings, the Fourier coefficients of six EEG frequency bands are extracted, and the defined spectral measure is computed based on the coefficients for each half-overlapped 20-second-long window. The computed spectral measure is applied to seizure prediction using a low-complexity methodology.

RESULTS

Within scalp EEG, we identified an early-warning indicator before an epileptic seizure occurs. Getting closer to the bifurcation point that triggers the transition from normal to seizure state, the power spectral density of low frequency bands of the perturbation of an attractor in the EEG, showed a relative increase. A low-complexity seizure prediction algorithm using this feature was evaluated, using ∼583h of scalp EEG in which 143 seizures in 16 patients were recorded. With the test dataset, the proposed method showed high sensitivity (86.67%) with a false prediction rate of 0.367h^-1 and average prediction time of 45.3min.

CONCLUSIONS

A novel seizure prediction method using scalp EEG, based on attractor state analysis, shows potential for application with real epilepsy patients. This is the first study in which the seizure-precursor phenomenon of an epileptic seizure is investigated based on attractor-based analysis of the macroscopic dynamics of the brain. With the scalp EEG, we first propose use of a spectral feature identified for seizure prediction, in which the dynamics of an attractor are excluded, and only the perturbation dynamics from the attractor are considered.

Intracellular, In Vivo, Dynamics of Thalamocortical Synapses in Visual Cortex

Seminal studies of the thalamocortical circuit in the visual system of the cat have been central to our understanding of sensory encoding. However, thalamocortical synaptic properties remain poorly understood. We used paired recordings, in the lateral geniculate nucleus (LGN) and primary visual cortex (V1), to provide the first in vivo characterization of sensory-driven thalamocortical potentials in V1. The amplitudes of EPSPs we characterized were smaller than those previously reported in vitro Consistent with prior findings, connected LGN-V1 pairs were only found when their receptive fields (RFs) overlapped, and the probability of connection increased steeply with degree of RF overlap and response similarity. However, surprisingly, we found no relationship between EPSP amplitudes and the similarity of RFs or responses, suggesting different connectivity models for intracortical and thalamocortical circuits. Putative excitatory regular-spiking (RS) and inhibitory fast-spiking (FS) V1 cells had similar EPSP characteristics, showing that in the visual system, feedforward excitation and inhibition are driven with equal strength by the thalamus. Similar to observations in the somatosensory cortex, FS V1 cells received less specific input from LGN. Finally, orientation tuning in V1 was not inherited from single presynaptic LGN cells, suggesting that it must emerge exclusively from the combined input of all presynaptic LGN cells. Our results help to decipher early visual encoding circuits and have immediate utility in providing physiological constraints to computational models of the visual system.SIGNIFICANCE STATEMENT To understand how the brain encodes the visual environment, we must understand the transfer of visual signals between various regions of the brain. Therefore, understanding synaptic dynamics is critical to our understanding of sensory encoding. This study provides the first characterization of visually evoked synaptic potentials between the visual thalamus and visual cortex in an intact animal. To record these potentials, we simultaneously recorded the extracellular potential of presynaptic thalamic cells and the intracellular potential of postsynaptic cortical cells in input layers of primary visual cortex. Our characterization of synaptic potentials in vivo disagreed with prior findings in vitro This study will increase our understanding of thalamocortical circuits and will improve computational models of visual encoding.

Extending the Stabilized Supralinear Network model for binocular image processing

The visual cortex is both extensive and intricate. Computational models are needed to clarify the relationships between its local mechanisms and high-level functions. The Stabilized Supralinear Network (SSN) model was recently shown to account for many receptive field phenomena in V1, and also to predict subtle receptive field properties that were subsequently confirmed in vivo. In this study, we performed a preliminary exploration of whether the SSN is suitable for incorporation into large, functional models of the visual cortex, considering both its extensibility and computational tractability. First, whereas the SSN receives abstract orientation signals as input, we extended it to receive images (through a linear-nonlinear stage), and found that the extended version behaved similarly. Secondly, whereas the SSN had previously been studied in a monocular context, we found that it could also reproduce data on interocular transfer of surround suppression. Finally, we reformulated the SSN as a convolutional neural network, and found that it scaled well on parallel hardware. These results provide additional support for the plausibility of the SSN as a model of lateral interactions in V1, and suggest that the SSN is well suited as a component of complex vision models. Future work will use the SSN to explore relationships between local network interactions and sophisticated vision processes in large networks.

