Use of the principles of computer statistical analysis for investigating the background impulse activity of neurons

A program for complex statistical analysis of the background impulse activity of neurons on a computer is proposed. The program includes: determination of the portion of the recording having a stable statistical structure; calculation of histograms of the probability density function of the interspike intervals (ISI) and statistical indexes related with them; correlation-spectral analysis of the ISI sequence; correlation-spectral analysis of the instants of appearance of impulses (from the frequency graph and graph of the function of recovery of impulse activity); and determination of the type and degree of relation of the lengths of adjacent ISI's and entropy analysis of this connection. A method is described for determining the portion of burst and group activity of the investigated neuron in the recording. The effectiveness of using the proposed program was checked by analyzing the background activity of pyramidal cells of the cat cortex. An analysis of neurons equal in frequency of background activity and rate of conduction of impulses in axons showed that the differences in the internal statistical structure of their impulses are very substantial.A. A. Bogomolets Institute of Physiology, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Neirofiziologiya, Vol. 2, No. 6, pp. 587–600, November–December, 1970.     

The amplitude principle of the structural-functional classification of cortical neurons

Some literature and author's experimental data are presented on functional and morphological characteristics of nerve cells by their electrophysiological parameters. The proposition is substantiated that in multineuron discharges reflecting the activity of microgroups of neighbouring cells, the absolute size of impulses indicates the distance of cortical neurones from the tip of the electrode, while amplitudes correlation may characterize the size of the cell and some of its functional properties. Arguments for this proposition are: latencies of impulse responses to afferent and antidromic stimulations and amplitude changes of multineuronal activity during movement of the electrode through the cortex thickness in acute experiments. As the electrode (with the tip diameter of 50 mcm) approaches a microgroup of neurons, the amplitude of the recorded impulse discharges increases, while the relation of big spikes to small ones remains almost the same.     

The temporal organization of the functional connection of the motor cortex neurons in the cat]

Conditioned food-procuring response to time (2 minutes interval) was elaborated in cats, multiunit activity of the motor cortex being recorded. On the basis of single spike trains discriminated from the multiunit activity the cross-correlation histograms were built and the spikes composing their peaks were analysed in real time. This secondary analysis of the histograms allowed to ascertain the dynamics of functional connections between the neurons during the phase of active waiting according to the distribution of coincident impulses. A concentration of coincident impulses of simultaneously recorded cells was observed in different moment of time. In some neuronal pairs the concentration of coincident impulses was revealed to the end of the conditioned interval. The data obtained are considered as a manifestation of the conditioned reaction at the level of neuronal interaction.     

Measuring kinetics of complex single ion channel data using mean-variance histograms.

The measurement of single ion channel kinetics is difficult when those channels exhibit subconductance events. When the kinetics are fast, and when the current magnitudes are small, as is the case for Na+, Ca2+, and some K+ channels, these difficulties can lead to serious errors in the estimation of channel kinetics. I present here a method, based on the construction and analysis of mean-variance histograms, that can overcome these problems. A mean-variance histogram is constructed by calculating the mean current and the current variance within a brief "window" (a set of N consecutive data samples) superimposed on the digitized raw channel data. Systematic movement of this window over the data produces large numbers of mean-variance pairs which can be assembled into a two-dimensional histogram. Defined current levels (open, closed, or sublevel) appear in such plots as low variance regions. The total number of events in such low variance regions is estimated by curve fitting and plotted as a function of window width. This function decreases with the same time constants as the original dwell time probability distribution for each of the regions. The method can therefore be used: 1) to present a qualitative summary of the single channel data from which the signal-to-noise ratio, open channel noise, steadiness of the baseline, and number of conductance levels can be quickly determined; 2) to quantify the dwell time distribution in each of the levels exhibited. In this paper I present the analysis of a Na+ channel recording that had a number of complexities. The signal-to-noise ratio was only about 8 for the main open state, open channel noise, and fast flickers to other states were present, as were a substantial number of subconductance states. "Standard" half-amplitude threshold analysis of these data produce open and closed time histograms that were well fitted by the sum of two exponentials, but with apparently erroneous time constants, whereas the mean-variance histogram technique provided a more credible analysis of the open, closed, and subconductance times for the patch. I also show that the method produces accurate results on simulated data in a wide variety of conditions, whereas the half-amplitude method, when applied to complex simulated data shows the same errors as were apparent in the real data. The utility and the limitations of this new method are discussed.     

