Neural Coding with Graded Membrane Potential Changes and Spikes

The neural encoding of sensory stimuli is usually investigated for spike responses, although many neurons are known to convey information by graded membrane potential changes. We compare by model simulations how well different dynamical stimuli can be discriminated on the basis of spiking or graded responses. Although a continuously varying membrane potential contains more information than binary spike trains, we find situations where different stimuli can be better discriminated on the basis of spike responses than on the basis of graded responses. Spikes can be superior to graded membrane potential fluctuations if spikes sharpen the temporal structure of neuronal responses by amplifying fast transients of the membrane potential. Such fast membrane potential changes can be induced deterministically by the stimulus or can be due to membrane potential noise that is influenced in its statistical properties by the stimulus. The graded response mode is superior for discrimination between stimuli on a fine time scale.     

Response dynamics of bullfrog ON-OFF RGCs to different stimulus durations

Stimulus duration is an important feature of visual stimulation. In the present study, response properties of bullfrog ON-OFF retinal ganglion cells (RGCs) in exposure to different visual stimulus durations were studied. By using a multi-electrode recording system, spike discharges from ON-OFF RGCs were simultaneously recorded, and the cells’ ON and OFF responses were analyzed. It was found that the ON response characteristics, including response latency, spike count, as well as correlated activity and relative latency between pair-wise cells, were modulated by different light OFF intervals, while the OFF response characteristics were modulated by different light ON durations. Stimulus information carried by the ON and OFF responses was then analyzed, and it was found that information about different light ON durations was more carried by transient OFF response, whereas information about different light OFF intervals were more carried by transient ON response. Meanwhile, more than 80 % information about stimulus durations was carried by firing rate. These results suggest that ON-OFF RGCs are sensitive to different stimulus durations, and they can efficiently encode the information about visual stimulus duration by firing rate.     

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.     

Fitting of dynamic recurrent neural network models to sensory stimulus-response data

We present a theoretical study aiming at model fitting for sensory neurons. Conventional neural network training approaches are not applicable to this problem due to lack of continuous data. Although the stimulus can be considered as a smooth time-dependent variable, the associated response will be a set of neural spike timings (roughly the instants of successive action potential peaks) that have no amplitude information. A recurrent neural network model can be fitted to such a stimulus-response data pair by using the maximum likelihood estimation method where the likelihood function is derived from Poisson statistics of neural spiking. The universal approximation feature of the recurrent dynamical neuron network models allows us to describe excitatory-inhibitory characteristics of an actual sensory neural network with any desired number of neurons. The stimulus data are generated by a phased cosine Fourier series having a fixed amplitude and frequency but a randomly shot phase. Various values of amplitude, stimulus component size, and sample size are applied in order to examine the effect of the stimulus to the identification process. Results are presented in tabular and graphical forms at the end of this text. In addition, to demonstrate the success of this research, a study involving the same model, nominal parameters and stimulus structure, and another study that works on different models are compared to that of this research.     

Encoding Stimulus Information by Spike Numbers and Mean Response Time in Primary Auditory Cortex

Neurons can transmit information about sensory stimuli via their firing rate, spike latency, or by the occurrence of complex spike patterns. Identifying which aspects of the neural responses actually encode sensory information remains a fundamental question in neuroscience. Here we compared various approaches for estimating the information transmitted by neurons in auditory cortex in two very different experimental paradigms, one measuring spatial tuning and the other responses to complex natural stimuli. We demonstrate that, in both cases, spike counts and mean response times jointly carry essentially all the available information about the stimuli. Thus, in auditory cortex, whereas spike counts carry only partial information about stimulus identity or location, the additional availability of relatively coarse temporal information is sufficient in order to extract essentially all the sensory information available in the spike discharge pattern, at least for the relatively short stimuli (< ∼ 100 ms) commonly used in auditory research.     

