Deviation of spontaneous firing in frog medullar auditory units from the renewal point process

Statistical characteristics of spontaneous activity (distribution of interspike intervals, hazard function, autocorrelation function, autocorrelation function for the process with mixed intervals, and interdependence between adjoining intervals) were analyzed for 123 neurons of the frog medullar dorsal nucleus (homolog of the mammalian cochlear nucleus). In the majority of cells, this activity was distinct from the Poisson process, and firing periodicity was noticed in some cases. In addition, deviations of the spontaneous activity from the renewal process were usually observed. Weak yet reliable positive interspike-interval correlation was typical of most neurons; however, a negative correlation between short adjoining intervals was recorded for some units. These data suggest the effects of memory in the activity of single neurons of the auditory system.     

On the existence of spontaneous neuronal bursting activity at the periphery of the amphibian auditory pathway

The firing activity of 104 neurons from the medullar dorsal nucleus (homologous to the mammalian cochlear nucleus complex) of immobilized common frogs (Rana t. temporaria) was recorded extracellularly in the absence of external auditory stimuli. This background activity was analyzed by using stochastic point process parameters such as the coefficient of variation, local coefficient of variation, interdependence of neighboring intervals, interpulse interval distribution, autocorrelation, and hazard function. All these parameters were put in correspondence with bursting rate, i.e., relative number of interpulse intervals grouped in clusters, or bursts, determined by the proposed method. Neurons with pronounced refractoriness, as a rule, exhibited lower bursting rates whereas neurons with a distinct maximum of the correlation function showed higher values than expected from a random Poisson process. However, even in the latter group of cells, bursting rates usually did not decrease after random shuffling of all the interpulse intervals. As a result, we must admit the absence of clustered spontaneous activity in second-order auditory neurons in the amphibian species studied. These data are compared with the specificities of spontaneous firing activity in different parts of the mammalian auditory pathway.     

Statistical characteristics of spontaneous and evoked unit activity in the cat superior colliculus

Spontaneous and evoked unit activity of the superior colliculus was studied in cats immobilized with gallamine or with the spinal cord divided (encephalé isolé). Statistical parameters of unit activity were calculated in light and darkness and in the presence of a moving photic stimulus. Spontaneously active neurons were divided into four main groups: 1) with a mean interspike interval of about 300 msec, coefficient of variation 1.9, and with two modes in the autocorrelation histogram; 2) with similar statistical parameters but distinguished by correlation with saccadic eye movements; 3) histogram of interspike intervals exponential in type, autocorrelation histogram flat, mean interval and standard deviation about 100 msec; 4) with symmetrical distribution of interspike intervals, mean interval about 50 msec, coefficient of variation 0.4–0.5. Spontaneous activity in light and darkness differed only in the neurons of the second group. Comparison of the statistical parameters of the spontaneous and evoked activity shows that encoding of the stimulus could be carried out by neurons of groups 3 and 4. In some cases the mode of the histogram of interspike intervals and the standard deviation changed significantly and activity appeared regularly in the autocorrelation histogram.     

Sensitivity of the motor unit unfused tetanus to changes in the pattern of motoneuronal firing

The effects of decreasing as well as increasing the interpulse intervals on the tension produced by motor units in the rat medial gastrocnemius muscle were investigated. The increase and decrease in tension, resulting from these changes in interpulse intervals were observed and compared for each motor unit in tetani fused to a various degree. It was found that amplitudes of both changes in tension were the same when the tetanic fusion index was approximately 0.70 and the tension corresponded to 40-50% of the maximal tetanic tension. This observation concerned the all three types of motor units. We also studied the effects of introducing a short interpulse interval ("doublet") at the beginning of the stimulation. The doublet produced an increased tetanic tension with a more fused profile, however the tension was similarly sensitive to an increase as well as a decrease in the interpulse interval when the tetanic fusion index was also about 0.70. Therefore, the extent of tetanic fusion determines the sensitivity of motor unit tetani to changes in a pattern of stimulation. The tetanus of the fusion index about 0.70 can be considered as the most sensitive to changes in the pattern of motoneuronal firing.     

