Nonequilibrium voltage fluctuations in biological membranes. I. General framework of charge transport in discrete systems and related voltage noise

This paper continues our work on the theory of nonequilibrium voltage noise generated by electric transport processes in membranes. Introducing the membrane voltage as a further variable, a system of kinetic equations linearized in voltage is derived by which generally the time-dependent behaviour of charge-transport processes under varying voltage can be discussed. Using these equations, the treatment of voltage noise can be based on the usual master equation approach to steady-state fluctuations of scalar quantities. Thus, a general theoretical approach to nonequilibrium voltage noise is presented, completing our approach to current fluctuations which had been developed some years ago. It is explicitly shown that at equilibrium the approach yields agreement with the Nyquist relation, while at nonequilibrium this relation is not valid. A further general property of voltage noise is the reduction of low-frequency noise with increasing number of transport units as a consequence of the interactions via the electric field. In a second paper, the approach will be applied for a number of special transport mechanisms, such as ionic channels, carriers or electrogenic pumps.     

Increasing model structural complexity inhibits the growth of initial condition errors

One source of inaccuracy in non-linear deterministic ecological models is the growth of initial condition errors. A size-resolved pelagic ecosystem model is used to investigate the effects of changing model structural complexity on the growth rate of initial condition errors. Structural complexity is altered by (1) changing the number of biological size-classes; and (2) changing prey size-ranges which changes the number of linkages for the same number of size-classes. Ensembles of model runs with tiny variations in initial conditions are undertaken and member divergence used to estimate ensemble spread (a measure of the growth of initial condition errors). Increasing prey ranges and therefore the number of linkages greatly reduced the rate of growth of initial condition errors, but ecosystem behaviour is also altered, restricting the generality of the result. At more than 123 size-classes, increasing the number of size-classes while not changing either the model equations or parameters does not alter ecosystem behaviour for over 200 days. In this case, increasing structural complexity through increasing the number of size-classes did not alter the growth of initial condition errors for the first 30 days of the simulations, but afterwards reduced error growth. There are many advantages of parsimonious ecological models with small numbers of classes and linkages, but they are more likely to suffer from the growth of initial condition errors than structurally complex models.     

Slow potential changes due to transport number effects in cells with unstirred membrane invaginations or dendrites

Summary Many neurones are extremely invaginated and possess branching processes, axons and dendrites. In general, they are surrounded by a restricted diffusion space. Many of these cells exhibit large, slow potential changes during the passage of current across their membranes. Whenever currents cross membranes separating aqueous solutions, differences in transport numbers of the major permeant ions give rise to local concentration changes of these ions adjacent to the membranes, which will result in various electrical and osmotic effects. These transport number effects are expected to be enhanced by the presence of membrane invaginations. Dendrites are equivalent to reversed invaginations and there should be significant changes in concentrations of permeant ions within them. In general, the effects of such changes on the electrical response of a cell will be greater when the concentration of a major permeant ion is low. The effects have been modelled in terms of two nondimensional parameters: the invagination transport number parameter and the relative area occupied by the invaginations A. If these two parameters are known, the magnitudes and time course of the slow potential changes can immediately be estimated and the time course converted to real time, if the length of the invaginations (l) and ionic diffusion coefficient (D) within them are also known. Both analytical and numerical solutions have been given and predictions compared. It is shown that in the case of large currents and potentials the analytical solution predictions will underestimate the magnitudes and rates of onset of the voltage responses. The relative magnitude of the transport number effect within the invaginations (or dendrites) and other transport number contributions to slow potential changes have also been assessed and order-of-magnitude values of these are estimated for some biological data.     

The RCE: a Riparian, Channel, and Environmental Inventory for small streams in the agricultural landscape

1. The Riparian, Channel and Environmental (RCE) Inventory has been developed to assess the physical and biological condition of small streams in the lowland, agricultural landscape. It consists of sixteen characteristics which define the structure of the riparian zone, stream channel morphology, and the biological condition in both habitats. 2. The inventory is based on the view that in landscapes where non-point source pollution and agriculture dominate, the environmental condition of small streams can be assessed by an appraisal of the physical condition of the riparian zone and stream channel. It is assumed that disturbance of this physical structure is a major cause for reduction of stream biological structure and function. This assumption is supported by a case study using fifteen Italian stream locations in which the RCE was found to be positively correlated to the benthic macroinvertebrate community as measured by the Extended Biotic Index (r = 0.80, P < 0.001) and the Shannon Diversity Index (r = 0.73; P < 0.001). 3. The inventory is designed for quick use to cover a large number of streams in a short period of time. When used it generates a numerical score which can be used to compare the physical and biological condition between different streams within a region. The numerical score is divided into five, colour-coded classes to facilitate use in streammonitoring programmes and to allow comparison with biological indices.     

