| The transportation of glucose, the primary energy source of all eukaryotic cells, from the bloodstream to the cells is catalyzed by a family of glucose transporters (GLUTs), among which GLUT4 is insulin stimulated and regulated. To study the insulin-stimulated glucose transport, we analyze the hybrid metabolic and signaling pathway models constructed by Sedaghat, et al. by applying multiple strategies based on dynamic sensitivity analysis, concentration control analysis, non-equilibrium thermodynamics, and nonlinear dynamics. In dynamic sensitivity analysis, we have calculated the time-dependent sensitivities of the concentration of the membrane GLUT4 with respect to all the reaction parameters (reaction rate constants and initial concentrations of the effectors). The roles of feedbacks are investigated by using dynamic sensitivities. In addition, the integrated sensitivities of the membrane GLUT4 have been used to rank the accumulated influence of each reaction parameter on the membrane GLUT4. Results are consistent with experimental facts and predictions of drug targets in the literature. Furthermore, a strategy is developed using dynamic concentration and sensitivity analyses to control certain outputs of the insulin pathways. The objective is to enhance the accumulated action of the membrane GLUT4 for a fixed amount of insulin input.; In the application of non-equilibrium thermodynamics, we calculate the fluxes, chemical affinities, and energy dissipated rates associated with each of the reaction steps of the pathways. The flux and chemical affinity associated with the GLUT4 translocation to the plasma membrane show clear sign of backflow, after the insulin application is suddenly switched off. This backflow results in the decrease in the concentration of membrane GLUT4, thus the reduction of glucose transport. Stimulated by these results, we have carried out a study of insulin dosage delivery aimed at enhancing the duration of the high concentration period of membrane GLUT4, that is, increasing insulin efficiency using various insulin input functions. Negative feedback and/or delay often cause oscillatory behaviors of a network system. This phenomenon reveals itself in the present insulin model as well. Nonlinear dynamical analysis and power spectra have been applied to the study of the complex oscillations associated with effectors concentrations. |
