Variability Of Spike Trains Research Articles

Estimation of the instantaneous spike train variability

The variability of neuronal spike trains is usually measured by the Fano factor or the coefficient of variation of interspike intervals, but their estimation is problematic, especially with limited amount of data. In this paper we show that it is in fact possible to estimate a quantity equivalent to the Fano factor and the squared coefficient of variation based on the intervals from only one specific (random) time. This leads to two very simple but precise Fano factor estimators, that can be interpreted as estimators of instantaneous variability. We derive their properties, evaluate their accuracy in various situations and show that they are often more accurate than the standard estimators. The presented estimators are particularly suitable for the case where variability changes rapidly.

Subthalamic nucleus stabilizes movements by reducing neural spike variability in monkey basal ganglia

The subthalamic nucleus projects to the external and internal pallidum, the modulatory and output nuclei of the basal ganglia, respectively, and plays an indispensable role in controlling voluntary movements. However, the precise mechanism by which the subthalamic nucleus controls pallidal activity and movements remains elusive. Here, we utilize chemogenetics to reversibly reduce neural activity of the motor subregion of the subthalamic nucleus in three macaque monkeys (Macaca fuscata, both sexes) during a reaching task. Systemic administration of chemogenetic ligands prolongs movement time and increases spike train variability in the pallidum, but only slightly affects firing rate modulations. Across-trial analyses reveal that the irregular discharges in the pallidum coincides with prolonged movement time. Reduction of subthalamic activity also induces excessive abnormal movements in the contralateral forelimb, which are preceded by subthalamic and pallidal phasic activity changes. Our results suggest that the subthalamic nucleus stabilizes pallidal spike trains and achieves stable movements.

Removing nonlinear misalignment in neuronal spike trains using the Fisher-Rao registration framework

BackgroundThe temporal precision in neural spike train data is critically important for understanding functional mechanism in the nervous systems. However, the timing variability of spiking activity can be highly nonlinear in practical observations due to behavioral variability or unobserved/unobservable cognitive states. New methodIn this study, we propose to adopt a powerful nonlinear method, referred to as the Fisher-Rao Registration (FRR), to remove such nonlinear phase variability in discrete neuronal spike trains. We also develop a smoothing procedure on the discrete spike train data in order to use the FRR framework. Comparison with existing methodsWe systematically compare the FRR with the state-of-the-art linear and nonlinear methods in terms of model efficiency and effectiveness. ResultsWe show that the FRR has superior performance and the advantages are well illustrated with simulation and real experimental data. ConclusionsIt is found the FRR framework provides more appropriate alignment performance to understand the temporal variability in neuronal spike trains.

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.

Spontaneous Multimodal Neural Transmission Suggests That Adult Spinal Networks Maintain an Intrinsic State of Readiness to Execute Sensorimotor Behaviors

Spontaneous action potential discharge (spAP) is both ubiquitous and functionally relevant during neural development. spAP remains a prominent feature of supraspinal networks in maturity, even during unconsciousness. Evidence suggests that spAP persists in mature spinal networks during wakefulness, and one function of spAP in this context could be maintenance of a "ready state" to execute behaviors. The extent to which spAP persists in mature spinal networks during unconsciousness remains unclear, and its function(s), if any, are likewise unresolved. Here, we attempt to reconcile some of the questions and contradictions that emerge from the disintegrated picture of adult spinal spAP currently available. We recorded simultaneously from large populations of spinal interneurons in vivo in male rats, characterizing the spatial distribution of spAP in the lumbar enlargement and identifying subgroups of spontaneously active neurons. We find (1) concurrent spAP throughout the dorsoventral extent of the gray matter, with a diverse yet strikingly consistent mixture of neuron types across laminae; (2) the proportion of neurons exhibiting spAP in deeper, sensorimotor integrative regions is comparable to that in more superficial, sensory-dominant regions; (3) firing rate, but not spike train variability, varies systematically with region; and (4) spAP includes multimodal neural transmission consistent with executing a spinally-mediated behavior. These findings suggest that adult spAP may continue to support a state of readiness to execute sensorimotor behaviors even during unconsciousness. Such functionality has implications for our understanding of how perception is translated into action, of experience-dependent modification of behavior, and (mal)adaptative responses to injury or disease.SIGNIFICANCE STATEMENT Neurons often discharge action potentials (APs) seemingly spontaneously, that is, in the absence of ongoing behaviors or overt stimuli. This phenomenon is particularly evident during neural development, where spontaneous AP discharge (spAP) is ubiquitous in the central nervous system and is crucial to establishing connectivity among functionally related groups of neurons. The function(s) of spAP in adult spinal networks, if any, have remained enigmatic, especially during unconsciousness. Here, we report evidence that one such function could be to support an intrinsic state of readiness to execute sensorimotor behaviors. This finding has implications for our understanding of how perception is translated into action, of experience-dependent modification of behavior, and (mal)adaptative responses to injury or disease.

