Predicting the synaptic information efficacy in cortical layer 5 pyramidal neurons using a minimal integrate-and-fire model

Synaptic information efficacy (SIE) is a statistical measure to quantify the efficacy of a synapse. It measures how much information is gained, on the average, about the output spike train of a postsynaptic neuron if the input spike train is known. It is a particularly appropriate measure for assessing the input–output relationship of neurons receiving dynamic stimuli. Here, we compare the SIE of simulated synaptic inputs measured experimentally in layer 5 cortical pyramidal neurons in vitro with the SIE computed from a minimal model constructed to fit the recorded data. We show that even with a simple model that is far from perfect in predicting the precise timing of the output spikes of the real neuron, the SIE can still be accurately predicted. This arises from the ability of the model to predict output spikes influenced by the input more accurately than those driven by the background current. This indicates that in this context, some spikes may be more important than others. Lastly we demonstrate another aspect where using mutual information could be beneficial in evaluating the quality of a model, by measuring the mutual information between the model’s output and the neuron’s output. The SIE, thus, could be a useful tool for assessing the quality of models of single neurons in preserving input–output relationship, a property that becomes crucial when we start connecting these reduced models to construct complex realistic neuronal networks.     

Firing pattern and synchronization property analysis in a network model of the olfactory bulb

In the olfactory system, both the temporal spike structure and spatial distribution of neuronal activity are important for processing odor information. In this paper, a biophysically-detailed, spiking neuronal model is used to simulate the activity of olfactory bulb. It is shown that by varying some key parameters such as maximal conductances of Ks and Nap the spike train of single neuron can exhibit various firing patterns. Synchronization in coupled neurons is also investigated as the coupling strength varying in the situation of two neurons and network. It is illustrated that the coupled neurons can exhibit different types of pattern when the coupling strength varies. These results may be instructive to understand information transmission in olfactory system.     

Measuring spike timing distance in the Hindmarsh–Rose neurons

In the present paper, a simple spike timing distance is defined which can be used to measure the degree of synchronization with the information only encoded in the precise timing of the spike trains. Via calculating the spike timing distance defined in this paper, the spike train similarity of uncoupled Hindmarsh–Rose neurons in bursting or spiking states with different initial conditions is investigated and the results are compared with other spike train distance measures. Later, the spike timing distance measure is applied to study the synchronization of coupled or common noise-stimulated neurons. Counterintuitively, the addition of weak coupling or common noise doesn’t enhance the degree of synchronization although after critical values, both of them can induce complete synchronizations. More interestingly, the common noise plays opposite roles for weak and strong enough couplings. Finally, it should be noted that the measure defined in this paper can be extended to measure large neuronal ensembles and the lag synchronization.     

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.     

Selectivity of stimulus induced responses in cultured hippocampal networks on microelectrode arrays

Sensory information can be encoded using the average firing rate and spike occurrence times in neuronal network responses to external stimuli. Decoding or retrieving stimulus characteristics from the response pattern generally implies that the corresponding neural network has a selective response to various input signals. The role of various spiking activity characteristics (e.g., spike rate and precise spike timing) for basic information processing was widely investigated on the level of neural populations but gave inconsistent evidence for particular mechanisms. Multisite electrophysiology of cultured neural networks grown on microelectrode arrays is a recently developed tool and currently an active research area. In this study, we analyzed the stimulus responses represented by network-wide bursts evoked from various spatial locations (electrodes). We found that the response characteristics, such as the burst initiation time and the spike rate, can be used to retrieve information about the stimulus location. The best selectivity in the response spiking pattern could be found for a small subpopulation of neurones (electrodes) at relatively short post-stimulus intervals. Such intervals were unique for each culture due to the non-uniform organization of the functional connectivity in the network during spontaneous development.     

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.     

Uncovering the synchronization dynamics from correlated neuronal activity quantifies assembly formation

 Synchronous network excitation is believed to play an outstanding role in neuronal information processing. Due to the stochastic nature of the contributing neurons, however, those synchronized states are difficult to detect in electrode recordings. We present a framework and a model for the identification of such network states and of their dynamics in a specific experimental situation. Our approach operationalizes the notion of neuronal groups forming assemblies via synchronization based on experimentally obtained spike trains. The dynamics of such groups is reflected in the sequence of synchronized states, which we describe as a renewal dynamics. We furthermore introduce a rate function which is dependent on the internal network phase that quantifies the activity of neurons contributing to the observed spike train. This constitutes a hidden state model which is formally equivalent to a hidden Markov model, and all its parameters can be accurately determined from the experimental time series using the Baum-Welch algorithm. We apply our method to recordings from the cat visual cortex which exhibit oscillations and synchronizations. The parameters obtained for the hidden state model uncover characteristic properties of the system including synchronization, oscillation, switching, background activity and correlations. In applications involving multielectrode recordings, the extracted models quantify the extent of assembly formation and can be used for a temporally precise localization of system states underlying a specific spike train. Received: 30 March 1993/Accepted in revised form: 16 April 1994     

To spike,or when to spike?