Spectral and spatial tuning of onset and offset response functions in auditory cortical fields A1 and CL of rhesus macaques

The mammalian auditory cortex is necessary for spectral and spatial processing of acoustic stimuli. Most physiological studies of single neurons in the auditory cortex have focused on the onset and sustained portions of evoked responses, but there have been far fewer studies on the relationship between onset and offset responses. In the current study, we compared spectral and spatial tuning of onset and offset responses of neurons in primary auditory cortex (A1) and the caudolateral (CL) belt area of awake macaque monkeys. Several different metrics were used to determine the relationship between onset and offset response profiles in both frequency and space domains. In the frequency domain, a substantial proportion of neurons in A1 and CL displayed highly dissimilar best stimuli for onset- and offset-evoked responses, although even for these neurons, there was usually a large overlap in the range of frequencies that elicited onset, and offset responses and distributions of tuning overlap metrics were mostly unimodal. In the spatial domain, the vast majority of neurons displayed very similar best locations for onset- and offset-evoked responses, along with unimodal distributions of all tuning overlap metrics considered. Finally, for both spectral and spatial tuning, a slightly larger fraction of neurons in A1 displayed nonoverlapping onset and offset response profiles, relative to CL, which supports hierarchical differences in the processing of sounds in the two areas. However, these differences are small compared with differences in proportions of simple cells (low overlap) and complex cells (high overlap) in primary and secondary visual areas.NEW & NOTEWORTHY In the current study, we examine the relationship between the tuning of neural responses evoked by the onset and offset of acoustic stimuli in the primary auditory cortex, as well as a higher-order auditory area-the caudolateral belt field-in awake rhesus macaques. In these areas, the relationship between onset and offset response profiles in frequency and space domains formed a continuum, ranging from highly overlapping to highly nonoverlapping.

Functional implications of orientation maps in primary visual cortex

Stimulus orientation in the primary visual cortex of primates and carnivores is mapped as iso-orientation domains radiating from pinwheel centres, where orientation preferences of neighbouring cells change circularly. Whether this orientation map has a function is currently debated, because many mammals, such as rodents, do not have such maps. Here we show that two fundamental properties of visual cortical responses, contrast saturation and cross-orientation suppression, are stronger within cat iso-orientation domains than at pinwheel centres. These differences develop when excitation (not normalization) from neighbouring oriented neurons is applied to different cortical orientation domains and then balanced by inhibition from un-oriented neurons. The functions of the pinwheel mosaic emerge from these local intra-cortical computations: Narrower tuning, greater cross-orientation suppression and higher contrast gain of iso-orientation cells facilitate extraction of object contours from images, whereas broader tuning, greater linearity and less suppression of pinwheel cells generate selectivity for surface patterns and textures.

Stimulus orientation in the primary visual cortex of primates and carnivores is mapped into a geometrical mosaic but the functional implications of these maps remain debated. Here the authors reveal an association between the structure of cortical orientation maps in cats, and the functions of local cortical circuits in processing patterns and contours.

Orientation selectivity in rat primary visual cortex emerges earlier with low-contrast and high-luminance stimuli

In natural vision, rapid and sustained variations in luminance and contrast change the reliability of information available about a visual scene, and markedly affect both neuronal and behavioural responses. The hallmark property of neurons in primary visual cortex (V1), orientation selectivity, is unaffected by changes in stimulus contrast, but it remains unclear how sustained differences in mean luminance and contrast affect the time-course of orientation selectivity, and the amount of information that neurons carry about orientation. We used reverse correlation with characterize the temporal dynamics of orientation selectivity in rat V1 neurons under four luminance-contrast conditions. We show that orientation selectivity and mutual information between neuronal responses and stimulus orientation are invariant to contrast or mean luminance. Critically, the time-course of the emergence of orientation selectivity was affected by both factors; response latencies were longer for low- than high-luminance gratings, and surprisingly, response latencies were also longer for high- than low-contrast gratings. Modelling suggests that luminance-modulated changes in feedforward gain, in combination with hyperpolarization caused by high contrasts can account for our physiological data. The hyperpolarization at high contrasts may increase signal-to-noise ratios, whereas a more depolarized membrane may lead to greater sensitivity to weak stimuli.

