A transduction model of the Meissner corpuscle

I propose a transduction model of the Meissner corpuscle that integrates ideas put forth by Freeman and Johnson and results obtained by Looft. The principal development in the present model is its specification that RA receptor potentials are updated as a linear function of stimulus velocity above baseline; the model thus readily accommodates non-sinusoidal input. It also incorporates modifications to Freeman and Johnson's model proposed by Slavík and Bell, namely a period of refractoriness lasting 1 ms followed by a period of hyperexcitability lasting 13.5 ms. The model is applied to various psychophysical and physiological situations: psychophysical threshold vs. frequency, RA afferent impulse rates vs. intensity, impulse regularity vs. frequency, phase retardation vs. frequency, and responses to non-repeating noise and to complex stimuli. Model output closely matches psychophysical and neurophysiological data. The proposed model thus reliably predicts RA afferent responses to arbitrary stimuli and may facilitate the development of theories relating psychophysical phenomena to their underlying neural representations.     

Phase-locked responses in the Limulus lateral eye. Theoretical and experimental investigation.

The 1:1 phase locking of the neural discharge to sinusoidally modulated stimuli was investigated both theoretically and experimentally. On the theoretical side, a neural encoder model, the self-inhibited leaky integrator, was considered, and the phase of the locked impulse was computed for each frequency in the locking range by imposing the condition that the "leaky integral" u(t) of the driving signal should reach the threshold for the first time one stimulus period after the preceding impulse. As u(t) can be a nonmonotonic function, this approach leads to results that sometimes differ from those reported in the literature. It turns out that the phase excursion is often much smaller than the values of about 180 degrees predicted from previous analysis. Moreover, our analysis shows a peculiar effect; the phase locking frequency range narrows when the input modulation depth increases. The theoretical predictions are then compared with phase-locked discharge patterns recorded from visual cells of the Limulus lateral eye, stimulated by sinusoidally modulated light or depolarizing current. The phases of the locked spikes at each of a number of modulation frequencies have been measured. The predictions offered by the model fit the experimental data, although there are some difficulties in determining the effective driving signal.     

Sensory transduction in an insect mechanoreceptor: Linear and nonlinear properties

Mechanotransduction in the femoral tactile spine of the cockroach, Periplaneta americana, was examined as a function of displacement of the spine axially in its socket. Linear behaviour was analyzed by measurement of the frequency response function between displacement and action potential output using sinusoidal stimulation and random noise stimulation. The measured frequency response functions can be well fitted by a relationship which is a fractional power of complex frequency. This power was close to 0.5 for all experiments. To distinguish between the effects of nonlinearity and of inherent variability, the averaged responses of the preparation to repeated sequences of pseudorandom noise were compared to those from experiments in which continuous pseudorandom noise were used. The lack of sensitivity of the coherence function to these two methods of measurement suggests that mechanical stimuli are encoded into action potentials with a large signal-to-noise ratio. The low value of the coherence function which is characteristics of insect mechanoreceptors is therefore due to the strong non-linearity of their responses. To investigate the nonlinear properties of transduction, the second-order frequency response function of the tactile spine was measured for random noise stimulation experiments. Two models of the transduction process were considered in which a linear element with memory was cascaded with a nonlinear element without memory in the two possible configurations. Comparison of the experimental second-order frequency response functions with predictions based upon these two models and the measured first-order frequency response suggests that the transduction mechanism can be modelled by a linear element, which may be associated with the viscoelastic properties of the dendritic tubular body, and a zeromemory nonlinearity, which is most likely to be rectification by the dendritic membrane.     

Hyperpolarizing photoreceptors in the eyes of the giant clamTridacna: physiological evidence for both spiking and nonspiking cell types

Summary Intracellular studies on photoreceptors in the eyes of the giant clamTridacna give evidence for two types of light-sensitive cells, both of which are hyperpolarized by light. These cells are distinguished by the presence or absence of spikes and corresponding characteristics of the receptor potential. In non-spiking (NS) receptors, the average resting potential in the dark is low (-15 mV) and peak receptor potentials are large (to 100 mV) and adapt rapidly to light. Spiking (S) receptors have higher average resting potentials (-45 mV), but receptor potentials do not exceed 20 mV and also do not adapt to light. The spikes in S-receptors are small (3–8 mV), occur spontaneously at low levels of illumination and are inhibited by light. Bursts of spikes arise on the repolarizing off-component of the receptor potential. Light adaptation increases the excitability of S-receptors in terms of a higher frequency and shorter latency of the off response burst. The receptor potential in both cells is due to a light-activated increase in membrane conductance to potassium ions. Membrane conductance decreases in NS-receptors in relation to light adaptation. Unlike the scallop eye, no depolarizing photoreceptors are present.Abbreviations NS non-spiking photoreceptors - S spiking photoreceptors - SW seawater     

Model of the dynamics of receptor potential in a mechanoreceptor.

