Optimal heterogeneity for coding in spiking neural networks

Neural populations within macaque early vestibular pathways are adapted to encode natural self-motion

How the activities of large neural populations are integrated in the brain to ensure accurate perception and behavior remains a central problem in systems neuroscience. Here, we investigated population coding of naturalistic self-motion by neurons within early vestibular pathways in rhesus macaques (Macacca mulatta). While vestibular neurons displayed similar dynamic tuning to self-motion, inspection of their spike trains revealed significant heterogeneity. Further analysis revealed that, during natural but not artificial stimulation, heterogeneity resulted primarily from variability across neurons as opposed to trial-to-trial variability. Interestingly, vestibular neurons displayed different correlation structures during naturalistic and artificial self-motion. Specifically, while correlations due to the stimulus (i.e., signal correlations) did not differ, correlations between the trial-to-trial variabilities of neural responses (i.e., noise correlations) were instead significantly positive during naturalistic but not artificial stimulation. Using computational modeling, we show that positive noise correlations during naturalistic stimulation benefits information transmission by heterogeneous vestibular neural populations. Taken together, our results provide evidence that neurons within early vestibular pathways are adapted to the statistics of natural self-motion stimuli at the population level. We suggest that similar adaptations will be found in other systems and species.

Neural heterogeneity controls computations in spiking neural networks

The brain is composed of complex networks of interacting neurons that express considerable heterogeneity in their physiology and spiking characteristics. How does this neural heterogeneity influence macroscopic neural dynamics, and how might it contribute to neural computation? In this work, we use a mean-field model to investigate computation in heterogeneous neural networks, by studying how the heterogeneity of cell spiking thresholds affects three key computational functions of a neural population: the gating, encoding, and decoding of neural signals. Our results suggest that heterogeneity serves different computational functions in different cell types. In inhibitory interneurons, varying the degree of spike threshold heterogeneity allows them to gate the propagation of neural signals in a reciprocally coupled excitatory population. Whereas homogeneous interneurons impose synchronized dynamics that narrow the dynamic repertoire of the excitatory neurons, heterogeneous interneurons act as an inhibitory offset while preserving excitatory neuron function. Spike threshold heterogeneity also controls the entrainment properties of neural networks to periodic input, thus affecting the temporal gating of synaptic inputs. Among excitatory neurons, heterogeneity increases the dimensionality of neural dynamics, improving the network's capacity to perform decoding tasks. Conversely, homogeneous networks suffer in their capacity for function generation, but excel at encoding signals via multistable dynamic regimes. Drawing from these findings, we propose intra-cell-type heterogeneity as a mechanism for sculpting the computational properties of local circuits of excitatory and inhibitory spiking neurons, permitting the same canonical microcircuit to be tuned for diverse computational tasks.

Diversity-induced trivialization and resilience of neural dynamics

Heterogeneity is omnipresent across all living systems. Diversity enriches the dynamical repertoire of these systems but remains challenging to reconcile with their manifest robustness and dynamical persistence over time, a fundamental feature called resilience. To better understand the mechanism underlying resilience in neural circuits, we considered a nonlinear network model, extracting the relationship between excitability heterogeneity and resilience. To measure resilience, we quantified the number of stationary states of this network, and how they are affected by various control parameters. We analyzed both analytically and numerically gradient and non-gradient systems modeled as non-linear sparse neural networks evolving over long time scales. Our analysis shows that neuronal heterogeneity quenches the number of stationary states while decreasing the susceptibility to bifurcations: a phenomenon known as trivialization. Heterogeneity was found to implement a homeostatic control mechanism enhancing network resilience to changes in network size and connection probability by quenching the system's dynamic volatility.

Controlling morpho-electrophysiological variability of neurons with detailed biophysical models

Variability, which is known to be a universal feature among biological units such as neuronal cells, holds significant importance, as, for example, it enables a robust encoding of a high volume of information in neuronal circuits and prevents hypersynchronizations. While most computational studies on electrophysiological variability in neuronal circuits were done with single-compartment neuron models, we instead focus on the variability of detailed biophysical models of neuron multi-compartmental morphologies. We leverage a Markov chain Monte Carlo method to generate populations of electrical models reproducing the variability of experimental recordings while being compatible with a set of morphologies to faithfully represent specifi morpho-electrical type. We demonstrate our approach on layer 5 pyramidal cells and study the morpho-electrical variability and in particular, find that morphological variability alone is insufficient to reproduce electrical variability. Overall, this approach provides a strong statistical basis to create detailed models of neurons with controlled variability.

Nonmonotonic enhancement of diversity-induced resonance in systems of mobile oscillators

Diversity is omnipresent in natural and synthetic extended systems, the phenomenon of diversity-induced resonance (DIR), wherein a moderate degree of the diversity can provoke an optimal collective response, provides researchers a brand-new strategy to amplify and utilize the weak signal. As yet the relevant advances focus mostly on the ideal situations where the interactions among elements are uncorrelated with the physical proximity of agents. Such a consideration overlooks interactions mediated by the motion of agents in space. Here, we investigate the signal response of an ensemble of spatial mobile heterogeneous bistable oscillators with two canonical interacting modes: dynamic and preset. The oscillators are considered as mass points and perform random walks in a two-dimensional square plane. Under the dynamic scheme, the oscillators can only interact with other oscillators within a fixed vision radius. For the preset circumstance, the interaction among oscillators occurs only when all of them are in a predefined region at the same moment. We find that the DIR can be obtained in both situations. Additionally, the strength of resonance nonmonotonically rises with respect to the increase of moving speed, and the optimal resonance is acquired by an intermediate magnitude of speed. Finally, we propose reduced equations to guarantee the occurrence of such mobility-optimized DIR on the basis of the fast switching approximation theory and also examine the robustness of such phenomenon through the excitable FitzHugh-Nagumo model and a different spatial motion mechanism. Our results reveal for the first time that the DIR can be optimized by the spatial mobility and thus has promising potential application in the communication of mobile agents.

Receptive field sizes and neuronal encoding bandwidth are constrained by axonal conduction delays

Studies on population coding implicitly assume that spikes from the presynaptic cells arrive simultaneously at the integrating neuron. In natural neuronal populations, this is usually not the case-neuronal signaling takes time and populations cover a certain space. The spread of spike arrival times depends on population size, cell density and axonal conduction velocity. Here we analyze the consequences of population size and axonal conduction delays on the stimulus encoding performance in the electrosensory system of the electric fish Apteronotus leptorhynchus. We experimentally locate p-type electroreceptor afferents along the rostro-caudal body axis and relate locations to neurophysiological response properties. In an information-theoretical approach we analyze the coding performance in homogeneous and heterogeneous populations. As expected, the amount of information increases with population size and, on average, heterogeneous populations encode better than the average same-size homogeneous population, if conduction delays are compensated for. The spread of neuronal conduction delays within a receptive field strongly degrades encoding of high-frequency stimulus components. Receptive field sizes typically found in the electrosensory lateral line lobe of A. leptorhynchus appear to be a good compromise between the spread of conduction delays and encoding performance. The limitations imposed by finite axonal conduction velocity are relevant for any converging network as is shown by model populations of LIF neurons. The bandwidth of natural stimuli and the maximum meaningful population sizes are constrained by conduction delays and may thus impact the optimal design of nervous systems.

