Presynaptic Spike Trains Research Articles

Temporal filters in response to presynaptic spike trains: interplay of cellular, synaptic and short-term plasticity time scales.

Temporal filters, the ability of postsynaptic neurons to preferentially select certain presynaptic input patterns over others, have been shown to be associated with the notion of information filtering and coding of sensory inputs. Short-term plasticity (depression and facilitation; STP) has been proposed to be an important player in the generation of temporal filters. We carry out a systematic modeling, analysis and computational study to understand how characteristic postsynaptic (low-, high- and band-pass) temporal filters are generated in response to periodic presynaptic spike trains in the presence STP. We investigate how the dynamic properties of these filters depend on the interplay of a hierarchy of processes, including the arrival of the presynaptic spikes, the activation of STP, its effect on the excitatory synaptic connection efficacy, and the response of the postsynaptic cell. These mechanisms involve the interplay of a collection of time scales that operate at the single-event level (roughly, during each presynaptic interspike-interval) and control the long-term development of the temporal filters over multiple presynaptic events. These time scales are generated at the levels of the presynaptic cell (captured by the presynaptic interspike-intervals), short-term depression and facilitation, synaptic dynamics and the post-synaptic cellular currents. We develop mathematical tools to link the single-event time scales with the time scales governing the long-term dynamics of the resulting temporal filters for a relatively simple model where depression and facilitation interact at the level of the synaptic efficacy change. We extend our results and tools to account for more complex models. These include multiple STP time scales and non-periodic presynaptic inputs. The results and ideas we develop have implications for the understanding of the generation of temporal filters in complex networks for which the simple feedforward network we investigate here is a building block.

Transmission of temporally correlated spike trains through synapses with short-term depression.

Short-term synaptic depression, caused by depletion of releasable neurotransmitter, modulates the strength of neuronal connections in a history-dependent manner. Quantifying the statistics of synaptic transmission requires stochastic models that link probabilistic neurotransmitter release with presynaptic spike-train statistics. Common approaches are to model the presynaptic spike train as either regular or a memory-less Poisson process: few analytical results are available that describe depressing synapses when the afferent spike train has more complex, temporally correlated statistics such as bursts. Here we present a series of analytical results—from vesicle release-site occupancy statistics, via neurotransmitter release, to the post-synaptic voltage mean and variance—for depressing synapses driven by correlated presynaptic spike trains. The class of presynaptic drive considered is that fully characterised by the inter-spike-interval distribution and encompasses a broad range of models used for neuronal circuit and network analyses, such as integrate-and-fire models with a complete post-spike reset and receiving sufficiently short-time correlated drive. We further demonstrate that the derived post-synaptic voltage mean and variance allow for a simple and accurate approximation of the firing rate of the post-synaptic neuron, using the exponential integrate-and-fire model as an example. These results extend the level of biological detail included in models of synaptic transmission and will allow for the incorporation of more complex and physiologically relevant firing patterns into future studies of neuronal networks.

Synaptic transmission of spike trains with arbitrary interspike intervals

Short-term synaptic depression, caused by depletion of releasable neurotransmitter vesicles, modulates the strength of neuronal connections in an activity-dependent manner [1,2]. Quantifying the statistics of this form of synaptic transmission requires the development of stochastic models linking probabilistic neurotransmitter release with the spike-train statistics of the presynaptic population [3,4]. A common approach has been to model the presynaptic spike train as either regular or a memory-less Poisson process [5] few analytical results are available that describe the behaviour of a depressing synapse when the afferent spike train has more complex, temporally correlated statistics. Recently, we have derived a series of results that allow for the fraction of occupied release sites and the neurotransmitter release probability to be calculated for a presynaptic spike train with arbitrary interspike interval (ISI) statistics. The results take a particularly compact form when the presynaptic spike times are generated by a renewal process, i.e. when the ISIs are independent. This encompasses a broad range of models that are currently used for circuit and network analyses, including the class of integrate-and-fire models. Our approach also allows for the postsynaptic voltage mean and variance to be calculated, which in turn allows for an approximation of the firing rate of a neuron driven by depressing synapses from non-Poissonian presynaptic neurons (Figure 1). These results will allow for the incorporation of more complex and physiologically relevant firing patterns

Curvature of dendritic nonlinearities modulates higher-order spiking correlations

