Coefficient of variation of interspike intervals greater than 0.5. How and when?

Logarithmically scaled, gamma distributed neuronal spiking

Naturally log-scaled quantities abound in the nervous system. Distributions of these quantities have non-intuitive properties, which have implications for data analysis and the understanding of neural circuits. Here, we review the log-scaled statistics of neuronal spiking and the relevant analytical probability distributions. Recent work using log-scaling revealed that interspike intervals of forebrain neurons segregate into discrete modes reflecting spiking at different timescales and are each well-approximated by a gamma distribution. Each neuron spends most of the time in an irregular spiking 'ground state' with the longest intervals, which determines the mean firing rate of the neuron. Across the entire neuronal population, firing rates are log-scaled and well approximated by the gamma distribution, with a small number of highly active neurons and an overabundance of low rate neurons (the 'dark matter'). These results are intricately linked to a heterogeneous balanced operating regime, which confers upon neuronal circuits multiple computational advantages and has evolutionarily ancient origins.

Functional Neuroanatomy of the Rat Nucleus Incertus–Medial Septum Tract: Implications for the Cell-Specific Control of the Septohippocampal Pathway

The medial septum (MS) is critically involved in theta rhythmogenesis and control of the hippocampal network, with which it is reciprocally connected. MS activity is influenced by brainstem structures, including the stress-sensitive, nucleus incertus (NI), the main source of the neuropeptide relaxin-3 (RLN3). In the current study, we conducted a comprehensive neurochemical and electrophysiological characterization of NI neurons innervating the MS in the rat, by employing classical and viral-based neural tract-tracing and electrophysiological approaches, and multiplex fluorescent in situ hybridization. We confirmed earlier reports that the MS is innervated by RLN3 NI neurons and documented putative glutamatergic (vGlut2 mRNA-expressing) neurons as a relevant NI neuronal population within the NI–MS tract. Moreover, we observed that NI neurons innervating MS can display a dual phenotype for GABAergic and glutamatergic neurotransmission, and that 40% of MS-projecting NI neurons express the corticotropin-releasing hormone-1 receptor. We demonstrated that an identified cholecystokinin (CCK)-positive NI neuronal population is part of the NI–MS tract, and that RLN3 and CCK NI neurons belong to a neuronal pool expressing the calcium-binding proteins, calbindin and calretinin. Finally, our electrophysiological studies revealed that MS is innervated by A-type potassium current-expressing, type I NI neurons, and that type I and II NI neurons differ markedly in their neurophysiological properties. Together these findings indicate that the MS is controlled by a discrete NI neuronal network with specific electrophysiological and neurochemical features; and these data are of particular importance for understanding neuronal mechanisms underlying the control of the septohippocampal system and related behaviors.

The Jacobi diffusion process as a neuronal model

The Jacobi process is a stochastic diffusion characterized by a linear drift and a special form of multiplicative noise which keeps the process confined between two boundaries. One example of such a process can be obtained as the diffusion limit of the Stein's model of membrane depolarization which includes both excitatory and inhibitory reversal potentials. The reversal potentials create the two boundaries between which the process is confined. Solving the first-passage-time problem for the Jacobi process, we found closed-form expressions for mean, variance, and third moment that are easy to implement numerically. The first two moments are used here to determine the role played by the parameters of the neuronal model; namely, the effect of multiplicative noise on the output of the Jacobi neuronal model with input-dependent parameters is examined in detail and compared with the properties of the generic Jacobi diffusion. It appears that the dependence of the model parameters on the rate of inhibition turns out to be of primary importance to observe a change in the slope of the response curves. This dependence also affects the variability of the output as reflected by the coefficient of variation. It often takes values larger than one, and it is not always a monotonic function in dependency on the rate of excitation.