Distinct Subthreshold Mechanisms Underlying Rate-Coding Principles in Primate Auditory Cortex

A key computational principle for encoding time-varying signals in auditory and somatosensory cortices of monkeys is the opponent model of rate coding by two distinct populations of neurons. However, the subthreshold mechanisms that give rise to this computation have not been revealed. Because the rate-coding neurons are only observed in awake conditions, it is especially challenging to probe their underlying cellular mechanisms. Using a novel intracellular recording technique that we developed in awake marmosets, we found that the two types of rate-coding neurons in auditory cortex exhibited distinct subthreshold responses. While the positive-monotonic neurons (monotonically increasing firing rate with increasing stimulus repetition frequency) displayed sustained depolarization at high repetition frequency, the negative-monotonic neurons (opposite trend) instead exhibited hyperpolarization at high repetition frequency but sustained depolarization at low repetition frequency. The combination of excitatory and inhibitory subthreshold events allows the cortex to represent time-varying signals through these two opponent neuronal populations.

Calcium imaging with genetically encoded indicators in behaving primates

Understanding the neural basis of behaviour requires studying brain activity in behaving subjects using complementary techniques that measure neural responses at multiple spatial scales, and developing computational tools for understanding the mapping between these measurements. Here we report the first results of widefield imaging of genetically encoded calcium indicator (GCaMP6f) signals from V1 of behaving macaques. This technique provides a robust readout of visual population responses at the columnar scale over multiple mm² and over several months. To determine the quantitative relation between the widefield GCaMP signals and the locally pooled spiking activity, we developed a computational model that sums the responses of V1 neurons characterized by prior single unit measurements. The measured tuning properties of the GCaMP signals to stimulus contrast, orientation and spatial position closely match the predictions of the model, suggesting that widefield GCaMP signals are linearly related to the summed local spiking activity.

DOI:http://dx.doi.org/10.7554/eLife.16178.001

An important question in brain research is how neurons and the circuits they form process information to produce behavior. To understand what happens in a human brain, it is necessary to study a brain of similar complexity, such as that of a primate. Examining how the neurons in a brain region called the visual cortex process information about what we see is especially informative. This is because animals can be taught to perform different visual tasks, and because the visual cortex is relatively easy to access. In principle, therefore, it should be possible to use modern genetic and imaging techniques to study the primate visual system, but, until now, that has not been the case.

Like much of the brain, the visual cortex consists of different classes of neurons that can excite, inhibit or modulate the activity of neighboring neurons. One way to study how these different classes of neurons interact with each other is to alter the animal’s DNA, such that only one cell type stands out during the experiment, allowing its role in the brain to be closely monitored. This technique has been used to study the interactions among neurons in the rodent brain, because rodent DNA is easy to alter. However, it is not easy to manipulate primate DNA.

Seidemann et al. have, therefore, developed a new technique that can target a specific class of neurons, allowing the activity of just these cells to be distinguished from the rest. The method uses specially designed harmless viruses to produce foreign proteins in the excitatory neurons of the visual cortex in an adult macaque. The optical properties of the proteins change when the neuron they are in is active, allowing the activity of the excitatory neurons to be detected and tracked in awake animals while they perform a visual task.

Previously, the activity of neurons in the primate visual cortex could only be measured using dyes that indiscriminately reported the activity of all the neurons present. Seidemann et al. found that, in addition to being more selective than the dye-based method, the new technique also more accurately depicted neuronal action potentials, which are the primary units of information in the brain.

