Recurrent networks of submucous neurons controlling intestinal secretion: a modeling study

Secretomotor neurons, immunoreactive for vasoactive intestinal peptide (VIP), are important in controlling chloride secretion in the small intestine. These neurons form functional synapses with other submucosal VIP neurons and transmit via slow excitatory postsynaptic potentials (EPSPs). Thus they form a recurrent network with positive feedback. Intrinsic sensory neurons within the submucosa are also likely to form recurrent networks with positive feedback, provide substantial output to VIP neurons, and receive input from VIP neurons. If positive feedback within recurrent networks is sufficiently large, then neurons in the network respond to even small stimuli by firing at their maximum possible rate, even after the stimulus is removed. However, it is not clear whether such a mechanism operates within the recurrent networks of submucous neurons. We investigated this question by performing computer simulations of realistic models of VIP and intrinsic sensory neuron networks. In the expected range of electrophysiological properties, we found that activity in the VIP neuron network decayed slowly after cessation of a stimulus, indicating that positive feedback is not strong enough to support the uncontrolled firing state. The addition of intrinsic sensory neurons produced a low stable firing rate consistent with the common finding that basal secretory activity is, in part, neurogenic. Changing electrophysiological properties enables these recurrent networks to support the uncontrolled firing state, which may have implications with hypersecretion in the presence of enterotoxins such as cholera-toxin.     

Searching for Optimal Sensory Signals: Iterative Stimulus Reconstruction in Closed-Loop Experiments

Shaped by evolutionary processes, sensory systems often represent behaviorally relevant stimuli with higher fidelity than other stimuli. The stimulus dependence of neural reliability could therefore provide an important clue in a search for relevant sensory signals. We explore this relation and introduce a novel iterative algorithm that allows one to find stimuli that are reliably represented by the sensory system under study. To assess the quality of a neural representation, we use stimulus reconstruction methods. The algorithm starts with the presentation of an initial stimulus (e.g. white noise). The evoked spike train is recorded and used to reconstruct the stimulus online. Within a closed-loop setup, this reconstruction is then played back to the sensory system. Iterating this procedure, the newly generated stimuli can be better and better reconstructed. We demonstrate the feasibility of this method by applying it to auditory receptor neurons in locusts. Our data show that the optimal stimuli often exhibit pronounced sub-threshold periods that are interrupted by short, yet intense pulses. Similar results are obtained for simple model neurons and suggest that these stimuli are encoded with high reliability by a large class of neurons.     

Background-activity-dependent properties of a network model for working memory that incorporates cellular bistability

In models of working memory, transient stimuli are encoded by feature-selective persistent neural activity. Network models of working memory are also implicitly bistable. In the absence of a brief stimulus, only spontaneous, low-level, and presumably nonpatterned neural activity is seen. In many working-memory models, local recurrent excitation combined with long-range inhibition (Mexican hat coupling) can result in a network-induced, spatially localized persistent activity or “bump state” that coexists with a stable uniform state. There is now renewed interest in the concept that individual neurons might have some intrinsic ability to sustain persistent activity without recurrent network interactions. A recent visuospatial working-memory model (Camperi and Wang 1998) incorporates both intrinsic bistability of individual neurons within a firing rate network model and a single population of neurons on a ring with lateral inhibitory coupling. We have explored this model in more detail and have characterized the response properties with changes in background synaptic input I_o and stimulus width. We find that only a small range of I_o yields a working-memory-like coexistence of bump and uniform solutions that are both stable. There is a rather larger range where only the bump solution is stable that might correspond instead to a feature-selective long-term memory. Such a network therefore requires careful tuning to exhibit working-memory-like function. Interestingly, where bumps and uniform stable states coexist, we find a continuous family of stable bumps representing stimulus width. Thus, in the range of parameters corresponding to working memory, the model is capable of capturing a two-parameter family of stimulus features including both orientation and width.     

