Receiver operating characteristic analysis. Application to the study of quantum fluctuation effects in optic nerve of Rana pipiens.

Receiver operating characteristic (ROC) analysis of nerve messages is described. The hypothesis that quantum fluctuations provide the only limit to the ability of frog ganglion cells to signal luminance change information is examined using ROC analysis. In the context of ROC analysis, the quantum fluctuation hypothesis predicts (a) the detectability of a luminance change signal should rise proportionally to the size of the change, (b) detectability should decrease as the square root of background, an implication of which is the deVries-Rose law, and (c) ROC curves should exhibit a shape particular to underlying Poisson distributions. Each of these predictions is confirmed for the responses of dimming ganglion cells to brief luminance decrements at scotopic levels, but none could have been tested using classical nerve message analysis procedures.     

ROC curve estimation when covariates affect the verification process

A receiver operating characteristic (ROC) curve is commonly used to measure the accuracy of a medical test. It is a plot of the true positive fraction (sensitivity) against the false positive fraction (1-specificity) for increasingly stringent positivity criterion. Bias can occur in estimation of an ROC curve if only some of the tested patients are selected for disease verification and if analysis is restricted only to the verified cases. This bias is known as verification bias. In this paper, we address the problem of correcting for verification bias in estimation of an ROC curve when the verification process and efficacy of the diagnostic test depend on covariates. Our method applies the EM algorithm to ordinal regression models to derive ML estimates for ROC curves as a function of covariates, adjusted for covariates affecting the likelihood of being verified. Asymptotic variance estimates are obtained using the observed information matrix of the observed data. These estimates are derived under the missing-at-random assumption, which means that selection for disease verification depends only on the observed data, i.e., the test result and the observed covariates. We also address the issues of model selection and model checking. Finally, we illustrate the proposed method on data from a two-phase study of dementia disorders, where selection for verification depends on the screening test result and age.     

Probability of Occurrence of Discrete Potential Waves in the Eye of Limulus

Discrete potential waves can be recorded from cells in the eye of Limulus both in darkness and in dim illumination. With constant illumination the frequency of these waves is linearly related to light intensity and the distribution of intervals between waves follows an exponential function. The latency of waves evoked by short flashes of light is usually long and variable and the number of waves evoked by a flash varies randomly, obeying approximately a Poisson distribution. The results of experiments with flashes of light have been compared with the predictions derived from the hypotheses that one, two, or three quanta of light are required for production of one wave. The agreement of the data with the theory can be considered acceptable for the "one quantum" hypothesis, is less satisfactory for the "two quanta" hypothesis, and is very poor for the "three quanta" hypothesis.     

A model for the variability of maintained discharges and responses to flashes of light

Previous studies of the variability of firing of retinal ganglion cells have led to apparently contradictory conclusions. To a first approximation, maintained discharges derive their variability from a noise source that is linearly added to the signal setting the mean firing rate. On the other hand, the variability of responses to abrupt changes in lighting seems to result from a nonlinear interaction between signal and noise. In both the cat and the goldfish retinae, the variance of rate is a fractional power function of the mean response amplitude (impulses/s). The exponent of that power function depends on the duration of the period in which the response is sampled after each transition in luminance; longer durations have a larger exponent. These results are difficult to explain with any simple model. The variability of the maintained discharges also deviates from the predictions of simple additivity. We propose a model for the variability of responses to abrupt changes in lighting that incorporates variability of the form observed for maintained discharges. The parameters of our model that provide the best fits to the variability of responses also provide a reasonable fit to the variability of maintained discharges. Thus, a single explanation can account for the variability of maintained discharges and responses of ganglion cells.     

Quantal Mechanism of Transmitter Release during Progressive Depletion of the Presynaptic Stores at a Ganglionic Synapse : The action of hemicholinium-3 and thiamine deprivation

In the present experiments we interfered with the mechanism of acetylcholine (ACh) synthesis in the rat superior cervical ganglion by impairing the supply of either the choline group (hemicholinium no. 3 [HC-3]treatment) or the acetyl group (thiamine deprivation). Under both conditions stimulation causes in the ganglion a progressive decline in ACh output associated with a depletion of transmitter tissue content. ACh release from the terminals of a single preganglionic fiber was estimated from the quantum content value of the evoked excitatory postsynaptic potentials (EPSP's) recorded intracellularly in the ganglion neuron under test. The present observations indicate that Poisson statistics describe transmitter release at either low or high release levels. Furthermore, the progressive decline in the rate of ACh output occurring during repetitive stimulation is shown to correspond to a progressive decrease in the number of transmitter quanta released per impulse and not to any modification in the size of individual quanta. Some 8,000 transmitter quanta proved to represent the presynaptic transmitter store initially present in those terminals on a neuron that are activated by stimulation of a single preganglionic fiber. Speculations are considered about synaptic efficacy and nerve connections in rat autonomic ganglia. It is suggested that six preganglionic fibers represent the mean input to a ganglion neuron.     

