Search

1AbstractA cornerstone of theoretical neuroscience is the circuit model: a system of equations that captures a hypothesized neural mechanism. Such models are valuable when they give rise to an experimentally observed phenomenon – whether behavioral or a pattern of neural activity – and thus can offer insights into neural computation. The operation of these circuits, like all models, critically depends on the choice of model parameters. A key step is then to identify the model parameters consistent with observed phenomena: to solve the inverse problem. In this work, we present a novel technique, emergent property inference (EPI), that brings the modern probabilistic modeling toolkit to theoretical neuroscience. When theorizing circuit models, theoreticians predominantly focus on reproducing computational properties rather than a particular dataset. Our method uses deep neural networks to learn parameter distributions with these computational properties. This methodology is introduced through a motivational example inferring conductance parameters in a circuit model of the stomatogastric ganglion. Then, with recurrent neural networks of increasing size, we show that EPI allows precise control over the behavior of inferred parameters, and that EPI scales better in parameter dimension than alternative techniques. In the remainder of this work, we present novel theoretical findings gained through the examination of complex parametric structure captured by EPI. In a model of primary visual cortex, we discovered how connectivity with multiple inhibitory subtypes shapes variability in the excitatory population. Finally, in a model of superior colliculus, we identified and characterized two distinct regimes of connectivity that facilitate switching between opposite tasks amidst interleaved trials, characterized each regime via insights afforded by EPI, and found conditions where these circuit models reproduce results from optogenetic silencing experiments. Beyond its scientific contribution, this work illustrates the variety of analyses possible once deep learning is harnessed towards solving theoretical inverse problems.

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.

In the visual system, the response to a stimulus in a neuron’s receptive field can be modulated by stimulus context, and the strength of these contextual influences vary with stimulus intensity. Recent work has shown how a theoretical model, the stabilized supralinear network (SSN), can account for such modulatory influences, using a small set of computational mechanisms. While the predictions of the SSN have been confirmed in primary visual cortex (V1), its computational principles apply with equal validity to any cortical structure. We have therefore tested the generality of the SSN by examining modulatory influences in the middle temporal area (MT) of the macaque visual cortex, using electrophysiological recordings and pharmacological manipulations. We developed a novel stimulus that can be adjusted parametrically to be larger or smaller in the space of all possible motion directions. We found, as predicted by the SSN, that MT neurons integrate across motion directions for low-contrast stimuli, but that they exhibit suppression by the same stimuli when they are high in contrast. These results are analogous to those found in visual cortex when stimulus size is varied in the space domain. We further tested the mechanisms of inhibition using pharmacologically manipulations of inhibitory efficacy. As predicted by the SSN, local manipulation of inhibitory strength altered firing rates, but did not change the strength of surround suppression. These results are consistent with the idea that the SSN can account for modulatory influences along different stimulus dimensions and in different cortical areas.Significance StatementVisual neurons are selective for specific stimulus features in a region of visual space known as the receptive field, but can be modulated by stimuli outside of the receptive field. The SSN model has been proposed to account for these and other modulatory influences, and tested in V1. As this model is not specific to any particular stimulus feature or brain region, we wondered whether similar modulatory influences might be observed for other stimulus dimensions and other regions. We tested for specific patterns of modulatory influences in the domain of motion direction, using electrophysiological recordings from MT. Our data confirm the predictions of the SSN in MT, suggesting that the SSN computations might be a generic feature of sensory cortex.

Systems neuroscience seeks explanations for how the brain implements a wide variety of perceptual, cognitive and motor tasks. Conversely, artificial intelligence attempts to design computational systems based on the tasks they will have to solve. In the case of artificial neural networks, the three components specified by design are the objective functions, the learning rules, and architectures. With the growing success of deep learning, which utilizes brain-inspired architectures, these three designed components have increasingly become central to how we model, engineer and optimize complex artificial learning systems. Here we argue that a greater focus on these components would also benefit systems neuroscience. We give examples of how this optimization-based framework can drive theoretical and experimental progress in neuroscience. We contend that this principled perspective on systems neuroscience will help to generate more rapid progress.

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 to the factors that cancel, rather than tight, meaning that the net input is very small relative to the cancelling 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., 21 pages, 2 figures

Physical features of sensory stimuli are fixed, but sensory perception is context dependent. The precise mechanisms that govern contextual modulation remain unknown. Here, we trained mice to switch between two contexts: passively listening to pure tones and performing a recognition task for the same stimuli. Two-photon imaging showed that many excitatory neurons in auditory cortex were suppressed during behavior, while some cells became more active. Whole-cell recordings showed that excitatory inputs were affected only modestly by context, but inhibition was more sensitive, with PV+, SOM+, and VIP+ interneurons balancing inhibition and disinhibition within the network. Cholinergic modulation was involved in context switching, with cholinergic axons increasing activity during behavior and directly depolarizing inhibitory cells. Network modeling captured these findings, but only when modulation coincidently drove all three interneuron subtypes, ruling out either inhibition or disinhibition alone as sole mechanism for active engagement. Parallel processing of cholinergic modulation by cortical interneurons therefore enables context-dependent behavior.

