Membrane potential changes of skeletomotor neurons in response to random stretches of the triceps surae muscles in decerebrate cats

 The properties of membrane potential changes of skeletomotor neurons (S, FR, and FF) innervating triceps surae muscles during pseudorandom stretching of these muscles were studied in decerebrate cats. Peak amplitudes of pseudorandom muscle stretches ranged from 119 μm to 4.15 mm peak-to-peak. Sequences of ten identical stretching periods were applied for averaging. Shapes of membrane potential changes and probability density distribution of amplitudes of the input and output signals and power spectra suggest that the skeletomotor neuron membrane has nonlinear properties. First- and second-order Wiener kernels were determined by applying the cross-correlation (Lee-Schetzen) method. The results suggest that the transfer function between muscle stretches and subthreshold membrane potentials is a Wiener-type cascade. This cascade is consistent with a linear, second-order, underdamped transfer function followed by a simple quadratic nonlinearity [linear (L) system followed by nonlinear (N) system, or LN cascade]. Including the nonlinear component calculated from the second-order Wiener kernel improved the model significantly over its linear counterpart, especially in S-type motoneurons. Qualitatively similar results were obtained with all types of motoneurons studied. Received: 1 April 1993/Accepted in revised form: 24 March 1994     

Time coupling of skeletomotor discharges in response to pseudo-random transsynaptic and transmembrane stimulation

Firing pattern of skeletomotor neurones innervating triceps surae muscles in response to pseudorandom muscle stretching and white noise modulated transmembrane current stimulation was investigated in decerebrate cats. Pseudo-random muscle stretching (upper cut-off frequency 60 Hz, amplitude (standard deviation) ranging from 18.5 m to 40 m) was applied to triceps surae muscles. Membrane potential changes and action potentials of skeletomotor neurones were recorded intracellularly. White noise modulated current was applied through the same (recording) microelectrode. Sequences of ten identical 5 s periods of either muscle stretching or transmembrane current stimulation were applied. Skeletomotor neurones belonging to slow motor units (rheobase less than 8.5 nA) generated action potentials in response to both pseudo-random muscle stretching and transmembrane current stimulation, while firing threshold of those belonging to fast motor units could not be reached by the muscle stretches applied. Peri-spike averaging of muscle length and injected current records showed that the action potentials appeared at the peak of either depolarizing current wave or muscle stretching both preceded by a change in opposite direction (the spikes coinciding with the peak in muscle length PSA being actually elicited by muscle spindle action potentials triggered at the moment of the peak stretching velocity). Time coupling of action potentials occurred during both muscle stretching and transmembrane stimulation, being more tight in the latter case as well as when larger amplitudes of the stimuli were applied. It is supposed that discharges from muscle spindle primary endings phase-locked to small pseudo-random muscle length changes may, due to the time coupling of skeletomotor action potentials, provoke a synchronous firing of skeletomotor neurones, mostly of those belonging to slow motor units. Possible effects of such a firing pattern on the resulting muscle reflex contraction and the stretch reflex stability as well as a possibility of it being provoked by fusimotor discharges are discussed.     

Retinal responses to white-noise modulated current stimuli

Electric current was injected into a rabbit's eye with white-noise modulations of the current amplitude. A variable D.C. bias was added to the whitenoise stimulus to study the effects of stimulus bias. For each bias level, the ERG response to the electrical stimulus was cross-correlated with the random stimulus to estimate first-and second-order Wiener kernels. The kernels indicated both linear and nonlinear characteristics of the Electrical ERG. The results for the zero biased stimulus are particularly relevant for clinical testing because the root mean square (RMS) level of the stimulus was less than 0.2 mA.This work was supported by NIH Grant Number EY03022     

Sympathetic outflow enhances the stretch reflex response in the relaxed soleus muscle in humans.