Testing of information condensation in a model reverberating spiking neural network

Information about external world is delivered to the brain in the form of structured in time spike trains. During further processing in higher areas, information is subjected to a certain condensation process, which results in formation of abstract conceptual images of external world, apparently, represented as certain uniform spiking activity partially independent on the input spike trains details. Possible physical mechanism of condensation at the level of individual neuron was discussed recently. In a reverberating spiking neural network, due to this mechanism the dynamics should settle down to the same uniform/ periodic activity in response to a set of various inputs. Since the same periodic activity may correspond to different input spike trains, we interpret this as possible candidate for information condensation mechanism in a network. Our purpose is to test this possibility in a network model consisting of five fully connected neurons, particularly, the influence of geometric size of the network, on its ability to condense information. Dynamics of 20 spiking neural networks of different geometric sizes are modelled by means of computer simulation. Each network was propelled into reverberating dynamics by applying various initial input spike trains. We run the dynamics until it becomes periodic. The Shannon's formula is used to calculate the amount of information in any input spike train and in any periodic state found. As a result, we obtain explicit estimate of the degree of information condensation in the networks, and conclude that it depends strongly on the net's geometric size.     

The Possible Role of Spike Patterns in Cortical Information Processing

When the same visual stimulus is presented across many trials, neurons in the visual cortex receive stimulus-related synaptic inputs that are reproducible across trials (S) and inputs that are not (N). The variability of spike trains recorded in the visual cortex and their apparent lack of spike-to-spike correlations beyond that implied by firing rate fluctuations, has been taken as evidence for a low S/N ratio. A recent re-analysis of in vivo cortical data revealed evidence for spike-to-spike correlations in the form of spike patterns. We examine neural dynamics at a higher S/N in order to determine what possible role spike patterns could play in cortical information processing. In vivo-like spike patterns were obtained in model simulations. Superpositions of multiple sinusoidal driving currents were especially effective in producing stable long-lasting patterns. By applying current pulses that were either short and strong or long and weak, neurons could be made to switch from one pattern to another. Cortical neurons with similar stimulus preferences are located near each other, have similar biophysical properties and receive a large number of common synaptic inputs. Hence, recordings of a single neuron across multiple trials are usually interpreted as the response of an ensemble of these neurons during one trial. In the presence of distinct spike patterns across trials there is ambiguity in what would be the corresponding ensemble, it could consist of the same spike pattern for each neuron or a set of patterns across neurons. We found that the spiking response of a neuron receiving these ensemble inputs was determined by the spike-pattern composition, which, in turn, could be modulated dynamically as a means for cortical information processing.     

Adaptive Spike Threshold Enables Robust and Temporally Precise Neuronal Encoding

Neural processing rests on the intracellular transformation of information as synaptic inputs are translated into action potentials. This transformation is governed by the spike threshold, which depends on the history of the membrane potential on many temporal scales. While the adaptation of the threshold after spiking activity has been addressed before both theoretically and experimentally, it has only recently been demonstrated that the subthreshold membrane state also influences the effective spike threshold. The consequences for neural computation are not well understood yet. We address this question here using neural simulations and whole cell intracellular recordings in combination with information theoretic analysis. We show that an adaptive spike threshold leads to better stimulus discrimination for tight input correlations than would be achieved otherwise, independent from whether the stimulus is encoded in the rate or pattern of action potentials. The time scales of input selectivity are jointly governed by membrane and threshold dynamics. Encoding information using adaptive thresholds further ensures robust information transmission across cortical states i.e. decoding from different states is less state dependent in the adaptive threshold case, if the decoding is performed in reference to the timing of the population response. Results from in vitro neural recordings were consistent with simulations from adaptive threshold neurons. In summary, the adaptive spike threshold reduces information loss during intracellular information transfer, improves stimulus discriminability and ensures robust decoding across membrane states in a regime of highly correlated inputs, similar to those seen in sensory nuclei during the encoding of sensory information.     

