Activation of passive iron as a model for the excitation of nerve

The activation by cathodic polarization of passive iron in concentrated nitric acid (d = 1.4) has been investigated. 1. For short current pulses (1 msec. or less) a transient activation occurs when the product of current density and time exceeds a certain value. This limiting value is here designated as the "threshold." It is of the order of magnitude of 200 x 10(-6) coulomb/cm.(2). 2. After activation and repassivation the threshold is temporarily several times higher than before. This "refractory state" is due to the presence of nitrous acid and of oxide layers. The return of the threshold to normal values occurs in seconds or minutes, depending on the variety of iron wire. 3. Immediately after a subthreshold current pulse the threshold is reduced (summation). However, if the second pulse occurs a certain interval of time after the first the wire exhibits a certain degree of refractoriness (Gildemeister effect). 4. Oscillographic measurements reveal the existence of a latent period between the application of the stimulating pulse and the establishment of the active state. The duration of this latent period depends on the strength of the current pulse. 5. There exists a minimum current density (rheobase) below which no activation occurs however long the current is applied. Depending on the variety of iron used this current density varies between about 1 and 10 ma./cm.(2). To produce activation a current of rheobasic strength does not have to be applied for an infinite time but only for about 100 msec. (maximum utilization time). Activation becomes manifest some time after termination of the activating pulse. 6. With currents of slowly increasing strength it is possible to reach current strengths several times higher than rheobase without obtaining activation (accomodation). Accomodation to a large extent depends on the variety of iron used. Details are given for currents increasing with a time constant of 0.5 second. 7. Potential measurements on wires in the refractory state show the existence of after potentials. Wires in the refractory state which are cathodically polarized show peculiar oscillograms. Both types of experiments point to the formation of nitrous acid as an essential element in the course of events. 8. With current densities only slightly above rheobase all wires exhibit simple activations only. With higher current densities certain types of wires exhibit periodic activations. The range of current densities in which such periodic activations occur varies with the type of wire. The lower limit is sometimes quite close to the rheobase. 9. A theory of periodic activations is presented which is modelled on the theory of self-excitatory electrical oscillations. As variables describing the state of the wire, the "degree of activation" and the "degree of refractoriness" are introduced. In the physicochemical system an autocatalytic process corresponds to the "falling characteristic" of electrical oscillations. The theory leads to a rational view of the interrelations between threshold, rheobase, accomodafion, refractoriness, and rhythm. The phenomena of conduction are not discussed here but their relation to the theory is briefly touched upon.     

Residency Time as an Indicator of Reproductive Restraint in Male Burying Beetles

The cost of reproduction theory posits that there are trade-offs between current and future reproduction because resources that are allocated to current offspring cannot be used for future reproductive opportunities. Two adaptive reproductive strategies have been hypothesized to offset the costs of reproduction and maximize lifetime fitness. The terminal investment hypothesis predicts that as individuals age they will allocate more resources to current reproduction as a response to decreasing residual reproductive value. The reproductive restraint hypotheses predicts that as individuals age they will allocate fewer resources to current reproduction to increase the chance of surviving for an additional reproductive opportunity. In this study, we test for adaptive responses to advancing age in male burying beetles, Nicrophorus orbicollis. Burying beetles use facultative biparental care, but the male typically abandons the brood before the female. Previous work in male burying beetles has suggested several factors to explain variation in male residency time, but no study has observed male behavior throughout their entire reproductive lifetimes to determine whether males change residency time in an adaptive way with age. We compared residency time of males that reproduced biparentally, uniparentally, and on different-sized carcasses to determine if they used an adaptive reproductive strategy. Males did not increase residency time as they aged when reproducing biparentally, but decreased residency time with age when reproducing uniparentally. A decrease in parental care with age is consistent with a reproductive restraint strategy. When female age increased over time, males did not increase their residency time to compensate for deteriorating female condition. To our knowledge, this is the first test of adaptive reproductive allocation strategies in male burying beetles.     

A generalized model of optimal diets

The scope of current optimal diet theory is greatly restricted by certain rather stringent assumptions upon which it rests. One of these is that the type of prey a predator encounters next is not influenced by the last type encountered. The purpose of this paper is to relax this and certain other assumptions and, in so doing, arrive at a set of rules for determining the structure of the optimal diet which are analogous to, but more general than, those of current theory. Once obtained, these rules are contrasted with their earlier analogues. The major findings are that (1) prey types are not necessarily added to the optimal diet in order of decreasing energy to handling time ratio, and (2) the abundance of a type initially excluded from the diet is not necessarily irrelevant in determining whether or not that type will be included in the future. These findings show that, in the more general case considered, the structure of the optimal diet may be quite different than predicted by current theory.     

