Visual apparent motion and some preferred paths in the rotation group SO(3)

The sequential presentation of two distinct stimulus objects to the visual system will, under certain conditions, induce an apparentmotion effect, called beta motion, in which the first object appears to smoothly transform into the second. This study is concerned with the kinds of paths selected by the visual system in effecting beta motion in which the metric structure of the object is preserved throughout. Two schemes are advanced according to which the visual system might operate. The first concentrates upon the manifold M in which the object appears to transform and the second upon the group G of transformations of M onto itself in which the particular transformation describing this motion lie. Under the identification of M with the 2-sphere S ², each scheme specifies the action-minimizing curves in the rotation group SO(3) for a particular “natural” Riemannian metric. An experiment is described in which a determination is made of the actual paths taken by an object under-going various rigid-motion beta motions. The results obtained indicate that the visual system behaves more in accordance with the second scheme than with the first. A generalization of this result is briefly discussed.     

A Model for the Propagation of Action Potentials in Non-Uniformly Excitable Media

Electrophysiological properties of cardiac tissue change as a function of position. We define the "excitability" as the propagation velocity of an excitation pulse through the tissue, and study a simple FitzHugh-Nagumo (FHN) model of heart tissue whose excitability changes with position. The propagation velocity is shown to be a good continuous measure of the excitability for both limit cycle and excitable tissue. The influence of the spatial dependence of the excitability is examined for several normal and pathological situations. A novel transient effect is observed for a train of pulses propagating across an excitability step. Copyright 1999 Academic Press.     

Continuation and bifurcation analysis of a periodically forced excitable system

The response of an excitable cell to periodic electrical stimulation is modeled using the FitzHugh-Nagumo (FHN) system submitted to a gaussian-shaped pacing, the width of which is small compared with the action potential duration. The influence of the amplitude and the period of the stimulation is studied using numerical continuation and bifurcation techniques (AUTO97 software). Results are discussed in the light of prior experimental and theoretical findings. In particular, agreement with the documented behavior of periodically stimulated cardiac cells and squid axons is discussed. As previously reported, we find many different "M:N" periodic solutions, period-doubling sequences leading to seemingly chaotic regimes, and bistability phenomena. In addition, the use of continuation techniques has allowed us to track unstable solutions of the system and thus to determine how the different stable rhythms are connected with each other in a bifurcation diagram. Depending on the stimulus amplitude, the aspect of the bifurcation diagram with the stimulus period as main varying parameter can vary from very simple to very complex. In its most developed structure, this bifurcation diagram consists of a main "tree" of period-2(P) branches, where the 1:1, 1:0, 2:2, 2:1,... rhythms are located, and of several closed loops made up of period-{N x 2(P)} branches (N>2), isolated from each other and from the main tree. It is mainly on such loops that N:1 rhythms (N>2) on one hand, and N:N-1 or Wenckebach rhythms (N>2) on the other hand, are located. Stable M:N and M:N-1 rhythms (M>or=N) can be found on the same branch of solutions. They are separated by a region of unstable solutions at small stimulus amplitudes, but this region shrinks gradually as the stimulus amplitude is raised, until it finally disappears. We believe that this property is related to the excitability characteristics of the FHN system. It would be interesting to know if it has any correspondence in the behavior of real excitable cells.     

Synergistic inhibition of the maximum conductance of Kv1.5 channels by extracellular K+ reduction and acidification

Voltage-gated potassium (Kv) channels exist in the membranes of all living cells. Of the functional classes of Kv channels, the Kv1 channels are the largest and the best studies and are known to play essential roles in excitable cell function, providing an essential counterpoin to the various inward currents that trigger excitability. The serum potassium concentration [K _o ⁺ ] is tightly regulated in mammals and disturbances can cause significant functional alterations in the electrical behavior of excitable tissues in the nervous system and the heart. At least some of these changes may be mediated by Kv channels that are regulated by changes in the extracellular K⁺ concentration. As well as changes in serum [K _o ⁺ ], tissue acification is a frequent pathological condition known to inhibit Shaker and Kv1 voltage-gated potassium channels. In recent studies, it has become recognized that the acidification-induced inhibition of some Kv1 channels is K _o ⁺ -dependent, and the suggestion has been made that pH and K _o ⁺ may regulate the channels via a common mechanism. Here we discuss P/C type inactivation as the common pathway by which some Kv channels become unavailable at acid pH and lowered K _o ⁺ . It is suggested that binding of protons to a regulatory site in the outer pore mouth of some Kv channels favors transitions to the inactivated state, whereas K⁺ ions exert countereffects. We suggest that modulation of the number of excitable voltage-gated K⁺ channels in the open vs inactivated states of the channels by physiological H⁺ and K⁺ concentrations represents an important pathway to control Kv channel function in health and disease.     

