Neural circuit models for computations in early visual cortex

Some cortical circuit models study the mechanisms of the transforms from visual inputs to neural responses. They model neural properties such as feature tunings, pattern sensitivities, and how they depend on intracortical connections and contextual inputs. Other cortical circuit models are more concerned with computational goals of the transform from visual inputs to neural responses, or the roles of the neural responses in the visual behavior. The appropriate complexity of a cortical circuit model depends on the question asked. Modeling neural circuits of many interacting hypercolumns is a necessary challenge, which is providing insights to cortical computations, such as visual saliency computation, and linking physiology with global visual cognitive behavior such as bottom-up attentional selection.     

Criticality enhances the multilevel reliability of stimulus responses in cortical neural networks

Cortical neural networks exhibit high internal variability in spontaneous dynamic activities and they can robustly and reliably respond to external stimuli with multilevel features–from microscopic irregular spiking of neurons to macroscopic oscillatory local field potential. A comprehensive study integrating these multilevel features in spontaneous and stimulus–evoked dynamics with seemingly distinct mechanisms is still lacking. Here, we study the stimulus–response dynamics of biologically plausible excitation–inhibition (E–I) balanced networks. We confirm that networks around critical synchronous transition states can maintain strong internal variability but are sensitive to external stimuli. In this dynamical region, applying a stimulus to the network can reduce the trial-to-trial variability and shift the network oscillatory frequency while preserving the dynamical criticality. These multilevel features widely observed in different experiments cannot simultaneously occur in non-critical dynamical states. Furthermore, the dynamical mechanisms underlying these multilevel features are revealed using a semi-analytical mean-field theory that derives the macroscopic network field equations from the microscopic neuronal networks, enabling the analysis by nonlinear dynamics theory and linear noise approximation. The generic dynamical principle revealed here contributes to a more integrative understanding of neural systems and brain functions and incorporates multimodal and multilevel experimental observations. The E–I balanced neural network in combination with the effective mean-field theory can serve as a mechanistic modeling framework to study the multilevel neural dynamics underlying neural information and cognitive processes.     

Balanced input allows optimal encoding in a stochastic binary neural network model: an analytical study

Recent neurophysiological experiments have demonstrated a remarkable effect of attention on the underlying neural activity that suggests for the first time that information encoding is indeed actively influenced by attention. Single cell recordings show that attention reduces both the neural variability and correlations in the attended condition with respect to the non-attended one. This reduction of variability and redundancy enhances the information associated with the detection and further processing of the attended stimulus. Beyond the attentional paradigm, the local activity in a neural circuit can be modulated in a number of ways, leading to the general question of understanding how the activity of such circuits is sensitive to these relatively small modulations. Here, using an analytically tractable neural network model, we demonstrate how this enhancement of information emerges when excitatory and inhibitory synaptic currents are balanced. In particular, we show that the network encoding sensitivity--as measured by the Fisher information--is maximized at the exact balance. Furthermore, we find a similar result for a more realistic spiking neural network model. As the regime of balanced inputs has been experimentally observed, these results suggest that this regime is functionally important from an information encoding standpoint.     

Characterising neural representation in terms of the dynamics of cell membrane potential activity: a control theoretic approach using differential geometry

Experimental and theoretical results seem to demand that the study of neural representations in the brain considers both the subthreshold and suprathreshold dynamic activity of the neural membrane potential, rather than be solely focussed on stimulus representation in trains of action potentials. In a dynamical systems formulation, the membrane potential can be regarded as the "state" of the neuron, evolving continuously over time and space, within an infinite dimensional space, in response to ever changing inputs. Formally, the state of the neuron, together with future inputs, is sufficient to fully determine the future behaviour of the neuron. In this paper, the characterisation of membrane potential activity is approached from a control theoretic viewpoint as a "reachability" problem, in which the effect of particular stimulus-evoked synaptic inputs is seen as driving the cell from some initial state of the neuron to a particular terminal state on a given manifold. It is shown that a fluctuating subthreshold membrane potential induced by synaptic background activity, and the cooperative interaction of excitatory and inhibitory inputs, may be important factors in allowing the cell to "reach" a maximal subset of all possible membrane potential states, through the action of its synaptic inputs.     