Descending pathways increase sensory neural response heterogeneity to facilitate decoding and behavior

The functional role of heterogeneous spiking responses of otherwise similarly tuned neurons to stimulation, which has been observed ubiquitously, remains unclear to date. Here, we demonstrate that such response heterogeneity serves a beneficial function that is used by downstream brain areas to generate behavioral responses that follows the detailed timecourse of the stimulus. Multi-unit recordings from sensory pyramidal cells within the electrosensory system of Apteronotus leptorhynchus were performed and revealed highly heterogeneous responses that were similar for all cell types. By comparing the coding properties of a given neural population before and after inactivation of descending pathways, we found that heterogeneities were beneficial as decoding was then more robust to the addition of noise. Taken together, our results not only reveal that descending pathways actively promote response heterogeneity within a given cell type, but also uncover a beneficial function for such heterogeneity that is used by the brain to generate behavior.

Intrinsic neural diversity quenches the dynamic volatility of neural networks

Heterogeneity is the norm in biology. The brain is no different: Neuronal cell types are myriad, reflected through their cellular morphology, type, excitability, connectivity motifs, and ion channel distributions. While this biophysical diversity enriches neural systems' dynamical repertoire, it remains challenging to reconcile with the robustness and persistence of brain function over time (resilience). To better understand the relationship between excitability heterogeneity (variability in excitability within a population of neurons) and resilience, we analyzed both analytically and numerically a nonlinear sparse neural network with balanced excitatory and inhibitory connections evolving over long time scales. Homogeneous networks demonstrated increases in excitability, and strong firing rate correlations-signs of instability-in response to a slowly varying modulatory fluctuation. Excitability heterogeneity tuned network stability in a context-dependent way by restraining responses to modulatory challenges and limiting firing rate correlations, while enriching dynamics during states of low modulatory drive. Excitability heterogeneity was found to implement a homeostatic control mechanism enhancing network resilience to changes in population size, connection probability, strength and variability of synaptic weights, by quenching the volatility (i.e., its susceptibility to critical transitions) of its dynamics. Together, these results highlight the fundamental role played by cell-to-cell heterogeneity in the robustness of brain function in the face of change.

Mapping thalamic innervation to individual L2/3 pyramidal neurons and modeling their 'readout' of visual input

The thalamus is the main gateway for sensory information from the periphery to the mammalian cerebral cortex. A major conundrum has been the discrepancy between the thalamus's central role as the primary feedforward projection system into the neocortex and the sparseness of thalamocortical synapses. Here we use new methods, combining genetic tools and scalable tissue expansion microscopy for whole-cell synaptic mapping, revealing the number, density and size of thalamic versus cortical excitatory synapses onto individual layer 2/3 (L2/3) pyramidal cells (PCs) of the mouse primary visual cortex. We find that thalamic inputs are not only sparse, but remarkably heterogeneous in number and density across individual dendrites and neurons. Most surprising, despite their sparseness, thalamic synapses onto L2/3 PCs are smaller than their cortical counterparts. Incorporating these findings into fine-scale, anatomically faithful biophysical models of L2/3 PCs reveals how individual neurons with sparse and weak thalamocortical synapses, embedded in small heterogeneous neuronal ensembles, may reliably 'read out' visually driven thalamic input.

Coding of object location by heterogeneous neural populations with spatially dependent correlations in weakly electric fish

Understanding how neural populations encode sensory stimuli remains a central problem in neuroscience. Here we performed multi-unit recordings from sensory neural populations in the electrosensory system of the weakly electric fish Apteronotus leptorhynchus in response to stimuli located at different positions along the rostro-caudal axis. Our results reveal that the spatial dependence of correlated activity along receptive fields can help mitigate the deleterious effects that these correlations would otherwise have if they were spatially independent. Moreover, using mathematical modeling, we show that experimentally observed heterogeneities in the receptive fields of neurons help optimize information transmission as to object location. Taken together, our results have important implications for understanding how sensory neurons whose receptive fields display antagonistic center-surround organization encode location. Important similarities between the electrosensory system and other sensory systems suggest that our results will be applicable elsewhere.

Efficient parameter calibration and real-time simulation of large-scale spiking neural networks with GeNN and NEST

Spiking neural networks (SNNs) represent the state-of-the-art approach to the biologically realistic modeling of nervous system function. The systematic calibration for multiple free model parameters is necessary to achieve robust network function and demands high computing power and large memory resources. Special requirements arise from closed-loop model simulation in virtual environments and from real-time simulation in robotic application. Here, we compare two complementary approaches to efficient large-scale and real-time SNN simulation. The widely used NEural Simulation Tool (NEST) parallelizes simulation across multiple CPU cores. The GPU-enhanced Neural Network (GeNN) simulator uses the highly parallel GPU-based architecture to gain simulation speed. We quantify fixed and variable simulation costs on single machines with different hardware configurations. As a benchmark model, we use a spiking cortical attractor network with a topology of densely connected excitatory and inhibitory neuron clusters with homogeneous or distributed synaptic time constants and in comparison to the random balanced network. We show that simulation time scales linearly with the simulated biological model time and, for large networks, approximately linearly with the model size as dominated by the number of synaptic connections. Additional fixed costs with GeNN are almost independent of model size, while fixed costs with NEST increase linearly with model size. We demonstrate how GeNN can be used for simulating networks with up to 3.5 · 10⁶ neurons (> 3 · 10¹²synapses) on a high-end GPU, and up to 250, 000 neurons (25 · 10⁹ synapses) on a low-cost GPU. Real-time simulation was achieved for networks with 100, 000 neurons. Network calibration and parameter grid search can be efficiently achieved using batch processing. We discuss the advantages and disadvantages of both approaches for different use cases.

Interaction between Functional Connectivity and Neural Excitability in Autism: A Novel Framework for Computational Modeling and Application to Biological Data

Functional connectivity (FC) and neural excitability may interact to affect symptoms of autism spectrum disorder (ASD). We tested this hypothesis with neural network simulations, and applied it with functional magnetic resonance imaging (fMRI). A hierarchical recurrent neural network embodying predictive processing theory was subjected to a facial emotion recognition task. Neural network simulations examined the effects of FC and neural excitability on changes in neural representations by developmental learning, and eventually on ASD-like performance. Next, by mapping each neural network condition to subject subgroups on the basis of fMRI parameters, the association between ASD-like performance in the simulation and ASD diagnosis in the corresponding subject subgroup was examined. In the neural network simulation, the more homogeneous the neural excitability of the lower-level network, the more ASD-like the performance (reduced generalization and emotion recognition capability). In addition, in homogeneous networks, the higher the FC, the more ASD-like performance, while in heterogeneous networks, the higher the FC, the less ASD-like performance, demonstrating that FC and neural excitability interact. As an underlying mechanism, neural excitability determines the generalization capability of top-down prediction, and FC determines whether the model's information processing will be top-down prediction-dependent or bottom-up sensory-input dependent. In fMRI datasets, ASD was actually more prevalent in subject subgroups corresponding to the network condition showing ASD-like performance. The current study suggests an interaction between FC and neural excitability, and presents a novel framework for computational modeling and biological application of a developmental learning process underlying cognitive alterations in ASD.

