Computer Analysis Dynamics of Background Impulse Activity of Neurons in Situ and in Vitro

IMPUffiE COMPUTER ANALYSIS DINAMICS OF BACKGROUND IMPULSE ACTIVITY OF NEURONS IN SITU AND IN VITRO

M.B. Shtark, A.S. Ratushnjak, V.J. Stratievski, N.A. Karasev, L.V. Voskresenskaja Institut of Automation and Electrometr,y Siberian Branch of Academy of Science USSR, Novosibirsk, USSR ABSTRACT Statistical characteristics of background impulse activity of pyramide neurons of hippocampus in situ and in vitro were compared. The results of statistical analysis have shown a good coincidence of numerical characteristics of distribution of inter-impulse intervals: mathematical expectancies, standard deviations,coefficients of asymmetry and excess in impulse flows of the compared series. This coincidence can serve as one of proofs of preservation of normal functional properties and "organospecificity" by the neurons is tissue culture. On the other hand, some differences were found in the structure of the compared flows, which the authors attribute to essential differences between the neuronal networks in the objects studied. INTRODUCTION The problem of the study of regularities of formation and of the structure of impulse flow of neurons requires application of the most powerful statistical methods with the help of computers. At the first stage, comparison of impulse flows of neurons in maximally different situations seems the most efficient. The aim of this comparison is to confront structural and functional differences with the differences in their statistical characteristics. The

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most suitable for this is the comparison of impulse flows of central neurons which fucntion under the condition of extremely simple nerve network in culture of nervous tissue (CNT), with the flows of single cells. METHOD The object for this work were hippocampal neurons of the rat. The impulse flows of the neurons were recorded by means of usual microelectrode techniques from neurons in situ and in vitro. In latter case, the microelectrode was impaled under visual control. The culturing was carried out after Bornstain(1). In 10-20 days, the culture on a coverslip was transferred to a chamber for electrophySiological studies, in which the physiological temperature and the medium was kept constant. The signals recorded from the cells were amplivied and transmitted to an oscilloscope for visual control of the process, converted into standard,rectangular impulses by means of special device and recorded on a magnetic tape. For the control of the mean discharge frequency and for the choice of stationary regions during the experiment, the "Didac" computer was used. The sequence of interimpulse - intervals (Ill) converted by means of input device was introduced into computers ''Minsk-22'' and

processed according to the programm block described below. The general properties of III distribution were evaluated by intervals histogramms of the first order{IH). For the quantitative estimation of the distribution, values of its numeric characteristics were built: mathematical expectancy, mean square deviation,asYmmetdeviation,asymmetry coefficients and excess and of the first four initial moments. By the IH of the first order, plots of logarithms of the reliability function were built for the comparison of the distribution with the exponential one and ext1mation of the distribution for the extimation within given intervals, and the curves of postimpulse probability (PP) for the study of distribution function of the lengths of III close to zero, for its comparison with the exponential distribution in the region of short and middle intervals, and for the more accurate location of intermodal minima. For the description of grouping of the impulses and evaluation of correlation properties of the flow, correlation fields of adjacent intervals, III of the 1-4th oraers and auto-correlograms (ACG) were constructed. The ACG were built after Herstein and Kiang by means of summa1-Sth orders. tion of the IH of the 1-8th Then the distributions were built for the numerical characteristics of the dif~ distributions of III in series, the dif~ ferences between which were estimated by corresponding criteria. RESULTS The background impulse activity of neurons in the culture was recorded in explants from the 7 day of culturing. The explants fill the 7th day did not show any background activity or did so very seldom. Statistical characteristics of the back-

