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

In this third of three papers, we develop a reaction-diffusion model for O2 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/HbO2) absorbance spectra during O2 efflux from intact murine RBCs show that membrane-impermeant inhibitor p-chloromercuribenzenesulfonate (pCMBS) reduces the HbO2-deoxygenation rate constant (kHbO2) by [~]61%. SF experiments show that kHbO2 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 HbO2 dissociation in the intact RBC (i.e., kHbO2); HbO2, Hb, and O2 diffusion through RBC cytosol; transmembrane O2 diffusion; and O2 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 kHbO2 decreases cannot reflect changes only in RBC size/shape or [Hb/HbO2]. Instead, membrane O2 permeability (PM,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 kHbO2 sensitivities to eight key parameters (e.g., [Hb/HbO2], diffusion constants, kHbO2[->]Hb+O2, thicknessEUF, diameterSphere) shows that no reasonable changes explain the kHbO2 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 O2 offloading, even for a WT mouse. Key PointsO_LIIn this third of three papers, we develop a novel reaction-diffusion model for O2 offloading from a red blood cell (RBC), treated as a sphere with diameter approximating RBC thickness. C_LIO_LIUsing physical constants and parameter values from the literature and papers #1 and #2, we generate simulations that reproduce observed hemoglobin desaturation (rate constant, kHbO2) of intact RBCs from wild-type mice. C_LIO_LITo simulate kHbO2 decreases (9%, 17%, 30%) observed in RBCs from knockouts (KOs: aquaporin-1, Rhesus A-glycoprotein, both) we must decrease membrane O2 permeability (PM,O2) by far greater percentages (22%, 36%, 55%). C_LIO_LIAnalyses of simulated-kHbO2 sensitivity to kinetic and geometric parameters suggest that reasonable parameter-value changes cannot explain experimentally observed kHbO2 decreases in RBCs from KOs. Thus, experimentally observed kHbO2 decreases must reflect decreases in PM,O2. C_LIO_LITo accommodate for poikilocytes, we develop a linear-combination approach (poikilocytes + biconcave disks, BCDs) to extract the kHbO2 and PM,O2 of just BCDs. C_LI