The mammalian glycine receptor: biology and structure of a neuronal chloride channel protein

Glycine is a major inhibitory neurotransmitter in the central nervous system (CNS) of vertebrates and invertebrates. The postsynaptic receptor for this amino acid is an oligomeric glycoprotein which, upon binding of glycine, transiently forms an anion-selective transmembrane channel. Agonist-mediated receptor activation is antagonized by strychnine, a high-affinity ligand of the glycine receptor (GlyR). Biochemical and immunological data show that affinity-purified preparations of the mammalian GlyR contain three polypeptides of M_r 48,000, 58,000 and 93,000. These polypeptides have different functional properties and/or topologies in the postsynaptic membrane of the glycinergic synapse. The primary sequence of the M_r 48,000 subunit deduced by cDNA cloning exhibits structural and amino-acid homology to nicotinic acetylcholine and GABA_a receptor proteins, indicating a common evolutionary relationship between the different neurotransmitter-gated ion channels of excitable membranes. Monoclonal antibodies against the GlyR allow its histochemical localization in different regions of the CNS. GlyR deficiencies have been implicated in the pathogenesis of spasticity and spinal cord degeneration in mouse and man.     

Integrate-and-fire models with nonlinear leakage

Can we express biophysical neuronal models as integrate-and-fire (IF) models with leakage coefficients which are no longer constant, as in the conventional leaky IF model, but functions of membrane potential and other biophysical variables? We illustrate the answer to this question using the FitzHugh-Nagumo (FHN) model as an example. A novel IF type model, the IF-FHN model, which approximates to the FHN model, is obtained. The leakage coefficient derived in the IF-FHN model has nonmonotonic relationship with membrane potential, revealing at least in part the intrinsic mechanisms underlying the FHN models. The IF-FHN model correspondingly exhibits more complex behaviour than the standard IF model. For example, in some parameter regions, the IF-FHN model has a coefficient of variation of the output interspike interval which is independent of the number of inhibitory inputs, being close to unity over the whole range, comparable to the FHN model as we noted previously (Brown et al., 1999).     

Induced pacemaker activity on toad skin

The electrical transients produced on the isolated abdominal skin obtained from Bufo arenarum Hensel, under the influence of inward current pulses of constant intensity have been studied. When both faces of the skin are bathed with Ringer''s solution, short pulses of inward current give rise to transient variations of the potential difference between both faces of the skin with "all-or-nothing" characteristics (action potentials, AP). When the outer face is bathed with a modified Ringer solution with low sodium content (2.4 mM), the transients are longer and they are only evident when the pulse is several hundred milliseconds long. With even longer pulses (several seconds) a repetitive activity can be elicited, with the electrical characteristics of a "pacemaker" activity. In all these "excitability" phenomena Na⁺ may be replaced by Li⁺ in the outer solution. The logarithm of the duration of AP''s is inversely related to the logarithm of the increase in concentration of Na⁺ or Li⁺ in the solution bathing the external face of the skin. The duration of AP''s is increased when the Ca⁺⁺ concentration in the outer solution is raised. This effect is more evident with low sodium concentration on the outside. The evolution of the slope conductance during repetitive activity has been determined. The site and mechanisms of the "excitable" behavior of the skin and the induced repetitive activity are discussed. Under the experimental conditions employed the behavior of the skin is compared with that of normally excitable plasma membranes.     

Statistical Distance as a Measure of Physiological Dysregulation Is Largely Robust to Variation in Its Biomarker Composition

