Mathematical Modeling of NO Diffusion and Reaction

Diffusion Distance

Despite its well-documented importance, the mechanism for nitric oxide (NO) transport in vivo is still unclear. In particular, the effect of hemoglobin-NO interaction and the range of NO action have not been characterized in the microcirculation, where blood flow is optimally regulated. Using a mathematical model and experimental data on NO production and degradation rates, we investigated factors that determine the effective diffusion distance of NO in the microcirculation. This distance is defined as the distance within which NO concentration is greater than the equilibrium dissociation constant (0.25 µM) of solubleguanylyl cyclase, the target enzyme for NO action. We found that the size of the vessel is an important factor in determining the effective diffusion distance of NO. In ~30- to 100-µm-ID microvessels the luminal NO concentrations and the abluminal effective diffusion distance are maximal. Furthermore, the model suggests that if the NO-erythrocyte reaction rate is as fast as the rate reported for the in vitro NO-hemoglobin reaction, the NO concentration in the vascular smooth muscle will be insufficient to stimulate smooth muscle guanylyl cyclase effectively. In addition, the existence of an erythrocyte-free layer near the vascular wall is important in determining the effective NO diffusion distance. These results suggest that 1) the range of NO action may exhibit significant spatial heterogeneity in vivo, depending on the size of the vessel and the local chemistry of NO degradation, 2) the NO binding/reaction constant with hemoglobin in the red blood cell may be much smaller than that with free hemoglobin, and 3) the microcirculation is the optimal site for NO to exert its regulatory function. Because NO exhibits vasodilatory function and antiatherogenic activity, the high NO concentration and its long effective range in the microcirculation may serve as intrinsic factors to prevent the development of systemic hypertension and atherosclerotic pathology in microvessels. 

 

Production and Reaction Rates

Vaughn, M.W., L. Kuo, and J.C. Liao (1998) “Estimation of nitric oxide production and reaction rates in tissue using a mathematical model" Am.J. Physiol. 274:H2163-H2176.

Nitric oxide (NO) produced by the vascular endothelium is an important biologic messenger that regulates vessel tone and permeability and inhibits platelet adhesion and aggregation. NO exerts its control of vessel tone by interacting with guanylyl cyclase in the vascular smooth muscle to initiate a series of reactions that lead to vessel dilation. Previous efforts to investigate this interaction by mathematical modeling of NO diffusion and reaction have been hampered by the lack of information on the production and degradation rate of NO. We use a mathematical model and previously published experimental data to estimate the rate of NO production, 6.8 × 1014
µmol · µm2 · s-1; the NO diffusion coefficient, 3,300 µm2 s1; and the NO consumption rate coefficient in the vascular smooth muscle, 0.01 s-1 (1st-order rate expression) or 0.05 µM-1 · s-1 (2nd-order rate expression). The modeling approach is discussed in detail. It provides a general framework for modeling the NO produced from the endothelium and for estimating relevant physical parameters.