Standard Deviation Of Interspike Intervals Research Articles

Towards systematic, data-driven validation of a collaborative, multi-scale model of Caenorhabditis elegans.

The OpenWorm Project is an international open-source collaboration to create a multi-scale model of the organism Caenorhabditis elegans At each scale, including subcellular, cellular, network and behaviour, this project employs one or more computational models that aim to recapitulate the corresponding biological system at that scale. This requires that the simulated behaviour of each model be compared with experimental data both as the model is continuously refined and as new experimental data become available. Here we report the use of SciUnit, a software framework for model validation, to attempt to achieve these goals. During project development, each model is continuously subjected to data-driven 'unit tests' that quantitatively summarize model-data agreement, identifying modelling progress and highlighting particular aspects of each model that fail to adequately reproduce known features of the biological organism and its components. This workflow is publicly visible via both GitHub and a web application and accepts community contributions to ensure that modelling goals are transparent and well-informed.This article is part of a discussion meeting issue 'Connectome to behaviour: modelling C. elegans at cellular resolution'.

Temperature-driven coherence resonance and stochastic resonance in a thermochemical system.

We perform the stochastic analysis of a thermochemical system using a master equation which describes a chemical reaction and includes discrete and continuous temperature jumps. We study the time evolution of the system selecting the temperature of the thermostat as an easily tunable control parameter. Depending on the thermostat temperature, the system can be in an excitable, oscillatory, or stationary regime. Stochastic time series for the system temperature are generated and the distributions of interspike intervals are analyzed in the three dynamical regimes separated by a homoclinic bifurcation and a Hopf bifurcation. Different constructive roles of internal fluctuations are exhibited. A noise-induced transition is observed in the vicinity of the Hopf bifurcation. Coherence resonance and stochastic resonance are found in the oscillatory regime. In a range of thermostat temperatures, a nontrivial behavior of the highly nonlinear system is revealed by the existence of both a minimum and a maximum in the scaled standard deviation of interspike intervals as a function of particle number. This high sensitivity to system size illustrates that controlling dynamics in nanoreactors may remain a difficult task.

Firing rate and pattern heterogeneity in the globus pallidus arise from a single neuronal population

Intrinsic heterogeneity in networks of interconnected cells has profound effects on synchrony and spike-time reliability of network responses. Projection neurons of the globus pallidus (GPe) are interconnected by GABAergic inhibitory synapses and in vivo fire continuously but display significant rate and firing pattern heterogeneity. Despite being deprived of most of their synaptic inputs, GPe neurons in slices also fire continuously and vary greatly in their firing rate (1-70 spikes/s) and in regularity of their firing. We asked if this rate and pattern heterogeneity arises from separate cell types differing in rate, local synaptic interconnections, or variability of intrinsic properties. We recorded the resting discharge of GPe neurons using extracellular methods both in vivo and in vitro. Spike-to-spike variability (jitter) was measured as the standard deviation of interspike intervals. Firing rate and jitter covaried continuously, with slow firing being associated with higher variability than faster firing, as would be expected from heterogeneity arising from a single physiologically distinct cell type. The relationship between rate and jitter was unaffected by blockade of GABA and glutamate receptors. When the firing rate of individual neurons was altered with constant current, jitter changed to maintain the rate-jitter relationship seen across neurons. Long duration (30-60 min) recordings showed slow and spontaneous bidirectional drift in rate similar to the across-cell heterogeneity. Paired recordings in vivo and in vitro showed that individual cells wandered in rate independently of each other. Input conductance and rate wandered together, in a manner suggestive that both were due to fluctuations of an inward current.

Firing Variability Is Higher than Deduced from the Empirical Coefficient of Variation

A convenient and often used summary measure to quantify the firing variability in neurons is the coefficient of variation (CV), defined as the standard deviation divided by the mean. It is therefore important to find an estimator that gives reliable results from experimental data, that is, the estimator should be unbiased and have low estimation variance. When the CV is evaluated in the standard way (empirical standard deviation of interspike intervals divided by their average), then the estimator is biased, underestimating the true CV, especially if the distribution of the interspike intervals is positively skewed. Moreover, the estimator has a large variance for commonly used distributions. The aim of this letter is to quantify the bias and propose alternative estimation methods. If the distribution is assumed known or can be determined from data, parametric estimators are proposed, which not only remove the bias but also decrease the estimation errors. If no distribution is assumed and the data are very positively skewed, we propose to correct the standard estimator. When defining the corrected estimator, we simply use that it is more stable to work on the log scale for positively skewed distributions. The estimators are evaluated through simulations and applied to experimental data from olfactory receptor neurons in rats.

Calcium signals driven by single channel noise.