Mechanoreceptors are physiological units that convert mechanical stimuli to neural responses. An important one in the skin is the Pacinian corpuscle, which consists of a nerve ending surrounded by a capsule that is made up of alternating layers of fluid and elastic shells. In this paper a capsule model is coupled to a model for the dendrite via a variable representing the hoop strain imposed by the capsule on the receptor membrane of the dendrite. The transient behavior of the receptor potential due to step and periodic displacement-type stimuli imposed on the outer membrane of the capsule is investigated, and the results are compared to those of analogous experiments. The model is used to develop hypotheses concerning the role of the capsule as a filter for mechanical stimuli.     

Ovoid geometry of the Pacinian corpuscle is not the determining factor for mechanical excitation

Static displacements in Pacinian corpuscles (PCs) were measured using video microscopy. Mechanical stimuli of 10-40 microm steps were applied to the PC capsule surfaces using cylindrical contacts with different diameters. Displacements parallel to the stimulation axis were measured at various locations in the focal plane of the optical setup. In contrast to previous data in the literature, the displacements within the corpuscle were found to be linearly related to the indentation amplitude. Displacements decreased as a function of lamella depth, with a more negative slope close to the surface and less negative slope at deeper locations. The experimental data were compared to the predictions of a previous mechanical model, and to the results of two new models: (1) elastic semi-infinite continuum model; (2) ovoid isotropic finite-element model. Although the previous model did not specify displacement boundary conditions, it predicted the current experimental results well. On the other hand, the experimental displacements were found to be smaller than those predicted by the semi-infinite continuum and finite-element models. However, both semi-infinite continuum and finite-element models yielded close results, which show that the three-dimensional ovoid geometry of the corpuscle is not the primary factor for determining the displacements in physiological conditions. Furthermore, simulations with the finite-element model using a wide range of material properties yielded similar results. This supports the hypothesis that a homogeneous isotropic model for the PC cannot predict experimental results. The modeling analyses suggest that the experimental results are largely affected by the displacement of the incompressible interlamellar fluid and the layered structure of the corpuscle.     

家鸽Herbst小体对振动的反应特征

鸟类的Herbst小体是一种形态特殊的感觉性神经末梢器官.本文利用电生理学方法,研究了家鸽腿部胫骨-腓骨之间的Herbst小体对振动刺激的反应特征.这种小体对振动刺激非常敏感,当振动频率在600—800赫时,它们有反应的最低阈值约为0.3微米.不同的Herbst小体的反应阈值与频率的关系曲线表明:这种小体具有明显的带通滤波的特征,对振动反应的最佳频率范围为400—1000赫.在适宜频率、超阈值强度的振动刺激下,Herbst小体能以1:1的方式作出反应,即相对于每次正弦波振动刺激都有一个锁相的神经脉冲产生.在背根脊神经节内的细胞外记录表明:对振动敏感的神经节细胞具有和Herbst小体完全相似的反应特征.     

Ovoid geometry of the Pacinian corpuscle is not the determining factor for mechanical excitation

