Single Interspike Intervals Research Articles

Sodium channel slow inactivation normalizes firing in axons with uneven conductance distributions

The Na+ channels that are important for action potentials show rapid inactivation, a state in which they do not conduct, although the membrane potential remains depolarized.1,2 Rapid inactivation is a determinant of millisecond-scale phenomena, such as spike shape and refractory period. Na+ channels also inactivate orders of magnitude more slowly, and this slow inactivation has impacts on excitability over much longer timescales than those of a single spike or a single inter-spike interval.3,4,5,6,7,8,9,10 Here, we focus on the contribution of slow inactivation to the resilience of axonal excitability11,12 when ion channels are unevenly distributed along the axon. We study models in which the voltage-gated Na+ and K+ channels are unevenly distributed along axons with different variances, capturing the heterogeneity that biological axons display.13,14 In the absence of slow inactivation, many conductance distributions result in spontaneous tonic activity. Faithful axonal propagation is achieved with the introduction of Na+ channel slow inactivation. This "normalization" effect depends on relations between the kinetics of slow inactivation and the firing frequency. Consequently, neurons with characteristically different firing frequencies will need to implement different sets of channel properties to achieve resilience. The results of this study demonstrate the importance of the intrinsic biophysical properties of ion channels in normalizing axonal function.

Models of stochastic hbox {Ca}^{2+} spiking

Complexity and limited knowledge render it impractical to write down the equations describing a cellular system completely. Cellular biophysics uses hypotheses-based modelling instead. How can we set up models with predictive power beyond the experimental examples used to develop them? The two textbook systems of cellular biophysics, hbox {Ca}^{2+} signalling and neuronal membrane potential dynamics, both face this question. Both systems also have a non-equilibrium feature in common: on different time scales and for different observables, they exhibit stochastic spiking, i.e., sequences of stereotypical events that are separated by statistically distributed intervals, the interspike intervals (ISI). Here we review recent progress on the description of hbox {Ca}^{2+} spikes in terms of blips, puffs and cellular hbox {Ca}^{2+} spikes and focus on stochastic models that can explain the statistics of the single ISIs, in particular its mean and variance and the cell-to-cell variability of these statistics. We also review models of the stochastic integrate-and-fire type and measures like the spike-train power spectrum or the serial correlation coefficient that are used to describe neuronal spike trains. These concepts from computational neuroscience might be applicable for understanding long-term memory effects in hbox {Ca}^{2+} spiking that extend beyond a single ISI, such as cumulative refractoriness.

Spike-Interval Triggered Averaging Reveals a Quasi-Periodic Spiking Alternative for Stochastic Resonance in Catfish Electroreceptors

Catfish detect and identify invisible prey by sensing their ultra-weak electric fields with electroreceptors. Any neuron that deals with small-amplitude input has to overcome sensitivity limitations arising from inherent threshold non-linearities in spike-generation mechanisms. Many sensory cells solve this issue with stochastic resonance, in which a moderate amount of intrinsic noise causes irregular spontaneous spiking activity with a probability that is modulated by the input signal. Here we show that catfish electroreceptors have adopted a fundamentally different strategy. Using a reverse correlation technique in which we take spike interval durations into account, we show that the electroreceptors generate a supra-threshold bias current that results in quasi-periodically produced spikes. In this regime stimuli modulate the interval between successive spikes rather than the instantaneous probability for a spike. This alternative for stochastic resonance combines threshold-free sensitivity for weak stimuli with similar sensitivity for excitations and inhibitions based on single interspike intervals.

Millisecond Timescale Disinhibition Mediates Fast Information Transmission through an Avian Basal Ganglia Loop

Avian song learning shares striking similarities with human speech acquisition and requires a basal ganglia (BG)-thalamo-cortical circuit. Information processing and transmission speed in the BG is thought to be limited by synaptic architecture of two serial inhibitory connections. Propagation speed may be critical in the avian BG circuit given the temporally precise control of musculature during vocalization. We used electrical stimulation of the cortical inputs to the BG to study, with fine time resolution, the functional connectivity within this network. We found that neurons in thalamic and cortical nuclei that are not directly connected with the stimulated area can respond to the stimulation with extremely short latencies. Through pharmacological manipulations, we trace this property back to the BG and show that the cortical stimulation triggers fast disinhibition of the thalamic neurons. Surprisingly, feedforward inhibition mediated by striatal inhibitory neurons onto BG output neurons sometimes precedes the monosynaptic excitatory drive from cortical afferents. The fast feedforward inhibition lengthens a single interspike interval in BG output neurons by just a few milliseconds. This short delay is sufficient to drive a strong, brief increase in firing probability in the target thalamic neurons, evoking short-latency responses. By blocking glutamate receptors in vivo, we show that thalamic responses do not appear to rely on excitatory drive, and we show in a theoretical model that they could be mediated by postinhibitory rebound properties. Such fast signaling through disinhibition and rebound may be a crucial specialization for learning of rapid and temporally precise motor acts such as vocal communication.