Statistical moments of the interspike intervals for a neuron model driven by trichotomous noise.

The influence of a colored three-level input noise (trichotomous noise) on the spike generation of a perfect integrate-and-fire (PIF) model of neurons is studied. Using a first-passage-time formulation, exact expressions for the Laplace transform of the output interspike interval (ISI) density and for the statistical moments of the ISIs (such as the coefficient of variation, the skewness, the serial correlation coefficient, and the Fano factor) are derived. To model the anomalous subdiffusion that can arise from, e.g., the trapping properties of dendritic spines, the model is extended by including a random operational time in the form of an inverse strictly increasing Lévy-type subordinator, and exact formulas for ISI statistics are given for this case as well. Particularly, it is shown that at some parameter regimes, the ISI density exhibits a three-modal structure. The results for the extended model show that the ISI serial correlation coefficient and the Fano factor are nonmonotonic with respect to the input current, which indicates that at an intermediate value of the input current the variability of the output spike trains is minimal. Similarities and differences between the behavior of the presented models and the previously investigated PIF models driven by dichotomous noise are also discussed.

Robust point-process Granger causality analysis in presence of exogenous temporal modulations and trial-by-trial variability in spike trains.

Assessing directional influences between neurons is instrumental to understand how brain circuits process information. To this end, Granger causality, a technique originally developed for time-continuous signals, has been extended to discrete spike trains. A fundamental assumption of this technique is that the temporal evolution of neuronal responses must be due only to endogenous interactions between recorded units, including self-interactions. This assumption is however rarely met in neurophysiological studies, where the response of each neuron is modulated by other exogenous causes such as, for example, other unobserved units or slow adaptation processes. Here, we propose a novel point-process Granger causality technique that is robust with respect to the two most common exogenous modulations observed in real neuronal responses: within-trial temporal variations in spiking rate and between-trial variability in their magnitudes. This novel method works by explicitly including both types of modulations into the generalized linear model of the neuronal conditional intensity function (CIF). We then assess the causal influence of neuron i onto neuron j by measuring the relative reduction of neuron j's point process likelihood obtained considering or removing neuron i. CIF's hyper-parameters are set on a per-neuron basis by minimizing Akaike's information criterion. In synthetic data sets, generated by means of random processes or networks of integrate-and-fire units, the proposed method recovered with high accuracy, sensitivity and robustness the underlying ground-truth connectivity pattern. Application of presently available point-process Granger causality techniques produced instead a significant number of false positive connections. In real spiking responses recorded from neurons in the monkey pre-motor cortex (area F5), our method revealed many causal relationships between neurons as well as the temporal structure of their interactions. Given its robustness our method can be effectively applied to real neuronal data. Furthermore, its explicit estimate of the effects of unobserved causes on the recorded neuronal firing patterns can help decomposing their temporal variations into endogenous and exogenous components.

Fano Factor: A Potentially Useful Information.

The Fano factor, defined as the variance-to-mean ratio of spike counts in a time window, is often used to measure the variability of neuronal spike trains. However, despite its transparent definition, careless use of the Fano factor can easily lead to distorted or even wrong results. One of the problems is the unclear dependence of the Fano factor on the spiking rate, which is often neglected or handled insufficiently. In this paper we aim to explore this problem in more detail and to study the possible solution, which is to evaluate the Fano factor in the operational time. We use equilibrium renewal and Markov renewal processes as spike train models to describe the method in detail, and we provide an illustration on experimental data.