Static displacements in Pacinian corpuscles (PCs) were measured using video microscopy. Mechanical stimuli of 10–40?µm steps were applied to the PC capsule surfaces using cylindrical contactors with different diameters. Displacements parallel to the stimulation axis were measured at various locations in the focal plane of the optical setup. In contrast to previous data in the literature, the displacements within the corpuscle were found to be linearly related to the indentation amplitude. Displacements decreased as a function of lamella depth, with a more negative slope close to the surface and less negative slope at deeper locations. The experimental data were compared to the predictions of a previous mechanical model, and to the results of two new models: () elastic semi-infinite continuum model; () ovoid isotropic finite-element model. Although the previous model did not specify displacement boundary conditions, it predicted the current experimental results well. On the other hand, the experimental displacements were found to be smaller than those predicted by the semi-infinite continuum and finite-element models. However, both semi-infinite continuum and finite-element models yielded close results, which show that the three-dimensional ovoid geometry of the corpuscle is not the primary factor for determining the displacements in physiological conditions. Furthermore, simulations with the finite-element model using a wide range of material properties yielded similar results. This supports the hypothesis that a homogeneous isotropic model for the PC cannot predict experimental results. The modeling analyses suggest that the experimental results are largely affected by the displacement of the incompressible interlamellar fluid and the layered structure of the corpuscle.     

The refractory state of the generator and propagated potentials in a pacinian corpuscle

A propagated potential produced in the Pacinian corpuscle in response to mechanical stimuli leaves a refractory state of 7 to 10 msec. duration. The refractory state is presumably produced at the first intracorpuscular node of Ranvier. The recovery of receptor excitability for producing an all-or-none response to mechanical stimulation follows the same time course as that of the electrically excited axon. Upon progressive reduction of stimulus interval (mechanical), the propagated potential falls progressively to 75 per cent of its resting magnitude and becomes finally blocked within the corpuscle. A non-propagated all-or-none potential, presumably corresponding to activity of the first node, is then detected. The critical firing level for all-or-none potentials increases progressively during the relative refractory period of the all-or-none potential, as the stimulus interval is shortened. Thus generator potentials up to 85 per cent of a propagated potential can be produced in absence of all-or-none activity. Generator potentials show: gradual over-all increase in amplitude and rate of rise as a function of stimulus strength; constant latency; and spontaneous fluctuations in amplitude. A generator potential leaves a refractory state (presumably at the non-myelinated ending) so that the amplitude of a second generator response which falls on its refractory trail is directly related to the time elapsed after the first generator response and inversely to its amplitude. The generator potential develops independently of any refractory state left by a preceding all-or-none potential.     

What Is the Most Realistic Single-Compartment Model of Spike Initiation?

A large variety of neuron models are used in theoretical and computational neuroscience, and among these, single-compartment models are a popular kind. These models do not explicitly include the dendrites or the axon, and range from the Hodgkin-Huxley (HH) model to various flavors of integrate-and-fire (IF) models. The main classes of models differ in the way spikes are initiated. Which one is the most realistic? Starting with some general epistemological considerations, I show that the notion of realism comes in two dimensions: empirical content (the sort of predictions that a model can produce) and empirical accuracy (whether these predictions are correct). I then examine the realism of the main classes of single-compartment models along these two dimensions, in light of recent experimental evidence.     

Precision of intracellular calcium spike timing in primary rat hepatocytes

Extracellular stimuli are often encoded in the frequency, amplitude and duration of spikes in the intracellular concentration of calcium ([Ca2+]i). However, the timing of individual [Ca2+]i-spikes in relation to the dynamics of an extracellular stimulus is still an open question. To address this question, we use a systems biology approach combining experimental and theoretical methods. Using computer simulations, we predict that more naturalistic pulsed stimuli generate precisely-timed [Ca2+]i-spikes in contrast to the application of constant stimuli of the same dose. These computational results are confirmed experimentally in single primary rat hepatocytes upon alpha1-adrenergic stimulation. Hormonal signalling in analogy to neuronal signalling thus has the potential to make use of temporal coding on the level of single cells. The [Ca2+]i-signalling cascade provides a first example for increasing the information capacity of an intracellular regulatory signal beyond the known coding mechanisms of amplitude (AM) and frequency modulation (FM).     

The temporal resolution of neural codes: does response latency have a unique role?

