A theory of steady-state activity in nerve-fiber networks II: The simple circuit

It is found that for a simple circuit of neurons, if this contains an odd number of inhibitory fibers, or none at all, or if the product of the activity parameters is less than unity, then the stimulus pattern always determines uniquely the steady-state activity. For circuits not of one of these types, it is possible to classify exclusively and exhaustively all possible activity patterns into three types, here called “odd”, “even”, and “mixed”. For any pattern of odd type and any pattern of even type there always exists a stimulus pattern consistent with both, but in no other way can such an association of activity patterns be made.     

Responses of ganglioglomerular nerve activity to respiratory stimuli in the cat

We studied the responses of the ganglioglomerular nerve (GGN) efferents to brief periods of hypoxia and hypercapnia and to several levels of steady-state arterial PO2 and PCO2 and to intravascular injection of cyanide in thirteen anesthetized cats. The cats breathed spontaneously. A branch of the GGN which was cut close to the carotid body was divided into several filaments, and the activity of each filament was tested until clean and identifiable action potentials were obtained. The GGN efferent activity, breath-by-breath inspiratory volume, tracheal PO2 and PCO2 and arterial blood pressure were recorded simultaneously. We found that the GGN contained spontaneously active fibers which showed a range of responses to the respiratory stimuli. Fifty-eight percent of the filaments with dominant cardiovascular rhythm showed the least response to blood gas stimuli. Forty-two percent showed clear responses to hypoxia and hypercapnia. These responses developed slowly with the onset of the stimulus but decreased promptly with the withdrawal of the stimulus. These GGN efferents were also promptly stimulated by sodium cyanide. The steady-state response curve to hypoxia was hyperbolic and to hypercapnia it was linear. Some of these fibers showed stronger respiratory rhythms than others. The responses of these GGN efferents were associated with the respiratory responses to hypoxia and hypercapnia. For the same respiratory drive, however, the steady-state hypoxic stimulus elicited a greater GGN response than did hypercapnia.     

Note on the mathematical biophysics of temporal sequences of stimuli

Some general considerations are given regarding the effects of temporal sequences of stimuli in a neuronic network, which consists of a set of parallel chains of excitatory fibers with cross-connections made of inhibitory fibers. It is shown that, in general, the excitation produced by any individual stimulus of the series is a function of the order and duration of the previous stimuli, and that the effect of each stimulus thus depends on the whole temporal pattern considered.     

Adaptation in auditory-nerve fibers: A revised model

Adaptation of firing rates in auditory-nerve fibers appears to reflect two distinct processes. Rapid adaptation occupies the first few milliseconds of response and is superimposed upon short-term adaptation which has a time constant of about 40 ms. The properties of the two processes are reviewed and compared, and a phenomenological model is developed that successfully accounts for them. The model consists of several stages which have been tentatively associated with underlying physiological processes. In the first stage stimulus intensity is transformed by a static nonlinearity, followed by a low-pass filter. The filtered output may correspond to the hair-cell receptor potential. It modulates the release of a substance that possibly represents synaptic transmitter. Adaptation is produced by the depletion of transmitter which is located in three stores in cascade. A global store with fixed concentration controls the steady-state response and replenishes a local store which is responsible for short-term adaptation. The local store seplenishes a rapidly depleted immediate store. Flow between stores is proportional to concentration gradients with the following exceptions. The immediate store is subdivided into independent volumes or sites and there is no flow among sites or back to the local store. A given site becomes activated only when the receptor potential exceeds its particular activation value and the number of activated sites is proportional to the receptor potential. The flow of transmitter from the immediate store is assumed to be proportional to neural firing rate, with some minor modifications described in the text. The properties of the model are determined from the underlying equations and from a computer simulation. The model produces realistic response properties including PST histograms, onset and steady-state rate-intensity functions, incremental and decremental responses, response modulation for amplitude modulated stimuli, and period histograms for low-frequency tones.     

