A nonlinear compartmental model of Sr metabolism. I. Non-steady-state kinetics and model building.

A model of Sr metabolism was developed by using plasma and urinary Sr kinetic data obtained in groups of postmenopausal women who received four different oral doses of Sr and collected during the Sr administration period (25 days) and for 28 days after cessation of treatment. A nonlinear compartmental formalism that is appropriate for study of non-steady-state kinetics and allows dissociation of variables pertaining to Sr metabolism (system 1) from those indirectly operating on it (system 2) was used. At each stage of model development, the dose-dependent model response was fitted to the four sets of data considered simultaneously (1 set per dose). A seven-compartment model with internal Sr distribution and intestinal, urinary, and bone metabolic pathways was selected. It includes two kinds of nonlinearities: those accounting for saturable intestinal and bone processes, which behave as intrinsic nonlinearities because they are directly dependent on Sr, and extrinsic nonlinearities (dependent on system 2), which suggest the cooperative involvement of plasma Sr changes in modulating some intestinal and bone mineral metabolic pathways. With the set of identified parameter values, the initial steady-state model predictions are relevant to known physiology, and some peculiarities of model behavior for long-term Sr administration were simulated.

A nonlinear compartmental model of Sr metabolism. II. Its physiological relevance for Ca metabolism.

We have studied the peculiarities of the nonlinear compartmental model for human Sr metabolism (Staub JF, Foos E, Courtin B, Jochemsen R, and Perault-Staub AM. Am J Physiol Regul Integr Comp Physiol 284: R819-R834, 2003), including its physiological reliability in the context of Sr-Ca similarity-dissimilarity. We found it to be relevant to Ca metabolism, except for discrimination against Sr relative to Ca at urinary and intestinal levels. The main findings are as follows: 1) the saturable part of intestinal absorption, shared by Sr and Ca, does not seem to be responsible for the discrimination of the transcellular pathway; 2) although there is little discrimination in bone, the physicochemical behaviors of Sr and Ca at the bone surface differ, at least quantitatively; and 3) Sr behaves as a "tracer" for Ca metabolic pathways and, under non-steady-state conditions, can also reveal self-regulatory processes. It is suggested that they depend on Ca2+ (cationic)-sensing receptors that are apparently more sensitive to Sr than to Ca. Acting on gastrointestinal and osteoblast lineage cells, these slow processes might contribute to adaptive, rather than homeostatic, regulation of Ca metabolism. Understanding these features could help clarify the pharmacological and therapeutic effects of oral Sr.

Spatio-temporal self-organization of bone mineral metabolism and trabecular structure of primary bone.

A nonlinear two-variable reaction-diffusion model of bone mineral metabolism, built from an overall self-oscillatory compartmental model of calcium metabolism in vivo, has been studied for its ability to generate spatial and spatio-temporal self-organizations in a two-dimensional space. Analytical and numerical results confirm the theoretical properties previously described for this kind of model. In particular, it is shown that, for a given set of reactional parameter values and certain values of the ratio of the two diffusion coefficients, there exists a set of unstable wavenumbers leading spontaneously to the development, from the homogeneous steady state, of either different types of stationary spatial patterns (hexagonal, striped and re-entrant hexagonal patterns) or more or less complex spatio-temporal expressions. We discuss the relevance of analogies established between some spatial or spatio-temporal structures predicted by the model and some peculiar features of the primary bone trabecular architecture which appear during embryonic ossification.

Modelling of in vivo calcium metabolism. II. Minimal structure or maximum dynamic diversity: the interplay of biological constraints.

The temporal behaviour of the nonlinear compartmental model we have developed for rat calcium metabolism is discussed with respect to the theoretical properties of the self-oscillating autocatalytic subunit around which the model is constructed. Depending on the approximations made, this subunit is described by a minimal two-variable model, SU2, or by a three-variable one, SU3. The diversity of the theoretical dynamic behaviours possible with SU2 is greatly increased with SU3. But the identification of SU3 parameter values in three different experimental situations reveals that biological constraints efficiently preserve a simple circadian rhythm for bone metabolism. This analysis indicates the significant contribution of the available bone crystal pool to the dynamic organization of this tissue, and hence to extracellular calcium homeostasis.

Modelling of in vivo calcium metabolism. I. Optimal cooperation between constant and rhythmic behaviours.