Modified histogram subtraction technique for analysis of flow cytometry data

Analysis of flow cytometry histogram data by the subjective selection of an integration window can be a tedious and time-consuming task and is often inaccurate. A new method for automated calculation of the percent positive from immunofluorescence histograms is presented. This new method is a modification of the currently used method of channel-by-channel histogram subtraction. Its accuracy is compared to that of the channel-by-channel histogram subtraction method and to another currently used automated method, which selects an integration window by finding the channels that contain the most fluorescent 2% of a control histogram. The new histogram subtraction method is objective, easy to use, and is more accurate than other currently used automated analysis methods. PASCAL source code is given for each method of analysis.     

An analysis of interneuronal connections in the auditory cortex of awake cats]

A statistical analysis has been made of the interaction of the auditory cortex units in alert cats with chronically implanted electrodes. Three neurones with an amplitude ratio of 4:2:1 were singled out from the multineuronal activity. The dependence between the firing of two neurones was determined by the cross interval histograms. The relationships between 78 pairs of units were studied in 26 three units microsystems. About a third of the studied pairs functioned independently. The number of pairs with one-way and two-way connections was about equal (26 and 30 respectively). The neurones which generated spikes of high and medium amplitude, had the largest number of two-way connections. One-way connections were equally represented in all the three neurones, though with regard to direction they depended on the amplitude characteristics of the spikes. In neurones with large and medium spikes, output connections predominated, while in neurones with small spikes input connections predominated considerably. The connection could be of inhibitory, excitatory or mixed type. The inhibitory type of connections was the most frequent occurrence (57 out of 86). At prolonged recording (6 to 16 min) of spike activity, most of the functional connections persisted.     

UP States Protect Ongoing Cortical Activity from Thalamic Inputs

Cortical neurons in vitro and in vivo fluctuate spontaneously between two stable membrane potentials: a depolarized UP state and a hyperpolarized DOWN state. UP states temporally correspond with multineuronal firing sequences which may be important for information processing. To examine how thalamic inputs interact with ongoing cortical UP state activity, we used calcium imaging and targeted whole-cell recordings of activated neurons in thalamocortical slices of mouse somatosensory cortex. Whereas thalamic stimulation during DOWN states generated multineuronal, synchronized UP states, identical stimulation during UP states had no effect on the subthreshold membrane dynamics of the vast majority of cells or on ongoing multineuronal temporal patterns. Both thalamocortical and corticocortical PSPs were significantly reduced and neuronal input resistance was significantly decreased during cortical UP states – mechanistically consistent with UP state insensitivity. Our results demonstrate that cortical dynamics during UP states are insensitive to thalamic inputs.     

Multineuronal cortical activity in dogs with a defensive instrumental conditioned reflex

By methods of correlation analysis, interrelations were studied of neurones with high, mean and low amplitudes of spikes singled out by amplitude principle from background multineuronal activity of the motor and somatosensory cortical zones, recorded by chronically implanted semi-microelectrodes in dogs. In trained animals, a high positive correlation was observed of singled out neurones discharges, particularly between the neurones with low and mean amplitude of spikes. By the method of cross-interval histogram, dependent relations were revealed of the neurones with different amplitude characteristic mainly of one-sided excitatory character.     

