Age structure in predator-prey systems: Intraspecific carnivore interaction,passive diffusion,and the paradox of enrichment

An existing arthropod predator-prey model incorporating age structure in the carnivore through the use of the von Foerster equation is extended to include the effects of intraspecific carnivore interaction and passive diffusion or migration. A linear stability analysis of the community equilibrium point of that differential-integral equation system is performed and the resulting secular equation analyzed by the method of D-partitions. These stability results are then compared to those obtained by employing an analogous differential equation model without age structure, in particular as they relate to the so-called paradox of enrichment. In the absence of passive diffusion, it is shown that, unlike for a differential equation model, the paradox of enrichment can occur even with a carnivore which exhibits intraspecific competition. This destabilizing effect of age structure is seen to occur most dramatically when interspecific interactions are large, while the effect of passive diffusion is to offset that tendency and restabilize the system. These predictions are in accordance with relevant experimental evidence involving mites.     

The hypercycle,traveling waves,and Wright's equation

A formal relation between the hypercycle equation and the delay differential equation of E. M. Wright is exhibited using a traveling waves approach. Several unsolved questions in either problem can be related and interpreted, in particular new motivation for the study of Wright's equation is obtained.     

Cellular calcium signals: nature, registration, and quantitative estimation

Calcium ions play a central role in the regulation of cellular activity. Calcium influx across the plasma membrane occurs through ion channels (voltage- and receptor-operated channels). Two intracellular channels responsible for releasing Ca2+ from the internal stores are ryanodine and IP3 receptors. Two mechanisms for Ca2+ extrusion have been identified in the sarcolemma (Ca2+ pump and Na+/Ca2+ exchanger) and one in the sarcoplasmic membrane (Ca2+ pump). Hierarchical organization of intracellular calcium signalling is presented. It is considered of opening of the single channels or of groups channels to give quarks and sparks. The methods for the determination of the intracellular Ca2+ concentration are discussed. The equation connecting [Ca2+]i with double wavelengths parameter R was obtained proceeding from three fluorescent forms of indo-1 (L, LM and LP). Using this equation permits improving calculation of [Ca2+]i.     

A classic learning opportunity from Fenn, Rahn, and Otis (1946): the alveolar gas equation

The alveolar gas equation, the focus of a classic paper by Fenn, Rahn, and Otis, provides a framework for understanding the mechanisms involved in pulmonary gas exchange as well as the limits of human performance. The classic 1946 paper by Fehn, Rahn, and Otis gives your students an opportunity to learn about the alveolar gas equation from the physiologists who pioneered it and demonstrates that mathematics and data graphics are fundamental tools with which to learn respiratory physiology. In this essay, I outline avenues of discovery by which your students can explore the alveolar gas equation. Meaningful learning stems from inspiration: to learn, you must be inspired to learn. If anyone can inspire learning in respiratory physiology, it is Wallace Fenn, Hermann Rahn, and Arthur Otis.     

Equations and calculations for fermentations of butyric acid bacteria. Reprinted from Biotechnology and Bioengineering, Vol. XXVI, Pp 174-187 (1984)

A stoichiometric equation has been derived which describes the interrelations among the various products and biomass in fermentations of butyric acid bacteria. The derivation of the equation is based on an assumed ATP yield, two biological regularities, and the biochemistry of product formation of the fermentations. The equation obeys the constraints imposed on growth and product formation by thermodynamics and the biochemical topology. The validity of the equation is tested using a variety of fermentation data from the literature. The uses, improvements, limitations, and extensions of the equation are also discussed in detail. For example, the fermentation equation is used to calculate the maximal possible yields of the main fermentation products.     

Blood flow: Theory,effective viscosity and effects of particle distribution

A study is made of blood flow by assuming that the blood constitutes a suspension of cells in plasma instead of a simple homogeneous fluid. A macroscopic theory governing the motion of plasma in a plasma-cell system is derived from the local volume averaging method for a system without mass transfer between the phases, and its characteristic length is much larger than the size of the cells. The equations governing the motion of the local averaged fluid quantities include one additional term in the equation of motion and two additional terms in the energy equation. These terms represent, respectively, the force exerted upon the fluid by the particles, and the rate of heat transfer and work kone upon the fluid by the particles. The theory is applied to obtain the effective viscosity as the explicit function of the volume concentration of the cells by assuming that the cells behave like rigid spherical particles with slip-collision, and the plasma is an compressible Newtonian fluid. Comparison with existing experimental results shows a good agreement. The theory is also used to obtain the effects of cell distribution upon the overall effective viscosity in a circular tube. The quantitative result shows that there is a decrease in overall effective viscosity as the concentration of cells increases toward the center of the tube, and the overall effective viscosity is smaller than the flow with evenly distributed cells.     