Seidemann et al. now plan to use a similar method to study the activity of the inhibitory neurons of the primate visual cortex. Further examination of both excitatory and inhibitory neurons at much higher magnification, using a different microscopy technique, will also reveal more subtle features of their responses during visual tasks.

DOI:http://dx.doi.org/10.7554/eLife.16178.002

Categorically distinct types of receptive fields in early visual cortex

In the visual cortex, distinct types of neurons have been identified based on cellular morphology, response to injected current, or expression of specific markers, but neurophysiological studies have revealed visual receptive field (RF) properties that appear to be on a continuum, with only two generally recognized classes: simple and complex. Most previous studies have characterized visual responses of neurons using stereotyped stimuli such as bars, gratings, or white noise and simple system identification approaches (e.g., reverse correlation). Here we estimate visual RF models of cortical neurons using visually rich natural image stimuli and regularized regression system identification methods and characterize their spatial tuning, temporal dynamics, spatiotemporal behavior, and spiking properties. We quantitatively demonstrate the existence of three functionally distinct categories of simple cells, distinguished by their degree of orientation selectivity (isotropic or oriented) and the nature of their output nonlinearity (expansive or compressive). In addition, these three types have differing average values of several other properties. Cells with nonoriented RFs tend to have smaller RFs, shorter response durations, no direction selectivity, and high reliability. Orientation-selective neurons with an expansive output nonlinearity have Gabor-like RFs, lower spontaneous activity and responsivity, and spiking responses with higher sparseness. Oriented RFs with a compressive nonlinearity are spatially nondescript and tend to show longer response latency. Our findings indicate multiple physiologically defined types of RFs beyond the simple/complex dichotomy, suggesting that cortical neurons may have more specialized functional roles rather than lying on a multidimensional continuum.

Inhibitory stabilization and visual coding in cortical circuits with multiple interneuron subtypes

Recent anatomical and functional characterization of cortical inhibitory interneurons has highlighted the diverse computations supported by different subtypes of interneurons. However, most theoretical models of cortex do not feature multiple classes of interneurons and rather assume a single homogeneous population. We study the dynamics of recurrent excitatory-inhibitory model cortical networks with parvalbumin (PV)-, somatostatin (SOM)-, and vasointestinal peptide-expressing (VIP) interneurons, with connectivity properties motivated by experimental recordings from mouse primary visual cortex. Our theory describes conditions under which the activity of such networks is stable and how perturbations of distinct neuronal subtypes recruit changes in activity through recurrent synaptic projections. We apply these conclusions to study the roles of each interneuron subtype in disinhibition, surround suppression, and subtractive or divisive modulation of orientation tuning curves. Our calculations and simulations determine the architectural and stimulus tuning conditions under which cortical activity consistent with experiment is possible. They also lead to novel predictions concerning connectivity and network dynamics that can be tested via optogenetic manipulations. Our work demonstrates that recurrent inhibitory dynamics must be taken into account to fully understand many properties of cortical dynamics observed in experiments.

Synaptic Basis for Differential Orientation Selectivity between Complex and Simple Cells in Mouse Visual Cortex

In the primary visual cortex (V1), orientation-selective neurons can be categorized into simple and complex cells primarily based on their receptive field (RF) structures. In mouse V1, although previous studies have examined the excitatory/inhibitory interplay underlying orientation selectivity (OS) of simple cells, the synaptic bases for that of complex cells have remained obscure. Here, by combining in vivo loose-patch and whole-cell recordings, we found that complex cells, identified by their overlapping on/off subfields, had significantly weaker OS than simple cells at both spiking and subthreshold membrane potential response levels. Voltage-clamp recordings further revealed that although excitatory inputs to complex and simple cells exhibited a similar degree of OS, inhibition in complex cells was more narrowly tuned than excitation, whereas in simple cells inhibition was more broadly tuned than excitation. The differential inhibitory tuning can primarily account for the difference in OS between complex and simple cells. Interestingly, the differential synaptic tuning correlated well with the spatial organization of synaptic input: the inhibitory visual RF in complex cells was more elongated in shape than its excitatory counterpart and also was more elongated than that in simple cells. Together, our results demonstrate that OS of complex and simple cells is differentially shaped by cortical inhibition based on its orientation tuning profile relative to excitation, which is contributed at least partially by the spatial organization of RFs of presynaptic inhibitory neurons.

