Mathematical modeling of the effects of Wnt-10b on bone metabolism
Abstract
Bone health is determined by many factors including bone metabolism. At any time, many bone multicellular units (BMU) are going through a remodeling cycle. Depending on different signaling factors, the cycle will end with the same amount of bone as at the beginning of the remodeling cycle (healthy) or increased or decreased amounts of bone. These changes contribute to chronic bone diseases such as osteoporosis. Osteoporosis results in brittle bones that are easily fractured. Recently immune cells have been identified as major signaling factors for this process. However, it is unclear how and to what extent they affect bone metabolism. One strategy to better understand this phenomenon is to consider different foods or medicines that activate immune cells. Lactobacillus rhamnosus GG (LGG), for example, is a probiotic that increases butyrate production in the gut. Butyrate has been shown to indirectly increase bone density through a series of interconnected processes throughout the body that involve immune cells (Tyagi et al., 2018). One key process is the increase of Wnt-10b within the bone compartment by stimulated regulatory T cells. This process has been shown to increase bone volume. Here, we focus on how Wnt-10b has been shown to alter osteoblastogenesis, osteoblast apoptosis rate, and osteoblast bone formation rate, which collectively lead to the increase of bone density (Wend et al., 2012). To model this change, we adapted a previously published and well-cited model of bone remodeling (Graham et al., 2013). The resulting model is a single compartment system that includes ordinary differential equations for cell types typically involved in remodeling such as osteoclasts, osteoblasts, and osteocytes and a delayed differential equation that tracks the amount of bone present at the remodeling site. Our alterations to the original model consist of extending it past a single remodeling cycle, implementing a reaction to Wnt-10b, and including a delayed relationship for the formation of the bone matrix. Three new parameters were estimated and validated using normalized data collected on mice (Bennett et al., 2005, 2007; Roser-Page et al., 2014). The values of the parameters were found using MATLAB nonlinear least-squares solver lsqcurvefit and delayed differential equation solver dde23. The completed model connects Wnt-10b to bone metabolism. Interestingly, we nd that this model predicts that osteoblast population does not change with Wnt-10b, but pre-osteoblast and osteoclast populations do. This model improves the understanding of immune cell disturbances to bone health and can help identify targets for medical intervention of bone loss.
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- OSU Theses [15752]