Sensitivity and functional characteristics of modern chemoluminescence meters

The paper describes the following quantum phenomenon discovered by B. N. Tarusov, A. I. Zhuravlev and A. I. Polivoda in 1961: spontaneous endogenous biochemiluminescence of animal tissues and cells in the spectral range of 320-1100 nm. It initiated studies of the role of electron-excited states and quanta in metabolism, i.e. it started the development of quantum biology of animal organisms. Intensity of this ultra-weak luminescence is determined and its classification is presented according to sensitivity towards fixation ability: a) ultra-weak 10-10(2) quanta/sec (spontaneous luminescence of blood plasma and serum, mitochondria suspension at 37 degrees C); b) ultra-weak 10(2)-10(3) quanta/sec (spontaneous luminescence of lipids and urea at 37 degrees C); weak 10(5)-10(6) quanta/sec (luminol-dependent luminescence of the blood immunocompetent cells, initiated by peroxides and luminescence catalysts in serum, plasma, lipids, suspension of organelles; d) 10(6) quanta/sec and higher (fixed by the eye or photoelement luminescence of glow worms, bacteria or ATP-triggered luciferin-luciferase reactions).     

Temporal pattern sensitive and nonsensitive responses in the cat's retinal ganglion cells

In order to characterize temporal pattern sensitivity in the cat ganglion cells, a new analysis technique by semi-Markov models which was developed in the previous papers (Tsukada et al., 1975–1977) was applied to input-output relations of the receptive-field. Three types of statistical spot stimuli positioned in the center region of receptive fields were used. Each type of stimulus has an identical histogram in the inter-stimulus intervals and therefore the same mean and variance, but different correlations between adjacent inter-stimulus intervals (Type 1, positive; Type 2, negative; and Type 3, independent processes). From the output spike trains of cat retinal ganglion cells to each stimulus, mean, variance, and histogram were computed. As the result of investigating these data, we could draw the following conclusion from the resultant output interval histograms. The receptive-field-center responses of cat ganglion cells can be classified into two groups (Types L and N) according to the difference of responsiveness to the three types of statistical spot stimuli. A Type L response has the same histogram in interspike intervals for all three stimuli, and is not sensitive to the temporal pattern, while a Type N response has three different forms depending on each type of stimulus showing high sensitivity to the temporal pattern. These results were also simulated by the Markov chain model and discussed with relation to neural coding and classification of ganglion cell types.     

Quantum relations in photoreactivation of Colpidium

1. The amount of visible or long ultraviolet light (UV) required to photoreactivate Colpidium colpoda injured with known dosages of short UV (2654 A) was determined. 2. The effect of the short UV was tested by the delay in division of exposed animals compared to controls. Photoreactivation was tested by the effect of postillumination on the delay of division of treated colpidia compared to controls. 3. Colpidia were used in two physiological states: well fed and starved in balanced medium for 48 hours. The latter are much more sensitive to short UV although less susceptible of photoreactivation. 4. Photoreactivation occurred over the entire span from 3350 A to 4350 A for the well fed colpidia, from 3130 A to 5490 (green) for starved colpidia. 5. The photoreactivating effect of a single quantum of blue (4350 A) or long UV (3660 A) delivered per quantum of 2654 A used to injure colpidia was too slight to be considered significant. The effect of 10 quanta was usually more pronounced, but only after 100 quanta had been delivered was the photoreactivation nearly maximal for well fed colpidia. 6. The quantum requirement for maximal photoreactivation of the starved animals was greater at all wave lengths tried: 3660, 4050, 4350, and 5460 A being of the order of 800 incident quanta per incident quantum of 2654 A. 7. The transmission of UV(2654 A), blue, yellow, and red light by a suspension of colpidia was determined. 8. Large dosages of blue, violet, or long UV were slightly injurious to starved colpidia. In a few cases large dosages of 3660 A killed starved colpidia, especially after a non-lethal dose of short UV(2654 A). 9. Photoreactivation seems to be a balance between the slight injurious effect produced by the visible light or UV of long wave lengths and the injury produced by short wave length UV. 10. Possible reasons for the large number of quanta of photoreactivating light required per quantum of short UV are discussed.     

