Interspike interval patterns of taste neurons in the hamster solitary nucleus

The central nervous system first processes taste informationin the solitary nucleus, which has been almost exclusively studiedin terms of average firing rate. We analyzed interspike intervals(ISI's) of 25 taste-responsive single units in the hamster (Mesocricetusauratus) solitary nucleus. ISI's were measured during spontaneousactivity and during stimulation with NaCl, KCl, sucrose, ora mixture of the three, and graphed on semi-logarithmic plots.Two different ISI patterns were evident: simple (13 units) andcomplex (12 units). Simple ISI patterns had a single broad peakat 284.7 ± 70.4 ms spontaneous and 78.8 ± 12.8ms stimulated. All complex ISI patterns had one distinct, sharppeak for an interval about 10 ms (11.3 ± 0.4 ms: spontaneous,9.3 ± 0.5 ms: stimulated), and a second, broader peakat 273.9 ± 45.9 ms spontaneous and 71.5 ± 14.6ms stimulated. As rate of firing increased peaks in ISI patternspredictably moved towards lower intervals, but ISI pattern-typedid not change. This constancy of ISI pattern held for responsesof a unit across all stimuli and did not depend upon the stimulusspecificity or location of the unit within the rostral poleof the solitary nucleus. Apparently, the pattern that a tasteneuron generates is intrinsic to the neuron and may relate tothe way it processes tast information.     

Interspike interval dependency from arterial chemoreceptors

The carotid body impulse generator has been previously characterized as a Poisson-type random process. We examined the validity of this characterization by analyzing sinus nerve spike trains for interspike interval dependency. Fifteen single chemoreceptive afferents were recorded in vivo under hypoxic-hypercapnic conditions, and approximately 1,000 consecutive interspike intervals for each fiber were timed and analyzed for serial dependence. The same set of intervals placed in shuffled order served as a control series without serial dependence. The original spike interval trains showed significantly negative first-order serial correlation coefficients and less variability in joint interval distributions than did the shuffled interval trains. These results suggest that the chemoreceptor afferent train is not random and may reflect a negative feedback system operating within the carotid body that limits variation about a mean frequency.     

Interspike interval correlations in neuron models with adaptation and correlated noise

The generation of neural action potentials (spikes) is random but nevertheless may result in a rich statistical structure of the spike sequence. In particular, contrary to the popular renewal assumption of theoreticians, the intervals between adjacent spikes are often correlated. Experimentally, different patterns of interspike-interval correlations have been observed and computational studies have identified spike-frequency adaptation and correlated noise as the two main mechanisms that can lead to such correlations. Analytical studies have focused on the single cases of either correlated (colored) noise or adaptation currents in combination with uncorrelated (white) noise. For low-pass filtered noise or adaptation, the serial correlation coefficient can be approximated as a single geometric sequence of the lag between the intervals, providing an explanation for some of the experimentally observed patterns. Here we address the problem of interval correlations for a widely used class of models, multidimensional integrate-and-fire neurons subject to a combination of colored and white noise sources and a spike-triggered adaptation current. Assuming weak noise, we derive a simple formula for the serial correlation coefficient, a sum of two geometric sequences, which accounts for a large class of correlation patterns. The theory is confirmed by means of numerical simulations in a number of special cases including the leaky, quadratic, and generalized integrate-and-fire models with colored noise and spike-frequency adaptation. Furthermore we study the case in which the adaptation current and the colored noise share the same time scale, corresponding to a slow stochastic population of adaptation channels; we demonstrate that our theory can account for a nonmonotonic dependence of the correlation coefficient on the channel’s time scale. Another application of the theory is a neuron driven by network-noise-like fluctuations (green noise). We also discuss the range of validity of our weak-noise theory and show that by changing the relative strength of white and colored noise sources, we can change the sign of the correlation coefficient. Finally, we apply our theory to a conductance-based model which demonstrates its broad applicability.     

Interspike interval statistics in the Ornstein-Uhlenbeck neuronal model with signal-dependent noise

The stochastic leaky integrate-and-fire (LIF) continuous model is studied under the condition that the amplitude of noise is a function of the input signal. The coefficient of variation (CV) of interspike intervals (ISIs) is investigated for different types of dependencies between the noise and the signal. Finally, we present the CV and the ISI density resulting from the special choice of parameters of the input that gave rise to a contra-intuitive behavior of the transfer function in Lánsky and Sacerdote [Phys. Lett. A 285 (2001) 132].     

