Mathematical modeling of intracrine androgen metabolism in prostate cancer: Methodological aspects

Progression of castration-recurrent/resistant prostate cancer (CRPC) relies in part on dihydrotestosterone derived from intratumoral androgen metabolism. Mathematical modeling provides a valuable tool for studies of androgen metabolism in CRPC. This modeling approach integrates existing knowledge about complex biologic systems and provides a means of interrogating the effects of various interventions. We sought to model a single reaction in the androgen biosynthesis network, namely the oxidation of androsterone (AND) to androstanedione (5α-dione) by four 3α-oxidoreductase enzymes, as an initial effort to establish the feasibility of our modeling approach.

Models were constructed for two cell culture systems, a non-prostate cancer cell line (CV-1) and a prostate cancer cell line (LAPC-4), using the SimBiology app (version 5.3) in MATLAB (version 8.6). The models included components for substrate (AND), product (5α-dione), each of the four enzymes, and each of the four enzyme-substrate complexes. Each enzymatic reaction consisted of a reversible enzyme-substrate binding step and an irreversible catalysis step. Rates of change for each component were described using ordinary differential equations.

Mathematical models were developed with model parameter values derived from literature sources or from existing experimental data, which included gene expression measurements and substrate and product concentrations determined using liquid chromatography-tandem mass spectrometry. The models for both cell lines adequately described substrate and product concentrations observed after 12 h treatment with AND.

This modeling approach represents an adaptable, extensible and mechanistic framework that reflects androgen metabolism. The models can be expanded systematically to describe the complex androgen metabolic pathways important for study of novel therapies for CRPC.