Note on the coefficient of variations of neuronal spike trains

It is known that many neurons in the brain show spike trains with a coefficient of variation (CV) of the interspike times of approximately 1, thus resembling the properties of Poisson spike trains. Computational studies have been able to reproduce this phenomenon. However, the underlying models were too complex to be examined analytically. In this paper, we offer a simple model that shows the same effect but is accessible to an analytic treatment. The model is a random walk model with a reflecting barrier; we give explicit formulas for the CV in the regime of excess inhibition. We also analyze the effect of probabilistic synapses in our model and show that it resembles previous findings that were obtained by simulation.

Skellam process with resetting: a neural spike train model

This paper introduces the Skellam process with resetting. Resetting is a modification that accommodates the modeling of neural spike trains. We show this as a biologically plausible model, which codes the information content of neural spike trains with three, potentially, time-varying functions. We show that the interspike interval distribution under this model follows a mixture of gamma distributions, a flexible class covering a wide range of commonly used models. Through simulation studies and the analyses of connected retinal ganglion and lateral geniculate nucleus cells, we evaluate the performance of this model. Copyright © 2016 John Wiley & Sons, Ltd.

Lognormal firing rate distribution reveals prominent fluctuation-driven regime in spinal motor networks

When spinal circuits generate rhythmic movements it is important that the neuronal activity remains within stable bounds to avoid saturation and to preserve responsiveness. Here, we simultaneously record from hundreds of neurons in lumbar spinal circuits of turtles and establish the neuronal fraction that operates within either a 'mean-driven' or a 'fluctuation-driven' regime. Fluctuation-driven neurons have a 'supralinear' input-output curve, which enhances sensitivity, whereas the mean-driven regime reduces sensitivity. We find a rich diversity of firing rates across the neuronal population as reflected in a lognormal distribution and demonstrate that half of the neurons spend at least 50 % of the time in the 'fluctuation-driven' regime regardless of behavior. Because of the disparity in input-output properties for these two regimes, this fraction may reflect a fine trade-off between stability and sensitivity in order to maintain flexibility across behaviors.

Dynamics of on-off neural firing patterns and stochastic effects near a sub-critical Hopf bifurcation

On-off firing patterns, in which repetition of clusters of spikes are interspersed with epochs of subthreshold oscillations or quiescent states, have been observed in various nervous systems, but the dynamics of this event remain unclear. Here, we report that on-off firing patterns observed in three experimental models (rat sciatic nerve subject to chronic constrictive injury, rat CA1 pyramidal neuron, and rabbit blood pressure baroreceptor) appeared as an alternation between quiescent state and burst containing multiple period-1 spikes over time. Burst and quiescent state had various durations. The interspike interval (ISI) series of on-off firing pattern was suggested as stochastic using nonlinear prediction and autocorrelation function. The resting state was changed to a period-1 firing pattern via on-off firing pattern as the potassium concentration, static pressure, or depolarization current was changed. During the changing process, the burst duration of on-off firing pattern increased and the duration of the quiescent state decreased. Bistability of a limit cycle corresponding to period-1 firing and a focus corresponding to resting state was simulated near a sub-critical Hopf bifurcation point in the deterministic Morris-Lecar (ML) model. In the stochastic ML model, noise-induced transitions between the coexisting regimes formed an on-off firing pattern, which closely matched that observed in the experiment. In addition, noise-induced exponential change in the escape rate from the focus, and noise-induced coherence resonance were identified. The distinctions between the on-off firing pattern and stochastic firing patterns generated near three other types of bifurcations of equilibrium points, as well as other viewpoints on the dynamics of on-off firing pattern, are discussed. The results not only identify the on-off firing pattern as noise-induced stochastic firing pattern near a sub-critical Hopf bifurcation point, but also offer practical indicators to discriminate bifurcation types and neural excitability types.

Analysis of interspike interval of dorsal horn neurons evoked by different needle manipulations at ST36

OBJECTIVES

Previous research has suggested that different manual acupuncture (MA) manipulations may have different physiological effects. Recent studies have demonstrated that neural electrical signals are generated or changed when acupuncture is administered. In order to explore the effects of different MA manipulations on the neural system, an experiment was designed to record the discharges of wide dynamic range (WDR) neurons in the spinal dorsal horn evoked by MA at different frequencies (0.5, 1, 2 and 3 Hz) at ST36.

