Adaptive Spike Threshold Enables Robust and Temporally Precise Neuronal Encoding

Neural processing rests on the intracellular transformation of information as synaptic inputs are translated into action potentials. This transformation is governed by the spike threshold, which depends on the history of the membrane potential on many temporal scales. While the adaptation of the threshold after spiking activity has been addressed before both theoretically and experimentally, it has only recently been demonstrated that the subthreshold membrane state also influences the effective spike threshold. The consequences for neural computation are not well understood yet. We address this question here using neural simulations and whole cell intracellular recordings in combination with information theoretic analysis. We show that an adaptive spike threshold leads to better stimulus discrimination for tight input correlations than would be achieved otherwise, independent from whether the stimulus is encoded in the rate or pattern of action potentials. The time scales of input selectivity are jointly governed by membrane and threshold dynamics. Encoding information using adaptive thresholds further ensures robust information transmission across cortical states i.e. decoding from different states is less state dependent in the adaptive threshold case, if the decoding is performed in reference to the timing of the population response. Results from in vitro neural recordings were consistent with simulations from adaptive threshold neurons. In summary, the adaptive spike threshold reduces information loss during intracellular information transfer, improves stimulus discriminability and ensures robust decoding across membrane states in a regime of highly correlated inputs, similar to those seen in sensory nuclei during the encoding of sensory information.     

Evolution of heterogeneity (i(2)) estimates and their 95% confidence intervals in large meta-analyses

Background

Assessment of heterogeneity is essential in systematic reviews and meta-analyses of clinical trials. The most commonly used heterogeneity measure, I², provides an estimate of the proportion of variability in a meta-analysis that is explained by differences between the included trials rather than by sampling error. Recent studies have raised concerns about the reliability of I² estimates, due to their dependence on the precision of included trials and time-dependent biases. Authors have also advocated use of 95% confidence intervals (CIs) to express the uncertainty associated with I² estimates. However, no previous studies have explored how many trials and events are required to ensure stable and reliable I² estimates, or how 95% CIs perform as evidence accumulates.

Methodology/Principal Findings

To assess the stability and reliability of I² estimates and their 95% CIs, in relation to the cumulative number of trials and events in meta-analysis, we looked at 16 large Cochrane meta-analyses - each including a sufficient number of trials and events to reliably estimate I² - and monitored the I² estimates and their 95% CIs for each year of publication. In 10 of the 16 meta-analyses, the I² estimates fluctuated more than 40% over time. The median number of events and trials required before the cumulative I² estimates stayed within +/−20% of the final I² estimate was 467 and 11. No major fluctuations were observed after 500 events and 14 trials. The 95% confidence intervals provided good coverage over time.

Conclusions/Significance

I² estimates need to be interpreted with caution when the meta-analysis only includes a limited number of events or trials. Confidence intervals for I² estimates provide good coverage as evidence accumulates, and are thus valuable for reflecting the uncertainty associated with estimating I².     

Adaptation and accommodation in the squid axon

Current clamp data of the squid axon indicate that there is a qualitative change in the adaptive response as the magnitude of the current step is increased. Large stimulus currents have a strong inhibitory effect on spike generation and on active responses in general. Such currents always lead to only one action-potential and to the elimination of post-spike subthreshold oscillation. In view of a direct connection between stimulus current and potassium current I _K, the potassium channel of the Hodgkin-Huxley model is reinterpreted in a natural way such that the K⁺ conductance is directly dependent on I _K in addition to a voltage dependence. The I-_Kdependence seems to dominate whenever the stimulus current is greater than approximately 35 μA/cm². For current ramps, and large current steps, such a current formulation leads to good agreement with the data.     

A critical assessment of different measures of the information carried by correlated neuronal firing

Information theoretic measures have been proposed as a quantitative framework to clarify the role of correlated neuronal activity in the brain. In this paper we review some recent methods that allow precise assessments of the role of correlation in stimulus coding and decoding by the nervous system. We present new results that make explicit links between types of encoding and decoding mechanisms based on correlations. We illustrate the concepts by showing that the spike trains of pairs of neurons in rat somatosensory cortex can be decoded almost perfectly without including knowledge of correlation in the read-out model, although in this neural system correlations between spike times contribute appreciably to stimulus encoding.     

