A Minimal Mathematical Model of Calcium Homeostasis

Raposo, João Filipe; Sobrinho, L. G.; Ferreira, H. G.

doi:10.1210/jc.2002-011870

Cited by 56 publications

(54 citation statements)

References 42 publications

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“…This model was further used to examine 3 steps in active calcium absorption, i.e., Ca entry, facilitated diffusion and Ca extrusion, and showed enhanced Ca absorption by calbindinD 9K (Feher et al, 1992;Slepchenko and Bronner, 2001). Urine excretion has not been individually modeled, but only as a part of the calcium balance model (Hurwitz et al, 1987a;Peterson and Riggs, 2010;Raposo et al, 2002). The bone remodeling process has been modeled as a function of bone cells and their regulators (Komarova, 2005;Komarova et al, 2003;Kroll, 2000;Lemaire et al, 2004;Rattanakul et al, 2003).…”

Section: Mechanistic Modeling In Calcium Studiesmentioning

confidence: 99%

Review on Application of Biosystem Modeling: Introducing 3 Model-based Approaches in Studying Ca Metabolism

Lee

Cho²

2012

Journal of Biosystems Engineering

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Purpose:This review aims at introducing 3 modeling approaches classified into 3 categories based on the purpose (estimation or prediction), structure (linear or non-linear) and phase (steady-state or dynamic-state); 1) statistical approaches, 2) kinetic modeling and 3) mechanistic modeling. We hope that this review can be a useful guide in the model-based approach of calcium metabolism as well as illustrates an application of engineering tools in studying biosystems. Background: The meaning of biosystems has been expanded, including agricultural/food system as well as biological systems like genes, cells and metabolisms. This expansion has required a useful tool for assessing the biosystems and modeling has arisen as a method that satisfies the current inquiry. To suit for the flow of the era, examining the system which is a little bit far from the traditional biosystems may be interesting issue, which can enlarge our insights and provide new ideas for prospective biosystem-researches. Herein, calcium metabolic models reviewed as an example of application of modeling approaches into the biosystems. Review: Calcium is an essential nutrient widely involved in animal and human metabolism including bone mineralization and signaling pathways. For this reason, the calcium metabolic system has been studied in various research fields of academia and industries. To study calcium metabolism, model-based system analyses have been utilized according to the purpose, subject characteristics, metabolic sites of interest, and experimental design. Either individual metabolic pathways or a whole homeostasis has been modeled in a number of studies.

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Section: Mechanistic Modeling In Calcium Studiesmentioning

confidence: 99%

Review on Application of Biosystem Modeling: Introducing 3 Model-based Approaches in Studying Ca Metabolism

Lee

Cho²

2012

Journal of Biosystems Engineering

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“…These parameter values were derived based on existing data as well as heuristic parameter fitting [1]. A perturbation to a specific state variable was introduced around a steady-state reference, and the dynamical system responses were evaluated.…”

Section: Numerical Simulationmentioning

confidence: 99%

“…The physiological system that regulates the balances of calcium and phosphorus in our body comprises a large number of regulatory components as well as a complex network of molecular and cellular interactions [1]. Since simple, logical reasoning is seldom possible, building mathematical models and conducting computational simulations are often useful to our understanding of a mechanism of actions of key regulatory factors.…”

Section: Introductionmentioning

confidence: 99%

“…Since simple, logical reasoning is seldom possible, building mathematical models and conducting computational simulations are often useful to our understanding of a mechanism of actions of key regulatory factors. We have previously developed two versions of mathematical models for calcium and phosphorus metabolism, focusing on the role of parathyroid hormone (PTH) and 1,25(OH) 2 D with and without inclusion of the role of FGF23 [1,2]. These models were able to explain the transient alterations in the concentrations of calcium in the serum and the urine by considering a rapid exchangeable pool of calcium (*100 mmol).…”

