The distribution of the intervals between neural impulses in the maintained discharges of retinal ganglion cells

Simulated neural impulse trains were generated by a digital realization of the integrate-and-fire model. The variability in these impulse trains had as its origin a random noise of specified distribution. Three different distributions were used: the normal (Gaussian) distribution (no skew, normokurtic), a first-order gamma distribution (positive skew, leptokurtic), and a uniform distribution (no skew, platykurtic). Despite these differences in the distribution of the variability, the distributions of the intervals between impulses were nearly indistinguishable. These inter-impulse distributions were better fit with a hyperbolic gamma distribution than a hyperbolic normal distribution, although one might expect a better approximation for normally distributed inverse intervals. Consideration of why the inter-impulse distribution is independent of the distribution of the causative noise suggests two putative interval distributions that do not depend on the assumed noise distribution: the log normal distribution, which is predicated on the assumption that long intervals occur with the joint probability of small input values, and the random walk equation, which is the diffusion equation applied to a random walk model of the impulse generating process. Either of these equations provides a more satisfactory fit to the simulated impulse trains than the hyperbolic normal or hyperbolic gamma distributions. These equations also provide better fits to impulse trains derived from the maintained discharges of ganglion cells in the retinae of cats or goldfish. It is noted that both equations are free from the constraint that the coefficient of variation (CV) have a maximum of unity. The concluding discussion argues against the random walk equation because it embodies a constraint that is not valid, and because it implies specific parameters that may be spurious.     

The facilitated probability of quantal secretion within an array of calcium channels of an active zone at the amphibian neuromuscular junction

A Monte Carlo analysis has been made of the phenomenon of facilitation, whereby a conditioning impulse leaves nerve terminals in a state of heightened release of quanta by a subsequent test impulse, this state persisting for periods of hundreds of milliseconds. It is shown that a quantitative account of facilitation at the amphibian neuromuscular junction can be given if the exocytosis is triggered by the combined action of a low-affinity calcium-binding molecule at the site of exocytosis and a high-affinity calcium-binding molecule some distance away. The kinetic properties and spatial distribution of these molecules at the amphibian neuromuscular junction are arrived at by considering the appropriate values that the relevant parameters must take to successfully account for the experimentally observed amplitude and time course of decline of F1 and F2 facilitation after a conditioning impulse, as well as the growth of facilitation during short trains of impulses. This model of facilitation correctly predicts the effects on facilitation of exogenous buffers such as BAPTA during short trains of impulses. In addition, it accounts for the relative invariance of the kinetics of quantal release due to test-conditioning sequences of impulses as well as due to change in the extent of calcium influx during an impulse.     

The analytical characteristics of the dynamics of interneuronal functional connections during conditioned-reflex activity]

The dynamics of functional relations between neurons was studied in the frontal cortex of dogs performing reversal conditioning task. To reveal the functionally relevant relationships between the temporal patterns of correlated firing and behavioral events, we developed an original processing technique. The technique included the following procedures: a) isolation of the "coupled spikes" (CS) from simultaneously recorded impulse trains: b) search for the temporal patterns of correlated firings and their classification by clustering single trials with similar temporal distribution of CS; c) assessment of behavioral significance of the identified patterns by evaluation of the probabilities of coincidence of behavioral events and different CS patterns. Significant correlations between impulse trains were revealed in 38 neuronal pairs of 456 analyzed. The effects of change in behavioral context on the CS dynamics during the task performance were found in 87% of neuronal pairs with correlated activity. In 17 pairs the behavioral conditions were identified, under which potentially connected neurons fired independently during all the periods of the behavioral task. The potentialities of the advanced processing technique are discussed. We suggest that this analysis can provide useful information about the temporal distribution of correlated firings under conditions of nonstereotyped behavior, when an animal reacts in the dynamically organized experimental context.     

