Modelling the ontogeny of ectotherms exhibiting indeterminate growth

Numerous growth functions exist to describe the ontogeny of animals. Such functions (e.g., von Bertalanffy's equation, thermal-unit growth coefficient) are currently applied to ectotherms even though they fail to provide analytical expressions that adapt to a wide range of fluctuating temperatures. The underlying mechanisms responsible for the ontogeny of ectotherms exhibiting indeterminate growth have not yet been summarised in terms of a simple but meaningful mathematical equation. Here, a growth function is developed, with parameters having physical or biological interpretation that accommodates indeterminate growth under fluctuating temperatures assuming the latter vary seasonally. The equation is derived as a special case of von Bertalanffy's equation providing realistic growth trajectories throughout the ontogeny of several groups of ectotherms (R²>0.90). The results suggest that the effect of temperature on growth trajectory supersedes that of reproduction in an environment with fluctuating temperature. Furthermore, values of the allometric weight exponent (0<b<0.75) indicate that the rules of body surface and body weight do not apply under certain circumstances. Finally, the growth function circumvents problems associated with models based on thermodynamic and chemical kinetic principles (e.g., inability to predict growth of organisms in which ontogeny exceeds 3 months) and on rule of thermal summation (e.g., reliable only in a certain range of temperature). The growth function can handle a wide range of temperature fluctuations, encompass life stages and apply to key organisms in ecology, fisheries and agriculture.     

Model for calcium dependent oscillatory growth in pollen tubes

Experiments have shown that pollen tubes grow in an oscillatory mode, the mechanism of which is poorly understood. We propose a theoretical growth model of pollen tubes exhibiting such oscillatory behaviour. The pollen tube and the surrounding medium are represented by two immiscible fluids separated by an interface. The physical variables are pressure, surface tension, density and viscosity, which depend on relevant biological quantities, namely calcium concentration and thickness of the cell wall. The essential features generally believed to control oscillating growth are included in the model, namely a turgor pressure, a viscous cell wall which yields under pressure, stretch-activated calcium channels which transport calcium ions into the cytoplasm and an exocytosis rate dependent on the cytosolic calcium concentration in the apex of the cell. We find that a calcium dependent vesicle recycling mechanism is necessary to obtain an oscillating growth rate in our model. We study the variation in the frequency of the growth rate by changing the extracellular calcium concentration and the density of ion channels in the membrane. We compare the predictions of our model with experimental data on the frequency of oscillation versus growth speed, calcium concentration and density of calcium channels.     

一类受马氏调制的连续型传染病模型

本文借鉴保险上的方法来考虑这样一个传染病模型,即在一个区域中,初始有一定的传染病人,假设一方面病人不断增加,且传染率受当时病人数目的影响;另一方面病人减少（死亡或治愈）的发生频率及数目受一外界环境的影响,而外界环境假定为一有限状态的马氏过程。在这些假设下,我们得出初始状态为i时疾病灭绝的概率以及平稳状态下的疾病灭绝概率。     

Unstable, self-limiting thermochemical temperature oscillations in Macrozamia cycads

Field measurements and laboratory experiments on the Australian cycads Macrozamia lucida and Macrozamia macleayi demonstrate that their cones' diel peak thermogenic temperature increase varies systematically with cone stage, with single thermogenic temperature peaks occurring daily for up to 2 weeks and reaching 12 degrees C above ambient at midstage. The initiation, magnitude and timing of those peaks are strongly modulated by ambient temperature; the period between successive thermogenic temperature peaks is not circadian, and light is neither necessary nor sufficient to initiate a thermogenic event. A mathematical analysis is developed that provides a unified explanation of the experimental results. It describes these unstable, self-limiting thermogenic events in terms of conservation of energy and a first-order chemical reaction rate model that includes an Arrhenius equation dependence of the cone's metabolic heating rate on the cone temperature.     

Investigating the mechanisms of photosynthetic proteins using continuum electrostatics

Computational methods based on continuum electrostatics are widely used in theoretical biochemistry to analyze the function of proteins. Continuum electrostatic methods in combination with quantum chemical and molecular mechanical methods can help to analyze even very complex biochemical systems. In this article, applications of these methods to proteins involved in photosynthesis are reviewed. After giving a short introduction to the basic concepts of the continuum electrostatic model based on the Poisson-Boltzmann equation, we describe the application of this approach to the docking of electron transfer proteins, to the comparison of isofunctional proteins, to the tuning of absorption spectra, to the analysis of the coupling of electron and proton transfer, to the analysis of the effect of membrane potentials on the energetics of membrane proteins, and to the kinetics of charge transfer reactions. Simulations as those reviewed in this article help to analyze molecular mechanisms on the basis of the structure of the protein, guide new experiments, and provide a better and deeper understanding of protein functions.     