METHODS

Microelectrode extracellular recordings were used to record the discharges of WDR neurons evoked by different MA manipulations. Approximate firing rate and coefficient of variation of interspike interval (ISI) were used to extract the characteristic parameters of the neural electrical signals after spike sorting, and the neural coding of the evoked discharges by different MA manipulations was obtained.

RESULTS

Our results indicated that the neuronal firing rate and time sequences of ISI showed distinct clustering properties for different MA manipulations, which could distinguish them effectively.

CONCLUSIONS

The combination of firing rate and ISI codes carries information about the acupuncture stimulus frequency. Different MA manipulations appear to change the neural coding of electrical signals in the spinal dorsal horn through WDR neurons.

A new method of spike modelling and interval analysis

Here we develop a new model of spike firing, based on the leaky integrate and fire model, modified to simulate afterpotentials. We also develop new analysis techniques, applying these to recorded and model generated data in order to make a comparative analysis and develop the model as a hypothesis for the functional components of the neuron. The model is based in this first instance on hypothalamic oxytocin neurons. We demonstrate how model parameters and cell properties relate to features observed in inter-spike intervals histograms, and the limits of these in being able to detect patterning features in spike recordings. A new technique, spike train analysis, is able to detect previously unobserved patterning, showing a dependence of spike intervals on previous firing activity. This effect is reproduced in the model by adding the small amplitude but long lasting after hyper-polarising potential (AHP). A fit measure based on log likelihood is used to compare model generated data to recorded spike intervals, taking account of interval dependence on previous activity. This measure is used with the simplex multiple parameter search algorithm to develop an automated method for fitting the model to recorded data.

Difficulty of visual search modulates neuronal interactions and response variability in the frontal eye field

The frontal eye field (FEF) is involved in selecting visual targets for eye movements. To understand how populations of FEF neurons interact during target selection, we recorded activity from multiple neurons simultaneously while macaques performed two versions of a visual search task. We used a multivariate analysis in a point process statistical framework to estimate the instantaneous firing rate and compare interactions among neurons between tasks. We found that FEF neurons were engaged in more interactions during easier visual search tasks compared with harder search tasks. In particular, eye movement-related neurons were involved in more interactions than visual-related neurons. In addition, our analysis revealed a decrease in the variability of spiking activity in the FEF beginning approximately 100 ms before saccade onset. The minimum in response variability occurred approximately 20 ms earlier for the easier search task compared with the harder one. This difference is positively correlated with the difference in saccade reaction times for the two tasks. These findings show that a multivariate analysis can provide a measure of neuronal interactions and characterize the spiking activity of FEF neurons in the context of a population of neurons.

Sensitive dependence of the coefficient of variation of interspike intervals on the lower boundary of membrane potential for the leaky integrate-and-fire neuron model

After the report of Softky and Koch [Softky, W.R., Koch, C., 1993. The highly irregular firing of cortical cells is inconsistent with temporal integration of random EPSPs. J. Neurosci. 13, 334-350], leaky integrate-and-fire models have been investigated to explain high coefficient of variation (CV) of interspike intervals (ISIs) at high firing rates observed in the cortex. The purpose of this paper is to study the effect of the position of a lower boundary of membrane potential on the possible value of CV of ISIs based on the diffusional leaky integrate-and-fire models with and without reversal potentials. Our result shows that the irregularity of ISIs for the diffusional leaky integrate-and-fire neuron significantly changes by imposing a lower boundary of membrane potential, which suggests the importance of the position of the lower boundary as well as that of the firing threshold when we study the statistical properties of leaky integrate-and-fire neuron models. It is worth pointing out that the mean-CV plot of ISIs for the diffusional leaky integrate-and-fire neuron with reversal potentials shows a close similarity to the experimental result obtained in Softky and Koch [Softky, W.R., Koch, C., 1993. The highly irregular firing of cortical cells is inconsistent with temporal integration of random EPSPs. J. Neurosci. 13, 334-350].