Analysis of flow cytometric data of irradiated cell populations

Summary Flow cytometry (FCM) and autoradiography have been applied to determine changes in the cell kinetics of irradiated cells. Synchronized L-929 cells were irradiated with 10 Gy of X-rays when progressing from G₁-to S-phase of the cell cycle. In this study three methods to analyse DNA histograms were tested for applicability on FCM data obtained from cell populations blocked or retarded in the cycle: A) the Gaussian integral method, B) the peak-half-reflection method, and C) the rectangle method. Since histograms from synchronized cells are heavily distorted as compared to those obtained from exponentially growing cells and are quite similar to histograms from irradiated cells, they were used to test the suitability of the evaluation methods. Comparing the evaluated FCM data with the autoradiographic results from the same experimental series, the Gaussian integral method proved to be superior to the two other relatively simple approximation methods. The FCM histograms of irradiated cells were therefore analyzed only by the Gaussian integral method. It was shown that a considerable fraction of cells is still in the S-phase 25 h post irradiation, the DNA synthesis of which has ceased, as shown by autoradiography. This indicated that parallel measurements using FCM and autoradiography yield additional information on cell kinetic changes that cannot be obtained from applying one of the two methods used.     

The assessment of the strength of the interaction between neurons of the cat motor cortex in a conditioned reflex to time]

The work was conducted on cats with recording multineuronal activity of the motor cortex at the elaboration of conditioned reflex to time. Strength of interaction was estimated between the adjacent and remote neurones in the limits of 0.5 m. The dynamics of strengths of interneuronal interaction in most cases did not correlate with the dynamics of impulses frequency of the studied neurones. Changes of strengths of interaction between mutually remote neurones at CRT were met more frequently than between the adjacent ones, what may serve as one more evidence of the hypothesis on more strict structure of connections within microsystems and greater plasticity of connections between microsystems.     

Analysis of extracellular potentials using an IBM PC

1. A system has been developed for using IBM PC-compatible computers in combination with a Grafitek Data Logging Interface to record spike trains on magentic discs for later analysis. 2. The times and amplitudes of spikes detected on two input channels are recorded, together with a third channel containing information on computer-generated stimuli and keyboard-activated event markers. In excess of 50,000 spikes can be recorded with a computer having 640 k of Random Access Memory. 3. The recorded spike trains can be reconstructed on the computer monitor and keyboard-controlled window discriminators can be used to select the spikes for analysis by amplitude. 4. The same recorded data can be analysed to produce displays of spike count against time, amplitude histograms, inter-spike interval histograms, peri-stimulus time histograms(PSTH), raster displays and auto- and cross-correlations between activity on the two channels. Each spike is identified by number, allowing easy location of the start and finish of the section of data to be analysed, and the PSTH, raster and correlation analyses allow pretriggering to investigate event occurring before stimulation. 5. The axes of the displays histograms can be adjusted to produce optimum displays, and hard copy can be produced on dot matrix printers or digital plotters. 6. Quantitative analysis enables comparison between different recordings and treatments.     

Formals for histogram analysis of Purkinje cell interspike intervals

A hypothesis has been advanced proposing that the resting discharge of Purkinje cells depends on two factors: 1) tonic excitatory inflow and 2) Puasson's inhibitory inflow. This is why variety of interspike intervals is supposed to be the result of non-regular arrival of inhibitory impulses. From these assumptions an analytical expression was derived allowing to calculate probabilities of interspike intervals of various durations. The histograms of interspike intervals obtained analitically were found to coincide satisfactory with those obtained in experiments (Fig. 3, a, b). The analysis of real histograms based on the presented theory allowed to compare excitatory and inhibitory inflows to individual Purkinje Cells. It was found that, on the average, those cells which had large excitatory inflow, had also large inhibitory one, and vice versa (Fig. 4). It was also found that small decrease (about 20 percent) of excitatory inflow, or corresponding increase of inhibitory inflow, resulted in complete inhibition of most Purkinje cells.     