Current noise around steady states in discrete transport systems

Subject of this paper is the transport noise in discrete systems. The transport systems are given by a number (n) of binding sites separated by energy barriers. These binding sites may be in contact with constant outer reservoirs. The state of the system is characterized by the occupation numbers of particles (current carriers) at these binding sites. The change in time of the occupation numbers is generated by individual “jumps” of particles over the energy barriers, building up the flux matter (for charged particles: the electric current). In the limit n → ∞ continuum processes as e.g. usual diffusion are included in the transport model. The fluctuations in occupation numbers and other quantities linearly coupled to the occupation numbers may be treated with the usual master equation approach. The treatment of the fluctuations in fluxes (current) makes necessary a different theoretical approach which is presented in this paper under the assumption of vanishing interactions between the particles. This approach may be applied to a number of different transport systems in biology and physics (ion transport through porous channels in membranes, carrier mediated ion transport through membranes, jump diffusion e.g. in superionic conductors). As in the master equation approach the calculation of correlations and noise spectra may be reduced to the solution of the macroscopic equations for the occupation numbers. This result may be regarded as a generalization to non-equilibrium current fluctuations of the usual Nyquist theorem relating the current (voltage) noise spectrum in thermal equilibrium to the macroscopic frequency dependent admittance.The validity of the general approach is demonstrated by the calculation of the autocorrelation function and spectrum of current noise for a number of special examples (e.g, pores in membrances, carrier mediated ion transport).     

Heritability of dispersal in the great reed warbler

Dispersal is commonly considered to be a condition‐dependent behaviour with no or low heritability. Here, we show that dispersal in the great reed warbler (Acrocephalus arundinaceus) has a high heritability. Analyses of capture–recapture data of male great reed warblers gathered from the species’ whole Swedish breeding range revealed a remarkable offspring–parent resemblance in dispersal behaviour (philopatry vs. inter‐population dispersal). Also, the degree of dispersal differed between cohorts, which shows that dispersal was partly conditionally dependent. The offspring to mid‐parent estimate of heritability was 0.50. In a previous study of the same data set of male offspring, we did not detect associations between dispersal and several relevant environmental, parental and offspring condition factors. Thus, our results indicate that variation in dispersal partly has a genetic basis in great reed warblers.     

Evaluation of consistency in quantification of gene copy number by real‐time reverse transcription quantitative polymerase chain reaction and virus titer by plaque‐forming assay for human respiratory syncytial virus

The plaque‐forming assay is the standard technique for determining viral titer, and a critical measurement for investigating viral replication. However, this assay is highly dependent on experimental technique and conditions. In the case of human respiratory syncytial virus (RSV) in particular, it can be difficult to objectively confirm the accuracy of plaque‐forming assay because the plaques made by RSV are often small and unclear. In recent studies, RT‐qPCR methods have emerged as a supportive procedure for assessment of viral titer, yielding highly sensitive and reproducible results. In this report, we compare the viral replication, as determined by plaque‐forming assay, and the copy numbers of RSV genes NS1, NS2, N, and F, as determined by RT‐qPCR. Two real‐time PCR systems, SYBR Green and TaqMan probe, gave highly similar results for measurement of copy numbers of RSV N genes of virus subgroups A. We determined the RSV gene copy numbers in the culture cell supernatant and cell lysate measured at various multiplicities of infection. We found that copy number of the RSV N gene in the culture supernatant and cell lysate was highly correlated with plaque‐forming units. In conclusion, RT‐qPCR measurement of RSV gene copy number was highly dependent on viral titer, and the detailed comparison between each gene copy number and virus titer should be useful and supportive in confirming RSV plaque‐forming assay and virus dynamics. The technique may also be used to estimate the amount of RSV present in clinical specimens.

     

Enriched partial correlations in genome-wide gene expression profiles of hybrids (A. thaliana): a systems biological approach towards the molecular basis of heterosis

Heterosis is a well-known phenomenon but the underlying molecular mechanisms are not yet established. To contribute to the understanding of heterosis at the molecular level, we analyzed genome-wide gene expression profile data of Arabidopsis thaliana in a systems biological approach. We used partial correlations to estimate the global interaction structure of regulatory networks. Our hypothesis states that heterosis comes with an increased number of partial correlations which we interpret as increased numbers of regulatory interactions leading to enlarged adaptability of the hybrids. This hypothesis is true for mid-parent heterosis for our dataset of gene expression in two homozygous parental lines and their reciprocal crosses. For the case of best-parent heterosis just one hybrid is significant regarding our hypothesis based on a resampling analysis. Summarizing, both metabolome and gene expression level of our illustrative dataset support our proposal of a systems biological approach towards a molecular basis of heterosis.     

