Theoretical analysis of insulin-dependent glucose uptake heterogeneity in 3D bioreactor cell culture

Three-dimensional (3D) cell cultures in bioreactors are becoming relevant as models for biological and physiological in vitro studies. In such systems, mathematical models can assist the experiment design that links the macroscopic properties to single-cell responses. We investigated the relationship between biochemical stimuli and cell response within a 3D cell culture in scaffold with heterogeneous porosity. Specifically, we studied the effect of insulin on the local glucose metabolism as a function of 3D pore size distribution. The multiscale mathematical model combines the mass transport within a 3D scaffold and a signaling pathways model. It considers the scaffold heterogeneity, and it describes spatiotemporal concentration of metabolites, biochemical stimuli, and cell density. The signaling model was integrated into this model, linking the local insulin concentration at cell membrane to the glucose uptake rate through glucose transporter type 4 (GLUT4) translocation from the cytosol to the cell membrane. The integrated model determines the cell response heterogeneities in a single channel, hence the biological response distribution in a 3D system. It also provides macroscopic outcomes to evaluate the feasibility of an experimental measurement of the system response. From our analysis, it became apparent that the flow rate is the most important operative variable, and that an optimum value ensures a fast and detectable cell response. This model on insulin-dependent glucose consumption rate offers insight into the cell metabolism physiology, which is a fundamental requirement for the study metabolic disorder such as Type 2 diabetes mellitus, in which the physiological insulin-dependent glucose metabolism is impaired.