Statistical Determination of Rainfall-Runoff Erosivity Indices for Single Storms in the Chinese Loess Plateau

Correlation analysis is popular in erosion- or earth-related studies, however, few studies compare correlations on a basis of statistical testing, which should be conducted to determine the statistical significance of the observed sample difference. This study aims to statistically determine the erosivity index of single storms, which requires comparison of a large number of dependent correlations between rainfall-runoff factors and soil loss, in the Chinese Loess Plateau. Data observed at four gauging stations and five runoff experimental plots were presented. Based on the Meng’s tests, which is widely used for comparing correlations between a dependent variable and a set of independent variables, two methods were proposed. The first method removes factors that are poorly correlated with soil loss from consideration in a stepwise way, while the second method performs pairwise comparisons that are adjusted using the Bonferroni correction. Among 12 rainfall factors, I ₃₀ (the maximum 30-minute rainfall intensity) has been suggested for use as the rainfall erosivity index, although I ₃₀ is equally correlated with soil loss as factors of I ₂₀, EI ₁₀ (the product of the rainfall kinetic energy, E, and I ₁₀), EI ₂₀ and EI ₃₀ are. Runoff depth (total runoff volume normalized to drainage area) is more correlated with soil loss than all other examined rainfall-runoff factors, including I ₃₀, peak discharge and many combined factors. Moreover, sediment concentrations of major sediment-producing events are independent of all examined rainfall-runoff factors. As a result, introducing additional factors adds little to the prediction accuracy of the single factor of runoff depth. Hence, runoff depth should be the best erosivity index at scales from plots to watersheds. Our findings can facilitate predictions of soil erosion in the Loess Plateau. Our methods provide a valuable tool while determining the predictor among a number of variables in terms of correlations.     

THEORY AND MEASUREMENT OF VISUAL MECHANISMS : I. A VISUAL DISCRIMINOMETER. II. THRESHOLD STIMULUS INTENSITY AND RETINAL POSITION

Monocular threshold stimulus intensities (ΔI_o, photons) were measured along the 0–180° meridian of human retinae for three observers. The test image was small (= 0.08°) and of short duration (= 0.20 second). ΔI_o was found to decrease as the angular distance from the fovea was increased. Actual counts of the number of retinal elements per mm.² along the 0–180° meridian (Østerberg) were compared with the obtained results. No direct correlation was found to exist between visual sensitivity and the number of retinal elements. Binocular threshold stimuli were also measured along the same meridian. The form of the function relating binocular visual sensitivity and retinal position was discovered to be essentially similar to that for monocular sensitivity, but is more symmetrical about the center of the fovea. The magnitude of the binocular measurement is in each case smaller than that of the monocular threshold stimulus intensity for the more sensitive eye. The ratio is statistically equal to 1.4 (a fact which suggests Piper''s rule). These results are shown to be consistent with the hypothesis that the process critical for the eventuation of the threshold response is localized in the central nervous system. They are not consistent with the view that the quantitative properties of visual data are directly determined by properties of the peripheral retina.     

Contributions of <Emphasis Type="Italic">I</Emphasis><Subscript>h</Subscript> to feature selectivity in layer II stellate cells of the entorhinal cortex