On the information received by sensory receptors

It is hypothesized that a sensory neuron, a neuron issuing from a sensory receptor, encodes the rate at which entropy or uncertainty is removed at the receptor level. This hypothesis is tested for the case of the entropy associated with the magnitude of a signal (stimulus) applied at the sensory receptor. A simple mathematical model of the process is presented and a number of well-known stimulus-response relationships are seen to emerge. For example, the adaptation of a receptor may be seen to occur as a consequence of reduced uncertainty regarding stimulus intensity. A general equation relating stimulus and response is developed, and this equation will simplify, depending upon the ratio of signal power to noise power, to either a logarithmic or a power law.     

Manifestations of dynamic coding of the amplitude-modulated sounds on the level of auditory nerve fibres

Average firing rate of the auditory nerve fiber as function of the level of the tone with the frequency equal to characteristic frequency of the fibers, can be defined as an input-output characteristic. It is known that the steepening of the input-output characteristic of the real auditory nerve fiber is more, and the width is less than the spontaneous activity of the fiber. The latter characterizes fiber's ability to generate spikes, if the stimulus is absent. However it is known, that the real auditory nerve fibers with low spontaneous activity reproduce amplitude modulation of the signals much better, than the fibers with high spontaneous activity. From the results of simulation experiments, it follows that the dynamic properties of the auditory nerve fibers, providing fine tuning or adaptation of a fiber threshold under the stimulus level but not the static input-output characteristics, are the reason of fibers reproduction of stimuli amplitude modulations. However the auditory nerve fibers with high spontaneous activity due to abrupt input-output characteristic are capable to reproduce modulations of sounds whose levels are lower than a threshold of the fiber, if a weak signal adds to a weak broadband noise. This is a phenomenon of stochastic resonance found in the reactions of auditory nerve fibers.     

Short-term adaptation and incremental responses of single auditory-nerve fibers

In response to tone bursts of constant sound intensity, mammalian auditory-nerve fibers produce a maximum firing rate at onset, followed by an adaptation to a quasi-steady firing rate within about 150 msec. On the basis of two fundamental findings, it appears that the adaptation is additive, or linear, in nature and does not result from a multiplicative gain change. Basically, a given increment in stimulus intensity produces the same change in firing rate before and after the adaptation. In addition, the relative amount of adaptation, i.e. the ratio of driven onset firing rate to driven steady-state firing rate, is independent of tone intensity. Nonlinear effects that appear in the experimental results may be accounted for by two static nonlinearities, one preceding and one following the linear adaptation stage.     

Rat extraocular muscle

Summary Multiply-innervated fibers from rat superior oblique extraocular muscle were followed in sequential serial sections using histochemistry. Sudan black and adenosine-triphosphase (ATPase) histochemical staining reactions were used to identify these fibers in the muscle's global layer and orbital surface layer. Regional differences in ATPase staining occurred along the length of multiply-innervated fibers from the orbital surface layer. In their middle third where these fibers appear ‘morphologically-fast’ and contain endplatelike endings, they were found to exhibit a dual ATPase activity. In their distal third where they appear ‘morphologically-slow’ and contain simple, superficial endings, they had an alkaline-labile and acid-stabile ATPase activity profile. In contrast, the multiply-innervated fibers of the global layer exhibited a homogeneous ATPase activity, i.e., alkaline-labile and acid-stabile pattern. This histochemical homogeneity parallels their uniform morphologically-slow profile. These fibers contain only multiple superficial endings. It would appear that the histochemical and ultrastructural profile of a fiber is dependent upon the type and location of the motor innervation.     

Sensory stimulation-dependent plasticity in the cerebellar cortex of alert mice

In vitro studies have supported the occurrence of cerebellar long-term depression (LTD), an interaction between the parallel fibers and Purkinje cells (PCs) that requires the combined activation of the parallel and climbing fibers. To demonstrate the existence of LTD in alert animals, we investigated the plasticity of local field potentials (LFPs) evoked by electrical stimulation of the whisker pad. The recorded LFP showed two major negative waves corresponding to trigeminal (broken into the N2 and N3 components) and cortical responses. PC unitary extracellular recording showed that N2 and N3 occurred concurrently with PC evoked simple spikes, followed by an evoked complex spike. Polarity inversion of the N3 component at the PC level and N3 amplitude reduction after electrical stimulation of the parallel fiber volley applied on the surface of the cerebellum 2 ms earlier strongly suggest that N3 was related to the parallel fiber-PC synapse activity. LFP measurements elicited by single whisker pad stimulus were performed before and after trains of electrical stimuli given at a frequency of 8 Hz for 10 min. We demonstrated that during this later situation, the stimulation of the PC by parallel and climbing fibers was reinforced. After 8-Hz stimulation, we observed long-term modifications (lasting at least 30 min) characterized by a specific decrease of the N3 amplitude accompanied by an increase of the N2 and N3 latency peaks. These plastic modifications indicated the existence of cerebellar LTD in alert animals involving both timing and synaptic modulations. These results corroborate the idea that LTD may underlie basic physiological functions related to calcium-dependent synaptic plasticity in the cerebellum.     