Correlated activity of neurons in the sensorimotor cortex of rabbits in the state of defensive dominanta and "animal hypnosis"

A hidden excitation focus (dominanta focus) was produced in the rabbit's CNS by threshold electrical stimulation of the left forelimb with the frequency of 0.5 Hz. As a rule, after the formation of the focus, pairs of neurons with prevailing two-second rhythm in their correlated activity were revealed both in the left and right sensorimotor cortices (with equal probabilities 29.3 and 32.4%, respectively). After "animal hypnosis" induction, the total percent of neuronal pairs with the prevalent dominanta-induced rhythm decreased significantly only in the right hemisphere (21%). After the termination of the "animal hypnosis" state, percent of neuronal pairs in the right cortex with prevailing two-second rhythm significantly increasead if the neurons in a pair were neighboring and decreased if they were remote from each other. Similar changes after the hypnotization were not found in the left cortex. Analysis of correlated activity of neuronal pairs with regard to amplitude characteristics showed that for both the right and left hemispheres, the prevalence of the two-second rhythm was more frequently observed in crosscorrelation histograms constructed regarding discharges of neurons with the lowest spike amplitude (in the right hemisphere) or the lowest and mean amplitudes (in the left hemisphere) selected from multiunit records.     

Repetitive excitation of bursts of action potentials in the rat hippocampus following single shock stimulation

1. Post-stimulus time (PST) histograms of rat hippocampal cells were recorded in vivo following single-shock stimulation of the fornix. 2. The PST histograms displayed a series of peaks of decreasing amplitude, similar to damped oscillatory responses previously recorded in cats and rabbits. 3. The effect of increased background activity was investigated by recording histograms with concurrent pulse train stimulation of the contralateral hippocampus. The histograms showed a decreased latency to the onset of the second peak. 4. Damped oscillatory activity seen in the in vivo rat preparation could not be elicited in the in vitro rat slice preparation. Thus species differences cannot account for the absence in slice studies of this type of damped oscillatory activity. 5. We conclude that the level of spontaneous activity is one factor contributing to the genesis of multiple peaks in histograms in the in vivo preparation.     

Fractal dimension and histogram method: Algorithm and some preliminary results of noise-like time series analysis

In the present work a methodological background for the histogram method of time series analysis is developed. Connection between shapes of smoothed histograms constructed on the basis of short segments of time series of fluctuations and the fractal dimension of the segments is studied. It is shown that the fractal dimension possesses all main properties of the histogram method. Based on it a further development of fractal dimension determination algorithm is proposed. This algorithm allows more precision determination of the fractal dimension by using the “all possible combination” method. The application of the method to noise-like time series analysis leads to results, which could be obtained earlier only by means of the histogram method based on human expert comparisons of histograms shapes.     

II. USE OF THE METHOD TO MONITOR THE IN VIVO KINETICS OF CELL POPULATIONS PERTURBED BY HYDROXYUREA

In a previous report, we described a new method called FP_i analysis to analyze time sequences of DNA histograms taken from a perturbed population of cells. In this paper we utilize the method to analyze the in vivo kinetic response of bone marrow and of lung metastases of the B16 tumor to various chemotherapeutic agents. We show that the technique allows useful kinetic data to be obtained with minimal processing of the raw histograms, thus allowing fast analysis of the data. We also show that, in order to monitor the kinetic response of living tissues, it is essential to collect multiparameter distributions; to monitor only the one dimensional fluorescence histogram can give rise to misleading results. Using these multiparameter histograms, we are also able to monitor the growth fraction of the lung metastases during treatment, allowing discrimination between cell synchrony and cell recruitment from the resting compartment.     

A practical graphical method for estimating the fraction of cells in S in DNA histograms from clinical tumor samples containing aneuploid cell populations

A graphical method for the analysis of unperturbed DNA histograms is presented in which the area of the normalized histogram subtended by the fraction of cells in S is represented by a trapezoid whose dimensions are dependent on features common to all such histograms. The technique takes measurement variability into account. This method was applied to a variety of synthetic DNA histograms. Overall, calculated values for the fraction of cells in S correlated well with actual values. This method was applied to 36 diploid cases of non-Hodgkin lymphoma; results correlated well with those obtained by a computer-based method. The results of the graphical-method were also highly reproducible between different observers. The graphical method can be used in the presence of aneuploid cell populations. Techniques for calculating S fractions in the presence of aneuploidy in clinical samples are described. These techniques were applied to synthetic histograms of mixed diploid and aneuploid populations. Calculated values correlated well with actual values.     