Stochastic description of complex and simple spike firing in cerebellar Purkinje cells

Cerebellar Purkinje cells generate two distinct types of spikes, complex and simple spikes, both of which have conventionally been considered to be highly irregular, suggestive of certain types of stochastic processes as underlying mechanisms. Interestingly, however, the interspike interval structures of complex spikes have not been carefully studied so far. We showed in a previous study that simple spike trains are actually composed of regular patterns and single interspike intervals, a mixture that could not be explained by a simple rate-modulated Poisson process. In the present study, we systematically investigated the interspike interval structures of separated complex and simple spike trains recorded in anaesthetized rats, and derived an appropriate stochastic model. We found that: (i) complex spike trains do not exhibit any serial correlations, so they can effectively be generated by a renewal process, (ii) the distribution of intervals between complex spikes exhibits two narrow bands, possibly caused by two oscillatory bands (0.5-1 and 4-8 Hz) in the input to Purkinje cells and (iii) the regularity of regular patterns and single interspike intervals in simple spike trains can be represented by gamma processes of orders, which themselves are drawn from gamma distributions, suggesting that multiple sources modulate the regularity of simple spike trains.

The parameters of the stochastic leaky integrate-and-fire neuronal model

Five parameters of one of the most common neuronal models, the diffusion leaky integrate-and-fire model, also known as the Ornstein-Uhlenbeck neuronal model, were estimated on the basis of intracellular recording. These parameters can be classified into two categories. Three of them (the membrane time constant, the resting potential and the firing threshold) characterize the neuron itself. The remaining two characterize the neuronal input. The intracellular data were collected during spontaneous firing, which in this case is characterized by a Poisson process of interspike intervals. Two methods for the estimation were applied, the regression method and the maximum-likelihood method. Both methods permit to estimate the input parameters and the membrane time constant in a short time window (a single interspike interval). We found that, at least in our example, the regression method gave more consistent results than the maximum-likelihood method. The estimates of the input parameters show the asymptotical normality, which can be further used for statistical testing, under the condition that the data are collected in different experimental situations. The model neuron, as deduced from the determined parameters, works in a subthreshold regimen. This result was confirmed by both applied methods. The subthreshold regimen for this model is characterized by the Poissonian firing. This is in a complete agreement with the observed interspike interval data.

Increased Noise Level of Purkinje Cell Activities Minimizes Impact of Their Modulation during Sensorimotor Control

While firing rate is well established as a relevant parameter for encoding information exchanged between neurons, the significance of other parameters is more conjectural. Here, we show that regularity of neuronal spike activities affects sensorimotor processing in tottering mutants, which suffer from a mutation in P/Q-type voltage-gated calcium channels. While the modulation amplitude of the simple spike firing rate of their floccular Purkinje cells during optokinetic stimulation is indistinguishable from that of wild-types, the regularity of their firing is markedly disrupted. The gain and phase values of tottering's compensatory eye movements are indistinguishable from those of flocculectomized wild-types or from totterings with the flocculus treated with P/Q-type calcium channel blockers. Moreover, normal eye movements can be evoked in tottering when the flocculus is electrically stimulated with regular spike trains mimicking the firing pattern of normal simple spikes. This study demonstrates the importance of regularity of firing in Purkinje cells for neuronal information processing.

Information transmission and recovery in neural communication channels revisited

Nerve cells in the brain generate all-or-none electric events-spikes-that are transmitted to other nerve cells via chemical synapses. An important issue in neuroscience is how neurons encode and transmit information using spike trains. Recently, signal transduction through two neurons connected by an excitatory chemical synapse was studied by Eguia et al. [Phys. Rev. E 62, 7111 (2000)]. They reported an apparent violation of the data processing inequality: The mutual information between the input signal and the output of the first neuron can be lower than the mutual information between the input signal and the output of the second neuron, that only receives input from the first neuron. We investigate whether it is possible, using a different method, to retrieve, from the first neuron's spike train, all the information about the input that is present in the second neuron's output. We find that single interspike intervals (ISI's) from the first neuron, at a resolution of 0.5 time units, contain more information about the input signal than those of the second neuron. Using a classification procedure based on the ISI return map, we recover 71% of the input entropy using the first neuron's spike train, and only 42% using the second neuron's spike train. Hence for these spike-train observables the data processing inequality is not violated.