Characterizing neural spiking covariability is essential for understanding the collective activity of neural populations. Recent experiments have provided evidence of statistical dependencies among groups of neurons beyond that expected by the firing rates and pairwise alone [1-3]. These correlations (HOCs) can be generated by common input [4] or motifs within the network architecture [5], yet a complete mechanistic understanding is lacking. We explore a novel mechanism through which higher-order can be modulated: dendritic nonlinearities. We simulated the spiking activity of a simple exponential integrate-and-fire model neuron in response to two correlated presynaptic spike trains and background noise. The synaptic conductances were either summed linearly at the soma or were filtered through a nonlinear dendritic transfer function (see Figure ​Figure1),1), which was chosen to have a similar magnitude of effect on nonlinear EPSP summation as observed by active dendritic properties in pyramidal cells [6]. Using maximum entropy techniques, correlations in the circuit were quantified as the probability of synchronous triplet spiking between the postsynaptic cell and its two presynaptic inputs beyond what could be captured by the firing rates and pairwise alone, normalized by the product of the standard deviations. We found that superlinear dendrites significantly increased the level of triplet. On the other hand, saturating dendrites decorrelated triplets. These results reveal that HOCs in spiking activity are modulated by the curvature of the dendritic transfer function. Finally, this study demonstrates how intrinsic single-cell properties can tune spiking covariability in neural populations. Figure 1 A. Transfer functions depicting the summation of synaptic inputs for linear dendrites. B. Transfer function for saturating dendritic nonlinearities (solid line), as well as the identity (dotted line). C. Same as B for superlinear dendrites. D-F. Triplet ...

Statistical structure of neural spiking under non-Poissonian or other non-white stimulation.

Nerve cells in the brain generate sequences of action potentials with a complex statistics. Theoretical attempts to understand this statistics were largely limited to the case of a temporally uncorrelated input (Poissonian shot noise) from the neurons in the surrounding network. However, the stimulation from thousands of other neurons has various sorts of temporal structure. Firstly, input spike trains are temporally correlated because their firing rates can carry complex signals and because of cell-intrinsic properties like neural refractoriness, bursting, or adaptation. Secondly, at the connections between neurons, the synapses, usage-dependent changes in the synaptic weight (short-term plasticity) further shape the correlation structure of the effective input to the cell. From the theoretical side, it is poorly understood how these correlated stimuli, so-called colored noise, affect the spike train statistics. In particular, no standard method exists to solve the associated first-passage-time problem for the interspike-interval statistics with an arbitrarily colored noise. Assuming that input fluctuations are weaker than the mean neuronal drive, we derive simple formulas for the essential interspike-interval statistics for a canonical model of a tonically firing neuron subjected to arbitrarily correlated input from the network. We verify our theory by numerical simulations for three paradigmatic situations that lead to input correlations: (i) rate-coded naturalistic stimuli in presynaptic spike trains; (ii) presynaptic refractoriness or bursting; (iii) synaptic short-term plasticity. In all cases, we find severe effects on interval statistics. Our results provide a framework for the interpretation of firing statistics measured in vivo in the brain.

Stein's neuronal model with pooled renewal input.

The input of Stein's model of a single neuron is usually described by using a Poisson process, which is assumed to represent the behaviour of spikes pooled from a large number of presynaptic spike trains. However, such a description of the input is not always appropriate as the variability cannot be separated from the intensity. Therefore, we create and study Stein's model with a more general input, a sum of equilibrium renewal processes. The mean and variance of the membrane potential are derived for this model. Using these formulas and numerical simulations, the model is analyzed to study the influence of the input variability on the properties of the membrane potential and the output spike trains. The generalized Stein's model is compared with the original Stein's model with Poissonian input using the relative difference of variances of membrane potential at steady state and the integral square error of output interspike intervals. Both of the criteria show large differences between the models for input with high variability.

Correlated neuronal activity and its relationship to coding, dynamics and network architecture.

Correlated neuronal activity and its relationship to coding, dynamics and network architecture.

The impact of short term synaptic depression and stochastic vesicle dynamics on neuronal variability

