(341e) Parameter Estimation for Sparse Biological Data: Glucose-Dependence of Renin-Angiotensin System in Podocytes Cells during Diabetic Kidney Disease

Diabetic kidney disease (DKD) is the primary cause of end-stage renal failure. Hyperglycemia is known to initiate and exacerbate the pathophysiology of DKD. Podocytes are terminally differentiated glomerular epithelial cells that play a key role in maintaining the structure and function of glomerular filtration barrier in kidneys. Podocytes express a local renin-angiotensin system (RAS) that is altered in hyperglycemia. Studies have shown that angiotensin II (ANG II), which is a RAS peptide, is modulated in hyperglycemic conditions and triggers podocyte injury and apoptosis. The progression of DKD could be slowed by controlling the ANG II levels to prevent irreversible podocyte loss. However, experimental evidence for glucose-dose-dependency of ANG II is scarce in the literature. Hence, for better understanding of the underlying mechanism, we use mathematical modeling to describe the glucose-stimulated RAS signaling in podocytes that produces ANG II.

We have formulated a mathematical model to describe the glucose-sensitive reaction network that triggers the synthesis of ANG II. The local podocyte RAS signaling pathway is represented by a system of ordinary differential equations to track RAS peptides, enzymes, and receptors without explicit glucose-dependence. The system is assumed to be at steady state, thus the model reduces to a system of nonlinear equations. Previous experimental studies were used to estimate the unknown parameters and kinetic constants for the model. Due to sparse experimental data on RAS at sufficiently many glucose states, two different approaches were used to parameterize the model to add glucose-dependency through the parameters: (1) parameterizing the RAS model at normal and high glucose states where all the RAS components are known or estimated and approximating the parameters for intermediate glucose states where no RAS component information is available by considering glucose-dependent linear mathematical functions for each of the sensitive parameters, and (2) fitting the parameters for the RAS model with different proposed glucose-dependent mathematical functions to experimental data from the literature for ANG II vs. glucose [1]. In both the approaches, only the sensitive parameters were varied whereas the non-sensitive parameters were assumed to be independent of glucose.

The model was used to study the change in ANG II concentrations in hyperglycemic conditions with varying glucose levels. The results showed a rise in ANG II levels with increasing glucose concentrations consistent with experimental observations. Sensitivity analysis was conducted. The two parameter estimation approaches resulted in multiple candidate models that are reasonable for glucose-dependence of podocyte intracellular RAS.

Using this model, we were also able to discriminate between possible models for the glucose dose-dependency of ANG II production in podocytes. The key RAS-modulating biomarkers can be identified by studying their effect on ANG II levels. The model can also be used to study the effect of different combinations of various ANG II modulating therapies, which could be useful for drug development.

References: [1] Durvasula & Shankland. 2008. Am J Physiol-Renal Physiol, 294, F830-F839.