Measurement of variability dynamics in cortical spike trains

We propose a method for the time-resolved joint analysis of two related aspects of single neuron variability, the spiking irregularity measured by the squared coefficient of variation (CV(2)) of the ISIs and the trial-by-trial variability of the spike count measured by the Fano factor (FF). We provide a calibration of both estimators using the theory of renewal processes, and verify it for spike trains recorded in vitro. Both estimators exhibit a considerable bias for short observations that count less than about 5-10 spikes on average. The practical difficulty of measuring the CV(2) in rate modulated data can be overcome by a simple procedure of spike train demodulation which was tested in numerical simulations and in real spike trains. We propose to test neuronal spike trains for deviations from the null-hypothesis FF=CV(2). We show that cortical pyramidal neurons, recorded under controlled stationary input conditions in vitro, comply with this assumption. Performing a time-resolved joint analysis of CV(2) and FF of a single unit recording from the motor cortex of a behaving monkey we demonstrate how the dynamic change of their quantitative relation can be interpreted with respect to neuron intrinsic and extrinsic factors that influence cortical variability in vivo. Finally, we discuss the effect of several additional factors such as serial interval correlation and refractory period on the empiric relation of FF and CV(2).     

Coarse-Grained Clustering Dynamics of Heterogeneously Coupled Neurons

We study a population of spiking neurons which are subject to independent noise processes and a strong common time-dependent input. We show that the response of output spikes to independent noise shapes information transmission of such populations even when information transmission properties of single neurons are left unchanged. In particular, we consider two Poisson models in which independent noise either (i) adds and deletes spikes (AD model) or (ii) shifts spike times (STS model). We show that in both models suprathreshold stochastic resonance (SSR) can be observed, where the information transmitted by a neural population is increased with addition of independent noise. In the AD model, the presence of the SSR effect is robust and independent of the population size or the noise spectral statistics. In the STS model, the information transmission properties of the population are determined by the spectral statistics of the noise, leading to a strongly increased effect of SSR in some regimes, or an absence of SSR in others. Furthermore, we observe a high-pass filtering of information in the STS model that is absent in the AD model. We quantify information transmission by means of the lower bound on the mutual information rate and the spectral coherence function. To this end, we derive the signal–output cross-spectrum, the output power spectrum, and the cross-spectrum of two spike trains for both models analytically.     

Estimating the correlation between bursty spike trains and local field potentials

To further understand rhythmic neuronal synchronization, an increasingly useful method is to determine the relationship between the spiking activity of individual neurons and the local field potentials (LFPs) of neural ensembles. Spike field coherence (SFC) is a widely used method for measuring the synchronization between spike trains and LFPs. However, due to the strong dependency of SFC on the burst index, it is not suitable for analyzing the relationship between bursty spike trains and LFPs, particularly in high frequency bands. To address this issue, we developed a method called weighted spike field correlation (WSFC), which uses the first spike in each burst multiple times to estimate the relationship. In the calculation, the number of times that the first spike is used is equal to the spike count per burst. The performance of this method was demonstrated using simulated bursty spike trains and LFPs, which comprised sinusoids with different frequencies, amplitudes, and phases. This method was also used to estimate the correlation between pyramidal cells in the hippocampus and gamma oscillations in rats performing behaviors. Analyses using simulated and real data demonstrated that the WSFC method is a promising measure for estimating the correlation between bursty spike trains and high frequency LFPs.     

Methods for estimating neural firing rates,and their application to brain–machine interfaces

Neural spike trains present analytical challenges due to their noisy, spiking nature. Many studies of neuroscientific and neural prosthetic importance rely on a smoothed, denoised estimate of a spike train’s underlying firing rate. Numerous methods for estimating neural firing rates have been developed in recent years, but to date no systematic comparison has been made between them. In this study, we review both classic and current firing rate estimation techniques. We compare the advantages and drawbacks of these methods. Then, in an effort to understand their relevance to the field of neural prostheses, we also apply these estimators to experimentally gathered neural data from a prosthetic arm-reaching paradigm. Using these estimates of firing rate, we apply standard prosthetic decoding algorithms to compare the performance of the different firing rate estimators, and, perhaps surprisingly, we find minimal differences. This study serves as a review of available spike train smoothers and a first quantitative comparison of their performance for brain–machine interfaces.     