Stellate cells (SCs) of the entorhinal cortex generate prominent subthreshold oscillations that are believed to be important contributors to the hippocampal theta rhythm. The slow inward rectifier I _h is expressed prominently in SCs and has been suggested to be a dominant factor in their integrative properties. We studied the input-output relationships in stellate cells (SCs) of the entorhinal cortex, both in control conditions and in the presence of the I _h antagonist ZD7288. Our results show that I _h is responsible for SCs’ subthreshold resonance, and contributes to enhanced spiking reliability to theta-rich stimuli. However, SCs still exhibit other traits of rhythmicity, such as subthreshold oscillations, under I _h blockade. To clarify the effects of I _h on SC spiking, we used a generalized form of principal component analysis to show that SCs select particular features with relevant temporal signatures from stimuli. The spike-selected mix of those features varies with the frequency content of the stimulus, emphasizing the inherent nonlinearity of SC responses. A number of controls confirmed that this selectivity represents a stimulus-induced change in the cellular input-output relationship rather than an artifact of the analysis technique. Sensitivity to slow features remained statistically significant in ZD7288. However, with I _h blocked, slow stimulus features were less predictive of spikes and spikes conveyed less information about the stimulus over long time scales. Together, these results suggest that I _h is an important contributor to the input-output relationships expressed by SCs, but that other factors in SCs also contribute to subthreshold oscillations and nonlinear selectivity to slow features. Action Editor: Xiao-Jing Wang     

CRITICAL ILLUMINATION FOR RESPONSE TO FLICKERED LIGHT,WITH DRAGONFLY LARVAE (ANAX), IN RELATION TO AREA OF EYE

Arthropods with large convex eyes provide curves of critical illumination for response as a function of flicker frequency (or of visual acuity) which depart from the probability integral type characteristically found for F – log I with vertebrates. By means of experiments with Anax nymphs in which various parts of the eye have been opaqued it is shown that the special shape of the flicker curve is due to the mechanical disadvantage of the periphery of the eye in the reception of light, which is overcome by higher intensities. It is not due to a fixed spatial pattern of intrinsic individual excitabilities of the ommatidia. Reduction of retinal area decreases F_max., and increases log I for F/F_max. = 50 per cent. The direct proportionality of I_m to P.E._1I is independent of area. Certain relations of these facts to the theory of response to flicker have been discussed.     

The influence of cortical feature maps on the encoding of the orientation of a short line

The inhomogeneous distribution of the receptive fields of cortical neurons influences the cortical representation of the orientation of short lines seen in visual images. We construct a model of the response of populations of neurons in the human primary visual cortex by combining realistic response properties of individual neurons and cortical maps of orientation and location preferences. The encoding error, which characterizes the difference between the parameters of a visual stimulus and their cortical representation, is calculated using Fisher information as the square root of the variance of a statistically efficient estimator. The error of encoding orientation varies considerably with the location and orientation of the short line stimulus as modulated by the underlying orientation preference map. The average encoding error depends only weakly on the structure of the orientation preference map and is much smaller than the human error of estimating orientation measured psychophysically. From this comparison we conclude that the actual mechanism of orientation perception does not make efficient use of all the information available in the neuronal responses and that it is the decoding of visual information from neuronal responses that limits psychophysical performance. Action Editor: Terrence Sejnowski     

Plants as bioindicator for temperature interpolation purposes: Analyzing spatial correlation between botany based index of thermophily and integrated temperature characteristics

The success of interpolation techniques relies heavily on the density and regularity of field reference data points. For instance temperature interpolations in the Arctic are hampered by few and scattered meteorological stations. The major objective of this study is to analyze the spatial relationship between plants, defined in terms of an index of thermophily (I_t) and temperature distribution. The study area is located in Kongsfjorden, northwest Spitsbergen (Svalbard). A systematic recording of floristic data covering the study area was made within quadrates of 1 km × 1 km (93 units). For each of them, the I_t was calculated. I_t provides a synthetic measure by which plants are taken as temperature indicators at a long time scale. Temperature values were recorded by means of 39 temperature loggers during the summer 2000. The model for spatial interpolation of temperature was developed using multiple regression of remote sensed data (Landsat TM) and topographical features derived from a digital elevation model (DEM). Continuous temperature layers were calculated at a spatial resolution of 50 m × 50 m, and aggregated to a resolution of 1 km × 1 km in order to correspond with the observed botanical units. Different maps were produced showing spatial distribution of the modelled temperature and I_t. Correlations between the I_t and temperature values derived from the modelled temperature layers were systematically explored. Correlation between the I_t and temperatures works well as standard deviation of residues is 0.7 °C only. Highest correlations (r) of I_t and the spatial distribution of temperature were obtained for: (a) maximum average temperature for August, excluding all areas higher than 100 m above sea level (0.75), (b) average daily maximum temperature for July–October (0.67), (c) average temperature for July and August (0.64, 0.65), and (d) when temperature range is >8 °C (0.55). Areas with low correlations between I_t and temperature were mainly attributed to the fact that these measurements represent (a) different time scales and (b) different spatial scales. However, results from this study have shown that calculating I_t provide a mean for restoring selected temperature parameters and thus can contribute to fill in and extend the network of field data points for temperature interpolation purposes.     