SIGNIFICANCE STATEMENT

Simple and complex cells, two classes of principal neurons in the primary visual cortex (V1), are generally thought to be equally selective for orientation. In mouse V1, we report that complex cells, identified by their overlapping on/off subfields, has significantly weaker orientation selectivity (OS) than simple cells. This can be primarily attributed to the differential tuning selectivity of inhibitory synaptic input: inhibition in complex cells is more narrowly tuned than excitation, whereas in simple cells inhibition is more broadly tuned than excitation. In addition, there is a good correlation between inhibitory tuning selectivity and the spatial organization of inhibitory inputs. These complex and simple cells with differential degree of OS may provide functionally distinct signals to different downstream targets.

Origin and Function of Tuning Diversity in Macaque Visual Cortex

Neurons in visual cortex vary in their orientation selectivity. We measured responses of V1 and V2 cells to orientation mixtures and fit them with a model whose stimulus selectivity arises from the combined effects of filtering, suppression, and response nonlinearity. The model explains the diversity of orientation selectivity with neuron-to-neuron variability in all three mechanisms, of which variability in the orientation bandwidth of linear filtering is the most important. The model also accounts for the cells' diversity of spatial frequency selectivity. Tuning diversity is matched to the needs of visual encoding. The orientation content found in natural scenes is diverse, and neurons with different selectivities are adapted to different stimulus configurations. Single orientations are better encoded by highly selective neurons, while orientation mixtures are better encoded by less selective neurons. A diverse population of neurons therefore provides better overall discrimination capabilities for natural images than any homogeneous population.

Functional characterization of spikelet activity in the primary visual cortex

KEY POINTS

In vivo whole-cell patch-clamp recordings in cat visual cortex revealed small deflections in the membrane potential of neurons, termed spikelets. Spikelet statistics and functional properties suggest these deflections originate from a single, nearby cell. Spikelets shared a number sensory selectivities with the principal neuron including orientation selectivity, receptive field location and eye preference. Principal neurons and spikelets did not, however, generally share preferences for depth (binocular disparity). Cross-correlation of spikelet activity and membrane potential revealed direct effects on the membrane potential of some principal neurons, suggesting that these cells were synaptically coupled or received common input from the cortical network. Other spikelet-neuron pairs revealed indirect effects, likely to be the result of correlated network events.

ABSTRACT

Intracellular recordings in the neocortex reveal not only the membrane potential of neurons, but small unipolar or bipolar deflections that are termed spikelets. Spikelets have been proposed to originate from various sources, including active dendritic mechanisms, gap junctions and extracellular signals. Here we examined the functional characteristics of spikelets measured in neurons from cat primary visual cortex in vivo. Spiking statistics and our functional characterization of spikelet activity indicate that spikelets originate from a separate, nearby cell. Spikelet kinetics and lack of a direct effect on spikelet activity from hyperpolarizing current injection suggest they do not arise from electrical coupling to the principal neuron being recorded. Spikelets exhibited matched orientation tuning preference and ocular dominance to the principal neuron. In contrast, binocular disparity preferences of spikelets and the principal neuron were unrelated. Finally, we examined the impact of spikelets on the principal neuron's membrane potential; we did observe some records for which spikelets were correlated with the membrane potential of the principal neuron, suggesting that these neurons were synaptically coupled or received common input from the cortical network.

Orientation selectivity in cat primary visual cortex: local and global measurement

In this study, we investigated orientation selectivity in cat primary visual cortex (V1) and its relationship with various parameters. We found a strong correlation between circular variance (CV) and orthogonal-topreferred response ratio (O/P ratio), and a moderate correlation between tuning width and O/P ratio. Moreover, the suppression far from the peak that accounted for the lower CV in cat V1 cells also contributed to the narrowing of the tuning width of cells. We also studied the dependence of orientation selectivity on the modulation ratio for each cell, which is consistent with robust entrainment of the neuronal response to the phase of the drifting grating stimulus. In conclusion, the CV (global measure) and tuning width (local measure) are signifi cantly correlated with the modulation ratio.

