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Notes: Abstract This communication compares the well known phenomenon of respiratory driving by the respiratory pump through the Breuer Hering reflex with a model (Segundo, 1979) of a neuronal pacemaker (i.e. regularly firing) interactions via IPSP's. The assumption involves a linear dependence (“delay function”) of the postsynaptic interval lengthening (or “delay”) produced by the IPSP's on the position (or “phase”) with respect to the preceding spike of the latter's arrival. Cats anesthetized and paralized with gallamine were artificially ventilated using a computer driven respirator. The pump period and the respiratory period (identified by the phrenic discharge) corresponded to the model's presynaptic pacemaker interval and to that of the post synaptic one, respectively. The delay of the respiratory period by an inflation was related linearly and in increasing manner to the latter's phase with respect to the inspiration onset. In the steady state, plots of average respiratory period versus pump period consisted in a succession of broad “paradoxical” segments with positive slopes 3, 2, 1, 1/2, 1/3 in which respiration was locked with the pump as predicted by the model. The locked condition were less easy to reach when FA CO 2increased or when level of anaesthesia decreased. The limits of paradoxical segments were different when measured using pump periods that increased or using periods that decreased. There was therefore a hysteresis as if the delay function parameters changed, a behavior that was not part of the model that assumed fixed characteristics. These modifications were related to dependency of each cycle on the preceding one. The model proposed for simple neuronal pacemaker interactions can thus be applied satisfactorily to the drive of the complex respiratory neuronal oscillator by the respiratory pump through Breuer Hering reflex, providing nevertheless some additonal assumptions concerning respiratory cycle interdependency are introduced to account for the hysteresis phenomenon. The Breuer Hering reflex could be considered as the equivalent of IPSP acting on the central respiratory oscillator. FA CO 2increase and anesthesia level decrease produced the same effect as the addition of noise to the model's presynaptic pacemaker, thus leading to the hypothesis that they act by adding noise (e.g., randomly distributed excitatory input) at the level of Breuer Hering reflex inhibition.

Notes: Abstract A mathematical model designed originally for pacemaker neurons and post synaptic potentials represents acceptably respiratory driving by a pump through the Hering-Breuer reflex (Vibert et al. 1981). Discrepancies with the respiratory embodiment arose firstly in the zig-zag plots of average driving and driven intervals where the boundaries between positively and negatively-sloped segments differed, and where a hysteresis-like dependence on the order of the observations occurred. Secondly, they arose from the fact that estimates of the slope A and intercept B of the linear dependence of the delay on the arrival phase of the driver differed when based on the model's formulae but using different aspects of the same data. The question thus arose as to which model shortcomings cause discrepancies with this particular embodiment. This communication presents computer simulations that explore the consequences of modifying, or imposing variabilities, upon several parameters. A reflects how the driver's (i.e. the inflation's) consequences increase as it arrives later in the driven (i.e. phrenic) cycle: when it departs from around 0.7, (as required by the model) and approaches 1. The positively sloped segments broaden at the expense of the negatively-sloped ones which disappear when A reaches 1. The intercept B reflects the effect of the driver when it arrives just after the driven event: its increases shift a relatively unchanged plot up and to the right. When the driving period I exhibits variability or the driver one N exhibits variability or trends, as happens often with the respiratory embodiment, the model-predicted behavior remains acceptably natural-like: in particular, that with a jittery driven period mimics well observations on cats with high CO2 or superficially anesthetized. For each driving period, the driven intervals pertained to a limited number of classes (e.g. to one, two or three) which occurred in an invariant sequence.