This article reviews the nature of the neural code in non-human primate cortex and assesses the potential for neurons to carry two or more signals simultaneously. Neurophysiological recordings from visual and motor systems indicate that the evidence for a role for precisely timed spikes relative to other spike times (ca. 1-10 ms resolution) is inconclusive. This indicates that the visual system does not carry a signal that identifies whether the responses were elicited when the stimulus was attended or not. Simulations show that the absence of such a signal reduces, but does not eliminate, the increased discrimination between stimuli that are attended compared with when the stimuli are unattended. The increased accuracy asymptotes with increased gain control, indicating limited benefit from increasing attention. The absence of a signal identifying the attentional state under which stimuli were viewed can produce the greatest discrimination between attended and unattended stimuli. Furthermore, the greatest reduction in discrimination errors occurs for a limited range of gain control, again indicating that attention effects are limited. By contrast to precisely timed patterns of spikes where the timing is relative to other spikes, response latency provides a fine temporal resolution signal (ca. 10 ms resolution) that carries information that is unavailable from coarse temporal response measures. Changes in response latency and changes in response magnitude can give rise to different predictions for the patterns of reaction times. The predictions are verified, and it is shown that the standard method for distinguishing executive and slave processes is only valid if the representations of interest, as evidenced by the neural code, are known. Overall, the data indicate that the signalling evident in neural signals is restricted to the spike count and the precise times of spikes relative to stimulus onset (response latency). These coding issues have implications for our understanding of cognitive models of attention and the roles of executive and slave systems.     

The effects of temperature on signalling in ocellar neurons of the desert locust, <Emphasis Type="Italic">Schistocerca gregaria</Emphasis>

In Schistocerca gregaria ocellar pathways, large second-order L-neurons use graded potentials to communicate signals from the ocellar retina to third-order neurons in the protocerebrum. A third-order neuron, DNI, converts graded potentials into axonal spikes that have been shown in experiments at room temperature to be sparse and precisely timed. I investigated effects of temperature changes that a locust normally experiences on these signals. With increased temperature, response latency decreases and frequency responses of the neurons increase. Both the graded potential responses in the two types of neuron and the spikes in DNI report greater detail about a fluctuating light stimulus. Over a rise from 22 to 35°C the power spectrum of the L-neuron response encompasses higher frequencies and its information capacity increases from about 600 to 1,700 bits/s. DNI generates spikes more often during a repeated stimulus but at all temperatures it reports rapid decreases in light rather than providing a continual measure of light intensity. Information rate carried by spike trains increases from about 50 to 185 bits/s. At warmer temperatures, increased performance by ocellar interneurons may contribute to improved aerobatic performance by delivering spikes earlier and in response to smaller, faster light stimuli.     

Cartilage electromechanics--II. A continuum model of cartilage electrokinetics and correlation with experiments

We have formulated a continuum model for linear electrokinetic transduction in cartilage. Expressions are derived for the streaming potential and streaming current induced by oscillatory, uniaxial confined compression of the tissue, as well as the mechanical stress generated by a current density or potential difference applied to the tissue. The experimentally observed streaming potential and current-generated stress response, measured on the same specimens, are compared with the predictions of the theory over a wide frequency range. The theory compares well with the data for reasonable values of cartilage intrinsic mechanical parameters and electrokinetic coupling coefficients. Experiments also show a linear relationship between the stimulus amplitude and the transduction response amplitude, within the range of stimulus amplitudes of interest. This observation is shown to be consistent with the predictions of the linear theory.     

Receptor clustering and signal processing in E. coli chemotaxis

Chemotaxis in Escherichia coli is one of the most thoroughly studied model systems for signal transduction. Receptor-kinase complexes, organized in clusters at the cell poles, sense chemoeffector stimuli and transmit signals to flagellar motors by phosphorylation of a diffusible response regulator protein. Despite the apparent simplicity of the signal transduction pathway, the high sensitivity, wide dynamic range and integration of multiple stimuli of this pathway remain unexplained. Recent advances in computer modeling and in quantitative experimental analysis suggest that cooperative protein interactions in receptor clusters play a crucial role in the signal processing during bacterial chemotaxis.     

Consequences of chemosensory phenomena for leukocyte chemotactic orientation

The stochastic nature of cell surface receptor-ligand binding is known to limit the accuracy of detection of chemoattractant gradients by leukocytes (11, 12), thus limiting the orientation ability that is crucial to the chemotactic response in host defense. The probabilistic cell orientation model of Lauffenburger (11) is extended here to assess the consequences of recently discovered receptor phenomena: “down-regulation” of total surface receptor number, spatial asymmetry of surface receptors, and existence of a higher-affinity receptor subpopulation. In general, a reduction in orientation accuracy is predicted by inclusion of these phenomena. An orientation signal based on a simple model of chemosensory adaptation (i.e., a spatial difference inrelative receptor occupancy) is found to be functionally different from the signal suggested by an experimental correlation (i.e., a spatial difference inabsolute receptor occupancy). However, in the context of receptor “signal noise,” the signal based on adaptation yields predictions in better qualitative agreement with the experimental orientation data of Zigmond (10). From this cell orientation model we can estimate the effective timeaveraging period required for noise diminution to a level allowing orientation predictions to match observed levels. This time-averaging period presumably reflects the time constant for receptor signal transduction and locomotory response.     