Dynamics of diluted attractor neural networks with delays

We present an analysis of the attractors of a deterministic dynamics in formal neural networks characterized by binary threshold units and a nonsymmetric connectivity. It is shown that in these networks a stored pattern or a pattern sequence is represented by a cloud of attractors rather than by a single attractor. Dilution, which we describe by a power-law scaling, and delayed couplings are shown to equip this type of network with a dynamic behaviour that is interesting enough for simplified models of biological motor systems. Received: 27 November 1992/Accepted in revised form: 22 September 1993     

Iron and Pathogenesis of Shigella: Iron Acquisition in the Intracellular Environment

Shigella species are able to grow in a variety of environments, including intracellularly in host epithelial cells. Shigella have a number of different iron transport systems that contribute to their ability to grow in these diverse environments. Siderophore iron uptake systems, heme transporters, and ferric and ferrous iron transport systems are present in these bacteria, and the genes encoding some of these systems appear to have spread among the Shigella species by horizontal transmission. Iron is not only essential for growth of Shigella but also plays an important role in regulation of metabolic processes and virulence determinants in Shigella. This regulation is mediated by the repressor protein Fur and the small RNA RyhB.     

Vocalization during Agonistic Behaviour in Cottus gobio L. (Cottidae): An Acoustic Threat Display

Agonistic behaviour in the river bullhead C. gobio consists of visual (raising gill covers and fins, lowering the head, darkening) and acoustic (single knock sounds and trains of knock sounds) threat displays, rarely followed by attacks and bites. This study investigates the relationship of vocalizations with size, dominance, territory dimensions and sex of the opponents. Four groups, each consisting of a big male, a small male and a female, were each investigated for three different days. The number of won contests of each individual, the numbers of each sound produced during these encounters and the tank part where encounters took place were determined. Subordinate fish emit fewer sounds but relatively far more trains of knock sounds than dominant ones. They produce relatively more sounds under shelters whereas dominants do this on uncovered areas. α-fish produce more calls during agonistic encounters with β-fish than Ω fish. In β-individuals no such difference was noted. Basically no sex related behaviour could be observed. In each area of the tank one individual won most contests (= territory). Dimensions of territories differed significantly between individuals in each tank (α-, β-, Ω-fish). In no case were all three individuals able to maintain territories. Relative sizes of fish correlate significantly with relative numbers of successful encounters and with territory dimensions. Furthermore, both parameters are positively correlated with the numbers of sounds emitted by an individual. Sound production in C. gobio functions as an acoustical threat display. Because of the high energy costs of sound emission underwater it might be a very effective method of assessing the fighting ability of an opponent.     

The effect of potassium diffusion through the Schwann cell layer on potassium conductance of the squid axon

Summary The accumulation of K⁺ ions in the intermembranous spaces of the Schwann cell layer during K⁺ ion current flow may lead to appreciable changes of the K⁺ equilibrium potential. Thus, for an evaluation of the K⁺ conductance of the axolemma, the transport of K⁺ ions through the Schwann cell layer has to be characterized quantitatively. In the present work this is done for a simplified model of the geometrical arrangement of the slit-like channels traversing the Schwann cell region.The K⁺ transport through the slits is treated for two cases: (a) Assuming that electro-kinetic volume flow does not affect K⁺ transport. In this case, pure diffusion of K⁺ ions accounts for their removal from the intermembranous spaces. Estimates on electro-kinetic volume flow show that this case applies to axons ofLoligo forbesi in voltage clamps of fairly small depolarizations. (b) For the case of appreciable electro-kinetic volume flow, evidence is adduced that its main effect is a widening of the slits through the Schwann cell layer. This physical situation could be treated only for the steady-state of convective diffusion of K⁺ ions in the slits.This case is applied to experiments on large depolarizing voltage clamps forLoligo pealii axons. It is shown that a widening of the slits to up to eight times the resting width is to be expected.In both cases (a) and (b), marked deviations of the K⁺ conductance of the axolemma from the Hodgkin-Huxley conductance result. The series resistance of the Schwann cell layer and the decay of after-effects of trains of action potentials are described by the theory.     