Spontaneous Activity in Crustacean Neurons

Single units which discharged with regular spontaneous rhythms without intentional stimulation were observed in the ventral nerve cord by intracellular recording close to the sixth abdominal ganglion. These units were divided into two groups: group A units in which interspike intervals varied less than 10 msec.; group B units in which interspike intervals varied within a range of 10 to 30 msec. Group A units maintained "constant" interspike intervals and could not be discharged by sensory inputs, while the majority of group B units could be discharged by appropriate sensory nerve stimulation. Both group A and B units discharged to direct stimulation when the stimulating and recording electrodes were placed in the same ganglionic intersegment, and directly evoked single spikes reset the spontaneous rhythm. In group B units, presynaptic volleys reset the spontaneous rhythm of some units; but in others, synaptically evoked spikes were interpolated within the spontaneous rhythm without resetting. The phenomenon of enhancement could also be demonstrated in spontaneously active units as a result of repetitive stimulation. It is concluded that endogenous pacemaker activity is responsible for much of the regular spontaneous firing observed in crayfish central neurons, and that interaction of evoked responses with such pacemaker sites can produce a variety of effects dependent upon the anatomical relationships between pacemaker and synaptic regions.     

A model-independent test for the presence of regulatory equilibrium and non-random structure in island species trajectories

Aims To test a key prevision of the dynamic equilibrium theory of island biogeography, namely that changes in species numbers on islands over time (hereafter, species trajectories) are equilibrial, and to characterize aspects of the dynamical properties of species change over time using a model‐independent test. Methods We tested for regulatory equilibrium and non‐random structure in species numbers through time by comparing observed correlation coefficients at lag‐k for species trajectories from four true islands and two habitat islands. First, we estimated the shape of the autocorrelation function for each observed species trajectory by calculating correlation coefficients of the observed data between pairs of values N_t?k and N_t separated by lag‐k (k = 1, 2, …, N ? 1). Second, we tested the observed correlation coefficients at each lag against a distribution of correlation coefficients generated by randomly ordering observed numbers in the species trajectories. Results The patterns of autocorrelation functions for all but one of the observed species trajectories did not exhibit evidence of regulatory equilibrium, and, in fact, closely matched what would be expected from a non‐stationary or ‘random walk’ process. The majority of the correlation coefficients generated from the observed species trajectories did not deviate significantly from correlation coefficients produced by the randomized trajectories. However, there was strong evidence of unusual positive autocorrelation at small time lags for birds on islands measured annually (2‐ to 4‐year lags) and for arthropods on islands measured weekly (7‐ to 8‐week lags), suggesting some degree of structure in change in species richness over time. Main conclusions The autocorrelation function patterns for all but one of the observed species trajectories showed various forms of non‐stationarity. These types of patterns suggest that the numbers of species through time gradually wandered away from their initial sizes. Our model‐independent test of individual correlation coefficients revealed significant structure in the observed species trajectories. These trajectories appear to be non‐random at relatively short lag intervals, indicating a process with short memory.     

Evaluation of Postspike Changes in Neuronal Excitability by Comparing Ordinary and Shuffled Autocorrelation Functions

Responses of single neurons to tonal signals amplitude-modulated by repeating segments of lowfrequency noise were studied in the dorsal (cochlear) medullary nucleus and midbrain auditory center (torus semicircularis) of the grass frog Rana temporaria. An autocorrelation function of the response to a total presentation and a shuffled autocorrelation function were derived. The latter was obtained by correlating the impulse response to each segment of the modulated signal with responses to all other segments with the exception of the initial one. After the necessary normalization, the function differed from the initial autocorrelation only in lacking postspike changes in excitability. A delay dependence of the ratio of the two functions directly demonstrated the time course of the postspike change in excitability of the studied cell. The majority of second-order neurons, which are in the dorsal nucleus of the medulla oblongata, were characterized only by brief intervals of absolute and relative refractoriness. However, cells with excitability that was markedly facilitated immediately after the refractory period were observed even in this nucleus. Neurons with a complex pattern of postspike changes in excitability were detected in the torus semicircularis. In these cells, a comparatively long postspike decrease in excitability was usually interrupted by intervals in which the neuron sensitivity was significantly higher than normal. The results demonstrate that spike generation has a marked effect on subsequent activity in brainstem auditory units. The effects may play an important role in the formation of the temporal pattern of neuronal responses to auditory signals.     