Historic and functional biology: the inadequacy of a system theory of evolution

In the first half of the 20th century neo-Kantianism in a broad sense proved itself the main conceptual and methodological background of the central European biology. As such it contributed much to the victory on the typological, idealistic-morphological and psycho-vitalistic interpretations of life. On the other hand it could not give tools to the biologists for working out a strictly darwinian evolution theory. Kant's theory of organism was conceived without evolution as a theory of the internal functionality of the organism. There was only some 'play' with the evolutionary differentiation of the species. Since then the disputes around the work of August Weismann, a synthetical evolution theory which is now behind time, arose. This theory developed from coinciding claims, elaborated by geneticists, mathematicians, and by biologists studying development, natural history and systematics. This was done under a strong influence of marxist ideas. Through the interweaving of such different approaches it was possible for this evolutionary synthesis to influence successfully the development of evolution research during more than 40 years. Philosophically speaking modern evolution theory means therefore an aversion, even a positive abolition of Kantian positions. A number of biologists however--as L. von Bertalanffy--refused to adhere to a misinterpreted Kantian methodology and oriented themselves to an approach via system theory, which obtained a place in evolution research. In fact this is a Kantian approach as well. They only repeated the Kantian dilemma of the evolution which can also be found in Lamarck and Hegel. The system theory of the functionality of the organism never reaches to the level of the evolving species, but remains always on the level of epigenetic thinking, because of its philosophical origin. This paper points out the consequences of this still current dilemma. At the same time an all-enclosing reflection on the methodological, epistemological and the important historical questions of evolutionary biology in its scientific context is recommended.     

Global change,biodiversity, and ecosystem services: What can we learn from studies of pollination?

The study of global environmental change and its effect on biodiversity and ecosystem function is at an exciting crossroads, at which ideas developed largely through theory and small-scale experiments are now being tested with ecosystem services as they are delivered to people in real-world landscapes. Pollinators and pollination are emerging as a model system for exploring these questions, which inherently required working large spatio-temporal scales. In this Invited View, I discuss current questions that are at the leading edge of this research. I first point out some surprising knowledge gaps in our understanding of pollinators’ response to global change. I then outline several ways in which current understanding of the biodiversity-ecosystem functioning relationship might be transformed by studies conducted at large spatio-temporal scales. Specifically, I propose two hypotheses that relate to the number of species required to saturate ecosystem function, and to the mechanisms through which biodiversity stabilizes ecosystem function over space or time.     

Gene mobility and the concept of relatedness

Cooperation is rife in the microbial world, yet our best current theories of the evolution of cooperation were developed with multicellular animals in mind. Hamilton’s theory of inclusive fitness is an important case in point: applying the theory in a microbial setting is far from straightforward, as social evolution in microbes has a number of distinctive features that the theory was never intended to capture. In this article, I focus on the conceptual challenges posed by the project of extending Hamilton’s theory to accommodate the effects of gene mobility. I begin by outlining the basics of the theory of inclusive fitness, emphasizing the role that the concept of relatedness is intended to play. I then provide a brief history of this concept, showing how, over the past fifty years, it has departed from the intuitive notion of genealogical kinship to encompass a range of generalized measures of genetic similarity. I proceed to argue that gene mobility forces a further revision of the concept. The reason in short is that, when the genes implicated in producing social behaviour are mobile, we cannot talk of an organism’s genotype simpliciter; we can talk only of an organism’s genotype at a particular stage in its life cycle. We must therefore ask: with respect to which stage(s) in the life cycle should relatedness be evaluated? For instance: is it genetic similarity at the time of social interaction that matters to the evolution of social behaviour, or is it genetic similarity at the time of reproduction? I argue that, strictly speaking, it is neither of these: what really matters to the evolution of social behaviour is diachronic genetic similarity between the producers of fitness benefits at the time they produce them and the recipients of those benefits at the end of their life-cycle. I close by discussing the implications of this result. The main payoff is that it makes room for a possible new mechanism for the evolution of altruism in microbes that does not require correlated interaction among bearers of the genes for altruism. The importance of this mechanism in nature remains an open empirical question.     

