Sharpening of directional selectivity from neural output of rabbit retina

The estimation of motion direction from time varying retinal images is a fundamental task of visual systems. Neurons that selectively respond to directional visual motion are found in almost all species. In many of them already in the retina direction selective neurons signal their preferred direction of movement. Scientific evidences suggest that direction selectivity is carried from the retina to higher brain areas. Here we adopt a simple integrate-and-fire neuron model, inspired by recent work of Casti et al. (2008), to investigate how directional selectivity changes in cells postsynaptic to directional selective retinal ganglion cells (DSRGC). Our model analysis shows that directional selectivity in the postsynaptic cells increases over a wide parameter range. The degree of directional selectivity positively correlates with the probability of burst-like firing of presynaptic DSRGCs. Postsynaptic potentials summation and spike threshold act together as a temporal filter upon the input spike train. Prior to the intricacy of neural circuitry between retina and higher brain areas, we suggest that sharpening is a straightforward result of the intrinsic spiking pattern of the DSRGCs combined with the summation of excitatory postsynaptic potentials and the spike threshold in postsynaptic neurons.     

A review of the integrate-and-fire neuron model: II. Inhomogeneous synaptic input and network properties

The integrate-and-fire neuron model describes the state of a neuron in terms of its membrane potential, which is determined by the synaptic inputs and the injected current that the neuron receives. When the membrane potential reaches a threshold, an action potential (spike) is generated. This review considers the model in which the synaptic input varies periodically and is described by an inhomogeneous Poisson process, with both current and conductance synapses. The focus is on the mathematical methods that allow the output spike distribution to be analyzed, including first passage time methods and the Fokker–Planck equation. Recent interest in the response of neurons to periodic input has in part arisen from the study of stochastic resonance, which is the noise-induced enhancement of the signal-to-noise ratio. Networks of integrate-and-fire neurons behave in a wide variety of ways and have been used to model a variety of neural, physiological, and psychological phenomena. The properties of the integrate-and-fire neuron model with synaptic input described as a temporally homogeneous Poisson process are reviewed in an accompanying paper (Burkitt in Biol Cybern, 2006).     

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

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

Emergence of resonances in neural systems: the interplay between adaptive threshold and short-term synaptic plasticity

In this work we study the detection of weak stimuli by spiking (integrate-and-fire) neurons in the presence of certain level of noisy background neural activity. Our study has focused in the realistic assumption that the synapses in the network present activity-dependent processes, such as short-term synaptic depression and facilitation. Employing mean-field techniques as well as numerical simulations, we found that there are two possible noise levels which optimize signal transmission. This new finding is in contrast with the classical theory of stochastic resonance which is able to predict only one optimal level of noise. We found that the complex interplay between adaptive neuron threshold and activity-dependent synaptic mechanisms is responsible for this new phenomenology. Our main results are confirmed by employing a more realistic FitzHugh-Nagumo neuron model, which displays threshold variability, as well as by considering more realistic stochastic synaptic models and realistic signals such as poissonian spike trains.     

Synaptic depression increases the selectivity of a neuron to its preferred pattern and binarizes the neural code

The preferred pattern of a neuron is defined here by the set of features detected by its excitatory inputs. It is shown that the Leaky integrate-and-fire (LIF) model of a neuron has a poor selectivity to its preferred pattern. Its response is determined by the total current injected by input spike trains. Thus, a few inputs with a high activity (an incomplete pattern) can elicit the same response as many inputs (a complete pattern) with a weak activity. A theoretical model of depressing synapse with linear recovery is proposed which eliminates this problem. Using this model, the time-averaged current injected in the soma by a spike train becomes independent on its frequency. The neural code thus becomes binary, and the response strength of the target neuron depends only on the number of active inputs. Simulations show that a biological model of strong synaptic depression has effects similar to those of the ideal linear model. The best selectivity is obtained with long somatic decay time constants (>50 ms) and with depression recovery time constants larger or equal to the somatic decay time constant. Thus, by eliminating information carried in the input firing rate, a neuron can improve its pattern recognition performance.     

Influence of temporal correlation of synaptic input on the rate and variability of firing in neurons

The spike trains that transmit information between neurons are stochastic. We used the theory of random point processes and simulation methods to investigate the influence of temporal correlation of synaptic input current on firing statistics. The theory accounts for two sources for temporal correlation: synchrony between spikes in presynaptic input trains and the unitary synaptic current time course. Simulations show that slow temporal correlation of synaptic input leads to high variability in firing. In a leaky integrate-and-fire neuron model with spike afterhyperpolarization the theory accurately predicts the firing rate when the spike threshold is higher than two standard deviations of the membrane potential fluctuations. For lower thresholds the spike afterhyperpolarization reduces the firing rate below the theory's predicted level when the synaptic correlation decays rapidly. If the synaptic correlation decays slower than the spike afterhyperpolarization, spike bursts can occur during single broad peaks of input fluctuations, increasing the firing rate over the prediction. Spike bursts lead to a coefficient of variation for the interspike intervals that can exceed one, suggesting an explanation of high coefficient of variation for interspike intervals observed in vivo.     