Measurement of time-dependent changes in the irregularity of neural spiking

Irregularity of firing in spike trains has been associated with coding processes and information transfer or alternatively treated as noise. Previous studies of irregularity have mainly used the coefficient of variation (CV) of the interspike interval distribution. Proper estimation of CV requires a constant underlying firing rate, a condition that most experimental situations do not fulfill either within or across trials. Here we introduce a novel irregularity metric based on the ratio of adjacent intervals in the spike train. The new metric is not affected by firing rate and is very localized in time so that it can be used to examine the time course of irregularity relative to an alignment marker. We characterized properties of the new metric with simulated spike trains of known characteristics and then applied it to data recorded from 108 single neurons in the motor cortex of two monkeys during performance of a precision grip task. Fifty-six cells were antidromically identified as pyramidal tract neurons (PTNs). Sixty-one cells (30 PTNs) exhibited significant temporal modulation of their irregularity during task performance with the contralateral hand. The irregularity modulations generally differed in sign and latency from the modulations of firing rate. High irregularity tended to occur during the task phases requiring the most detailed control of movement, whereas neural firing became more regular during the steady hold phase. Such irregularity modulation could have important consequences for the response of downstream neurons and may provide insight into the nature of the cortical code.

Including Long-Range Dependence in Integrate-and-Fire Models of the High Interspike-Interval Variability of Cortical Neurons

Many different types of integrate-and-fire models have been designed in order to explain how it is possible for a cortical neuron to integrate over many independent inputs while still producing highly variable spike trains. Within this context, the variability of spike trains has been almost exclusively measured using the coefficient of variation of interspike intervals. However, another important statistical property that has been found in cortical spike trains and is closely associated with their high firing variability is long-range dependence. We investigate the conditions, if any, under which such models produce output spike trains with both interspike-interval variability and long-range dependence similar to those that have previously been measured from actual cortical neurons. We first show analytically that a large class of high-variability integrate-and-fire models is incapable of producing such outputs based on the fact that their output spike trains are always mathematically equivalent to renewal processes. This class of models subsumes a majority of previously published models, including those that use excitation-inhibition balance, correlated inputs, partial reset, or nonlinear leakage to produce outputs with high variability. Next, we study integrate-and-fire models that have (non-Poissonian) renewal point process inputs instead of the Poisson point process inputs used in the preceding class of models. The confluence of our analytical and simulation results implies that the renewal-input model is capable of producing high variability and long-range dependence comparable to that seen in spike trains recorded from cortical neurons, but only if the interspike intervals of the inputs have infinite variance, a physiologically unrealistic condition. Finally, we suggest a new integrate-and-fire model that does not suffer any of the previously mentioned shortcomings. By analyzing simulation results for this model, we show that it is capable of producing output spike trains with interspike-interval variability and long-range dependence that match empirical data from cortical spike trains. This model is similar to the other models in this study, except that its inputs are fractional-gaussian-noise-driven Poisson processes rather than renewal point processes. In addition to this model's success in producing realistic output spike trains, its inputs have longrange dependence similar to that found in most subcortical neurons in sensory pathways, including the inputs to cortex. Analysis of output spike trains from simulations of this model also shows that a tight balance between the amounts of excitation and inhibition at the inputs to cortical neurons is not necessary for high interspike-interval variability at their outputs. Furthermore, in our analysis of this model, we show that the superposition of many fractional-gaussian-noise-driven Poisson processes does not approximate a Poisson process, which challenges the common assumption that the total effect of a large number of inputs on a neuron is well represented by a Poisson process.

The discharge variability of neocortical neurons during high-conductance states

In vivo recordings have shown that the discharge of cortical neurons is often highly variable and can have statistics similar to a Poisson process with a coefficient of variation around unity. To investigate the determinants of this high variability, we analyzed the spontaneous discharge of Hodgkin-Huxley type models of cortical neurons, in which in vivo-like synaptic background activity was modeled by random release events at excitatory and inhibitory synapses. By using compartmental models with active dendrites, or single compartment models with fluctuating conductances and fluctuating currents, we found that a high discharge variability was always paralleled with a high-conductance state, while some active and passive cellular properties had only a minor impact. Furthermore, a balance between excitation and inhibition was not a necessary condition for high discharge variability. We conclude that the fluctuating high-conductance state caused by the ongoing activity in the cortical network in vivo may be viewed as a natural determinant of the highly variable discharges of these neurons.