A theory of measurement error and its implications for spatial and temporal gradient sensing during chemotaxis. II. The effects of non-equilibrated ligand binding

Cells generally chemotax along a direction in which their receptor occupancy gradient--whether spatial or temporal--is maximum. Occupancy differentials are, however, often so small as to be masked by thermal noise; i.e., by fluctuations inherent in the stochastic nature of ligand binding. Such fluctuations therefore impose a fundamental limit on the sensitivity of a cell's ability to detect a chemoattractant gradient. In order to pursue the implications of this limit, fluctuation theories have been developed. The theories assume that the signal is some function of the receptor occupancy gradient, allow an estimate of the standard deviation about the mean signal, and permit an evaluation of, among other things, the extent to which a receptor defect can impair an effective response. Previous theories have assumed an equilibrated ligand-receptor interaction. In this paper we introduce a generalized definition of a signal caused by a receptor occupancy gradient that allows us to develop a non-equilibrium theory of thermal noise. We show that previous formulations are a special case of the current development. More specifically, we find the following. Swimming cells subject to Brownian tumbling must generally average their signals over a very long time period to achieve a signal-to-noise ratio less than or equal to 1. Spatial gradient detection is possible with ligand-receptor equilibrium constants less than 10(3)M-1, but since such ligands are rare, theory predicts that tumbling cells will generally not detect gradients by measuring spatial occupancy differentials. These conclusions hold irrespective of whether chemical equilibrium is achieved. For crawling cells not subject to Brownian tumbling, a range of affinities exists in which spatial or temporal gradient detection is possible. In general a spatial mechanism is more efficient for low affinity ligands (dissociation times less than 0.3 s), whereas a temporal mechanism is more efficient for higher K. In this case the detection of gradients in slowly dissociating ligand will be facilitated if signal processing begins prior to chemical equilibration. An important new parameter is indicated by the theory. The definitions of a temporal gradient signal is based on estimating and comparing average occupancy over two time intervals displaced by a time t1. The theory predicts an optimal t1, of order milliseconds, that leads to the shortest minimum averaging time. For t1 values at and longer than the optimum, and for all averaging times exceeding some minimum, the cell will detect a temporal signal.(ABSTRACT TRUNCATED AT 400 WORDS)     

Towards a theory of insect epidemiology

An attempt is made to consolidate and extend some of our current thoughts on insect epidemiology using graphical reproduction models. Starting with a simple model with a single equilibrium point, the elementary hypothesis is proposed that epidemics erupt when this equilibrium point increases substantially through improvement of the insect's habitat. The extension of this model to more than one coincident equilibria, some of which may be locally stable, is discussed and generalized using the theory of habitat suitability. Use of equilibrium manifolds is suggested to permit greater dimensionality. Lastly, an explanation of insect epidemics, based on the effects of time delays in the response of density-dependent processes, is elaborated and generalized. The influence of spatial dimensions and insect dispersal on the theory is discussed.     

Influence of temporal correlation of synaptic input on the rate and variability of firing in neurons

The spike trains that transmit information between neurons are stochastic. We used the theory of random point processes and simulation methods to investigate the influence of temporal correlation of synaptic input current on firing statistics. The theory accounts for two sources for temporal correlation: synchrony between spikes in presynaptic input trains and the unitary synaptic current time course. Simulations show that slow temporal correlation of synaptic input leads to high variability in firing. In a leaky integrate-and-fire neuron model with spike afterhyperpolarization the theory accurately predicts the firing rate when the spike threshold is higher than two standard deviations of the membrane potential fluctuations. For lower thresholds the spike afterhyperpolarization reduces the firing rate below the theory's predicted level when the synaptic correlation decays rapidly. If the synaptic correlation decays slower than the spike afterhyperpolarization, spike bursts can occur during single broad peaks of input fluctuations, increasing the firing rate over the prediction. Spike bursts lead to a coefficient of variation for the interspike intervals that can exceed one, suggesting an explanation of high coefficient of variation for interspike intervals observed in vivo.     

Fractal approach to the description of the auroral region

The plasma of the auroral region, where energetic particles precipitate from the magnetosphere into the ionosphere, is highly inhomogeneous and nonstationary. In this case, traditional methods of classical plasma physics turn out to be inapplicable. In order to correctly describe the dynamic regimes, transition processes, fluctuations, and self-similar scalings in this region, nonlinear dynamics methods based of the concepts of fractal geometry and percolation theory can be used. In this work, the fractal geometry and percolation theory are used to describe the spatial structure of the ionospheric conductivity. The topological properties, fractal dimensions, and connective indices characterizing the structure of the Pedersen and Hall conductivities on the nightside auroral zone are investigated theoretically. The restrictions imposed on the fractal estimates by the condition of ionospheric current percolation are analyzed. It is shown that the fluctuation scalings of the electric fields and auroral glow observed in the auroral zone fit well the restrictions imposed by the critical condition on the percolation of the Pedersen current. Thus, it is demonstrated that the fractal approach is a promising and convenient method for studying the properties of the ionosphere.     