The relevance of nonlinear dynamics to calcium metabolism led us to reevaluate the role of Ca-regulating hormones in Ca homeostasis. We suggest that, firstly, the main Ca metabolic functions in rat-bone and gut--are organized as dynamic entities able to generate various temporal expressions, including self-oscillating patterns and, secondly, Ca homeostasis results from interaction between both metabolic and hormonal oscillators. Following this schema, a major role for the hormonal system, with its circadian pattern, could be to act directly on metabolic functions or indirectly through feeding behaviour, in order to optimize, coordinate and synchronize the Ca fluxes at ECF level.

Regulation of plasma calcium and phosphate in calcitonin-infused rats.

The effects of long-term constant infusion of moderate doses (2-32 ng/h) of salmon calcitonin (sCT) on plasma Ca (and its radionuclide 45Ca), Pi, Mg, and on endogenous rat CT (rCT) metabolism were investigated in the rat. Daily variations were included. 1) The plasma concentrations of Ca and Pi fell and that of Mg increased transiently during infusion, with the duration of responses (1-3 days) depending on the sCT dose. Rats infused with 8 ng/h sCT remained sensitive to CT after 7 and 14 days, as indicated by the effects of minipump removal and of a bolus injection of exogenous sCT on plasma mineral concentrations. 2) In contrast to control rats, the well-established daily variations in plasma Ca and Pi levels were no longer observed after 7 and 14 days of sCT infusion (8 ng/h), but normal variations persisted for plasma Mg, circulating rCT, rCT mRNA, and rCT thyroid content. 3) Statistical analysis of plasma mineral data, collected at five sequential times during days 7 and 14, showed that the means were not significantly different and that the daily variations were essentially identical on days 7 and 14 in control rats. In contrast, the variability of measurements for plasma Ca and Pi, but not for Mg, increased significantly between days 7 and 14 in infused rats, and the mean differences were significantly lower in infused rats on day 7 than in control rats. These results are consistent with a transitory loss of the daily variations for Ca and Pi (day 7) and the later (day 14) spontaneous recovery of some variations in these parameters, although the individuals remain unsynchronized.(ABSTRACT TRUNCATED AT 250 WORDS)

A physiological view of in vivo calcium dynamics: the regulation of a nonlinear self-organized system.

Our aim is neither to re-evaluate the term homeostasis, nor to summarize the conventional concepts in the field of calcium metabolism and its regulation, nor even to comment on their advantages and their limitations (excellent recent reviews have been published). This paper is rather a position article and references to the current literature will be made only if they contribute to a better understanding of our proposals; in contrast, emphasis will be placed on a literature which has, until now, remained unfamiliar to the field of calcium metabolism. The text is organized around three related features which are largely dictated by the characteristics of our recently published compartmental self-oscillatory model for rat calcium metabolism: (a) The circadian behavior associated with calcium dynamics in vivo may be viewed as a "key" temporal behavior for investigating the spatiotemporal organization of calcium metabolism in the normal rat. Within the bone, a large part of this circadian behavior should stem from the physico-chemical properties of the transformations of calcium-phosphate associations at the extracellular fluid (ECF)/mature bone interface; (b) an important part of the maintenance of a nearly constant plasma calcium concentration (homeostasis) results from interaction between nonlinear oscillators belonging to both calcium metabolism and calcium-regulating hormones. This implies that: firstly, calcium metabolism, like any biological system, is a complex dynamic system which has evolved over a long period and whose metabolic components--gut, kidney, bone--are organized as dynamic entities, adapted to periodic relationships with the external environment. The intrinsic nature of the circadian behavior of bone calcium efflux proposed here is a sufficient demonstration of this. Secondly, the existence of rhythmic variations in the main calcium regulating hormones, parathyroid hormone (PTH), calcitonin (CT) and vitamin D (VitD), are in agreement with this argument. As developed below, fascinating properties emerge from interaction between oscillators (hormones and target organs) which provide a new perspective on calcium regulation; and (c) one of the striking properties of the kind of nonlinear dynamic system required for this representation of calcium metabolism is that periodicity is only one of many temporal expressions. Thus, qualitative diversity in the temporal expression of calcium metabolism can be expected with varying experimental situations and different modes of temporal regulation of calcium metabolism might be physiologically effective, depending on the species studied.(ABSTRACT TRUNCATED AT 400 WORDS)

Calcium metabolism in the rat: a temporal self-organized model.