Neuronal variability plays a central role in neural coding and impacts the dynamics of neuronal networks. Unreliability of synaptic transmission is a major source of neural variability: synaptic neurotransmitter vesicles are released probabilistically in response to presynaptic action potentials and are recovered stochastically in time. The dynamics of this process of vesicle release and recovery interacts with variability in the arrival times of presynaptic spikes to shape the variability of the postsynaptic response. We use continuous time Markov chain methods to analyze a model of short term synaptic depression with stochastic vesicle dynamics coupled with three different models of presynaptic spiking: one model in which the timing of presynaptic action potentials are modeled as a Poisson process, one in which action potentials occur more regularly than a Poisson process (sub-Poisson) and one in which action potentials occur more irregularly (super-Poisson). We use this analysis to investigate how variability in a presynaptic spike train is transformed by short term depression and stochastic vesicle dynamics to determine the variability of the postsynaptic response. We find that sub-Poisson presynaptic spiking increases the average rate at which vesicles are released, that the number of vesicles released over a time window is more variable for smaller time windows than larger time windows and that fast presynaptic spiking gives rise to Poisson-like variability of the postsynaptic response even when presynaptic spike times are non-Poisson. Our results complement and extend previously reported theoretical results and provide possible explanations for some trends observed in recorded data.

Individual and collective properties of computationally efficient motoneuron models of types S and F with active dendrites

The input–output properties of motoneurons (MNs) and motor units (MUs) may be modulated by different physiological variables, including neuromodulators released by presynaptic neurons from the brainstem. Monoamines, such as serotonin and norepinephrine, act on MNs mainly by activating dendritic L-type Ca++ channels, generating a persistent inward current (PIC), which may change the input–output properties of the MU. If the firing properties of individual MNs and also the features of the force generated by the MUs can be changed, it follows that the descending monoaminergic systems may modulate the overall dynamics of motor control. The purpose of the present study is to investigate the effects of neuromodulation on the input–output properties of mathematically modeled type-specified MUs. Computationally efficient models are presented for S- and F-type mammalian MNs as well as a MN pool commanding muscle units of the Soleus muscle. The single models have a dendritic L-type Ca++ channel, generating a PIC, along with somatic currents that are responsible for spike-generating mechanisms and the afterhyperpolarization. The S-type active-dendrite (AD) MN model resulted highly excitable and discharged in a self-sustained manner after an excitatory input (bistability). An inhibitory activity turned off this self-sustained discharge. In addition, this low-threshold MN model showed a significant reduction in interspike interval (ISI) variability in comparison with an equivalent passive-dendrite (PD) MN model discharging at a similar mean rate. The frequency response gain from presynaptic spike train rate modulation to output spike train modulation had a clear valley from about 1–10Hz for the S-type AD MN model, whereas the PD model showed a gain increase instead. On the other hand, the frequency responses of PD and AD F-type models were similarly shaped, with the AD model having a higher gain at high frequencies. These results suggest that in motor behaviors where steady or low frequency activity is required, such as posture, PICs would aid low-threshold MNs to respond with regular spikes, reducing output variability, and would attenuate the effects of high-frequency input disturbances, helping maintain system steadiness. At the same time, high-threshold MNs being more responsive to high-frequency disturbances would contribute with the necessary activity to correct for postural deviations from a desired position. Simulation results from the neuromuscular model have shown that the PIC activation profoundly affects muscle force generation, with the neuromodulatory activity acting in the adjustment of the motor output. Both individual and collective results presented here expand the understanding of the versatility of monoaminergic neuromodulation in adjusting both the MN input–output coding and the control of force generation.

Short term synaptic depression with stochastic vesicle dynamics imposes a high-pass filter on presynaptic information

The filtering properties of synapses are modulated by a form of short term depression arising from the depletion of neurotransmitter vesicles. The uptake and release of these vesicles is stochastic in nature, but a widely used model of synaptic depression does not take this stochasticity into account. While this model of synaptic depression accurately captures the trial-averaged synaptic response to a presynaptic spike train [1], it fails to capture variability introduced by stochastic vesicle dynamics [2]. Our goal is to understand the impact of stochastic vesicle dynamics on filtering and information transfer in depressing synapses. We derive compact, closed-form expressions for the synaptic filter induced by short term synaptic depression when stochastic vesicle dynamics are taken into account and when they are not. We find that stochasticity in vesicle uptake and release fundamentally alters the way in which a synapse filters presynaptic information. Predictably, the variability introduced by this stochasticity reduces the rate at which information is transmitted through a synapse. Additionally, this variability introduces frequency-dependence to the transfer of information through a synapse: a model that ignores synaptic variability transmits slowly varying signals with the same fidelity as faster varying signals [3,4], but a model that takes this variability into account transmits faster varying signals with higher fidelity than slower signals (Figure ​(Figure1).1). Differences between the models persist even when the presynaptic cell makes many contacts onto the postsynaptic cell. We extend our analysis to the population level and conclude that a slowly varying signal must be encoded by a large presynaptic population if it is to be reliably transmitted through depressing synapses, but faster varying signals can be reliably encoded by smaller populations. Our results provide useful analytical tools for understanding the filtering properties of depressing synapses and have important consequences for neural coding in the presence of short term synaptic depression. Figure 1 The linear information rate, IL(g;s), which represents the information per unit time available to an optimal linear decoder that estimates a rate-coded presynaptic signal, s(t), by observing a postsynaptic conductance, g(t). The linear information rate ...