Summary Correlated variability in cortical activity is ubiquitously quenched following stimulus onset, in a stimulus-dependent manner. These modulations have been attributed to circuit dynamics involving either multiple stable states (“attractors”) or chaotic activity. Here we show that a qualitatively different dynamical regime, involving fluctuations about a single, stimulus-driven attractor in a loosely balanced excitatory-inhibitory network (the stochastic “stabilized supralinear network”), best explains these modulations. Given the supralinear input/output functions of cortical neurons, increased stimulus drive strengthens effective network connectivity. This shifts the balance from interactions that amplify variability to suppressive inhibitory feedback, quenching correlated variability around more strongly driven steady states. Comparing to previously published and original data analyses, we show that this mechanism, unlike previous proposals, uniquely accounts for the spatial patterns and fast temporal dynamics of variability suppression. Specifying the cortical operating regime is key to understanding the computations underlying perception., Highlights • A simple network model explains stimulus-tuning of cortical variability suppression • Inhibition stabilizes recurrently interacting neurons with supralinear I/O functions • Stimuli strengthen inhibitory stabilization around a stable state, quenching variability • Single-trial V1 data are compatible with this model and rules out competing proposals, Stimuli suppress cortical correlated variability. Hennequin et al. show that a cortical operating regime of inhibitory stabilization around a single stable state—the “stabilized supralinear network”—explains this suppression’s tuning and timing, while alternative proposed regimes do not.

How does attentional modulation of neural activity enhance performance? Here we use a deep convolutional neural network as a large-scale model of the visual system to address this question. We model the feature similarity gain model of attention, in which attentional modulation is applied according to neural stimulus tuning. Using a variety of visual tasks, we show that neural modulations of the kind and magnitude observed experimentally lead to performance changes of the kind and magnitude observed experimentally. We find that, at earlier layers, attention applied according to tuning does not successfully propagate through the network, and has a weaker impact on performance than attention applied according to values computed for optimally modulating higher areas. This raises the question of whether biological attention might be applied at least in part to optimize function rather than strictly according to tuning. We suggest a simple experiment to distinguish these alternatives., eLife digest Imagine you have lost your cell phone. Your eyes scan the cluttered table in front of you, searching for its familiar blue case. But what is happening within the visual areas of your brain while you search? One possibility is that neurons that represent relevant features such as 'blue' and 'rectangular' increase their activity. This might help you spot your phone among all the other objects on the table. Paying attention to specific features improves our performance on visual tasks that require detecting those features. The 'feature similarity gain model' proposes that this is because attention increases the activity of neurons sensitive to specific target features, such as ‘blue’ in the example above. But is this how the brain solves such challenges in practice? Previous studies examining this issue have relied on correlations. They have shown that increases in neural activity correlate with improved performance on visual tasks. But correlation does not imply causation. Lindsay and Miller have now used a computer model of the brain’s visual pathway to examine whether changes in neural activity cause improved performance. The model was trained to use feature similarity gain to detect an object within a set of photographs. As predicted, changes in activity like those that occur in the brain did indeed improve the model’s performance. Moreover, activity changes at later stages of the model's processing pathway produced bigger improvements than activity changes earlier in the pathway. This may explain why attention affects neural activity more at later stages in the visual pathway. But feature similarity gain is not the only possible explanation for the results. Lindsay and Miller show that another pattern of activity change also enhanced the model’s performance, and propose an experiment to distinguish between the two possibilities. Overall, these findings increase our understanding of how the brain processes sensory information. Work is ongoing to teach computers to process images as efficiently as the human visual system. The computer model used in this study is similar to those used in state-of-the-art computer vision. These findings could thus help advance artificial sensory processing too.

Neurons in sensory cortex integrate multiple influences to parse objects and support perception. Across multiple cortical areas, integration is characterized by two neuronal response properties: (1) surround suppression: modulatory contextual stimuli suppress responses to driving stimuli; (2) “normalization”: responses to multiple driving stimuli add sublinearly. These properties depend on input strength: for weak driving stimuli, contextual influences more weakly suppress or facilitate and summation becomes linear or supralinear. Understanding the circuit operations underlying integration is critical to understanding cortical function and disease. We present a simple, general theory. A wealth of integrative properties including the above emerge robustly from four properties of cortical circuitry: (1) supralinear neuronal input/output functions; (2) sufficiently strong recurrent excitation; (3) feedback inhibition; (4) simple spatial properties of intracortical connections. Integrative properties emerge dynamically as circuit properties, with excitatory and inhibitory neurons showing similar behaviors. In new recordings in visual cortex, we confirm key model predictions.