Auslösung von Elementarprozessen durch einzelne Lichtquanten im Fliegenauge

Summary Light quanta impinging upon the photopigments located in the rhabdomeric receptor structures of the fly's compound eyes trigger photochemical reactions which in turn elicit miniature receptor potentials (bumps). The paper mainly deals with the problem whether a single quantum of light is sufficient, or whether a coincidence of quanta and/or elementary photochemical events is necessary to trigger a miniature receptor potential.The experiments were based on tests of the optomotor responses of fixed flying flies suspended in a rotating patterned cylinder with periodic distributions of inner surface brightness. The tests were made under two different light programs: 1) Illumination constant in time 2) Illumination by periodic light pulse sequences with various frequencies. Average light fluxes absorbed by the receptors were equal in both programs. Theoretical considerations lead to the following conclusions: The strength of the optomotor responses to the light programs 1 and 2 should not differ from each other in the case of single quantum processes. However for multiquantum processes light program 2 should be more effective than light program 1 as it favours the coincidence of quantum absorptions per unit time. But these theoretical conclusions are valid only if two conditions are fulfilled in the experiments: a) The pulse frequency of light program 2 has to be kept below a certain limit which is determined by the kinetics of the photochemical systems. Otherwise light program 2 gets averaged in time and in principle can be not more effective than light program 1. b) The rates of quanta absorbed by the receptors have to be kept low enough to guarantee that the concentration of unbleached pigment molecules remains practically unchanged as compared with the concentration in darkness. Accordingly the test experiments were carried out with light pulse frequencies ranging from 500 to 1/120 cycles per second. Intensities were used which corresponded to an average quantum flux effective for one rhabdomeric structure ranging between 10 and 250 quanta per second.The interpretation of the experimental results is in accordance with the hypothesis that one single quantum of light is sufficient to trigger an elementary photochemical reaction and that in turn one single photochemical event can elicit a miniature receptor potential. At present time the experiments do not allow conclusions about the possible occurrence of coincidence-functions of synapses at the level of the first optical ganglion which receive their information via fibers leading off from the receptors.In one of the appendices of the paper, the transinformation flux into a receptor is calculated, taking into consideration the Poisson noise of the quanta disrupting the signal at extremely low quantum rates.

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Ein Teil der in dieser Arbeit abgedruckten Ergebnisse wurde bereits in zwei vorläufigen Mitteilungen publiziert, Reichardt (1965, 1966).     

Morphology and mosaic of on- and off-beta cells in the cat retina and some functional considerations

The beta type of ganglion cell can be subdivided in Golgi-stained whole mounts of the cat retina according to the branching level of the dendritic tree in the inner plexiform layer. The dendritic branching level of on-beta cells is nearer to the cell body; that of off-beta cells is about 10 micrometers further outwards. After horseradish peroxidase (HRP) injection into the lateral geniculate nucleus all beta cells were labelled. In this way it is shown that about 55% of all ganglion cells, irrespective of retinal topography, are beta cells. The spatial distribution of on- and off-beta cells was studied from the HRP-labelled material. On-beta cells form a lattice with regular inter-cell spacings; off-beta cells are also regularly arrayed. The two lattices are superimposed independently of each other. Beta cells are commonly assumed to be associated with the resolution of fine detail in the cat vision system. The mosaic of beta cells imposes some constraints and permits some predictions to be made with respect to the cat's visual discrimination.     

Multiplication and refractoriness in the cat's retinal-ganglion-cell discharge at low light levels

Measurements of the pulse-interval distribution and pulse-number distribution for cat retinal ganglion cells in darkness and light have been carried out by Barlow, Levick, and Yoon. The experimental results for an on-center brisk-sustained cell are in accord with a mathematical model incorporating four features: Poisson quantum fluctuations, additive dark noise, multiplication noise (random multiple neural spikes per absorbed quantum), and refractoriness. The data cannot be properly explained by a model lacking any one of these features. Parameters extracted from the model are in good agreement with physiological values.     