Nonlinear modeling of neural population dynamics for hippocampal prostheses

Developing a neural prosthesis for the damaged hippocampus requires restoring the transformation of population neural activities performed by the hippocampal circuitry. To bypass a damaged region, output spike trains need to be predicted from the input spike trains and then reinstated through stimulation. We formulate a multiple-input, multiple-output (MIMO) nonlinear dynamic model for the input–output transformation of spike trains. In this approach, a MIMO model comprises a series of physiologically-plausible multiple-input, single-output (MISO) neuron models that consist of five components each: (1) feedforward Volterra kernels transforming the input spike trains into the synaptic potential, (2) a feedback kernel transforming the output spikes into the spike-triggered after-potential, (3) a noise term capturing the system uncertainty, (4) an adder generating the pre-threshold potential, and (5) a threshold function generating output spikes. It is shown that this model is equivalent to a generalized linear model with a probit link function. To reduce model complexity and avoid overfitting, statistical model selection and cross-validation methods are employed to choose the significant inputs and interactions between inputs. The model is applied successfully to the hippocampal CA3–CA1 population dynamics. Such a model can serve as a computational basis for the development of hippocampal prostheses.     

Neonatal seizures induced persistent changes in intrinsic properties of CA1 rat hippocampal cells

We investigated the effects of repeated early-life seizures induced by flurothyl inhalation on intrinsic membrane properties of hippocampal pyramidal neurons from young rats (postnatal day 15-20). Intracellular recordings of CA1 and CA3 pyramidal neurons from flurothyl-treated and control rats revealed no significant differences in resting membrane potential, input resistance, membrane time constant, and action potential characteristics. In CA1 pyramidal cells from flurothyl-treated rats, the spike frequency adaptation and afterhyperpolarizing potential following a spike train were markedly reduced when compared with controls. In contrast, no significant alterations in the firing properties of CA3 pyramidal neurons were found. It is concluded that neonatal seizures lead to persistent changes in intrinsic membrane properties of CA1 pyramidal neurons. These alterations are consistent with an increase in neuronal excitability and may contribute to the behavioral deficit and epileptogenic predisposition observed in rats that experienced repeated neonatal seizures.     

Rate maintenance and resonance in the entorhinal cortex

Throughout the brain, neurons encode information in fundamental units of spikes. Each spike represents the combined thresholding of synaptic inputs and intrinsic neuronal dynamics. Here, we address a basic question of spike train formation: how do perithreshold synaptic inputs perturb the output of a spiking neuron? We recorded from single entorhinal principal cells in vitro and drove them to spike steadily at ～5 Hz (theta range) with direct current injection, then used a dynamic‐clamp to superimpose strong excitatory conductance inputs at varying rates. Neurons spiked most reliably when the input rate matched the intrinsic neuronal firing rate. We also found a striking tendency of neurons to preserve their rates and coefficients of variation, independently of input rates. As mechanisms for this rate maintenance, we show that the efficacy of the conductance inputs varied with the relationship of input rate to neuronal firing rate, and with the arrival time of the input within the natural period. Using a novel method of spike classification, we developed a minimal Markov model that reproduced the measured statistics of the output spike trains and thus allowed us to identify and compare contributions to the rate maintenance and resonance. We suggest that the strength of rate maintenance may be used as a new categorization scheme for neuronal response and note that individual intrinsic spiking mechanisms may play a significant role in forming the rhythmic spike trains of activated neurons; in the entorhinal cortex, individual pacemakers may dominate production of the regional theta rhythm.     

Perineuronal nets ensheath fast spiking, parvalbumin-immunoreactive neurons in the medial septum/diagonal band complex