Role of delayed nonsynaptic neuronal plasticity in long-term associative memory

BACKGROUND: It is now well established that persistent nonsynaptic neuronal plasticity occurs after learning and, like synaptic plasticity, it can be the substrate for long-term memory. What still remains unclear, though, is how nonsynaptic plasticity contributes to the altered neural network properties on which memory depends. Understanding how nonsynaptic plasticity is translated into modified network and behavioral output therefore represents an important objective of current learning and memory research. RESULTS: By using behavioral single-trial classical conditioning together with electrophysiological analysis and calcium imaging, we have explored the cellular mechanisms by which experience-induced nonsynaptic electrical changes in a neuronal soma remote from the synaptic region are translated into synaptic and circuit level effects. We show that after single-trial food-reward conditioning in the snail Lymnaea stagnalis, identified modulatory neurons that are extrinsic to the feeding network become persistently depolarized between 16 and 24 hr after training. This is delayed with respect to early memory formation but concomitant with the establishment and duration of long-term memory. The persistent nonsynaptic change is extrinsic to and maintained independently of synaptic effects occurring within the network directly responsible for the generation of feeding. Artificial membrane potential manipulation and calcium-imaging experiments suggest a novel mechanism whereby the somal depolarization of an extrinsic neuron recruits command-like intrinsic neurons of the circuit underlying the learned behavior. CONCLUSIONS: We show that nonsynaptic plasticity in an extrinsic modulatory neuron encodes information that enables the expression of long-term associative memory, and we describe how this information can be translated into modified network and behavioral output.     

Network, cellular and molecular mechanisms of plasticity in simple nervous systems

In the present study we will try to single out several principles of the nervous system functioning essential for describing mechanisms of learning and memory basing on our own experimental investigation of cellular mechanisms of memory in the nervous system of gastropod molluscs and literature data: main changes in functioning due to learning occur in effectivity of synaptic inputs and in the intrinsic properties of postsynaptic neurons; due to learning some synaptic inputs of neurons selectively change its effectivity due to pre- and postsynaptic changes, but the induction of plasticity always starts in postsynapse, maintaining of long-term memory in postsynapse is also shown; reinforcement is not related to activity of the neural chain receptor-sensory neuron-interneuron-motoneuron-effector; reinforcement is mediated via activity of modulatory neurons, and in some cases can be exerted by a single neuron; activity of modulatory neurons is necessary for development of plastic modifications of behavior (including associative), but is not needed for recall of conditioned responses. At the same time, the modulatory neurons (in fact they constitute a neural reinforcement system) are necessary for recall of context associative memory; changes due to learning occur at least in two independent loci in the nervous system. A possibility for erasure of memory with participation of nitroxide is experimentally and theoretically based.     

A persistent cellular change in a single modulatory neuron contributes to associative long-term memory

Most neuronal models of learning assume that changes in synaptic strength are the main mechanism underlying long-term memory (LTM) formation. However, we show here that a persistent depolarization of membrane potential, a type of cellular change that increases neuronal responsiveness, contributes significantly to a long-lasting associative memory trace. The use of a model invertebrate network with identified neurons and known synaptic connectivity had the advantage that the contribution of this cellular change to memory could be evaluated in a neuron with a known function in the learning circuit. Specifically, we used the well-understood motor circuit underlying molluscan feeding and showed that a key modulatory neuron involved in the initiation of feeding ingestive movements underwent a long-term depolarization following behavioral associative conditioning. This depolarization led to an enhanced single cell and network responsiveness to a previously neutral tactile conditioned stimulus, and the persistence of both matched the time course of behavioral associative memory. The change in the membrane potential of a key modulatory neuron is both sufficient and necessary to initiate a conditioned response in a reduced preparation and underscores its importance for associative LTM.     