Short term synaptic depression imposes a frequency dependent filter on synaptic information transfer.

Depletion of synaptic neurotransmitter vesicles induces a form of short term depression in synapses throughout the nervous system. This plasticity affects how synapses filter presynaptic spike trains. The filtering properties of short term depression are often studied using a deterministic synapse model that predicts the mean synaptic response to a presynaptic spike train, but ignores variability introduced by the probabilistic nature of vesicle release and stochasticity in synaptic recovery time. We show that this additional variability has important consequences for the synaptic filtering of presynaptic information. In particular, a synapse model with stochastic vesicle dynamics suppresses information encoded at lower frequencies more than information encoded at higher frequencies, while a model that ignores this stochasticity transfers information encoded at any frequency equally well. This distinction between the two models persists even when large numbers of synaptic contacts are considered. Our study provides strong evidence that the stochastic nature neurotransmitter vesicle dynamics must be considered when analyzing the information flow across a synapse.

A two-stage cascade nonlinear dynamical model of single neurons for the separation and quantification of pre- and post-synaptic mechanisms of synaptic transmission.

Neurons receive pre-synaptic spike trains and transform them into post-synaptic spike trains. This spike train to spike train temporal transformation underlies all cognitive functions performed by neurons, e.g., learning and memory. The transformation is a highly nonlinear dynamical process that involves both pre- and post-synaptic mechanisms. The ability to separate and quantify the nonlinear dynamics of pre- and post-synaptic mechanism is needed to gain insights into this transformation. In this study, we developed a Volterra kernel based two-stage cascade model of synaptic transmission using synaptically-driven intracellular activities, to which broadband stimulation conditions were imposed. The first stage of the model represents the pre-synaptic mechanisms and describes the nonlinear dynamical transformation from pre-synaptic spike trains to transmitter vesicle release strengths. The vesicle release strengths were obtained from the intracellularly recorded excitatory post-synaptic currents (EPSCs). The second stage of the model represents the post-synaptic mechanisms and describes the nonlinear dynamical transformation from release strengths to excitatory post-synaptic potentials (EPSPs). One application of this cascade model is to analyze the pre- and post-synaptic mechanism change induced by long-term potentiation (LTP). This future application is expected to shed new light on the expression locus of LTP.

Interaction between synaptic dynamics and synaptic configuration determines the phase of the response to rhythmic inputs

The postsynaptic response of a neuron to time-varying inputs is determined by the interaction of presynaptic spike times with the short-term dynamics of each synapse. For a neuron driven by stochastic synapses and operating in afluctuation-driven regime, synaptic depression results in a quite different postsynaptic response to a large population input depending on how correlated in time the spikes across individual synapses are [1,2]. Here we show that not only the rate but the phase of the postsynaptic response to a rhythmic population input varies as a function of synaptic dynamics and synaptic configuration, which contributes to input correlations. In computer simulations, a single- compartment spiking model neuron is fed inputs via a synaptic pathway containing M=512 vesicle release sites. The pathway is configured in different ways by assigning release sites equally between varying numbers of active zones (N). Each active zone is driven by a particular input spike train. Spike trains to different active zones have the same time-varying mean frequency but individual spikes are uncorrelated in time. A completely uncorrelated pathway consists of 512 active zones containing a single release site, each driven by an independent presynaptic spike train. In contrast, a completely correlated pathway consists of a single active zone containing 512 releasable vesicles that may all release independently on the arrival of a spike from a single presynaptic cell. Each release site is modelled stochastically: a site may or may not contain a vesicle; an empty release site may be refilled at a fixed rate; a full site may release its vesicle with a given probability on arrival of a presynaptic spike. The refilling rate may be slow compared to the arrival rate of spikes, resulting in synaptic depression. The probability of vesicle release may increase with each spike, decaying back to baseline at a slow rate, resulting in facilitation of release. In the results shown here, the refilling rate is 2/s and the facilitation decay rate is also 2/s. The input signal is a 30Hz carrier frequency that is modulated sinusoidally between 50Hz and 10Hz at different modulation frequencies. This signal is carried by up to 512 independent non-homogeneous Poisson-distributed spike trains. The phase of the output spiking response (obtained from multiple runs with the same and different input trains), relative to the input signal, is plotted against the number of active zones (N) in Figure ​Figure1.1. At all modulation frequencies (0.1, 1, 3Hz) and in all configurations, synaptic depression results in the output response leading the input oscillations. The lead increases as the inputs become more correlated (decreasing N). The effect is amplified by facilitation for correlated synapses (N=1 or 2), but reduced for less correlated pathways. Also, the lead decreases with increasing modulation frequency for correlated synapses, but is maximal at 1Hz for uncorrelated pathways. Figure 1 Phase of response to rhythmic population inputs for different synaptic configurations and modulation frequencies. D: depression; D+F: depression + facilitation.