Animal experiments suggest that an increase in sympathetic outflow can depress muscle spindle sensitivity and thus modulate the stretch reflex response. The results are, however, controversial, and human studies have failed to demonstrate a direct influence of the sympathetic nervous system on the sensitivity of muscle spindles. We studied the effect of increased sympathetic outflow on the short-latency stretch reflex in the soleus muscle evoked by tapping the Achilles tendon. Nine subjects performed three maneuvers causing a sustained activation of sympathetic outflow to the leg: 3 min of static handgrip exercise at 30% of maximal voluntary contraction, followed by 3 min of posthandgrip ischemia, and finally during a 3-min mental arithmetic task. Electromyography was measured from the soleus muscle with bipolar surface electrodes during the Achilles tendon tapping, and beat-to-beat changes in heart rate and mean arterial blood pressure were monitored continuously. Mean arterial pressure was significantly elevated during all three maneuvers, whereas heart rate was significantly elevated during static handgrip exercise and mental arithmetic but not during posthandgrip ischemia. The peak-to-peak amplitude of the short-latency stretch reflex was significantly increased during mental arithmetic (P < 0.05), static handgrip exercise (P < 0.001), and posthandgrip ischemia (P < 0.005). When expressed in percent change from rest, the mean peak-to-peak amplitude increased by 111 (SD 100)% during mental arithmetic, by 160 (SD 103)% during static handgrip exercise, and by 90 (SD 67)% during posthandgrip ischemia. The study clearly indicates a facilitation of the short-latency stretch reflex during increased sympathetic outflow. We note that the enhanced stretch reflex responses observed in relaxed muscles in the absence of skeletomotor activity support the idea that the sympathetic nervous system can exert a direct influence on the human muscle spindles.     

Contrast gain control in the lower vertebrate retinas [published erratum appears in J Gen Physiol 1995 Aug;106(2):following 388]

Control of contrast sensitivity was studied in two kinds of retina, that of the channel catfish and that of the kissing gourami. The former preparation is dominantly monochromatic and the latter is bichromatic. Various stimuli were used, namely a large field of light, a spot- annulus configuration and two overlapping stimuli of red and green. Recordings were made from horizontal, amacrine, and ganglion cells and the results were analyzed by means of Wiener's theory, in which the kernels are the contrast (incremental) sensitivity. Modulation responses from horizontal cells are linear, in that the waveform and amplitude of the first-order kernels are independent of the depth of modulation. In the N (sustained) amacrine and ganglion cells, contrast sensitivity was low for a large modulation input and was high for a small modulation input, providing an example of contrast gain control. In most of the cells, the contrast gain control did not affect the dynamics of the response because the waveform of the first-order kernels remained unchanged when the contrast sensitivity increased more than fivefold. The signature of the second-order kernels also remained unchanged over a wide range of modulation. The increase in the contrast sensitivity for the second-order component, as defined by the amplitude of the kernels, was much larger than for the first-order component. This observation suggests that the contrast gain control proceeded the generation of the second-order nonlinearity. An analysis of a cascade of the Wiener type shows that the control of contrast sensitivity in the proximal retinal cells could be modeled by assuming the presence of a simple (static) saturation nonlinearity. Such a nonlinearity must exist somewhere between the horizontal cells and the amacrine cells. The functional implications of the contrast gain control are as follows: (a) neurons in the proximal retina exhibit greater sensitivity to input of lower contrast; (b) saturation of a neuronal response can be prevented because of the lower sensitivity for an input with large contrast, and (c) over a large range of modulation depths, the amplitude of the response remains approximately constant.     

Nonlinear analysis of the human visual evoked response

Using time-domain correlation techniques, the first- and second-order Wiener kernels have been calculated for the system mediating the human visual evoked response. The first-order kernels indicate the linear element is a resonant one, with a natural frequency near 20 Hz, and a memory of approximately 250 ms. The transport delay associated with this element is approximately 56 ms. The second-order kernels indicate a quadratic nonlinear element with a memory less than 20 ms. The analytic form of this element can be approximated by a parabola shifted to the right of the origin. A close correspondance between the spectrum of the first-order kernel and the spectrum of the main diagonal of the second-order kernel suggests the nonlinear element preceeds the linear one. Tests of reproducibility on the first-order kernel and the main diagonal of the second-order kernel suggest they are reliable describing functions for the system mediating the human visual evoked response.     

