A physical model of sodium channel gating

Most current models of membrane ion channel gating are abstract compartmental models consisting of many undefined states connected by rate constants arbitrarily assigned to fit the known kinetics. In this paper is described a model with states that are defined in terms of physically plausible real systems which is capable of describing accurately most of the static and dynamic properties measured for the sodium channel of the squid axon. The model has two components. The Q-system consists of charges and dipoles that can move in response to an electric field applied across the membrane. It would contain and may compose the gating charge that is known to transfer prior to channel opening. The N-system consists of a charged group or dipole that is constrained to move only in the plane of the membrane and thus does not interact directly with the trans-membrane electric field but can interact electrostatically with the Q-system. The N-system has only two states, its resting state (channel closed) and its excited state (channel open) and its response time is very short in comparison with that of the Q-system. On depolarizing the membrane the the N-system will not make a transition to its open state until a critical amount of Q-charge transfer has occurred. Using only four adjustable parameters that are fully determined by fitting the equilibrium properties of the model to those of the sodium channel in the squid axon, the model is then able to describe with some accuracy the kinetics of channel opening and closing and includes the Cole and Moore delay. In addition to these predictions of the behaviour of assemblies of channels the model predicts some of the individual channel properties measured by patch clamp techniques.     

A finite-difference electromagnetic deposition/thermoregulatory model: comparison between theory and measurements

The rate of the electromagnetic energy deposition and the resultant thermoregulatory response of a block model of a squirrel monkey exposed to plane-wave fields at 350 MHz were calculated using a finite-difference procedure. Noninvasive temperature measurements in live squirrel monkeys under similar exposure conditions were obtained using Vitek probes. Calculations exhibit reasonable correlation with the measured data, especially for the rise in colonic temperature.     

Invertebrate predator-prey body size relationships: an explanation for upper triangular food webs and patterns in food web structure?

Summary It has been suggested by Cohen and Newman (1985) that many of the patterns in published food webs can be derived from a stochastic model in which the species are arranged in a trophic hierarchy (the cascade model). We suggest that, if predators are larger than their prey, a trophic hierarchy can be generated on the basis of body size Empirical evidence from the literature shows that there is a positive relationship between predator and prey size for a range of invertebrates and that predators are usually larger than their prey. Using experimental data on an aquatic food web we show that body size can lead to the type of trophic hierarchy used in the cascade model, suggesting that many food web patterns may be a product of body size. This conclusion is discussed with respect to the limitations of the food web data and the relationship between static and dynamic models of web structure.     

Calculation of leaf photosynthetic parameters from light-response curves for ecophysiological applications

Measurement of the light response of photosynthetic CO₂ uptake is often used as an implement in ecophysiological studies. A method is described to calculate photosynthetic parameters, such as the maximum rate of whole electron transport and dissimilative respiration in the light, from the light response of CO₂ uptake. Examples of the light-response curves of flag leaves and ears of wheat (Triticum aestivum cv. ARKAS) are shown.Abbreviations and symbols A net photosynthesis rate - D ¹ rate of dissimilative respiration occurring in the light - f loss factor - I incident PPFD - I effective absorbed PPFD - J rate of whole electron transport - J _m maximum rate of whole electron transport - p ^c intercellular CO₂ partial pressure - PPFD photosynthetic photon flux density - q effectivity factor for the use of light (electrons/quanta) - absorption coefficient - I ^* CO₂ compensation point in the absence of dissimilative respiration (bar) - II conversion factor for calculation of CO₂ uptake from the rate of whole electron transport - convexity factor Gas-exchange rates relate to the projective area and are given in mol·m^-2·s^-1. Electron-transport rates are given in mol electrons·m^-2·s^-1; PPFD is given in mol quanta·m^-2·s^-1.     

A method for the estimation of gene flow parameters from a population structure caused by restricted gene flow and genetic drift

Summary A method has been developed which enables the estimation of the plant gene flow parameters _p (pollen dispersal), _s (seed dispersal) and t (outcrossing rate) from a selection-free continuously structured population in equilibrium. The method uses Wright's F-coefficients and introduces a new F-function which describes the genetic similarity as a function of the spatial distance. The method has been elaborated for wind pollinated plant species but can be modified for insect pollination and for animal species. In practice allozymes will provide for the necessary neutral genetic variation. The more loci used and the more intermediate the gene frequencies, the more reliable the results. For the estimation of _p and t together (when the outcrossing rate is not known) at least two chromosomally unlinked loci are required. The method for estimating _s depends on whether the plant species is annual or perennial. The mechanism of selfing has been analysed by the explanation of the value of t by three components: population density (d), pollen flow (_p) and relative fertilization potential of own pollen (Z). The concepts of neighbourhood size and isolation by distance, developed by Wright, who used a single gene flow parameter , have been extended to the situation which is realistic for seed plants, using all three parameters _p, _s and t. When _p is large with respect to _s, _s largely determines the value of the neighbourhood size, whereas _p is the most dominating factor in isolation by distance. The use of local effective population size and mean gene transport per generation instead of neighbourhood size and neighbourhood area, respectively, is proposed to avoid confusion. Computer simulations have been carried out to check the validity and the reliability of the method. Populations of 200 plants, using two or three loci with intermediate allele frequencies, gave good results in the calculation of _p with known value of t and of _s and N_e. With unknown t, especially with lower values of t, larger populations of at least 1,000 plants are necessary to obtain reasonably accurate results for _p and mean gene transport per generation M.Grassland Species Research Group Publication No. 81     