Rotating stripes and the impulse response of the eye: I. Uniform illumination

A rotating striped pattern produces an unexpected visual effect: a band of relatively high contrast is seen obliquely across the striped pattern, moving steadily around with the pattern and lagging behind the perpendicular to the stripes. Photographs of the moving pattern display similar effects. An analysis of the effect (based on a simple linear model) shows that the perceived contrast observed at any instant across the pattern represents the temporal modulation transfer function of the eye and the asymmetrical shape of the lines is a display of the phase transfer function. The analysis establishes and uses an analogy with the amplitude distribution in a Fraunhofer diffraction pattern. The temporal impulse response of the eye is related to the perceived contrast in the same way that the aperture function is to the amplitude distribution in the diffraction pattern. The binocularly perceived contrast distribution is considered as the interference or phasor addition of the two monocularly perceived effects, and the clinical potential of this approach is illustrated. In addition, since the band itself is not an object with a physical boundary, but a perceptual consequence of blurring and spatial averaging, the effect provides a means for investigating the perceived location of moving objects in general.     

A model for impulse frequency modulation used in neural encoding

The impulse rate at the output of a neural encoder can be interpreted as the sum of the mean impulse rate plus a noise component. From literature models are known which describe the transient phenomena of the encoder as far as the mean impulse rate is concerned. In this paper in addition the noise phenomenon is treated by a model which is in agreement with results derived from measurements. This model consists of two parts, a multiplicative and an additive estimator. The first one is similar to the automatic gain control system known from literature. This system estimates the amplification of the impulse rate due to the step input of the neural encoder. Multiplying the impulse rate with the inverse of this factor inhibits the change of the impulse rate. The second estimator calculates the step size of the impulse rate which is subtracted from the output of the encoder. Again the change of the impulse rate is inhibited. The comparison of the impulse rates simulated by the model and given by published measurements shows a good agreement for the properties of the mean impulse rate and the variance of the imposed noise.     

Screening Method Based on Walking Plantar Impulse for Detecting Musculoskeletal Senescence and Injury

No consensus has been reached on how musculoskeletal system injuries or aging can be explained by a walking plantar impulse. We standardize the plantar impulse by defining a principal axis of plantar impulse. Based upon this standardized plantar impulse, two indexes are presented: plantar pressure record time series and plantar-impulse distribution along the principal axis of plantar impulse. These indexes are applied to analyze the plantar impulse collected by plantar pressure plates from three sources: Achilles tendon ruptures; elderly people (ages 62–71); and young people (ages 19–23). Our findings reveal that plantar impulse distribution curves for Achilles tendon ruptures change irregularly with subjects’ walking speed changes. When comparing distribution curves of the young, we see a significant difference in the elderly subjects’ phalanges plantar pressure record time series. This verifies our hypothesis that a plantar impulse can function as a means to assess and evaluate musculoskeletal system injuries and aging.     

Effect of doublet impulse sequences in the crayfish claw opener muscles and the computer-simulated neuromuscular synapse

The effects of doublet impulse sequences of the excitatory motor axon on the movement of the claw opener muscles in the crayfish were examined. The excitatory motor axon was stimulated electrically with various patterns of doublet impulse sequences generated by a digital computer. Doublet impulse sequences of stimulation produced a larger sustained movement than an uniform impulse sequences at the same mean rate of stimulation. The movement was largest when the interval between the impulses of a doublet was about 5 ms. This interval generated a movement amplitude 25% greater than that for the uniform impulse sequence. A simple model was formulated to stimulate the neuromuscular synapse of the claw opener muscle. The relationship between stimulation sequences with alternating long and short intervals and responses (firing probabilities) of the neuromuscular synapse at the same mean rate was investigated. The responses was classified into two typical types which are noneffective Type I and effective Type II to the absolute refractory period (ARP). The characteristics which are larger responses with short intervals in Type I and reduction of responses in the ARP region of Type II formed a plateau peak of the experimental results. By incorporating the reduction of end-plate potential (EPP) as a property of nonlinear rule for temporal summation into the model, it was shown that Type I response is maximal with a plateau peak at short interval, agreeing well with the experimental results from the claw opener muscles.     