Effects of neuromodulation in a cortical network model of object working memory dominated by recurrent inhibition

Experimental evidence suggests that the maintenance of an item in working memory is achieved through persistent activity in selective neural assemblies of the cortex. To understand the mechanisms underlying this phenomenon, it is essential to investigate how persistent activity is affected by external inputs or neuromodulation. We have addressed these questions using a recurrent network model of object working memory. Recurrence is dominated by inhibition, although persistent activity is generated through recurrent excitation in small subsets of excitatory neurons.Our main findings are as follows. (1) Because of the strong feedback inhibition, persistent activity shows an inverted U shape as a function of increased external drive to the network. (2) A transient external excitation can switch off a network from a selective persistent state to its spontaneous state. (3) The maintenance of the sample stimulus in working memory is not affected by intervening stimuli (distractors) during the delay period, provided the stimulation intensity is not large. On the other hand, if stimulation intensity is large enough, distractors disrupt sample-related persistent activity, and the network is able to maintain a memory only of the last shown stimulus. (4) A concerted modulation of GABA _A and NMDA conductances leads to a decrease of spontaneous activity but an increase of persistent activity; the enhanced signal-to-noise ratio is shown to increase the resistance of the network to distractors. (5) Two mechanisms are identified that produce an inverted U shaped dependence of persistent activity on modulation. The present study therefore points to several mechanisms that enhance the signal-to-noise ratio in working memory states. These mechanisms could be implemented in the prefrontal cortex by dopaminergic projections from the midbrain.     

Habituation and dishabituation mediated by the peripheral and central neural circuits of the siphon of aplysia

The siphon withdrawal response evoked by a weak tactile (water drop) or light stimulus is mediated primarily by neurons in the siphon. Central neurons (abdominal ganglion) contribute very little since the response amplitude and latency are not changed following removal of the abdominal ganglion. Similarly, habituation and dishabituation of this withdrawal response are not different after removal of the abdominal ganglion, indicating that the peripheral neural circuit in the isolated siphon can mediate habituation itself, and thus has many of the properties attributed to central neurons. Responses evoked by electrical stimulation of the siphon nerve habituate, depending upon the stimulus intensity and interval. These habituated responses may be dishabituated by tactile or light stimulation of the siphon. These results show that each neural system, peripheral and central, has an excitatory modulatory influence on the other. Normally adaptive siphon responses must be shaped by the integrated activity of both of these neural systems.     

Habituation and dishabituation mediated by the peripheral and central neural circuits of the siphon of Aplysia.

The siphon withdrawal response evoked by a weak tactile (water drop) or light stimulus is mediated primarily by neurons in the siphon. Central neurons (abdominal ganglion) contribute very little since the response amplitude and latency are not changed following removal of the abdominal ganglion. Similarly, habituation and dishabituation of this withdrawal response are not different after removal of the abdominal ganglion, indicating that the peripheral neural circuit in the isolated siphon can mediate habituation itself, and thus has many of the properties attributed to central neurons. Response evoked by electrical stimulation of the siphon nerve habituate, depending upon the stimulus intensity and interval. These habituated responses may be dishabituated by tactile or light stimulation of the siphon. These results show that each neural system, peripheral and central, has an excitatory modulatory influence on the other. Normally adaptive siphon responses must be shaped by the integrated activity of both of these neural systems.     