Perineuronal nets, composed of extracellular matrix material, have previously been associated with parvalbumin-immunoreactive neurons in the medial septum/diagonal band (MS/DB) complex of the rat. The aim of this study was to correlate the presence of perineuronal nets with electrophysiological properties and parvalbumin immunoreactivity in MS/DB neurons. Intracellular recordings were made from cells in a brain slice preparation maintained in vitro, and neurons were characterized into four populations: (i) slow-firing neurons, (ii) burst-firing neurons, (iii) fast spiking neurons with narrow action potentials and a small degree of spike frequency adaptation, and (iv) regular spiking neurons with broader action potentials and a high degree of spike frequency adaptation. Following electrophysiological characterization, neurons were filled with biocytin, processed for parvalbumin immunoreactivity and stained for perineuronal nets using Wisteria floribunda lectin. The three substances were viewed with triple fluorescence. Fast spiking, nonadapting neurons, shown previously to contain parvalbumin immunoreactivity, were nearly all ensheathed by perineuronal nets. There was a population of small parvalbumin-immunoreactive neurons which did not possess perineuronal nets, and which were not encountered with the intracellular electrodes. The other three neuron types in the MS/DB did not contain parvalbumin immunoreactivity or perineuronal nets. In keeping with this neurochemical profile for electrophysiologically identified neurons, burst-firing neurons had action potential parameters more similar to those of regular spiking than of fast spiking neurons. We conclude that fast spiking neurons, presumed to be GABAergic septohippocampal projection neurons, are surrounded by supportive structures to enable the high level of neuronal discharge required for producing disinhibition of hippocampal pyramidal neurons.     

Heterogeneity among hippocampal pyramidal neurons revealed by their relation to theta-band oscillation and synchrony

Intracellular recordings were made in the dorsal hippocampal formation of urethane-anesthetized rats as the local field activity spontaneously cycled between a synchronous condition termed theta and an asynchronous condition termed LIA. All cells reported in this study were labeled with Neurobiotin and classified as theta-related or non-theta-related according to the system of Colom and Bland [Colom, L.V., Bland, B.H., 1987. State-dependent spike train dynamics of hippocampal formation neurons: evidence for theta-ON and theta-OFF cells. Brain Res. 422; 277-286]. The findings are the first demonstration that hippocampal pyramidal cells are functionally heterogeneous in relation to the generation of theta-band oscillation and synchrony. In field CA1 pyramidal cells formed theta-related subsets of phasic theta-ON cells and tonic theta-ON cells and non-theta-related subsets of simple spike discharging cells, complex spike discharging cells and "silent" cells. Similar findings were evident for CA3 pyramidal cells.     

Statistical technique for analysing functional connectivity of multiple spike trains

A new statistical technique, the Cox method, used for analysing functional connectivity of simultaneously recorded multiple spike trains is presented. This method is based on the theory of modulated renewal processes and it estimates a vector of influence strengths from multiple spike trains (called reference trains) to the selected (target) spike train. Selecting another target spike train and repeating the calculation of the influence strengths from the reference spike trains enables researchers to find all functional connections among multiple spike trains. In order to study functional connectivity an "influence function" is identified. This function recognises the specificity of neuronal interactions and reflects the dynamics of postsynaptic potential. In comparison to existing techniques, the Cox method has the following advantages: it does not use bins (binless method); it is applicable to cases where the sample size is small; it is sufficiently sensitive such that it estimates weak influences; it supports the simultaneous analysis of multiple influences; it is able to identify a correct connectivity scheme in difficult cases of "common source" or "indirect" connectivity. The Cox method has been thoroughly tested using multiple sets of data generated by the neural network model of the leaky integrate and fire neurons with a prescribed architecture of connections. The results suggest that this method is highly successful for analysing functional connectivity of simultaneously recorded multiple spike trains.     

Frequency-dependent synaptic potentiation, depression and spike timing induced by Hebbian pairing in cortical pyramidal neurons.

Experiments by Markram and Tsodyks (Nature, 382 (1996) 807-810) have suggested that Hebbian pairing in cortical pyramidal neurons potentiates or depresses the transmission of a subsequent pre-synaptic spike train at steady-state depending on whether the spike train is of low frequency or high frequency, respectively. The frequency above which pairing induced a significant decrease in steady-state synaptic efficacy was as low as about 20 Hz and this value depends on such synaptic properties as probability of release and time constant of recovery from short-term synaptic depression. These characteristics of cortical synapses have not yet been fully explained by neural models, notably the decreased steady-state synaptic efficacy at high pre-synaptic firing rates. This article suggests that this decrease in synaptic efficacy in cortical synapses was not observed at steady-state, but rather during a transition period preceding it whose duration is frequency-dependent. It is shown that the time taken to reach steady-state may be frequency-dependent, and may take considerably longer to occur at high than low frequencies. As a result, the pairing-induced decrease in synaptic efficacy at high pre-synaptic firing rates helps to localize the firing of the post-synaptic neuron to a short time interval following the onset of high-frequency pre-synaptic spike trains. This effect may "speed up the time scale" in response to high-frequency bursts of spikes, and may contribute to rapid synchronization of spike firing across cortical cells that are bound together by associatively learned connections.     