Temporal derivative computation in the dorsal raphe network revealed by an experimentally driven augmented integrate-and-fire modeling framework

By means of an expansive innervation, the serotonin (5-HT) neurons of the dorsal raphe nucleus (DRN) are positioned to enact coordinated modulation of circuits distributed across the entire brain in order to adaptively regulate behavior. Yet the network computations that emerge from the excitability and connectivity features of the DRN are still poorly understood. To gain insight into these computations, we began by carrying out a detailed electrophysiological characterization of genetically identified mouse 5-HT and somatostatin (SOM) neurons. We next developed a single-neuron modeling framework that combines the realism of Hodgkin-Huxley models with the simplicity and predictive power of generalized integrate-and-fire models. We found that feedforward inhibition of 5-HT neurons by heterogeneous SOM neurons implemented divisive inhibition, while endocannabinoid-mediated modulation of excitatory drive to the DRN increased the gain of 5-HT output. Our most striking finding was that the output of the DRN encodes a mixture of the intensity and temporal derivative of its input, and that the temporal derivative component dominates this mixture precisely when the input is increasing rapidly. This network computation primarily emerged from prominent adaptation mechanisms found in 5-HT neurons, including a previously undescribed dynamic threshold. By applying a bottom-up neural network modeling approach, our results suggest that the DRN is particularly apt to encode input changes over short timescales, reflecting one of the salient emerging computations that dominate its output to regulate behavior.

Noise Enhancement of Neural Information Processing

Cortical neurons in vivo function in highly fluctuating and seemingly noisy conditions, and the understanding of how information is processed in such complex states is still incomplete. In this perspective article, we first overview that an intense "synaptic noise" was measured first in single neurons, and computational models were built based on such measurements. Recent progress in recording techniques has enabled the measurement of highly complex activity in large numbers of neurons in animals and human subjects, and models were also built to account for these complex dynamics. Here, we attempt to link these two cellular and population aspects, where the complexity of network dynamics in awake cortex seems to link to the synaptic noise seen in single cells. We show that noise in single cells, in networks, or structural noise, all participate to enhance responsiveness and boost the propagation of information. We propose that such noisy states are fundamental to providing favorable conditions for information processing at large-scale levels in the brain, and may be involved in sensory perception.

Emergence of sensory attenuation based upon the free-energy principle

The brain attenuates its responses to self-produced exteroceptions (e.g., we cannot tickle ourselves). Is this phenomenon, known as sensory attenuation, enabled innately, or acquired through learning? Here, our simulation study using a multimodal hierarchical recurrent neural network model, based on variational free-energy minimization, shows that a mechanism for sensory attenuation can develop through learning of two distinct types of sensorimotor experience, involving self-produced or externally produced exteroceptions. For each sensorimotor context, a particular free-energy state emerged through interaction between top-down prediction with precision and bottom-up sensory prediction error from each sensory area. The executive area in the network served as an information hub. Consequently, shifts between the two sensorimotor contexts triggered transitions from one free-energy state to another in the network via executive control, which caused shifts between attenuating and amplifying prediction-error-induced responses in the sensory areas. This study situates emergence of sensory attenuation (or self-other distinction) in development of distinct free-energy states in the dynamic hierarchical neural system.

Loss of neuronal heterogeneity in epileptogenic human tissue impairs network resilience to sudden changes in synchrony

A myriad of pathological changes associated with epilepsy can be recast as decreases in cell and circuit heterogeneity. We thus propose recontextualizing epileptogenesis as a process where reduction in cellular heterogeneity, in part, renders neural circuits less resilient to seizure. By comparing patch clamp recordings from human layer 5 (L5) cortical pyramidal neurons from epileptogenic and non-epileptogenic tissue, we demonstrate significantly decreased biophysical heterogeneity in seizure-generating areas. Implemented computationally, this renders model neural circuits prone to sudden transitions into synchronous states with increased firing activity, paralleling ictogenesis. This computational work also explains the surprising finding of significantly decreased excitability in the population-activation functions of neurons from epileptogenic tissue. Finally, mathematical analyses reveal a bifurcation structure arising only with low heterogeneity and associated with seizure-like dynamics. Taken together, this work provides experimental, computational, and mathematical support for the theory that ictogenic dynamics accompany a reduction in biophysical heterogeneity.

Dynamics and Information Import in Recurrent Neural Networks

Recurrent neural networks (RNNs) are complex dynamical systems, capable of ongoing activity without any driving input. The long-term behavior of free-running RNNs, described by periodic, chaotic and fixed point attractors, is controlled by the statistics of the neural connection weights, such as the density d of non-zero connections, or the balance b between excitatory and inhibitory connections. However, for information processing purposes, RNNs need to receive external input signals, and it is not clear which of the dynamical regimes is optimal for this information import. We use both the average correlations C and the mutual information I between the momentary input vector and the next system state vector as quantitative measures of information import and analyze their dependence on the balance and density of the network. Remarkably, both resulting phase diagrams C(b, d) and I(b, d) are highly consistent, pointing to a link between the dynamical systems and the information-processing approach to complex systems. Information import is maximal not at the "edge of chaos," which is optimally suited for computation, but surprisingly in the low-density chaotic regime and at the border between the chaotic and fixed point regime. Moreover, we find a completely new type of resonance phenomenon, which we call "Import Resonance" (IR), where the information import shows a maximum, i.e., a peak-like dependence on the coupling strength between the RNN and its external input. IR complements previously found Recurrence Resonance (RR), where correlation and mutual information of successive system states peak for a certain amplitude of noise added to the system. Both IR and RR can be exploited to optimize information processing in artificial neural networks and might also play a crucial role in biological neural systems.

Synchronous inhibitory pathways create both efficiency and diversity in the retina

Complex connections in neural circuits make it difficult to quantitatively assign even the most basic neural computations to the actions of specific neurons. Retinal ganglion cells are most sensitive to changes in intensity across space and over time. This property, caused by a region known as the receptive field surround, improves information transmission about natural scenes. We dynamically manipulated individual interneurons to directly measure their effect on retinal receptive fields, finding that two inhibitory neuron types, horizontal cells and amacrine cells, synchronously create the same contribution to the receptive field surround at different spatial scales. By analyzing large populations of ganglion cells, we show that this arrangement increases diversity in retinal signaling while preserving maximal information transmission about natural scenes.