Where’s the Noise? Key Features of Spontaneous Activity and Neural Variability Arise through Learning in a Deterministic Network

Even in the absence of sensory stimulation the brain is spontaneously active. This background “noise” seems to be the dominant cause of the notoriously high trial-to-trial variability of neural recordings. Recent experimental observations have extended our knowledge of trial-to-trial variability and spontaneous activity in several directions: 1. Trial-to-trial variability systematically decreases following the onset of a sensory stimulus or the start of a motor act. 2. Spontaneous activity states in sensory cortex outline the region of evoked sensory responses. 3. Across development, spontaneous activity aligns itself with typical evoked activity patterns. 4. The spontaneous brain activity prior to the presentation of an ambiguous stimulus predicts how the stimulus will be interpreted. At present it is unclear how these observations relate to each other and how they arise in cortical circuits. Here we demonstrate that all of these phenomena can be accounted for by a deterministic self-organizing recurrent neural network model (SORN), which learns a predictive model of its sensory environment. The SORN comprises recurrently coupled populations of excitatory and inhibitory threshold units and learns via a combination of spike-timing dependent plasticity (STDP) and homeostatic plasticity mechanisms. Similar to balanced network architectures, units in the network show irregular activity and variable responses to inputs. Additionally, however, the SORN exhibits sequence learning abilities matching recent findings from visual cortex and the network’s spontaneous activity reproduces the experimental findings mentioned above. Intriguingly, the network’s behaviour is reminiscent of sampling-based probabilistic inference, suggesting that correlates of sampling-based inference can develop from the interaction of STDP and homeostasis in deterministic networks. We conclude that key observations on spontaneous brain activity and the variability of neural responses can be accounted for by a simple deterministic recurrent neural network which learns a predictive model of its sensory environment via a combination of generic neural plasticity mechanisms.     

Cellular mechanisms of behavioural plasticity in simple nervous systems

In the present study, we will try to single out several principles of the nervous system functioning essential for describing the mechanisms of learning and memory, basing on our own experimental investigation of cellular mechanisms of memory in the nervous system of gastropod molluscs and literature data as follows: (1) Main changes in functioning due to learning occur in the interneurons; (2) Due to learning some synaptic inputs of command neurons selectively change its effectivity; (3) Reinforcement is not related to activity of the neural chain receptor-sensory neuron-interneuron-motoneuron-effector; reinforcement is mediated via activity of modulatory neurons, and in some cases can be exerted by a single neuron; (4) Activity of modulatory neurons is necessary for development of plastic modifications of behaviour (including associative), but is not needed for recall of conditioned responses. At the same time, the modulatory neurons (in fact they constitute a neural reinforcement system) are necessary for recall of context associative memory; (5) Changes due to learning occur at least in two independent loci in the nervous system.     

Neuromodulation and flexibility in Central Pattern Generator networks

Central Pattern Generator (CPG) networks, which organize rhythmic movements, have long served as models for neural network organization. Modulatory inputs are essential components of CPG function: neuromodulators set the parameters of CPG neurons and synapses to render the networks functional. Each modulator acts on the network by many effects which may oppose one another; this may serve to stabilize the modulated state. Neuromodulators also determine the active neuronal composition in the CPG, which varies with state changes such as locomotor speed. The pattern of gene expression which determines the electrophysiological personality of each CPG neuron is also under modulatory control. It is not possible to model the function of neural networks without including the actions of neuromodulators.     

Sensory experience modifies spontaneous state dynamics in a large-scale barrel cortical model

Experimental evidence suggests that spontaneous neuronal activity may shape and be shaped by sensory experience. However, we lack information on how sensory experience modulates the underlying synaptic dynamics and how such modulation influences the response of the network to future events. Here we study whether spike-timing-dependent plasticity (STDP) can mediate sensory-induced modifications in the spontaneous dynamics of a new large-scale model of layers II, III and IV of the rodent barrel cortex. Our model incorporates significant physiological detail, including the types of neurons present, the probabilities and delays of connections, and the STDP profiles at each excitatory synapse. We stimulated the neuronal network with a protocol of repeated sensory inputs resembling those generated by the protraction-retraction motion of whiskers when rodents explore their environment, and studied the changes in network dynamics. By applying dimensionality reduction techniques to the synaptic weight space, we show that the initial spontaneous state is modified by each repetition of the stimulus and that this reverberation of the sensory experience induces long-term, structured modifications in the synaptic weight space. The post-stimulus spontaneous state encodes a memory of the stimulus presented, since a different dynamical response is observed when the network is presented with shuffled stimuli. These results suggest that repeated exposure to the same sensory experience could induce long-term circuitry modifications via 'Hebbian' STDP plasticity.     