Plastic changes in the spontaneous activity of pond snail neurons during rhythmic and associated intracellular electrostimulation

In experiments on spontaneously active neurones of the isolated CNS of pond snail, under contingent stimulation with selective auto-reinforcement of interpulse intervals longer than their mean background value, 70 per cent of neurones were capable of adaptive rearrangements of the initial firing frequency, leading to frequency minimization or maximization of influences applied to them. After control rhythmic stimulation, usually no substantial changes of spontaneous activity were observed. The detected phenomena of initial transformation of the spontaneous impulse activity are considered as a cellular analogue of the instrumental conditioned reflex.     

Auditory units in the medulla of the marsh frog with unusual patterns of spontaneous activity

Statistical properties of spontaneous firing were studied in 79 single auditory units located in the dorsal medullar (cochlear) nucleus of unanaesthetized curarized marsh frogs (Rana ridibunda). The great majority of these units showed irregular spontaneous activity with mean rates in the range 1–30 spikes · s^–1. In 53% of the cells the auto-renewal functions of the spontaneous activity monotonically rose to an asymptotic value, but 41% of the cells produced auto-renewal functions which showed a pronounced peak after a dead-time period. Five low-frequency auditory neurons revealed periodic firing in the absence of controlled stimuli. The preferred period did not correspond to the unit's best frequency but demonstrated a modest correlation with the best modulation frequency of the unit's response to amplitude-modulated tones and with the duration of the after-onset dip in peri-stimulus time histograms.Abbreviations AM amplitude modulation - ARF auto-renewal function - DMN dorsal medullar nucleus - PST peristimulus time - SA spontaneous activity - TID time interval distribution - RMG response modulation gain     

Comparison of spontaneous cortical unit activity in several brain areas of unanesthetized cats

Spontaneous unit activity in association area 5 and some projection areas of the cortex (first somatosensory, first and second auditory areas) were studied in cats immobilized with D-tubocurarine in which the index of specific spontaneous activity, the mean frequency, types of spontaneous activity, and statistical parameters — distribution of interspike intervals and autocorrelation function — were determined. The results showed that spontaneous unit activity in the association area differs from that in the projection areas in both intensity and character. A special feature of the spontaneous activity of the auditory areas was a well-marked volley distribution of activity. In the somatosensory area the level of spontaneous activity as reflected in all indices was the lowest. In the association cortex the largest number of neurons with spontaneous activity lay at a depth of 500–1000 µ corresponding to cortical layers III–IV. In the first auditory area neurons with spontaneous activity were concentrated at a depth of 1400 µ (layer V) and in the somatosensory area at a depth of 1000–1400 µ (alyers IV–V). The possible functional significance of these differences is discussed.A. A. Bogomolets Institute of Physiology, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Neirofiziologiya, Vol. 8, No. 1, pp. 13–21, January–February, 1976.     

Analysis of spontaneous unit activity in the cat pyramidal tract

For a statistical analysis of spontaneous activity of cortical pyramidal neurons (PN) of the cat, recordings were obtained from axons of those neurons descending in the lateral pyramidal tract in lumbar segments of the spinal cord. Spontaneous activity of all investigated PN is not random in sequence but has a complex temporal structure. Three types of spontaneous activity were distinguished by the character of distribution of the interspike intervals (ISI); the degree of grouping of the spikes into volleys separated by long intervals increases from type I to type III. Type III is more often found in PN with fast-conducting axons. As a rule the number of volleys in the spontaneous activity differed from that expected by the hypothesis of random spike sequence. In some cases repetition of volleys with an identical, or nearly identical, temporal structure was observed. It is postulated that the type of spontaneous activity is determined by the functional state of the neuron and by its morphological properties. Experiments were carried out on two groups of animals: 1) briefly anesthetized a long time before the recording was obtained, and then immobilized; 2) anesthetized with chloralose and Nembutal. The differences between the character of spontaneous PN activity were mainly in the degree of grouping of the spikes (which was greater in the second group). Significant positive correlation was found between the velocity of conduction along the PN axon and the mean ISI of the spontaneous activity.A. A. Bogomolets' Institute of Physiology, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Neirofiziologiya, Vol. 4, No. 1, pp. 3–11, January–February, 1972.     