Interspike background activity in extracelullarly recorded Purkinje neurons: spectral analysis

The aim of this study was to investigate the spectral characteristics of Purkinje cell interspike background activity caused by the occurrence of particular action potentials or by electrically induced enhancement of cerebellar inhibitory and excitatory input drive. Spontaneously active Purkinje neurons were extracellularly recorded in anesthetized rats before and after cessation of stimulation from the inferior olive (10) or locus coeruleus (LC). After A/D conversion (30 kHz), direct spectral analysis of extracted interspike background activity was done. Our results have shown that, in contrast to simple spikes, the occurrence of complex spikes induces changes in the spectra of interspike background activity. The different spectral changes of interspike background activity induced by LC and 10 stimulation also indicated the importance of this extracellularly recorded phenomenon.     

Spontaneous discharge patterns of mesencephalic neurons: interval histogram and mean interval relationship

Summary The spontaneous nerve impulse activity of 354 neurons of the mesencephalic reticular formation resp. the superior colliculus of unanesthetized curarized rats resp. cats has been recorded by microelectrodes and processed by means of a LINC computer. A relationship between the shape of interimpulse interval histogram (IH) and the mean interimpulse intervals (MI) of the same spike train has been found. Neurons with long MI's (low frequency of firing) are never characterized by symmetrical IH's, the exponential IH (characterizing random occurrence of impulses) being the most common in these cases. Neurons with symmetrical IH's are usually those with short MI's (fast firing rate). Longlasting recordings with changing MI show that the shape of IH's may not be considered in general a stable feature of certain neurons (in the majority of cases it changes together with the MI). Neurons with symmetrical IH's and short MI's may not be found in the superficial layers but in the depth of the superior colliculus only (having probably like the reticular formation integrative functions). A computer model is presented explaining the observed dependency of the IH shape on the MI duration in terms of the change in the mean frequency of common input process.     

Systematic regulation of spine sizes and densities in pyramidal neurons

Dendritic spines receive most excitatory inputs in the CNS. Recent evidence has demonstrated that the spine head volume is linearly correlated with the readily releasable pool of neurotransmitter and the PSD size. These correlations can be used to functionally interpret spine morphology. Using Golgi impregnations and light microscopy, we reconstructed 23000 spines from pyramidal neurons in layers 2/3, 4, 5 and 6 of mouse primary visual cortex and CA1 hippocampal region and measured their spine head diameters and densities. Spine head diameters and densities are variable within and across cells, although they are similar between apical and basal dendrites. When compared to other regions, layer 5 neurons have larger spine heads and CA1 neurons higher spine densities. Interestingly, we detect a correlation between spine head diameter and interspine distance within and across cells, whereby larger spines are spaced further away from each other than smaller spines. Finally, in CA1 neurons, spine head diameters are larger, and spine density lower, in distal apical dendrites (>200 microm from soma) compared to proximal regions. These results reveal that spine morphologies and densities, and therefore synaptic properties, are jointly modulated with respect to cortical region, laminar position, and, in some cases, even the position of the spine along the dendritic tree. Individual neurons also appear to regulate their apical and basal spine densities and morphologies in concert. Our data provide evidence for a homeostatic control of excitatory synaptic strength.     

Fire incidence,but not fire size,affects macropod densities

The regeneration of plants post‐fire has widely been shown to be attractive to vertebrate herbivores. However, there are few data relevant to the effect of fire size on herbivore densities. In dry eucalypt forest in one region and hummock sedgeland in another region, we used timed scat counts to test the effect of fire and fire size on Tasmanian macropod densities 6 months after burning. We also tested whether soil characteristics and the nature of ground cover related to the degree of attractiveness of post‐burn regeneration. Soil nutrients and higher covers of grasses and herbs in ground layer vegetation were associated with higher macropod densities. In dry eucalypt forest, fire incidence and fire size did not affect macropod density, while in hummock sedgeland, fire had a positive effect on macropod density, but fire size had no effect.     

Bifurcations of large networks of two-dimensional integrate and fire neurons

Recently, a class of two-dimensional integrate and fire models has been used to faithfully model spiking neurons. This class includes the Izhikevich model, the adaptive exponential integrate and fire model, and the quartic integrate and fire model. The bifurcation types for the individual neurons have been thoroughly analyzed by Touboul (SIAM J Appl Math 68(4):1045–1079, 2008). However, when the models are coupled together to form networks, the networks can display bifurcations that an uncoupled oscillator cannot. For example, the networks can transition from firing with a constant rate to burst firing. This paper introduces a technique to reduce a full network of this class of neurons to a mean field model, in the form of a system of switching ordinary differential equations. The reduction uses population density methods and a quasi-steady state approximation to arrive at the mean field system. Reduced models are derived for networks with different topologies and different model neurons with biologically derived parameters. The mean field equations are able to qualitatively and quantitatively describe the bifurcations that the full networks display. Extensions and higher order approximations are discussed.     