Measurement error and confidence intervals for ROC curves

Measurement error in a continuous test variable may bias estimates of the summary properties of receiver operating characteristics (ROC) curves. Typically, unbiased measurement error will reduce the diagnostic potential of a continuous test variable. This paper explores the effects of possibly heterogenous measurement error on estimated ROC curves for binormal test variables. Corrected estimators for specific points on the curve are derived under the assumption of known or estimated measurement variances for individual test results. These estimators and associated confidence intervals do not depend on normal assumptions for the distribution of the measurement error and are shown to be approximately unbiased for moderate size samples in a simulation study. An application from a study of emerging imaging modalities in breast cancer is used to demonstrate the new techniques.     

A comparative and quantitative study of small intensely fluorescent (SIF) cells in the sympathetic ganglia of some small mammals

This comparative study of the number of SIF cells in the ganglions of the rat, cat, rabbit, mouse and hamster has confirmed that the mean number of SIF cells in the same ganglion of different species varies greatly, for instance in the superior cervical ganglion (SCG) of the rat and the cat, in the stellate ganglion of the cat and the mouse, or in the inferior mesenteric ganglion of the hamster and the other species. There is also considerable variability among individuals of the same animal species. In the SCG, the only ganglion for which there are data on the number of neurons, the ratio of SIF cells to neurons is around 1% in the rat, 0.2% in the rabbit, 0.3% in the mouse and 0.05% in the cat, i.e. a twenty-fold difference between the cat and the rat. Williams et al. (1975) distinguished type 1 SIF cells, corresponding to interneurons, from type 2, which are purely endocrine cells. Type 2 appears to be predominant in all ganglia, except the rabbit SCG where type 1 is highly predominant, and in all species, except the rat, in which this distinction is not applicable. The possible implications of these data on ganglionic functioning are discussed.     

ROC graphs for assessing the ability of a diagnostic marker to detect three disease classes with an umbrella ordering

Receiver operating characteristic (ROC) curves and the area under these curves are commonly used to assess the ability of a continuous diagnostic marker (e.g., DNA methylation markers) to correctly classify subjects as having a particular disease or not (e.g., cancer). These approaches, however, are not applicable to settings where the gold standard yields more than two disease states or classes. ROC surfaces and the volume under the surfaces have been proposed for settings with more than two disease classes. These approaches, however, do not allow one to assess the ability of a marker to differentiate two disease classes from a third disease class without requiring a monotone order for the three disease classes under study. That is, existing approaches do not accommodate an umbrella ordering of disease classes. This article proposes the construction of an ROC graph that is applicable for an umbrella ordering. Furthermore, this article proposes that a summary measure for this umbrella ROC graph can be used to summarize the classification accuracy, and corresponding variance estimates can be obtained using U-statistics theory or bootstrap methods. The proposed methods are illustrated using data from a study assessing the ability of a DNA methylation marker to correctly classify lung specimens into three histologic classes: squamous cell carcinoma, large cell carcinoma, and nontumor lung.     

Rapid determination of enzyme kinetics from fluorescence: overcoming the inner filter effect

Fluorescence change is convenient for monitoring enzyme kinetics. Unfortunately, it loses linearity as the absorbance of the fluorescent substrate increases with concentration. When the sum of absorbance at excitation and emission wavelengths exceeds 0.08, this inner filtering effect (IFE) alters apparent initial velocities, K(m), and k(cat). The IFE distortion of apparent initial velocities can be corrected without doing fluorophore dilution assays. Using the substrate's extinction coefficients at excitation and emission wavelengths, the inner filter effect can be modeled during curve fitting for more accurate Michaelis-Menten parameters. A faster and simpler approach is to derive k(cat) and K(m) from progress curves. Strategies to obtain reliable and reproducible estimates of k(cat) and K(m) from only two or three progress curves are illustrated using matrix metalloproteinase 12 and alkaline phosphatase. Accurate estimates of concentration of enzyme-active sites and specificity constant k(cat)/K(m) (from one progress curve with [S]相似文献   

The morphology and topographic distribution of substance-P-like immunoreactive amacrine cells in the cat retina