Of all of the sensory areas, barrel cortex is among the best understood in terms of circuitry, yet least understood in terms of sensory function. We combined intracellular recording in rats with a multi-directional, multi-whisker stimulator system to estimate receptive fields by reverse correlation of stimuli to synaptic inputs. Spatiotemporal receptive fields were identified orders of magnitude faster than by conventional spike-based approaches, even for neurons with little spiking activity. Given a suitable stimulus representation, a linear model captured the stimulus-response relationship for all neurons with high accuracy. In contrast with conventional single-whisker stimuli, complex stimuli revealed markedly sharpened receptive fields, largely as a result of adaptation. This phenomenon allowed the surround to facilitate rather than to suppress responses to the principal whisker. Optimized stimuli enhanced firing in layers 4-6, but not in layers 2/3, which remained sparsely active. Surround facilitation through adaptation may be required for discriminating complex shapes and textures during natural sensing.

What causes critical periods (CPs) to open? For the best-studied case, ocular dominance plasticity in primary visual cortex in response to monocular deprivation (MD), the maturation of inhibition is necessary and sufficient. How does inhibition open the CP? We present a novel theory: the transition from pre-CP to CP plasticity arises because inhibition preferentially suppresses responses to spontaneous relative to visually-driven input activity, switching learning cues from internal to external sources. This differs from previous proposals in (1) arguing that the CP can open without changes in plasticity mechanisms when, through circuit development, activity patterns become more sensitive to sensory experience; (2) explaining not simply a transition from no plasticity to plasticity, but rather the change in outcome of MD-induced plasticity,from pre-CP to CP,. More broadly, hierarchical organization of sensory-motor pathways may develop through a cascade of CPs induced as circuit maturation progresses from “lower” to “higher” cortical areas.

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.

Early in development, the cat primary visual cortex (V1) is dominated by inputs driven by the contralateral eye. The pattern then reorganizes into ocular dominance columns that are roughly equally distributed between inputs serving the two eyes. This reorganization does not occur if the eyes are kept closed. The mechanism of this equalization is unknown. It has been argued that it is unlikely to involve Hebbian activity-dependent learning rules, on the assumption that these would favor an initially dominant eye. The reorganization occurs at the onset of the critical period (CP) for monocular deprivation (MD), the period when MD can cause a shift of cortical innervation in favor of the nondeprived eye. In mice, the CP is opened by the maturation of cortical inhibition, which does not occur if the eyes are kept closed. Here we show how these observations can be united: under Hebbian rules of activity-dependent synaptic modification, strengthening of intracortical inhibition can lead to equalization of the two eyes' inputs. Furthermore, when the effects of homeostatic synaptic plasticity or certain other mechanisms are incorporated, activity-dependent learning can also explain how MD causes a shift toward the open eye during the CP despite the drive by inhibition toward equalization of the two eyes' inputs. Thus, assuming similar mechanisms underlie the onset of the CP in cats as in mice, this and activity-dependent learning rules can explain the interocular equalization observed in cat V1 and its failure to occur without visual experience.

SummaryIn what regime does the cortical circuit operate? Our intracellular studies of surround suppression in cat primary visual cortex (V1) provide strong evidence on this question. Although suppression has been thought to arise from an increase in lateral inhibition, we find that the inhibition that cells receive is reduced, not increased, by a surround stimulus. Instead, suppression is mediated by a withdrawal of excitation. Thalamic recordings and previous work show that these effects cannot be explained by a withdrawal of thalamic input. We find in theoretical work that this behavior can only arise if V1 operates as an inhibition-stabilized network (ISN), in which excitatory recurrence alone is strong enough to destabilize visual responses but feedback inhibition maintains stability. We confirm two strong tests of this scenario experimentally and show through simulation that observed cell-to-cell variability in surround effects, from facilitation to suppression, can arise naturally from variability in the ISN.

SummaryIn cerebral cortex, ongoing activity absent a stimulus can resemble stimulus-driven activity in size and structure. In particular, spontaneous activity in cat primary visual cortex (V1) has structure significantly correlated with evoked responses to oriented stimuli. This suggests that, from unstructured input, cortical circuits selectively amplify specific activity patterns. Current understanding of selective amplification involves elongation of a neural assembly's lifetime by mutual excitation among its neurons. We introduce a new mechanism for selective amplification without elongation of lifetime: “balanced amplification.” Strong balanced amplification arises when feedback inhibition stabilizes strong recurrent excitation, a pattern likely to be typical of cortex. Thus, balanced amplification should ubiquitously contribute to cortical activity. Balanced amplification depends on the fact that individual neurons project only excitatory or only inhibitory synapses. This leads to a hidden feedforward connectivity between activity patterns. We show in a detailed biophysical model that this can explain the cat V1 observations.