Usually, the occurrence of random cell behavior is appointed to small copy numbers of molecules involved in the stochastic process. Recently, we demonstrated for a variety of cell types that intracellular Ca2+ oscillations are sequences of random spikes despite the involvement of many molecules in spike generation. This randomness arises from the stochastic state transitions of individual Ca2+ release channels and does not average out due to the existence of steep concentration gradients. The system is hierarchical due to the structural levels channel - channel cluster - cell and a corresponding strength of coupling. Concentration gradients introduce microdomains which couple channels of a cluster strongly. But they couple clusters only weakly; too weak to establish deterministic behavior on cell level. Here, we present a multi-scale modelling concept for stochastic hierarchical systems. It simulates active molecules individually as Markov chains and their coupling by deterministic diffusion. Thus, we are able to follow the consequences of random single molecule state changes up to the signal on cell level. To demonstrate the potential of the method, we simulate a variety of experiments. Comparisons of simulated and experimental data of spontaneous oscillations in astrocytes emphasize the role of spatial concentration gradients in Ca2+ signalling. Analysis of extensive simulations indicates that frequency encoding described by the relation between average and standard deviation of interspike intervals is surprisingly robust. This robustness is a property of the random spiking mechanism and not a result of control.

Are motoneurons involved in muscular dystrophy?

In the early seventies, a suggestion that even in muscular dystrophy a neurogenic factor may be involved, was formulated. The argument which followed this suggestion, resulted in eventual abandoning of this concept even by its author. This discussion however has never been supported by any systematic study of motoneuron activity in muscular dystrophy. We examined an activity of motoneurons supplying brachial biceps in eight controls and 26 patients affected by Duchenne muscular dystrophy by studying single motor unit (MU) potentials picked up by fine wire bipolar electrodes. In the majority of patients, MU firing rates were higher as compared to controls and increased more rapidly with increasing force level. The relationship between standard deviation of interspike intervals and their mean value, SD(x̄), was shifted towards the shorter intervals and lower SDs. The numerical values describing these changes were correlated with severity of the disease. There is evidence that the break-point of the function SD(x̄) is correlated with motoneuron properties, in particular with afterhyperpolarization duration. In muscular dystrophy, this break-point corresponds to the shorter interspike intervals. Therefore, we suggest that the motoneurons in muscular dystrophy are altered either in response to the muscle degeneration, or as a result of the disease itself.

Motoneurons are altered in muscular dystrophy

The activity of motoneurons supplying the brachial biceps muscle was examined in eight control subjects and 26 patients affected by Duchenne muscular dystrophy. The patients were subdivided into two groups: one whose motor units (MU) fired with normal rates (N group) and the other whose MU firing rates were higher as compared to controls (I group). Firing rates of motoneurons of patients from group I increased more rapidly with increasing force level. The relationship between the standard deviation of interspike intervals and their mean value, σ( T m ), was shifted towards the shorter intervals and lower standard deviations in both groups of patients. The numerical values describing these changes correlated with the severity of disease. The MU recruitment was comparable for control subjects and for patients. Experimental results as well as computer simulations indicate that the break-point of the function σ( T m ) is correlated with motoneuronal properties, and in particular with the afterhyperpolarization (AHP) duration. In muscular dystrophy this break-point corresponds to the shorter interspike intervals. Therefore, we propose that the motoneurons in muscular dystrophy are altered either in response to the muscle degeneration or as a result of the disease itself.

Convergence of auditory nerve fibers onto bushy cells in the ventral cochlear nucleus: implications of a computational model.

1. Convergence of auditory nerve (AN) fibers onto bushy cells of the ventral cochlear nucleus (VCN) was investigated with a model that describes the electrical membrane properties of these cells. The model consists of a single compartment, representing the soma, and includes three voltage-sensitive ion channels (fast sodium, delayed-rectifier-like potassium, and low-threshold potassium). These three channels have characteristics derived from voltage clamp data of VCN bushy cells. The model also contains a leakage channel, membrane capacitance, and synaptic inputs. The model accurately reproduces the membrane rectification seen in current clamp studies of bushy cells, as well as their unique current clamp responses. 2. In this study, the number and synaptic strength of excitatory AN inputs to the model were varied to investigate the relationship between input convergence parameters and response characteristics. From 1 to 20 excitatory synaptic inputs were applied through channels in parallel with the voltage-gated channels. Each synapse was driven by an independent AN spike train; spike arrivals produced brief (approximately 0.5 ms) conductance increases. The number (NS) and conductance (AE) of these inputs were systematically varied. The input spike trains were generated as a renewal point process that accurately models characteristics of AN fibers (refractoriness, adaptation, onset latency, irregularity of discharge, and phase locking). Adaptation characteristics of both high and low spontaneous rate (SR) AN fibers were simulated. 3. As NS and AE vary over the ranges 1-20 and 3-80 nS, respectively, the full range of response types seen in VCN bushy cells are produced by the model, with AN inputs typical of high-SR AN fibers. These include primarylike (PL), primarylike-with-notch (Pri-N), and onset-L (On-L). In addition, Onset responses, whose association with bushy cells in uncertain, and "dip" responses, which are not seen in the VCN, are produced. Dip responses occur with large NS and/or AE, and are due to depolarization block. When the AN inputs have the adaptation characteristics of low-SR AN fibers, PL--but not Pri-N or On-L responses--are produced. This suggests that neurons showing Pri-N and On-L responses must receive high-SR AN inputs. 4. The regularity of discharge of the model is compared with that of VCN bushy cells, using a measure derived from the mean and standard deviation of interspike intervals. Regularity is an important constraint on the model because the regularity of VCN bushy cells is the same as that of their AN inputs.(ABSTRACT TRUNCATED AT 400 WORDS)