Closed-loop Neuro-robotic Experiments to Test Computational Properties of Neuronal Networks

Information coding in the Central Nervous System (CNS) remains unexplored. There is mounting evidence that, even at a very low level, the representation of a given stimulus might be dependent on context and history. If this is actually the case, bi-directional interactions between the brain (or if need be a reduced model of it) and sensory-motor system can shed a light on how encoding and decoding of information is performed. Here an experimental system is introduced and described in which the activity of a neuronal element (i.e., a network of neurons extracted from embryonic mammalian hippocampi) is given context and used to control the movement of an artificial agent, while environmental information is fed back to the culture as a sequence of electrical stimuli. This architecture allows a quick selection of diverse encoding, decoding, and learning algorithms to test different hypotheses on the computational properties of neuronal networks.     

Upregulation of casein kinase 1ε in dorsal root ganglia and spinal cord after mouse spinal nerve injury contributes to neuropathic pain

Glycine receptors (GlyRs) play important roles in regulating hippocampal neural network activity and spinal nociception. Here we show that, in cultured rat hippocampal (HIP) and spinal dorsal horn (SDH) neurons, 17-β-estradiol (E₂) rapidly and reversibly reduced the peak amplitude of whole-cell glycine-activated currents (I _Gly). In outside-out membrane patches from HIP neurons devoid of nuclei, E₂ similarly inhibited I _Gly, suggesting a non-genomic characteristic. Moreover, the E₂ effect on I _Gly persisted in the presence of the calcium chelator BAPTA, the protein kinase inhibitor staurosporine, the classical ER (i.e. ERα and ERβ) antagonist tamoxifen, or the G-protein modulators, favoring a direct action of E₂ on GlyRs. In HEK293 cells expressing various combinations of GlyR subunits, E₂ only affected the I _Gly in cells expressing α2, α2β or α3β subunits, suggesting that either α2-containing or α3β-GlyRs mediate the E₂ effect observed in neurons. Furthermore, E₂ inhibited the GlyR-mediated tonic current in pyramidal neurons of HIP CA1 region, where abundant GlyR α2 subunit is expressed. We suggest that the neuronal GlyR is a novel molecular target of E₂ which directly inhibits the function of GlyRs in the HIP and SDH regions. This finding may shed new light on premenstrual dysphoric disorder and the gender differences in pain sensation at the CNS level.     

On-line continuous measurement of the oxygen consumption rate in mammalian cell culture

A method for on-line, continuous measurement of the oxygen consumption rate (Io₂) by mammalian cells on a microcarrier was developed and its reliability investigated. Utilizing the periodic dissolved oxygen (DO) fluctuation in the normal on-off control of DO, on-line, continuous measurement of Io₂ was carried out in which real-time estimation of the DO saturation concentration was made by measuring the gas-phase pressure and the gas-phase oxygen concentration. It was found that the continuously measured Io₂ value was quantitatively exact and could be applied commercially using the oxidation reaction of glucose by glucose oxidase.     

The lateral root initiation index: an integrative measure of primordium formation

Background and Aims

Lateral root initiation is an essential and continuous process in the formation of root systems; therefore, its quantitative analysis is indispensable. In this study a new measure of lateral root initiation is proposed and analysed, namely the lateral root initiation index (I_LRI), which defines how many lateral roots and/or primordia are formed along a parent-root portion corresponding to 100 cortical cells in a file.