Little is known about the internal circuitry of the primate lateral intraparietal area (LIP). During two versions of a delayed-saccade task, we found radically different network dynamics beneath similar population average firing patterns. When neurons are not influenced by stimuli outside their receptive fields (RFs), dynamics of the high-dimensional LIP network during slowly varying activity lie predominantly in one multi-neuronal dimension, as described previously. However, when activity is suppressed by stimuli outside the RF, slow LIP dynamics markedly deviate from a single dimension. The conflicting results can be reconciled if two LIP local networks, each underlying an RF location and dominated by a single multi-neuronal activity pattern, are suppressively coupled to each other. These results demonstrate the low dimensionality of slow LIP local dynamics, and suggest that LIP local networks encoding the attentional and movement priority of competing visual locations actively suppress one another.

Tetrodes allow isolation of multiple neurons at a single recording site by clustering spikes. Due to electrode drift and perhaps due to time-varying neuronal properties, positions and shapes of clusters change in time. As data is typically collected in sequential files, to track neurons across files one has to decide which clusters from different files belong to the same neuron. We report on a semi-automated neuron tracking procedure that uses computed similarities between the mean spike waveforms of the clusters. The clusters with the most similar waveforms are assigned to the same neuron, provided their similarity exceeds a threshold. To set this threshold, we calculate two distributions: of within-file similarities, and of best matches in the across adjacent file similarities. The threshold is set to the value that optimally separates the two distributions. We compare different measures of similarity (metrics) by their ability to separate these distributions. We find that these metrics do not differ drastically in their performance, but that taking into account the cross-channel noise correlation significantly improves performance of all metrics. We also demonstrate the method on an independent dataset and show that neurons, as assigned by the procedure, have consistent physiological properties across files.

Previously, we proposed a model of the circuitry underlying simple-cell responses in cat primary visual cortex (V1) layer 4. We argued that the ordered arrangement of lateral geniculate nucleus inputs to a simple cell must be supplemented by a component of feedforward inhibition that is untuned for orientation and responds to high temporal frequencies to explain the sharp contrast-invariant orientation tuning and low-pass temporal frequency tuning of simple cells. The temporal tuning also requires a significant NMDA component in geniculocortical synapses. Recent experiments have revealed cat V1 layer 4 inhibitory neurons with two distinct types of receptive fields (RFs): complex RFs with mixed ON/OFF responses lacking in orientation tuning, and simple RFs with normal, sharp-orientation tuning (although, some respond to all orientations). We show that complex inhibitory neurons can provide the inhibition needed to explain simple-cell response properties. Given this complex cell inhibition, antiphase or “push-pull” inhibition from tuned simple inhibitory neurons acts to sharpen spatial frequency tuning, lower responses to low temporal frequency stimuli, and increase the stability of cortical activity.

We develop a new analysis of the lateral geniculate nucleus (LGN) input to a cortical simple cell, demonstrating that this input is the sum of two terms, a linear term and a nonlinear term. In response to a drifting grating, the linear term represents the temporal modulation of input, and the nonlinear term represents the mean input. The nonlinear term, which grows with stimulus contrast, has been neglected in many previous models of simple cell response. We then analyze two scenarios by which contrast-invariance of orientation tuning may arise. In the first scenario, at larger contrasts, the nonlinear part of the LGN input, in combination with strong push-pull inhibition, counteracts the nonlinear effects of cortical spike threshold, giving the result that orientation tuning scales with contrast. In the second scenario, at low contrasts, the nonlinear component of LGN input is negligible, and noise smooths the nonlinearity of spike threshold so that the input-output function approximates a power-law function. These scenarios can be combined to yield contrast-invariant tuning over the full range of stimulus contrast. The model clarifies the contribution of LGN nonlinearities to the orientation tuning of simple cells and demonstrates how these nonlinearities may impact different models of contrast-invariant tuning.

We model the development of the functional circuit of layer 4 (the input-recipient layer) of cat primary visual cortex. The observed thalamocortical and intracortical circuitry codevelop under Hebb-like synaptic plasticity. Hebbian development yields opponent inhibition: inhibition evoked by stimuli anticorrelated with those that excite a cell. Strong opponent inhibition enables recognition of stimulus orientation in a manner invariant to stimulus contrast. These principles may apply to cortex more generally: Hebb-like plasticity can guide layer 4 of any piece of cortex to create opposition between anticorrelated stimulus pairs, and this enables recognition of specific stimulus patterns in a manner invariant to stimulus magnitude. Properties that are invariant across a cortical column are predicted to be those shared by opponent stimulus pairs; this contrasts with the common idea that a column represents cells with similar response properties.