Comparison of the Schwartz and CKD-EPI Equations for Estimating Glomerular Filtration Rate in Children,Adolescents, and Adults: A Retrospective Cross-Sectional Study

Background

Estimating kidney glomerular filtration rate (GFR) is of utmost importance in many clinical conditions. However, very few studies have evaluated the performance of GFR estimating equations over all ages and degrees of kidney impairment. We evaluated the reliability of two major equations for GFR estimation, the CKD-EPI and Schwartz equations, with urinary clearance of inulin as gold standard.

Methods and Findings

The study included 10,610 participants referred to the Renal and Metabolic Function Exploration Unit of Edouard Herriot Hospital (Lyon, France). GFR was measured by urinary inulin clearance (only first measurement kept for analysis) then estimated with isotope dilution mass spectrometry (IDMS)–traceable CKD-EPI and Schwartz equations. The participants’ ages ranged from 3 to 90 y, and the measured GFRs from 3 to 160 ml/min/1.73 m². A linear mixed-effects model was used to model the bias (mean ratio of estimated GFR to measured GFR). Equation reliability was also assessed using precision (interquartile range [IQR] of the ratio) and accuracy (percentage of estimated GFRs within the 10% [P10] and 30% [P30] limits above and below the measured GFR). In the whole sample, the mean ratio with the CKD-EPI equation was significantly higher than that with the Schwartz equation (1.17 [95% CI 1.16; 1.18] versus 1.08 [95% CI 1.07; 1.09], p < 0.001, t-test). At GFR values of 60–89 ml/min/1.73 m², the mean ratios with the Schwartz equation were closer to 1 than the mean ratios with the CKD-EPI equation whatever the age class (1.02 [95% CI 1.01; 1.03] versus 1.15 [95% CI 1.13; 1.16], p < 0.001, t-test). In young adults (18–40 y), the Schwartz equation had a better precision and was also more accurate than the CKD-EPI equation at GFR values under 60 ml/min/1.73 m² (IQR: 0.32 [95% CI 0.28; 0.33] versus 0.40 [95% CI 0.36; 0.44]; P30: 81.4 [95% CI 78.1; 84.7] versus 63.8 [95% CI 59.7; 68.0]) and also at GFR values of 60–89 ml/min/1.73 m². In all patients aged ≥65 y, the CKD-EPI equation performed better than the Schwartz equation (IQR: 0.33 [95% CI 0.31; 0.34] versus 0.40 [95% CI 0.38; 0.41]; P30: 77.6 [95% CI 75.7; 79.5] versus 67.5 [95% CI 65.4; 69.7], respectively). In children and adolescents (2–17 y), the Schwartz equation was superior to the CKD-EPI equation (IQR: 0.23 [95% CI 0.21; 0.24] versus 0.33 [95% CI 0.31; 0.34]; P30: 88.6 [95% CI 86.7; 90.4] versus 29.4 [95% CI 26.8; 32.0]). This study is limited by its retrospective design, single-center setting with few non-white patients, and small number of patients with severe chronic kidney disease.

Conclusions

The results from this study suggest that the Schwartz equation may be more reliable than the CKD-EPI equation for estimating GFR in children and adolescents and in adults with mild to moderate kidney impairment up to age 40 y.     

