In this study, we formulated a mathematical model of hypoxia-inducible factor 1 (HIF-1) mediated regulation of cellular energy metabolism describing the reprogramming of cell metabolic processes from oxidative phosphorylation to glycolysis under reduced oxygen levels. The model considers the dynamics of fifteen biochemical species and the proton concentration with the underlying reaction processes localized in three intracellular compartments, i.e. the cytoplasm, mitochondrion and nucleus. More than sixty parameters of the model were calibrated using both the published data and the system steady-state based identification procedure. The model was validated by generating predictions which could be compared to empirical observations. The model behaviors representing the cell metabolism switching over in response to transitioning from a normoxic to hypoxic environment are consistent with the current views of the role of HIF-1 in hypoxia.

In this paper, we derive an effective model for transport processes in periodically perforated elastic media, taking into account, e.g., cyclic elastic deformations as they occur in lung tissue due to respiratory movement. The underlying microscopic problem couples the deformation of the domain with a diffusion process within a mixed Lagrangian/Eulerian formulation. After a transformation of the diffusion problem onto the fixed domain, we use the formal method of two-scale asymptotic expansion to derive the upscaled model, which is nonlinearly coupled through effective coefficients. The effective model is implemented and validated using an application-inspired model problem. Numerical solutions for both, cell problems and macroscopic equations, are investigated and interpreted. We use simulations to qualitatively determine the effect of the deformation on the transport process.