Permanent coexistence in general models of three interacting species

We address the question of the long term coexistence of three interacting species whose dynamics are governed by the ordinary differential equations x _i = X _i f _i (i = 1, 2, 3). In order for any theory in this area to be useful in practice, it must utilize as little information as possible concerning the forms of the f _i , in view of the great difficulty of determining these experimentally. Here we obtain, under rather general conditions on the equations, a criterion for judging whether the species will coexist in a biologically realistic manner. This criterion depends only on the behaviour near the one or two species equilibria of the two dimensional subsystems, the behaviour there being relatively easy to examine experimentally. We show that with the exception of one class of cases, which is a generalization of a classical example of May and Leonard [21], invasibility at each such equilibrium suitably interpreted is both necessary and sufficient for a strong form of coexistence to hold. In the exceptional case, a single additional condition at the equilibria is enough to ensure coexistence.     

Analysis of Prinobius myardi Mulsant population dynamics in a Mediterranean cork oak stand

The dehesa is a silvopastoral system of a high economic and ecological significance in the Iberian Peninsula that is protected under the EEC/92/43 Habitat Directive. One of the most serious problems the dehesa system is currently facing is oak decline. This tree decay process is largely caused by three xylophagous cerambycids of which Prinobius myardi is the least known. In this study, we used a capture-mark-recapture method to identify the models best fitting the behaviour of this species with a view to estimating basic population parameters such as survival rate (phi), recapture rate (p) and transiency index (T). Prinobius myardi adults were captured by hand following visual detection in the trees of a cork oak (Quercus suber) plot located in the close vicinity of the Doñana National Park (SW Spain). Males exhibited a constant survival rate exceeding 85.4% throughout their flight period, a maximum transiency index of 1.82% and a recapture rate ranging from 42.50% to 76.90%. These results are suggestive of a sedentary behaviour in P. myardi males. By contrast, the small number of females captured precluded calculation of the previous parameters for this gender; in any case, field observations revealed a fleeing, less sedentary behaviour with respect to the males.     

Impact of mitochondrial electric field on modal occupancy in the Fröhlich model of cellular electromagnetism

Fröhlich model describes emission of electromagnetic field in the interior of biological cells by oscillating polar units, now mostly identified with microtubule filaments. Central element of this theory is the system of rate equations for the quantum occupancy numbers n _i of collective oscillation modes. These equations describe both linear and nonlinear properties of the system; presence of the latter can lead to condensation of the incoming energy into the lowest frequency mode – a phenomenon deemed to be of major importance for cell's biochemistry, because the excited mode can engage in chemical reactions while the major part of the system remains near the equilibrium, not exposed to energetic stress. This paper explores, using a simple model, the influence of strong static electric field created by mitochondria flanking the microtubules on nonlinear interactions and, in turn, on occupancy numbers. The computed results show that simultaneous presence of both sufficient metabolic pumping and adequately elevated static electric field is necessary for the full unfolding of the hallmark properties of the Fröhlich model. It is suggested that cancer-related mitochondrial dysfunction leading to metabolic transformation has additional adverse effect mediated by diminution of static fields which in turn reduces the nonlinear processes in the Fröhlich systems, essential for energy condensation in the fundamental mode.     

Karyological Differentiation in Sapindaceae with Special Reference to Serjania and Cardiospermum

New chromosome counts for 9 species and 2 genera of Sapindaceae are presented and compared with a review of all available chromosome numbers of the family. In 4 species diploid numbers differing from previous reports are found. In 4 species of the tribe Paullinieae (S. diversiflora, S. subdentata, C. grandiflorum and C. halicacabum) detailed studies on interphase nucleus structure, condensing behaviour and chromosome banding patterns are presented. The karyological differentiation of Paullinieae is generally characterized by dysploid reduction of chromosome numbers and the increase of chromosome size. Sequential staining of nuclei with CMA/DAPI and Giemsa-C-banding demonstrates diversification of constitutive heterochromatin (= hc) and different types of chromatin organization in Serjania and Cardiospermum. The obvious lack of polyploid series and the karyological evolution within the family is discussed. The outstanding small genome size found in Cardiospermum halicacabum is considered to be due to a secondary loss of DNA in the course of the change to herbaceous growth.     