Spatiotemporal burst coding for extracting features of spatiotemporally varying stimuli

Encoding features of spatiotemporally varying stimuli is quite important for understanding the neural mechanisms of various sensory coding. Temporal coding can encode features of time-varying stimulus, and population coding with temporal coding is adequate for encoding spatiotemporal correlation of stimulus features into spatiotemporal activity of neurons. However, little is known about how spatiotemporal features of stimulus are encoded by spatiotemporal property of neural activity. To address this issue, we propose here a population coding with burst spikes, called here spatiotemporal burst (STB) coding. In STB coding, the temporal variation of stimuli is encoded by the precise onset timing of burst spike, and the spatiotemporal correlation of stimuli is emphasized by one specific aspect of burst firing, or spike packet followed by silent interval. To show concretely the role of STB coding, we study the electrosensory system of a weakly electric fish. Weakly electric fish must perceive the information about an object nearby by analyzing spatiotemporal modulations of electric field around it. On the basis of well-characterized circuitry, we constructed a neural network model of the electrosensory system. Here we show that STB coding encodes well the information of object distance and size by extracting the spatiotemporal correlation of the distorted electric field. The burst activity of electrosensory neurons is also affected by feedback signals through synaptic plasticity. We show that the control of burst activity caused by the synaptic plasticity leads to extracting the stimulus features depending on the stimulus context. Our results suggest that sensory systems use burst spikes as a unit of sensory coding in order to extract spatiotemporal features of stimuli from spatially distributed stimuli.     

Timing as an intrinsic property of neural networks: evidence from in vivo and in vitro experiments

The discrimination and production of temporal patterns on the scale of hundreds of milliseconds are critical to sensory and motor processing. Indeed, most complex behaviours, such as speech comprehension and production, would be impossible in the absence of sophisticated timing mechanisms. Despite the importance of timing to human learning and cognition, little is known about the underlying mechanisms, in particular whether timing relies on specialized dedicated circuits and mechanisms or on general and intrinsic properties of neurons and neural circuits. Here, we review experimental data describing timing and interval-selective neurons in vivo and in vitro. We also review theoretical models of timing, focusing primarily on the state-dependent network model, which proposes that timing in the subsecond range relies on the inherent time-dependent properties of neurons and the active neural dynamics within recurrent circuits. Within this framework, time is naturally encoded in populations of neurons whose pattern of activity is dynamically changing in time. Together, we argue that current experimental and theoretical studies provide sufficient evidence to conclude that at least some forms of temporal processing reflect intrinsic computations based on local neural network dynamics.     

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.     

Associative fear learning enhances sparse network coding in primary sensory cortex

Several models of associative learning predict that stimulus processing changes during association formation. How associative learning reconfigures neural circuits in primary sensory cortex to "learn" associative attributes of a stimulus remains unknown. Using 2-photon in vivo calcium imaging to measure responses of networks of neurons in primary somatosensory cortex, we discovered that associative fear learning, in which whisker stimulation is paired with foot shock, enhances sparse population coding and robustness of the conditional stimulus, yet decreases total network activity. Fewer cortical neurons responded to stimulation of the trained whisker than in controls, yet their response strength was enhanced. These responses were not observed in mice exposed to a nonassociative learning procedure. Our results define how the cortical representation of a sensory stimulus is shaped by associative fear learning. These changes are proposed to enhance efficient sensory processing after associative learning.     

Sound representation methods for spectro-temporal receptive field estimation

The spectro-temporal receptive field (STRF) of an auditory neuron describes the linear relationship between the sound stimulus in a time-frequency representation and the neural response. Time-frequency representations of a sound in turn require a nonlinear operation on the sound pressure waveform and many different forms for this non-linear transformation are possible. Here, we systematically investigated the effects of four factors in the non-linear step in the STRF model: the choice of logarithmic or linear filter frequency spacing, the time-frequency scale, stimulus amplitude compression and adaptive gain control. We quantified the goodness of fit of these different STRF models on data obtained from auditory neurons in the songbird midbrain and forebrain. We found that adaptive gain control and the correct stimulus amplitude compression scheme are paramount to correctly modelling neurons. The time-frequency scale and frequency spacing also affected the goodness of fit of the model but to a lesser extent and the optimal values were stimulus dependant. Action Editor: Israel Nelken     

Detection of multiple stimulus features forces a trade-off in the pyramidal cell network of a gymnotiform electric fish's electrosensory lateral line lobe