Sensory receptive fields combine features that originate in different neural pathways. Retinal ganglion cell receptive fields compute intensity changes across space and time using a peripheral region known as the surround, a property that improves information transmission about natural scenes. The visual features that construct this fundamental property have not been quantitatively assigned to specific interneurons. Here, we describe a generalizable approach using simultaneous intracellular and multielectrode recording to directly measure and manipulate the sensory feature conveyed by a neural pathway to a downstream neuron. By directly controlling the gain of individual interneurons in the circuit, we show that rather than transmitting different temporal features, inhibitory horizontal cells and linear amacrine cells synchronously create the linear surround at different spatial scales and that these two components fully account for the surround. By analyzing a large population of ganglion cells, we observe substantial diversity in the relative contribution of amacrine and horizontal cell visual features while still allowing individual cells to increase information transmission under the statistics of natural scenes. Established theories of efficient coding have shown that optimal information transmission under natural scenes allows a diverse set of receptive fields. Our results give a mechanism for this theory, showing how distinct neural pathways synthesize a sensory computation and how this architecture both generates computational diversity and achieves the objective of high information transmission.

Heterogeneity in GnRH and kisspeptin neurons and their significance in vertebrate reproductive biology

Vertebrate reproduction is essentially controlled by the hypothalamus-pituitary-gonadal (HPG) axis, which is a central dogma of reproductive biology. Two major hypothalamic neuroendocrine cell groups containing gonadotropin-releasing hormone (GnRH) and kisspeptin are crucial for control of the HPG axis in vertebrates. GnRH and kisspeptin neurons exhibit high levels of heterogeneity including their cellular morphology, biochemistry, neurophysiology and functions. However, the molecular foundation underlying heterogeneities in GnRH and kisspeptin neurons remains unknown. More importantly, the biological and physiological significance of their heterogeneity in reproductive biology is poorly understood. In this review, we first describe the recent advances in the neuroendocrine functions of kisspeptin-GnRH pathways. We then view the recent emerging progress in the heterogeneity of GnRH and kisspeptin neurons using morphological and single-cell transcriptomic analyses. Finally, we discuss our views on the significance of functional heterogeneity of reproductive endocrine cells and their potential relevance to reproductive health.

Optimal responsiveness and information flow in networks of heterogeneous neurons

Cerebral cortex is characterized by a strong neuron-to-neuron heterogeneity, but it is unclear what consequences this may have for cortical computations, while most computational models consider networks of identical units. Here, we study network models of spiking neurons endowed with heterogeneity, that we treat independently for excitatory and inhibitory neurons. We find that heterogeneous networks are generally more responsive, with an optimal responsiveness occurring for levels of heterogeneity found experimentally in different published datasets, for both excitatory and inhibitory neurons. To investigate the underlying mechanisms, we introduce a mean-field model of heterogeneous networks. This mean-field model captures optimal responsiveness and suggests that it is related to the stability of the spontaneous asynchronous state. The mean-field model also predicts that new dynamical states can emerge from heterogeneity, a prediction which is confirmed by network simulations. Finally we show that heterogeneous networks maximise the information flow in large-scale networks, through recurrent connections. We conclude that neuronal heterogeneity confers different responsiveness to neural networks, which should be taken into account to investigate their information processing capabilities.

Neural network modeling of altered facial expression recognition in autism spectrum disorders based on predictive processing framework

The mechanism underlying the emergence of emotional categories from visual facial expression information during the developmental process is largely unknown. Therefore, this study proposes a system-level explanation for understanding the facial emotion recognition process and its alteration in autism spectrum disorder (ASD) from the perspective of predictive processing theory. Predictive processing for facial emotion recognition was implemented as a hierarchical recurrent neural network (RNN). The RNNs were trained to predict the dynamic changes of facial expression movies for six basic emotions without explicit emotion labels as a developmental learning process, and were evaluated by the performance of recognizing unseen facial expressions for the test phase. In addition, the causal relationship between the network characteristics assumed in ASD and ASD-like cognition was investigated. After the developmental learning process, emotional clusters emerged in the natural course of self-organization in higher-level neurons, even though emotional labels were not explicitly instructed. In addition, the network successfully recognized unseen test facial sequences by adjusting higher-level activity through the process of minimizing precision-weighted prediction error. In contrast, the network simulating altered intrinsic neural excitability demonstrated reduced generalization capability and impaired emotional clustering in higher-level neurons. Consistent with previous findings from human behavioral studies, an excessive precision estimation of noisy details underlies this ASD-like cognition. These results support the idea that impaired facial emotion recognition in ASD can be explained by altered predictive processing, and provide possible insight for investigating the neurophysiological basis of affective contact.

Efficient and robust coding in heterogeneous recurrent networks

Cortical networks show a large heterogeneity of neuronal properties. However, traditional coding models have focused on homogeneous populations of excitatory and inhibitory neurons. Here, we analytically derive a class of recurrent networks of spiking neurons that close to optimally track a continuously varying input online, based on two assumptions: 1) every spike is decoded linearly and 2) the network aims to reduce the mean-squared error between the input and the estimate. From this we derive a class of predictive coding networks, that unifies encoding and decoding and in which we can investigate the difference between homogeneous networks and heterogeneous networks, in which each neurons represents different features and has different spike-generating properties. We find that in this framework, 'type 1' and 'type 2' neurons arise naturally and networks consisting of a heterogeneous population of different neuron types are both more efficient and more robust against correlated noise. We make two experimental predictions: 1) we predict that integrators show strong correlations with other integrators and resonators are correlated with resonators, whereas the correlations are much weaker between neurons with different coding properties and 2) that 'type 2' neurons are more coherent with the overall network activity than 'type 1' neurons.

Neuronal heterogeneity modulates phase synchronization between unidirectionally coupled populations with excitation-inhibition balance

Several experiments and models have highlighted the importance of neuronal heterogeneity in brain dynamics and function. However, how such a cell-to-cell diversity can affect cortical computation, synchronization, and neuronal communication is still under debate. Previous studies have focused on the effect of neuronal heterogeneity in one neuronal population. Here we are specifically interested in the effect of neuronal variability on the phase relations between two populations, which can be related to different cortical communication hypotheses. It has been recently shown that two spiking neuron populations unidirectionally connected in a sender-receiver configuration can exhibit anticipated synchronization (AS), which is characterized by a negative phase lag. This phenomenon has been reported in electrophysiological data of nonhuman primates and human EEG during a visual discrimination cognitive task. In experiments, the unidirectional coupling could be accessed by Granger causality and can be accompanied by either positive or negative phase difference between cortical areas. Here we propose a model of two coupled populations in which the neuronal heterogeneity can determine the dynamical relation between the sender and the receiver and can reproduce phase relations reported in experiments. Depending on the distribution of parameters characterizing the neuronal firing patterns, the system can exhibit both AS and the usual delayed synchronization regime (DS, with positive phase) as well as a zero-lag synchronization regime and phase bistability between AS and DS. Furthermore, we show that our network can present diversity in their phase relations maintaining the excitation-inhibition balance.

