BackgroundThe complexity and multiscale nature of the mammalian immune response provides an excellent test bed for the potential of mathematical modeling and simulation to facilitate mechanistic understanding. Historically, mathematical models of the immune response focused on subsets of the immune system and/or specific aspects of the response. Mathematical models have been developed for the humoral side of the immune response, or for the cellular side, or for cytokine kinetics, but rarely have they been proposed to encompass the overall system complexity. We propose here a framework for integration of subset models, based on a system biology approach.ResultsA dynamic simulator, the Fully-integrated Immune Response Model (FIRM), was built in a stepwise fashion by integrating published subset models and adding novel features. The approach used to build the model includes the formulation of the network of interacting species and the subsequent introduction of rate laws to describe each biological process. The resulting model represents a multi-organ structure, comprised of the target organ where the immune response takes place, circulating blood, lymphoid T, and lymphoid B tissue. The cell types accounted for include macrophages, a few T-cell lineages (cytotoxic, regulatory, helper 1, and helper 2), and B-cell activation to plasma cells. Four different cytokines were accounted for: IFN-γ, IL-4, IL-10 and IL-12. In addition, generic inflammatory signals are used to represent the kinetics of IL-1, IL-2, and TGF-β. Cell recruitment, differentiation, replication, apoptosis and migration are described as appropriate for the different cell types. The model is a hybrid structure containing information from several mammalian species. The structure of the network was built to be physiologically and biochemically consistent. Rate laws for all the cellular fate processes, growth factor production rates and half-lives, together with antibody production rates and half-lives, are provided. The results demonstrate how this framework can be used to integrate mathematical models of the immune response from several published sources and describe qualitative predictions of global immune system response arising from the integrated, hybrid model. In addition, we show how the model can be expanded to include novel biological findings. Case studies were carried out to simulate TB infection, tumor rejection, response to a blood borne pathogen and the consequences of accounting for regulatory T-cells.ConclusionsThe final result of this work is a postulated and increasingly comprehensive representation of the mammalian immune system, based on physiological knowledge and susceptible to further experimental testing and validation. We believe that the integrated nature of FIRM has the potential to simulate a range of responses under a variety of conditions, from modeling of immune responses after tuberculosis (TB) infection to tumor formation in tissues. FIRM also has the flexibility to be expanded to include both complex and novel immunologi...

The testicular-hypothalamicpituitary 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), 5␣-dihydrotestosterone (DHT), and luteinizing hormone (LH), with metabolism of T to DHT by 5␣-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 5␣-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 ϳ17 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. rodent ventral prostate; androgen receptor; testosterone; 5␣-dihydrotestosterone; testicular-hypothalamic-pituitary axis THE HYPOTHALAMUS, PITUITARY, AND TESTES produce endocrine hormones responsible for regulation of the prostate and other male sexual functions (12, 46). Exogenous endocrine active compounds can disrupt these processes. Some pesticides (e.g., vinclozolin and linuron) are known to have antiandrogenic activity (19,20). Toxic effects of antiandrogens in male rodents range from developmental effects such as reproductive malformations, retained nipples, and undescended testes to pubertal effects such as delayed puberty and reduced weights of prostate and other reproductive organs. In the pharmaceutical setting, therapeutic drugs such as finasteride, dutasteride, bicalutamide, and flutamide are used to treat benign prostatic hyperplasia and/or prostate cancer by inhibiting androgendependent growth processes.The mechanisms of action of antiandrogens are generally of two forms. The first is the androgen antagonist, which binds to the androgen receptor (AR) but does not stimulate DNA transcription, such as the pharmaceutical compounds flutamide and bicalutamide or the environmental compound vinclozolin. The second is the 5␣-reductase inhibitor, which blocks th...

A systems-level mathematical model is presented that describes the effects of inhibiting the enzyme 5α-reductase (5aR) on the ventral prostate of the adult male rat under chronic administration of the 5aR inhibitor, finasteride. 5aR is essential for androgen regulation in males, both in normal conditions and disease states. The hormone kinetics and downstream effects on reproductive organs associated with perturbing androgen regulation are complex and not necessarily intuitive. Inhibition of 5aR decreases the metabolism of testosterone (T) to the potent androgen 5α-dihydrotestosterone (DHT). This results in decreased cell proliferation, fluid production and 5aR expression as well as increased apoptosis in the ventral prostate. These regulatory changes collectively result in decreased prostate size and function, which can be beneficial to men suffering from benign prostatic hyperplasia (BPH) and could play a role in prostate cancer. There are two distinct isoforms of 5aR in male humans and rats, and thus developing a 5aR inhibitor is a challenging pursuit. Several inhibitors are on the market for treatment of BPH, including finasteride and dutasteride. In this effort, comparisons of simulated vs. experimental T and DHT levels and prostate size are depicted, demonstrating the model accurately described an approximate 77% decrease in prostate size and nearly complete depletion of prostatic DHT following 21 days of daily finasteride dosing in rats. This implies T alone is not capable of maintaining a normal prostate size. Further model analysis suggests the possibility of alternative dosing strategies resulting in similar or greater effects on prostate size, due to complex kinetics between T, DHT and gene occupancy. With appropriate scaling and parameterization for humans, this model provides a multiscale modeling platform for drug discovery teams to test and generate hypotheses about drugging strategies for indications like BPH and prostate cancer, such as compound binding properties, dosing regimens, and target validation.

Genistein is an endocrine-active compound (EAC) found in soy products. It has been linked to beneficial effects such as mammary tumor growth suppression and adverse endocrine-related effects such as reduced birth weight in rats and humans. In its conjugated form, genistein is excreted in the bile, which is a significant factor in its pharmacokinetics. Experimental data suggest that genistein induces a concentration-dependent suppression of biliary excretion. In this article, we describe a physiologically based pharmacokinetic (PBPK) model that focuses on biliary excretion with the goal of accurately simulating the observed suppression. The mathematical model is a system of nonlinear differential equations with state-dependent delay to describe biliary excretion. The model was analyzed to examine local existence and uniqueness of a solution to the equations. Furthermore, unknown parameters were estimated, and the mathematical model was compared against published experimental data.