An extended model for a spiking neuron class

This paper proposes an extension to the model of a spiking neuron for information processing in artificial neural networks, developing a new approach for the dynamic threshold of the integrate-and-fire neuron. This new approach invokes characteristics of biological neurons such as the behavior of chemical synapses and the receptor field. We demonstrate how such a digital model of spiking neurons can solve complex nonlinear classification with a single neuron, performing experiments for the classical XOR problem. Compared with rate-coded networks and the classical integrate-and-fire model, the trained network demonstrated faster information processing, requiring fewer neurons and shorter learning periods. The extended model validates all the logic functions of biological neurons when such functions are necessary for the proper flow of binary codes through a neural network.     

Recording Light-evoked Postsynaptic Responses in Neurons in Dark-adapted,Mouse Retinal Slice Preparations Using Patch Clamp Techniques

The retina is the gateway to the visual system. To understand visual signal processing mechanisms, we investigate retinal neural network functions. Retinal neurons in the network comprise of numerous subtypes. More than 10 subtypes of bipolar cells, ganglion cells, and amacrine cells have been identified by morphological studies. Multiple subtypes of retinal neurons are thought to encode distinct features of visual signaling, such as motion and color, and form multiple neural pathways. However, the functional roles of each neuron in visual signal processing are not fully understood. The patch clamp method is useful to address this fundamental question. Here, a protocol to record light-evoked synaptic responses in mouse retinal neurons using patch clamp recordings in dark-adapted conditions is provided. The mouse eyes are dark-adapted O/N, and retinal slice preparations are dissected in a dark room using infrared illumination and viewers. Infrared light does not activate mouse photoreceptors and thus preserves their light responsiveness. Patch clamp is used to record light-evoked responses in retinal neurons. A fluorescent dye is injected during recordings to characterize neuronal morphological subtypes. This procedure enables us to determine the physiological functions of each neuron in the mouse retina.     

Visual pattern discrimination by population retinal ganglion cells’ activities during natural movie stimulation

In the visual system, neurons often fire in synchrony, and it is believed that synchronous activities of group neurons are more efficient than single cell response in transmitting neural signals to down-stream neurons. However, whether dynamic natural stimuli are encoded by dynamic spatiotemporal firing patterns of synchronous group neurons still needs to be investigated. In this paper we recorded the activities of population ganglion cells in bullfrog retina in response to time-varying natural images (natural scene movie) using multi-electrode arrays. In response to some different brief section pairs of the movie, synchronous groups of retinal ganglion cells (RGCs) fired with similar but different spike events. We attempted to discriminate the movie sections based on temporal firing patterns of single cells and spatiotemporal firing patterns of the synchronous groups of RGCs characterized by a measurement of subsequence distribution discrepancy. The discrimination performance was assessed by a classification method based on Support Vector Machines. Our results show that different movie sections of the natural movie elicited reliable dynamic spatiotemporal activity patterns of the synchronous RGCs, which are more efficient in discriminating different movie sections than the temporal patterns of the single cells’ spike events. These results suggest that, during natural vision, the down-stream neurons may decode the visual information from the dynamic spatiotemporal patterns of the synchronous group of RGCs’ activities.     

Activity-induced long-term potentiation of excitatory synapses in developing zebrafish retina in vivo

Neural activity-induced long-term potentiation (LTP) of synaptic transmission is believed to be one of the cellular mechanisms underlying experience-dependent developmental refinement of neural circuits. Although it is well established that visual experience and neural activity are critical for the refinement of retinal circuits, whether and how LTP occurs in the retina remain unknown. Using in?vivo perforated whole-cell recording and two-photon calcium imaging, we find that both repeated electrical and visual stimulations can induce LTP at excitatory synapses formed by bipolar cells on retinal ganglion cells in larval but not juvenile zebrafish. LTP induction requires the activation of postsynaptic N-methyl-D-aspartate receptors, and its expression involves arachidonic acid-dependent presynaptic changes in calcium dynamics and neurotransmitter release. Physiologically, both electrical and visual stimulation-induced LTP can enhance visual responses of retinal ganglion cells. Thus, LTP exists in developing retinae with a presynaptic locus and may serve for visual experience-dependent refinement of retinal circuits.     

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.     