Modification of an existing neural structure to support a second function will produce a trade-off between the two functions if they are in some way incompatible. The trade-off between two such sensory functions is modeled here in pyramidal neurons of the gymnotiform electric fish's medullar electrosensory lateral line lobe (ELL). These neurons detect two electric stimulus features produced when a nearby object interferes with the fish's autogenous electric field: (1) amplitude modulation across a cell's entire receptive field and (2) amplitude variation within a cell's receptive field produced by an object's edge. A model of sensory integration shows that detection of amplitude modulation and enhancement of spatial contrast involve an inherent mechanistic trade-off and that the severity of the trade-off depends on the particular algorithm of sensory integration. Electrophysiology data indicate that of the two algorithms for sensory integration modeled here for the gymnotiform fish Brachyhypopomus pinnicaudatus, the algorithm with the better trade-off function is used. Further, the intrinsic trade-off within single cells has been surmounted by the replication of ELL into multiple electrosensory map segments, each specialized to emphasize different sensory features. Accepted: 14 June 1997     

Firing pattern of bursting neurons under sinusoidal drive in mean-field modeling

Bursting has been observed in many sensory neurons, and is thought to be important in neural signaling, sleep, and some disorders of the brain. Bursting neurons have been studied via various types of conductance-based models at the single-neuron level. Important features of bursting have been reproduced by this type of model, but it is not certain how well the behavior of populations of bursting neurons can be represented solely by that of individual neurons. To study bursting neurons at the population level, a conductance-based model is incorporated into a mean-field model to yield a mean-field bursting model. The responses of the model to sinusoidal inputs are studied, showing that neurons with various different initial states are capable of phase-locked or intermittent firing, depending on their baseline voltage. Furthermore, depending on this voltage, the bursting frequency either slaves to the original unperturbed bursting frequency or approaches a steady value when the external driving frequency increases. Finally, use of white noise perturbations shows that the bursting frequency of the neurons remains the same even under a more general external stimulus.     

Stimulus detection after interruption of the feedforward response in a backward masking paradigm

In backward masking, a target stimulus is rendered invisible by the presentation of a second stimulus, the mask. When the mask is effective, neural responses to the target are suppressed. Nevertheless, weak target responses sometimes may produce a behavioural response. It remains unclear whether the reduced target response is a purely feedforward response or that it includes recurrent activity. Using a feedforward neural network of biological plausible spiking neurons, we tested whether a transient spike burst is sufficient for face categorization. After training the network, the system achieved face/non-face categorization for sets of grayscale images. In a backward masking paradigm, the transient burst response was cut off thereby reducing the feedforward target response. Despite the suppressed feedforward responses stimulus classification remained robust. Thus according to our model data stimulus detection is possible with purely, suppressed feedforward responses.     

To Burst or Not to Burst?

It is well known that some neurons tend to fire packets of action potentials followed by periods of quiescence (bursts) while others within the same stage of sensory processing fire in a tonic manner. However, the respective computational advantages of bursting and tonic neurons for encoding time varying signals largely remain a mystery. Weakly electric fish use cutaneous electroreceptors to convey information about sensory stimuli and it has been shown that some electroreceptors exhibit bursting dynamics while others do not. In this study, we compare the neural coding capabilities of tonically firing and bursting electroreceptor model neurons using information theoretic measures. We find that both bursting and tonically firing model neurons efficiently transmit information about the stimulus. However, the decoding mechanisms that must be used for each differ greatly: a non-linear decoder would be required to extract all the available information transmitted by the bursting model neuron whereas a linear one might suffice for the tonically firing model neuron. Further investigations using stimulus reconstruction techniques reveal that, unlike the tonically firing model neuron, the bursting model neuron does not encode the detailed time course of the stimulus. A novel measure of feature detection reveals that the bursting neuron signals certain stimulus features. Finally, we show that feature extraction and stimulus estimation are mutually exclusive computations occurring in bursting and tonically firing model neurons, respectively. Our results therefore suggest that stimulus estimation and feature extraction might be parallel computations in certain sensory systems rather than being sequential as has been previously proposed.     