Mechanisms That Modulate the Transfer of Spiking Correlations

Correlations between neuronal spike trains affect network dynamics and population coding. Overlapping afferent populations and correlations between presynaptic spike trains introduce correlations between the inputs to downstream cells. To understand network activity and population coding, it is therefore important to understand how these input correlations are transferred to output correlations.Recent studies have addressed this question in the limit of many inputs with infinitesimal postsynaptic response amplitudes, where the total input can be approximated by gaussian noise. In contrast, we address the problem of correlation transfer by representing input spike trains as point processes, with each input spike eliciting a finite postsynaptic response. This approach allows us to naturally model synaptic noise and recurrent coupling and to treat excitatory and inhibitory inputs separately.We derive several new results that provide intuitive insights into the fundamental mechanisms that modulate the transfer of spiking correlations.

Nonrenewal spike train statistics: causes and functional consequences on neural coding.

Many neurons display significant patterning in their spike trains (e.g. oscillations, bursting), and there is accumulating evidence that information is contained in these patterns. In many cases, this patterning is caused by intrinsic mechanisms rather than external signals. In this review, we focus on spiking activity that displays nonrenewal statistics (i.e. memory that persists from one firing to the next). Such statistics are seen in both peripheral and central neurons and appear to be ubiquitous in the CNS. We review the principal mechanisms that can give rise to nonrenewal spike train statistics. These are separated into intrinsic mechanisms such as relative refractoriness and network mechanisms such as coupling with delayed inhibitory feedback. Next, we focus on the functional roles for nonrenewal spike train statistics. These can either increase or decrease information transmission. We also focus on how such statistics can give rise to an optimal integration timescale at which spike train variability is minimal and how this might be exploited by sensory systems to maximize the detection of weak signals. We finish by pointing out some interesting future directions for research in this area. In particular, we explore the interesting possibility that synaptic dynamics might be matched with the nonrenewal spiking statistics of presynaptic spike trains in order to further improve information transmission.

Intrinsic Stability of Temporally Shifted Spike-Timing Dependent Plasticity

Spike-timing dependent plasticity (STDP), a widespread synaptic modification mechanism, is sensitive to correlations between presynaptic spike trains and it generates competition among synapses. However, STDP has an inherent instability because strong synapses are more likely to be strengthened than weak ones, causing them to grow in strength until some biophysical limit is reached. Through simulations and analytic calculations, we show that a small temporal shift in the STDP window that causes synchronous, or nearly synchronous, pre- and postsynaptic action potentials to induce long-term depression can stabilize synaptic strengths. Shifted STDP also stabilizes the postsynaptic firing rate and can implement both Hebbian and anti-Hebbian forms of competitive synaptic plasticity. Interestingly, the overall level of inhibition determines whether plasticity is Hebbian or anti-Hebbian. Even a random symmetric jitter of a few milliseconds in the STDP window can stabilize synaptic strengths while retaining these features. The same results hold for a shifted version of the more recent “triplet” model of STDP. Our results indicate that the detailed shape of the STDP window function near the transition from depression to potentiation is of the utmost importance in determining the consequences of STDP, suggesting that this region warrants further experimental study.

A Spiking Neuron as Information Bottleneck

Neurons receive thousands of presynaptic input spike trains while emitting a single output spike train. This drastic dimensionality reduction suggests considering a neuron as a bottleneck for information transmission. Extending recent results, we propose a simple learning rule for the weights of spiking neurons derived from the information bottleneck (IB) framework that minimizes the loss of relevant information transmitted in the output spike train. In the IB framework, relevance of information is defined with respect to contextual information, the latter entering the proposed learning rule as a "third" factor besides pre- and postsynaptic activities. This renders the theoretically motivated learning rule a plausible model for experimentally observed synaptic plasticity phenomena involving three factors. Furthermore, we show that the proposed IB learning rule allows spiking neurons to learn a predictive code, that is, to extract those parts of their input that are predictive for future input.