Spatial phase sensitivity of complex cells in primary visual cortex depends on stimulus contrast

Neurons in primary visual cortex are classified as simple, which are phase sensitive, or complex, which are significantly less phase sensitive. Previously, we have used drifting gratings to show that the phase sensitivity of complex cells increases at low contrast and after contrast adaptation while that of simple cells remains the same at all contrasts (Cloherty SL, Ibbotson MR. J Neurophysiol 113: 434-444, 2015; Crowder NA, van Kleef J, Dreher B, Ibbotson MR. J Neurophysiol 98: 1155-1166, 2007; van Kleef JP, Cloherty SL, Ibbotson MR. J Physiol 588: 3457-3470, 2010). However, drifting gratings confound the influence of spatial and temporal summation, so here we have stimulated complex cells with gratings that are spatially stationary but continuously reverse the polarity of the contrast over time (contrast-reversing gratings). By varying the spatial phase and contrast of the gratings we aimed to establish whether the contrast-dependent phase sensitivity of complex cells results from changes in spatial or temporal processing or both. We found that most of the increase in phase sensitivity at low contrasts could be attributed to changes in the spatial phase sensitivities of complex cells. However, at low contrasts the complex cells did not develop the spatiotemporal response characteristics of simple cells, in which paired response peaks occur 180° out of phase in time and space. Complex cells that increased their spatial phase sensitivity at low contrasts were significantly overrepresented in the supragranular layers of cortex. We conclude that complex cells in supragranular layers of cat cortex have dynamic spatial summation properties and that the mechanisms underlying complex cell receptive fields differ between cortical layers.

Non-linear Membrane Properties in Entorhinal Cortical Stellate Cells Reduce Modulation of Input-Output Responses by Voltage Fluctuations

The presence of voltage fluctuations arising from synaptic activity is a critical component in models of gain control, neuronal output gating, and spike rate coding. The degree to which individual neuronal input-output functions are modulated by voltage fluctuations, however, is not well established across different cortical areas. Additionally, the extent and mechanisms of input-output modulation through fluctuations have been explored largely in simplified models of spike generation, and with limited consideration for the role of non-linear and voltage-dependent membrane properties. To address these issues, we studied fluctuation-based modulation of input-output responses in medial entorhinal cortical (MEC) stellate cells of rats, which express strong sub-threshold non-linear membrane properties. Using in vitro recordings, dynamic clamp and modeling, we show that the modulation of input-output responses by random voltage fluctuations in stellate cells is significantly limited. In stellate cells, a voltage-dependent increase in membrane resistance at sub-threshold voltages mediated by Na⁺ conductance activation limits the ability of fluctuations to elicit spikes. Similarly, in exponential leaky integrate-and-fire models using a shallow voltage-dependence for the exponential term that matches stellate cell membrane properties, a low degree of fluctuation-based modulation of input-output responses can be attained. These results demonstrate that fluctuation-based modulation of input-output responses is not a universal feature of neurons and can be significantly limited by subthreshold voltage-gated conductances.

The membrane voltage of neurons in vivo is dominated by noisy “background” fluctuations generated by network-based synaptic activity from nearby cells. It has been speculated that membrane voltage fluctuations in neurons play an important role in scaling the relationship between input amplitude and spike rate response. For this to be true, neuronal spike input-output behavior must be sensitive to physiological membrane voltage fluctuations. Using a combination of single cell recordings and modeling, we investigated the mechanisms through which voltage fluctuations modulate neuronal input-output responses. We find that neurons that express an increase in membrane input resistance with depolarization show low levels of noise-mediated modulation of input-output responses due, in part, to voltage trajectories that suppress the likelihood of generating a spike in response to random current input fluctuations. Hence, non-linear membrane properties arising from certain types of voltage-gated conductances limit noise-based modulation of neuronal input-output responses.