The effect of fire interval on post‐fire understorey communities in Yellowstone National Park

Questions: How does the time interval between subsequent stand‐replacing fire events affect post‐fire understorey cover and composition following the recent event? How important is fire interval relative to broad‐ or local‐scale environmental variability in structuring post‐fire understorey communities? Location: Subalpine plateaus of Yellowstone National Park (USA) that burned in 1988. Methods: In 2000, we sampled understorey cover and Pinus contorta density in pairs of 12–yr old stands at 25 locations. In each pair, the previous fire interval was either short (7–100 yr) or long (100–395 yr). We analysed variation in understorey species richness, total cover, and cover of functional groups both between site pairs (using paired t‐tests) and across sites that experienced the short fire intervals (using regression and ordination). We regressed three principal components to assess the relative importance of disturbance and broad or local environmental variability on post‐fire understorey cover and richness. Results: Between paired plots, annuals were less abundant and fire‐intolerant species (mostly slow‐growing shrubs) were more abundant following long intervals between prior fires. However, mean total cover and richness did not vary between paired interval classes. Across a gradient of fire intervals ranging from 7–100 yr, total cover, species richness, and the cover of annuals and nitrogen‐fixing species all declined while the abundance of shrubs and fire‐intolerant species increased. The few exotics showed no response to fire interval. Across all sites, broad‐scale variability related to elevation influenced total cover and richness more than fire interval. Conclusions: Significant variation in fire intervals had only minor effects on post‐fire understorey communities following the 1988 fires in Yellowstone National Park.     

How noisy adaptation of neurons shapes interspike interval histograms and correlations

Channel noise is the dominant intrinsic noise source of neurons causing variability in the timing of action potentials and interspike intervals (ISI). Slow adaptation currents are observed in many cells and strongly shape response properties of neurons. These currents are mediated by finite populations of ionic channels and may thus carry a substantial noise component. Here we study the effect of such adaptation noise on the ISI statistics of an integrate-and-fire model neuron by means of analytical techniques and extensive numerical simulations. We contrast this stochastic adaptation with the commonly studied case of a fast fluctuating current noise and a deterministic adaptation current (corresponding to an infinite population of adaptation channels). We derive analytical approximations for the ISI density and ISI serial correlation coefficient for both cases. For fast fluctuations and deterministic adaptation, the ISI density is well approximated by an inverse Gaussian (IG) and the ISI correlations are negative. In marked contrast, for stochastic adaptation, the density is more peaked and has a heavier tail than an IG density and the serial correlations are positive. A numerical study of the mixed case where both fast fluctuations and adaptation channel noise are present reveals a smooth transition between the analytically tractable limiting cases. Our conclusions are furthermore supported by numerical simulations of a biophysically more realistic Hodgkin-Huxley type model. Our results could be used to infer the dominant source of noise in neurons from their ISI statistics.     

Long-term effects of prescribed fire on Cladium jamaicense crantz and Typha domingensis pers. densities

The importance of fire to the maintenance of herbaceous plant communities in Florida wetland ecosystems is widely acknowledged. However, despite the acceptance of fire as a natural and necessary disturbance, ecosystem responses to fire in these systems are still poorly understood. Of particular concern is the effect of fire on the dynamics of plant communities dominated by Cladium jamaicense Crantz and Typha domingensis Pers. High nutrient levels, primarily phosphorus, and prolonged hydroperiods have been associated with Typha expansion into Cladium dominated communities. Recent studies suggest that fire is a disturbance that may play a facilitative role in this process. The objective of this study was to monitor the long-term effects of a single prescribed fire on Cladium and Typha densities in a freshwater marsh in Florida. Transects located at two burned sites and one unburned site were sampled prior to and annually for four years following a prescribed, lightning-season fire. There was a significant increase (P < 0.01) in Typha at both burn sites for two years after the fire. However, this increase was temporary since Typha density declined to pre-burn levels in the third and fourth years post-burn. Cladium density at the burned sites either increased or remained unchanged throughout the study period. When the control site unexpectedly burned in the fourth year of the study, density changes of Typha were similar to those observed at the original burn sites. Overall, we did not see any lasting changes in Cladium and Typha as a result of the fires, even though soil nutrient levels and hydroperiods were within levels documented to enhance Typha expansion.     