Notes: Abstract The length of isolated slowly adapting stretch-receptor organs (SAO) from crayfish was submitted to approximately sinusoidal modulations of 0.030–0.800 mm at frequencies of about 0.2, 1.0 or 3.0 cps. Sines were imposed either by themselves (“clean”) or mixed with (“perturbed by”) fast irregular length fluctuations or “jitter”. The amplitude of the latter remained within a specified fraction of the modulation, usually two-thirds (or x0.66), though from one twentieth to twice (or x0.05–2.00) were explored. The afferent impulse discharge was recorded: rate over bins of about 1/10 of the period was plotted as function of ongoing time. Within stationary epochs, average cycles were analyzed primarily in terms of lengths and discharge intensities. Each point in the displays corresponded to a particular bin along the average cycle, the abscissa and the ordinate being the length and the corresponding discharge rate, respectively; points were numbered in the order of their generation. Similar displays were constructed for rate vs velocity, rate vs acceleration, and rate-change vs velocity. Experiments without jitter. The non-perturbed state. With 0.2 and 1.0 cps, the rate vs length display had a “clockwise loop with a flat extension to the left”. The SAO at its shortest did not discharge and remained silent for some time. As length augmented, it eventually started firing, reaching maximum rate while being stretched (lead) or at maximum length. While length decayed, the organ fired less, slowing down, stopping at a length greater than where it had started, and then remaining silent until the end of the cycle. With 3.0 cps, the display had a “counterclockwise loop with a flat extension on the left”. The SAO did not discharge at its shortest, and fired more during relaxation than during stretching, peaking when relaxing (lag) and stopping at a length greater than where it had started. Artificial introduction of time separations between length and rate converted displays into acceptably straight lines only in a few, usually 0.2 cps, cases. The rate vs length relation exhibited consistent departures from monotonic increase and from linearity: departures were large fractions of the overall swings involving flat extensions, leads, lags, saturation effects, asymmetric rate sensitivities, and “locking” (which was frequent with 1.0 or 3.0 cps and could conceivably be more common with faster modulations). Other experimental paradigms have demonstrated multivaiued steady-state-rate-length relations. The variability from cycle to cycle of the rate in a particular bin was high or low for bins with low or high rates, respectively. “Rate vs velocity” plots were counter-clockwise loops with a base upon the abscissae, higher rates when velocity was decaying than when augmenting, and maxima at non-negative velocities. “Rate-change vs velocity” plots showed shortening associated with either discharge, decreases or small changes, and lengthenings associated with discharge increases, greater when augmenting if at 0.2 cps or when decaying if at 3.0 cps. “Rate vs stimulus acceleration” plots were, for the three tested frequencies, counterclockwise loops with a base upon the abscissae and higher rates when acceleration was decaying than when augmenting, suggesting a particular role in sensing accelerations. The sensitivity to length was evaluated by comparing the rate-swings at each frequency using identical bin-widths and depths. This procedure is considered to be most meaningful physiologically. Sensitivity was contingent upon the bin-width: with small bins (30 and 120 ms) it was highest for 3.0 cps, with intermediate bins (160 ms) it was highest for 1.0 cps, and with larger bins it was practically uniform. Differences involved factors of under x1.7. Experiments with jitter. The perturbed state. Jitter changed radically the “rate vs length” displays, converting all of them into clockwise folium-like loops, which implied a shift from lag to lead at 3.0 cps. Introduction of appropriate lags brought points acceptably close to straight, positively sloped segments: this occurred often at 0.2 cps, sometimes at 1.0 cps, and exceptionally at 3.0 cps. Jitter altered the variability profile along the cycle, decreasing peak variability and not affecting or increasing the minimum; variability along the cycle was thus reduced and uniformed and identification of stimuli on the basis of discharges was improved. Jitter amplitude was an important issue. The larger ones, about the modulation size, increased the lowest bin-rates, particularly at 0.2 and 1.0 cps, and increased the peaks at 0.2 cps, decreasing them at 1.0 and 3.0 cps. The smaller jitter, about 1/10 of the modulation, affected the lowest rates little, but increased the peak rate at 0.2 cps, decreasing it at 1.0 and 3.0 cps; display shapes changed little. A qualitative model of the SAO involves subsystems with linear features, as well as rectification, stiction-like and saturation-like properties. Depending upon back-ground length, modulation depth, jitter and several other issues, the organ can perform frankly nonlinearly, piece-wise linearly or linearly. Within each context, a particular stimulus is of interest and can be referred to as the “signal”; others are not, and can be referred to as “noise”, acting as “perturbations”. Small, erratic perturbations influence strongly transduction of large steps or sines, simplifying and making it more proportionate. Large regular perturbations act upon small signals too, but their influence has been explored less extensively.

Notes: Abstract The crayfish stretch receptor organs provide the opportunity to study recurrent inhibition (RI) in pure experimental conditions. The slowly adapting organ (SAO) from the cephalothoraxabdomen joint of Procambarus darkii was isolated and its length set by anchoring one end and clamping the other with a movable forceps. Each impulse from the SAO triggered a shock to the common inhibitory fiber, after an adjustable delay called “phase”. Thus, RI acted upon the SAO. Under steady length conditions, the discharge rate with RI was proportional to the spontaneous discharge rate (i.e. to that without RI), and negatively correlated to the ratio of the phase to the spontaneous interspike interval. Under dynamic conditions, with the SAO submitted to under 0.3 mm length variations, sine-like with or without “white” noise, and periodic at 0.2, 1.0, or 3.0 cps, the effect of RI was basically the same in all conditions. While the lower rates of discharge were unchanged, the higher rates were reduced: thus the overall sensitivity of the SAO was decreased. The RI also decreased the discharge variability at the low rates; variability remained unaffected at the high rates. The general form of the response of the SAO was unaffected by RI, as indicated by displays of rate versus length, of rate versus velocity, or of change in rate versus velocity: only the widness of the loops changed. The effects of RI were compared to those of randomly arriving, Poisson-like IPSP's at the same overall rate: the latter did not exhibit the same dependence on the SAO firing rate.