Analysis of spontaneous unit activity of the cat caudate nucleus

Spontaneous unit activity recorded extracellularly from the caudate nucleus in acute experiments on cats was analyzed. A graph of the sliding mean frequency, an interspike interval histogram, correlogram, intensity function, and histogram of correlation between adjacent intervals were plotted for the spontaneous activity of each neuron. The spontaneous activity of neurons of the caudate nucleus showed considerable variability in time and its mean frequency varied for different neurons from 0.5 to 20 spikes/sec. Depending on the temporal pattern of the spikes and also on the statistical indices, spontaneous unit activity in the caudate nucleus was conventionally divided into two types: single and grouped. A switch from one type of activity to the other was observed for the same neuron. On the basis of the data as a whole it is impossible to regard the spontaneous unit activity of the caudate nucleus as a simple random (Poissonian) spike train.A. A. Bogomolets Institute of Physiology, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Neirofiziologiya, Vol. 9, No. 4, pp. 369–376, July–August, 1977.     

Effects of oxiracetam and piracetam on the electrical activity of neurons of the cerebral cortex

The effect of oxiracetam and piracetam on the spontaneous impulse neuronal activity of the somatosensory cortex of the cat and rabbit was studied. Oxiracetam and piracetam when applied microiontophoretically changed neuronal activity by depressing in the majority of the cases studied or sometimes facilitating the spontaneous firing rate. A small percentage of neurons (about 30%) remains unaffected by the application of the nootropics. In some cases oxiracetam and piracetam diminished the depress effect of morphine and DADLE on the spontaneous impulse neuronal activity.     

Statistical features of impulse trains in cat's lateral geniculate neurons

The spontaneous discharges which recorded extracellularly from cells in the lateral geniculate nucleus (LGN) of a cat were classified into the following 3 main groups depending upon the shapes of their interval histograms and autocorrelation functions: the gamma type whose interval histogram is fitted by a gamma distribution function and whose autocorrelation function has some periodic property which damps down within about several 10 ms, the burst type whose interval histogram has a peak in the first bin (less than 8 ms) and whose autocorrelation function has a large positive peak within several msec, and the multimodal type whose interval histogram has a complex shape with three or more peaks and whose autocorrelation function has a periodic property. Each type of spontaneous discharge seems to be inherent at scotopic and mesopic backgrounds, and the cells whose spontaneous discharges are the gamma type, the burst type, and the multimodal type are called here a gamma cell, burst cell, and the multimodal cell, respectively. Gamma cells are subdivided into X- and Y-cells (gamma-X and gamma-Y cells), but burst cells are all Y-cells and multimodal cells observed up to now are all X-cells. It is clear that these various types of cells are distributed significantly differently in each lamina. All the cells that we found up to now in lamina A were either burst cells or multimodal cells, but every type of cell was found in lamina A1. The majority of cells in lamina C were the gamma type. In most cases, the peak values of the PST histograms of gamma-Y cells (especially, on-center cells) are larger than those of burst cells. These results suggest that Y-cells projecting to area 17 from laminae A and A1 are the burst type, and Y-cells projecting to area 18 from laminae C and A1 are the gamma-Y type.     