Phylogenetic,ontogenetic and adult adaptive plasticity of rhythmic neural networks: a common neuromodulatory mechanism?

Neuromodulatory inputs are known to play a major role in the adaptive plasticity of rhythmic neural networks in adult animals. Using the crustacean stomatogastric nervous system, we have investigated the role of modulatory inputs in the development of rhythmic neural networks. We found that the same neuronal population is organised into a single network in the embryo, as opposed to the two networks present in the adult. However, these adult networks pre-exist in the embryo and can be unmasked by specific alterations of the neuromodulatory environment. Similarly, adult networks may switch back to the embryonic phenotype by manipulating neuromodulatory inputs. During development, we found that the early established neuromodulatory population display alteration in expressed neurotransmitter phenotypes, and that although the population of modulatory neurones is established early, with morphology and projection pattern similar to adult ones, their neurotransmitter phenotype may appear gradually. Therefore the abrupt switch from embryonic to adult network expression occurring at metamorphosis may be due to network reconfiguration in response to changes in modulatory input, as found in adult adaptive plasticity. Strikingly, related crustacean species express different motor outputs using the same basic network circuitry, due to species-specific alteration in neuromodulatory substances within homologous projecting neurones. Therefore we propose that alterations within neuromodulatory systems to a given rhythmic neural network displaying the same basic circuitry may account for the generation of different motor outputs throughout development (ontogenetic plasticity), adulthood (adaptive plasticity) and evolution (phylogenetic plasticity).Abbreviations CoG Commissural ganglion - OG Oesophageal ganglion - STG Stomatogastric ganglion - STNS Stomatogastric nervous system     

A single functional model of drivers and modulators in cortex

A distinction is commonly made between synaptic connections capable of evoking a response (“drivers”) and those that can alter ongoing activity but not initiate it (“modulators”). Here it is proposed that, in cortex, both drivers and modulators are an emergent property of the perceptual inference performed by cortical circuits. Hence, it is proposed that there is a single underlying computational explanation for both forms of synaptic connection. This idea is illustrated using a predictive coding model of cortical perceptual inference. In this model all synaptic inputs are treated identically. However, functionally, certain synaptic inputs drive neural responses while others have a modulatory influence. This model is shown to account for driving and modulatory influences in bottom-up, lateral, and top-down pathways, and is used to simulate a wide range of neurophysiological phenomena including surround suppression, contour integration, gain modulation, spatio-temporal prediction, and attention. The proposed computational model thus provides a single functional explanation for drivers and modulators and a unified account of a diverse range of neurophysiological data.     

Representational switching by dynamical reorganization of attractor structure in a network model of the prefrontal cortex

The prefrontal cortex (PFC) plays a crucial role in flexible cognitive behavior by representing task relevant information with its working memory. The working memory with sustained neural activity is described as a neural dynamical system composed of multiple attractors, each attractor of which corresponds to an active state of a cell assembly, representing a fragment of information. Recent studies have revealed that the PFC not only represents multiple sets of information but also switches multiple representations and transforms a set of information to another set depending on a given task context. This representational switching between different sets of information is possibly generated endogenously by flexible network dynamics but details of underlying mechanisms are unclear. Here we propose a dynamically reorganizable attractor network model based on certain internal changes in synaptic connectivity, or short-term plasticity. We construct a network model based on a spiking neuron model with dynamical synapses, which can qualitatively reproduce experimentally demonstrated representational switching in the PFC when a monkey was performing a goal-oriented action-planning task. The model holds multiple sets of information that are required for action planning before and after representational switching by reconfiguration of functional cell assemblies. Furthermore, we analyzed population dynamics of this model with a mean field model and show that the changes in cell assemblies' configuration correspond to those in attractor structure that can be viewed as a bifurcation process of the dynamical system. This dynamical reorganization of a neural network could be a key to uncovering the mechanism of flexible information processing in the PFC.     