On The Mechanism of Spontaneous Impulse Generation in the Pacemaker of the Heart

Rhythmic activity in Purkinje fibers of sheep and in fibers of the rabbit sinus can be produced or enhanced when a constant depolarizing current is applied. When extracellular calcium is reduced successively, the required current strength is less, and eventually spontaneous beating occurs. These effects are believed due to an increase in steady-state sodium conductance. A significant hyperpolarization occurs in fibers of the rabbit sinus bathed in a sodium-free medium, suggesting an appreciable sodium conductance of the "resting" membrane. During diastole, there occurs a voltage-dependent and, to a smaller extent, time-dependent reduction in potassium conductance, and a pacemaker potential occurs as a result of a large resting sodium conductance. It is postulated that the mechanism underlying the spontaneous heart beat is a high resting sodium current in pacemaker tissue which acts as the generator of the heart beat when, after a regenerative repolarization, the decrease in potassium conductance during diastole reestablishes the condition of threshold.     

Inability of chrysotile asbestos fibers to modulate the 2-acetylaminofluorene-induced UDS in primary cultures of rat hepatocytes

There is now growing evidence that asbestos fibers could act in association with genotoxic compounds, either as cocarcinogens or promoters, in the process of carcinogenesis. The hepatocyte/UDS assay system has been taken to advantage to investigate the capacity of fibers to modulate the effects of genotoxic compounds on the cell, as we previously demonstrated the hepatocytes can engage in phagocytosis of chrysotile fibers. Measurement of UDS was performed by a biochemical procedure involving liquid scintillation counting (LSC) of a purified DNA fraction as well as by radioautography. Both LSC and radioautography revealed that chrysotile asbestos fibers UICC B at concentrations up to 100 micrograms/ml do not elicit UDS, whereas 2-acetylaminofluorene (2-AAF) at low concentrations (0.05-0.625 micrograms/ml) significantly induces it in parallel positive controls. In an attempt to test the cocarcinogen hypothesis, cultures of hepatocytes were simultaneously exposed for 20 h to 2-AAF (0.05 and 0.25 micrograms/ml) and asbestos fibers (1 and 10 micrograms/ml) given as simple mixtures. It was found that the 2-AAF-induced UDS activity was the same whether fibers were present or not. This was observed with both UDS evaluation procedures at all concentration combinations selected. An analysis of variance applied to the data collected from several experiments confirmed that there was no significant 2-AAF-fiber interaction. Our data suggest the absence of intrinsic genotoxic properties for chrysotile fibers. They also indicate that the modulation of the cellular response to genotoxic agents by asbestos fibers is not detected under our test conditions and may require longer-term exposures to be expressed.     

Effects of acute sublethal exposure to coumaphos or diazinon on acquisition and discrimination of odor stimuli in the honey bee (Hymenoptera: Apidae)

Two organophosphate compounds, coumaphos and diazinon, were examined for effects of sublethal exposure on odor learning and generalization in honey bees, Apis mellifera L. Using proboscis extension response training as a measure of odor learning and discrimination, a series of two experiments tested whether these compounds would inhibit bees from learning a new odor or discriminating between different odors. Bees were exposed to coumaphos or diazinon in acetone applied to the thorax, or to coumaphos or diazinon in hexane injected intracranially. At no dose tested or exposure method used was coumaphos shown to inhibit acquisition of a novel odor stimulus, although it was shown to slightly reduce discriminatory ability when given by intracranial injection. Diazinon had effects on odor learning at several small doses, and a small injected dose was shown to significantly inhibit learning of an odor stimulus paired with a sucrose reward. When bee head acetylcholineasterase activity was measured after dermal applications of both pesticides, only the higher doses of diazinon showed reduced activity, indicating that externally-applied coumaphos shows no significant effect on bee brain acetylcholinesterase activity. These data suggest that acute application of coumaphos has only slight nonlethal effects upon the behavior of honey bees and should have little effect upon bee tasks that involve odor learning.     