Recent experimental reports have suggested that cortical networks can operate in regimes were sensory information is encoded by relatively small populations of spikes and their precise relative timing. Combined with the discovery of spike timing dependent plasticity, these findings have sparked growing interest in the capabilities of neurons to encode and decode spike timing based neural representations. To address these questions, a novel family of methodologically diverse supervised learning algorithms for spiking neuron models has been developed. These models have demonstrated the high capacity of simple neural architectures to operate also beyond the regime of the well established independent rate codes and to utilize theoretical advantages of spike timing as an additional coding dimension.     

Compromised axonal functionality after neurodegeneration,concussion and/or traumatic brain injury

Axonal swellings are almost universal in neurodegenerative diseases of the central nervous system, including Alzheimer’s and Parkinson’s disease. Concussions and traumatic brain injuries can also produce cognitive and behavioral deficits by compromising neuronal morphology. Using a spike metric analysis, we characterize computationally the effects of such axonal varicosities on spike train propagation by comparing Poisson spike train classes before and after propagation through a prototypical axonal enlargement, or focused axonal swelling. Misclassification of spike train classes and low-pass filtering of firing rate activity increases with more pronounced axonal injury. We show that confusion matrices and a calculation of the loss of transmitted information provide a very practical way to characterize how injured neurons compromise the signal processing and faithful conductance of spike trains. The method demonstrates that (i) neural codes encoded with low firing rates are more robust to injury than those encoded with high firing rates, (ii) classification depends upon the length of the spike train used to encode information, and (iii) axonal injuries reduce the variance of spike trains within a given stimulus class. The work introduces a novel theoretical and computational framework to quantify the interplay between electrophysiological dynamics with focused axonal swellings generated by injury or other neurodegenerative processes. It further suggests how pharmacology and plasticity may play a role in recovery of neural computation. Ultimately, the work bridges vast experimental observations of in vitro morphological pathologies with post-traumatic cognitive and behavioral dysfunction.     

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.     

Multiple Spike Time Patterns Occur at Bifurcation Points of Membrane Potential Dynamics

The response of a neuron to repeated somatic fluctuating current injections in vitro can elicit a reliable and precisely timed sequence of action potentials. The set of responses obtained across trials can also be interpreted as the response of an ensemble of similar neurons receiving the same input, with the precise spike times representing synchronous volleys that would be effective in driving postsynaptic neurons. To study the reproducibility of the output spike times for different conditions that might occur in vivo, we somatically injected aperiodic current waveforms into cortical neurons in vitro and systematically varied the amplitude and DC offset of the fluctuations. As the amplitude of the fluctuations was increased, reliability increased and the spike times remained stable over a wide range of values. However, at specific values called bifurcation points, large shifts in the spike times were obtained in response to small changes in the stimulus, resulting in multiple spike patterns that were revealed using an unsupervised classification method. Increasing the DC offset, which mimicked an overall increase in network background activity, also revealed bifurcation points and increased the reliability. Furthermore, the spike times shifted earlier with increasing offset. Although the reliability was reduced at bifurcation points, a theoretical analysis showed that the information about the stimulus time course was increased because each of the spike time patterns contained different information about the input.     

神经放电序列模式的一种识别方法及应用

提出了神经放电序列模式识别的一种新方法。首先,把放电序列用阶梯状的响应函数来表示,然后定义了其一阶、二阶形式导数以及形式积分。这三个特征量均有着不同的几何和物理意义,因此采用这三个特征量来刻画神经放电序列的模式,就可以较全面地表示其特征。对神经放电序列的重构也表明通过这几个特征量可以很好地反映序列中所包含的信息。作为应用例子,这种量化方法用来研究冷热感受器模型所产生的放电模式,结果表明它能够识别在不同温度条件下的放电模式。     

Studying spike trains using a van Rossum metric with a synapse-like filter

Spike trains are unreliable. For example, in the primary sensory areas, spike patterns and precise spike times will vary between responses to the same stimulus. Nonetheless, information about sensory inputs is communicated in the form of spike trains. A challenge in understanding spike trains is to assess the significance of individual spikes in encoding information. One approach is to define a spike train metric, allowing a distance to be calculated between pairs of spike trains. In a good metric, this distance will depend on the information the spike trains encode. This method has been used previously to calculate the timescale over which the precision of spike times is significant. Here, a new metric is constructed based on a simple model of synaptic conductances which includes binding site depletion. Including binding site depletion in the metric means that a given individual spike has a smaller effect on the distance if it occurs soon after other spikes. The metric proves effective at classifying neuronal responses by stimuli in the sample data set of electro-physiological recordings from the primary auditory area of the zebra finch fore-brain. This shows that this is an effective metric for these spike trains suggesting that in these spike trains the significance of a spike is modulated by its proximity to previous spikes. This modulation is a putative information-coding property of spike trains.     

