Inhibition-stabilized Networks Research Articles

Inhibitory stabilized network behaviour in a balanced neural mass model of a cortical column

Strong inhibitory recurrent connections can reduce the tendency for a neural network to become unstable. This is known as inhibitory stabilization; networks that are unstable in the absence of strong inhibitory feedback because of their unstable excitatory recurrent connections are known as Inhibition Stabilized Networks (ISNs). One of the characteristics of ISNs is their “paradoxical response”, where perturbing the inhibitory neurons with additional excitatory input results in a decrease in their activity after a temporal delay instead of increasing their activity. Here, we develop a model of populations of neurons across different layers of cortex. Within each layer, there is one population of inhibitory neurons and one population of excitatory neurons. The connectivity weights across different populations in the model are derived from a synaptic physiology database provided by the Allen Institute. The model shows a gradient of excitation–inhibition balance across different layers in the cortex, where superficial layers are more inhibitory dominated compared to deeper layers. To investigate the presence of ISNs across different layers, we measured the membrane potentials of neural populations in the model after perturbing inhibitory populations. The results show that layer 2/3 in the model does not operate in the ISN regime but layers 4 and 5 do operate in the ISN regime. These results accord with neurophysiological findings that explored the presence of ISNs across different layers in the cortex. The results show that there may be a systematic macroscopic gradient of inhibitory stabilization across different layers in the cortex that depends on the level of excitation–inhibition balance, and that the strength of the paradoxical response increases as the model moves closer to bifurcation points.

Optogenetics reveals paradoxical network stabilizations in hippocampal CA1 and CA3

Recurrent connectivity between excitatory neurons and the strength of feedback from inhibitory neurons are critical determinants of the dynamics and computational properties of neuronal circuits. Toward a better understanding of these circuit properties in regions CA1 and CA3 of the hippocampus, we performed optogenetic manipulations combined with large-scale unit recordings in rats under anesthesia and in quiet waking, using photoinhibition and photoexcitation with different light-sensitive opsins. In both regions, we saw striking paradoxical responses: subsets of cells increased firing during photoinhibition, while other cells decreased firing during photoexcitation. These paradoxical responses were more prominent in CA3 than in CA1, but, notably, CA1 interneurons showed increased firing in response to photoinhibition of CA3. These observations were recapitulated in simulations where we modeled both CA1 and CA3 as inhibition-stabilized networks in which strong recurrent excitation is balanced by feedback inhibition. To directly test the inhibition-stabilized model, we performed large-scale photoinhibition directed at (GAD-Cre) inhibitory cells and found that interneurons in both regions increased firing when photoinhibited, as predicted. Our results highlight the often-paradoxical circuit dynamics that are evidenced during optogenetic manipulations and indicate that, contrary to long-standing dogma, both CA1 and CA3 hippocampal regions display strongly recurrent excitation, which is stabilized through inhibition.

Paradoxical self-sustained dynamics emerge from orchestrated excitatory and inhibitory homeostatic plasticity rules

Self-sustained neural activity maintained through local recurrent connections is of fundamental importance to cortical function. Converging theoretical and experimental evidence indicates that cortical circuits generating self-sustained dynamics operate in an inhibition-stabilized regime. Theoretical work has established that four sets of weights (WE←E, WE←I, WI←E, and WI←I) must obey specific relationships to produce inhibition-stabilized dynamics, but it is not known how the brain can appropriately set the values of all four weight classes in an unsupervised manner to be in the inhibition-stabilized regime. We prove that standard homeostatic plasticity rules are generally unable to generate inhibition-stabilized dynamics and that their instability is caused by a signature property of inhibition-stabilized networks: the paradoxical effect. In contrast, we show that a family of "cross-homeostatic" rules overcome the paradoxical effect and robustly lead to the emergence of stable dynamics. This work provides a model of how-beginning from a silent network-self-sustained inhibition-stabilized dynamics can emerge from learning rules governing all four synaptic weight classes in an orchestrated manner.

Inhibitory stabilization and cortical computation

Neuronal networks with strong recurrent connectivity provide the brain with a powerful means to perform complex computational tasks. However, high-gain excitatory networks are susceptible to instability, which can lead to runaway activity, as manifested in pathological regimes such as epilepsy. Inhibitory stabilization offers a dynamic, fast and flexible compensatory mechanism to balance otherwise unstable networks, thus enabling the brain to operate in its most efficient regimes. Here we review recent experimental evidence for the presence of such inhibition-stabilized dynamics in the brain and discuss their consequences for cortical computation. We show how the study of inhibition-stabilized networks in the brain has been facilitated by recent advances in the technological toolbox and perturbative techniques, as well as a concomitant development of biologically realistic computational models. By outlining future avenues, we suggest that inhibitory stabilization can offer an exemplary case of how experimental neuroscience can progress in tandem with technology and theory to advance our understanding of the brain.

Competing inhibition-stabilized networks in sensory and memory processing.