Grafen,the Price equations,fitness maximization,optimisation and the fundamental theorem of natural selection

This paper is a commentary on the focal article by Grafen and on earlier papers of his on which many of the results of this focal paper depend. Thus it is in effect a commentary on the “formal Darwinian project”, the focus of this sequence of papers. Several problems with this sequence are raised and discussed. The first of these concerns fitness maximization. It is often claimed in these papers that natural selection leads to a maximization of fitness and that this view is claimed in Fisher’s “fundamental theorem of natural selection”. These claims are refuted, and various incorrect statements about the meaning and interpretation of the fundamental theorem of natural selection, in this sequence and in other papers by other authors, are discussed. Next, much of the work in this sequence rests on the first Price equation. In the deterministic (infinite population) case this equation is no more than the standard classical equation relating to changes in gene frequencies. In the stochastic case the equation gives the change in gene frequencies as the sum of two terms (the second of which vanishes in the deterministic case). These two terms are of essentially equal importance in the situation considered in the focal article, yet one of Grafen’s results ignores the second term in the stochastic analysis. This is associated with a wavering between deterministic and stochastic analyses and the use of the Price fitness concept and the classical fitness concept. These comments cast doubts on Grafen’s optimization theory.     

Photophysics, photochemistry, and reactivity: molecular aspects of perylenequinone reactions.

Density functional theory (DFT) and time-dependent density functional theory (TD-DFT) were used to elucidate the photochemistry and photophysics of eight different perylenequinones (PQ). The objective of this work has been to quantitatively investigate the photodynamic therapeutic potential of this family of compounds and give an overview of their photoreactivity. The effects of solvation were evaluated through single-point calculations using the integral equation formalism of the polarised continuum model. It is concluded that the eight studied perylenequinones can generate singlet oxygen (in aqueous solution) and superoxide radical anions, and that the autoionisation of two nearby PQ molecules is possible.     

Estimation of total water and fatness from weight and height: inaccurate for lean women

Mellits and Cheek have provided a regression equation which predicts total water, and by extension, fat, from weight and height of women. The equation has been used by many researchers as a convenient means to estimate fat when more complicated body composition estimation techniques are not possible. It is an essential component of evidence provide by Frisch for the critical fat hypothesis. The equation has not been validated on another sample, however, and has a large standard error. I test the Mellits and Cheek equation on five samples of young women, two of which show a normal range of heights and weights. The other three are athletic samples composed of lean women. In the normal samples mean fat percent determined by density (from underwater weighing) is closely approximated by the weight and height equation but not in the lean samples. When measured fat is regressed on estimated fat, correlations are low, and standard errors are high, suggesting that the Mellits and Cheek equation predicts poorly the body fat percentage of individual females. In summary, the Mellits and Cheek equation is moderately useful for the prediction of group means for body composition on samples with normal ranges of height and weight. It does not produce acceptable results on groups selected for extreme leanness or obesity. It is not recommended for fat prediction of individuals.     

The use of a metabolically structured model in the study of growth, nitrification, and denitrification by Thiosphaera pantotropha

Thiosphaera pantotropha is capable of aerobic heterotrophic nitrification and both aerobic and anaerobic denitrification. These phenomena have been studied in acetate-limited aerobic and anaerobic continuous cultures supplied with ammonia and nitrate. The internal reaction rates were defined, based on biochemical knowledge. The observable external conversion rates are related through a linear equation on the basis of the specified internal reaction rates. The linear equation is a Pirt relation extended for microbial systems with multiple electron donors (acetate and ammonia) and electron acceptors (oxygen and nitrate). The coefficients in this equation were estimated from the continuous culture measurements, and are composed of parameters involved in ATP production and consumption by the microorganism. It is shown that with realistic values for these parameters, the metabolically structured model describes the aerobic as well as the anaerobic experiments.     

Metabolic cost of walking: equation and model

Twenty years of published experience with the Workman-Armstrong equation for predicting walking VO2 is reviewed. The equation is reexpressed in currently accepted terminology, and it is shown that the equation serves well as a basic model of normal walking. Employing this model to analyze VO2/step leads to the elaboration of a three-compartment model of the metabolic cost of walking. This three-compartment model provides a rational estimate of the fraction of walking's metabolic cost that powers the actual walking movement. Doubt is expressed that "comfortable speed of walking" is definable in energy terms. It is suggested that the requirements of maintaining balance while walking may determine both the comfortable speed of walking and the curvilinearity of the relationship between ground-speed and freely chosen step frequency of walking.     