Volume transmission in activity-dependent regulation of myelinating glia

The importance of neural impulse activity in regulating neuronal plasticity is widely appreciated; increasingly, it is becoming apparent that activity-dependent communication between neurons and glia is critical in regulating many aspects of nervous system development and plasticity. This communication takes place not only at the synapse, but also between premyelinating axons and glia, which form myelin in the PNS and CNS. Recent work indicates that neural impulse activity releases ATP and adenosine from non-synaptic regions of neurons, which activates purinergic receptors on myelinating glia. Acting through this receptor system, neural impulse activity can regulate gene expression, mitosis, differentiation, and myelination of Schwann cells (SCs) and oligodendrocytes, helping coordinate nervous system development with functional activity in the perinatal period. ATP and adenosine have opposite effects on differentiation of Schwann cells and oligodendrocytes, providing a possible explanation for the opposite effects of impulse activity reported on myelination in the CNS and PNS.     

Effects of heating and cooling on nerve terminal impulses recorded from cold-sensitive receptors in the guinea-pig cornea

An in vitro preparation of the guinea-pig cornea was used to study the effects of changing temperature on nerve terminal impulses recorded extracellularly from cold-sensitive receptors. At a stable holding temperature (31-32.5 degrees C), cold receptors had an ongoing periodic discharge of nerve terminal impulses. This activity decreased or ceased with heating and increased with cooling. Reducing the rate of temperature change reduced the respective effects of heating and cooling on nerve terminal impulse frequency. In addition to changes in the frequency of activity, nerve terminal impulse shape also changed with heating and cooling. At the same ambient temperature, nerve terminal impulses were larger in amplitude and faster in time course during heating than those recorded during cooling. The magnitude of these effects of heating and cooling on nerve terminal impulse shape was reduced if the rate of temperature change was slowed. At 29, 31.5, and 35 degrees C, a train of 50 electrical stimuli delivered to the ciliary nerves at 10-40 Hz produced a progressive increase in the amplitude of successive nerve terminal impulses evoked during the train. Therefore, it is unlikely that the reduction in nerve terminal impulse amplitude observed during cooling is due to the activity-dependent changes in the nerve terminal produced by the concomitant increase in impulse frequency. Instead, the differences in nerve terminal impulse shape observed at the same ambient temperature during heating and cooling may reflect changes in the membrane potential of the nerve terminal associated with thermal transduction.     

Chemoattraction and chemotaxis in Dictyostelium discoideum: myxamoeba cannot read spatial gradients of cyclic adenosine monophosphate

Myxamoebae of the morphogenetic cellular slime mold Dictyostelium discoideum are thought to be able to accurately read and respond to directional information in spatial gradients of cyclic AMP. We examined the spatial and temporal mechanisms proposed for chemotaxis by comparing the behavior of spreading or evenly distributed cell populations after exposure to well-defined spatial gradients. The effects of gradient generation on cells were avoided by using predeveloped gradients. Qualitatively different responses were obtained using (a) isotropic, (b) static spatial, or (c) temporal (impulse) gradients in a simple chamber of penetrable micropore filters. We simulated models of chemotaxis and chemokinesis to aid our interpretations. The attractive and locomotory responses of populations were maximally stimulated by 0.05 microM cyclic AMP, provided that cellular phosphodiesterase was inhibited. But a single impulse of cyclic AMP during gradient development caused a greater and qualitatively different attraction. Attraction in spatial gradients was only transient, in that populations eventually developed a random distribution when confined to a narrow territory. Populations never accumulated nor lost their random distribution even in extremely steep spatial gradients. Attraction in spatial gradients was inducible only in spreading populations, not randomly distributed ones. Thus, spatial gradients effect biased-random locomotion: i.e., chemokinesis without adaptation. Cells cannot read gradients; the reaction of the cells is stochastic. Spatial gradients do not cause chemotaxis, which probably requires a sharp stimulant concentration increase (a temporal gradient) as a pulse or impulse. The results also bear on concepts of how embryonic cells might be able to decipher the positional information in a morphogen spatial gradient during development.     