Section: Introductionmentioning

confidence: 99%

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A mathematical model of calcium and phosphorus metabolism in two forms of hyperparathyroidism

et al. 2011

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Parathyroid hormone (PTH) plays a critical role in calcium and phosphorus metabolism. Interestingly, in two forms of hyperparathyroidism (excessive amount of PTH in the serum), the metabolic disturbances in patients with chronic kidney disease (CKD) significantly differ from those with primary hyperparathyroidism (PHP). Since an intuitive understanding of these PTH-linked regulatory mechanisms are hardly possible, we developed a mathematical model using clinical data (1586 CKD and 40 PHP patients). The model was composed of a set of ordinary differential equations, in which the regulatory mechanism of PTH together with other key factors such as 1,25-Dihydroxyvitamin D (1,25(OH) 2 D) and calcium was described in the tissues including bone, the kidney, the serum, and the parathyroid glands. In this model, an increase in PTH was induced by its autonomous production in PHP, while PTH in CKD was elevated by a decrease in feedback inhibition of 1,25(OH) 2 D in the serum, as well as an increase in stimulation by phosphorus in the serum. The model-based analysis revealed characteristic differences in the outcomes of hyperparathyroidism in CKD and PHP. The calcium exchange in bone, for instance, was predicted significantly higher in PHP than CKD. Furthermore, we evaluated the observed and predicted responses to the administration of calcimimetics, a recently developed synthetic drug that modulated efficacy of calcium-sensing receptors. The results herein support the notion that the described model would enable us to pose testable hypotheses about the actions of PTH, providing a quantitative analytical tool for evaluating treatment strategies of PHP and CKD.

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“…Mathematical modeling has become popular to depict the conceptually developed model and to evaluate and predict the metabolic variables involved in the mechanism. Mathematical modeling can be used to prove the conceptual model by simulating the model and comparing it to the actual data set (Komarova et al 2003;Raposo et al 2002). Also, it has been used to quantitatively estimate Ca parameters, which cannot be directly measured, by fitting the experimental data to examine the effect of regulators in Ca/bone metabolism (Hill et al 2008;Wastney et al 1996).…”

Section: Introductionmentioning

confidence: 99%

A Theoretical Modeling for Suggesting Unique Mechanism of Adolescent Calcium Metabolism

Lee

Cho

Okos

2013

Journal of Biosystems Engineering

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Purpose: Modeling has been used for elucidating the mechanism of complex biosystems. In spite of importance and uniqueness of adolescent calcium (Ca) metabolism characterized by a threshold Ca intake, its regulatory mechanism has not been covered and even not proposed. Hence, this study aims at model-based proposing potential mechanisms regulating adolescent Ca metabolism. Methods: Two different hypothetic mechanisms were proposed. The main mechanism is conceived based on Ca-protein binding which induces renal Ca filtration, while additional mechanism assumed that active renal Ca re-absorption regulated Ca metabolism in adolescents. Mathematical models were developed to represent the proposed mechanism and simulated them whether they could produce adolescent Ca profiles in serum and urine. Results: Simulation showed that both mechanisms resulted in the unique behavior of Ca metabolism in adolescents. Based on the simulation insulin-like growth factor-1 (IGF-1) is suggested as a potential regulator because it is related to both growth, a remarkable characteristic of adolescence, and Ca metabolism including absorption and bone accretion. Then, descriptive modeling is employed to conceptualize the hypothesized mechanisms governing adolescent Ca metabolism. Conclusions: This study demonstrated that modeling is a powerful tool for elucidating an unknown mechanism by simulating potential regulatory mechanisms in adolescent Ca metabolism. It is expected that various analytic applications would be plausible in the study of biosystems, particularly with combination of experimental and modeling approaches.

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A Minimal Mathematical Model of Calcium Homeostasis

Cited by 56 publications

References 42 publications

Review on Application of Biosystem Modeling: Introducing 3 Model-based Approaches in Studying Ca Metabolism

Review on Application of Biosystem Modeling: Introducing 3 Model-based Approaches in Studying Ca Metabolism

A mathematical model of calcium and phosphorus metabolism in two forms of hyperparathyroidism

A Theoretical Modeling for Suggesting Unique Mechanism of Adolescent Calcium Metabolism

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