Narrative event segmentation in the cortical reservoir

Recent research has revealed that during continuous perception of movies or stories, humans display cortical activity patterns that reveal hierarchical segmentation of event structure. Thus, sensory areas like auditory cortex display high frequency segmentation related to the stimulus, while semantic areas like posterior middle cortex display a lower frequency segmentation related to transitions between events. These hierarchical levels of segmentation are associated with different time constants for processing. Likewise, when two groups of participants heard the same sentence in a narrative, preceded by different contexts, neural responses for the groups were initially different and then gradually aligned. The time constant for alignment followed the segmentation hierarchy: sensory cortices aligned most quickly, followed by mid-level regions, while some higher-order cortical regions took more than 10 seconds to align. These hierarchical segmentation phenomena can be considered in the context of processing related to comprehension. In a recently described model of discourse comprehension word meanings are modeled by a language model pre-trained on a billion word corpus. During discourse comprehension, word meanings are continuously integrated in a recurrent cortical network. The model demonstrates novel discourse and inference processing, in part because of two fundamental characteristics: real-world event semantics are represented in the word embeddings, and these are integrated in a reservoir network which has an inherent gradient of functional time constants due to the recurrent connections. Here we demonstrate how this model displays hierarchical narrative event segmentation properties beyond the embeddings alone, or their linear integration. The reservoir produces activation patterns that are segmented by a hidden Markov model (HMM) in a manner that is comparable to that of humans. Context construction displays a continuum of time constants across reservoir neuron subsets, while context forgetting has a fixed time constant across these subsets. Importantly, virtual areas formed by subgroups of reservoir neurons with faster time constants segmented with shorter events, while those with longer time constants preferred longer events. This neurocomputational recurrent neural network simulates narrative event processing as revealed by the fMRI event segmentation algorithm provides a novel explanation of the asymmetry in narrative forgetting and construction. The model extends the characterization of online integration processes in discourse to more extended narrative, and demonstrates how reservoir computing provides a useful model of cortical processing of narrative structure.     

Predicting human perceptual decisions by decoding neuronal information profiles

Perception relies on the response of populations of neurons in sensory cortex. How the response profile of a neuronal population gives rise to perception and perceptual discrimination has been conceptualized in various ways. Here we suggest that neuronal population responses represent information about our environment explicitly as Fisher information (FI), which is a local measure of the variance estimate of the sensory input. We show how this sensory information can be read out and combined to infer from the available information profile which stimulus value is perceived during a fine discrimination task. In particular, we propose that the perceived stimulus corresponds to the stimulus value that leads to the same information for each of the alternative directions, and compare the model prediction to standard models considered in the literature (population vector, maximum likelihood, maximum-a-posteriori Bayesian inference). The models are applied to human performance in a motion discrimination task that induces perceptual misjudgements of a target direction of motion by task irrelevant motion in the spatial surround of the target stimulus (motion repulsion). By using the neurophysiological insight that surround motion suppresses neuronal responses to the target motion in the center, all models predicted the pattern of perceptual misjudgements. The variation of discrimination thresholds (error on the perceived value) was also explained through the changes of the total FI content with varying surround motion directions. The proposed FI decoding scheme incorporates recent neurophysiological evidence from macaque visual cortex showing that perceptual decisions do not rely on the most active neurons, but rather on the most informative neuronal responses. We statistically compare the prediction capability of the FI decoding approach and the standard decoding models. Notably, all models reproduced the variation of the perceived stimulus values for different surrounds, but with different neuronal tuning characteristics underlying perception. Compared to the FI approach the prediction power of the standard models was based on neurons with far wider tuning width and stronger surround suppression. Our study demonstrates that perceptual misjudgements can be based on neuronal populations encoding explicitly the available sensory information, and provides testable neurophysiological predictions on neuronal tuning characteristics underlying human perceptual decisions.     

