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.

Morphological study of amelogenesis in the rat lower incisor after thyro-parathyroidectomy, parathyroidectomy and thyroidectomy.

The effects of thyro-parathyroidectomy, parathyroidectomy or thyroidectomy upon enamel formation in the rat incisor were studied. One control group and four groups of surgically treated rats were used: parathyroid autotransplanted, thyroidectomized, parathyroidectomized, and thyro-parathyroidectomized. One month after surgery, the incisors were processed for light and electron microscopy. The present study revealed perturbations of the Tomes process morphology, of the rod pattern in the inner enamel formation, of the enamel surface, and of the mineralization after thyro-parathyroidectomy. After parathyroidectomy, only mineralization defects could be visualised. No effects were observed in enamel after thyroidectomy. A severe hypocalcemic state as seen in thyro-parathyroidectomized rats affects the enamel shape, and mineralization, and the morphology and function of secretory ameloblasts. Knowledge of the way in which the alteration of the enamel surface is produced should contribute to a better understanding of the development of tooth enamel.

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.

Effects of thyro-parathyroidectomy and parathyroidectomy upon dentinogenesis: Part I: Light microscopy.

In order to determine the differential effects of the thyroid hormones and the parathyroid hormone upon dentinogenesis in the rat incisor one control group (C) and four groups of surgically treated rats were studied: parathyroid autotransplanted (PTT), thyroidectomized (TX), parathyroidectomized (PTX), and thyro-parathyroidectomized group. One month after surgery the incisors were dissected and the tissues were prepared for light microscopy and morphometric measurements. This study revealed modifications in the TPTX rats as well as in the PTX rats: an enlargement of the predentin, alterations in the predentin appearance and the presence of mineralization defects. These results confirm that the effects observed are probably due to a PTH deficiency and/or hypocalcemia and suggest that their occurrence is associated with a determined stage of dentinogenesis in the rat.

Effects of thyro-parathyroidectomy and parathyroidectomy upon dentinogenesis: Part II: Electron microscopy.

An ultrastructural study was carried out in order to better characterize the findings observed in the first part of our study. The materials and methods are the same as those used in the preceding paper. This study reveals the occurrence of structures which display a symmetrical cross-banded pattern within the predentin and dentin of thyro-parathyroidectomized (TPTX) and parathyroidectomized (PTX) rats. A difference in the distribution of the symmetrical banded structures as dentinogenesis advances, as well as differences in the amount of the symmetrical banded structures between TPTX and PTX rats were observed. The symmetrical banded structures correspond with the so-called symmetrical SLS previously described in the incisor of normal and pathologic rats. The occurrence of these structures at a given stage of the incisor development suggests that the odontoblast is sensitive to the parathyroid hormone deficiency and/or hypocalcemia in a precise stage of its maturation.

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)

Circadian rhythms of calcitonin gene expression in the rat.

The daily changes in rat thyroid calcitonin and its specific mRNA concentrations, and the relationship between their dynamics and the plasma levels of calcitonin, calcium and phosphate over a 24-h period were investigated. The circulating calcitonin concentration rose during the daily dark period when plasma calcium and phosphate levels were minimal, indicating that plasma calcitonin rhythm cannot be generated directly by a linear effect of calcium on hormone secretion. Moreover, we established that the expression of the calcitonin gene also exhibited periodic dynamics observable at the pretranslational level: the gland content of hybridizable specific calcitonin RNA displayed daily rhythms; specific RNA levels peaked during the light period and were minimal during the first part of the dark period. Significant changes in thyroid calcitonin concentrations also occurred over a 24-h period. Statistical analyses which distinguished between variations over the 24-h period and residual variations were performed to test the relationships between the various parameters. The daily rhythms of hybridizable RNA, thyroid calcitonin and plasma minerals appeared to be in phase, while the plasma calcitonin concentration displayed variations out of phase with these rhythms. The implication of the correlations observed on the residual variations is discussed in comparison with the temporal relationship between the daily variations. The results fit the hypothesis that hormone production and secretion are self-oscillating processes. Plasma concentrations of calcium and phosphate might play a role in the synchronization of the calcitonin metabolism periodicity.

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.

The kinetics of intestinal calcium absorption in the rat: an analytical and model building study.

The experimental data obtained from in vivo single pass perfusion of duodenal, jejunal, and ileal intestinal segments of 33- and 50-day-old rats have been used to test a series of models for calcium absorption. Each model was checked for the statistical validity and goodness-of-fit with the experimental data. The model adopted for the duodenum and jejunum had two major components, one saturable and the other nonsaturable, and a minor secretory component. This model was not applicable to ileal calcium absorption. Here the secretory component appeared to be much more important, and the absorption parameters varied in such a manner as to suggest that this intestinal segment was capable of short term autoregulation of dietary calcium absorption.

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.

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.

A technique for multiple, high-rate blood samplings via an external cannula in rats.

A method for obtaining multiple, high-rate blood sample collections from rats without the use of anesthesia and anticoagulant is described. The surgical procedure consists of a bypass of the carotid via a cannula; this cannula forms a loop above the rat's head and is available for blood sampling. The method permits the investigation of high-frequency oscillations in blood components of rat.