Gain control of firing rate by shunting inhibition: roles of synaptic noise and dendritic saturation

Adjusting input-output gain is crucial for information processing by the brain. Gain control of subthreshold depolarization is commonly ascribed to increased membrane conductance caused by shunting inhibition. But contrary to its divisive effect on depolarization, shunting inhibition on its own fails to divisively modulate firing rate, apparently upsetting a critical tenet of neural models that use shunting inhibition to achieve gain control. Using a biophysically realistic neuron model, we show that divisive modulation of firing rate by shunting inhibition requires synaptic noise to smooth the relation between firing rate and somatic depolarization; although necessary, noise alone endows shunting inhibition with only a modest divisive effect on firing rate. In addition to introducing noise, synaptic input is associated with a nonlinear relation between somatic depolarization and excitation because of dendritic saturation; this nonlinearity dramatically enhances divisive modulation of firing rate by shunting inhibition under noisy conditions. Thus, shunting inhibition can act as a mechanism for firing rate gain control, but its modulatory effects (which include both divisive and subtractive components) are fully explained only when both synaptic noise and dendritic saturation are taken into account.

Temporal album

Transient synchronization has been used as a mechanism of recognizing auditory patterns using integrate-and-fire neural networks. We first extend the mechanism to vision tasks and investigate the role of spike dependent learning. We show that such a temporal Hebbian learning rule significantly improves accuracy of detection. We demonstrate how multiple patterns can be identified by a single pattern selective neuron and how a temporal album can be constructed. This principle may lead to multidimensional memories, where the capacity per neuron is considerably increased with accurate detection of spike synchronization.

Stages of spike time variability during neuronal responses to transient inputs

In cerebral cortex, cells tend to fire in response to strong transient fluctuations in input, produced by synchronous population activity, which reset the precision of firing and erase correlations between prior and future spike times. Here, using experiments and modeling, we study the accumulation of spike time variance in response to single decaying transient stimuli. All such responses go through distinct stages in time. When the stimulus is high, variance is held low, while at low stimulus levels near threshold, variance rises dramatically, approaching a Poisson level. This behavior was reproduced in a stochastically simulated Hodgkin-Huxley model, and in two simpler models, class 1 (Morris-Lecar) and class 2 (FitzHugh-Nagumo), incorporating Ornstein-Uhlenbeck noise. Early stage variance represents perturbation of uniform limit-cycle motion of the dynamical variables. Late stage variance reflects random motion of the dynamical variables captured within the basin of the resting fixed point. We show that the two stages have different sensitivities to the amplitude and time scale of noise, and relate this to coherence resonance. This rapid breakdown in reliability during responses to transient stimuli may restrict precise signalling by spike times to brief time windows, and limit the duration of coherent synchronous responses in the cortex.