In simplified models of neocortical circuits, inhibition is either modeled in a feedforward manner or through mutual inhibitory interactions that provide for competition between neuronal populations. By contrast, recent work has suggested a critical role for recurrent inhibition as a negative feedback element that stabilizes otherwise unstable recurrent excitation. Here, we show how models based upon a motif of recurrently connected "E-I" pairs of excitatory and inhibitory units can be used to describe experimental observations in sensory and memory networks. In a sensory network model of binocular rivalry, a model based on competing E-I motifs captures psychophysical observations about how incongruous images presented to the two eyes compete. In a model of cortical working memory, an architecturally similar model with modified synaptic time constants can mathematically accumulate signals into a working memory buffer in a manner that is robust to the abrupt removal of cells. These results suggest the inhibition-stabilized E-I motif as a fundamental building block for models of a wide array of neocortical dynamics.

Cortical Neural Activity Predicts Sensory Acuity Under Optogenetic Manipulation.

Excitatory and inhibitory neurons in the mammalian sensory cortex form interconnected circuits that control cortical stimulus selectivity and sensory acuity. Theoretical studies have predicted that suppression of inhibition in such excitatory-inhibitory networks can lead to either an increase or, paradoxically, a decrease in excitatory neuronal firing, with consequent effects on stimulus selectivity. We tested whether modulation of inhibition or excitation in the auditory cortex of male mice could evoke such a variety of effects in tone-evoked responses and in behavioral frequency discrimination acuity. We found that, indeed, the effects of optogenetic manipulation on stimulus selectivity and behavior varied in both magnitude and sign across subjects, possibly reflecting differences in circuitry or expression of optogenetic factors. Changes in neural population responses consistently predicted behavioral changes for individuals separately, including improvement and impairment in acuity. This correlation between cortical and behavioral change demonstrates that, despite the complex and varied effects that these manipulations can have on neuronal dynamics, the resulting changes in cortical activity account for accompanying changes in behavioral acuity.SIGNIFICANCE STATEMENT Excitatory and inhibitory interactions determine stimulus specificity and tuning in sensory cortex, thereby controlling perceptual discrimination acuity. Modeling has predicted that suppressing the activity of inhibitory neurons can lead to increased or, paradoxically, decreased excitatory activity depending on the architecture of the network. Here, we capitalized on differences between subjects to test whether suppressing/activating inhibition and excitation can in fact exhibit such paradoxical effects for both stimulus sensitivity and behavioral discriminability. Indeed, the same optogenetic manipulation in the auditory cortex of different mice could improve or impair frequency discrimination acuity, predictable from the effects on cortical responses to tones. The same manipulations sometimes produced opposite changes in the behavior of different individuals, supporting theoretical predictions for inhibition-stabilized networks.

Assessing the Role of Inhibition in Stabilizing Neocortical Networks Requires Large-Scale Perturbation of the Inhibitory Population.

Neurons within cortical microcircuits are interconnected with recurrent excitatory synaptic connections that are thought to amplify signals (Douglas and Martin, 2007), form selective subnetworks (Ko et al., 2011), and aid feature discrimination. Strong inhibition (Haider et al., 2013) counterbalances excitation, enabling sensory features to be sharpened and represented by sparse codes (Willmore et al., 2011). This balance between excitation and inhibition makes it difficult to assess the strength, or gain, of recurrent excitatory connections within cortical networks, which is key to understanding their operational regime and the computations that they perform. Networks that combine an unstable high-gain excitatory population with stabilizing inhibitory feedback are known as inhibition-stabilized networks (ISNs) (Tsodyks et al., 1997). Theoretical studies using reduced network models predict that ISNs produce paradoxical responses to perturbation, but experimental perturbations failed to find evidence for ISNs in cortex (Atallah et al., 2012). Here, we reexamined this question by investigating how cortical network models consisting of many neurons behave after perturbations and found that results obtained from reduced network models fail to predict responses to perturbations in more realistic networks. Our models predict that a large proportion of the inhibitory network must be perturbed to reliably detect an ISN regime robustly in cortex. We propose that wide-field optogenetic suppression of inhibition under promoters targeting a large fraction of inhibitory neurons may provide a perturbation of sufficient strength to reveal the operating regime of cortex. Our results suggest that detailed computational models of optogenetic perturbations are necessary to interpret the results of experimental paradigms.SIGNIFICANCE STATEMENT Many useful computational mechanisms proposed for cortex require local excitatory recurrence to be very strong, such that local inhibitory feedback is necessary to avoid epileptiform runaway activity (an “inhibition-stabilized network” or “ISN” regime). However, recent experimental results suggest that this regime may not exist in cortex. We simulated activity perturbations in cortical networks of increasing realism and found that, to detect ISN-like properties in cortex, large proportions of the inhibitory population must be perturbed. Current experimental methods for inhibitory perturbation are unlikely to satisfy this requirement, implying that existing experimental observations are inconclusive about the computational regime of cortex. Our results suggest that new experimental designs targeting a majority of inhibitory neurons may be able to resolve this question.