Place cell assemblies remain intact,despite reduced phase precession,after cholinergic disruption

The hippocampal theta rhythm is frequently viewed as a clocking mechanism that coordinates the spiking activity of neurons across the hippocampus to form coherent neural assemblies. Phase precession is a form of temporal coding evidencing this mechanism and is degraded following systemic pharmacological disruption of cholinergic signaling. However, whether neural assemblies are commensurately degraded, as would be predicted from a clocking mechanism hypothesis, remains unknown. To address this, we recorded the spiking activity of hippocampal place cells as rats completed laps on a circle track for chocolate drink before versus during the influence of a systemic muscarinic acetylcholine receptor antagonist. We compared the integrity of hippocampal ensembles using three approaches. The first approach used cross‐correlogram (CCG) analyses to ask if the relative spike‐timing between pairs of cells became less reliable. The second used a general linear model based analysis to ask whether the activity of simultaneously recorded neurons became any less predictive of the spiking activity of single neurons. Finally, the third approach used a reconstruction analysis to ask if the population activity was any less informative regarding the environmental position of the animal and whether theta sequences were impaired. The results of all three analyses paint a consistent picture: systemic cholinergic disruption did not degrade assembly integrity. These data demonstrate that place cell assemblies do not depend upon high quality phase precession.     

Pyramidal neurons in immature rat hippocampus are sensitive to beta-adrenergic agents.

The development of hippocampal neuronal sensitivities to the beta-noradrenergic agent, isoproterenol, was examined in tissue from immature rats. The in vitro hippocampal slice preparation was used to assess intracellularly recorded responses from hippocampal neurons to pressure-pulse and bath application of noradrenergic drugs. Effects of the drug on individual hippocampal CA3 pyramidal neurons were compared across several stages of development, ranging from postnatal day 4-5 (P4-5) to maturity. Isoproterenol, pressure-pulse applied to CA3c pyramidal cells, produced a depolarization of membrane potential and an increase in cell input resistance in tissue as young as P7. Spike frequency adaptation (in trains of action potentials triggered by depolarizing pulses) was reduced, as were the slow after-hyperpolarizations following the spike trains. All agonist effects were blocked by timolol, a beta-antagonist. Drug-induced changes in cell membrane and firing properties in immature tissue were qualitatively similar to beta-receptor-mediated noradrenergic effects in adult tissue. These results indicate that the beta-receptor-mediated component of the noradrenergic effect in rat hippocampus is physiologically functional by the seventh day of postnatal life; at earlier times (P4-5) these beta-receptor-mediated noradrenergic actions are, at best, equivocal.     

Role of the hippocampus in temporal and spatial navigation: an adaptive neural network

The hippocampus has been proposed to participate in either spatial or temporal mapping. As an alternative to these seemingly conflicting views, we hypothesized that the hippocampus computes 'aggregate predictions' of environmental events that are used to control associative learning. Aggregate predictions forecast what event is going to occur, when in time, and where in space. The hypothesis assumes that activity of hippocampal pyramidal neurons is proportional to the instantaneous value of the aggregate prediction, and that the computation of the aggregate prediction is impaired by hippocampal lesions. In order to test the 'aggregate prediction' hypothesis in both spatial and temporal tasks, this paper presents a real-time neural network capable of describing temporal discrimination and spatial learning in a unified fashion. The neural network incorporates detectors that can be tuned to a particular value of continuous temporal or spatial variables. In the temporal domain, computer simulations were carried out for temporal discrimination in classical conditioning and instrumental learning, classical conditioning under different interstimulus intervals (ISIs), and classical conditioning with mixed ISIs. In the spatial domain, computer simulations were carried out for place and cue learning. The paper shows that under the 'aggregate prediction' hypothesis the network correctly describes activity of hippocampal pyramidal neurons and the effect of hippocampal lesions in temporal and spatial learning. These results suggest that, rather than either a temporal or spatial function, the hippocampus is involved in the computation of variables common to both temporal and spatial navigation.     