Based on consideration of rat plasma Ca and 45Ca concentrations, we analyze the circadian behavior of Ca metabolism of the rat as the temporal expression of a self-organized system. We present a self-oscillatory model M for rat Ca metabolism based on a compartmental formalism, which includes a second-order autocatalytic process. M describes the entire mass of Ca as made up of eight compartments and predicts a distinction between 1) the amount of Ca deposited in zones of rapid bone growth and reutilized during bone maturation and 2) the amount of Ca in mature bone subdivided into four compartments. Two of these compartments, largely self-oscillating, may represent Ca-P associations at bone liquid/solid interface and are subject to osteoblast-osteocyte control. The other two compartments can be thought of as made up of a large expanding pool of hydroxyapatite (HA) crystals, which are largely unavailable as such, and a small pool or more available HA crystals. Bone Ca influx and rhythmic efflux play a major role in the regulation of Ca in extracellular fluid but must be dissociated from bone accretion and resorption. Application to Ca deficiency was analyzed. Conceptual consequences of the connection of Ca metabolism to a self-regulated system are discussed.

Circadian variations in plasma calcium and calcitonin: effect of calcium deficiency and fasting.

Circadian fluctuations of plasma calcium and immunoassayable calcitonin levels were studied in normal and calcium-deficient 2-month-old rats. The relationship between these parameters was also studied in animals which had been fasted for short periods. The plasma calcium rhythm persisted and was even amplified in rats placed on a 4-week calcium-deficient diet. In these rats, as in normal rats, the plasma calcium concentration diminished during the dark period. Calcitonin levels increased at the onset of the feeding period in normal rats but, in calcium-deficient rats, the pattern changed completely, with a major peak at the end of the light period and remaining at a low level during the dark feeding period. This modification of calcitonin rhythmicity appeared to be dependent on the degree of calcium deficiency. Fasting had little effect on calcitonin rhythms in either normal or calcium-deficient rats. It is concluded that the calcitonin rhythm is relatively independent of feeding per se and that there appears to be no simple relationship between plasma calcium and calcitonin concentrations. It is suggested that the results may best be interpreted as reflecting the presence of rhythmic endogenous phenomena which are intrinsic to calcium metabolism and its regulation in the rat.

Distribution and antigenic properties of the O-determinants of Salmonella zuerich (1, 9, 27 46).

Fractionation of the O-polysaccharide derived from Salmonella zuerich (1, 9, 27, 46) on a concanavalin A polymer permitted immunological and chemical analysis on the different fractions. The S. zuerich O-polysaccharide preparation is composed of two distinct populations of molecules: one, ZB1-, devoid of O-antigenic determinant 1, and the other, ZB1+, carrying the determinant 1. This determinant is linked to the presence of D-glucosyl residues on the side chain. O-polysaccharide molecules 1-, devoid of D-glucose, are shown to carry simultaneously both determinants 27 and 46. These determinants are not evenly distributed on the molecules. The expression of determinants 46 (-[Tyv]-betaMan-, where Tyv = tyvelose) seems to be restricted to a distinct specific configuration, and it is altered by the presence of either determinant 27 (-[Tyv]-alphaMan-) or determinant 1 (Glc-Gal-) in the close neighbourhood. Molecules 1+ are partially or completely substituted by glucosyl residues and react with anti-1 antibodies. They are characterized by the same uneven distribution of determinants 27 and 46 as molecules ZB1-. In conclusion, the O-polysaccharide chains are heterogeneous. They contain simultaneously factors 27, 46, and often also 1.

Isolation of an (O,H,Vi)-free immunoprotective antigenic fraction with mannose receptor-like activity from Salmonella typhi.

An antigenic fraction of Salmonella typhi strain TY6S, obtained from a bacterial pellet by washings with 1.5 M NaCl and ultracentrifugation in a 5%-20% sucrose density gradient, induced serum antibodies in rabbits that protected chicken embryos challenged with lethal doses of the virulent microorganism. The antigenic preparation was free of Vi, O, and H antigens. It contained about 85% protein and Rd1P+ lipopolysaccharide. The protein moiety comprised three polypeptides of 45,000, 32,000, and 20,000 daltons, respectively. In addition, the purified preparation exhibited the properties of a bacterial adhesin with receptor-like activity for mannosyl residues, as shown by agglutination of target cells containing these residues at their surfaces.

