Role of channels in the O₂ permeability of murine red blood cells. III. Mathematical modeling and simulations.

Abstract

In this third of three papers, we develop a reaction-diffusion model for O ₂ offloading from a red blood cell (RBC), treated as a sphere with diameter approximating RBC thickness. Stopped-flow (SF) analysis (paper #1) of hemoglobin/oxyhemoglobin (Hb/HbO ₂ ) absorbance spectra during O ₂ efflux from intact murine RBCs show that membrane-impermeant inhibitor p-chloromercuribenzenesulfonate (pCMBS) reduces the HbO ₂ -deoxygenation rate constant (k _HbO2 ) by ~61%. SF experiments show that k _HbO2 falls by (1) 9% for aquaporin-1 knockouts (AQP1-KOs), (2) 17% for Rhesus A-glycoprotein knockouts (RhAG-KOs), (3) 30% for double knockouts (dKOs), and (4) ~78% in dKOs/pCMBS. Here, we simulate HbO ₂ dissociation (rate constant, k _HbO2 → Hb); HbO ₂ , Hb, and O ₂ diffusion through RBC cytosol; transmembrane O ₂ diffusion; and O ₂ diffusion through extracellular unconvected fluid (EUF) to bulk extracellular fluid. Informed by automated-hematology data (paper #1) and imaging-flow-cytometry data (paper #2), simulations predict that observed k _HbO2 decreases cannot reflect changes in RBC size/shape or [Hb/HbO ₂ ]. Instead, membrane O ₂ permeability ( P _M,O2 ) must fall by (1) 22% to account for AQP1-KO data, (2) 36% for RhAG-KOs, (3) 55% for dKOs, and (4) 91% for dKOs/pCMBS. Exploring predicted k _HbO2 sensitivities to eight key parameters (e.g., [Hb/HbO ₂ ], diffusion constants, k _HbO2 → Hb, thickness _EUF , diameter _Sphere ) shows that no reasonable changes explain the k _HbO2 data. We introduce a linear-combination approach to accommodate for the presence of poikilocytes. Finally, contrary to common beliefs, the model predicts that, in the absence of inhibitors, the RBC membrane represents >30% of total diffusive "resistance" to O ₂ offloading, even for a WT mouse.