Zager, Schlosser, Tran, 2007

Model Status

This CellML version of the model has been checked in COR and PCEnv and the model runs to 'almost' recreate the published results. The only difference is the CellML model is missing the time delays. Although it is possible to express time delays in the CellML language, the software tools PCEnv and COR are currently unable to handle time delays. The units have been checked and are consistent. The author of the original model was involved in the process of translating the model into CellML and his help has been invaluable.

Model Structure

There are increasing concerns that environmental pollutants may disrupt the endocrine systems in both humans and wildlife. Of particular concern are compounds that can affect the functioning of the endocrine system. It has been suggested that these so called endocrine-active compounds (EAC) can have numerous health effects, both adverse and beneficial.

Phytoestrogens are a class of EAC that are naturally derived from plants. They can mimic the effects of endogenous estrogen by binding to the estrogen receptor and acting as either an agonist or an antagonist. Genistein is a phytoestrogen which is found in soy products. It has been linked to beneficial health effects, such as cancer prevention and mammary tumour growth suppression, but also to adverse effects such as endocrine disruption and enhanced carcinogenic tumour growth. As a consequence of these wide ranging effects, genistein has become the topic of many research investigations.

Physiologically based pharmacokinetic (PBPK) models are often developed to simulate the general dosimetry of a chemical. The CellML model described here is a translation of the PBPK model of genistein dosimetry published by Zager, Schlosser and Tran, 2007 (the complete original paper reference is cited below). Genistein undergoes enterohepatic circulation - from the liver to the gastrointestinal (GI) tract - where it is subsequently reabsorbed. There is a time delay while genistein passes down the bile duct, during which time it is not available for reabsorption, but once it has been secreted into the intestine it is cleaved from its conjugated form back into its pure form, after which it can be reabsorbed (see the diagram below). To incorporate this delay in the mathematical model, state-dependent delay-differential equations (DDEs) were included. The values of unknown parameters were estimated by fitting the model to biliary excretion data.

Schematic diagram of the genistein PBPK model. The upper components represent compartments containing the pure genistein (gen) while the lower components contain genistein that has undergone conjugation in the liver (con). B - plasma, rp - richly perfused tissues, pp - poorly perfused tissues, l - liver, GI - gastrointestinal tract, ROB - rest of body, Ab - bile-delayed compartment. The arrows represent genistein transfer as blood flows between the organs and the systemic circulation, and also genistein elimination in the urine (out of Ccon_ROB); these are all linear with the exception of the conversion of pure to conjugated genistein in the liver which follows Michaelis-Menton kinetics.

A delayed nonlinear PBPK model for genistein dosimetry in rats, Michael G. Zager, Paul M. Schlosser and Hien T. Tran, 2007, Bulletin of Mathematical Biology , 69, 93-117. (A PDF version of the article is available to journal subscribers on the Bulletin of Mathematical Biology website.) PubMed ID: 17024552