Endogenous nature of circadian rhythms in calcium metabolism.

Rats studied when the lights are on from 0600 to 1800 daily and fed only in the dark period displayed circadian rhythms in plasma calcium (ionized and total) and 45Ca concentrations, 6 and 8 days after 45Ca administration. In rats fed a calcium-deficient diet, the amplitude of daily variation of plasma ionized and total calcium increased markedly whereas plasma 45Ca daily fluctuation remained essentially unchanged. In the calcium-deficient rats, significant correlations between plasma calcium and 45Ca and between plasma calcium and magnesium were observed throughout the 24 h; circadian periodicity of calcium metabolism persisted in rats fasted overnight, regardless of the illumination schedule. Normal daily fluctuations in plasma 45Ca, lost after thyroparathyroidectomy (TPTX), were restored by feeding the TPTX rats a high-calcium diet. These results demonstrate clearly that circadian rhythms of calcium metabolism occurred irrespective of the light-dark schedule, the calcium supply through intestines and the thyroparathyroid system. An attractive suggestion is that circadian rhythmicity originates as a result of dynamic properties involving nonlinear processes of calcium metabolism.

[Regulation of calcium metabolism ; its rhythmic variations]. / Régulation du métabolisme calcique ; ses variations rhythmiques.

In rats fed a calcium-deficient diet, the amplitude of daily variation of plasma ionized and total calcium increased markedly whereas plasma 45Ca daily fluctuation remained essentially unchanged. Normal daily fluctuations in plasma 45Ca, lost after thyroparathyroidectomy, were restored by feeding rats a high-calcium diet. A suggestion is that circadian rhythmicity originates as a result of dynamic properties involving nonlinear processes of calcium metabolism.

[Specific blast transformation of rabbit spleen cells induced by a bacterial polysaccharide and inhibitory effect of peripheral blood lymphocytes (author's transl)]. / Transformation blastique spécifique des lymphocytes spléniques de lapins induite par un polyoside bactérien et effet inhibiteur des lymphocytes du sang périphérique.

Following immunization with bacteria (i.e. Salmonella johannesburg), rabbit spleen lymphocytes developed a specific blast response when the lymphocytes were stimulated with polysaccharide, the haptenic moiety of lipopolysaccharide. A clear cut dissociation was noted in the blast response induced by polysaccharide compared with those induced by lipopolysaccharide and lipid A. There was no correlation between the magnitude of the cellular responses and that of the antibody response. Moreover, there was less specificity at the cellular level than at the level of antibody secreted by cells. A decrease of 3H-thymidine incorporation was often observed after immunization, at the level of peripheral blood lymphocytes. An inhibitory effect of these cells was shown on the blast response of spleen lymphocytes with polysaccharide. A high blast response to Salmonella polysaccharide which could be observed in some non-immunized rabbits might be related to a natural sensitization of animals with the same or related unknown antigens which could not be recognized by anti-S. johannesburg antibodies.

Origin of the heterogeneity of cell wall O-polysaccharides from Salmonella zuerich (1,9,12,(46),27).

The heterogeneity of the cell wall O-polysaccharide of Salmonella zuerich (factor 1 present or absent) is probably not due to mutations in the stock since it was seen in essentially similar fashion (proportion one 1+ to four 1-forms) in four separate lots of polysaccharide extracted from separate culture batches. The results of indirect fluorescent antibody studies suggest that form variation of factor 1, occurring at an unusually high rate, is the most probable basis of the heterogeneity.

[Study of X antigen of Salmonella typhi responsible for the production of protective antibody towards chick embryo]. / Recherche sur l'antigène X responsable de la production des anticorps anti-Salmonella typhi, protecteurs pour l'embryon de poulet

Laboratory animals are not sensitive to human S. typhi strain (O+ Vi+). But the chick embryo is very susceptible to infection by this strain. This property can be used to test protective activity of immuno sera. Several antigenic fractions have been prepared from Ty6S strain (0- Vi+) by washing methods. The " outer layer " of the bacteria is easily removed by NaCl 0,5 M. Injected in rabbits this preparation produces the synthesis of protective antibodies. The active antigen X is spun down with the Vi antigen. The relation of X antigen to Vi antigen is being studied.