Processing of Auditory Midbrain Interspike Intervals by Model Neurons

A question central to sensory processing is how signal information is encoded and processed by single neurons. Stimulus features can be represented through rate coding (via firing rate), temporal coding (via firing synchronization to temporal periodicities), or temporal encoding (via intricate patterns of spike trains). Of the three, examples of temporal encoding are the least documented. One region in which temporal encoding is currently being explored is the auditory midbrain. Midbrain neurons in the plainfin midshipman generate different interspike interval (ISI) distributions depending on the frequencies of the concurrent vocal signals. However, these distributions differ only along certain lengths of ISIs, so that any neurons trying to distinguish the distributions would have to respond selectively to specific ISI ranges. We used this empirical observation as a realistic challenge with which to explore the plausibility of ISI-tuned neurons that could validate this form of temporal encoding. The resulting modeled cells—point neurons optimized through multidimensional searching—were successfully tuned to discriminate patterns in specific ranges of ISIs. Achieving this task, particularly with simplified neurons, strengthens the credibility of ISI coding in the brain and lends credence to its role in auditory processing.     

Leader neurons in leaky integrate and fire neural network simulations

In this paper, we highlight the topological properties of leader neurons whose existence is an experimental fact. Several experimental studies show the existence of leader neurons in population bursts of activity in 2D living neural networks (Eytan and Marom, J Neurosci 26(33):8465–8476, 2006; Eckmann et al., New J Phys 10(015011), 2008). A leader neuron is defined as a neuron which fires at the beginning of a burst (respectively network spike) more often than we expect by chance considering its mean firing rate. This means that leader neurons have some burst triggering power beyond a chance-level statistical effect. In this study, we characterize these leader neuron properties. This naturally leads us to simulate neural 2D networks. To build our simulations, we choose the leaky integrate and fire (lIF) neuron model (Gerstner and Kistler 2002; Cessac, J Math Biol 56(3):311–345, 2008), which allows fast simulations (Izhikevich, IEEE Trans Neural Netw 15(5):1063–1070, 2004; Gerstner and Naud, Science 326:379–380, 2009). The dynamics of our lIF model has got stable leader neurons in the burst population that we simulate. These leader neurons are excitatory neurons and have a low membrane potential firing threshold. Except for these two first properties, the conditions required for a neuron to be a leader neuron are difficult to identify and seem to depend on several parameters involved in the simulations themselves. However, a detailed linear analysis shows a trend of the properties required for a neuron to be a leader neuron. Our main finding is: A leader neuron sends signals to many excitatory neurons as well as to few inhibitory neurons and a leader neuron receives only signals from few other excitatory neurons. Our linear analysis exhibits five essential properties of leader neurons each with different relative importance. This means that considering a given neural network with a fixed mean number of connections per neuron, our analysis gives us a way of predicting which neuron is a good leader neuron and which is not. Our prediction formula correctly assesses leadership for at least ninety percent of neurons.     

Astrocytes regulate amino acid receptor current densities in embryonic rat hippocampal neurons

Embryonic rat hippocampal neurons were cultured in a serum-free defined medium (MEM/N3) either directly on poly-D -lysine (PDL) or on a confluent monolayer of postnatal cortical astrocytes, C6 glioma cells, or Rat2 fibroblasts. Neurons on PDL were grown in MEM/N3 or in MEM/N3 conditioned for 24 h by astrocytes or C6 cells. Membrane capacitance (C_m) and γ-aminobutyric acid (GABA)-, glycine-, kainate-, and N-methyl-D -aspartate (NMDA)-induced currents were quantified using whole-cell patch-clamp recordings. C_m as well as the amplitude and the density of these currents in neurons cultured on astrocytes were significantly greater than those in neurons grown on PDL after 24 and 48 h. C6 cells mimicked astrocytes in promoting C_m and GABA-, glycine-, and NMDA-evoked, but not kainate-evoked, currents. C_m and currents in neurons grown on Rat2 cells were comparable to those in neurons on PDL. Astrocytes maintained in culture for 3 months were noticeably less effective than freshly prepared ones just grown to confluence. Suppression of spontaneous cytoplasmic Ca²⁺ (Ca_c²⁺) elevations in astrocytes by 1,2-bis(2-aminophenoxy) ehane-N, N, N, N-tetraacetic acid acetoxymethyl ester (BAPTA-AM) loaded intracellularly blocked the observed modulatory effects. Medium conditioned by either astrocytes or C6 cells mimicked the effects of direct coculture of neurons on these cells in promoting C_m and amino acid-evoked currents. Inclusion of antagonists at GABA and glutamate receptors in coculture experiments blocked the observed effects. Thus, diffusible substances synthesized and/or secreted by astrocytes in a Ca_c²⁺-dependent manner can regulate neuronal growth and aminoacid receptor function, and these effects may involve neuronal GABA and glutamate receptors. © 1997 John Wiley & Sons, Inc. J Neurobiol 33: 848–864, 1997     