Methods

For data collection, a commonly used root clearing procedure was employed, and a new simple root clearing procedure is also proposed. The I_LRI was determined as 100dl, where d is the density of lateral root initiation events (number mm⁻¹) and l is the average fully elongated cortical cell length (mm).

Key Results

Analyses of different Arabidopsis thaliana genotypes and of a crop plant, tomato (Solanum lycopersicum), showed that I_LRI is a more precise parameter than others commonly used as it normalizes root growth for variations in cell length. Lateral root primordium density varied in the A. thaliana accessions Col, Ler, Ws, and C24; however, in all accessions except Ws, I_LRI was similar under the same growth conditions. The nitrogen/carbon ratio in the growth medium did not change the lateral root primordium density but did affect I_LRI. The I_LRI was also modified in a number of auxin-related mutants, revealing new root branching phenotypes in some of these mutants. The rate of lateral root initiation increased with Arabidopsis seedling age; however, I_LRI was not changed in plants between 8 and 14 d post-germination.

Conclusions

The I_LRI allows for a more precise comparison of lateral root initiation under different growth conditions, treatments, genotypes and plant species than other comparable methods.Key words: Arabidopsis thaliana, auxin, lateral root density, lateral root initiation index, mutant phenotype, pericycle, root architecture, root branching, root primordium, Solanum lycopersicum     

Partial pressure of oxygen in brain and peripheral nerve during damaging electrical stimulation

The studies were performed to elucidate the mechanism underlying the neural damage which may occur during prolonged electrical stimulation of either brain tissue or peripheral nerve. The partial pressure of oxygen (pO₂) was measured in the sciatic nerve and the cerebral cortex of adult cats before and during direct, local electrical stimulation of these neural tissues, using stimulus parameters capable of inducing neural injury. pO₂ was monitored by the polarographic method, employing a platinum microelectrode inserted into the tissue adjacent to or beneath the stimulating electrode. In the sciatic nerve there was no marked change in intrafascicular pO₂ in three cats upon initiation of the electrical stimulation. In a fourth animal intraneural pO₂ increased briefly upon intitiation of the stimulation. In no case did the intrafascicular compartment of nerves become significantly hypoxic. In the cerebral cortex, the start of stimulation was accompanied by a significant increase (approximately 12–15 Torr) in intracortical pO₂ beneath the stimulating electrode, and pO₂ remained at or above the pre-stimulus value for the duration of the stimulation. These results show that extracellular hypoxia is unlikely to be a significant factor in the neural injury induced in brain or peripheral nerve by prolonged electrical stimulation.     

Differential modulation of late sodium current by protein kinase A in R1623Q mutant of LQT3

AimsIn the type 3 long QT syndrome (LQT3), shortening of the QT interval by overdrive pacing is used to prevent life-threatening arrhythmias. However, it is unclear whether accelerated heart rate induced by β-adrenergic agents produces similar effects on the late sodium current (I_Na) to those by overdrive pacing therapy. We analyzed the β-adrenergic-like effects of protein kinase A and fluoride on I_Na in R1623Q mutant channels.Main methodscDNA encoding either wild-type (WT) or R1623Q mutant of hNa_v1.5 was stably transfected into HEK293 cells. I_Na was recorded using a whole-cell patch-clamp technique at 23 °C.Key findingsIn R1623Q channels, 2 mM pCPT-AMP and 120 mM fluoride significantly delayed macroscopic current decay and increased relative amplitude of the late I_Na in a time-dependent manner. Modulations of peak I_Na gating kinetics (activation, inactivation, recovery from inactivation) by fluoride were similar in WT and R1623Q channels. The effects of fluoride were almost completely abolished by concomitant dialysis with a protein kinase inhibitor. We also compared the effect of pacing with that of β-adrenergic stimulation by analyzing the frequency-dependence of the late I_Na. Fluoride augmented frequency-dependent reduction of the late I_Na, which was due to preferential delay of recovery of late I_Na. However, the increase in late I_Na by fluoride at steady-state was more potent than the frequency-dependent reduction of late I_Na.SignificanceDifferent basic mechanisms participate in the QT interval shortening by pacing and β-adrenergic stimulation in the LQT3.     