Evaluation of Frequency-Dependent Effects of Deep Brain Stimulation in a Cortex-Basal Ganglia-Thalamus Network Model of Parkinson's Disease.

Parkinson's disease (PD) is a chronic neurodegenerative disease whose motor symptoms are accompanied by an exaggerated power in the alpha-beta (7-35Hz) band and an increased synchronization of neurons encompassing the cortex-basal ganglia-thalamus network. Currently, deep brain stimulation (DBS) is used as an effective therapy for reducing the excessive power and synchrony observed in brain circuits, thereby ameliorating the PD symptoms. In the present study, we used a biologically plausible computational model of cortex-basal ganglia-thalamus network, which represents both healthy and PD conditions, to systematically investigate the effects of DBS frequency on the model outputs. DBS was applied to the subthalamic nucleus (STN) at different stimulation frequencies (40Hz to 300Hz). Spike train variability and spectral power in the 7-35Hz band were measured from the several nuclei represented in the model. In addition, the magnitude squared coherence between the nuclei was assessed. An increased DBS frequency tended to produce interspike intervals (ISIs) with higher variability as compared to PD condition. Also, DBS significantly reduced the alpha-beta power for almost all brain nuclei. The median of the magnitude-squared coherence matrix (which is a metric of global network synchronization) decreased significantly with the increase of DBS frequency.

The noise cancelation effects caused by spike-frequency adaptation in single neurons

Spike-frequency adaptation, which reduces the firing rate of a neuron during a constant stimulus, is a prominent property observed in many neurons. In this work, we studied the effects of the $$I_{\mathrm{AHP}}$$ spiking adaptation on the information transmission and efficiency of the Morris–Lecar (ML) neuron model in the spike-timing coding scheme. We showed that this kind of adaptation caused non-trivial spiking dynamics when the input rate was high. Under the stimulation of high-rate inputs, although $$I_{\mathrm{AHP}}$$ adaptation neurons could not outperform non-adaptation neurons in terms of information rate, $$I_{\mathrm{AHP}}$$ adaptation neurons yielded higher coding efficiency than non-adaptation neurons. We also found that the noise could enlarge the range of input rates that the adaptation takes effect to enhance coding efficiency. Increasing the calcium-activated $$\hbox {K}^{+}$$ current could also extend the range of input rates in which adaptation takes effect. Therefore, we argue that the $$I_{\mathrm{AHP}}$$ adaptation mechanism may play a role of adaptive noise cancelation mechanism in neuronal information processing, i.e., it maintains information transmission when neurons receive low-rate inputs but substantially enhancing coding efficiency for high-rate inputs and highly noise environments by suppressing the spike train variability caused by the noise.

Feedforward Thalamocortical Connectivity Preserves Stimulus Timing Information in Sensory Pathways.

Reliable timing of cortical spikes in response to visual events is crucial in representing visual inputs to the brain. Spikes in the primary visual cortex (V1) need to occur at the same time within a repeated visual stimulus. Two classical mechanisms are employed by the cortex to enhance reliable timing. First, cortical neurons respond reliably to a restricted set of stimuli through their preference for certain patterns of membrane potential due to their intrinsic properties. Second, intracortical networking of excitatory and inhibitory neurons induces lateral inhibition that, through the timing and strength of IPSCs and EPSCs, produces sparse and reliably timed cortical neuron spike trains to be transmitted downstream. Here, we describe a third mechanism that, through preferential thalamocortical synaptic connectivity, enhances the trial-to-trial timing precision of cortical spikes in the presence of spike train variability within each trial that is introduced between LGN neurons in the retino-thalamic pathway. Applying experimentally recorded LGN spike trains from the anesthetized cat to a detailed model of a spiny stellate V1 neuron, we found that output spike timing precision improved with increasing numbers of convergent LGN inputs. The improvement was consistent with the predicted proportionality of [Formula: see text] for n LGN source neurons. We also found connectivity configurations that maximize reliability and that generate V1 cell output spike trains quantitatively similar to the experimental recordings. Our findings suggest a general principle, namely intra-trial variability among converging inputs, that increases stimulus response precision and is widely applicable to synaptically connected spiking neurons.SIGNIFICANCE STATEMENT The early visual pathway of the cat is favorable for studying the effects of trial-to-trial variability of synaptic inputs and intra-trial variability of thalamocortical connectivity on information transmission into the visual cortex. We have used a detailed model to show that there are preferred combinations of the number of thalamic afferents and the number of synapses per afferent that maximize the output reliability and spike-timing precision of cortical neurons. This provides additional insights into how synchrony in thalamic spike trains can reduce trial-to-trial variability to produce highly reliable reporting of sensory events to the cortex. The same principles may apply to other converging pathways where temporally jittered spike trains can reliably drive the downstream neuron and improve temporal precision.