Extended monod kinetics for substrate, product, and cell inhibition

A generalized form of Monod kinetics is proposed to account for all kinds of product, cell, and substrate inhibition. This model assumes that there exists a critical inhibitor concentration above which cells cannot grow, and that the constants of the Monod equation are functions of this limiting inhibitor concentration. Methods for evaluating the constants of this rate form are presented. Finally the proposed kinetic form is compared with the available data in the literature, which unfortunately is very sparse. In all cases, this equation form fitted the data very well.     

Studies on a thermophilic bacillus: its isolation, properties, and temperature coefficient of growth

A thermophilic bacillus with minimal, optimal, and maximal growth temperatures of 40, 64.5, and 72 C, respectively, was isolated from soil. Biochemical and morphological studies place the isolate in group 1 of the classification of Walker and Wolf. After adaption to nitrate broth, the temperature coefficient for growth was found to be 20,400 cal/mol. When the temperature coefficient for growth of the isolate, psychrophilic bacteria, mesophilic bacteria, and a strain of Bacillus stearothermophilus are compared, there is no correlation with optimal temperature. The form of the Arrhenius equation, as used by some workers, is commented on.     

Coexistence of Flexibility and Stability of Proteins: An Equation of State

We consider a recently suggested “equation of state” for natively folded proteins, and verify its validity for a set of about 5800 proteins. The equation is based on a fractal viewpoint of proteins, on a generalization of the Landau-Peierls instability, and on a marginal stability criterion. The latter allows for coexistence of stability and flexibility of proteins, which is required for their proper function. The equation of state relates the protein fractal dimension , its spectral dimension , and the number of amino acids N. Using structural data from the protein data bank (PDB) and the Gaussian network model (GNM), we compute and for the entire set and demonstrate that the equation of state is well obeyed. Addressing the fractal properties and making use of the equation of state may help to engineer biologically inspired catalysts.     

Aqueous solutions of native and hydrophobically modified polysaccharides: temperature effect

Amphiphilic polysaccharides, obtained by the attachment of various hydrocarbon groups onto dextran, are studied in aqueous solutions. The viscosity of their aqueous solutions is examined as a function of concentration and temperature in the range 25-65 degrees C. Varying polymer concentration, viscosity follows a polynomial development of Huggins equation in which the coefficients can be calculated from the Huggins constant determined in the dilute domain (Matsuoka-Cowman equation). For all polymers, the solution viscosity follows an Arrhenius-like variation with temperature. The activation energy of the aqueous solutions is determined as a function of polymer concentration and structural characteristics (nature and amount of grafted hydrocarbon groups). The variation of activation energy with polymer concentration is shown to be consistent with predictions based on the Matsuoka-Cowman equation combined with the equation of Andrade. This conclusion is extended to other polysaccharides using data from the literature.     

Sex ratio at birth, polygyny, and fertility: a cross-national study

The sex ratio at birth may reflect frequency of intercourse that affects the timing of conception. If so, cross-national variation in polygyny and fertility might account for country differences in secondary sex ratios. Consistent with the timing of intercourse hypothesis, the birth sex ratios of 148 countries declined with total fertility rates and polygyny intensity, and increased with contraception use in correlational analysis. Regression analysis confirmed that polygyny was a negative predictor of the sex ratio (and contraception was a positive predictor), with level of economic development and mother's age controlled, but the effects disappeared with total fertility added to the equation. The sex ratio evidently declines with increases in fertility because more children are born at a later birth order when frequency of intercourse is lower.     

Cellobiase from Trichoderma viride: purification, properties, kinetics, and mechanism

Three distinct cellobiase components were isolated from a commercial Trichoderma viride cellulase preparation by repeated chromatography on DEAE cellulose eluting by a salt gradient. The purified cellobiase preparations were evaluated for physical properties, kinetics, and mechanism. Results from this work include: 1) development of one step enzyme purification procedure using DEAE-cellulose; 2) isolation of three chromatographically distinct, yet kinetically similar, cellobiase fractions of molecular weight of approximately 76,000; 3) determination of kinetics which shows that cellobiase hydrolyzes cellobiose by a noncompetitive mechanism and that the product, glucose, inhibits the enzyme, and 4) development of an equation, based on the mechanism of cellobiase action, which accurately predicts the time course of cellobiose hydrolysis over an eightfold range of substrate concentration and conversions of up to 90%. Based on the data presented in the paper, it is shown that product inhibition of cellobiase significantly retards the rate of cellobiose hydrolysis.