In cat retinal wholemounts, substance-P-like immunoreactivity (SP-IR) was localized in a distinct population of amacrines whose cell bodies were normally placed in the ganglion cell layer. Although displaced amacrines accounted for 80-95% of the SP-IR amacrines in peripheral retina, this proportion decreased considerably within the area centralis, accounting for 50-80% of the labelled cells at maximum density. The SP-IR cells in both the inner nuclear and ganglion cell layers gave rise to well-defined varicose dendrites of uniform appearance that stratified around 60% depth (S3/S4) of the inner plexiform layer. In addition, sparse fine dendrites in stratum 1 (S1) could sometimes be traced to inner nuclear cells and occasionally to displaced amacrines. The combined SP-IR cell density ranged from less than 50 cells mm-2 in the far periphery to more than 500 cells mm-2 in the area centralis; the maximum density showed little individual variation despite wide differences in the proportion of displaced cells. The 39,000 SP-IR amacrines in a mapped retina had a triangular topographic distribution, with intermediate isodensity lines extending vertically in superior retina and horizontally along both arms of the visual streak. Colocalization experiments established that all SP-IR cells in cat retina showed GABA-like immunoreactivity, and that the SP-IR amacrines were quite distinct from the cholinergic amacrines identified by choline acetyltransferase immunohistochemistry.     

Timing of quantal release from the retinal bipolar terminal is regulated by a feedback circuit

In isolation, a presynaptic terminal generally releases quanta according to Poisson statistics, but in a circuit its release statistics might be shaped by synaptic interactions. We monitored quantal glutamate release from retinal bipolar cell terminals (which receive GABA-ergic feedback from amacrine cells) by recording spontaneous EPSCs (sEPSCs) in their postsynaptic amacrine and ganglion cells. In about one-third of these cells, sEPSCs were temporally correlated, arriving in brief bursts (10-55 ms) more often than expected from a Poisson process. Correlations were suppressed by antagonizing the GABA(C) receptor (expressed on bipolar terminals), and correlations were induced by raising extracellular calcium or osmolarity. Simulations of the feedback circuit produced "bursty" release when the bipolar cell escaped intermittently from inhibition. Correlations of similar duration were present in the light-evoked sEPSCs and spike trains of sluggish-type ganglion cells. These correlations were suppressed by antagonizing GABA(C) receptors, indicating that glutamate bursts from bipolar terminals induce spike bursts in ganglion cells.     

Spatial properties of goldfish ganglion cells

We systematically classified goldfish ganglion cells according to their spatial summation properties using the same techniques and criteria used in cat and monkey research. Results show that goldfish ganglion cells can be classified as X-, Y-, or W-like based on their responses to contrast-reversal gratings. Like cat X cells, goldfish X-like cells display linear spatial summation. Goldfish Y-like cells, like cat Y cells, respond with frequency doubling at all spatial positions when the contrast-reversal grating consists of high spatial frequencies. There is also a third class of neurons, which is neither X- nor Y-like; many of these cells' properties are similar to those of the "not-X" cells found in the eel retina. Spatial filtering characteristics were obtained for each cell by drifting sinusoidal gratings of various spatial frequencies and contrasts across the receptive field of the cell at a constant temporal rate. The spatial tuning curves of the cell depend on the temporal parameters of the stimulus; at high drift rates, the tuning curves lose their low spatial frequency attenuation. To explore this phenomenon, temporal contrast response functions were derived from the cells' responses to a spatially uniform field whose luminance varied sinusoidally in time. These functions were obtained for the center, the surround, and the entire receptive field. The results suggest that differences in the cells' spatial filtering across stimulus drift rate are due to changes in the interaction of the center and surround mechanisms; at low temporal frequencies, the center and surround responses are out-of-phase and mutually antagonistic, but at higher temporal rates their responses are in-phase and their interaction actually enhances the cell's responsiveness.     

Receiver operating characteristic curves for Poisson signals

Receiver operating characteristic (ROC) curves for the detection of Poisson distributed signals were evaluated by computer simulation and found to be a set of nearly collinear points when plotted on probability axes. Approximate expressions were derived for the slope and intercept (d) of the line containing the points. The predictive value of these expressions was verified by measuring slopé and d of ROC curves produced from computer simulation of Poisson signals. Estimates of slope and d from empirical ROC curves were distributed according to the Gaussian probability density with variance approximately equal to 3/n, where n is the number of stimulus repetitions used to determine the ROC.