Firing-rate models for neurons with a broad repertoire of spiking behaviors

Capturing the response behavior of spiking neuron models with rate-based models facilitates the investigation of neuronal networks using powerful methods for rate-based network dynamics. To this end, we investigate the responses of two widely used neuron model types, the Izhikevich and augmented multi-adapative threshold (AMAT) models, to a range of spiking inputs ranging from step responses to natural spike data. We find (i) that linear-nonlinear firing rate models fitted to test data can be used to describe the firing-rate responses of AMAT and Izhikevich spiking neuron models in many cases; (ii) that firing-rate responses are generally too complex to be captured by first-order low-pass filters but require bandpass filters instead; (iii) that linear-nonlinear models capture the response of AMAT models better than of Izhikevich models; (iv) that the wide range of response types evoked by current-injection experiments collapses to few response types when neurons are driven by stationary or sinusoidally modulated Poisson input; and (v) that AMAT and Izhikevich models show different responses to spike input despite identical responses to current injections. Together, these findings suggest that rate-based models of network dynamics may capture a wider range of neuronal response properties by incorporating second-order bandpass filters fitted to responses of spiking model neurons. These models may contribute to bringing rate-based network modeling closer to the reality of biological neuronal networks.     

Why spikes? Hebbian learning and retrieval of time-resolved excitation patterns

Hebbian learning allows a network of spiking neurons to store and retrieve spatio-temporal patterns with a time resolution of 1 ms, despite the long postsynaptic and dendritic integration times. To show this, we introduce and analyze a model of spiking neurons, the spike response model, with a realistic distribution of axonal delays and with realistic postsynaptic potentials. Learning is performed by a local Hebbian rule which is based on the synchronism of presynaptic neurotransmitter release and some short-acting postsynaptic process. The time window of this synchronism determines the temporal resolution of pattern retrieval, which can be initiated by applying a short external stimulus pattern. Furthermore, a rate quantization is found in dependence upon the threshold value of the neurons, i.e., in a given time a pattern runsn times as often as learned, wheren is a positive integer (n 0). We show that all information about the spike pattern is lost if only mean firing rates (temporal average) or ensemble activities (spatial average) are considered. An average over several retrieval runs in order to generate a post-stimulus time histogram may also deteriorate the signal. The full information on a pattern is contained in the spike raster of a single run. Our results stress the importance, and advantage, of coding by spatio-temporal spike patterns instead of firing rates and average ensemble activity. The implications regarding modelling and experimental data analysis are discussed.     

Spike-based population coding and working memory

Compelling behavioral evidence suggests that humans can make optimal decisions despite the uncertainty inherent in perceptual or motor tasks. A key question in neuroscience is how populations of spiking neurons can implement such probabilistic computations. In this article, we develop a comprehensive framework for optimal, spike-based sensory integration and working memory in a dynamic environment. We propose that probability distributions are inferred spike-per-spike in recurrently connected networks of integrate-and-fire neurons. As a result, these networks can combine sensory cues optimally, track the state of a time-varying stimulus and memorize accumulated evidence over periods much longer than the time constant of single neurons. Importantly, we propose that population responses and persistent working memory states represent entire probability distributions and not only single stimulus values. These memories are reflected by sustained, asynchronous patterns of activity which make relevant information available to downstream neurons within their short time window of integration. Model neurons act as predictive encoders, only firing spikes which account for new information that has not yet been signaled. Thus, spike times signal deterministically a prediction error, contrary to rate codes in which spike times are considered to be random samples of an underlying firing rate. As a consequence of this coding scheme, a multitude of spike patterns can reliably encode the same information. This results in weakly correlated, Poisson-like spike trains that are sensitive to initial conditions but robust to even high levels of external neural noise. This spike train variability reproduces the one observed in cortical sensory spike trains, but cannot be equated to noise. On the contrary, it is a consequence of optimal spike-based inference. In contrast, we show that rate-based models perform poorly when implemented with stochastically spiking neurons.     

