Estimation of population firing rates and current source densities from laminar electrode recordings

This model study investigates the validity of methods used to interpret linear (laminar) multielectrode recordings. In computer experiments extracellular potentials from a synaptically activated population of about 1,000 pyramidal neurons are calculated using biologically realistic compartmental neuron models combined with electrostatic forward modeling. The somas of the pyramidal neurons are located in a 0.4 mm high and wide columnar cylinder, mimicking a stimulus-evoked layer-5 population in a neocortical column. Current-source density (CSD) analysis of the low-frequency part (<500 Hz) of the calculated potentials (local field potentials, LFP) based on the ‘inverse’ CSD method is, in contrast to the ‘standard’ CSD method, seen to give excellent estimates of the true underlying CSD. The high-frequency part (>750 Hz) of the potentials (multi-unit activity, MUA) is found to scale approximately as the population firing rate to the power 3/4 and to give excellent estimates of the underlying population firing rate for trial-averaged data. The MUA signal is found to decay much more sharply outside the columnar populations than the LFP.     

Reciprocal inhibition of human motoneurons with different firing frequencies

A study was made of the effect of reciprocal inhibition on individual firing motoneurons in the extensor carpi ulnaris and soleus muscle in human subjects. Peristimulus histograms (PSH) were plotted at different average frequency of motoneuron firing ( ) and the change in duration of interspike intervals (ISI) was analyzed. For reciprocal inhibition, as for other types of inhibition, is a factor in the effectiveness of motoneuron inhibition. The duration of inhibition apparent in the PSH, the sizes of zones of inhibition effectiveness in the ISIs and lengthening of the intervals are dependent on . For all motoneurons, the low range is most favorable for effective inhibition. The dependence of effectiveness of a volley on the time of its arrival within the ISI is also analyzed.Institute for Problems of Information Transmission, Russian Academy of Sciences, Moscow. Translated from Neirofiziologiya, Vol. 24, No. 6, pp. 643–653, November–December, 1992.     

Multiple firing of single muscle vasoconstrictor neurons during cardiac dysrhythmias in human heart failure.

Single vasoconstrictor nerve fibers in humans normally fire only once but have the capacity to fire as many as eight times, per cardiac interval. Our laboratory recently demonstrated that the mean firing frequency of individual vasoconstrictor fibers is more than doubled in the sympathoexcitation associated with congestive heart failure (Macefield VG, Rundqvist B, Sverrisdottir YB, Wallin BG, and Elam M. Circulation 100: 1708--1713, 1999). However, the propensity to fire only once per cardiac interval was retained. In the present retrospective study, we tested the hypothesis that vasoconstrictor fibers fire more than once per cardiac interval in response to transient sympathoexcitatory stimuli, providing one mechanism for further increase of an already augmented sympathetic discharge. Six patients with congestive heart failure (New York Heart Association functional class II--IV; left ventricular ejection range 13--37%, average 22%) were studied at rest and during premature ectopic heartbeats. Analyzed for a total of 60 premature beats, the average firing probability of 10 vasoconstrictor fibers increased from 61 to 80% in the prolonged cardiac interval (i.e., reduced diastolic pressure) after premature beats. The incidence of multiple within-burst firing increased markedly, with two spikes being more common than one. Our results illustrate two different mechanisms (increases in firing probability and multiple within-burst firing), and indirectly indicate a third mechanism (recruitment of previously silent fibers), for acute sympathoexcitatory responses.     

Threshold model for clustered firing of neurons

Two probabilistic threshold models for burst activity of cortical neurons are proposed. In model I every input impulse increases the summed effect of previous input impulses by one unit. The decay of the summed effect takes place in discrete steps of one unit. A response occurs on arrival of an input impulse, when a threshold value is attained.Although after a response the summed effect is not reset to zero, it cannot exceed the threshold either. The distribution of intervals can be resolved in two components, one for long and one for short intervals. In model II intervals of the short component are terminated by a multiple response instead of one response.     

Estimation of HLA phenotype frequencies from two- and three-locus haplotype frequencies

A procedure for estimating HLA phenotype frequencies from two- and three-locus haplotype frequencies is described. Formulae for this procedure are derived, and examples are presented to illustrate the application. The procedure is useful when multiple-locus phenotype frequencies from a laboratory control series are not available, or when a sufficiently large number of laboratory controls have not yet been typed for recently defined antigens or loci to yield stable multiple-locus rates for comparative purposes.     

The population firing rate in the presence of GABAergic tonic inhibition in single neurons and application to general anaesthesia

Tonic inhibition has been found experimentally in single neurons and affects the activity of neural populations. This kind of inhibition is supposed to set the background or resting level of neural activity and plays a role in the brains arousal system, e.g. during general anaesthesia. The work shows how to involve tonic inhibition in population rate-coding models by deriving a novel transfer function. The analytical and numerical study of the novel transfer function reveals the impact of tonic inhibition on the population firing rate. Finally, a first application to a recent neural field model for general anaesthesia discusses the origin of the loss of consciousness during anaesthesia.     