Firing statistics in the bistable regime of neurons with homoclinic spike generation

Neuronal voltage dynamics of regularly firing neurons typically has one stable attractor: either a fixed point (like in the subthreshold regime) or a limit cycle that defines the tonic firing of action potentials (in the suprathreshold regime). In two of the three spike onset bifurcation sequences that are known to give rise to all-or-none type action potentials, however, the resting-state fixed point and limit cycle spiking can coexist in an intermediate regime, resulting in bistable dynamics. Here, noise can induce switches between the attractors, i.e., between rest and spiking, and thus increase the variability of the spike train compared to neurons with only one stable attractor. Qualitative features of the resulting spike statistics depend on the spike onset bifurcations. This paper focuses on the creation of the spiking limit cycle via the saddle-homoclinic orbit (HOM) bifurcation and derives interspike interval (ISI) densities for a conductance-based neuron model in the bistable regime. The ISI densities of bistable homoclinic neurons are found to be unimodal yet distinct from the inverse Gaussian distribution associated with the saddle-node-on-invariant-cycle bifurcation. It is demonstrated that for the HOM bifurcation the transition between rest and spiking is mainly determined along the downstroke of the action potential-a dynamical feature that is not captured by the commonly used reset neuron models. The deduced spike statistics can help to identify HOM dynamics in experimental data.

On the Validity of Neural Mass Models

Modeling the dynamics of neural masses is a common approach in the study of neural populations. Various models have been proven useful to describe a plenitude of empirical observations including self-sustained local oscillations and patterns of distant synchronization. We discuss the extent to which mass models really resemble the mean dynamics of a neural population. In particular, we question the validity of neural mass models if the population under study comprises a mixture of excitatory and inhibitory neurons that are densely (inter-)connected. Starting from a network of noisy leaky integrate-and-fire neurons, we formulated two different population dynamics that both fall into the category of seminal Freeman neural mass models. The derivations contained several mean-field assumptions and time scale separation(s) between membrane and synapse dynamics. Our comparison of these neural mass models with the averaged dynamics of the population reveals bounds in the fraction of excitatory/inhibitory neuron as well as overall network degree for a mass model to provide adequate estimates. For substantial parameter ranges, our models fail to mimic the neural network's dynamics proper, be that in de-synchronized or in (high-frequency) synchronized states. Only around the onset of low-frequency synchronization our models provide proper estimates of the mean potential dynamics. While this shows their potential for, e.g., studying resting state dynamics obtained by encephalography with focus on the transition region, we must accept that predicting the more general dynamic outcome of a neural network via its mass dynamics requires great care.

Statistical Analysis of Decoding Performances of Diverse Populations of Neurons

A central theme in computational neuroscience is determining the neural correlates of efficient and accurate coding of sensory signals. Diversity, or heterogeneity, of intrinsic neural attributes is known to exist in many brain areas and is thought to significantly affect neural coding. Recent theoretical and experimental work has argued that in uncoupled networks, coding is most accurate at intermediate levels of heterogeneity. Here we consider this question with data from in vivo recordings of neurons in the electrosensory system of weakly electric fish subject to the same realization of noisy stimuli; we use a generalized linear model (GLM) to assess the accuracy of (Bayesian) decoding of stimulus given a population spiking response. The long recordings enable us to consider many uncoupled networks and a relatively wide range of heterogeneity, as well as many instances of the stimuli, thus enabling us to address this question with statistical power. The GLM decoding is performed on a single long time series of data to mimic realistic conditions rather than using trial-averaged data for better model fits. For a variety of fixed network sizes, we generally find that the optimal levels of heterogeneity are at intermediate values, and this holds in all core components of GLM. These results are robust to several measures of decoding performance, including the absolute value of the error, error weighted by the uncertainty of the estimated stimulus, and the correlation between the actual and estimated stimulus. Although a quadratic fit to decoding performance as a function of heterogeneity is statistically significant, the result is highly variable with low R2 values. Taken together, intermediate levels of neural heterogeneity are indeed a prominent attribute for efficient coding even within a single time series, but the performance is highly variable.

Diversity-induced resonance for optimally suprathreshold signals

Recent research has revealed that a system of coupled units with a certain degree of parameter diversity can generate an enhanced response to a subthreshold signal compared to that without diversity, exhibiting a diversity-induced resonance. We here show that diversity-induced resonance can also respond to a suprathreshold signal in a system of globally coupled bistable oscillators or excitable neurons, when the signal amplitude is in an optimal range close to the threshold amplitude. We find that such diversity-induced resonance for optimally suprathreshold signals is sensitive to the signal period for the system of coupled excitable neurons, but not for the coupled bistable oscillators. Moreover, we show that the resonance phenomenon is robust to the system size. Furthermore, we find that intermediate degrees of parameter diversity and coupling strength jointly modulate either the waveform or the period of collective activity of the system, giving rise to the resonance for optimally suprathreshold signals. Finally, with low-dimensional reduced models, we explain the underlying mechanism of the observed resonance. Our results extend the scope of the diversity-induced resonance effect.

Stability of motor cortex network states during learning-associated neural reorganizations

A substantial reorganization of neural activity and neuron-to-movement relationship in motor cortical circuits accompanies the emergence of reproducible movement patterns during motor learning. Little is known about how this tempest of neural activity restructuring impacts the stability of network states in recurrent cortical circuits. To investigate this issue, we reanalyzed data in which we recorded for 14 days via population calcium imaging the activity of the same neural populations of pyramidal neurons in layer 2/3 and layer 5 of forelimb motor and premotor cortex in mice during the daily learning of a lever-press task. We found that motor cortex network states remained stable with respect to the critical network state during the extensive reorganization of both neural population activity and its relation to lever movement throughout learning. Specifically, layer 2/3 cortical circuits unceasingly displayed robust evidence for operating at the critical network state, a regime that maximizes information capacity and transmission and provides a balance between network robustness and flexibility. In contrast, layer 5 circuits operated away from the critical network state for all 14 days of recording and learning. In conclusion, this result indicates that the wide-ranging malleability of synapses, neurons, and neural connectivity during learning operates within the constraint of a stable and layer-specific network state regarding dynamic criticality, and suggests that different cortical layers operate under distinct constraints because of their specialized goals.NEW & NOTEWORTHY The neural activity reorganizes throughout motor learning, but how this reorganization impacts the stability of network states is unclear. We used two-photon calcium imaging to investigate how the network states in layer 2/3 and layer 5 of forelimb motor and premotor cortex are modulated by motor learning. We show that motor cortex network states are layer-specific and constant regarding criticality during neural activity reorganization, and suggests that layer-specific constraints could be motivated by different functions.