Measurement of nonuniform current densities and current kinetics in Aplysia neurons using a large patch method

A large patch electrode was used to measure local currents from the cell bodies of Aplysia neurons that were voltage-clamped by a two-microelectrode method. Patch currents recorded at the soma cap, antipodal to the origin of the axon, and whole-cell currents were recorded simultaneously and normalized to membrane capacitance. The patch electrode could be reused and moved to different locations which allowed currents from adjacent patches on a single cell to be compared. The results show that the current density at the soma cap is smaller than the average current density in the cell body for three components of membrane current: the inward Na current (INa), the delayed outward current (Iout), and the transient outward current (IA). Of these three classes of ionic currents, IA is found to reach the highest relative density at the soma cap. Current density varies between adjacent patches on the same cell, suggesting that ion channels occur in clusters. The kinetics of Iout, and on rare occasions IA, were also found to vary between patches. Possible sources of error inherent to this combination of voltage clamp techniques were identified and the maximum amplitudes of the errors estimated. Procedures necessary to reduce errors to acceptable levels are described in an appendix.     

On the firing maps of a general class of forced integrate and fire neurons

Integrate and fire processes are fundamental mechanisms causing excitable and oscillatory behavior. Van der Pol [Philos. Mag. (7) 2 (11) (1926) 978] studied oscillations caused by these processes, which he called 'relaxation oscillations' and pointed out their relevance, not only to engineering, but also to the understanding of biological phenomena [Acta Med. Scand. Suppl. CVIII (108) (1940) 76], like cardiac rhythms and arrhythmias. The complex behavior of externally stimulated integrate and fire oscillators has motivated the study of simplified models whose dynamics are determined by iterations of 'firing circle maps' that can be studied in terms of Poincaré's rotation theory [Chaos 1 (1991) 20; Chaos 1 (1991) 13; SIAM J. Appl. Math. 41 (3) (1981) 503]. In order to apply this theory to understand the responses and bifurcation patterns of forced systems, it is fundamental to determine the regions in parameter space where the different regularity properties (e.g., continuity and injectivity) of the firing maps are satisfied. Methods for carrying out this regularity analysis for linear systems, have been devised and the response of integrate and fire neurons (with linear accumulation) to a cyclic input has been analyzed [SIAM J. Appl. Math. 41 (3) (1981) 503]. In this paper we are concerned with the most general class of forced integrate and fire systems, modelled by one first-order differential equation. Using qualitative analysis we prove theorems on which we base a new method of regularity analysis of the firing map, that, contrasting with methods previously reported in the literature, does not requires analytic knowledge of the solutions of the differential equation and therefore it is also applicable to non-linear integrate and fire systems. To illustrate this new methodology, we apply it to determine the regularity regions of a non-linear example whose firing maps undergo bifurcations that were unknown for the previously studied linear systems.     

Power-law inter-spike interval distributions infer a conditional maximization of entropy in cortical neurons

The brain is considered to use a relatively small amount of energy for its efficient information processing. Under a severe restriction on the energy consumption, the maximization of mutual information (MMI), which is adequate for designing artificial processing machines, may not suit for the brain. The MMI attempts to send information as accurate as possible and this usually requires a sufficient energy supply for establishing clearly discretized communication bands. Here, we derive an alternative hypothesis for neural code from the neuronal activities recorded juxtacellularly in the sensorimotor cortex of behaving rats. Our hypothesis states that in vivo cortical neurons maximize the entropy of neuronal firing under two constraints, one limiting the energy consumption (as assumed previously) and one restricting the uncertainty in output spike sequences at given firing rate. Thus, the conditional maximization of firing-rate entropy (CMFE) solves a tradeoff between the energy cost and noise in neuronal response. In short, the CMFE sends a rich variety of information through broader communication bands (i.e., widely distributed firing rates) at the cost of accuracy. We demonstrate that the CMFE is reflected in the long-tailed, typically power law, distributions of inter-spike intervals obtained for the majority of recorded neurons. In other words, the power-law tails are more consistent with the CMFE rather than the MMI. Thus, we propose the mathematical principle by which cortical neurons may represent information about synaptic input into their output spike trains.