The response of cortical neurons to in vivo-like input current: theory and experiment: II. Time-varying and spatially distributed inputs

The response of a population of neurons to time-varying synaptic inputs can show a rich phenomenology, hardly predictable from the dynamical properties of the membrane’s inherent time constants. For example, a network of neurons in a state of spontaneous activity can respond significantly more rapidly than each single neuron taken individually. Under the assumption that the statistics of the synaptic input is the same for a population of similarly behaving neurons (mean field approximation), it is possible to greatly simplify the study of neural circuits, both in the case in which the statistics of the input are stationary (reviewed in La Camera et al. in Biol Cybern, 2008) and in the case in which they are time varying and unevenly distributed over the dendritic tree. Here, we review theoretical and experimental results on the single-neuron properties that are relevant for the dynamical collective behavior of a population of neurons. We focus on the response of integrate-and-fire neurons and real cortical neurons to long-lasting, noisy, in vivo-like stationary inputs and show how the theory can predict the observed rhythmic activity of cultures of neurons. We then show how cortical neurons adapt on multiple time scales in response to input with stationary statistics in vitro. Next, we review how it is possible to study the general response properties of a neural circuit to time-varying inputs by estimating the response of single neurons to noisy sinusoidal currents. Finally, we address the dendrite–soma interactions in cortical neurons leading to gain modulation and spike bursts, and show how these effects can be captured by a two-compartment integrate-and-fire neuron. Most of the experimental results reviewed in this article have been successfully reproduced by simple integrate-and-fire model neurons.     

Integrated mechanisms of anticipation and rate-of-change computations in cortical circuits

Local neocortical circuits are characterized by stereotypical physiological and structural features that subserve generic computational operations. These basic computations of the cortical microcircuit emerge through the interplay of neuronal connectivity, cellular intrinsic properties, and synaptic plasticity dynamics. How these interacting mechanisms generate specific computational operations in the cortical circuit remains largely unknown. Here, we identify the neurophysiological basis of both the rate of change and anticipation computations on synaptic inputs in a cortical circuit. Through biophysically realistic computer simulations and neuronal recordings, we show that the rate-of-change computation is operated robustly in cortical networks through the combination of two ubiquitous brain mechanisms: short-term synaptic depression and spike-frequency adaptation. We then show how this rate-of-change circuit can be embedded in a convergently connected network to anticipate temporally incoming synaptic inputs, in quantitative agreement with experimental findings on anticipatory responses to moving stimuli in the primary visual cortex. Given the robustness of the mechanism and the widespread nature of the physiological machinery involved, we suggest that rate-of-change computation and temporal anticipation are principal, hard-wired functions of neural information processing in the cortical microcircuit.     

Switching neuronal state: optimal stimuli revealed using a stochastically-seeded gradient algorithm

Inducing a switch in neuronal state using energy optimal stimuli is relevant to a variety of problems in neuroscience. Analytical techniques from optimal control theory can identify such stimuli; however, solutions to the optimization problem using indirect variational approaches can be elusive in models that describe neuronal behavior. Here we develop and apply a direct gradient-based optimization algorithm to find stimulus waveforms that elicit a change in neuronal state while minimizing energy usage. We analyze standard models of neuronal behavior, the Hodgkin-Huxley and FitzHugh-Nagumo models, to show that the gradient-based algorithm: 1) enables automated exploration of a wide solution space, using stochastically generated initial waveforms that converge to multiple locally optimal solutions; and 2) finds optimal stimulus waveforms that achieve a physiological outcome condition, without a priori knowledge of the optimal terminal condition of all state variables. Analysis of biological systems using stochastically-seeded gradient methods can reveal salient dynamical mechanisms underlying the optimal control of system behavior. The gradient algorithm may also have practical applications in future work, for example, finding energy optimal waveforms for therapeutic neural stimulation that minimizes power usage and diminishes off-target effects and damage to neighboring tissue.