Nonlinear mechanisms for gain adaptation in locust photoreceptors.

Intracellular membrane potential responses were recorded from locust photoreceptors under two stimulus conditions: pairs of flashes to dark-adapted receptors, and white-noise modulated light at a range of background intensities from 500 to 15,000 effective photons per second. Nonlinear analysis of the input-output relationships were performed by estimating the Volterra and Wiener kernels of the system. The Volterra kernels obtained from the double-flash experiments were similar to the Wiener kernels obtained from the white-noise experiments, except for a change of time scale. The structure of the second-order kernels obtained with either method gave evidence for a gain control mechanism acting at an early stage of the cascade. Both feedforward and feedback nonlinearities could account for the observed system behavior at any one background level. The differences in amplitude between the kernels obtained at different background levels could be accounted for by an adaptation process which further decreased the gain of the system, acting on a slower time scale, also at some early stage of the cascade.     

Third-order reverse correlation analysis of muscle spindle primary afferent fiber responses to random muscle stretch

 The response of primary muscle spindle afferent fibers to muscle stretch is nonlinear. Now spindle responses (trains of action potentials) to band-limited Gaussian white noise length perturbations of the gastrocnemius muscles (input signal) are described in cats. The input noise upper cutoff frequency was clearly above the frequency range of physiological length changes in cat hindleg muscles. The input–output relation was analyzed by means of peri-spike averages (PSAs), which could be shown to correspond to the kernels of Wiener’s white noise approach to systems identification. The present approach (the reverse correlation analysis) was applied up to the third order. An experiment consisted of two recordings: one (the source recording) to determine PSAs and the other (the test recording) to provide an input signal for predicting responses. The predictions of different orders were compared with the actual neuronal response (the observation) of the test recording. Four different approximation procedures were developed to adapt prediction and observation and to determine weighting factors for the predictions of different orders. The approximations also yielded the value of the power density P of the input noise signal: at a variety of stimulus parameters, P from approximations had the same magnitude as P determined directly from the input signal amplitude spectrum. The prediction of a sequence of action potentials improved the higher the order of components. 37 of 42 action potentials of a test recording (the observation) could be confidently predicted from PSAs or kernels. Compared with the size of the linear first-order prediction curve, the relative sizes of the second and third-order prediction curves were: 1.0 : 0.47 : 0.26. Received: 15 November 1994/Accepted in revised form: 23 May 1995     

A dynamical model for reflex activated head movements in the horizontal plane

 We present a controls systems model of horizontal-plane head movements during perturbations of the trunk, which for the first time interfaces a model of the human head with neural feedback controllers representing the vestibulocollic (VCR) and the cervicocollic (CCR) reflexes. This model is homeomorphic such that model structure and parameters are drawn directly from anthropomorphic, biomechanical and physiological studies. Using control theory we analyzed the system model in the time and frequency domains, simulating neck movement responses to input perturbations of the trunk. Without reflex control, the head and neck system produced a second-order underdamped response with a 5.2 dB resonant peak at 2.1 Hz. Adding the CCR component to the system dampened the response by approximately 7%. Adding the VCR component dampened head oscillations by 75%. The VCR also improved low-frequency compensation by increasing the gain and phase lag, creating a phase minimum at 0.1 Hz and a phase peak at 1.1 Hz. Combining all three components (mechanics, VCR and CCR) linearly in the head and neck system reduced the amplitude of the resonant peak to 1.1 dB and increased the resonant frequency to 2.9 Hz. The closed loop results closely fit human data, and explain quantitatively the characteristic phase peak often observed. Received: 15 April 1996 / Accepted in revised form: 1 July 1996     