565

bround impulse activity were compared in 55 pyramide neurons of hippocampus of albino rats in situ, and in 51 neurons of the same structure in tissue culture. The distribution of inter-impulse intervals of all the impulse flows studied were characterized by positive values of coefficients of aSYmmetry asymmetry and excess. The distributions of values of mathematical expectancies of the lengths of interimpulse intervals, aSYmmetry asymmetry and excess coefficients did not show any significant differencies when checked by Student's inSignificant were the difcriterium. As insignificant ferences of distributions of standard devisions by Fisher's criterium. The same nonresults were obtained when checked by oonparametric criteria (Kolmogorov & Peerson) (fig. 1) Significant at ~5 per cent level were the distributions of variation coefficients in the series in situ and in vitro. The maxima of these distributions fell on the values of 1.0-1.2 and 0.7-0.9 respectively. Because of absence of evident and unequivocal differences in most statistical characteristics, ununiformity of the obtained data and impossibility, im most cases, of approximation of the realizations under study by means of theoretical distributions and classes of flows, an attempt was made at qualitative classification of impulse flows of the compared series. On the basis of study of interval histograms, functions of post-impulse probability (risk functions) and logarithms of reliability functions, three types of distribution of inter-impulse intervals intervalS were found. To the first type we referred unimodal distributions which were close to exponential ones. The second type consisted of unimodal distributions with significantly increased number of intervals intervalS of certain

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duration as compared to the exponential ones. Bimodal distributions with two (seldom more) such length ranges of inter-impulse intervals of higher probability separated from each other by expressed minima, were attributed to ~o the third type. ~ype. The evaluation of relation between inter-impulse intervals in~ervals on the basis of study of correlation fields and autocorrelograms showed ununiformity for this feature of flows with distributions of the second and third types. Except the flows having no visible dependence between the varian~ with inter-impulse intervals, two varian~ expressed periodicity were found. One of them, having distributions of the second type was referred to as "regular"; the other with third type distributions, as i 'lOWS characterized by in"periodic". The 1"10WS ter-impulse intervals distributed exponentially were aperiodic in all cases.As the result of such classification, each of the analysed impulse flows was attributed to one of five types: 1. "The simplest flow" - The flow without any after-effect. The inter-impulse intervals are independent and distributed exponentially, i.e. ot: an impulse at any The appearance of moment is equally probable. Such flows are characterized by values of variation coefficients close to zero, unimodal interval histograms with exponential decrease, functions of post-impulse probability oscillating near the straight line parallel to abscissa, plots of algorithm of reliability function approaching the straight line, sharply damped aperiodic autocorrelograms and correlation field symmetrical with respect to diagonal, condensing uniformly towards the region of the shortest intervals (fig. 3). The most intervals fall on the region of 10-20 msec. 2. "Simple quasi-periodical" - a flow

with restricted after-effect. The number of intervals of certain duration is sharply increased in comparison with the occasional ones, i.e. in the post-impulse period the time of maximal probability of spike appearance is isolated, but no dependence between the intervals is found. Thus, the probability of appearance of an impulse depends only on the time which has elapsed since the moment of the immediately previous spike. The maxima of intervals fall on 10-20 msec in the flows of neurons in Situ, situ, and in a less outlined region of short intervals in vitro. A considerable predominance of short intervals of stable duration in the impulse flows gives them the character of "firing" activity, but unlike the periodical flows, the duration of pauses between the firings are distributed uniformly. These flows are characterized by unimodal histograms with non-exponential decrease and a long "tail", a curve of post-impulse prosubsequent bability with one maximum and SUbsequent plateau, a sharper decrease of the logarithm of the function of reliability in the region of prevalent intervals, corresponding lines of condensation of the points of correlation fields. When interval histograms of different orders are summed, the autocorrelograms of these flows preserve one peak, corresponding to the mode of the histogram of the 1 st order (fig. 4). 3. "Regular" periodical flow with relatively stable intervals between impulses. Statistical characteristics are similar to those of regular flows of pace-maker neurons. 'l'he The values of variation coefficients are less than unit. The rH of different orders are clearly separated from each other by constant distances,and when summed give autocorrelograms characteristic for regular flows.