A Simple Model for Low Variability in Neural Spike Trains.

Neural noise sets a limit to information transmission in sensory systems. In several areas, the spiking response (to a repeated stimulus) has shown a higher degree of regularity than predicted by a Poisson process. However, a simple model to explain this low variability is still lacking. Here we introduce a new model, with a correction to Poisson statistics, that can accurately predict the regularity of neural spike trains in response to a repeated stimulus. The model has only two parameters but can reproduce the observed variability in retinal recordings in various conditions. We show analytically why this approximation can work. In a model of the spike-emitting process where a refractory period is assumed, we derive that our simple correction can well approximate the spike train statistics over a broad range of firing rates. Our model can be easily plugged to stimulus processing models, like a linear-nonlinear model or its generalizations, to replace the Poisson spike train hypothesis that is commonly assumed. It estimates the amount of information transmitted much more accurately than Poisson models in retinal recordings. Thanks to its simplicity, this model has the potential to explain low variability in other areas.

Ionic mechanisms underlying tonic and burst firing behavior in subfornical organ neurons: a combined experimental and modeling study.

Subfornical organ (SFO) neurons exhibit heterogeneity in current expression and spiking behavior, where the two major spiking phenotypes appear as tonic and burst firing. Insight into the mechanisms behind this heterogeneity is critical for understanding how the SFO, a sensory circumventricular organ, integrates and selectively influences physiological function. To integrate efficient methods for studying this heterogeneity, we built a single-compartment, Hodgkin-Huxley-type model of an SFO neuron that is parameterized by SFO-specific in vitro patch-clamp data. The model accounts for the membrane potential distribution and spike train variability of both tonic and burst firing SFO neurons. Analysis of model dynamics confirms that a persistent Na+ and Ca2+ currents are required for burst initiation and maintenance and suggests that a slow-activating K+ current may be responsible for burst termination in SFO neurons. Additionally, the model suggests that heterogeneity in current expression and subsequent influence on spike afterpotential underlie the behavioral differences between tonic and burst firing SFO neurons. Future use of this model in coordination with single neuron patch-clamp electrophysiology provides a platform for explaining and predicting the response of SFO neurons to various combinations of circulating signals, thus elucidating the mechanisms underlying physiological signal integration within the SFO. NEW & NOTEWORTHY Our understanding of how the subfornical organ (SFO) selectively influences autonomic nervous system function remains incomplete but theoretically results from the electrical responses of SFO neurons to physiologically important signals. We have built a computational model of SFO neurons, derived from and supported by experimental data, which explains how SFO neurons produce different electrical patterns. The model provides an efficient system to theoretically and experimentally explore how changes in the essential features of SFO neurons affect their electrical activity.