A spiking neuron model: applications and learning

This paper presents a biologically inspired, hardware-realisable spiking neuron model, which we call the Temporal Noisy-Leaky Integrator (TNLI). The dynamic applications of the model as well as its applications in Computational Neuroscience are demonstrated and a learning algorithm based on postsynaptic delays is proposed. The TNLI incorporates temporal dynamics at the neuron level by modelling both the temporal summation of dendritic postsynaptic currents which have controlled delay and duration and the decay of the somatic potential due to its membrane leak. Moreover, the TNLI models the stochastic neurotransmitter release by real neuron synapses (with probabilistic RAMs at each input) and the firing times including the refractory period and action potential repolarisation. The temporal features of the TNLI make it suitable for use in dynamic time-dependent tasks like its application as a motion and velocity detector system presented in this paper. This is done by modelling the experimental velocity selectivity curve of the motion sensitive H1 neuron of the visual system of the fly. This application of the TNLI indicates its potential applications in artificial vision systems for robots. It is also demonstrated that Hebbian-based learning can be applied in the TNLI for postsynaptic delay training based on coincidence detection, in such a way that an arbitrary temporal pattern can be detected and recognised. The paper also demonstrates that the TNLI can be used to control the firing variability through inhibition; with 80% inhibition to concurrent excitation, firing at high rates is nearly consistent with a Poisson-type firing variability observed in cortical neurons. It is also shown with the TNLI, that the gain of the neuron (slope of its transfer function) can be controlled by the balance between inhibition and excitation, the gain being a decreasing function of the proportion of inhibitory inputs. Finally, in the case of perfect balance between inhibition and excitation, i.e. where the average input current is zero, the neuron can still fire as a result of membrane potential fluctuations. The firing rate is then determined by the average input firing rate. Overall this work illustrates how a hardware-realisable neuron model can capitalise on the unique computational capabilities of biological neurons.

Responses of magnocellular neurons to osmotic stimulation involves coactivation of excitatory and inhibitory input: an experimental and theoretical analysis

How does a neuron, challenged by an increase in synaptic input, display a response that is independent of the initial level of activity? Here we show that both oxytocin and vasopressin cells in the supraoptic nucleus of normal rats respond to intravenous infusions of hypertonic saline with gradual, linear increases in discharge rate. In hyponatremic rats, oxytocin and vasopressin cells also responded linearly to intravenous infusions of hypertonic saline but with much lower slopes. The linearity of response was surprising, given both the expected nonlinearity of neuronal behavior and the nonlinearity of the oxytocin secretory response to such infusions. We show that a simple computational model can reproduce these responses well, but only if it is assumed that hypertonic infusions coactivate excitatory and inhibitory synaptic inputs. This hypothesis was tested first by applying the GABA(A) antagonist bicuculline to the dendritic zone of the supraoptic nucleus by microdialysis. During local blockade of GABA inputs, the response of oxytocin cells to hypertonic infusion was greatly enhanced. We then went on to directly measure GABA release in the supraoptic nucleus during hypertonic infusion, confirming the predicted rise. Together, the results suggest that hypertonic infusions lead to coactivation of excitatory and inhibitory inputs and that this coactivation may confer appropriate characteristics on the output behavior of oxytocin cells. The nonlinearity of oxytocin secretion that accompanies the linear increase in oxytocin cell firing rate reflects frequency-facilitation of stimulus-secretion coupling at the neurohypophysis.

Correlation between uncoupled conductance-based integrate-and-fire neurons due to common and synchronous presynaptic firing

We investigate the firing characteristics of conductance-based integrate-and-fire neurons and the correlation of firing for uncoupled pairs of neurons as a result of common input and synchronous firing of multiple synaptic inputs. Analytical approximations are derived for the moments of the steady state potential and the effective time constant. We show that postsynaptic firing barely depends on the correlation between inhibitory inputs; only the inhibitory firing rate matters. In contrast, both the degree of synchrony and the firing rate of excitatory inputs are relevant. A coefficient of variation CV > 1 can be attained with low inhibitory firing rates and (Poisson-modulated) synchronized excitatory synaptic input, where both the number of presynaptic neurons in synchronous firing assemblies and the synchronous firing rate should be sufficiently large. The correlation in firing of a pair of uncoupled neurons due to common excitatory input is initially increased for increasing firing rates of independent inhibitory inputs but decreases for large inhibitory firing rates. Common inhibitory input to a pair of uncoupled neurons barely induces correlated firing, but amplifies the effect of common excitation. Synchronous firing assemblies in the common input further enhance the correlation and are essential to attain experimentally observed correlation values. Since uncorrelated common input (i.e., common input by neurons, which do not fire in synchrony) cannot induce sufficient postsynaptic correlation, we conclude that lateral couplings are essential to establish clusters of synchronously firing neurons.