Neuronal On- and Off-type heterogeneities improve population coding of envelope signals in the presence of stimulus-induced noise

Understanding the mechanisms by which neuronal population activity gives rise to perception and behavior remains a central question in systems neuroscience. Such understanding is complicated by the fact that natural stimuli often have complex structure. Here we investigated how heterogeneities within a sensory neuron population influence the coding of a noisy stimulus waveform (i.e., the noise) and its behaviorally relevant envelope signal (i.e., the signal). We found that On- and Off-type neurons displayed more heterogeneities in their responses to the noise than in their responses to the signal. These differences in heterogeneities had important consequences when quantifying response similarity between pairs of neurons. Indeed, the larger response heterogeneity displayed by On- and Off-type neurons made their pairwise responses to the noise on average more independent than when instead considering pairs of On-type or Off-type neurons. Such relative independence allowed for better averaging out of the noise response when pooling neural activities in a mixed-type (i.e., On- and Off-type) than for same-type (i.e., only On-type or only Off-type), thereby leading to greater information transmission about the signal. Our results thus reveal a function for the combined activities of On- and Off-type neurons towards improving information transmission of envelope stimuli at the population level. Our results will likely generalize because natural stimuli across modalities are characterized by a stimulus waveform whose envelope varies independently as well as because On- and Off-type neurons are observed across systems and species.

Neural Synchrony Gives Rise to Amplitude- and Duration-Invariant Encoding Consistent With Perception of Natural Communication Stimuli

When confronted with a highly variable environment, it remains poorly understood how neural populations encode and classify natural stimuli to give rise to appropriate and consistent behavioral responses. Here we investigated population coding of natural communication signals with different attributes (i.e., amplitude and duration) in the electrosensory system of the weakly electric fish Apteronotus leptorhynchus. Our results show that, while single peripheral neurons encode the detailed timecourse of different stimulus waveforms, measures of population synchrony are effectively unchanged because of coordinated increases and decreases in activity. A phenomenological mathematical model reproduced this invariance and shows that this can be explained by considering homogeneous populations whose responses are solely determined by single neuron firing properties. Moreover, recordings from downstream central neurons reveal that synchronous afferent activity is actually decoded and thus most likely transmitted to higher brain areas. Finally, we demonstrate that the associated behavioral responses at the organism level are invariant. Our results provide a mechanism by which amplitude- and duration-invariant coding of behaviorally relevant sensory input emerges across successive brain areas thereby presumably giving rise to invariant behavioral responses. Such mechanisms are likely to be found in other systems that share anatomical and functional features with the electrosensory system (e.g., auditory, visual, vestibular).

Positive and negative couplings perform complementary roles in the signal amplification of globally coupled bistable oscillators

We investigate a system of globally coupled bistable oscillators subjected to a common weak signal, where the couplings are oscillator dependent with random signs: positive or negative. We find that neither purely positive nor purely negative couplings are optimal for signal amplification of the system; a mixture of both positive and negative couplings is more beneficial for the signal amplification. Our numerical results further show that different from the fully synchronous state caused by purely positive couplings or asynchronous state caused by purely negative couplings, the mixed positive and negative couplings can generate a clustering synchronous state, which allows the system to generate a resonancelike response to the weak signal, and thus, amplifies the signal. We finally propose a reduced model to analyze the mechanism underlying this resonancelike behavior, and find a complementary effect of these two types of couplings in signal amplification.

Homogeneous Intrinsic Neuronal Excitability Induces Overfitting to Sensory Noise: A Robot Model of Neurodevelopmental Disorder

Neurodevelopmental disorders, including autism spectrum disorder, have been intensively investigated at the neural, cognitive, and behavioral levels, but the accumulated knowledge remains fragmented. In particular, developmental learning aspects of symptoms and interactions with the physical environment remain largely unexplored in computational modeling studies, although a leading computational theory has posited associations between psychiatric symptoms and an unusual estimation of information uncertainty (precision), which is an essential aspect of the real world and is estimated through learning processes. Here, we propose a mechanistic explanation that unifies the disparate observations via a hierarchical predictive coding and developmental learning framework, which is demonstrated in experiments using a neural network-controlled robot. The results show that, through the developmental learning process, homogeneous intrinsic neuronal excitability at the neural level induced via self-organization changes at the information processing level, such as hyper sensory precision and overfitting to sensory noise. These changes led to multifaceted alterations at the behavioral level, such as inflexibility, reduced generalization, and motor clumsiness. In addition, these behavioral alterations were accompanied by fluctuating neural activity and excessive development of synaptic connections. These findings might bridge various levels of understandings in autism spectrum and other neurodevelopmental disorders and provide insights into the disease processes underlying observed behaviors and brain activities in individual patients. This study shows the potential of neurorobotics frameworks for modeling how psychiatric disorders arise from dynamic interactions among the brain, body, and uncertain environments.

Pattern Classification by Spiking Neural Networks Combining Self-Organized and Reward-Related Spike-Timing-Dependent Plasticity

Many recent studies have applied to spike neural networks with spike-timing-dependent plasticity (STDP) to machine learning problems. The learning abilities of dopamine-modulated STDP (DA-STDP) for reward-related synaptic plasticity have also been gathering attention. Following these studies, we hypothesize that a network structure combining self-organized STDP and reward-related DA-STDP can solve the machine learning problem of pattern classification. Therefore, we studied the ability of a network in which recurrent spiking neural networks are combined with STDP for non-supervised learning, with an output layer joined by DA-STDP for supervised learning, to perform pattern classification. We confirmed that this network could perform pattern classification using the STDP effect for emphasizing features of the input spike pattern and DA-STDP supervised learning. Therefore, our proposed spiking neural network may prove to be a useful approach for machine learning problems.

Neural activity of heterogeneous inhibitory spiking networks with delay

We study a network of spiking neurons with heterogeneous excitabilities connected via inhibitory delayed pulses. For globally coupled systems the increase of the inhibitory coupling reduces the number of firing neurons by following a winner-takes-all mechanism. For sufficiently large transmission delay we observe the emergence of collective oscillations in the system beyond a critical coupling value. Heterogeneity promotes neural inactivation and asynchronous dynamics and its effect can be counteracted by considering longer time delays. In sparse networks, inhibition has the counterintuitive effect of promoting neural reactivation of silent neurons for sufficiently large coupling. In this regime, current fluctuations are on one side responsible for neural firing of subthreshold neurons and on the other side for their desynchronization. Therefore, collective oscillations are present only in a limited range of coupling values, which remains finite in the thermodynamic limit. Out of this range the dynamics is asynchronous and for very large inhibition neurons display a bursting behavior alternating periods of silence with periods where they fire freely in absence of any inhibition.

Functional Diversity in the Retina Improves the Population Code

Within a given brain region, individual neurons exhibit a wide variety of different feature selectivities. Here, we investigated the impact of this extensive functional diversity on the population neural code. Our approach was to build optimal decoders to discriminate among stimuli using the spiking output of a real, measured neural population and compare its performance against a matched, homogeneous neural population with the same number of cells and spikes. Analyzing large populations of retinal ganglion cells, we found that the real, heterogeneous population can yield a discrimination error lower than the homogeneous population by several orders of magnitude and consequently can encode much more visual information. This effect increases with population size and with graded degrees of heterogeneity. We complemented these results with an analysis of coding based on the Chernoff distance, as well as derivations of inequalities on coding in certain limits, from which we can conclude that the beneficial effect of heterogeneity occurs over a broad set of conditions. Together, our results indicate that the presence of functional diversity in neural populations can enhance their coding fidelity appreciably. A noteworthy outcome of our study is that this effect can be extremely strong and should be taken into account when investigating design principles for neural circuits.

