2. ( 20 points) To examine how glucose is regulated in tumor cells, we can model two of the factors which affect glucose concentration those cells: - Diffusion across the cell membrane, which is governed by a transport coefficient KG and the concentration gradient between the intracellular and extracellular space. - Conversion of glucose within the cell into lactate and lipids, which can be modeled as a sum of two first-order reactions with apparent rate constants k1 (for the lactate production pathway) and k2 (for the lipogenesis pathway). The cell (system) can be visualized as: - GEC represents the concentration of glucose in the extracellular space. - KG is the diffusional transport coefficient for entry into the cell: The rate of glucose concentration across the cell membrane is (dtdG)in/out=KG(GECG);[KG has units 1/s and the direction of diffusion depends on the sign of (GECG)] - For each pathway glucose is converted in a first-order reaction with rate constants k1 or k2 obeying a general first-order reaction formula: (dtdG)conv=kG; [conversion rate constant k has units 1/s] Derive the system dynamic equation for glucose concentration in the liver cell, in instance where, GEC=(3e3t+4)(mM). Show derivation starting from the balance equation