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The points of correlation fields are localized in a certain region, being condensed towards its centre and varified at the peinter-1mpulse riphery (fig. 5). Maxima of inter-impulse intervals are in the region of 60-70 msec. This flow type is isolated only 1n in vitro. 4. "Complex quasi-periodic" - flow mith restricted after-effect. As the result of predominance of some intervals and lack of others there appear several (mostly 2) distribution modes which are, however, smoothed out when interval histograms of different orders are summed, because of absence of any dependence between the intervals. This is reflected 1n in the aperiodic character of autocorrelograms. The interval histograms are bimodal. The curves of post-impulse probability have two maxima and a minimum between themselves. On the correlation fields there are characteristic densities and ravifications in the regions of the predominant and absent interimpulse intervals (fig. 6). 5. "Periodic". - The flow with aftereffect in which the inter-impulse intervals are also. The after-effect, unlike the "comples periodical" one, consists in the tendency to alternation of short and long intervals which results in the fact that the bimodality of idistribution is not smoothed out when the histogram intervals of different orders are summed up (fig. 7). The distribution of different types of flows in the compared series is given in table 1. In Fig. 8, the distributions of the values of inter-impulse intervals are given, whose number predominates over the randomic one. Summary and conclusion The existence of stable background neuronal activity in hippocampal tissue culture evidences for the fact that in situ actiVity activity represents also a hippocampal

569

phenomenon. The role of extra-hippocampal influences seems to be restricted by the modulation of impulse flows generated in the circuits of the hippocampus. In particular, the role of stimuli of sensory imputs which are not controllable during the experiment in the origin of impulse activity seems to be less important. As little probable source of background activity under the reverberation of impulses in closed neuronal circuits as an after-effect of previous stimulation. One has to acknowledge that under these conditions of long-term informational isolation, the most probable sources of background activity are the endogenous oscillations of membrane potential of hippocampal pyramides and the spontaneous leakage of transmitter into the synaptic cleft. The absence of significant and unequivocal differences in statistical characteristics of impulse flows in the compared series permits to suggest that the two latter reasons are main also in the development of the background activity in situ. The absence of any significant differences in the distributions of basic numerical characteristics, together with the well known data on the sensitivity of these characteristics (e.g., the mean discharse frequency) to non-specific and noxious influences can be considered as an evidence for the preservation of fundamental functional properties by the neurons in culture. These facts corroborate the conclusions about the sources of the background activity, to which the ~he very fact of the existence exis~ence of this phenomenon in tissue culture leads. The predominance of variation coefficients close to zero in the "in situ" series is connected with relatively large number offlows approaching the Poissonian ones and referred to as "the simplest", in this series. The presence of such

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flows may be connected with superposition of a large number of insignificant differently directed influences, and their predominance in the in situ series - with the reduction of a part of such influences in tissue culture. The shift of the variation coefficients mode in the in vitro series towards lower values in connected with the presence of flows highly characteristic for this series, of regular type with low l ow variation coefficients. The character of these flows and their predominance in the culture allow to consider this form of .. . true activity as the closest to the ... spontaneous activity caused by endogenous oscillations of the membrane potential and or spontaneous leakage of the transmitter into the synaptic slit. (The choice between these two hypotheses seems to be not practicable by means of statistical analysis of impulse flows). In these hypotheses, "regular" flows can be considered as the initial ones, in the sense that there are no inhibiting of exciting modulating influences.

FIGURES Fig. 1. Distribution of the numerical statistical characteristics in compared series (in situ solid line): a) mathematical expectancies; b) standard deviations; c) coefficients of asymmetry and d) excess.

Fig. 2. Coefficients variations distribution. Fig. 3. "Simplest flow": a) interval histo gramm the 1 st order; histogramm b) function postimpulse probability's; c) correlation rield; field; d) logarithms of tthe he reliability function. Fig. 4. "Simplex quasiperiodical flow": a) function funct i on postimpalse probability's; b) correlation field. Pig Pig.. 5. "Regular flow": a) intervals histo gramms of the 1-4th orders; histogramms b) autocorrelogramm; c) correlation field. Fig. 6. "Periodical uPeriodical flow": a) interval histogramm of the 1 st order; b) autocorrelogramm; c,d) correlation field.

REFERENCES ( 1) Bornstein,M.B. Bornstein, M.B. Lab. Invest. I nvest. 1958, 77,, (1) 134-137.

Fig. 7. Distribution of the t he postimpalse postimpals e t he compared series serie s maximums in the (in situ - solid line).

TABL. 1 Types distribution

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