Synchronization transition in neuronal networks composed of chaotic or non-chaotic oscillators

Chaotic dynamics has been shown in the dynamics of neurons and neural networks, in experimental data and numerical simulations. Theoretical studies have proposed an underlying role of chaos in neural systems. Nevertheless, whether chaotic neural oscillators make a significant contribution to network behaviour and whether the dynamical richness of neural networks is sensitive to the dynamics of isolated neurons, still remain open questions. We investigated synchronization transitions in heterogeneous neural networks of neurons connected by electrical coupling in a small world topology. The nodes in our model are oscillatory neurons that – when isolated – can exhibit either chaotic or non-chaotic behaviour, depending on conductance parameters. We found that the heterogeneity of firing rates and firing patterns make a greater contribution than chaos to the steepness of the synchronization transition curve. We also show that chaotic dynamics of the isolated neurons do not always make a visible difference in the transition to full synchrony. Moreover, macroscopic chaos is observed regardless of the dynamics nature of the neurons. However, performing a Functional Connectivity Dynamics analysis, we show that chaotic nodes can promote what is known as multi-stable behaviour, where the network dynamically switches between a number of different semi-synchronized, metastable states.

Circuit variability interacts with excitatory-inhibitory diversity of interneurons to regulate network encoding capacity

Local interneurons (LNs) in the Drosophila olfactory system exhibit neuronal diversity and variability, yet it is still unknown how these features impact information encoding capacity and reliability in a complex LN network. We employed two strategies to construct a diverse excitatory-inhibitory neural network beginning with a ring network structure and then introduced distinct types of inhibitory interneurons and circuit variability to the simulated network. The continuity of activity within the node ensemble (oscillation pattern) was used as a readout to describe the temporal dynamics of network activity. We found that inhibitory interneurons enhance the encoding capacity by protecting the network from extremely short activation periods when the network wiring complexity is very high. In addition, distinct types of interneurons have differential effects on encoding capacity and reliability. Circuit variability may enhance the encoding reliability, with or without compromising encoding capacity. Therefore, we have described how circuit variability of interneurons may interact with excitatory-inhibitory diversity to enhance the encoding capacity and distinguishability of neural networks. In this work, we evaluate the effects of different types and degrees of connection diversity on a ring model, which may simulate interneuron networks in the Drosophila olfactory system or other biological systems.

Routes to Chaos Induced by a Discontinuous Resetting Process in a Hybrid Spiking Neuron Model

Several hybrid spiking neuron models combining continuous spike generation mechanisms and discontinuous resetting processes following spiking have been proposed. The Izhikevich neuron model, for example, can reproduce many spiking patterns. This model clearly possesses various types of bifurcations and routes to chaos under the effect of a state-dependent jump in the resetting process. In this study, we focus further on the relation between chaotic behaviour and the state-dependent jump, approaching the subject by comparing spiking neuron model versions with and without the resetting process. We first adopt a continuous two-dimensional spiking neuron model in which the orbit in the spiking state does not exhibit divergent behaviour. We then insert the resetting process into the model. An evaluation using the Lyapunov exponent with a saltation matrix and a characteristic multiplier of the Poincar'e map reveals that two types of chaotic behaviour (i.e. bursting chaotic spikes and near-period-two chaotic spikes) are induced by the resetting process. In addition, we confirm that this chaotic bursting state is generated from the periodic spiking state because of the slow- and fast-scale dynamics that arise when jumping to the hyperpolarization and depolarization regions, respectively.

Dichotomous Dynamics in E-I Networks with Strongly and Weakly Intra-connected Inhibitory Neurons

The interconnectivity between excitatory and inhibitory neural networks informs mechanisms by which rhythmic bursts of excitatory activity can be produced in the brain. One such mechanism, Pyramidal Interneuron Network Gamma (PING), relies primarily upon reciprocal connectivity between the excitatory and inhibitory networks, while also including intra-connectivity of inhibitory cells. The causal relationship between excitatory activity and the subsequent burst of inhibitory activity is of paramount importance to the mechanism and has been well studied. However, the role of the intra-connectivity of the inhibitory network, while important for PING, has not been studied in detail, as most analyses of PING simply assume that inhibitory intra-connectivity is strong enough to suppress subsequent firing following the initial inhibitory burst. In this paper we investigate the role that the strength of inhibitory intra-connectivity plays in determining the dynamics of PING-style networks. We show that networks with weak inhibitory intra-connectivity exhibit variations in burst dynamics of both the excitatory and inhibitory cells that are not obtained with strong inhibitory intra-connectivity. Networks with weak inhibitory intra-connectivity exhibit excitatory rhythmic bursts with weak excitatory-to-inhibitory synapses for which classical PING networks would show no rhythmic activity. Additionally, variations in dynamics of these networks as the excitatory-to-inhibitory synaptic weight increases illustrates the important role that consistent pattern formation in the inhibitory cells serves in maintaining organized and periodic excitatory bursts. Finally, motivated by these results and the known diversity of interneurons, we show that a PING-style network with two inhibitory subnetworks, one strongly intra-connected and one weakly intra-connected, exhibits organized and periodic excitatory activity over a larger parameter regime than networks with a homogeneous inhibitory population. Taken together, these results serve to better articulate the role of inhibitory intra-connectivity in generating PING-like rhythms, while also revealing how heterogeneity amongst inhibitory synapses might make such rhythms more robust to a variety of network parameters.

Coding of time-dependent stimuli in homogeneous and heterogeneous neural populations

We compare the information transmission of a time-dependent signal by two types of uncoupled neuron populations that differ in their sources of variability: i) a homogeneous population whose units receive independent noise and ii) a deterministic heterogeneous population, where each unit exhibits a different baseline firing rate ('disorder'). Our criterion for making both sources of variability quantitatively comparable is that the interspike-interval distributions are identical for both systems. Numerical simulations using leaky integrate-and-fire neurons unveil that a non-zero amount of both noise or disorder maximizes the encoding efficiency of the homogeneous and heterogeneous system, respectively, as a particular case of suprathreshold stochastic resonance. Our findings thus illustrate that heterogeneity can render similarly profitable effects for neuronal populations as dynamic noise. The optimal noise/disorder depends on the system size and the properties of the stimulus such as its intensity or cutoff frequency. We find that weak stimuli are better encoded by a noiseless heterogeneous population, whereas for strong stimuli a homogeneous population outperforms an equivalent heterogeneous system up to a moderate noise level. Furthermore, we derive analytical expressions of the coherence function for the cases of very strong noise and of vanishing intrinsic noise or heterogeneity, which predict the existence of an optimal noise intensity. Our results show that, depending on the type of signal, noise as well as heterogeneity can enhance the encoding performance of neuronal populations.