The effect of pulsed microwaves on passive electrical properties and interspike intervals of snail neurons

The effects of pulsed microwaves (2.45 GHz, 10 microseconds, 100 pps, SAR: 81.5 kW/kg peak, 81.5 W/kg average) on membrane input resistance and action potential (AP) interval statistics were studied in spontaneously active ganglion neurons of land snails (Helix aspersa), at strictly constant temperature (20.8 +/- .07 degrees C worst case). Statistical comparison with sham-irradiated neurons revealed a significant increase in the mean input resistance of neurons exposed to pulsed microwaves (P < or = .05). Pulsed microwaves had no visible effect on mean AP firing rate; this observation was confirmed by analysis of interspike intervals (ISIs). Using an integrator model for spontaneously active neurons, we found the net input current to be more variable in neurons exposed to pulsed microwaves. The mean input current was not affected. The standard deviation of ISIs and the autocorrelation of the input current were marginally affected, but these changes were not consistent across neurons. Although the observed effects were less obvious than those reported in other studies, they represent evidence of a direct interaction between neurons and pulsed microwaves, in the absence of macroscopic temperature changes. The data do not suggest a single, specific mechanism for such interaction.

Regularity and latency of units in ventral cochlear nucleus: implications for unit classification and generation of response properties.

1. The responses of neurons in the ventral cochlear nucleus (VCN) of decerebrate cats are described with regard to their regularity of discharge and latency. Regularity is measured by estimating the mean and standard deviation of interspike intervals as a function of time during responses to short tone bursts (25 ms). This method extends the usual interspike-interval analysis based on interval histograms by allowing the study of temporal changes in regularity during transient responses. The coefficient of variation (CV), equal to the ratio of standard deviation to mean interspike interval, is used as a measure of irregularity. Latency is measured as the mean and standard deviation of the latency of the first spike in response to short tone bursts, with 1.6-ms rise times. 2. The regularity and latency properties of the usual PST histogram response types are shown. Five major PST response type classes are used: chopper, primary-like, onset, onset-C, and unusual. The presence of a prepotential in a unit's action potentials is also noted; a prepotential implies that the unit is recorded from a bushy cell. 3. Units with chopper PST histograms give the most regular discharge. Three varieties of choppers are found. Chop-S units (regular choppers) have CVs less than 0.35 that are approximately constant during the response; chop-S units show no adaptation of instantaneous rate, as measured by the inverse of the mean interspike interval. Chop-T units have CVs greater than 0.35, show an increase in irregularity during the response and show substantial rate adaptation. Chop-U units have CVs greater than 0.35, show a decrease in irregularity during the response, and show a variety of rate adaptation behaviors, including negative adaptation (an increase in rate during a short-tone response). Irregular choppers (chop-T and chop-U units) rarely have CVs greater than 0.5. Choppers have the longest latencies of VCN units; all three groups have mean latencies at least 1 ms longer than the shortest auditory nerve (AN) fiber mean latencies. 4. Chopper units are recorded from stellate cells in VCN (35, 42). Our results for chopper units suggest a model for stellate cells in which a regularly firing action potential generator is driven by the summation of the AN inputs to the cell, where the summation is low-pass filtered by the membrane capacitance of the cell.(ABSTRACT TRUNCATED AT 400 WORDS)

Quantitative analysis of depth spiking in relation to seizure foci in patients with temporal lobe epilepsy

The statistical properties of interictal EEG spiking in medial temporal lobe sites were analyzed in 14 patients with medically refractory complex partial seizures in whom the anatomical origins of seizure episodes had been inferred through the assessment of electrographic seizure records. An automatic spike recognition system programmed for a minicomputer was optimized and used to quantify spike abnormalities. The relationship of spike properties across recording sites within patients was found to exhibit stability across a period of days. Within each patient, the temporal lobe which appeared to be most likely to initiate electrographic seizure episodes was found to contain a site or sites exhibiting the maximum mean spike rate, the minimum standard deviation of interspike intervals, and the minimum coefficient of variation in spiking. Certain values of these measures of spiking may be indicative of a strong likelihood of eventual seizure initiation from the region being monitored. The degree of lateralization of depth spike activity was found to correlate perfectly with the suitability of patients from unilateral temporal lobectomy as judged by electrographic seizure recordings. While the relation between depth spike occurrence and the apparent origin of seizure episodes was found to be a very close one, a relation between depth spike occurrence and time of seizure onset was usually not evident. These data indicate the usefulness of interictal depth spike activity in predicting the electrographic locus of depth originating seizure episodes as well as the potential usefulness of such information in forming a surgical prognosis.