Spatial and temporal correlations of spike trains in frog retinal ganglion cells

For a neuron, firing activity can be in synchrony with that of others, which results in spatial correlation; on the other hand, spike events within each individual spike train may also correlate with each other, which results in temporal correlation. In order to investigate the relationship between these two phenomena, population neurons’ activities of frog retinal ganglion cells in response to binary pseudo-random checker-board flickering were recorded via a multi-electrode recording system. The spatial correlation index (SCI) and temporal correlation index (TCI) were calculated for the investigated neurons. Statistical results showed that, for a single neuron, the SCI and TCI values were highly related—a neuron with a high SCI value generally had a high TCI value, and these two indices were both associated with burst activities in spike train of the investigated neuron. These results may suggest that spatial and temporal correlations of single neuron’s spiking activities could be mutually modulated; and that burst activities could play a role in the modulation. We also applied models to test the contribution of spatial and temporal correlations for visual information processing. We show that a model considering spatial and temporal correlations could predict spikes more accurately than a model does not include any correlation.     

Visual pattern recognition based on spatio-temporal patterns of retinal ganglion cells’ activities

Neural information is processed based on integrated activities of relevant neurons. Concerted population activity is one of the important ways for retinal ganglion cells to efficiently organize and process visual information. In the present study, the spike activities of bullfrog retinal ganglion cells in response to three different visual patterns (checker-board, vertical gratings and horizontal gratings) were recorded using multi-electrode arrays. A measurement of subsequence distribution discrepancy (MSDD) was applied to identify the spatio-temporal patterns of retinal ganglion cells' activities in response to different stimulation patterns. The results show that the population activity patterns were different in response to different stimulation patterns, such difference in activity pattern was consistently detectable even when visual adaptation occurred during repeated experimental trials. Therefore, the stimulus pattern can be reliably discriminated according to the spatio-temporal pattern of the neuronal activities calculated using the MSDD algorithm.     

Receptive-field modification in rat visual cortex induced by paired visual stimulation and single-cell spiking

Experience-dependent plasticity of visual cortical receptive fields (RFs) involves synaptic modifications in the underlying neural circuits, but the site and mechanism of these modifications remain to be elucidated. Using in vivo whole-cell recordings, we show that pairing visual stimulation at a given retinal location with spiking of a single neuron in developing rat visual cortex induces rapid RF modifications. The time course of the response to the visual stimulus at the paired RF location is altered, with an enhancement of the response preceding the spike time and a reduction following the spike. Such bidirectional modification is consistent with spike timing-dependent plasticity. Response modification also occurs at nearby locations, the direction and magnitude of which are correlated with the change at the paired location. In addition, changes at unpaired locations show a negative correlation with the initial strength of the response, which may facilitate rapid modification of the spatial RF profile.     

A key role of starburst amacrine cells in originating retinal directional selectivity and optokinetic eye movement.

The directional selectivity of retinal ganglion cell responses represents a primitive pattern recognition that operates within a retinal neural circuit. The cellular origin and mechanism of directional selectivity were investigated by selectively eliminating retinal starburst amacrine cells, using immunotoxin-mediated cell targeting techniques. Starburst cell ablation in the adult retina abolished not only directional selectivity of ganglion cell responses but also an optokinetic eye reflex derived by stimulus movement. Starburst cells therefore serve as the key element that discriminates the direction of stimulus movement through integrative synaptic transmission and play a pivotal role in information processing that stabilizes image motion.     

The chronotron: a neuron that learns to fire temporally precise spike patterns

In many cases, neurons process information carried by the precise timings of spikes. Here we show how neurons can learn to generate specific temporally precise output spikes in response to input patterns of spikes having precise timings, thus processing and memorizing information that is entirely temporally coded, both as input and as output. We introduce two new supervised learning rules for spiking neurons with temporal coding of information (chronotrons), one that provides high memory capacity (E-learning), and one that has a higher biological plausibility (I-learning). With I-learning, the neuron learns to fire the target spike trains through synaptic changes that are proportional to the synaptic currents at the timings of real and target output spikes. We study these learning rules in computer simulations where we train integrate-and-fire neurons. Both learning rules allow neurons to fire at the desired timings, with sub-millisecond precision. We show how chronotrons can learn to classify their inputs, by firing identical, temporally precise spike trains for different inputs belonging to the same class. When the input is noisy, the classification also leads to noise reduction. We compute lower bounds for the memory capacity of chronotrons and explore the influence of various parameters on chronotrons' performance. The chronotrons can model neurons that encode information in the time of the first spike relative to the onset of salient stimuli or neurons in oscillatory networks that encode information in the phases of spikes relative to the background oscillation. Our results show that firing one spike per cycle optimizes memory capacity in neurons encoding information in the phase of firing relative to a background rhythm.     

Reverse spikeology: predicting single spikes.

Neural models that simulate single spike trains can help us understand the basic principles of neural coding in vision. Keat et al. (2001) develop a hybrid model that combines spatiotemporal filtering with nonlinear spike generation. The model does a good job of predicting the responses of single retinal ganglion cells and thalamic relay neurons.