A retinal circuit model accounting for wide-field amacrine cells

In previous experimental studies on the visual processing in vertebrates, higher-order visual functions such as the object segregation from background were found even in the retinal stage. Previously, the “linear–nonlinear” (LN) cascade models have been applied to the retinal circuit, and succeeded to describe the input-output dynamics for certain parts of the circuit, e.g., the receptive field of the outer retinal neurons. And recently, some abstract models composed of LN cascades as the circuit elements could explain the higher-order retinal functions. However, in such a model, each class of retinal neurons is mostly omitted and thus, how those neurons play roles in the visual computations cannot be explored. Here, we present a spatio-temporal computational model of the vertebrate retina, based on the response function for each class of retinal neurons and on the anatomical inter-cellular connections. This model was capable of not only reproducing the spatio-temporal filtering properties of the outer retinal neurons, but also realizing the object segregation mechanism in the inner retinal circuit involving the “wide-field” amacrine cells. Moreover, the first-order Wiener kernels calculated for the neurons in our model showed a reasonable fit to the kernels previously measured in the real retinal neuron in situ.     

Octanoate increases cytosolic Ca2+ concentration and membrane conductance in ovine pancreatic acinar cells

 In order to investigate the cellular mechanisms involved in amylase release in response to stimulation with short-chain fatty acids, changes in intracellular calcium concentration ([Ca²⁺]_i), membrane current and amylase release were measured in pancreatic acinar cells of sheep. Both octanoate and acetylcholine raised [Ca²⁺]_i in acinar cells in a concentration-dependent manner. The rise in [Ca²⁺]_i in response to the stimulation with octanoate (10 mmol ⋅ l^-1) was reduced in a medium without CaCl₂, but was markedly enhanced by reintroduction of CaCl₂ into the medium up to 2.56 mmol ⋅ l^-1. Perfusion of the cells with a medium containing octanoate (5 mmol ⋅ l^-1) or acetylcholine (0.5 μmol ⋅ l^-1) immediately raised inward current across the cell membrane at a holding-membrane potential of −30 mV. The inward current became greater as the holding potential became more negative. The equilibrium potential was 1.8 mV and 3.9 mV for octanoate and acetylcholine, respectively, being consistent with that for Cl^-. Although intracellular application of octanoate through a patch-clamp pipette also raised inward current after several minutes in some cells (4 out of 12), this possibility was significantly smaller than that for extracellular application. In other cells, even though the intracellular application of octanoate did not cause an increase in current, it always caused responses immediately after introduction of the fatty acid into the medium. Stimulation with fatty acid as well as acetylcholine raised amylase release in a concentration-dependent manner in cells dispersed from tissue segments with crude collagenase and trypsin inhibitor. Without trypsin inhibitor, crude collagenase significantly and selectively reduced the octanoate (10 mmol ⋅ l^-1)-induced amylase release. Dispersion with crude collagenase and trypsin significantly reduced both responses induced by octanoate and acetylcholine (5.5 μmol ⋅ l^-1). We conclude that fatty acids and acetylcholine increase [Ca²⁺]_i, which consequently evokes a rise in transmembrane ion (Cl^-) conductance and amylase release, and that trypsin-sensitive protein(s) in the cell membrane are involved in secretory processes activated by stimulation with fatty acids in ovine pancreatic acinar cells. Accepted: 14 May 1996     