Relative spike timing in stochastic oscillator networks of the Hermissenda eye

The role of relative spike timing on sensory coding and stochastic dynamics of small pulse-coupled oscillator networks is investigated physiologically and mathematically, based on the small biological eye network of the marine invertebrate Hermissenda. Without network interactions, the five inhibitory photoreceptors of the eye network exhibit quasi-regular rhythmic spiking; in contrast, within the active network, they display more irregular spiking but collective network rhythmicity. We investigate the source of this emergent network behavior first analyzing the role of relative input to spike–timing relationships in individual cells. We use a stochastic phase oscillator equation to model photoreceptor spike sequences in response to sequences of inhibitory current pulses. Although spike sequences can be complex and irregular in response to inputs, we show that spike timing is better predicted if relative timing of spikes to inputs is accounted for in the model. Further, we establish that greater noise levels in the model serve to destroy network phase-locked states that induce non-monotonic stimulus rate-coding, as predicted in Butson and Clark (J Neurophysiol 99:146–154, 2008a; J Neurophysiol 99:155–165, 2008b). Hence, rate-coding can function better in noisy spiking cells relative to non-noisy cells. We then study how relative input to spike–timing dynamics of single oscillators contribute to network-level dynamics. Relative timing interactions in the network sharpen the stimulus window that can trigger a spike, affecting stimulus encoding. Also, we derive analytical inter-spike interval distributions of cells in the model network, revealing that irregular Poisson-like spike emission and collective network rhythmicity are emergent properties of network dynamics, consistent with experimental observations. Our theoretical results generate experimental predictions about the nature of spike patterns in the Hermissenda eye.     

Noise,not stimulus entropy,determines neural information rate

In the quest for deciphering the neural code, theoretical advances were made which allow for the determination of the information rate inherent in the spike trains of nerve cells. However, up to now, the dependence of the information rate on stimulus parameters has not been studied in any neuron in a systematic way. Here, I investigate the information carried by the spike trains of H1, a motion-sensitive visual interneuron of the blowfly (Calliphora vicina) using a moving grating as a stimulus. Stimulus parameters fall in two classes: those that have only a minor effect on the information rate like increasing the frequency bandwidth or the maximum amplitude of the stimulus velocity, and those which dramatically affect the neural information rate, like varying the spatial size or the contrast of the visual pattern being moved. It appears that, for a broad range of complex stimuli, the neuron covers the stimulus with its whole response repertoire regardless of the stimulus entropy, with the information rate being limited by the noise of the stimulus and the neural hardware.     

Pattern recall in networks of chaotic neurons

This research investigates the potential utility of chaotic dynamics in neural information processing. A novel chaotic spiking neural network model is presented which is composed of non-linear dynamic state (NDS) neurons. The activity of each NDS neuron is driven by a set of non-linear equations coupled with a threshold based spike output mechanism. If time-delayed self-connections are enabled then the network stabilises to a periodic pattern of activation. Previous publications of this work have demonstrated that the chaotic dynamics which drive the network activity ensure that an extremely large number of such periodic patterns can be generated by this network. This paper presents a major extension to this model which enables the network to recall a pattern of activity from a selection of previously stabilised patterns.     

Sensory gating and its modulation by cannabinoids: electrophysiological, computational and mathematical analysis

Gating of sensory information can be assessed using an auditory conditioning-test paradigm which measures the reduction in the auditory evoked response to a test stimulus following an initial conditioning stimulus. Recording brainwaves from specific areas of the brain using multiple electrodes is helpful in the study of the neurobiology of sensory gating. In this paper, we use such technology to investigate the role of cannabinoids in sensory gating in the CA3 region of the rat hippocampus. Our experimental results show that application of the exogenous cannabinoid agonist WIN55,212-2 can abolish sensory gating. We have developed a phenomenological model of cannabinoid dynamics incorporated within a spiking neural network model of CA3 with synaptically interacting pyramidal and basket cells. Direct numerical simulations of this model suggest that the basic mechanism for this effect can be traced to the suppression of inhibition of slow GABA_B synapses. Furthermore, by working with a simpler mathematical firing rate model we are able to show the robustness of this mechanism for the abolition of sensory gating.     

Feedback enhances feedforward figure-ground segmentation by changing firing mode

In the visual cortex, feedback projections are conjectured to be crucial in figure-ground segregation. However, the precise function of feedback herein is unclear. Here we tested a hypothetical model of reentrant feedback. We used a previous developed 2-layered feedforward spiking network that is able to segregate figure from ground and included feedback connections. Our computer model data show that without feedback, neurons respond with regular low-frequency (～9 Hz) bursting to a figure-ground stimulus. After including feedback the firing pattern changed into a regular (tonic) spiking pattern. In this state, we found an extra enhancement of figure responses and a further suppression of background responses resulting in a stronger figure-ground signal. Such push-pull effect was confirmed by comparing the figure-ground responses with the responses to a homogenous texture. We propose that feedback controls figure-ground segregation by influencing the neural firing patterns of feedforward projecting neurons.     