THEORY AND MEASUREMENT OF VISUAL MECHANISMS : III. ΔI AS A FUNCTION OF AREA,INTENSITY, AND WAVE-LENGTH,FOR MONOCULAR AND BINOCULAR STIMULATION

Measurements of ΔI as a function of retinal area illuminated have been obtained at various levels of standard intensity I ₁, using "white" light and light of three modal wave-lengths (λ465, 525, 680), for monocular stimulation and for simultaneous excitation of the two eyes ("binocular"), using several methods of varying (rectangular) area and retinal location, with control of exposure time. For data homogeneous with respect to method of presentation, log ΔI_m = -Z log A + C, where ΔI = Ĩ ₂ – I ₁, A is area illuminated, and C is a terminal constant (= log ΔI_m for A = 1 unit) depending on the units in which ΔI and A are expressed, and upon I ₁. The equation is readily deduced on dimensional grounds, without reference to specific theories of the nature of ΔI or of retinal area in terms of its excitable units. Z is independent of the units of I and A. Experimentally it is found to be the same for monocular and binocular excitations, as is to be expected. Also as is expected it is not independent of λ, and it is markedly influenced by the scheme according to which A is varied; it depends directly upon the rate at which potentially excitable elements are added when A is made to increase. For simultaneous excitation of the two eyes (when of very nearly equivalent excitability), ΔĪ_B is less than for stimulation of either eye alone, at all levels of I ₁, A, λ. The mean ratio (ΔĪ_L + ΔĪ_R)/2 to ΔI^B was 1.38. For white light, doubling A on one retina reduces ΔI_m in the ratio 1.21, or a little less than for binocular presentation under the same conditions. These facts are consistent with the view that the properties of ΔI are quantitatively determined by events central to the retina. The measure σ_1ΔI of organic variation in discrimination of intensities and ΔI_m are found to be in simple proportion, independent of I ₁, A, λ (and exposure time). Variability (σ_1ΔI) is not a function of the mode of presentation, save that it may be slightly higher when both retinas are excited, and its magnitude (for a given level of ΔI_m) is independent of the law according to which the adjustable intensity I ₂ is instrumentally controlled.     

THEORY AND MEASUREMENT OF VISUAL MECHANISMS : X. MODIFICATIONS OF THE FLICKER RESPONSE CONTOUR,AND THE SIGNIFICANCE OF THE AVIAN PECTEN