CA1 pyramidal cells have diverse biophysical properties, affected by development, experience, and aging

Neuron types (e.g., pyramidal cells) within one area of the brain are often considered homogeneous, despite variability in their biophysical properties. Here we review literature demonstrating variability in the electrical activity of CA1 hippocampal pyramidal cells (PCs), including responses to somatic current injection, synaptic stimulation, and spontaneous network-related activity. In addition, we describe how responses of CA1 PCs vary with development, experience, and aging, and some of the underlying ionic currents responsible. Finally, we suggest directions that may be the most impactful in expanding this knowledge, including the use of text and data mining to systematically study cellular heterogeneity in more depth; dynamical systems theory to understand and potentially classify neuron firing patterns; and mathematical modeling to study the interaction between cellular properties and network output. Our goals are to provide a synthesis of the literature for experimentalists studying CA1 PCs, to give theorists an idea of the rich diversity of behaviors models may need to reproduce to accurately represent these cells, and to provide suggestions for future research.

Coexistence of critical sensitivity and subcritical specificity can yield optimal population coding

The vicinity of phase transitions selectively amplifies weak stimuli, yielding optimal sensitivity to distinguish external input. Along with this enhanced sensitivity, enhanced levels of fluctuations at criticality reduce the specificity of the response. Given that the specificity of the response is largely compromised when the sensitivity is maximal, the overall benefit of criticality for signal processing remains questionable. Here, it is shown that this impasse can be solved by heterogeneous systems incorporating functional diversity, in which critical and subcritical components coexist. The subnetwork of critical elements has optimal sensitivity, and the subnetwork of subcritical elements has enhanced specificity. Combining segregated features extracted from the different subgroups, the resulting collective response can maximize the trade-off between sensitivity and specificity measured by the dynamic-range-to-noise ratio. Although numerous benefits can be observed when the entire system is critical, our results highlight that optimal performance is obtained when only a small subset of the system is at criticality.

Optimized Parallel Coding of Second-Order Stimulus Features by Heterogeneous Neural Populations

Efficient processing of sensory input is essential to ensure an organism's survival in its natural environment. Growing evidence suggests that sensory neurons can optimally encode natural stimuli by ensuring that their tuning opposes stimulus statistics, such that the resulting neuronal response contains equal power at all frequencies (i.e., is "white"). Such temporal decorrelation or whitening has been observed across modalities, but the effects of neural heterogeneities on determining tuning and thus responses to natural stimuli have not been investigated. Here, we investigate how heterogeneities in sensory pyramidal neurons organized in three parallel maps representing the body surface determine responses to second-order electrosensory stimulus features in the weakly electric fish Apteronotus leptorhynchus While some sources of heterogeneities such as ON- and OFF-type responses to first-order did not affect responses to second-order electrosensory stimulus features, other sources of heterogeneity within and across the maps strongly determined responses. We found that these cells effectively performed a fractional differentiation operation on their input with exponents ranging from zero (no differentiation) to 0.4 (strong differentiation). Varying adaptation in a simple model explained these heterogeneities and predicted a strong correlation between fractional differentiation and adaptation. Using natural stimuli, we found that only a small fraction of neurons implemented temporal whitening. Rather, a large fraction of neurons did not perform any significant whitening and thus preserved natural input statistics in their responses. We propose that this information is needed to properly decode optimized information sent in parallel through temporally whitened responses based on context.

SIGNIFICANCE STATEMENT

We demonstrate that heterogeneities in the same sensory neuron type can either have no or significant influence on their responses to second-order stimulus features. While an ON- or OFF-type response to first-order stimulus attributes has no significant influence on responses to second-order stimulus features, we found that only a small fraction of sensory neurons optimally encoded natural stimuli through high-pass filtering, thereby implementing temporal whitening. Surprisingly, a large fraction of sensory neurons performed little if no filtering of stimuli, thereby preserving natural stimulus statistics. We hypothesize that this pathway is necessary to properly decode optimized information contained in temporally whitened responses based on context.

Optimal Detection of a Localized Perturbation in Random Networks of Integrate-and-Fire Neurons

Experimental and theoretical studies suggest that cortical networks are chaotic and coding relies on averages over large populations. However, there is evidence that rats can respond to the short stimulation of a single cortical cell, a theoretically unexplained fact. We study effects of single-cell stimulation on a large recurrent network of integrate-and-fire neurons and propose a simple way to detect the perturbation. Detection rates obtained from simulations and analytical estimates are similar to experimental response rates if the readout is slightly biased towards specific neurons. Near-optimal detection is attained for a broad range of intermediate values of the mean coupling between neurons.

The Influence of Mexican Hat Recurrent Connectivity on Noise Correlations and Stimulus Encoding

Noise correlations are a common feature of neural responses and have been observed in many cortical areas across different species. These correlations can influence information processing by enhancing or diminishing the quality of the neural code, but the origin of these correlations is still a matter of controversy. In this computational study we explore the hypothesis that noise correlations are the result of local recurrent excitatory and inhibitory connections. We simulated two-dimensional networks of adaptive spiking neurons with local connection patterns following Gaussian kernels. Noise correlations decay with distance between neurons but are only observed if the range of excitatory connections is smaller than the range of inhibitory connections (“Mexican hat” connectivity) and if the connection strengths are sufficiently strong. These correlations arise from a moving blob-like structure of evoked activity, which is absent if inhibitory interactions have a smaller range (“inverse Mexican hat” connectivity). Spatially structured external inputs fixate these blobs to certain locations and thus effectively reduce noise correlations. We further investigated the influence of these network configurations on stimulus encoding. On the one hand, the observed correlations diminish information about a stimulus encoded by a network. On the other hand, correlated activity allows for more precise encoding of stimulus information if the decoder has only access to a limited amount of neurons.

Qualitative changes in phase-response curve and synchronization at the saddle-node-loop bifurcation

Prominent changes in neuronal dynamics have previously been attributed to a specific switch in onset bifurcation, the Bogdanov-Takens (BT) point. This study unveils another, relevant and so far underestimated transition point: the saddle-node-loop bifurcation, which can be reached by several parameters, including capacitance, leak conductance, and temperature. This bifurcation turns out to induce even more drastic changes in synchronization than the BT transition. This result arises from a direct effect of the saddle-node-loop bifurcation on the limit cycle and hence spike dynamics. In contrast, the BT bifurcation exerts its immediate influence upon the subthreshold dynamics and hence only indirectly relates to spiking. We specifically demonstrate that the saddle-node-loop bifurcation (i) ubiquitously occurs in planar neuron models with a saddle node on invariant cycle onset bifurcation, and (ii) results in a symmetry breaking of the system's phase-response curve. The latter entails an increase in synchronization range in pulse-coupled oscillators, such as neurons. The derived bifurcation structure is of interest in any system for which a relaxation limit is admissible, such as Josephson junctions and chemical oscillators.