Physiological dysregulation may underlie aging and many chronic diseases, but is challenging to quantify because of the complexity of the underlying systems. Recently, we described a measure of physiological dysregulation, D_M, that uses statistical distance to assess the degree to which an individual’s biomarker profile is normal versus aberrant. However, the sensitivity of D_M to details of the calculation method has not yet been systematically assessed. In particular, the number and choice of biomarkers and the definition of the reference population (RP, the population used to define a “normal” profile) may be important. Here, we address this question by validating the method on 44 common clinical biomarkers from three longitudinal cohort studies and one cross-sectional survey. D_Ms calculated on different biomarker subsets show that while the signal of physiological dysregulation increases with the number of biomarkers included, the value of additional markers diminishes as more are added and inclusion of 10-15 is generally sufficient. As long as enough markers are included, individual markers have little effect on the final metric, and even D_Ms calculated from mutually exclusive groups of markers correlate with each other at r~0.4-0.5. We also used data subsets to generate thousands of combinations of study populations and RPs to address sensitivity to differences in age range, sex, race, data set, sample size, and their interactions. Results were largely consistent (but not identical) regardless of the choice of RP; however, the signal was generally clearer with a younger and healthier RP, and RPs too different from the study population performed poorly. Accordingly, biomarker and RP choice are not particularly important in most cases, but caution should be used across very different populations or for fine-scale analyses. Biologically, the lack of sensitivity to marker choice and better performance of younger, healthier RPs confirm an interpretation of D_M physiological dysregulation and as an emergent property of a complex system.     

Dietary analysis reveals differences in the prey use of two sympatric bat species

One mechanism for morphologically similar and sympatric species to avoid competition and facilitate coexistence is to feed on different prey items within different microhabitats. In the current study, we investigated and compared the diet of the two most common and similar‐sized bat species in Japan—Murina ussuriensis (Ognev, 1913) and Myotis ikonnikovi (Ognev, 1912)—to gain more knowledge about the degree of overlap in their diet and their foraging behavior. We found that both bat species consumed prey from the orders of Lepidoptera and Diptera most frequently, while the proportion of Dipterans was higher in the diet of M. ikonnikovi. Furthermore, we found a higher prey diversity in the diet of M. ikonnikovi compared to that of M. ussuriensis that might indicate that the former is a more generalist predator than the latter. In contrast, the diet of M. ussuriensis contained many Lepidopteran families. The higher probability of prey items likely captured via gleaning to occur in the diet of M. ussuriensis in contrast to M. ikonnikovi indicates that M. ussuriensis might switch between aerial‐hawking and gleaning modes of foraging behavior. We encourage further studies across various types of habitats and seasons to investigate the flexibility of the diet composition and foraging behavior of these two bat species.     

Collision of two action potentials in a single excitable cell

BackgroundIt is a common incident in nature, that two waves or pulses run into each other head-on. The outcome of such an event is of special interest, because it allows conclusions about the underlying physical nature of the pulses. The present experimental study dealt with the head-on meeting of two action potentials (AP) in a single excitable plant cell (Chara braunii internode).MethodsThe membrane potential was monitored with multiple sensors along a single excitable cell. In control experiments, an AP was excited electrically at either end of the cell cylinder. Subsequently, stimuli were applied simultaneously at both ends of the cell in order to generate two APs that met each other head-on.ResultsWhen two action potentials propagated into each other, the pulses did not penetrate but annihilated (N = 26 experiments in n = 10 cells).ConclusionsAPs in excitable plant cells did not penetrate upon meeting head-on. In the classical electrical model, this behavior is specifically attributed to relaxation of ion channel proteins. From an acoustic point of view, annihilation can be viewed as a result of nonlinear material properties (e.g. a phase change).General significanceThe present results suggest that APs in excitable animal and plant cells belong to a similar class of nonlinear phenomena. Intriguingly, other excitation waves in biology (intracellular waves, cortical spreading depression, etc.) also annihilate upon collision and are thus expected to follow the same underlying principles as the observed action potentials.     

Odor of achlorophyllous plants’ seeds drives seed‐dispersing ants

Seed dispersal by ants is an important means of migration for plants. Many myrmecochorous plants have specialized appendages in their seeds called elaiosome, which provides nutritional rewards for ants, and enable effective seed dispersal. However, some nonmyrmecochorous seeds without elaiosomes are also dispersed by ant species, suggesting the additional mechanisms other than elaiosomes for seed dispersal by ants. The seeds of the achlorophyllous and myco‐heterotrophic herbaceous plant Monotropastrum humile are very small without elaiosomes; we investigated whether odor of the seeds could mediate seed dispersal by ants. We performed a bioassay using seeds of M. humile and the ant Nylanderia flavipes to demonstrate ant‐mediated seed dispersal. We also analyzed the volatile odors emitted from M. humile seeds and conducted bioassays using dummy seeds coated with seed volatiles. Although elaiosomes were absent from the M. humile seeds, the ants carried the seeds to their nests. They also carried the dummy seeds coated with the seed volatile mixture to the nest and left some dummy seeds inside the nest and discarded the rest of the dummy seeds outside the nest with a bias toward specific locations, which might be conducive to germination. We concluded that, in M. humile seeds, volatile odor mixtures were sufficient to induce seed‐carrying behavior by the ants even without elaiosomes.     