Existence of two calcium currents recorded at normal calcium concentrations in single frog atrial cells

A low threshold calcium current (ICALT) was found in Cs+-loaded frog atrial cells in addition to the classical (high threshold) calcium current (ICaHT), and was investigated at physiological Ca2+ concentrations using the whole-cell patch-clamp technique. The threshold potentials were approximately -60 mV for ICaLT and -40 mV for ICaHT. The amplitude and time course of ICaLT were almost unaffected by exchanging Ca2+ for Ba2+ or Sr2+, while those of ICaLT were modified. ICaLT was inhibited by Ni2+ (40 x 10(-6) M) but was not affected by Cd2+ (20 x 10(-6) M) while ICaHT was inhibited by Cd2+ and only slightly reduced by Ni2+ at the same concentrations. Co2+ (10(-3) M) inhibited both types of calcium currents while La3+ (5 x 10(-6) M) had a greater blocking effect on ICaHT. ICaLT was neither modified by dihydropyridines (nisoldipine, Bay K) nor by adrenergic agonists (adrenaline, noradrenaline, isoprenaline), in contrast with the effects of these agents on ICaHT. Angiotensin II (40 x 10(-9) M) increased and atrial natriuretic factor (0.1 x 10(-6) M) decreased ICaLT while ICaHT, was not modified by these two substances.     

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.     

Estimation of allele frequencies for VNTR loci

VNTR loci provide valuable information for a number of fields of study involving human genetics, ranging from forensics (DNA fingerprinting and paternity testing) to linkage analysis and population genetics. Alleles of a VNTR locus are simply fragments obtained from a particular portion of the DNA molecule and are defined in terms of their length. The essential element of a VNTR fragment is the repeat, which is a short sequence of basepairs. The core of the fragment is composed of a variable number of identical repeats that are linked in tandem. A sample of fragments from a population of individuals exhibits substantial variation in length because of variation in the number of repeats. Each distinct fragment length defines an allele, but any given fragment is measured with error. Therefore the observed distribution of fragment lengths is not discrete but is continuous, and determination of distinct allele classes is not straightforward. A mixture model is the natural statistical method for estimating the allele frequencies of VNTR loci. In this article we develop nonparametric methods for obtaining the distribution of allele sizes and estimates of their frequencies. Methods for obtaining maximum-likelihood estimates are developed. In addition, we suggest an empirical Bayes method to improve the maximum-likelihood estimates of the gene frequencies; the empirical Bayes procedure effects a local smoothing. The latter method works particularly well when measurement error is large relative to the repeat size, because the estimated distribution of allele frequencies when maximum likelihood is used is unreliable because of an alternating pattern of over- and underestimation. We define alleles and estimate the allele frequencies for two VNTR loci from the human genome (D17S79 and D2S44), from data obtained from Lifecodes, Inc.     

Regularly firing neurons in the inferior colliculus have a weak interaural intensity difference sensitivity

The spike discharge regularity may be important in the processing of information in the auditory pathway. It has already been shown that many cells in the central nucleus of the inferior colliculus fire regularly in response to monaural stimulation by the best frequency tones. The aim of this study was to find how the regularity of units was affected by adding ipsilateral tone, and how interaural intensity difference sensitivity is related to regularity. Single unit recordings were performed from 66 units in the inferior colliculus of the anaesthetized guinea pig in response to the best frequency tone. Regularity of firing was measured by calculating the coefficient of variation as a function of time of a unit’s response. There was a positive correlation between coefficient of variation and interaural intensity difference sensitivity, indicating that highly regular units had very weak and irregular units had strong interaural intensity difference sensitivity responses. Three effects of binaural interaction on the sustained regularity were observed: constant coefficient of variation despite change in rate (66% of the units), negative (20%) and positive (13%) rate–CV relationships. A negative rate-coefficient of variation relationship was the dominant pattern of binaural interaction on the onset regularity.     

Functional interactions in hierarchically organized neural networks studied with spatiotemporal firing patterns and phase-coupling frequencies

A scalable hardware/software hybrid module--called Ubidule--endowed with bio-inspired ontogenetic and epigenetic features is configured to run a neural networks simulation with developmental and evolvable capabilities. We simulated the activity of hierarchically organized spiking neural networks characterized by an initial developmental phase featuring cell death followed by spike timing dependent synaptic plasticity in presence of background noise. An upstream 'sensory' network received a spatiotemporally organized external input and downstream networks were activated only via the upstream network. Precise firing sequences, formed by recurrent patterns of spikes intervals above chance levels, were observed in all recording conditions, thus suggesting the build-up of a connectivity able to sustain temporal information processing. The activity of a Ubinet--a network of Ubidules--is analyzed by means of virtual electrodes that recorded neural signals similar to EEG. The analysis of these signals was compared with a small set of human recordings and revealed common patterns of shift in quadratic phase coupling. The results suggest some interpretations of changes and plasticity of functional interactions between cortical areas driven by external stimuli and by learning/cognitive     

Estimation of cancer mortality rates: a Bayesian analysis of small frequencies

A Bayesian method is presented for estimating mortality rates of specific diseases when the frequency of deaths over a specified time period is assumed to have a Poisson distribution with mean proportional to the population size. The estimators use information from related populations, each having its own rate which is assumed distributed according to a common prior distribution about which some information is available. The study was motivated by an epidemiological study on the geographic variation of cancer mortality in the state of Missouri. Data from this study are used to illustrate the method and to compare it to a somewhat simpler empirical Bayes method.     