Neighboring neurons in cat primary visual cortex (V1) have similar preferred orientation, direction, and spatial frequency. How diverse is their degree of tuning for these properties? To address this, we used single-tetrode recordings to simultaneously isolate multiple cells at single recording sites and record their responses to flashed and drifting gratings of multiple orientations, spatial frequencies, and, for drifting gratings, directions. Orientation tuning width, spatial frequency tuning width, and direction selectivity index (DSI) all showed significant clustering: pairs of neurons recorded at a single site were significantly more similar in each of these properties than pairs of neurons from different recording sites. The strength of the clustering was generally modest. The percent decrease in the median difference between pairs from the same site, relative to pairs from different sites, was as follows: for different measures of orientation tuning width, 29–35% (drifting gratings) or 15–25% (flashed gratings); for DSI, 24%; and for spatial frequency tuning width measured in octaves, 8% (drifting gratings). The clusterings of all of these measures were much weaker than for preferred orientation (68% decrease) but comparable to that seen for preferred spatial frequency in response to drifting gratings (26%). For the above properties, little difference in clustering was seen between simple and complex cells. In studies of spatial frequency tuning to flashed gratings, strong clustering was seen among simple-cell pairs for tuning width (70% decrease) and preferred frequency (71% decrease), whereas no clustering was seen for simple-complex or complex-complex cell pairs.

A central theme in neural coding concerns the role of response variability and noise in determining the information transmission of neurons. This issue was investigated in single cells of the lateral geniculate nucleus of barbiturate-anesthetized cats by quantifying the degree of precision in and the information transmission properties of individual spike train responses to full field, binary (bright or dark), flashing stimuli. We found that neuronal responses could be highly reproducible in their spike timing (approximately 1-2 ms standard deviation) and spike count (approximately 0.3 ratio of variance/mean, compared with 1.0 expected for a Poisson process). This degree of precision only became apparent when an adequate length of the stimulus sequence was specified to determine the neural response, emphasizing that the variables relevant to a cell's response must be controlled to observe the cell's intrinsic response precision. Responses could carry as much as 3.5 bits/spike of information about the stimulus, a rate that was within a factor of two of the limit the spike train could transmit. Moreover, there appeared to be little sign of redundancy in coding: on average, longer response sequences carried at least as much information about the stimulus as would be obtained by adding together the information carried by shorter response sequences considered independently. There also was no direct evidence found for synergy between response sequences. These results could largely, but not entirely, be explained by a simple model of the response in which one filters the stimulus by the cell's impulse response kernel, thresholds the result at a fairly high level, and incorporates a postspike refractory period.

We study a recently proposed “correlation-based,” push-pull model of the circuitry of layer 4 of cat visual cortex. This model was previously shown to explain the contrast-invariance of cortical orientation tuning. Here we show that it can simultaneously account for several contrast-dependent (c-d) “nonlinearities” in cortical responses. These include an advance with increasing contrast in the temporal phase of response to a sinusoidally modulated stimulus; a change in shape of the temporal frequency tuning curve, so that higher temporal frequencies may give little or no response at low contrast but reasonable responses at high contrast; and contrast saturation that occurs at lower contrasts in cortex than in the lateral geniculate nucleus (LGN). In the context of the model circuit, these properties arise from a mixture of nonlinear cellular and synaptic mechanisms: short-term synaptic depression, spike-rate adaptation, contrast-induced changes in cellular conductance, and the nonzero spike threshold. The former three mechanisms are sufficient to explain the experimentally observed increase in c-d phase advance in cortex relative to LGN. The c-d changes in temporal frequency tuning arise as a threshold effect: voltage modulations in response to higher-frequency inputs are only slightly above threshold at lower contrast, but become robustly suprathreshold at higher contrast. The other three nonlinear mechanisms also play a crucial role in this result, allowing contrast dependence of temporal frequency tuning to coexist with contrast-invariance of orientation tuning. Contrast saturation, and the observation that responses to stimuli of increasing temporal frequency saturate at increasingly high contrasts, can be induced both by the model's push-pull inhibition and by synaptic depression. Previous proposals explained these nonlinear response properties by assuming contrast-invariant orientation tuning as a starting point, and adding normalization by shunting inhibition derived equally from cells of all preferred orientations. The present proposal simultaneously explains both contrast-invariant orientation tuning and these contrast-dependent nonlinearities and requires only processing that is local in orientation, in agreement with intracellular measurements.

Hebbian models of development and learning require both activity-dependent synaptic plasticity and a mechanism that induces competition between different synapses. One form of experimentally observed long-term synaptic plasticity, which we call spike-timing-dependent plasticity (STDP), depends on the relative timing of pre- and postsynaptic action potentials. In modeling studies, we find that this form of synaptic modification can automatically balance synaptic strengths to make postsynaptic firing irregular but more sensitive to presynaptic spike timing. It has been argued that neurons in vivo operate in such a balanced regime. Synapses modifiable by STDP compete for control of the timing of postsynaptic action potentials. Inputs that fire the postsynaptic neuron with short latency or that act in correlated groups are able to compete most successfully and develop strong synapses, while synapses of longer-latency or less-effective inputs are weakened.