Behavior of integrate-and-fire and Hodgkin-Huxley models with correlated inputs

We assess, both numerically and theoretically, how positively correlated Poisson inputs affect the output of the integrate-and-fire and Hodgkin-Huxley models. For the integrate-and-fire model the variability of efferent spike trains is an increasing function of input correlation, and of the ratio between inhibitory and excitatory inputs. Interestingly for the Hodgkin-Huxley model the variability of efferent spike trains is a decreasing function of input correlation, and for fixed input correlation it is almost independent of the ratio between inhibitory and excitatory inputs. In terms of the signal to noise ratio of efferent spike trains the integrate-and-fire model works better in an environment of asynchronous inputs, but the Hodgkin-Huxley model has an advantage for more synchronous (correlated) inputs. In conclusion the integrate-and-fire and Hodgkin-Huxley models respond to correlated inputs in totally opposite ways.

Balance between four types of synaptic input for the integrate-and-fire model

We consider the integrate-and-fire model with AMPA, NMDA, GABA(A)and GABA(B)synaptic inputs, with model parameters based upon experimental data. An analytical approach is presented to determine when a post-synaptic balance between excitation and inhibition can be achieved. Secondly, we compare the model behaviour subject to these four types of input, with its behaviour subject to conventional point process inputs. We conclude that point processes are not a good approximation, even away from exact presynaptic balance. Thirdly, numerical simulations are presented which demonstrate that we can treat NMDA and GABA(B)as DC currents. Finally, we conclude that a balanced input is plausible neither pre-synaptically nor post-synaptically for the model and parameters we employed.

Near Poisson-type firing produced by concurrent excitation and inhibition

The effect of inhibition on the firing variability is examined in this paper using the biologically-inspired temporal noisy-leaky integrator (TNLI) neuron model. The TNLI incorporates hyperpolarising inhibition with negative current pulses of controlled shapes and it also separates dendritic from somatic integration. The firing variability is observed by looking at the coefficient of variation (C(V)) (standard deviation/mean interspike interval) as a function of the mean interspike interval of firing (delta tM) and by comparing the results with the theoretical curve for random spike trains, as well as looking at the interspike interval (ISI) histogram distributions. The results show that with 80% inhibition, firing at high rates (up to 200 Hz) is nearly consistent with a Poisson-type variability, which complies with the analysis of cortical neuron firing recordings by Softky and Koch [1993, J. Neurosci. 13(1) 334-530]. We also demonstrate that the mechanism by which inhibition increases the C(V) values is by introducing more short intervals in the firing pattern as indicated by a small initial hump at the beginning of the ISI histogram distribution. The use of stochastic inputs and the separation of the dendritic and somatic integration which we model in TNLI, also affect the high firing, near Poisson-type (explained in the paper) variability produced. We have also found that partial dendritic reset increases slightly the firing variability especially at short ISIs.

Stochastic resonance tuned by correlations in neural models

The idea that neurons might use stochastic resonance (SR) to take advantage of random signals has been extensively discussed in the literature. However, there are a few key issues that have not been clarified and thus it is difficult to assess that whether SR in neuronal models occurs inside plausible physiology parameter regions or not. We propose and show that neurons can adjust correlations between synaptic inputs, which can be measured in experiments and are dynamical variables, to exhibit SR. The benefit of such a mechanism over the conventional SR is also discussed.

Impact of correlated inputs on the output of the integrate- and-fire model

For the integrate-and-fire model with or without reversal potentials, we consider how correlated inputs affect the variability of cellular output. For both models, the variability of efferent spike trains measured by coefficient of variation (CV) of the interspike interval is a nondecreasing function of input correlation. When the correlation coefficient is greater than 0.09, the CV of the integrate-and-fire model without reversal potentials is always above 0.5, no matter how strong the inhibitory inputs. When the correlation coefficient is greater than 0.05, CV for the integrate-and-fire model with reversal potentials is always above 0. 5, independent of the strength of the inhibitory inputs. Under a given condition on correlation coefficients, we find that correlated Poisson processes can be decomposed into independent Poisson processes. We also develop a novel method to estimate the distribution density of the first passage time of the integrate-and-fire model.