Changes in interspike interval during propagation: Quantitative description

The intervals between nerve impulses can change substantially during propagation because of conduction velocity aftereffects of previous impulse activity. Effects of such changes on interval histograms and on statistical parameters of spike trains were evaluated for Poisson spike trains and for trains generated by a clock with added random delays. The distribution of short intervals was significantly changed during propagation for these spike trains. Substantial changes in serial correlation coefficients were found in trains with certain initial interval distributions. The relevance of these effects to neural coding is discussed.     

Characterizing and correcting for the dynamic response of a bag-in-box system

A bag-in-box system (BBS) whose volume is monitored by a mechanical spirometer tends to have a slow response if the volume of the box is large, and this may significantly affect its measurement of gas flow. We describe a device for creating reproducible gas flows with which the impulse response of a BBS may be conveniently determined. Two computational techniques for correcting a BBS flow measurement for the effects of the impulse response were investigated: 1) an exponential model method that assumes a second-order model of the BBS dynamics and 2) a Fourier transform-based method of deconvolution known as Wiener filtering. Both correction methods produced a significant increase in the accuracy of BBS flow estimations, with the Wiener filter giving superior results.     

Inhibition of Impulse Activity in a Sensory Neuron by an Electrogenic Pump

The crayfish tonic stretch receptor neuron manifests three phenomena: (a) Impulse frequency in response to a depolarizing current decays exponentially to half the initial rate with a time constant of about 4 sec. (b) One or more extra impulses superimposed on steady activity result in a lengthening of the interspike interval immediately following the last extra impulse which is proportional to the number of extra impulses. However, above a "threshold' number of impulses the proportionality constant becomes abruptly larger. (c) Following trains of impulses, the resting potential of the cell is hyperpolarized by an amount proportional to impulse number. Such posttetanic hyperpolarization (PTH) decays approximately exponentially with a time constant of 11 sec, but this varies with membrane potential. These effects are attributed to the incremental increase of an inhibitory (hyperpolarizing) current with a long (relative to interspike interval) decay constant. We suggest that this inhibitory current is the result of increased electrogenic Na pumping stimulated by Na entering with each impulse. Evidence is presented that the three effects are reversibly inhibited by conditions which depress active Na transport: (a) Li substituted for Na in the bath; (b) application of strophanthidin; (c) K removal; (d) treatment with cyanide; (e) cooling. We conclude that a single process is responsible for the three responses described above and identify that process as electrogenic Na pumping. Our observations also indicate that electrogenic pumping contributes to this neuron's resting potential.     

Effect of local SHF-irradiation of the rat foot on impulse activity in the tibial nerve

In experiments on rats the effects of 2.45 GHz microwave radiation on impulse activity of the afferent structures were studied in single afferent fibres of n. tibialis. Microwaves of both low and high intensity (from 0.04 to 100 mW/cm2) were shown to modify the impulse activity of the afferents which was mainly displayed by the increase in a current average frequency of impulse activity.     

Theoretical approach to modelling and analysis of the bioprocess with product inhibition and impulse effect

This work presents the first mathematical model of a bioprocess with product inhibition and impulse effect. To begin with, an exemplary mathematical bioprocess model with product inhibition and impulse effect is formulated. Then, according to the model, the analysis of bioprocess stability is presented. The article expresses the product oscillation period, which provides the precise feeding time frame for the regulator bioprocess to achieve an equivalent stable output as that of a bioprocess with impulse effect in the same production environment. Moreover, in this work, the optimization of the production process with respect to the tunable parameters is investigated, and analytical expressions of their optimal values are provided. Numerical simulations using biological data are presented to illustrate the main results.     