Partially isolated cortical islands prepared in vivo become epileptogenic within weeks of the injury. In this model of chronic epileptogenesis, recordings from cortical slices cut through the injured area and maintained in vitro often show evoked, long- and variable-latency multiphasic epileptiform field potentials that also can occur spontaneously. These events are initiated in layer V and are synchronous with polyphasic long-duration excitatory and inhibitory potentials (currents) in neurons that may last several hundred milliseconds. Stimuli that are significantly above threshold for triggering these epileptiform events evoke only a single large excitatory postsynaptic potential (EPSP) followed by an inhibitory postsynaptic potential (IPSP). We investigated the physiological basis of these events using simulations of a layer V network consisting of 500 compartmental model neurons, including 400 principal (excitatory) and 100 inhibitory cells. Epileptiform events occurred in response to a stimulus when sufficient N-methyl-d-aspartate (NMDA) conductance was activated by feedback excitatory activity among pyramidal cells. In control simulations, this activity was prevented by the rapid development of IPSPs. One manipulation that could give rise to epileptogenesis was an increase in the threshold of inhibitory interneurons. However, previous experimental data from layer V pyramidal neurons of these chronic epileptogenic lesions indicate: upregulation, rather than downregulation, of inhibition; alterations in the intrinsic properties of pyramidal cells that would tend to make them more excitable; and sprouting of their intracortical axons and increased numbers of presumed synaptic contacts, which would increase recurrent EPSPs from one cell onto another. Consistent with this, we found that increasing the excitability of pyramidal cells and the strength of NMDA conductances, in the face of either unaltered or increased inhibition, resulted in generation of epileptiform activity that had characteristics similar to those of the experimental data. Thus epileptogenesis such as occurs after chronic cortical injury can result from alterations of intrinsic membrane properties of pyramidal neurons together with enhanced NMDA synaptic conductances.

Neurons in the primary visual cortex of higher mammals respond selectively to light/dark borders of a particular orientation. The receptive fields of simple cells, a type of orientation-selective cell, consist of adjacent, oriented regions alternately receiving ON-center and OFF-center excitatory input. I show that this segregation of inputs within receptive fields can occur through an activity-dependent competition between ON-center and OFF-center inputs, just as segregation of inputs between different postsynaptic cells into ocular dominance columns appears to occur through activity-dependent competition between left-eye and right-eye inputs. These different outcomes are proposed to result, not from different mechanisms, but from different spatial structures of the correlations in neural activity among the competing inputs in each case. Simple cells result if ON-center inputs are best correlated with other ON-center inputs, and OFF with OFF, at small retinotopic separations, but ON-center inputs are best correlated with OFF-center inputs at larger separations. This hypothesis leads robustly to development of simple cell receptive fields selective for orientation and spatial frequency, and to the continuous and periodic arrangement of preferred orientation across the cortex. Input correlations determine the mean preferred spatial frequency and degree of orientation selectivity. Estimates of these correlations based on measurements in adult cat retina (Mastronarde, 1983a,b) produce quantitative predictions for the mean preferred spatial frequencies of cat simple cells across eccentricities that agree with experiments (Movshon et al., 1978b). Intracortical interactions are the primary determinant of cortical organization. Simple cell spatial phases can play a key role in this organization, so arrangements of spatial phases and preferred orientations may need to be studied together to understand either alone. Possible origins for other cortical features including spatial frequency clusters, afferent ON/OFF segregation, blobs, pinwheels, and opponent inhibition within simple cell receptive fields are suggested. A number of strong experimental tests of the hypothesis are proposed.

Cholinergic synaptic vesicles purified from the electric organ of the marine ray, Discopyge ommata, contain 2 different size classes of GTP- binding proteins: one or more with an apparent molecular weight (MW) between 37 and 41 kDa, and 3 major and at least 2 minor proteins with MW between 20 and 29 kDa. These GTP-binding proteins were detectable using the alpha 32P-GTP overlay technique and covalent modification with bacterial toxins. The higher MW GTP-binding proteins are ADP- ribosylated by pertussis toxin and 2 of the lower MW GTP-binding proteins are sensitive to botulinum toxin.

We model the effects of excitation and inhibition on the gain of cortical neurons. Previous theoretical work has concluded that excitation or inhibition alone will not cause a multiplicative gain change in the curve of firing rate versus input current. However, such gain changesin vivoare measured in the curve of firing rate versus stimulus parameter. We find that when this curve is considered, and when the nonlinear relationships between stimulus parameter and input current and between input current and firing ratein vivoare taken into account, then simple excitation or inhibition alone can induce a multiplicative gain change. In particular, the power-law relationship between voltage and firing rate that is induced by neuronal noise is critical to this result. This suggests an unexpectedly simple mechanism that may underlie the gain modulations commonly observed in cortex. More generally, it suggests that a smaller input will multiplicatively modulate the gain of a larger one when both converge on a common cortical target.