A theory of steady-state activity in nerve-fiber networks: IV.N circuits with a common synapse

Conditions under which either of two distinct activity patterns may arise from the same stimulus pattern are deduced for the case of a net-work which consists ofN simple circuits all jointed at a common synapse. If the product of the activity parameters of all the fibers in any circuit is called the activity parameter of the circuit, or, more briefly, the circuit parameter, then the condition for the existence of such mutually consistent activity patterns is that there be a sum of circuit paramaters which is not less than unity.     

A generalized activating function for predicting virtual electrodes in cardiac tissue.

To fully understand the mechanisms of defibrillation, it is critical to know how a given electrical stimulus causes membrane polarizations in cardiac tissue. We have extended the concept of the activating function, originally used to describe neuronal stimulation, to derive a new expression that identifies the sources that drive changes in transmembrane potential. Source terms, or virtual electrodes, consist of either second derivatives of extracellular potential weighted by intracellular conductivity or extracellular potential gradients weighted by derivatives of intracellular conductivity. The full response of passive tissue can be considered, in simple cases, to be a convolution of this "generalized activating function" with the impulse response of the tissue. Computer simulations of a two-dimensional sheet of passive myocardium under steady-state conditions demonstrate that this source term is useful for estimating the effects of applied electrical stimuli. The generalized activating function predicts oppositely polarized regions of tissue when unequally anisotropic tissue is point stimulated and a monopolar response when a point stimulus is applied to isotropic tissue. In the bulk of the myocardium, this new expression is helpful for understanding mechanisms by which virtual electrodes can be produced, such as the hypothetical "sawtooth" pattern of polarization, as well as polarization owing to regions of depressed conductivity, missing cells or clefts, changes in fiber diameter, or fiber curvature. In comparing solutions obtained with an assumed extracellular potential distribution to those with fully coupled intra- and extracellular domains, we find that the former provides a reliable estimate of the total solution. Thus the generalized activating function that we have derived provides a useful way of understanding virtual electrode effects in cardiac tissue.     

Spectro-temporal interpretation of activity patterns of auditory neurons

Sensory receptors transform an external sensory stimulus into an internal neural activity pattern. This mapping is studied through its inverse. An earlier paper showed that within the context of a neuron model composed of a linear filter followed by an exponential pulse generator and a Gaussian stimulus ensemble a unique "most plausible" first-order stimulus estimate can be constructed. This method, applicable only to neurons showing phase-lock, is extended to neurons without phase-lock. In this situation second-order spectro-temporal stimulus estimates are produced; examples are given from simulation. The method is applied to activity of neurons in the auditory system of the frog.     

The structure of steady-state enzyme kinetic equations: a graph-theoretical algorithm for obtaining conditions for reduction in degree by common-factor cancellation

Many enzyme kinetic steady-state equations are so complicated that analysis of their predictions, preferably by graph-theoretical methods, without deriving the equations is desirable. An example of such a method is given here. It is a graph-theoretical algorithm for determining non-trivial relations between the rate constants of a mechanism that cause the numerator and denominator of its rate expression have a common factor so permitting the degree of the expression to be reduced. An algorithm for writing the several different forms of the reduced rate equation is also given. The algorithm is applied to some standard simple enzymic mechanisms that give relatively complicated rate equations.In the case of a 2:2 equation, the sign of curvature in a double reciprocal plot depends on the sign of the expression in the common-factor condition.     