Learning Nonlinear Dynamics in Efficient, Balanced Spiking Networks Using Local Plasticity Rules

The brain uses spikes in neural circuits to perform many dynamical computations. The computations are performed with properties such as spiking efficiency, i.e. minimal number of spikes, and robustness to noise. A major obstacle for learning computations in artificial spiking neural networks with such desired biological properties is due to lack of our understanding of how biological spiking neural networks learn computations. Here, we consider the credit assignment problem, i.e. determining the local contribution of each synapse to the network's global output error, for learning nonlinear dynamical computations in a spiking network with the desired properties of biological networks. We approach this problem by fusing the theory of efficient, balanced neural networks (EBN) with nonlinear adaptive control theory to propose a local learning rule. Locality of learning rules are ensured by feeding back into the network its own error, resulting in a learning rule depending solely on presynaptic inputs and error feedbacks. The spiking efficiency and robustness of the network are guaranteed by maintaining a tight excitatory/inhibitory balance, ensuring that each spike represents a local projection of the global output error and minimizes a loss function. The resulting networks can learn to implement complex dynamics with very small numbers of neurons and spikes, exhibit the same spike train variability as observed experimentally, and are extremely robust to noise and neuronal loss.

Ergodicity and parameter estimates in auditory neural circuits

This paper discusses ergodic properties and circular statistical characteristics in neuronal spike trains. Ergodicity means that the average taken over a long time period and over smaller population should equal the average in less time and larger population. The objectives are to show simple examples of design and validation of a neuronal model, where the ergodicity assumption helps find correspondence between variables and parameters. The methods used are analytical and numerical computations, numerical models of phenomenological spiking neurons and neuronal circuits. Results obtained using these methods are the following. They are: a formula to calculate vector strength of neural spike timing dependent on the spike train parameters, description of parameters of spike train variability and model of output spiking density based on assumption of the computation realized by sound localization neural circuit. Theoretical results are illustrated by references to experimental data. Examples of neurons where spike trains have and do not have the ergodic property are then discussed.

Robust transmission of rate coding in the inhibitory Purkinje cell to cerebellar nuclei pathway in awake mice.

Neural coding through inhibitory projection pathways remains poorly understood. We analyze the transmission properties of the Purkinje cell (PC) to cerebellar nucleus (CN) pathway in a modeling study using a data set recorded in awake mice containing respiratory rate modulation. We find that inhibitory transmission from tonically active PCs can transmit a behavioral rate code with high fidelity. We parameterized the required population code in PC activity and determined that 20% of PC inputs to a full compartmental CN neuron model need to be rate-comodulated for transmission of a rate code. Rate covariance in PC inputs also accounts for the high coefficient of variation in CN spike trains, while the balance between excitation and inhibition determines spike rate and local spike train variability. Overall, our modeling study can fully account for observed spike train properties of cerebellar output in awake mice, and strongly supports rate coding in the cerebellum.

Spike Pattern Structure Influences Synaptic Efficacy Variability under STDP and Synaptic Homeostasis. I: Spike Generating Models on Converging Motifs.

In neural systems, synaptic plasticity is usually driven by spike trains. Due to the inherent noises of neurons and synapses as well as the randomness of connection details, spike trains typically exhibit variability such as spatial randomness and temporal stochasticity, resulting in variability of synaptic changes under plasticity, which we call efficacy variability. How the variability of spike trains influences the efficacy variability of synapses remains unclear. In this paper, we try to understand this influence under pair-wise additive spike-timing dependent plasticity (STDP) when the mean strength of plastic synapses into a neuron is bounded (synaptic homeostasis). Specifically, we systematically study, analytically and numerically, how four aspects of statistical features, i.e., synchronous firing, burstiness/regularity, heterogeneity of rates and heterogeneity of cross-correlations, as well as their interactions influence the efficacy variability in converging motifs (simple networks in which one neuron receives from many other neurons). Neurons (including the post-synaptic neuron) in a converging motif generate spikes according to statistical models with tunable parameters. In this way, we can explicitly control the statistics of the spike patterns, and investigate their influence onto the efficacy variability, without worrying about the feedback from synaptic changes onto the dynamics of the post-synaptic neuron. We separate efficacy variability into two parts: the drift part (DriftV) induced by the heterogeneity of change rates of different synapses, and the diffusion part (DiffV) induced by weight diffusion caused by stochasticity of spike trains. Our main findings are: (1) synchronous firing and burstiness tend to increase DiffV, (2) heterogeneity of rates induces DriftV when potentiation and depression in STDP are not balanced, and (3) heterogeneity of cross-correlations induces DriftV together with heterogeneity of rates. We anticipate our work important for understanding functional processes of neuronal networks (such as memory) and neural development.