Trial-to-Trial Variability of Spiking Delay Activity in Prefrontal Cortex Constrains Burst-Coding Models of Working Memory

A hallmark neuronal correlate of working memory (WM) is stimulus-selective spiking activity of neurons in PFC during mnemonic delays. These observations have motivated an influential computational modeling framework in which WM is supported by persistent activity. Recently, this framework has been challenged by arguments that observed persistent activity may be an artifact of trial-averaging, which potentially masks high variability of delay activity at the single-trial level. In an alternative scenario, WM delay activity could be encoded in bursts of selective neuronal firing which occur intermittently across trials. However, this alternative proposal has not been tested on single-neuron spike-train data. Here, we developed a framework for addressing this issue by characterizing the trial-to-trial variability of neuronal spiking quantified by Fano factor (FF). By building a doubly stochastic Poisson spiking model, we first demonstrated that the burst-coding proposal implies a significant increase in FF positively correlated with firing rate, and thus loss of stability across trials during the delay. Simulation of spiking cortical circuit WM models further confirmed that FF is a sensitive measure that can well dissociate distinct WM mechanisms. We then tested these predictions on datasets of single-neuron recordings from macaque PFC during three WM tasks. In sharp contrast to the burst-coding model predictions, we only found a small fraction of neurons showing increased WM-dependent burstiness, and stability across trials during delay was strengthened in empirical data. Therefore, reduced trial-to-trial variability during delay provides strong constraints on the contribution of single-neuron intermittent bursting to WM maintenance.SIGNIFICANCE STATEMENT There are diverging classes of theoretical models explaining how information is maintained in working memory by cortical circuits. In an influential model class, neurons exhibit persistent elevated memorandum-selective firing, whereas a recently developed class of burst-coding models suggests that persistent activity is an artifact of trial-averaging, and spiking is sparse in each single trial, subserved by brief intermittent bursts. However, this alternative picture has not been characterized or tested on empirical spike-train data. Here we combine mathematical analysis, computational model simulation, and experimental data analysis to test empirically these two classes of models and show that the trial-to-trial variability of empirical spike trains is not consistent with burst coding. These findings provide constraints for theoretical models of working memory.     

Precise feature based time scales and frequency decorrelation lead to a sparse auditory code

Sparse redundancy reducing codes have been proposed as efficient strategies for representing sensory stimuli. A prevailing hypothesis suggests that sensory representations shift from dense redundant codes in the periphery to selective sparse codes in cortex. We propose an alternative framework where sparseness and redundancy depend on sensory integration time scales and demonstrate that the central nucleus of the inferior colliculus (ICC) of cats encodes sound features by precise sparse spike trains. Direct comparisons with auditory cortical neurons demonstrate that ICC responses were sparse and uncorrelated as long as the spike train time scales were matched to the sensory integration time scales relevant to ICC neurons. Intriguingly, correlated spiking in the ICC was substantially lower than predicted by linear or nonlinear models and strictly observed for neurons with best frequencies within a "critical band," the hallmark of perceptual frequency resolution in mammals. This is consistent with a sparse asynchronous code throughout much of the ICC and a complementary correlation code within a critical band that may allow grouping of perceptually relevant cues.     

Peptidergic transmission in the brain. I. Vasopressin-like signal in the hippocampus

Studies of the action of arginine vasopressin (AVP) in the rat hippocampal slice have produced a model of the peptide's neural action. AVP excites local circuit inhibitory interneurons and causes consequent inhibition of pyramidal cells that is apparent as a reduction in the amplitude of the evoked population spike in field potential recording. Here we show that applied AVP does the same thing to the evoked population spike in the whole animal. Then we show that stimulation of the source of hippocampampal AVP, the medial amygdaloid nucleus, also inhibits the evoked population spike. Analysis of the synaptic potential indicates that the same mechanisms are employed by exogenously applied and endogenously released peptide. The inhibition can only be obtained by stimulating those brain structures known to project vasopressin fibers to the hippocampus. The stimulus-response characteristics and kinetics of the endogenous signal correspond to the properties of peptidergic signals in simple systems. The results are taken to support a transmitter role for AVP in the rat hippocampus.