White noise analysis of a chromatic type horizontal cell in the Xenopus retina

The dynamics of color-coded signal transmission in the light-adapted Xenopus retina were studied by a combination of white noise (Wiener) analysis and simultaneous recordings from two types of horizontal cells: chromatic-type horizontal cells (C-HCs) are hyperpolarized by blue light and depolarized by red light, whereas luminosity-type horizontal cells (L-HCs) are hyperpolarized by all wave-lengths. The retina was stimulated by two superimposed fields of red and blue light modulated by two independent white noise signals, and the resulting intracellular responses were decomposed into red and blue components (first-order kernels). The first-order kernels predict the intracellular responses with a small degree of error (3.5-9.5% in terms of mean square error) under conditions where modulated responses exceeded 30 mV in amplitude peak-to-peak, thus demonstrating that both red and blue modulation responses are linear. Moreover, there is little or no interaction between the red- and blue-evoked responses; i.e., nearly identical first-order kernels were obtained for one color whether the other color was modulated or not. In C-HCs (but not L-HCs), there were consistent differences in the dynamics of the red and blue responses. In the C-HC, the cutoff frequency of the red response was higher than for the blue (approximately 12 vs 5 Hz), and the red kernel was more bandpass than the blue. In the L-HC, kernel waveform and cutoff frequencies were similar for both colors (approximately 12 Hz or greater), and the time-to-peak of the L-HC kernel was always shorter than either the red or blue C-HC kernel. These results have implications for the mechanisms underlying color coding in the distal retina, and they further suggest that nonlinear phenomena, such as voltage-dependent conductances in HCs, do not contribute to the generation of modulation responses under the experimental conditions used here.     

Effects of saturated fatty acids on amylase release from exocrine pancreatic segments of sheep,rats, hamsters,field voles and mice

 Stimulatory effects of saturated fatty acids consisting of 4 (butyrate), 8 (octanoate), 12 (laurate) and 16 (palmitate) carbon atoms, as well as acetylcholine on pancreatic amylase release were assessed in tissue segments isolated from sheep, rats, hamsters, field voles and mice. The amount of amylase release induced by the fatty acids (1 μmol ⋅ l^-1 to 10 mml ⋅ l^-1) and by acetylcholine (10 nmol ⋅ l^-1 to 100 μmol ⋅ l^-1) increased in a concentration-dependent manner, and the maximum response in response to the fatty acids was obtained at the maximal dose used. The maximum increase in amylase release in response to butyrate or octanoate was highly and significantly (r=0.974, P<0.001) dependent on the log value of the mean body mass in the following order: sheep>rats>hamsters>field voles>mice. On the other hand, the response to laurate and palmitate was variable among animal species. Addition of atropine (1.4 μmol ⋅ l^-1) to the medium did not reduce the responses to octanoate stimulation, but significantly reduced acetylcholineinduced responses, implying that the effects of the fatty acids were not mediated through activation of muscarinic acetylcholine receptors. Reduction of calcium ion concentration in the medium significantly inhibited the responses induced by the fatty acids and acetylcholine, suggesting that amylase release depends on extracellular calcium ions. Accepted: 14 May 1996     

Picophytoplankton biomass, community structure and productivity in the Great Astrolabe Lagoon, Fiji

 Phytoplankton biomass, community structure and productivity of the Great Astrolabe lagoon and surrounding ocean were studied using measurements of chlorophyll concentration and carbon uptake. The contribution of picophytoplankton to biomass, productivity and community structure was estimated by size fractionation, ¹⁴C-incubation and flow cytometry analysis. Picoplankton red fluorescence was demonstrated to be a proxy for chlorophyll <3 μm. Consequently, the percentage contribution to chl a<3 μm from each picoplankton group could be calculated using regression estimated values of ψ _i (fg chl a per unit of red fluorescence). In the lagoon, average chlorophyll concentration was 0.8 mg m^-3 with 45% of phytoplankton <3 μm. Primary production reached 1.3 g C m^-2 day^-1 with 53% due to phytoplankton <3 μm. Synechococcus was the most abundant group at all stations, followed by Prochlorococcus and picoeukaryotes. At all stations, Prochlorococcus represented less than 4% of the chl a <3 μm, Synechococcus between 85 and 95%, and Picoeukaryotes between 5 and 10%. In the upper 40 m of surrounding oceanic waters, phytoplankton biomass was dominated by the >3 μm size fraction. In deeper water, the <1 μm size fraction dominated. Prochlorococcus was the most abundant picoplankton group and their contributions to the chlorophyll a<3 μm were close to that of the picoeukaryotes (50% each). Accepted: 27 May 1999     