Many phenomenological models of the responses of simple cells in primary visual cortex have concluded that a cell's firing rate should be given by its input raised to a power greater than one. This is known as an expansive power-law nonlinearity. However, intracellular recordings have shown that a different nonlinearity, a linear-threshold function, appears to give a good prediction of firing rate from a cell's low-pass-filtered voltage response. Using a model based on a linear-threshold function, Anderson et al. showed that voltage noise was critical to converting voltage responses with contrast-invariant orientation tuning into spiking responses with contrast-invariant tuning. We present two separate results clarifying the connection between noise-smoothed linear-threshold functions and power-law nonlinearities. First, we prove analytically that a power-law nonlinearity is the only input-output function that converts contrast-invariant input tuning into contrast-invariant spike tuning. Second, we examine simulations of a simple model that assumes instantaneous spike rate is given by a linear-threshold function of voltage and voltage responses include significant noise. We show that the resulting average spike rate is well described by an expansive power law of the average voltage (averaged over multiple trials), provided that average voltage remains less than about 1.5 SDs of the noise above threshold. Finally, we use this model to show that the noise levels recorded by Anderson et al. are consistent with the degree to which the orientation tuning of spiking responses is more sharply tuned relative to the orientation tuning of voltage responses. Thus neuronal noise can robustly generate power-law input-output functions of the form frequently postulated for simple cells.

In cortical simple cells of cat striate cortex, the response to a visual stimulus of the preferred orientation is partially suppressed by simultaneous presentation of a stimulus at the orthogonal orientation, an effect known as “cross-orientation inhibition.” It has been argued that this is due to the presence of inhibitory connections between cells tuned for different orientations, but intracellular studies suggest that simple cells receive inhibitory input primarily from cells with similar orientation tuning. Furthermore, response suppression can be elicited by a variety of nonpreferred stimuli at all orientations. Here we study a model circuit that was presented previously to address many aspects of simple cell orientation tuning, which is based on local intracortical connectivity between cells of similar orientation tuning. We show that this model circuit can account for many aspects of cross-orientation inhibition and, more generally, of response suppression by nonpreferred stimuli and of other nonlinear properties of responses to stimulation with multiple gratings.

Cells in cerebral cortex fail to respond to fast-moving stimuli that evoke strong responses in the thalamic nuclei innervating the cortex. The reason for this behavior has remained a mystery. We study an experimentally motivated model of the thalamic input-recipient layer of cat primary visual cortex that accounts for many aspects of cortical orientation tuning. In this circuit, inhibition dominates over excitation, but temporal modulations of excitation and inhibition occur out of phase with one another, allowing excitation to transiently drive cells. We show that this circuit provides a natural explanation of cortical low-pass temporal frequency tuning, provided N-methyl-D-aspartate (NMDA) receptors are present in thalamocortical synapses in proportions measured experimentally. This suggests a new and unanticipated role for NMDA conductances in shaping the temporal response properties of cortical cells, and suggests that common cortical circuit mechanisms underlie both spatial and temporal response tuning.

The origin of orientation selectivity in the responses of simple cells in cat visual cortex serves as a model problem for understanding cortical circuitry and computation. The feed-forward model posits that this selectivity arises simply from the arrangement of thalamic inputs to a simple cell. Much evidence, including a number of recent intracellular studies, supports a primary role of the thalamic inputs in determining simple cell response properties, including orientation tuning. This mechanism alone, however, cannot explain the invariance of orientation tuning to changes in stimulus contrast. Simple cells receive push-pull inhibition: ON inhibition in OFF subregions and vice versa. Addition of such inhibition to the feed-forward model can account for this contrast invariance, provided the inhibition is sufficiently strong. The predictions of “normalization” and “feedback” models are reviewed and compared with the predictions of this modified feed-forward model and with experimental results. The modified feed-forward and the feedback models ascribe fundamentally different functions to cortical processing.

We explore the hypothesis that binocular simple cells in cat areas 17 and 18 show subregion correspondence , defined as follows: within the region of overlap of the two eye’s receptive fields, their ON subregions lie in corresponding locations, as do their OFF subregions. This hypothesis is motivated by a developmental model ([Erwin and Miller, 1998][1]) that suggested that simple cells could develop binocularly matched preferred orientations and spatial frequencies by developing subregion correspondence. Binocular organization of simple cell receptive fields is commonly characterized by two quantities: interocular position shift, the distance in visual space between the center positions of the two eye’s receptive fields; and interocular phase shift, the difference in the spatial phases of those receptive fields, each measured relative to its center position. The subregion correspondence hypothesis implies that interocular position and phase shifts are linearly related. We compare this hypothesis with the null hypothesis, assumed by most previous models of binocular organization, that the two types of shift are uncorrelated. We demonstrate that the subregion correspondence and null hypotheses are equally consistent with previous measurements of binocular response properties of individual simple cells in the cat and other species and with measurements of the distribution of interocular phase shifts versus preferred orientations or versus interocular position shifts. However, the observed tendency of binocular simple cells in the cat to have “tuned excitatory” disparity tuning curves with preferred disparities tightly clustered around zero ([Fischer and Kruger, 1979][2]; [Ferster, 1981][3]; [LeVay and Voigt, 1988][4]) follows naturally from the subregion correspondence hypothesis but is inconsistent with the null hypothesis. We describe tests that could more conclusively differentiate between the hypotheses. The most straightforward test requires simultaneous determination of the receptive fields of groups of three or more binocular simple cells. [1]: #ref-18 [2]: #ref-23 [3]: #ref-20 [4]: #ref-36

