Modelling growth responses of soil nitrifiers to additions of ammonium sulphate and ammonium chloride

Summary Following the addition of 0–75 mole N g^–1 as ammonium chloride or ammonium sulphate to a sandy loam soil the nitrate formed was measured daily for a period of 15–17 days. The nitrate produced as a function of time was described using the Monod equation for microbial growth. An optimisation technique is described for obtaining, from the nitrification time course data, the maximum specific growth rate, the affinity constantant and an index limited by the concentration of ammonium in soil solution. Additions of more than 7.3 moles N g^–1 soil as ammonium chloride were found to inhibit nitrification. The inhibition was interpreted as being caused by osmotic pressure or by chloride ion. A similar effect was not found with ammonium sulphate, because the salt concentration in the soil solution was restricted by the precipitation of calcium sulphate. The model developed was capable of accounting for nitrate production in the soil under non-steady state conditions of substrate concentrations and nitrifier biomass.     

Diffusion of inorganic carbon across an unstirred layer: a simplified quantitative approach

Abstract The quantitative approach used here is based on a model comprising a well-stirred medium, an unstirred layer, and a CO₂ absorbing leaf. The unstirred layer is divided up by planes into a number of sub-layers. Within each plane the concentration of each solute is everywhere the same as is the electric potential. These variables constitute the basic data. Thus the planes were characterized by their pH value. An equation is derived which enables the calculation of the basic data of a plane from the known data of another plane. In this way it is possible to calculate the basic data for all planes. From these data the rate of assimilation, the thickness of the unstirred layer and its sub-layers, the fluxes across the sub-layers and the conversions among the carbon components can be estimated. The CO₂ flux decreases, and the HCO^?₃ flux increases towards the leaf. There are negative fluxes of OH^& and CO^2–₃. H⁺ fluxes are of minor importance and can be ignored if the pH of the medium is higher than 8.0, provided no non-inorganic C buffers with appropriate pK_a are present. The significance of the carbon diffusion facilitating effect of an inorganic carbon system is expressed in various ways. The values obtained represent maxima, as the assumption is made that the equilibrium reactions are very fast. It is argued that even better effects are possible if the back-diffusion of CO^2–₃ could be prevented by lowering the pH of the unstirred layer.     

Global asymptotic stability of the size distribution in probabilistic models of the cell cycle

Probabilistic models of the cell cycle maintain that cell generation time is a random variable given by some distribution function, and that the probability of cell division per unit time is a function only of cell age (and not, for instance, of cell size). Given the probability density, f(t), for time spent in the random compartment of the cell cycle, we derive a recursion relation for _n(x), the probability density for cell size at birth in a sample of cells in generation n. For the case of exponential growth of cells, the recursion relation has no steady-state solution. For the case of linear cell growth, we show that there exists a unique, globally asymptotically stable, steady-state birth size distribution, _*(x). For the special case of the transition probability model, we display _*(x) explicitly.This work was supported by the National Science Foundation under grants MCS8301104 (to J.J.T.) and MCS8300559 (to K.B.H.), and by the National Institutes of Health under grant GM27629 (to J.J.T.).     

A prediction model for parasitic gastro-enteritis in lambs

Paton G., Thomas R. J. and Waller P. J. 1984. A prediction model for parasitic gastroenteritis in lambs. International Journal for Parasitology14: 439–445. The parasite Ostertagia circumcincta is a major cause of parasitic gastro-enteritis in lambs in temperate countries. A prediction model is described, based on a mathematical representation of the external and internal stages of the life-cycle.The model is used to predict the numbers of infective larvae on a permanent experimental paddock grazed by ewes and lambs in 1973 and 1974. The “moisture status” of the surface layer of the pasture was found to be of fundamental importance for the successful prediction of the development and survival of the pre-infective larval stages. For the years studied the contribution to the summer wave of infection by lamb derived larvae was particularly significant.     

Dose dependent responses of cattle to Theileria parva stabilate

Dolan T. T., Young A.S., Losos G.J., McMillan I., Minder Ch.E. and Soulsby K. 1984. Dose dependent responses of Theileria parva stabilate. International Journal for Parasitology14: 89–95. A tick derived stabilate of Theileria parva (Maguga) was titrated in a large group of Boran (Bos indicus) cattle of the same age, sex and origin. The infectivity data was analysed using the independent action model. The cattle were identified as heterogeneous in their response to infection with 75% showing one ID₅₀ (0.0014) and 25% showing another (0.01). The disease responses of the cattle given different dose levels were compared for a variety of parameters. The results obtained showed these parameters to be dose dependent including the time to onset of piroplasm parasitaemia. The stabilate is of large volume and can be used for controlled challenge in immunity studies and for comparison of susceptibility between cattle of different breeds and from different epidemiological backgrounds.     

General method for the derivation and numerical solution of epithelial transport models

Summary A general method is presented for the formulation and numerical evaluation of mathematical models describing epithelial transport. The method is based on the principles of conservation of mass, and maintenance of electroneutrality within the cells and bathing solutions. It is therefore independent of the specific membrane transport mechanisms, and can be used to evaluate different models describing arbitrary transport processes (including passive, active and cotransport processes). Detailed numerical methods are presented that allow computation of steady-state and transient responses under open-circuit, current-clamp and voltage-clamp conditions, using a general-purpose laboratory minicomputer. To evaluate the utility of this approach, a specific model is presented that is consistent with the Koefoed-Johnson and Ussing hypothesis of sodium transport in tight epithelia (Acta Physiol. Scand. 42:298–308, 1958). This model considers passive transport of an arbitrary number of permeant solutes, active transport of sodium and potassium, and osmotically induced water transport across the apical and basolateral membranes. Results of the model are compared to published experimental measurements in rabbit urinary bladder epithelium.     

Growth and development of immature life stages ofPropylaea 14-punctata L. andCoccinella 7-punctata L. [Col.: Coccinellidae] simulated by the metabolic pool model

The conversion of aphid prey tissue (Acyrthosiphon pisum Harris) into predator biomass (immature life stages ofPropylaea 14-punctata L. andCoccinella 7-punctata L.) is calculated by plotting weight gain against assimilation (i.e. consumption minus egestion). This concept is added to the metabolic pool model byGutierrez et al. (1981) that enables the simulation of growth and development of a predator on a physiological basis. Physiological time is expressed in daydegrees above lower development thresholds for both species. Visual examination of observed and calculated values showed that the model satisfactorily describes the growth patterns of the above predators.      

A Monte Carlo method for the simulation of kinetie models

The purpose of this note is to illustrate the feasibility of simulating kinetic systems, such as commonly encountered in photosynthesis research, using the Monte Carlo (MC) method. In this approach, chemical events are considered at the molecular level where they occur randomly and the macroscopic kinetic evolution results from averaging a large number of such events. Their repeated simulation is easily accomplished using digital computing. It is shown that the MC approach is well suited to the capabilities and resources of modern microcomputers. A software package is briefly described and discussed, allowing a simple programming of any kinetic model system and its resolution. The execution is reasonably fast and accurate; it is not subject to such instabilities as found with the conventional analytical approach.Abbreviations MC Monte Carlo - RN random number - PSU photosynthetic unit Dedicated to Prof. L.N.M. Duysens on the occasion of his retirement.