Cyclic GMP alters the firing rate and thermosensitivity of hypothalamic neurons

The rostral hypothalamus, especially the preoptic-anterior hypothalamus (POAH), contains temperature-sensitive and -insensitive neurons that form synaptic networks to control thermoregulatory responses. Previous studies suggest that the cyclic nucleotide cGMP is an important mediator in this neuronal network, since hypothalamic microinjections of cGMP analogs produce hypothermia in several species. In the present study, immunohistochemisty showed that rostral hypothalamic neurons contain cGMP, guanylate cyclase (necessary for cGMP synthesis), and CNG A2 (an important cyclic nucleotide-gated channel). Extracellular electrophysiological activity was recorded from different types of neurons in rat hypothalamic tissue slices. Each recorded neuron was classified according to its thermosensitivity as well as its firing rate response to 2-100 microM 8-bromo-cGMP (a membrane-permeable cGMP analog). cGMP has specific effects on different neurons in the rostral hypothalamus. In the POAH, the cGMP analog decreased the spontaneous firing rate in 45% of temperature-sensitive and -insensitive neurons, an effect that is likely due to cGMP-enhanced hyperpolarizing K(+) currents. This decreased POAH activity could attenuate thermoregulatory responses and produce hypothermia during exposures to cool or neutral ambient temperatures. Although 8-bromo-cGMP did not affect the thermosensitivity of most POAH neurons, it did increase the warm sensitivity of neurons in other hypothalamic regions located dorsal, lateral, and posterior to the POAH. This increased thermosensitivity may be due to pacemaker currents that are facilitated by cyclic nucleotides. If some of these non-POAH thermosensitive neurons promote heat loss or inhibit heat production, then their increased thermosensitivity could contribute to cGMP-induced decreases in body temperature.     

A joint interspike interval difference stochastic spike train analysis: detecting local trends in the temporal firing patterns of single neurons

We introduce a stochastic spike train analysis method called joint interspike interval difference (JISID) analysis. By design, this method detects changes in firing interspike intervals (ISIs), called local trends, within a 4-spike pattern in a spike train. This analysis classifies 4-spike patterns that have similar incremental changes. It characterizes the higher-order serial dependence in spike firing relative to changes in the firing history. Mathematically, this spike train analysis describes the statistical joint distribution of consecutive changes in ISIs, from which the serial dependence of the changes in higher-order intervals can be determined. It is similar to the joint interspike interval (JISI) analysis, except that the joint distribution of consecutive ISI differences (ISIDs) is quantified. The graphical location of points in the JISID scatter plot reveals the local trends in firing (i.e., monotonically increasing, monotonically decreasing, or transitional firing). The trajectory of these points in the serial-JISID plot traces the time evolution of these trends represented by a 5-spike pattern, while points in the JISID scatter plot represent trends of a 4-spike pattern. We provide complete theoretical interpretations of the JISID analysis. We also demonstrate that this method indeed identifies firing trends in both simulated spike trains and spike trains recorded from cultured neurons. Received: 13 May 1997 / Accepted in revised form: 9 December 1998     

Leptin counteracts the hypoxia-induced inhibition of spontaneously firing hippocampal neurons: a microelectrode array study

Besides regulating energy balance and reducing body-weight, the adipokine leptin has been recently shown to be neuroprotective and antiapoptotic by promoting neuronal survival after excitotoxic and oxidative insults. Here, we investigated the firing properties of mouse hippocampal neurons and the effects of leptin pretreatment on hypoxic damage (2 hours, 3% O(2)). Experiments were carried out by means of the microelectrode array (MEA) technology, monitoring hippocampal neurons activity from 11 to 18 days in vitro (DIV). Under normoxic conditions, hippocampal neurons were spontaneously firing, either with prevailing isolated and randomly distributed spikes (11 DIV), or with patterns characterized by synchronized bursts (18 DIV). Exposure to hypoxia severely impaired the spontaneous activity of hippocampal neurons, reducing their firing frequency by 54% and 69%, at 11 and 18 DIV respectively, and synchronized their firing activity. Pretreatment with 50 nM leptin reduced the firing frequency of normoxic neurons and contrasted the hypoxia-induced depressive action, either by limiting the firing frequency reduction (at both ages) or by increasing it to 126% (in younger neurons). In order to find out whether leptin exerts its effect by activating large conductance Ca(2+)-activated K(+) channels (BK), as shown on rat hippocampal neurons, we applied the BK channel blocker paxilline (1 μM). Our data show that paxilline reversed the effects of leptin, both on normoxic and hypoxic neurons, suggesting that the adipokine counteracts hypoxia through BK channels activation in mouse hippocampal neurons.