Coordination theory of leaf nitrogen distribution in a canopy

It has long been observed that leaf nitrogen concentrations decline with depth in closed canopies in a number of plant communities. This phenomenon is generally believed to be related to a changing radiation environment and it has been suggested by some researchers that plants allocate nitrogen in order to optimize total whole canopy photosynthesis. Although optimization theory has been successfully utilized to describe a variety of physiological and ecological phenomena, it has some shortcomings that are subject to criticism (e.g., time constraints, oversimplifications, lack of insights, etc.). In this paper we present an alternative to the optimization theory of plant canopy nitrogen distribution, which we term coordination theory. We hypothesize that plants allocate nitrogen to maintain a balance between two processes, each of which is dependent on leaf nitrogen content and each of which potentially limits photosynthesis. These two processes are defined as W_c, the Rubiscolimited rate of carboxylation, and W_j, the electron transport-limited rate of carboxylation. We suggest that plants allocate nitrogen differentially to, leaves in different canopy layers in such a way that W_c and W_j remain roughly balanced. In this scheme, the driving force for the allocation of nitrogen within a canopy is the difference between the leaf nitrogen content that is required to bring W_c and W_j into balance and the current nitrogen content. We show that the daily carbon assimilation of a canopy with a nitrogen distribution resulting from this internal coordination of W_c and W_j is very similar to that obtained using optimization theory.     

Multigenerational interstitial growth of biological tissues

This study formulates a theory for multigenerational interstitial growth of biological tissues whereby each generation has a distinct reference configuration determined at the time of its deposition. In this model, the solid matrix of a growing tissue consists of a multiplicity of intermingled porous permeable bodies, each of which represents a generation, all of which are constrained to move together in the current configuration. Each generation’s reference configuration has a one-to-one mapping with the master reference configuration, which is typically that of the first generation. This mapping is postulated based on a constitutive assumption with regard to that generations’ state of stress at the time of its deposition. For example, the newly deposited generation may be assumed to be in a stress-free state, even though the underlying tissue is in a loaded configuration. The mass content of each generation may vary over time as a result of growth or degradation, thereby altering the material properties of the tissue. A finite element implementation of this framework is used to provide several illustrative examples, including interstitial growth by cell division followed by matrix turnover.     

Interpreting power spectra from nonstationary membrane current fluctuations

It is often desirable to characterize membrane current fluctuations from ionic channels under conditions in which the mean current and the variance of the fluctuations change with time. A simple theory is developed that relates the power spectrum to the channel characteristics under such nonstationary conditions, assuming that the mean current time-course has been removed from the fluctuation records. Strategies for removing the mean time-course are discussed, the spectra are calculated from simulated channel fluctuations for comparison with the theory.     

How the leopard got its spots: a phylogenetic view of the evolution of felid coat patterns

The current theory of felid coat pattern evolution proposes that the primitive pattern is one of relatively large spots that break down into smaller spots (here denoted flecks) and rosettes while at the same time leading to various striped patterns as sidelines. We have coded the coat patterns of felids into uniform, flecks, rosettes, vertical stripes, small blotches and blotches and show by mapping these character states onto phylogenies of the family that the current theory is flawed. Instead, the primitive pattern appears to be flecks and it is from this type that nearly all other types have developed. The robustness of this hypothesis is shown by the fact that it remains unchanged regardless of which of several quite different, competing phylogenies of the family is used. The pattern of transformations reconstructed is not predicted by current theories of pattern formation and we suggest that modellers pay closer attention to the phylogenetic histories of the features that they model.     

Hydrogen ion modulation of Ca channel current in cardiac ventricular cells. Evidence for multiple mechanisms

We have investigated the effects of H ions on (L-type) Ca channel current in isolated ventricular cells. We find that the current amplitude is enhanced in solutions that are alkaline relative to pH 7.4 and reduced in solutions acidic to this pH. We measured pH0-induced shifts in channel gating and analyzed our results in terms of surface potential theory. The shifts are well described by changes in surface potential caused by the binding of H ions to negative charges on the cell surface. The theory predicts a pK of 5.8 for this binding. Gating shifts alone cannot explain all of our observations on modulation of current amplitude. Our results suggest that an additional mechanism contributes to modification of the current amplitude.     