Sparsity and Compressed Coding in Sensory Systems

Considering that many natural stimuli are sparse, can a sensory system evolve to take advantage of this sparsity? We explore this question and show that significant downstream reductions in the numbers of neurons transmitting stimuli observed in early sensory pathways might be a consequence of this sparsity. First, we model an early sensory pathway using an idealized neuronal network comprised of receptors and downstream sensory neurons. Then, by revealing a linear structure intrinsic to neuronal network dynamics, our work points to a potential mechanism for transmitting sparse stimuli, related to compressed-sensing (CS) type data acquisition. Through simulation, we examine the characteristics of networks that are optimal in sparsity encoding, and the impact of localized receptive fields beyond conventional CS theory. The results of this work suggest a new network framework of signal sparsity, freeing the notion from any dependence on specific component-space representations. We expect our CS network mechanism to provide guidance for studying sparse stimulus transmission along realistic sensory pathways as well as engineering network designs that utilize sparsity encoding.     

Variable synaptic strengths controls the firing rate distribution in feedforward neural networks

Heterogeneity of firing rate statistics is known to have severe consequences on neural coding. Recent experimental recordings in weakly electric fish indicate that the distribution-width of superficial pyramidal cell firing rates (trial- and time-averaged) in the electrosensory lateral line lobe (ELL) depends on the stimulus, and also that network inputs can mediate changes in the firing rate distribution across the population. We previously developed theoretical methods to understand how two attributes (synaptic and intrinsic heterogeneity) interact and alter the firing rate distribution in a population of integrate-and-fire neurons with random recurrent coupling. Inspired by our experimental data, we extend these theoretical results to a delayed feedforward spiking network that qualitatively capture the changes of firing rate heterogeneity observed in in-vivo recordings. We demonstrate how heterogeneous neural attributes alter firing rate heterogeneity, accounting for the effect with various sensory stimuli. The model predicts how the strength of the effective network connectivity is related to intrinsic heterogeneity in such delayed feedforward networks: the strength of the feedforward input is positively correlated with excitability (threshold value for spiking) when firing rate heterogeneity is low and is negatively correlated with excitability with high firing rate heterogeneity. We also show how our theory can be used to predict effective neural architecture. We demonstrate that neural attributes do not interact in a simple manner but rather in a complex stimulus-dependent fashion to control neural heterogeneity and discuss how it can ultimately shape population codes.     

Spectro-temporal interpretation of activity patterns of auditory neurons

Sensory receptors transform an external sensory stimulus into an internal neural activity pattern. This mapping is studied through its inverse. An earlier paper showed that within the context of a neuron model composed of a linear filter followed by an exponential pulse generator and a Gaussian stimulus ensemble a unique "most plausible" first-order stimulus estimate can be constructed. This method, applicable only to neurons showing phase-lock, is extended to neurons without phase-lock. In this situation second-order spectro-temporal stimulus estimates are produced; examples are given from simulation. The method is applied to activity of neurons in the auditory system of the frog.     

Transitions between asynchronous and synchronous states: a theory of correlations in small neural circuits

The study of correlations in neural circuits of different size, from the small size of cortical microcolumns to the large-scale organization of distributed networks studied with functional imaging, is a topic of central importance to systems neuroscience. However, a theory that explains how the parameters of mesoscopic networks composed of a few tens of neurons affect the underlying correlation structure is still missing. Here we consider a theory that can be applied to networks of arbitrary size with multiple populations of homogeneous fully-connected neurons, and we focus its analysis to a case of two populations of small size. We combine the analysis of local bifurcations of the dynamics of these networks with the analytical calculation of their cross-correlations. We study the correlation structure in different regimes, showing that a variation of the external stimuli causes the network to switch from asynchronous states, characterized by weak correlation and low variability, to synchronous states characterized by strong correlations and wide temporal fluctuations. We show that asynchronous states are generated by strong stimuli, while synchronous states occur through critical slowing down when the stimulus moves the network close to a local bifurcation. In particular, strongly positive correlations occur at the saddle-node and Andronov-Hopf bifurcations of the network, while strongly negative correlations occur when the network undergoes a spontaneous symmetry-breaking at the branching-point bifurcations. These results show how the correlation structure of firing-rate network models is strongly modulated by the external stimuli, even keeping the anatomical connections fixed. These results also suggest an effective mechanism through which biological networks may dynamically modulate the encoding and integration of sensory information.