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.     

Ordination of vegetation change in Guadalupe Mountains,New Mexico,USA

Vegetation change over a nine-year period was studied in Guadalupe Mountains, New Mexico. Permanent transects in desert shrub vegetation were sampled in 1972 and 1980. Emphasis was given to shrubs because of their importance to big game diets. Univariate paired t-tests and reciprocal averaging ordination were used to detect and display coordinated changes in species composition over time. Despite apparently less browsing pressure in desert shrub vegetation in 1980 there were few significant changes in species composition. In addition, preferred forage species showed reduced reproduction while species of intermediate and poor forage value dis-played increased reproduction during this time. These data do not support traditional rangeland succession theory which states that enhanced reproduction of preferred species should follow grazing or browsing pressure reduction.     

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.     

Manganese-histidine cluster as the functional center of the water oxidation complex in photosynthesis

The recent model of Kambara and Govindjee for water oxidation [Kambara T. and Govindjee (1985) Proc. Natl. Acad. Sci. U.S.A., 82:6119–6123] has been extended in this paper by examining all the data in order to identify the most likely candidate for the redox-active ligand (RAL), suggested to operate between the water oxidizing complex (WOC) and Z, the electron donor to the reaction center P680. We have concluded that a very suitable candidate for RAL is the imidazole moiety of a histidine residue. The electrochemical data available on imidazole derivatives play heavily in this identification of RAL. Thus, we suggest that histidine might play the role of an electron mediator between the WOC and Z. A model of S-states in terms of their plausible chemical identity is presented here.Abbreviations J electronic spin of ion - P680 reaction center chlorophyll - RAL Redox active ligand - S_n state of the oxygen-evolving system - WOC water oxidation complex - Z electron donor to P680 Dedicated to Prof. L.N.M. Duysens on the occasion of his retirement     

The versatility of proteolytic enzymes

The growing realization of their physiological importance has generated renewed interest in the study of proteolytic enzymes. Modern methods of protein chemistry and molecular biology have revealed new insights into the protein and gene structure of a variety of protein precursors and their processing by limited proteolysis. Examples are given in this review for transmembrane processes and the role of signal peptidases of both eukaryotic and prokaryotic origin, the processing of prohormones and precursors of growth factors, protein components of blood coagulation, fibrinolysis, and of the complement system, and a group of granulocyte proteases, including the mast cell serine proteases. The relationship of homologous domains found in many of these proteases and their zymogens to protein evolution is a recurrent theme of this discussion.