Fluorescence correlation spectroscopy for detecting submicroscopic clusters of fluorescent molecules in membranes

The formation of cell surface receptor clusters has been implicated of confirmed in the mechanism of signal transduction across biological membranes for a variety of processes, including receptor-mediated phagocytosis and endocytosis and cellular response to hormones and neurotransmitters. Flourescence correlation spectroscopy (FCS) is one technique that may provide insight into the kinetics and extent of receptor aggregation. Recent theoretical and experimental developments in FCS for the investigation of submicroscopic clusters of fluorescence molecules are described and the potential applications of the technique to receptor aggregation are reviewed.     

Contrasting effects of the persistent Na+ current on neuronal excitability and spike timing

The persistent Na+ current, INaP, is known to amplify subthreshold oscillations and synaptic potentials, but its impact on action potential generation remains enigmatic. Using computational modeling, whole-cell recording, and dynamic clamp of CA1 hippocampal pyramidal cells in brain slices, we examined how INaP changes the transduction of excitatory current into action potentials. Model simulations predicted that INaP increases afterhyperpolarizations, and, although it increases excitability by reducing rheobase, INaP also reduces the gain in discharge frequency in response to depolarizing current (f/I gain). These predictions were experimentally confirmed by using dynamic clamp, thus circumventing the longstanding problem that INaP cannot be selectively blocked. Furthermore, we found that INaP increased firing regularity in response to sustained depolarization, although it decreased spike time precision in response to single evoked EPSPs. Finally, model simulations demonstrated that I(NaP) increased the relative refractory period and decreased interspike-interval variability under conditions resembling an active network in vivo.     

Langevin equation,Fokker-Planck equation and cell migration

Cell migration can be characterized by two independent variables: the speed,v, and the migration angle, ϕ. Each variable can be described by a stochastic differential equation—a Langevin equation. The migration behaviour of an ensemble of cells can be predicted due to the stochastic processes involved in the signal transduction/response system of each cell. Distribution functions, correlation functions, etc. are determined by using the corresponding Fokker-Planck equation. The model assumptions are verified by experimental results. The theoretical predictions are mainly compared with the galvanotactic response of human granulocytes. The coefficient characterizing the mean effect of the signal transduction/response system of the cell is experimentally determined to 0.08 mm/V sec (galvanotaxis) or 0.7 mm/sec (chemotaxis) and the characteristic time characterizing stochastic effects in the signal transduction/response system is experimentally determined as 30 sec. The temporal directed response induced by electric field pulses is investigated: the experimental cells react slower but are more sensitive than predicted by theory.     

Optic nerve responses to visual stimuli in squid

Summary Single unit optic nerve responses were studied in isolated eye-optic lobe preparations ofLoligo opalescens. Units could be classified as fast or slow. Fast units were invariably receptor cell axons; slow units might be either receptor cell axons or centrifugal axons.On, on-off, andoff units could be found within these classes. A given unit was not stable with respect to these latter attributes which depended greatly on the history and level of illumination. The curve which relates quantal content of a brief flash to number of spikes in the response has a logarithmic phase, but it saturates as brightness is increased further. An inhibitory component has been demonstrated following the response to a flash. It is probably responsible for the non-monotonic relationship between frequency and light intensity which is observed for sustained stimuli. Background light or previous illumination can lead to a facilitation of the response to a flash.The authors share equally in credit and responsibility for this paper and for the research reported here. We thank Dr. A. Hurley and Dr. T. H. Bullock for valuable comments and suggestions and L. Ball and S. St. John for technical assistance. This research was supported by PHS grants NS 09342 to GDL and EY 29405 to PHH, by a grant from the Sloan Foundation to the group in Neurosciences at UCSD and NSF grants GB 24816 and GD 28838 to the Scripps Institution of Oceanography for operation of the Alpha Helix Research Program.