On the asymptotics of marginal regression splines with longitudinal data

There have been studies on how the asymptotic efficiency ofa nonparametric function estimator depends on the handling ofthe within-cluster correlation when nonparametric regressionmodels are used on longitudinal or cluster data. In particular,methods based on smoothing splines and local polynomial kernelsexhibit different behaviour. We show that the generalized estimationequations based on weighted least squares regression splinesfor the nonparametric function have an interesting property:the asymptotic bias of the estimator does not depend on theworking correlation matrix, but the asymptotic variance, andtherefore the mean squared error, is minimized when the truecorrelation structure is specified. This property of the asymptoticbias distinguishes regression splines from smoothing splines.     

Myosin V随机步长分布的动力学分析

Myosin V利用ATP水解所释放的自由能,朝肌动蛋白微丝正端作连续的定向运动,平均步长约为36nm。最近几年,诸多实验数据表明,myosin V步长并不固定为36nm,马达各步长值和相应步长出现概率的柱状图符合高斯分布;且在负载力大于2pN的情况下会出现“中间步长”和“后退步子”的现象。可根据已有实验数据,同时考虑马达在跃迁过程中所受的溶液摩擦阻力、常负载力和高斯随机力对其跃迁距离的影响,提出一种跃迁模型,并以此为基础对上述现象进行理论解释。     

Functional response of a parasitoid Ganaspidium utilis （Hymenoptera： Eucoilidae） on the leafminer Liriomyza trifolii （Diptera： Agromyzidae）

Functional response of a solitary, larval-pupal endoparasitoid of Liriomyza leafminers, Ganaspidium utilis Beardsley, was estimated on Liriomyza trifolii Burgess at three temperatures （17℃, 25℃, 29℃ ） and host densities. A type Ⅱ random parasitoid equation （RPE） was used to estimate instantaneous search rate and handling time. The instantaneous search rate increased as temperature increased. All of the RPE regressions obtained for functional response of G. utilis at different temperatures were significant （P〈0.01）. The slope of RPE regression lines was lower across the temperatures. At 29±2℃, the maximum number of larvae parasitized was 7.8 per day. It decreased to 7.2 larvae parasitized at 25±2℃. At 17±2℃, no significant increment of parasitization was observed due to the host density increments. The estimated handling time was lowest at 17±2℃ and highest at 25 ± 2℃, respectively. The ability of G. utilis to find and parasitize L. trifolii over a wide range of temperatures makes them a good candidate for biological control of Liriomyza leafminers.     

Standing crop and aboveground biomass partitioning of a dwarf mangrove forest in Taylor River Slough,Florida

The structure and standing crop biomass of a dwarf mangrove forest, located in the salinity transition zone ofTaylor River Slough in the Everglades National Park, were studied. Although the four mangrove species reported for Florida occurred at the study site, dwarf Rhizophora mangle trees dominated the forest. The structural characteristics of the mangrove forest were relatively simple: tree height varied from 0.9 to 1.2 meters, and tree density ranged from 7062 to 23 778 stems ha^–1. An allometric relationship was developed to estimate leaf, branch, prop root, and total aboveground biomass of dwarf Rhizophora mangle trees. Total aboveground biomass and their components were best estimated as a power function of the crown area times number of prop roots as an independent variable (Y = B × X^–0.5083). The allometric equation for each tree component was highly significant (p<0.0001), with all r² values greater than 0.90. The allometric relationship was used to estimate total aboveground biomass that ranged from 7.9 to 23.2 ton ha^–1. Rhizophora mangle contributed 85% of total standing crop biomass. Conocarpus erectus, Laguncularia racemosa, and Avicennia germinans contributed the remaining biomass. Average aboveground biomass allocation was 69% for prop roots, 25% for stem and branches, and 6% for leaves. This aboveground biomass partitioning pattern, which gives a major role to prop roots that have the potential to produce an extensive root system, may be an important biological strategy in response to low phosphorus availability and relatively reduced soils that characterize mangrove forests in South Florida.