Mechanism of inhibition defines CETP activity: a mathematical model for CETP in vitro.

Because cholesteryl ester transfer protein (CETP) inhibition is a potential HDL-raising therapy, interest has been raised in the mechanisms and consequences of CETP activity. To explore these mechanisms and the dynamics of CETP in vitro, a mechanistic mathematical model was developed based upon the shuttle mechanism for lipid transfer. Model parameters were estimated from eight published experimental datasets, and the resulting model captures observed dynamics of CETP in vitro. Simulations suggest the shuttle mechanism yields behaviors consistent with experimental observations. Three key findings predicted from model simulations are: 1) net CE transfer activity from HDL to VLDL and LDL can be significantly altered by changing the balance of homoexchange versus heteroexchange of neutral lipids via CETP; 2) lipemia-induced increases in CETP activity are more likely caused by increases in lipoprotein particle size than particle number; and 3) the inhibition mechanisms of the CETP inhibitors torcetrapib and JTT-705 are significantly more potent than a classic competitive inhibition mechanism with the irreversible binding mechanism having the most robust response. In summary, the model provides a plausible representation of CETP activity in vitro, corroborates strong evidence for the shuttle hypothesis, and provides new insights into the consequences of CETP activity and inhibition on lipoproteins.

Response to continuous and pulsatile PTH dosing: a mathematical model for parathyroid hormone receptor kinetics.

In this paper, we propose a mathematical model for parathyroid hormone receptor (PTH1R) kinetics, focusing on the receptor's response to PTH dosing to discern bone formation responses from bone resorption. The PTH1R is a major target for new osteoporosis treatments, as pulsatile PTH dosing has been shown to induce net bone formation in both animals and humans, and PTH(1-34) was recently FDA approved for the treatment of post-menopausal osteoporosis. PTH has also been shown to cause net bone loss when given continuously, so that the net action of PTH on bone is dependent on the dosing pattern. We have developed a simplified two-state receptor kinetics model for the PTH1R, based on the concepts of Segel et al., to distinguish the activity of active and inactive receptor and receptor-ligand complexes. The goal is to develop a plausible model of the minimal essential biological relationships necessary for understanding the responses to PTH dosing. A two-state model is able to effectively discriminate between continuous and pulsatile PTH dosing using the active species as surrogates for the downstream anabolic response. For continuous PTH dosing, the model predicts a desensitized system dominated by the inactive receptor and complex, consistent with downstream net bone loss that has been demonstrated experimentally. Using pulsatile PTH dosing, the model system predicts a highly sensitized state dominated by the active receptor and complex, corresponding to net bone formation. These results are consistent with the hypothesis that the kinetics of the receptor plays a critical role in the downstream effects of PTH dosing. Moreover, these results indicate that within a range of biologically relevant PTH doses, the two-state model is able to capture the differential behavior of the system for both continuous and pulsatile PTH dosing. The development of such a model provides a rational basis for developing more biologically extensive models that may support the design of optimal dosing strategies for PTH-based anti-osteoporosis treatments. Moreover, this model provides a unique starting point from which to design experiments investigating PTH receptor biology.

Probabilistic methods for addressing uncertainty and variability in biological models: application to a toxicokinetic model.

Population variability and uncertainty are important features of biological systems that must be considered when developing mathematical models for these systems. In this paper we present probability-based parameter estimation methods that account for such variability and uncertainty. Theoretical results that establish well-posedness and stability for these methods are discussed. A probabilistic parameter estimation technique is then applied to a toxicokinetic model for trichloroethylene using several types of simulated data. Comparison with results obtained using a standard, deterministic parameter estimation method suggests that the probabilistic methods are better able to capture population variability and uncertainty in model parameters.

Perspectives on mathematical modeling for receptor-mediated processes.

Mathematical modeling is a potent in silico tool that can help investigate, interpret, and predict the behavior of biological systems. The first step is to develop a working hypothesis of the biology. Then by "translating" the biological phenomena into equations, models can harness the power of mathematical analysis techniques to explore the dynamics and interactions of the biological components. Models can be used together with traditional experimental models to help design new experiments, test hypotheses, identify mechanisms, and predict outcomes. This article reviews the process of building, calibrating, and using mathematical models in the context of the kinetics of receptor and signal transduction biology. An example model related to the androgen receptor-mediated regulation of the prostate is presented to illustrate the steps in the modeling process and to highlight the potential for mathematical modeling in this area.

Mathematical model for the androgenic regulation of the prostate in intact and castrated adult male rats.

The testicular-hypothalamic-pituitary axis regulates male reproductive system functions. Understanding these regulatory mechanisms is important for assessing the reproductive effects of environmental and pharmaceutical androgenic and antiandrogenic compounds. A mathematical model for the dynamics of androgenic synthesis, transport, metabolism, and regulation of the adult rodent ventral prostate was developed on the basis of a model by Barton and Anderson (1997). The model describes the systemic and local kinetics of testosterone (T), 5alpha-dihydrotestosterone (DHT), and luteinizing hormone (LH), with metabolism of T to DHT by 5alpha-reductase in liver and prostate. Also included are feedback loops for the positive regulation of T synthesis by LH and negative regulation of LH by T and DHT. The model simulates maintenance of the prostate as a function of hormone concentrations and androgen receptor (AR)-mediated signal transduction. The regulatory processes involved in prostate size and function include cell proliferation, apoptosis, fluid production, and 5alpha-reductase activity. Each process is controlled through the occupancy of a representative gene by androgen-AR dimers. The model simulates prostate dynamics for intact, castrated, and intravenous T-injected rats. After calibration, the model accurately captures the castration-induced regression of the prostate compared with experimental data that show that the prostate regresses to approximately 17 and 5% of its intact weight at 14 and 30 days postcastration, respectively. The model also accurately predicts serum T and AR levels following castration compared with data. This model provides a framework for quantifying the kinetics and effects of environmental and pharmaceutical endocrine active compounds on the prostate.