Molecular and epidemiological characterization of recurrent Mycobacterium ulcerans infections in Benin

BackgroundBuruli ulcer is a neglected tropical disease caused by Mycobacterium ulcerans, an environmental mycobacterium. Although transmission of M. ulcerans remains poorly understood, the main identified risk factor for acquiring Buruli ulcer is living in proximity of potentially contaminated water sources. Knowledge about the clinical features of Buruli ulcer and its physiopathology is increasing, but little is known about recurrence due to reinfection.Methodology/Principal findingsWe describe two patients with Buruli ulcer recurrence due to reinfection with M. ulcerans, as demonstrated by comparisons of DNA from the strains isolated at the time of the first diagnosis and at recurrence. Based on the spatial distribution of M. ulcerans genotypes in this region and a detailed study of the behavior of these two patients with respect to sources of water as well as water bodies and streams, we formulated hypotheses concerning the sites at which they may have been contaminated.Conclusions/SignificanceSecond episodes of Buruli ulcer may occur through reinfection, relapse or a paradoxical reaction. We formally demonstrated that the recurrence in these two patients was due to reinfection. Based on the sites at which the patients reported engaging in activities relating to water, we were able to identify possible sites of contamination. Our findings indicate that the non-random distribution of M. ulcerans genotypes in this region may provide useful information about activities at risk.     

描述神经元相互作用的非线性动力学方程的解析解

神经系统是由大量神经元构成的非线性动力系统,动力学行为十分复杂ＦＨＮ模型提供了在该系统中观察时间周期振荡这种非线性现象的实验证据．本文利用扰动法从理论上求出了ＦＨＮ模型所给出的非线性动力学方程的解析解,为进一步深入研究神经系统的动力学行为提供了理论依据     

Rotating wave solutions of the FitzHugh–Nagumo equations

This paper will treat the bifurcation and numerical simulation of rotating wave (RW) solutions of the FitzHugh-Nagumo (FHN) equations. These equations are often used as a simple mathematical model of excitable media. The dependence of the solutions on a uniformly applied current, and also on the diffusion coefficients or domain size will be studied. Ranges of applied current and/or diffusion coefficients in which RW solutions are observed will be described using bifurcation theory and continuation methods. The bifurcation of time-periodic solutions of these FHN equations without diffusion is described first. Similar methods are then used to find RW solutions on a circular ring and numerical simulations are described. These results are then extended to investigate RW solutions on annular rings of finite cross-section. Scaling arguments are used to show how the existence of solutions depends on either the diffusion coefficient or on the size of the region.     

Subunit structure of three glyceraldehyde 3-phosphate dehydrogenases of some flowering plants.

A procedure is described for the purification of three glyceraldehyde phosphate dehydrogenases from a batch of beet leaves. Glyceraldehyde 3-phosphate:NADP⁺ reductase, nonphosphorylating (EC 1.2.1.9) has been purified over 1500-fold. The M_r of this enzyme is 190,000 and its subunits have an M_r of 53,000, suggesting a tetramer as the active form. Its pI is 6.0. Cytosolic glyceraldehyde 3-phosphate dehydrogenase, NAD dependent (EC 1.2.1.12), has an M_r of 145,000 and subunits of M_r 37,000. It is dissociated to inactive dimers by ATP, whereas NAD⁺ in the presence of reductant promotes its reactivation. The amino acid composition is related to glyceraldehyde 3-phosphate dehydrogenases from animal sources and is most similar to pea seed glyceraldehyde 3-phosphate dehydrogenase. The enzyme exhibits a range of pI values from 5 to 7, but a second electrofocusing in the presence of dithioerythritol results in a single main form with pI 5.33, consistent with the behavior in polyacrylamide and cellulose acetate gel electrophoresis. Chloroplast NAD(P)-glyceraldehyde 3-phosphate dehydrogenase (EC 1.2.1.13) has been obtained from beet, pea, Ranunculus, Arum, and maize leaves. The stable form is an oligomer of about 800,000 M_r (±10%), while a minor, possibly damaged fraction elutes as a retarded peak from agarose columns. The M_r 800,000 form is reversibly dissociated to protomers of M_r 160,000 by NADP⁺, with increase of apparent NADP-dependent activity. Two subunits are present in similar amounts in all association states and after all treatments: α with M_r 36,000, and β with M_r 41,000. The form found in density gradient ultracentrifugation has an M_r of 390,000. Isoelectric points of the various forms lie between pH 4.1 and 4.7 for all species, with a main peak usually at pI 4.45. The amino acid composition of beet chloroplast glyceraldehyde phosphate dehydrogenase is not closely related to that of beet leaf NAD-dependent glyceraldehyde 3-phosphate dehydrogenase.     

