Mathematical Model for Glucose Dependence of the Local Renin-Angiotensin System in Podocytes.

Diabetic kidney disease (DKD) is the primary cause of kidney failure. Diabetic hyperglycemia primarily damages podocyte cells. Podocytes express a local renin-angiotensin system (RAS) that produces angiotensin II (ANG II). ANG II levels are elevated by hyperglycemia, triggering podocyte injury. Quantitative descriptions of glucose dose dependency of ANG II are scarce in the literature. For better understanding of the mechanism of glycemic injury in DKD, a mathematical model is developed to describe the glucose-stimulated local RAS in podocytes. The model of the RAS signaling pathway in podocytes tracks peptides and enzymes without explicit glucose dependence. Local and global sensitivity analyses are used to identify the key parameters to be estimated in the model. Three approaches are explored to incorporate glucose dependency through linear ramp functions for the sensitive parameters. The first approach uses inferences from literature data to estimate the parameter values, while the other approaches reduce the number of assumptions by using least-squares regression to estimate all or a subset of the parameters. Physiological parameter values and RAS peptide concentrations ranges are used to discriminate between plausible models for the glucose dose dependency. This is the first model of the theory of the local RAS mechanism specific to podocyte cells to track ANG II levels in a range of glycemic conditions that may contribute to podocyte damage in DKD. The ability to track ANG II behavior could enable prediction of its downstream effects on podocytes and provide opportunities to better characterize pathophysiological features of DKD progression.

Mathematical Modeling of Tuberculosis Granuloma Activation.

Tuberculosis (TB) is one of the most common infectious diseases worldwide. It is estimated that one-third of the world's population is infected with TB. Most have the latent stage of the disease that can later transition to active TB disease. TB is spread by aerosol droplets containing Mycobacterium tuberculosis (Mtb). Mtb bacteria enter through the respiratory system and are attacked by the immune system in the lungs. The bacteria are clustered and contained by macrophages into cellular aggregates called granulomas. These granulomas can hold the bacteria dormant for long periods of time in latent TB. The bacteria can be perturbed from latency to active TB disease in a process called granuloma activation when the granulomas are compromised by other immune response events in a host, such as HIV, cancer, or aging. Dysregulation of matrix metalloproteinase 1 (MMP-1) has been recently implicated in granuloma activation through experimental studies, but the mechanism is not well understood. Animal and human studies currently cannot probe the dynamics of activation, so a computational model is developed to fill this gap. This dynamic mathematical model focuses specifically on the latent to active transition after the initial immune response has successfully formed a granuloma. Bacterial leakage from latent granulomas is successfully simulated in response to the MMP-1 dynamics under several scenarios for granuloma activation.