Network-State Modulation of Power-Law Frequency-Scaling in Visual Cortical Neurons

Various types of neural-based signals, such as EEG, local field potentials and intracellular synaptic potentials, integrate multiple sources of activity distributed across large assemblies. They have in common a power-law frequency-scaling structure at high frequencies, but it is still unclear whether this scaling property is dominated by intrinsic neuronal properties or by network activity. The latter case is particularly interesting because if frequency-scaling reflects the network state it could be used to characterize the functional impact of the connectivity. In intracellularly recorded neurons of cat primary visual cortex in vivo, the power spectral density of Vm activity displays a power-law structure at high frequencies with a fractional scaling exponent. We show that this exponent is not constant, but depends on the visual statistics used to drive the network. To investigate the determinants of this frequency-scaling, we considered a generic recurrent model of cortex receiving a retinotopically organized external input. Similarly to the in vivo case, our in computo simulations show that the scaling exponent reflects the correlation level imposed in the input. This systematic dependence was also replicated at the single cell level, by controlling independently, in a parametric way, the strength and the temporal decay of the pairwise correlation between presynaptic inputs. This last model was implemented in vitro by imposing the correlation control in artificial presynaptic spike trains through dynamic-clamp techniques. These in vitro manipulations induced a modulation of the scaling exponent, similar to that observed in vivo and predicted in computo. We conclude that the frequency-scaling exponent of the Vm reflects stimulus-driven correlations in the cortical network activity. Therefore, we propose that the scaling exponent could be used to read-out the “effective” connectivity responsible for the dynamical signature of the population signals measured at different integration levels, from Vm to LFP, EEG and fMRI.

Locomotor Recovery after Spinal Cord Lesions in the Lamprey Is Associated with Functional and Ultrastructural Changes below Lesion Sites

While axonal regeneration continues to be the major focus of research into spinal injury, there is growing evidence for changes in functional properties below lesion sites. In this study we have used the lamprey, a model system for studying axonal regeneration after spinal injury, to examine whether functional and ultrastructural changes below lesion sites might also contribute to the recovery of locomotor function in this system. In the current study, the majority of the animals showed good functional recovery 10 weeks after lesioning, even when there was no physiological evidence for regeneration across the lesion site (although animals that recovered poorly always lacked regeneration). Excitability was increased below, but not above, the lesion site, as shown by the significantly greater ventral root responses following electrical stimulation of the spinal cord, a depolarization of the resting membrane potential, and an increase in input resistance and excitability in spinal cord neurons. Synaptic properties were also affected: a slow postsynaptic depolarization developed during presynaptic spike trains, and there was an increase in the frequency and amplitude of tetrodotoxin (TTX)-resistant miniature excitatory postsynaptic potentials (mEPSPs). There were also changes in synaptic ultrastructure, including a reduction of the synaptic gap and an increase in synaptic vesicle pools at asymmetric (putative excitatory) synapses. These results provide the first evidence for functional changes below lesion sites in the lamprey, and suggest that locomotor recovery reflects an interaction between regenerated axons and altered networks below lesion sites. The lamprey offers a tractable model system in which to investigate how interactions between altered locomotor networks and regenerated axons are organized to promote locomotor recovery.

Dependence of Neuronal Correlations on Filter Characteristics and Marginal Spike Train Statistics

Correlated neural activity has been observed at various signal levels (e.g., spike count, membrane potential, local field potential, EEG, fMRI BOLD). Most of these signals can be considered as superpositions of spike trains filtered by components of the neural system (synapses, membranes) and the measurement process. It is largely unknown how the spike train correlation structure is altered by this filtering and what the consequences for the dynamics of the system and for the interpretation of measured correlations are. In this study, we focus on linearly filtered spike trains and particularly consider correlations caused by overlapping presynaptic neuron populations. We demonstrate that correlation functions and statistical second-order measures like the variance, the covariance, and the correlation coefficient generally exhibit a complex dependence on the filter properties and the statistics of the presynaptic spike trains. We point out that both contributions can play a significant role in modulating the interaction strength between neurons or neuron populations. In many applications, the coherence allows a filter-independent quantification of correlated activity. In different network models, we discuss the estimation of network connectivity from the high-frequency coherence of simultaneous intracellular recordings of pairs of neurons.