Mathematical Modeling of the Gut–Bone Axis and Implications of Butyrate Treatment on Osteoimmunology

Butyrate, a short-chain fatty acid produced by the gut microbiota, has pivotal roles in the regulation of the immune system. Recent studies have revealed that butyrate increases the differentiation of peripheral regulatory T cells in the gut-bone axis and promotes osteoblasts' bone forming activity. However, the mechanism of the therapeutic benefit of butyrate in bone remodeling remains incompletely understood. Here, we develop a multicompartment mathematical model to quantitatively predict the contribution of butyrate on the expansion of regulatory T cells in the gut, blood, and bone compartments. We investigate the interplay between regulatory T cell-derived TGF-β and CD8+ T cell-derived Wnt-10b with changes in gut butyrate concentration. In addition, we connect our model to a detailed model of bone metabolism to study the impacts of butyrate and Wnt-10b on trabecular bone volume. Our results indicate both direct and indirect immune-mediated impacts of butyrate on bone metabolism.