(448e) Model-Based Identification of Therapeutic Intervention Targets in Calcium-Related Pathologies

Calcium (Ca) homeostasis is the maintenance of a stable plasma Ca concentration in the human body in the presence of Ca variability in the physiological environment (e.g. by ingestion and/or excretion). For normal physiological function, the total plasma Ca concentration must be maintained within a very narrow range (2.2-2.4mM) [1]. Meeting such stringent requirements is the task of a regulatory system that employs parathyroid hormone (PTH) and calcitriol (CTL) to regulate Ca flux between the plasma and the kidneys, intestines and bones. Chronic imbalances in plasma Ca levels are associated with disorders of the regulatory organs, which cause abnormal hormonal secretion and activity. These changes in hormonal activity may lead to long-term problems, such as, osteoporosis (increased loss of bone mineral density), which arises from primary hyperparathyroidism (PHPT) – hyper secretion of PTH [2].

We previously proposed a representation of the physiological process of Ca regulation in the form of a control system block diagram comprising: sensor, controller, actuators and process [3]. Mathematical models were generated for each component sub-process by applying standard conservation of mass principles augmented with available mechanistic information. The resulting model is a system of ordinary differential equations (ODE) that describe the dynamics of: (i) PTH in the controller; (ii) calcitriol from the kidneys in the actuator; (iii) bone cells (osteoblasts and osteoclasts) from the bone in the actuator; and (iv) plasma calcium (the “process”). The overall model was subsequently validated with published clinical data. Finally known pathological conditions were accurately simulated through induced irregularities in the control system components which represent defects in the Ca homeostatic system. The irregularities include defects of the sensor, controller and/or actuator.

In this presentation, we focus on our approach to identifying potential targets for therapeutic intervention in PHPT and chronic kidney disease (CKD). We apply sensitivity analysis to models of the pathological conditions corresponding to PHPT and CKD to identify the intrinsic parameters that have the most influence on the key hormones/ions (PTH, CTL, Ca and phosphate). Additionally, we explore the extent to which each of these parameters affects the different hormones/ions and explain the physiological significance of these findings in the two pathologies. Furthermore, we show that our analysis is consistent with the clinical results of calcimimetic therapy in PHPT and CKD. Calcimimetics constitutes a class of drugs used to reduce PTH secretion through targeting of the calcium-sensing receptors on the parathyroid gland. We anticipate using this approach in hypothesizing therapeutic intervention targets for other Ca-related pathologies.

1. Kovacs, W.J. and S.R. Ojeda, Textbook of Endocrine Physiology. 6th ed2012, Oxford: Oxford University Press. xii, 462 p.

2. Fraser, W.D., Hyperparathyroidism. Lancet, 2009. 374(9684): p. 145-58.

3. Christie, C.R., L.E.K. Achenie, and B.A. Ogunnaike, A Control Engineering Perspective to Modeling Calcium Regulation and Related Pathologies, in Annual Meeting October 28-    November 2,2012.