Response of Black-Capped Chickadees to House Finch Mycoplasma gallisepticum

Tests for the presence of pathogen DNA or antibodies are routinely used to survey for current or past infections. In diseases that emerge following a host jump estimates of infection rate might be under- or overestimated. We here examine whether observed rates of infection are biased for a non-focal host species in a model system. The bacterium Mycoplasma gallisepticum is a widespread pathogen in house finches (Haemorhous mexicanus), a fringillid finch, but an unknown proportion of individuals of other songbird species are also infected. Our goal is to determine the extent to which detection of M. gallisepticum DNA or antibodies against the bacteria in a non-fringillid bird species is over- or underestimated using black-capped chickadees Poecile atricapillus, a species in which antibodies against M. gallisepticum are frequently detected in free-living individuals. After keeping black-capped chickadees in captivity for 12 weeks, during which period the birds remained negative for M. gallisepticum, four were inoculated with M. gallisepticum and four were sham inoculated in both eyes to serve as negative controls. Simultaneously we inoculated six house finches with the same isolate of M. gallisepticum as a positive control. All inoculated birds of both species developed infections detectable by qPCR in the conjunctiva. For the 6 weeks following inoculation we detected antibodies in all M. gallisepticum-inoculated house finches but in only three of the four M. gallisepticum-inoculated black-capped chickadees. All house finches developed severe eye lesions but none of the black-capped chickadees did. Modeling the Rapid Plate Agglutination test results of black-capped chickadees shows that the rate of false-positive tests would be not more than 3.2%, while the estimated rate of false negatives is 55%. We conclude that the proportion of wild-caught individuals in which we detect M. gallisepticum-specific antibodies using Rapid Plate Agglutination is, if anything, substantially underestimated.     

Dynamics of excitable elements with time-delayed coupling

Motivated by recent experiments on intracellular calcium release we study the effects of different types of coupling on the dynamics of arrays of excitable elements. We intend to find a mechanism that produces a sustained activity of the elements following a spike. While instantaneous diffusive coupling does not exhibit this property, we show that, for a coupling term with temporal delay, signals from adjacent elements can serve as mutual excitations and thus prolong the duration of the signal. We propose that time delayed coupling is generated by diffusion between isolated clusters of calcium channels. Our model could thus provide an explanation for two different release modes observed in the Ca²⁺ system.     

Neural Circuit Recording from an Intact Cockroach Nervous System

The cockroach ventral nerve cord preparation is a tractable system for neuroethology experiments, neural network modeling, and testing the physiological effects of insecticides. This article describes the scope of cockroach sensory modalities that can be used to assay how an insect nervous system responds to environmental perturbations. Emphasis here is on the escape behavior mediated by cerci to giant fiber transmission in Periplaneta americana. This in situ preparation requires only moderate dissecting skill and electrophysiological expertise to generate reproducible recordings of neuronal activity. Peptides or other chemical reagents can then be applied directly to the nervous system in solution with the physiological saline. Insecticides could also be administered prior to dissection and the escape circuit can serve as a proxy for the excitable state of the central nervous system. In this context the assays described herein would also be useful to researchers interested in limb regeneration and the evolution of nervous system development for which P. americana is an established model organism.     

Calcium wave propagation by calcium-induced calcium release: An unusual excitable system

We discuss in detail the behaviour of a model, proposed by Goldbeteret al. (1990.Proc. natn. Acad. Sci. 87, 1461–1465), for intracellular calcium wave propagation by calcium-induced calcium release, focusing our attention on excitability and the propagation of waves in one spatial dimension. The model with no diffusion behaves like a generic excitable system, and threshold behaviour, excitability and oscillations can be understood within this general framework. However, when diffusion is included, the model no longer behaves like a generic excitable system; the fast and slow variables are not distinct and previous results on excitable systems do not necessarily apply. We consider a piecewise linear simplification of the model, and construct travelling pulse and periodic plane wave solutions to the simplified model. The analogous behaviour in the full model is studied numerically. Goldbeter's model for calciuminduced calcium release is an excitable system of a type not previously studied in detail.