Predictive Coding of Dynamical Variables in Balanced Spiking Networks

Two observations about the cortex have puzzled neuroscientists for a long time. First, neural responses are highly variable. Second, the level of excitation and inhibition received by each neuron is tightly balanced at all times. Here, we demonstrate that both properties are necessary consequences of neural networks that represent information efficiently in their spikes. We illustrate this insight with spiking networks that represent dynamical variables. Our approach is based on two assumptions: We assume that information about dynamical variables can be read out linearly from neural spike trains, and we assume that neurons only fire a spike if that improves the representation of the dynamical variables. Based on these assumptions, we derive a network of leaky integrate-and-fire neurons that is able to implement arbitrary linear dynamical systems. We show that the membrane voltage of the neurons is equivalent to a prediction error about a common population-level signal. Among other things, our approach allows us to construct an integrator network of spiking neurons that is robust against many perturbations. Most importantly, neural variability in our networks cannot be equated to noise. Despite exhibiting the same single unit properties as widely used population code models (e.g. tuning curves, Poisson distributed spike trains), balanced networks are orders of magnitudes more reliable. Our approach suggests that spikes do matter when considering how the brain computes, and that the reliability of cortical representations could have been strongly underestimated.     

Identifying temporal codes in spontaneously active sensory neurons

The manner in which information is encoded in neural signals is a major issue in Neuroscience. A common distinction is between rate codes, where information in neural responses is encoded as the number of spikes within a specified time frame (encoding window), and temporal codes, where the position of spikes within the encoding window carries some or all of the information about the stimulus. One test for the existence of a temporal code in neural responses is to add artificial time jitter to each spike in the response, and then assess whether or not information in the response has been degraded. If so, temporal encoding might be inferred, on the assumption that the jitter is small enough to alter the position, but not the number, of spikes within the encoding window. Here, the effects of artificial jitter on various spike train and information metrics were derived analytically, and this theory was validated using data from afferent neurons of the turtle vestibular and paddlefish electrosensory systems, and from model neurons. We demonstrate that the jitter procedure will degrade information content even when coding is known to be entirely by rate. For this and additional reasons, we conclude that the jitter procedure by itself is not sufficient to establish the presence of a temporal code.     

Oscillations in Large-Scale Cortical Networks: Map-Based Model

We develop a new computationally efficient approach for the analysis of complex large-scale neurobiological networks. Its key element is the use of a new phenomenological model of a neuron capable of replicating important spike pattern characteristics and designed in the form of a system of difference equations (a map). We developed a set of map-based models that replicate spiking activity of cortical fast spiking, regular spiking and intrinsically bursting neurons. Interconnected with synaptic currents these model neurons demonstrated responses very similar to those found with Hodgkin-Huxley models and in experiments. We illustrate the efficacy of this approach in simulations of one- and two-dimensional cortical network models consisting of regular spiking neurons and fast spiking interneurons to model sleep and activated states of the thalamocortical system. Our study suggests that map-based models can be widely used for large-scale simulations and that such models are especially useful for tasks where the modeling of specific firing patterns of different cell classes is important.     

Functional interactions in hierarchically organized neural networks studied with spatiotemporal firing patterns and phase-coupling frequencies

A scalable hardware/software hybrid module--called Ubidule--endowed with bio-inspired ontogenetic and epigenetic features is configured to run a neural networks simulation with developmental and evolvable capabilities. We simulated the activity of hierarchically organized spiking neural networks characterized by an initial developmental phase featuring cell death followed by spike timing dependent synaptic plasticity in presence of background noise. An upstream 'sensory' network received a spatiotemporally organized external input and downstream networks were activated only via the upstream network. Precise firing sequences, formed by recurrent patterns of spikes intervals above chance levels, were observed in all recording conditions, thus suggesting the build-up of a connectivity able to sustain temporal information processing. The activity of a Ubinet--a network of Ubidules--is analyzed by means of virtual electrodes that recorded neural signals similar to EEG. The analysis of these signals was compared with a small set of human recordings and revealed common patterns of shift in quadratic phase coupling. The results suggest some interpretations of changes and plasticity of functional interactions between cortical areas driven by external stimuli and by learning/cognitive