Membrane potential and its electrode-recorded counterpart in an electrical model of an olfactory sensillum

Insect receptor neurons are surrounded with auxiliary cells and encased in a hair. Their electrical activity is usually recorded with an electrode located at the tip of the hair. Analytical expressions giving the membrane potential along the sensory dendrite and the tip-recorded potential are derived for a neuron in steady-state conditions. They formally close the gap between theoretical models and experimental measurements, when transduction mechanisms and active membrane properties are not taken into account. It is shown that the tip-recorded potential reflects correctly the relative variations of the dendritic membrane potential as a function of stimulus intensity over a large range of parameters. The geometric and electrical characteristics of the sensillum that need be known to compute the dendritic membrane potential from the tip-recorded potential are given.     

An analysis of a sample of afferent discharges provoked in frog dorsal root by a passive movement

Summary Discharges of individual fibers from the IX-th frog dorsal root, under stretching of the hind leg by falling weights, have been recorded. About 1/3 of the recorded fibers are leading off from rapidly adapting receptors. The fibers coming from slowly adapting receptors and those not responding to the applied stimulus are analyzed with some details.The number of pulse per second as a function of time and load is examined. It has been found that a group of fibers increases the rate of firing regularly with the load, a second group gives the greatest response in intermediate zones of the loads scale and a third group shows a higher threshold.Some remarks on the aggregate message reaching the spinal cord are developed.     

Control of endogenous phosphorylation of the major cAMP-dependent protein kinase substrate in adipocytes by insulin and beta-adrenergic stimulation

In isolated, 32Pi-loaded, rat adipocytes, we have examined phosphorylation of the major cAMP-dependent protein kinase (A-kinase) substrate, a protein that appears to be associated with the lipid storage droplet and migrates in sodium dodecyl sulfate-polyacrylamide gel electrophoresis as a 65-67-kDa doublet. In control cells, a strong phosphorylation signal is detected as the (+/- cAMP) A-kinase activity ratio ranges from approximately 0.1 to approximately 0.3-0.4 with increasing isoproterenol concentrations. By contrast, insulin-treated cells exhibiting A-kinase activity ratios over the range of 0.1-0.25 contain less 32P in the 65-67-kDa protein than control cells exhibiting identical A-kinase activity ratios. At higher activity ratios (greater than 0.3), this reduction in phosphorylation of the 65-67-kDa protein by insulin disappears. It is concluded that insulin stimulates a phosphatase activity that acts on the 65-67-kDa protein. Insulin actions aside, these studies reveal two interesting phenomena. 1) Whereas elevated, steady-state A-kinase activities are established rapidly (1-2 min) upon isoproterenol stimulation, phosphorylation of the 65-67-kDa substrate proceeds through a burst, followed by a decline to a steady-state level by 10-12 min. An "adaptation" mechanism, providing for a constant response to a constant stimulus, may underlie this lack of parallelism between the time course of phosphorylation and A-kinase activity. 2) Removal of [32Pi] orthophosphate immediately before isoproterenol stimulation leads to a rapid (t approximately 10 min) loss in labeling of the 65-67-kDa protein, whereas the phosphorylation state of other phosphoproteins are not changed. These data suggest that elevation of A-kinase activity leads to a rapid exchange of external Pi with an ATP pool that is used by A-kinase.     

Stimulus interaction between CO2 and almitrine in the cat carotid chemoreceptors

The hypothesis that augmentation of the carotid chemoreceptor response to hypoxia by almitrine is due in part to an increased response to CO2 was tested by using single or few fiber preparation of carotid body chemosensory fibers in 12 cats anesthetized with alpha-chloralose. To differentiate between the plausible mechanisms of effects, we also tested the responsiveness of the afferents to cyanide and nicotine before and after almitrine. After a saturation dose of almitrine (1 mg.kg-1 followed by 0.5 mg.kg-1.h-1) the chemosensory responses to CO2 strikingly increased even during hyperoxia: the afferents showing an increased transient peak activity at the onset of hypercapnia, an augmented steady-state response to CO2 stimulus, and a decreased arterial PCO2 stimulus threshold. Thus, the effect of almitrine on carotid chemoreceptor response to hypoxia could be explained, at least in part, by its multiplicative stimulus interaction with CO2. After almitrine, the chemoreceptor response to cyanide, which is dependent on arterial PO2, was not particularly augmented relative to those of nicotine. Accordingly, the O2-sensing mechanism does not appear to be the primary site of almitrine effect. The results also indicate that the site of CO2 chemoreception resides downstream from those of hypoxia.