Due 2/12/2019 Problem 1:

Insulin is transported from the capillary to the interstitial space of tissues, particularly muscle tissue, to support glucose uptake by cells. The human insulin protein is a dimer composed of 51 amino acids, and has a molecular mass of 5808 Da. It has a molecular diameter of 2.7 nm. The length of a blood capillary is 1 mm, dimeter is 10 µm, and capillary wall thickness is 0.5 µm. The capillary wall contains intracellular pores with diameter of 7 nm for mass transport across the capillary wall. The pores cover 0.1% of the surface of the capillary wall and the rest is covered by endothelial cells such that only those compounds that have appreciable solubility in the cell lipid bilayer can diffuse through. Insulin does not have appreciable solubility in the cell lipid bilayer. Therefore, the overall insulin mass transfer, not including mass transfer by pinocytosis, through the capillary wall is given by the following equation: 𝑁𝑁𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖,𝑡𝑡 = 𝑁𝑁𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖,𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 + 𝑁𝑁𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖,𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 Where Ninsulin,conv is the transport of insulin by convention through the capillary pores and Ninsulin,diff is the transport of insulin by diffusion through the capillary pores given by the following equations: 𝑁𝑁𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖,𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 = 𝐶𝐶𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖,𝑐𝑐𝑐𝑐𝑐𝑐 (1 − 𝜎𝜎) 𝐽𝐽𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 𝑁𝑁𝑂𝑂2,𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 = 𝑃𝑃𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖,𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 𝑆𝑆 (𝐶𝐶𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖,𝑐𝑐𝑐𝑐𝑐𝑐 − 𝐶𝐶𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖,𝑖𝑖𝑖𝑖𝑖𝑖) In the above equations, Cinsulin,cap and Cinsulin,int are the concentrations of insulin in the capillary and in the tissue interstitial space, σ is the reflection coefficient of insulin, Jfilt is the capillary filtration rate, Pinsulin,pore is the insulin permeability in the pores of the capillary, S is the total surface area of a capillary, Dinsulin is the insulin diffusion coefficient in plasma, and twall is the thickness of the capillary wall. The following values are given for muscle tissue under saturation insulin infusion: Cinsulin,cap = 22000 picomoles/liter Cinsulin,int = 0 Wall tortuosity = τ = 2 Jfilt = 5.75×10-9 cm3/h per capillary (1 mm long) Dinsulin = 150 μm2/s A. Determine the reflection coefficient and the ratio of capillary membrane to plasma diffusion coefficient (Dm/D) for insulin. B. Use the results in part A to find the contribution of each mechanism to insulin transport through the capillary wall (percent convection and percent diffusion). C. Determine the total insulin transport through the capillary wall in picomoles/h. D. What would the total insulin transport reduce to when the Cinsulin,int increases to 19000 picomoles/liter as insulin is transported to the interstitial space (the same Cinsulin,cap)?