CompuCell3D Simulations Reproduce Mesenchymal Cell Migration on Flat Substrates

Mesenchymal cell crawling is a critical process in normal development, in tissue function, and in many diseases. Quantitatively predictive numerical simulations of cell crawling thus have multiple scientific, medical, and technological applications. However, we still lack a low-computational-cost approach to simulate mesenchymal three-dimensional (3D) cell crawling. Here, we develop a computationally tractable 3D model (implemented as a simulation in the CompuCell3D simulation environment) of mesenchymal cells crawling on a two-dimensional substrate. The Fürth equation, the usual characterization of mean-squared displacement (MSD) curves for migrating cells, describes a motion in which, for increasing time intervals, cell movement transitions from a ballistic to a diffusive regime. Recent experiments have shown that for very short time intervals, cells exhibit an additional fast diffusive regime. Our simulations’ MSD curves reproduce the three experimentally observed temporal regimes, with fast diffusion for short time intervals, slow diffusion for long time intervals, and intermediate time -interval-ballistic motion. The resulting parameterization of the trajectories for both experiments and simulations allows the definition of time- and length scales that translate between computational and laboratory units. Rescaling by these scales allows direct quantitative comparisons among MSD curves and between velocity autocorrelation functions from experiments and simulations. Although our simulations replicate experimentally observed spontaneous symmetry breaking, short-timescale diffusive motion, and spontaneous cell-motion reorientation, their computational cost is low, allowing their use in multiscale virtual-tissue simulations. Comparisons between experimental and simulated cell motion support the hypothesis that short-time actomyosin dynamics affects longer-time cell motility. The success of the base cell-migration simulation model suggests its future application in more complex situations, including chemotaxis, migration through complex 3D matrices, and collective cell motion.     

Development of a local size hierarchy causes regular spacing of trees in an even-aged Abies forest: analyses using spatial autocorrelation and the mark correlation function

Background and Aims

During the development of an even-aged plant population, the spatial distribution of individuals often changes from a clumped pattern to a random or regular one. The development of local size hierarchies in an Abies forest was analysed for a period of 47 years following a large disturbance in 1959.

Methods

In 1980 all trees in an 8 × 8 m plot were mapped and their height growth after the disturbance was estimated. Their mortality and growth were then recorded at 1- to 4-year intervals between 1980 and 2006. Spatial distribution patterns of trees were analysed by the pair correlation function. Spatial correlations between tree heights were analysed with a spatial autocorrelation function and the mark correlation function. The mark correlation function was able to detect a local size hierarchy that could not be detected by the spatial autocorrelation function alone.

Key Results

The small-scale spatial distribution pattern of trees changed from clumped to slightly regular during the 47 years. Mortality occurred in a density-dependent manner, which resulted in regular spacing between trees after 1980. The spatial autocorrelation and mark correlation functions revealed the existence of tree patches consisting of large trees at the initial stage. Development of a local size hierarchy was detected within the first decade after the disturbance, although the spatial autocorrelation was not negative. Local size hierarchies that developed persisted until 2006, and the spatial autocorrelation became negative at later stages (after about 40 years).

Conclusions

This is the first study to detect local size hierarchies as a prelude to regular spacing using the mark correlation function. The results confirm that use of the mark correlation function together with the spatial autocorrelation function is an effective tool to analyse the development of a local size hierarchy of trees in a forest.Key words: Abies, local size hierarchy, mark correlation function, pair correlation function, regenerating forest, regular spacing, spatial autocorrelation     

Correlation of the neuronal impulse activity of different areas of the neocortex in rabbits in the switching of positive and inhibitory conditioned reflexes

By cross-correlation method conjugation in impulse activity of pairs of simultaneously recorded units in the visual and sensorimotor areas of the neocortex (representations of the conditioned and unconditioned stimuli) was studied during the switching of defensive positive and inhibitory reflexes in rabbits. 30-second fragments of impulse activity were analyzed in intervals before and after three presentations of positive and inhibitory conditioned stimuli (CS). The activity of single pairs of units in the process of stimuli presentation was characterized by instability. Only in 29% of 51 units' pairs the presence or absence of correlation between their discharges was stable. Analysis of activity of 75 pairs of units showed differences in impulse activity in inhibitory and positive tonic reflexes. The number of pairs of correlated units in about 30 s after inhibitory CS decreased (27%) in comparison with the interval before its action (52%). In the inhibitory tonic conditioned reflex, temporal intervals of discharges of one unit correlated with discharges of the second unit undergo changes. The obtained results testify that such parameter as the number of pairs of units with correlated activity in intersignal time interval is very important for the realization of motor reaction to conditioned stimuli.     

