Role of channels in the O 2 permeability of murine red blood cells III. Mathematical modeling

In this third of three papers, we develop a reaction-diffusion model for ${\text{O}}_2$ 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 $(\text{Hb}/{\text{HbO}}_2)$ absorbance spectra during ${\text{O}}_2$ efflux from intact murine RBCs show that membrane-impermeant inhibitor p-chloromercuribenzenesulfonate (pCMBS) reduces the ${\text{HbO}}_2$ -deoxygenation rate constant $\left(k_{{\text{HbO}}_2}\right)$ by ~61%. SF experiments show that $k_{{\text{HbO}}_2}$ 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 ${\text{HbO}}_2$ dissociation in the intact RBC (i.e., $k_{{\text{HbO}}_2}$ ); ${\text{HbO}}_2$ , Hb, and ${\text{O}}_2$ diffusion through RBC cytosol; transmembrane ${\text{O}}_2$ diffusion; and ${\text{O}}_2$ 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 $k_{{\text{HbO}}_2}$ decreases cannot reflect changes only in RBC size/shape or $\left(\text{Hb}/{\text{HbO}}_2\right)$ . Instead, membrane ${\text{O}}_2$ permeability $\left(P_{\text{M},{\text{O}}_2}\right)$ 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 $k_{{\text{HbO}}_2}$ sensitivities to eight key parameters (e.g., $\left(\text{Hb}/{\text{HbO}}_2\right)$ , diffusion constants, $k_{{\text{HbO}}_2\to \text{Hb}+{\text{O}}_2}$ , ${\text{thickness}}_{\text{EUF}}$ , ${\text{diameter}}_{\text{Sphere}}$ ) shows that no reasonable changes explain the $k_{{\text{HbO}}_2}$ 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 ${\text{O}}_2$ offloading, even for a WT mouse.