1. When there is projected on the retina (man, monocularly) the shadow of a grid which forms a visual field in several distinct pieces (not including the fovea in the present tests), the ordinary properties of the flicker recognition contour (F vs. log I) as a function of the light-time cycle fraction (t_L) can be markedly disturbed. In the present experiments flicker was produced by the rotation of a cylinder with opaque vertical stripes. In the absence of such a grid shadow the "cone" segments of the contours form a set in which F_max. and the abscissa of inflection are opposite but rectilinear functions of t_L, while the third parameter of the probability integral (σ''_{log I}) remains constant. This is the case also with diverse other animals tested. In the data with the grid, however, analysis shows that even for low values of t_L (up to 0.50) there occurs an enhancement of the production of elements of neural effect, so that F_max. rises rather than falls as ordinarily with increase of t_L, although σ''_{log I} stays constant and hence the total number of acting units is presumed not to change. This constitutes valid evidence for neural integration of effects due to the illumination of separated retinal patches. Beginning at t_L = 0.75, and at 0.90, the slope of the "cone" curve is sharply increased, and the maximum F is far above its position in the absence of the grid. The decrease of σ''_{log I} (the slope constant) signifies, in terms of other information, an increase in the number of acting cone units. The abscissa of inflection is also much lowered, relatively, whereas without the grid it increases as t_L is made larger. These effects correspond subjectively to the fact that at the end-point flicker is most pronounced, on the "cone" curve, along the edges of the grid shadow where contrast is particularly evident with the longer light-times. The "rod" portion of the F - log I contour is not specifically affected by the presence of the grid shadow. Its form is obtainable at t_L = 0.90 free from the influence of summating "cone" contributions, because then almost no overlapping occurs. Analysis shows that when overlapping does occur a certain number of rod units are inhibited by concurrent cone excitation, and that the mean contribution of elements of neural action from each of the non-inhibited units is also reduced to an extent depending on the degree of overlap. The isolated "rod" curve at t_L = 0.90 is quite accurately in the form of a probability integral. The data thus give a new experimental proof of the occurrence of two distinct but interlocking populations of visual effects, and experimentally justify the analytical procedures which have been used to separate them. 2. The changing form of the F - log I contour as a function of t_L, produced in man when the illuminated field is divided into parts by a shadow pattern, is normally found with the bird Taeniopygia castenotis (Gould), the zebra finch. The retina has elements of one general structural type (cones), and the F - log I contour is a simplex symmetrical probability integral. The eye of this bird has a large, complex, and darkly pigmented pecten, which casts a foliated shadow on the retina. The change in form of the F - log I curve occurs with t_L above 0,50, and at t_L = 0.90 is quite extreme. It is more pronounced than the one that is secured in the human data with the particular grid we have used, but there is no doubt that it could be mimicked completely by the use of other grids. The increase of flicker acuity due to the pecten shadow is considerable, when the dark spaces are brief relative to the light. The evidence thus confirms the suggestion (Menner) drawn from comparative natural history that the visual significance of the avian pecten might be to increase the sensory effect of small moving images. It is theoretically important that (as in the human experiment) this may be brought about by an actual decrease of effective retinal area illuminated. It is also significant theoretically that despite the presence of shadows of pecten or of grid, and of the sensory influences thus introduced, the probability integral formulation remains effective.     

Action of aldosterone on frog skin in the presence and absence of in vitro molting effects

The molting which occurs in frog skin following exposure to high concentrations of aldosterone interferes with the interpretation of physiological measurements. Exposure of skins from frogs maintained in standard smooth tanks to 5 · 10^?7 M aldosterone caused within a few hours erratic responses in short-circuit current I₀ and conductance κ followed by sustained stimulation of I₀ and κ; 10^?8 M aldosterone caused only stimulation of I₀ and κ. Storage of frogs in “rough tanks” eliminated in vitro molting on exposure to 5 · 10^?7 M aldosterone. I₀ and κ were then superimposable for 3 h, after which I₀ increased far more rapidly than κ. These results are consistent with an early effect on permeability of the active pathway and later effects on metabolism, either a direct effect on the pump or enhanced interaction between transport and metabolism.     

Equatorial x-ray intensities and isometric force levels in frog sartorius muscle.

Isometric force levels, ranging between 0 and 100% of maximal force P₀ at 2 to 3 °C, were elicited in frog sartorius muscle by means of rapidly cooling a Ringer solution containing 1·25 to 2·0 mm-caffeine. Equatorial X-ray diffraction patterns were obtained in the resting state and during contraction. The ratio of the intensities $\text{I}{}_{11}\text{I}{}_{10}$ increased with force almost linearly, with a slight upward curvature. The individual intensities for the contracting state were normalized relative to both the intensity of the undiffracted beam and the intensity of each reflection in the resting state. These normalized intensities were found to vary in a reciprocal way: I₁₀ decreased while I₁₁ increased throughout the range of forces studied.The gradual change in $\text{I}{}_{11}\text{I}{}_{10}$ with force level indicates that this ratio is a sensitive measure of the number of cross-bridges in the isometric state. A two-state model in which myosin projections are either in a resting or attached state and in which force is proportional to the fraction of projections in the attached state was applied to the experimental data of the individual reflections. I₁₀ deviates from this model in a way that suggests that formation of the first few cross-bridges may decrease the regularity of the remaining unattached myosin projections.