On the Spike Train Variability Characterized by Variance-to-Mean Power Relationship.

We propose a statistical method for modeling the non-Poisson variability of spike trains observed in a wide range of brain regions. Central to our approach is the assumption that the variance and the mean of interspike intervals are related by a power function characterized by two parameters: the scale factor and exponent. It is shown that this single assumption allows the variability of spike trains to have an arbitrary scale and various dependencies on the firing rate in the spike count statistics, as well as in the interval statistics, depending on the two parameters of the power function. We also propose a statistical model for spike trains that exhibits the variance-to-mean power relationship. Based on this, a maximum likelihood method is developed for inferring the parameters from rate-modulated spike trains. The proposed method is illustrated on simulated and experimental spike trains.

Ambiguity and nonidentifiability in the statistical analysis of neural codes

Many experimental studies of neural coding rely on a statistical interpretation of the theoretical notion of the rate at which a neuron fires spikes. For example, neuroscientists often ask, "Does a population of neurons exhibit more synchronous spiking than one would expect from the covariability of their instantaneous firing rates?" For another example, "How much of a neuron's observed spiking variability is caused by the variability of its instantaneous firing rate, and how much is caused by spike timing variability?" However, a neuron's theoretical firing rate is not necessarily well-defined. Consequently, neuroscientific questions involving the theoretical firing rate do not have a meaning in isolation but can only be interpreted in light of additional statistical modeling choices. Ignoring this ambiguity can lead to inconsistent reasoning or wayward conclusions. We illustrate these issues with examples drawn from the neural-coding literature.

Afferent-hair cell connectivity as a possible source of spike train irregularity in turtle vestibular bouton afferents

Vestibular afferents have been categorized as “regular” or “irregular” depending on the variability of their spike trains [1,2]. It is thought that the difference in regularity among afferents results from differences in the types of voltage-dependent conductances present in the cell. For example afferents may differ in their complements of potassium A, D, and M currents or in currents that produce a small vs. prominent afterhyperpolarization (AHP) [3-5]. Because bouton afferents from turtle utricle vary widely in morphology depending on their location in the utricle, we sought to determine if afferent morphology might also play a role in spike train irregularity. Although we found that morphology itself is not a factor in determining spike train variability, we did find that spike train variability can be affected by afferent/hair cell connectivity. Morphological reconstructions of bouton afferents from the lateral extrastriolar (LES), striola, juxtastriola and medial extrastriolar (MES) regions of turtle utricle were done with Neurolucida. Models based on these reconstructions were constructed for 16 afferents. Voltage-dependent conductance distributions in different regions (axon, soma, terminal arbor, varicosities, nodes, myelin) were identical in each cell model. Given the locations of synapses in the terminal arbor and the density of hair cells in each region, we were able to estimate the number of synapses formed between individual hair cells and an afferent. In the LES, striola and juxtastriola most synapses on an afferent were formed with unique hair cells, whereas in the MES single hair cells more often made multiple synapses with an afferent. To determine the effect of this difference in connectivity we modeled Poisson release from hair cells to synapses in the terminal arbor to generate spike trains. The coefficient of variation (cv) as a function of interspike interval (ISI) was calculated to estimate spike train variability with different average release rates. We found that cv as a function of ISI was nearly identical for LES, striola and juxtastriola afferents, but was the same for MES afferents only if connectivity in the MES was assumed to be one afferent synapse per hair cell. However, cv was much larger when the MES afferents were modeled with multiple synapses between an afferent and a hair cell, as calculated from synaptic location and hair cell density. To see if we could make an LES afferent more irregular, we modified connectivity to have more multiple synapses between individual hair cells and the afferent. As predicted, cv increased. These results suggest that afferent-hair cell connectivity may be a source of spike train irregularity. Given the large number of multiple contacts between a calyx and its presynaptic hair cell, we expect that connectivity contributes to spike train variability in calyx-bearing (calyx and dimorph) afferents.