Guanosine 3',5'-cyclic monophosphate reduces the response of the Moth's olfactory receptor neuron to pheromone

The effects of the membrane-permeable dibutyryl guanosine 3', 5'-cyclic monophosphate (db-cGMP) on the bombykol-elicited receptor current and nerve impulse activity were studied using the open sensillum recording technique. db-cGMP was applied to the outer dendritic membrane of the olfactory receptor neuron of the moth Bombyx mori. db-cGMP reduced the amplitude of the overall receptor current activated by a pulse of strong pheromone stimuli as well as diminished the nerve impulse frequency elicited by continuously applied weak pheromone stimuli. The observed inhibition of the response to pheromone was due to size reduction of an elementary receptor current that elicits the nerve impulses and underlies the overall receptor current. It is suggested that cGMP is a factor which may adjust cell sensitivity to odour and play a role in olfactory adaptation.     

Effect of vasopressin and enkephalin analogs on the chemoreactive properties of the sensorimotor cortex neurons in rats

On immobile rats it has been shown that subcuteneous injection of two different neuropeptides causes different distribution of activating, inhibiting and areactive cells resulting from microionoforetically administrated acetylcholine and noradrenaline without altering the mean frequency of the background unit activity sensorimotor cortical neurons. At the same time the alteration in the pattern of neurons impulse activity has been revealed, which acquires the character of packet activity with a specific packet length of 2-3, 4-6, 7-10 impulses. Depending on the injected neuropeptide reliable but almost contrary effects of the packet activity alterations have been observed. These effects have been suggested to result from the alteration of the chemoreactive properties of the neuron membranes and the corresponding reorganisations of interneuron attitudes.     

Impulse response functions of terrestrial carbon cycle models: method and application

To provide a common currency for model comparison, validation and manipulation, we suggest and describe the use of impulse response functions, a concept well-developed in other fields, but only partially developed for use in terrestrial carbon cycle modelling. In this paper, we describe the derivation of impulse response functions, and then examine (i) the dynamics of a simple five-box biosphere carbon model; (ii) the dynamics of the CASA biosphere model, a spatially explicit NPP and soil carbon biogeochemistry model; and (iii) various diagnostics of the two models, including the latitudinal distribution of mean age, mean residence time and turnover time. We also (i) deconvolve the past history of terrestrial NPP from an estimate of past carbon sequestration using a derived impulse response function to test the performance of impulse response functions during periods of historical climate change; (ii) convolve impulse response functions from both the simple five-box model and the CASA model against a historical record of atmospheric δ¹³C to estimate the size of the terrestrial ¹³C isotopic disequilibrium; and (iii) convolve the same impulse response functions against a historical record of atmospheric ¹⁴C to estimate the ¹⁴C content and isotopic disequilibrium of the terrestrial biosphere at the 1° × 1° scale. Given their utility in model comparison, and the fact that they facilitate a number of numerical calculations that are difficult to perform with the complex carbon turnover models from which they are derived, we strongly urge the inclusion of impulse response functions as a diagnostic of the perturbation response of terrestrial carbon cycle models.     

Adaptation-promoting effect of IP3, Ca2+, and phorbol ester on the sugar taste receptor cell of the blowfly, Phormia regina.

The fly has a receptor cell highly specialized for the taste of sugars. We introduced inositol 1,4,5-trisphosphate (IP3), Ca2+, or a phorbol ester, 12-deoxyphorbol 13-isobutylate 20-acetate (DPBA), into the cell and investigated their effects on the response to sucrose. The sugar receptor cell generates impulses during constant stimulation with sucrose, but the impulse frequency gradually declines as the cell adapts to the stimulus. Thus, this gradual reduction of the impulse frequency is a direct manifestation of adaptation of the cell. These reagents accelerated the gradual reduction of the impulse frequency, although the initial impulse frequency was little affected. In contrast to these reagents, glycoletherdiamine-tetraacetate (EGTA) retarded the gradual reduction of the impulse frequency. Moreover, when IP3 and DPBA were applied together, the gradual reduction of the impulse frequency was more accelerated than when either IP3 or DPBA was applied. When IP3 and EGTA were applied together, however, the accelerating effect of IP3 tended to be canceled. Based on these results, we hypothesized that an intracellular cascade involving inositol phospholipid hydrolysis, intracellular Ca2+ mobilization, and protein kinase C-mediated phosphorylation promotes adaptation of the sugar receptor cell.