A sensitive cytochemical staining method for glucose-6-phosphate dehydrogenase activity in individual erythrocytes. I. Optimalization of the staining procedure

A sensitive cytochemical staining method for glucose-6-phosphate dehydrogenase activity in individual human erythrocytes is described. This staining method can be used for the rapid routine discrimination of patients with a deficiency of the enzyme in its homozygote or heterozygote form, but also for quantitative localization of its activity in individual erythrocytes. The staining procedure in its optimal form consists of a treatment of the erythrocytes with sodium nitrite, then a "fixation" in 0.025% glutaraldehyde (under NADP+ protection of the active site of the enzyme), followed by incubation of the cells in suspension in the presence of tetranitro BT, 1-methoxyphenazine methosulphate and polyvinyl alcohol. Using this new technique, a sharp localization is obtained of the glucose-6-phosphate dehydrogenase activity, which enables discrimination between red cells with different levels of enzyme activity, as a consequence of enzyme deficiencies or age changes.     

A functional statistical analysis of the action potentials in the brain multineuronal activity of waking cats

In the present work a method is substantiated of the correction of singled out impulses series by identification of parameters of neurones discharges (PD) during a long period of recording (up to 120 days) of the neuronal activity by means of chronically implanted nichrome semimicroelectrode in different brain part of alert cats.     

How voltage-gated ion channels alter the functional properties of ganglion and amacrine cell dendrites

The present study compares the structure and function of retinal ganglion and amacrine cell dendrites. Although a superficial similarity exists between amacrine and ganglion cell dendrites, a comparison between the branching pattern of the two cell types reveals differences which can only be appreciated at the microscopic level. Whereas decremental branching is found in ganglion cells, a form of non-decremental or "trunk branching" is observed in amacrine cell dendrites. Physiological differences are also observed in amacrine vs ganglion cells in which many amacrine cells generate dendritic impulses which can be readily distinguished from those of the soma, while separate dendritic impulses in ganglion cell dendrites have not been reported. Despite these differences, both amacrine and ganglion cell dendrites appear to contain voltage-gated ion channels, including TTX-sensitive sodium channels. One way to account for separate dendritic impulses in amacrine cells is to have a higher density of sodium channels and we generally find in modeling studies that a dendritic sodium channel density that is more than about 50% of that in the soma is required for excitatory, synaptic currents to give rise to local dendritic spike activity. Under these conditions, impulses can be generated in the dendrites and propagate for some distance along the dendritic tree. When the soma generates impulse activity in amacrine cells, it can activate, antidromically, the entire dendritic tree. Although ganglion cell dendrites do not appear to generate independent impulses, the presence of voltage-gated ion channels in these structures appears to be important for their function. Modeling studies demonstrate that when dendrites lack voltage-gated ion channels, impulse activity evoked by current applied to the cell body is generated at rates that are much higher than those observed physiologically. However, by placing ion channels in the dendrites at a reduced density compared to those of amacrine cells, the firing rate of ganglion cells becomes more physiological and the relationship between frequency and current (F/I relationship) can be precisely matched with physiological data. Recent studies have demonstrated the presence of T-type calcium channels in ganglion cells and our analysis suggests that they are found in higher density in the dendrites compared to the soma. This is the first voltage-gated ion channel which appears more localized to the dendrites than other cell copartments and this difference alone cries for an interpretation. The presence of a significant T-type calcium channel density in the dendrites can influence their integrative properties in several important ways. First, excitatory synaptic currents can be augmented by the activation of T-type calcium channels, although this is more likely to occur for transient rather than sustained synaptic currents because T-type currents show strong inactivation properties. In addition, T-type calcium channels may serve to limit the electrical load which dendrites impose on the spike initiation process and thus enhance the speed with which impulses can be triggered by the impulse generation site. This role whill enhance the safety factor for impulses traveling in the orthograde direction.