Timing Precision in Population Coding of Natural Scenes in the Early Visual System

The timing of spiking activity across neurons is a fundamental aspect of the neural population code. Individual neurons in the retina, thalamus, and cortex can have very precise and repeatable responses but exhibit degraded temporal precision in response to suboptimal stimuli. To investigate the functional implications for neural populations in natural conditions, we recorded in vivo the simultaneous responses, to movies of natural scenes, of multiple thalamic neurons likely converging to a common neuronal target in primary visual cortex. We show that the response of individual neurons is less precise at lower contrast, but that spike timing precision across neurons is relatively insensitive to global changes in visual contrast. Overall, spike timing precision within and across cells is on the order of 10 ms. Since closely timed spikes are more efficient in inducing a spike in downstream cortical neurons, and since fine temporal precision is necessary to represent the more slowly varying natural environment, we argue that preserving relative spike timing at a ~10-ms resolution is a crucial property of the neural code entering cortex.     

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.     

Reading spike timing without a clock: intrinsic decoding of spike trains

The precise timing of action potentials of sensory neurons relative to the time of stimulus presentation carries substantial sensory information that is lost or degraded when these responses are summed over longer time windows. However, it is unclear whether and how downstream networks can access information in precise time-varying neural responses. Here, we review approaches to test the hypothesis that the activity of neural populations provides the temporal reference frames needed to decode temporal spike patterns. These approaches are based on comparing the single-trial stimulus discriminability obtained from neural codes defined with respect to network-intrinsic reference frames to the discriminability obtained from codes defined relative to the experimenter''s computer clock. Application of this formalism to auditory, visual and somatosensory data shows that information carried by millisecond-scale spike times can be decoded robustly even with little or no independent external knowledge of stimulus time. In cortex, key components of such intrinsic temporal reference frames include dedicated neural populations that signal stimulus onset with reliable and precise latencies, and low-frequency oscillations that can serve as reference for partitioning extended neuronal responses into informative spike patterns.     

A joint interspike interval difference stochastic spike train analysis: detecting local trends in the temporal firing patterns of single neurons

We introduce a stochastic spike train analysis method called joint interspike interval difference (JISID) analysis. By design, this method detects changes in firing interspike intervals (ISIs), called local trends, within a 4-spike pattern in a spike train. This analysis classifies 4-spike patterns that have similar incremental changes. It characterizes the higher-order serial dependence in spike firing relative to changes in the firing history. Mathematically, this spike train analysis describes the statistical joint distribution of consecutive changes in ISIs, from which the serial dependence of the changes in higher-order intervals can be determined. It is similar to the joint interspike interval (JISI) analysis, except that the joint distribution of consecutive ISI differences (ISIDs) is quantified. The graphical location of points in the JISID scatter plot reveals the local trends in firing (i.e., monotonically increasing, monotonically decreasing, or transitional firing). The trajectory of these points in the serial-JISID plot traces the time evolution of these trends represented by a 5-spike pattern, while points in the JISID scatter plot represent trends of a 4-spike pattern. We provide complete theoretical interpretations of the JISID analysis. We also demonstrate that this method indeed identifies firing trends in both simulated spike trains and spike trains recorded from cultured neurons. Received: 13 May 1997 / Accepted in revised form: 9 December 1998     

Spike generating dynamics and the conditions for spike-time precision in cortical neurons

Temporal precision of spiking response in cortical neurons has been a subject of intense debate. Using a canonical model of spike generation, we explore the conditions for precise and reliable spike timing in the presence of Gaussian white noise. In agreement with previous results we find that constant stimuli lead to imprecise timing, while aperiodic stimuli yield precise spike timing. Under constant stimulus the neuron is a noise perturbed oscillator, the spike times follow renewal statistics and are imprecise. Under an aperiodic stimulus sequence, the neuron acts as a threshold element; the firing times are precisely determined by the dynamics of the stimulus. We further study the dependence of spike-time precision on the input stimulus frequency and find a non-linear tuning whose width can be related to the locking modes of the neuron. We conclude that viewing the neuron as a non-linear oscillator is the key for understanding spike-time precision.     

Recurrent Network Models for Perfect Temporal Integration of Fluctuating Correlated Inputs

Temporal integration of input is essential to the accumulation of information in various cognitive and behavioral processes, and gradually increasing neuronal activity, typically occurring within a range of seconds, is considered to reflect such computation by the brain. Some psychological evidence suggests that temporal integration by the brain is nearly perfect, that is, the integration is non-leaky, and the output of a neural integrator is accurately proportional to the strength of input. Neural mechanisms of perfect temporal integration, however, remain largely unknown. Here, we propose a recurrent network model of cortical neurons that perfectly integrates partially correlated, irregular input spike trains. We demonstrate that the rate of this temporal integration changes proportionately to the probability of spike coincidences in synaptic inputs. We analytically prove that this highly accurate integration of synaptic inputs emerges from integration of the variance of the fluctuating synaptic inputs, when their mean component is kept constant. Highly irregular neuronal firing and spike coincidences are the major features of cortical activity, but they have been separately addressed so far. Our results suggest that the efficient protocol of information integration by cortical networks essentially requires both features and hence is heterotic.