Changes in distribution and behaviour of two congeneric mayflies in a boreal river and its seasonal tributaries

Both Parameletus chelifer and P. minor had univoltine life-cycles. For a period of 6–10 months almost no nymphs of either species were found. The first nymphs appeared near midstream in winter and later in spring when the ice had broken up, they were found in great numbers close to the bank of the main river. During spring, nymphs of P. chelifer colonized the newly flooded littoral faster, and a seasonal stream in an alluvial meadow in greater numbers, than did nymphs of P. minor. Both species also colonized 10 seasonal tributaries which showed that the springtime upstream colonization was a common behaviour. During the colonization of the seasonal stream in the alluvial meadow, the diel activity pattern changed in nymphs of both species. In the main river small nymphs showed a nocturnal activity, while large nymphs were active during day-time. In the seasonal stream, both small and large nymphs showed a diurnal activity. However, when the stream was flooded, small nymphs of both species showed nocturnal activity again. In both species, diurnal activity of mature nymphs continued during emergence. Reasons for shifts in diel activity are discussed.     

Analysis and Application of an Equilibrium Model forin vitroBioassay Systems with Three Components: Receptor, Hormone and Hormone-Binding-Protein

A simple theoretical framework is presented for bioassay studies using three componentin vitrosystems. An equilibrium model is used to derive equations useful for predicting changes in biological response after addition of hormone-binding-protein or as a consequence of increased hormone affinity. Sets of possible solutions for receptor occupancy and binding protein occupancy are found for typical values of receptor and binding protein affinity constants. Unique equilibrium solutions are dictated by the initial condition of total hormone concentration. According to the occupancy theory of drug action, increasing the affinity of a hormone for its receptor will result in a proportional increase in biological potency. However, the three component model predicts that the magnitude of increase in biological potency will be a small fraction of the proportional increase in affinity. With typical initial conditions a two-fold increase in hormone affinity for its receptor is predicted to result in only a 33% increase in biological response. Under the same conditions an 11-fold increase in hormone affinity for receptor would be needed to produce a two-fold increase in biological potency. Some currently used bioassay systems may be unrecognized three component systems and gross errors in biopotency estimates will result if the effect of binding protein is not calculated. An algorithm derived from the three component model is used to predict changes in biological response after addition of binding protein toin vitrosystems. The algorithm is tested by application to a published data set from an experimental study in anin vitrosystem (Limet al., 1990,Endocrinology127,1287–1291). Predicted changes show good agreement (within 8%) with experimental observations.     

Multilayered‐Electrode‐Based Triboelectric Nanogenerators with Managed Output Voltage and Multifold Enhanced Charge Transport

The open‐circuit voltage of a triboelectric nanogenerator (TENG) increases with the tribo‐charge density and the separated distance between two tribo‐surfaces, which can reach several thousand volts and is much higher than the working voltage required by most electrical devices and energy storage units. Therefore, improving the effective efficiency of TENGs requires reducing the output voltage and enhancing the transferred charges. Here, a multilayered‐electrode‐based TENG (ME‐TENG) is developed in which the output voltage can be managed by controlling the charge flow in a process of multiple (N) steps, which results in N times lower voltage but N times higher total charge transport. The ME‐TENG is demonstrated to work in various modes, including multichannel, single‐channel, and double‐tribo‐surface structures. The effects of insulator layer thickness and total layer number on the output voltage are simulated by the finite element method. The output voltage can be modulated from 14 to 102 V by changing the insulator layer number between two adjacent working electrodes, based on which the 8‐bit logic representations of the characters in the ACSII code table are demonstrated. The ME‐TENG provides a novel method to manage the output power and has potential applications in self‐powered sensors array and human–machine interfacing with logic communications.     

Courtship Behaviour and Mating in Two Cow Dung Inhabiting Sphaerocerid Flies (Diptera: Sphaeroceridae)

Adults and larvae of Coproica lugubris and Chaetopodella scutellaris (Diptera: Sphaeroceridae) occur in great numbers on cow droppings. Courtship behaviour and copulation were analyzed and compared. Striking differences were found in the complexity and number of courtship patterns. In contrast to C. lugubris, where males usually mount females without performing any displays, courtship of Ch. scutellaris is rather complex: a male approaches a female and positions himself facing her; he then starts to circle her in a fashion very similar to a male courtship pattern in Drosophila species. Females usually respond to circling with a typical behaviour pattern I called swaying. Its function is discussed. The complex courtship behaviour of Ch. scutellaris is interpreted as a mechanism for female choice. In Ch. scutellaris copulation takes about 60 min longer than in C. lugubris, but the mechanism based upon this obvious difference is not understood. Females of both species can effectively prevent males from copulating.