Mathematical Modeling of Estrogen-Mediated Inflammation in the Gut and Immune System

Postmenopausal osteoporosis is a chronic inflammatory disease characterized by decreased bone mass and increased bone fracture risk. Estrogen deficiency during menopause plays a major role in post-menopausal osteoporosis by influencing bone, immune, and gut cell activity. In the gut, estrogen loss decreases tight junction proteins that bind epithelial cells of the intestinal barrier together. This increases gut permeability and alters the balance of T cells, increasing inflammatory T helper (Th17) cells and decreasing anti-inflammatory regulatory T cells (Tregs). Prebiotic dietary fibers are a promising treatment modality for gut-mediated inflammation and bone loss associated with estrogen deficiency. In a previous study, we investigated the effect of butyrate (a prebiotic by-product) on Treg levels in the gut, blood, and bone starting with healthy conditions. However, a gap remains in our mechanistic understanding of how estrogen affects systemic inflammation separately and in combination with prebiotic fibers. We developed a two-compartment dynamic model of estrogen in the gut and immune system to investigate the mechanisms of gut-mediated inflammation induced by estrogen-deficient conditions. Our initial model contains ODEs for estrogen, naive T cells, Tregs, and Th17 cells in gut and blood compartments. Estrogen is modeled using physiological mass balance equations considering its production, migration, and elimination. We integrate our estrogen model with an adapted version of our previous butyrate model, adding a population balance for Th17 cells and terms for bidirectional migration of Tregs and Th17 cells. Estrogen interactions with cells are modeled using Hill-type activation and inhibition functions. Our mathematical model predicts changes in T cell dynamics associated with changes in endogenous estrogen levels. We compare our predictions to in vivo results of estrogen, Tregs, and Th17 levels in the gut and blood after surgical menopause in mice. In the future, we will leverage this model to investigate whether the effect of prebiotic fiber treatment on estrogen-deficient bone loss is significantly affected by gut-mediated inflammation. The emphasis in this preprint is on the methods, particularly those for literature-based model parameterization.