The foraging benefits of information and the penalty of ignorance

Patch use theory and the marginal value theorem predict that a foraging patch should be abandoned when the costs and benefits of foraging in the patch are equal. This has generally been interpreted as all patches being abandoned when their instantaneous intake rate equals the foraging costs. Bayesian foraging – patch departure is based on a prior estimate of patch qualities and sampling information from the current patch – predicts that instantaneous quitting harvest rates sometimes are not constant across patches but increase with search time in the patch. That is, correct Bayesian foraging theory has appeared incompatible with the widely accepted cost–benefit theories of foraging. In this paper we reconcile Bayesian foraging with cost–benefit theories. The general solution is that a patch should be left not when instantaneous quitting harvest rate reaches a constant level, but when potential quitting harvest rate does. That is, the forager should base its decision on the value now and in the future until the patch is left. We define the difference between potential and instantaneous quitting harvest rates as the foraging benefit of information, FBI. For clumped prey the FBI is positive, and by including this additional benefit of patch harvest the forager is able to reduce its penalty of ignorance.     

Endothelial nitric oxide synthase,vascular integrity and human exceptional longevity

Aging is the sum of the deleterious changes that occur as time goes by. It is the main risk factor for the development of cardiovascular disease, and aging of the vasculature is the event that most often impacts on the health of elderly people. The “free-radical theory of aging” was proposed to explain aging as a consequence of the accumulation of reactive oxygen species (ROS). However, recent findings contradict this theory, and it now seems that mechanisms mediating longevity act through induction of oxidative stress. In fact, calorie restriction ? a powerful way of delaying aging ? increases ROS accumulation due to stimulation of the basal metabolic rate; moreover, reports show that antioxidant therapy is detrimental to healthy aging. We also now know that genetic manipulation of the insulin-like-growth-factor-1/insulin signal (IIS) has a profound impact on the rate of aging and that the IIS is modulated by calorie restriction and physical exercise. The IIS regulates activation of nitric oxide synthase (eNOS), the activity of which is essential to improving lifespan through calorie restriction, as demonstrated by experiments on eNOS knockout mice. Indeed, eNOS has a key role in maintaining vascular integrity during aging by activating vasorelaxation and allowing migration and angiogenesis. In this review, we will overview current literature on these topics and we will try to convince the reader of the importance of vascular integrity and nitric oxide production in determining healthy aging.     

Can unified theories of biodiversity explain mammalian macroecological patterns?

The idea of a unifying theory of biodiversity linking the diverse array of macroecological patterns into a common theoretical framework is very appealing. We explore this idea to examine currently proposed unified theories of biodiversity (UTBs) and their predictions. Synthesizing the literature on the macroecological patterns of mammals, we critically evaluate the evidence to support these theories. We find general qualitative support for the UTBs' predictions within mammals, but rigorous testing is hampered by the types of data typically collected in studies of mammals. In particular, abundance is rarely estimated for entire mammalian communities or of individual species in multiple locations, reflecting the logistical challenges of studying wild mammal populations. By contrast, there are numerous macroecological patterns (especially allometric scaling relationships) that are extremely well characterized for mammals, but which fall outside the scope of current UTBs. We consider how these theories might be extended to explain mammalian biodiversity patterns more generally. Specifically, we suggest that UTBs need to incorporate the dimensions of geographical space, species' traits and time to reconcile theory with pattern.     

Jensen’s Inequality and the Impact of Short-Term Environmental Variability on Long-Term Population Growth Rates

It is well established in theory that short-term environmental fluctuations could affect the long-term growth rates of wildlife populations, but this theory has rarely been tested and there remains little empirical evidence that the effect is actually important in practice. Here we develop models to quantify the effects of daily, seasonal, and yearly temperature fluctuations on the average population growth rates, and we apply them to long-term data on the endangered Black-faced Spoonbill (Platalea minor); an endothermic species whose population growth rates follow a concave relationship with temperature. We demonstrate for the first time that the current levels of temperature variability, particularly seasonal variability, are already large enough to substantially reduce long-term population growth rates. As the climate changes, our results highlight the importance of considering the ecological effects of climate variability and not just average conditions.