We extend previous models for separate development of ocular dominance and orientation selectivity in cortical layer 4 by exploring conditions permitting combined organization of both properties. These conditions are expressed in terms of functions describing the degree of correlation in the firing of two inputs from the lateral geniculate nucleus (LGN), as a function of their retinotopic separation and their “type” (ON center or OFF center and left eye or right eye).The development of ocular dominance requires that the correlations of an input with other inputs of the same eye be stronger than or equal to its correlations with inputs of the opposite eye and strictly stronger at small retinotopic separations. This must be true after summing correlations with inputs of both center types. The development of orientation-selective simple cells requires that (1) an input’s correlations with other inputs of the same center type be stronger than its correlations with inputs of the opposite center type at small retinotopic separation; and (2) this relationship reverse at larger retinotopic separations within an arbor radius (the radius over which LGN cells can project to a common cortical point). This must be true after summing correlations with inputs serving both eyes.For orientations to become matched in the two eyes, correlated activity within the receptive fields must be maximized by specific between-eye alignments of ON and OFF subregions. Thus the correlations between the eyes must differ depending on center type, and this difference must vary with retinotopic separation within an arbor radius.These principles are satisfied by a wide class of correlation functions. Combined development of ocularly matched orientation maps and ocular dominance maps can be achieved either simultaneously or sequentially. In the latter case, the model can produce a correlation between the locations of orientation map singularities and local ocular dominance peaks similar to that observed physiologically.The model’s main prediction is that the above correlations should exist among inputs to cortical layer 4 simple cells before vision. In addition, mature simple cells are predicted to have certain relationships between the locations of the ON and OFF subregions of the left and right eyes’ receptive fields.

The origin of orientation selectivity in visual cortical responses is a central problem for understanding cerebral cortical circuitry. In cats, many experiments suggest that orientation selectivity arises from the arrangement of lateral geniculate nucleus (LGN) afferents to layer 4 simple cells. However, this explanation is not sufficient to account for the contrast invariance of orientation tuning.To understand contrast invariance, we first characterize the input to cat simple cells generated by the oriented arrangement of LGN afferents. We demonstrate that it has two components: a spatial-phase-specific component (i.e., one that depends on receptive field spatial phase), which is tuned for orientation, and a phase-nonspecific component, which is untuned. Both components grow with contrast.Second, we show that a correlation-based intracortical circuit, in which connectivity between cell pairs is determined by the correlation of their LGN inputs, is sufficient to achieve well tuned, contrast-invariant orientation tuning. This circuit generates both spatially opponent, “antiphase” inhibition (“push–pull”), and spatially matched, “same-phase” excitation. The inhibition, if sufficiently strong, suppresses the untuned input component and sharpens responses to the tuned component at all contrasts. The excitation amplifies tuned responses. This circuit agrees with experimental evidence showing spatial opponency between, and similar orientation tuning of, the excitatory and inhibitory inputs received by a simple cell. Orientation tuning is primarily input driven, accounting for the observed invariance of tuning width after removal of intracortical synaptic input, as well as for the dependence of orientation tuning on stimulus spatial frequency.The model differs from previous push–pull models in requiring dominant rather than balanced inhibition and in predicting that a population of layer 4 inhibitory neurons should respond in a contrast-dependent manner to stimuli of all orientations, although their tuning width may be similar to that of excitatory neurons. The model demonstrates that fundamental response properties of cortical layer 4 can be explained by circuitry expected to develop under correlation-based rules of synaptic plasticity, and shows how such circuitry allows the cortex to distinguish stimulus intensity from stimulus form.

Development of orientation-selective receptive fields in primary visual cortex of higher mammals can occur through activity-dependent competition between ON-center and OFF-center inputs. This competition yields orientation and spatial-frequency-selective `simple cells' if the dark activity of ON (or OFF)-center inputs is best correlated with that of other ON (or OFF)-center inputs at small retinotopic separations and with that of OFF (ON)-center inputs at larger separations. Features of cat and monkey cortical organization emerge, including continuous and periodic arrangement of preferred orientation across the cortex. A new feature, systematic variation of receptive field spatial phase, is predicted. Experimental tests of this hypothesis are proposed.