Nonlinear kernels of the human ERG

In this paper we examine the use of a symmetric binary random stimulus for eliciting the ERG, and for calculating the first-order and second-order kernels of a nonlinear functional expansion of the response. We show that if the stimulus is represented in a non-dimensional form, then the units in which all kernels are measured are the same as the units used to measure the response, microvolts in the case of the ERG: further, contributions from all kernels to the response can be added without scale factors. We present the first-order and second-order kernels measured for a population of 15 normal subjects in a clinical setting. The measurements were made at various levels of adaptation ranging from photopic to scotopic conditions. The second-order kernels illustrate the processes of rapid adaptation (<100 ms) in the retina.This research was supported in part by Grants No. EY01526, EY01774, EY01775, and RR07003 from the National Institutes of Health     

On the parameter estimation for diffusion models of single neuron's activities

 For the Ornstein-Uhlenbeck neuronal model a quantitative method is proposed for the estimation of the two parameters characterizing the unkown input process, namely the neuron’s mean input per unit time μ and the infinitesimal standard deviation per unit time σ. This method is based on the experimentally observed first- and second-order moments of interspike intervals. The dependence of the estimates μ^ and σ^ on the moments of the observed interspike intervals and on the neuronal parameters is clarified, and a comparison is made between the estimates based on the classical Wiener model and those yielded by the Ornstein-Uhlenbeck model. Comprehensive tables are included in which the displayed values of μ^ and σ^ have been calculated in terms of physiologically realistic pairs of first- and second-order moments. Our method is finally applied to interspike interval data recorded from neurons in the mesencephalic reticular formation of the cat during hypothetical sleep, slow-wave sleep stage, and wake stage. Received: 10 October 1994/Accepted in revised form: 21 March 1995     

The dynamic nonlinear behavior of fly photoreceptors evoked by a wide range of light intensities.

Fly photoreceptor cells were stimulated with steps of light over a wide intensity range. First- and second-order Volterra kernels were then computed from sequences of combined step responses. Diagonal values of the second-order Volterra kernels were much greater than the off-diagonal values, and the diagonal values were roughly proportional to the corresponding first-order kernels, suggesting that the response could be approximated by a static nonlinearity followed by a dynamic linear component (Hammerstein model). The amplitudes of the second-order kernels were much smaller in light-adapted than in dark-adapted photoreceptors. Hammerstein models constructed from the step input/output measurements gave reasonable approximations to the actual photoreceptor responses, with light-adapted responses being relatively better fitted. However, Hammerstein models could not account for several features of the photoreceptor behavior, including the dependence of the step response shape on step amplitude. A model containing an additional static nonlinearity after the dynamic linear component gave significantly better fits to the data. These results indicate that blowfly photoreceptors have a strong early gain control nonlinearity acting before the processes that create the characteristic time course of the response, in addition to the nonlinearities caused by membrane conductances.     

Dynamics of cockroach ocellar neurons

The incremental responses from the second-order neurons of the ocellus of the cockroach, Periplaneta americana, have been measured. The stimulus was a white-noise-modulated light with various mean illuminances. The kernels, obtained by cross-correlating the white-noise input against the resulting response, provided a measure of incremental sensitivity as well as of response dynamics. We found that the incremental sensitivity of the second-order neurons was an exact Weber-Fechner function; white-noise-evoked responses from second-order neurons were linear; the dynamics of second-order neurons remain unchanged over a mean illuminance range of 4 log units; the small nonlinearity in the response of the second-order neuron was a simple amplitude compression; and the correlation between the white-noise input and spike discharges of the second-order neurons produced a first-order kernel similar to that of the cell's slow potential. We conclude that signal processing in the cockroach ocellus is simple but different from that in other visual systems, including vertebrate retinas and insect compound eyes, in which the system's dynamics depend on the mean illuminance.