Distribution of calcium ATPase in the sarcoplasmic reticulum of fast- and slow-twitch muscles determined with monoclonal antibodies

Summary Four monoclonal antibodies against the calcium ATPase in sarcoplasmic reticulum (SR) of rabbit fast-twitch skeletal muscle were characterized using SDS-PAGE, Western blots and immunofluorescence. The ultrastructural distribution of the antigens was determined using post-embedding immunolabeling. The antibodies recognized the calcium ATPase in the SR but not in transverse (T-) tubule or plasma membranes. The antibody, D12, had the same binding affinity for the calcium ATPase from fast-twitch (rabbit sternomastoid) and slow-twitch (rabbit soleus) fibers and the affinity fell by 30% after fixation for electron microscopy in both types of muscle fiber. Ultrastructural studies revealed that the density of D12 antibody binding to the terminal cisternae membrane of extensor digitorum longus (edl) and sternomastoid fibers was on average seven times greater than in the slow-twitch soleus and semimembranosus fibers. Since the affinity of the ATPase for the antibody was the same in SR from fast- and slow-twitch muscles, the concentration of calcium ATPase in the terminal cisternae membrane of fast-twitch fibers was seven times greater than in slow-twitch fibers. This conclusion was supported by the fact that the concentration of calcium ATPase in light SR membranes was six times greater in SR from fast-twitch fibers than in SR from slow-twitch fibers. The results provide strong evidence that the different calcium accumulation rates in mammalian fast- and slow-twitch muscles are due to different concentrations of calcium ATPase molecules in the SR membrane.     

Isolation and culture of cells derived from human cerebral microvessels

Summary Microvessels were isolated from non-neoplastic human cerebral cortical fragments resected for treatment of intractable seizure disorder. The microvessels were incubated in modified Lewis medium with 20 or 30% fetal bovine serum. Within 1–2 weeks, two cell populations emerged from the isolates. One type of cells had polygonal morphology, showed density-dependent contact inhibition at confluence in vitro, showed lectin-binding characteristics of endothelium (but only moderate positivity for factor VIII antigen), demonstrated induction of -glutamyl trans-peptidase when exposed to astrocyte-conditioned media, and responded to insulin by a pronounced increase in DNA synthesis. The other variety of cells grew in vitro more slowly in irregular strands separated by clear zones, showed ultrastructural features of smooth muscle, and isoelectric focusing of cell proteins revealed the presence of smooth-musclespecific -isoactin. Both types of cells could be serially subcultured. The ability to isolate and grow the two cell types, tentatively identified as human cerebral microvascular endothelium and smooth muscle, may facilitate studies of human blood-brain barrier function as well as the pathogenesis of cerebral microangiopathies unique to the human brain.Funded by Canadian Heart Foundation, Heart and Stroke Foundation of Ontario and UCLA Biomedical Research Support Grant     

Reutilisation of tritiated thymidine in studies of regenerating skeletal muscle

Summary Two different aspects of tritiated thymidine (³H-Tdr) reutilisation in skeletal muscle were examined. Injection of a high dose (7 Ci/g) of ³H-Tdr into mice prior to crush injury of skeletal muscle resulted in heavy labelling (grain counts) of myotube nuclei 9 d later. In contrast, myotube nuclei were essentially unlabelled when a low dose (1 Ci/g) of ³H-Tdr was injected at similar times with respect to injury. It was concluded that labelling seen after the high dose was due to reutilisation of ³H-Tdr. (Such ³H-Tdr reutilisation can account for the results of Sloper et al. (1970) which previously supported the concept of a circulating muscle precursor cell.) When replicating muscle precursors were labelled directly with ³H-Tdr 48 h after injury, the percentages of labelled myotube nuclei and the distribution of nuclear grain counts were similar with either high or low dose.We also investigated whether the light labelling seen in regenerated myotube nuclei after 9 d, when ³H-Tdr had been injected before the onset of myogenesis (as found by McGeachie and Grounds 1987), was due to ³H-Tdr reutilisation or, alternatively, to proliferation of local cells in the wound which subsequently gave rise to muscle precursors. Labelling of myotube nuclei was compared in mice injected with ³H-Tdr either 2 h before, or 2 h after injury. In another experiment, mice were injected 12 h after injury and lesions sampled 1, 12 or 36 h later, to see whether local cells were replicating 12 h after injury, and what labelled cells subsequently entered to wound. No difference was found in myotube labelling between mice injected before or after injury, and no cells replicating locally in the wound at 12 h after injury were observed. The results clearly show that the light labelling was due to ³H-Tdr reutilisation.