Periodic Forcing of Inhibition-Stabilized Networks: Nonlinear Resonances and Phase-Amplitude Coupling.

Inhibition-stabilized networks (ISNs) are neural architectures with strong positive feedback among pyramidal neurons balanced by strong negative feedback from inhibitory interneurons, a circuit element found in the hippocampus and the primary visual cortex. In their working regime, ISNs produce damped oscillations in the [Formula: see text]-range in response to inputs to the inhibitory population. In order to understand the properties of interconnected ISNs, we investigated periodic forcing of ISNs. We show that ISNs can be excited over a range of frequencies and derive properties of the resonance peaks. In particular, we studied the phase-locked solutions, the torus solutions, and the resonance peaks. Periodically forced ISNs respond with (possibly multistable) phase-locked activity, whereas networks with sustained intrinsic oscillations respond more dynamically to periodic inputs with tori. Hence, the dynamics are surprisingly rich, and phase effects alone do not adequately describe thenetwork response. This strengthens the importance of phase-amplitude coupling as opposed to phase-phase coupling in providing multiple frequencies for multiplexing and routing information.

Optimal architectures for fast-learning, flexible networks

Event Abstract Back to Event Optimal architectures for fast-learning, flexible networks Vladimir Itskov1*, Anda Degeratu2 and Carina Curto1 1 University of Nebraska-Lincoln, United States 2 Max Planck Institute, Germany New memories (patterns) in some brain areas, such as hippocampus, can be encoded quickly. Irrespective of the plasticity mechanism (or learning rule) used to encode patterns via changes in synaptic weights, rapid learning is perhaps most easily accomplished if new patterns can be learned via only small modifications of the initial synaptic weights. It may thus be desirable for fast-learning and flexible neural networks to have architectures which enable large numbers of patterns to be encoded by only small perturbations of the synaptic efficacies. What kinds of network architectures have this property? We define the perturbative capacity of a network to be the number of memory patterns that can be learned under small perturbations of the (effective) synaptic weights. We propose that candidate architectures for fast-learning, flexible networks should be networks with high perturbative capacity. What are optimal architectures that maximize a network’s perturbative capacity? We investigate this question for threshold-linear networks. Here the memory patterns encoded by the recurrent network are groups of neurons that co-fire at a stable fixed point for some external input. We prove that for an arbitrary matrix of effective synaptic weights, the network’s memory patterns correspond to stable submatrices. This enables us to study the perturbative capacity of a network by analyzing the eigenvalues of submatrices under small perturbations of the synaptic weights. In the case of symmetric threshold-linear networks, we find (analytically) the set of optimal network architectures that have maximal perturbative capacity. For these networks, any of the possible memory patterns can be selectively encoded via small perturbations of the synaptic weights. We show that these architectures correspond to a highly restricted set of possible sign patterns governing the effective interactions between principal neurons, and we completely describe these patterns. In particular, we find that at least one half of the effective weights must be inhibitory, and thus the optimal architectures reflect inhibition-stabilized networks with a significant level of inhibition. Finally, we study a larger class of threshold-linear networks (where the matrices are no longer assumed symmetric), and find that our qualitative results continue to hold. The optimal architectures we discover provide a benchmark for comparison to experimentally obtainable estimates of the effective interactions between pyramidal neurons in fast-learning networks. They also give clues as to the differences we might expect between recurrent networks in areas such as the hippocampus, and more rigid networks in areas such as primary sensory cortices, where it may be undesirable for the allowed response patterns to be sensitive to small perturbations in synaptic weights. Conference: Computational and Systems Neuroscience 2010, Salt Lake City, UT, United States, 25 Feb - 2 Mar, 2010. Presentation Type: Poster Presentation Topic: Poster session III Citation: Itskov V, Degeratu A and Curto C (2010). Optimal architectures for fast-learning, flexible networks. Front. Neurosci. Conference Abstract: Computational and Systems Neuroscience 2010. doi: 10.3389/conf.fnins.2010.03.00214 Copyright: The abstracts in this collection have not been subject to any Frontiers peer review or checks, and are not endorsed by Frontiers. They are made available through the Frontiers publishing platform as a service to conference organizers and presenters. The copyright in the individual abstracts is owned by the author of each abstract or his/her employer unless otherwise stated. Each abstract, as well as the collection of abstracts, are published under a Creative Commons CC-BY 4.0 (attribution) licence (https://creativecommons.org/licenses/by/4.0/) and may thus be reproduced, translated, adapted and be the subject of derivative works provided the authors and Frontiers are attributed. For Frontiers’ terms and conditions please see https://www.frontiersin.org/legal/terms-and-conditions. Received: 04 Mar 2010; Published Online: 04 Mar 2010. * Correspondence: Vladimir Itskov, University of Nebraska-Lincoln, Lincoln, United States, vitskov2@math.unl.edu Login Required This action requires you to be registered with Frontiers and logged in. To register or login click here. 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