Notes: Summary The upper and middle pons and the lower mesencephalon of the cat were explored with extracellular microelectrodes in a search for respiratory related units (RRU). The preparation used, the unanesthetized normocapnic cat, resulted in an “isolated respiratory center” by eliminating input from, as well as output to, lung and thorax. Observations were done in standard experimental conditions which allowed quantitative comparisons of anatomical structures with respect to RRU density (RRUD), RRUD to total unit density (UD) ratio, and a respiratory modulation index (RMI). Units were recorded in 22 anatomical structures; of 3614 units kept for analysis, 46.9% had a definite respiratory rhythm. The phase relations of frequency variation ere classified into five main categories: 1) tonic expiratory (E) or 2) inspiratory (I) patterns, 3) phase spanning inspiratory-expiratory (IE) or 4) expiratoryinspiratory (EI) patterns, and 5) tonic early expiratory depressed (EED) pattern. Densely packed RRU were recorded in anatomical structures known to be involved in the command of respiratory accessory musculature (trigeminal system) or thought to be part of the pneumotaxic machinery (nucleus parabrachialis median's, Kölliker-Fuse nucleus). In these structures, RRU proportion was 57–89% of the total neuronal activity. On the other hand, definite RRU (10–26%) were recorded in structures which are not thought to have a respiratory function (such as inferior colliculus or griseum centralis) where isolate RRU were scattered among non-respiratory tonic units. This group includes nuclei sometimes considered as having a pneumotaxic function. The pontine reticular formation represents an intermediate category (RRU = 35.6%) where clusters of RRU alternate with non-respiratory modulated cells. The possible role of these clusters is discussed in relation to the hypothesis of multiple coupled respiratory oscillators. Variance analysis of RRUD, RRUD to UD ratio and RMI shows highly significant differences between the three preceding categories of structures.

Notes: Abstract Multimodal soma diameter spectra for neurones of the cat retinal ganglion cell layer have been represented by three subpopulations of independent, normal diameter distribution. Recurrent computation according to the technique of Vibert and Caille (1978) has extracted best fit populations for samples from various regions of central and peripheral retina. The model subpopulations from all these regions did not differ significantly in their relative proportions or variance. Significant progressive variation between subpopulations representing different regions of retina were observed only in the mean diameter of the α and β mode cells. The parameters of the γ mode population were statistically uniform across the retina. The cat retina thus appears to be more homogeneously organized than has been suggested elsewhere.

Notes: Abstract A method is proposed to estimate the number of subpopulations which compose a heterogeneous experimental population. The method consists of reconstructing a population sample by adding computed subpopulations, postulated to be independent. The assumption is made that each subpopulation fits a normal distribution; the method may also be generalized to other distributions laws; each subpopulation can thus be entirely defined by its mean, variance and relative weight. Recurrent adjustments of number and parameters of subpopulations are carried out in order to minimize the difference between synthetized and experimental populations. This difference was measured by the quadratic distance χ2 between the two populations. Mean, variance and weight of the computed population must then be close to those of the experimental population in order to consider the results as acceptable. This method is discussed with regard to others proposed in the literature.

Notes: Abstract There is experimental evidence that neuronal electrical activity directly influences neurite outgrowth during the development of the nervous system. Using model studies, Van Ooyen and Van Pelt extensively investigated the effect of this phenomenon upon network development and architecture. Their studies are based on the experimental observations that there is an optimal range of electrical activity at which neurite outgrowth takes place. In their model, neurite growth occurs if the activity level of the neuron is below a certain threshold, otherwise the neurite retracts. We extend their results to include a more complete description of the relationship between electrical activity and neurite outgrowth. This takes into account the experimental observation that outgrowth ceases not only when neuronal activity is too high, but also when it is below a certain threshold. The modified model displays a wider range of behaviours during network development. In some cases, for example, growth is only transient and is followed by a total loss of connections in the network. As a consequence of the larger spectrum of possible behaviours, the mechanisms for control of network formation, by the network's internal dynamics as well as by external inputs, are also increased.