Some properties of auditory neuron’s model trained by firing caused by tones modulated by low-frequency noise

In many sensory systems the formation of burst firing can be observed along a way from the periphery to the central nuclei. We investigate the putative transformation of spontaneous activity in the auditory pathway using a neuron model trained by real firing recorded in the auditory nuclei of the frog. The model has 200 separate inputs (neuronal spines). It is supposed that every spine is a coincidence detector. Its output (synaptic potential) sharply increases at emergence of the precisely certain interpulse interval in an input pulse sequence. If the total synaptic potentials excess a threshold, the model generates output spike, which changes weight of all spines according to the simplified Hebb principle. The model was trained by real firing caused in the auditory nuclei of the frog by tones modulated by low-frequency noise in the frequency ranges of 0–15 Hz, 0–50 Hz or 0–150 Hz. After that training the synaptic weights of every spine essentially changed. Thus, along with some increase of weights of spines tuned to boundary frequencies of modulating noise, the most characteristic change was the emphasizing weights of spines tuned to short interpulse intervals. As a result the spontaneous activity passed through the trained model became much more bursting. Efficiency of a signal transmission in model was higher when input spontaneous activity of real cells contains bursts of spikes. Results of modeling are discussed in connection with modern physiological data demonstrating the functional advantage of bursting.     

Types of spontaneous discharges of muscle receptors

Characteristics of discharges of 462 muslce spindle receptors located in the deefferented triceps surae muscle with a divided tendon were analyzed in anesthetized cats. Of the total number, 205 units had spontaneous activity which, depending on its stability, could be divided into three types. A long continuous spike train was generated by 87% of units. Distributions of interspike intervals were unimodal and symmetrical. Spontaneous activity of this type was more regular in secondary than in primary endings. Action potentials in 8% of units were grouped in volleys and interval distributions were bimodal. Spontaneous activity of the remaining 5% of units was characterized by sporadically appearing spikes with long intervals between them. The first two types of spontaneous activity cannot be placed in the category of stochastic processes. Threshold discharges during static stretching of the muscle sufficient to cause the appearance of a long spike train were studied in 231 of 257 initially "silent" units. By the same criteria these discharges were divided into corresponding types. Comparison of the characteristics of spontaneous activity and evoked responses suggests that they share the same mechanism of origin. It is concluded that the spontaneous discharge can be regarded as a static response of the receptors due not to an externally applied stretching load, but to the action of internal factors, depending on interaction between extrafusal and intrafusal muscle fibers.I. P. Pavlov Institute of Physiology, Academy of Sciences of the USSR, Leningrad. Translated from Neirofiziologiya, Vol. 13, No. 3, pp. 315–321, May–June, 1981.     

Activity patterns of cochlear ganglion neurones in the starling

Spontaneous activity and responses to simple tonal stimuli were studied in cochlear ganglion neurones of the starling. Both regular and irregular spontaneous activity were recorded. Non-auditory cells have their origin in the macula lagenae. Mean spontaneous rate for auditory cells (all irregularly spiking) was 45 spikes s-1. In half the units having characteristic frequencies (CFs) less than 1.5 kHz, time-interval histograms (TIHs) of spontaneous activity showed regularly-spaced peaks or 'preferred' intervals. The spacing of the peak intervals was, on average, 15% greater than the CF-period interval of the respective units. In TIH of lower-frequency cells without preferred intervals, the modal interval was also on average about 15% longer than the CF-period interval. Apparently, the resting oscillation frequency of these cells lies below their CF. Tuning curves (TCs) of neurones to short tone bursts show no systematic asymmetry as in mammals. Below CF 1 kHz, the low-frequency flanks of the TCs are, on average, steeper than the high-frequency flanks. Above CF 1 kHz, the reverse is true. The cochlear ganglion and nerve are tonotopically organized. Low-frequency fibres arise apically in the papilla basilaris and are found near non-auditory (lagenar) fibres. Discharge rates to short tones were monotonically related to sound pressure level. Saturation rates often exceeded 300 spikes s-1. 'On-off' responses and primary suppression of spontaneous activity were observed. A direct comparison of spontaneous activity and tuning-curve symmetry revealed that, apart from quantitative differences, fundamental qualitative differences exist between starling and guinea-pig primary afferents.