Mathematical modeling of the interaction between oxygen, nitric oxide and superoxide

Nitric oxide release by deoxymyoglobin nitrite reduction during cardiac ischemia: A mathematical model

Interactions between cardiac myoglobin (Mb), nitrite, and nitric oxide (NO) are vital in regulating O₂ storage, transport, and NO homeostasis. Production of NO through the reduction of endogenous myocardial nitrite by deoxygenated myoglobin has been shown to significantly reduce myocardial infarction damage and ischemic injury. We developed a mathematical model for a cardiac arteriole and surrounding myocardium to examine the hypothesis that myoglobin switches functions from being a strong NO scavenger to an NO producer via the deoxymyoglobin nitrite reductase pathway. Our results predict that under ischemic conditions of flow, blood oxygen level, and tissue pH, deoxyMb nitrite reduction significantly elevates tissue and smooth muscle cell NO. The size of the effect is consistent at different flow rates, increases with decreasing blood oxygen and tissue pH and, in extreme pathophysiological conditions, NO can even be elevated above the normoxic levels. Our simulations suggest that cardiac deoxyMb nitrite reduction is a plausible mechanism for preserving or enhancing NO levels using endogenous nitrite despite the rate-limiting O₂ levels for endothelial NO production. This NO could then be responsible for mitigating deleterious effects under ischemic conditions.

A mathematical model for the role of N2O3 in enhancing nitric oxide bioavailability following nitrite infusion

Nitrite infusion into the bloodstream has been shown to elicit vasodilation and protect against ischemia-reperfusion injury through nitric oxide (NO) release in hypoxic conditions. However, the mechanism by which nitrite-derived NO escapes scavenging by hemoglobin in the erythrocyte has not been fully elucidated, owing in part to the difficulty in measuring the reactions and transport on NO in vivo. We developed a mathematical model for an arteriole and surrounding tissue to examine the hypothesis that dinitrogen trioxide (N2O3) acts as a stable intermediate for preserving NO. Our simulations predict that with hypoxia and moderate nitrite concentrations, the N2O3 pathway can significantly preserve the NO produced by hemoglobin nitrite reductase in the erythrocyte and elevate NO reaching the smooth muscle cells. Nitrite retains its ability to increase NO bioavailability even at varying flow conditions, but there is minimal effect under normoxia or very low nitrite concentrations. Our model demonstrates a viable pathway for reconciling experimental findings of potentially beneficial effects of nitrite infusions despite previous models showing negligible NO elevation associated with hemoglobin nitrite reductase. Our results suggest that additional mechanisms may be needed to explain the efficacy of nitrite-induced vasodilation at low infusion concentrations.

Nitric oxide and the cardiovascular system

Nitric oxide (NO) generated by endothelial cells to relax vascular smooth muscle is one of the most intensely studied molecules in the past 25 years. Much of what is known about NO regulation of NO is based on blockade of its generation and analysis of changes in vascular regulation. This approach has been useful to demonstrate the importance of NO in large scale forms of regulation but provides less information on the nuances of NO regulation. However, there is a growing body of studies on multiple types of in vivo measurement of NO in normal and pathological conditions. This discussion will focus on in vivo studies and how they are reshaping the understanding of NO's role in vascular resistance regulation and the pathologies of hypertension and diabetes mellitus. The role of microelectrode measurements in the measurement of [NO] will be considered because much of the controversy about what NO does and at what concentration depends upon the measurement methodology. For those studies where the technology has been tested and found to be well founded, the concept evolving is that the stresses imposed on the vasculature in the form of flow-mediated stimulation, chemicals within the tissue, and oxygen tension can cause rapid and large changes in the NO concentration to affect vascular regulation. All these functions are compromised in both animal and human forms of hypertension and diabetes mellitus due to altered regulation of endothelial cells and formation of oxidants that both damage endothelial cells and change the regulation of endothelial nitric oxide synthase.

Bang-bang model for regulation of local blood flow

The classical model of metabolic regulation of blood flow in muscle tissue implies the maintenance of basal tone in arterioles of resting muscle and their dilation in response to exercise and/or tissue hypoxia via the evoked production of vasodilator metabolites by myocytes. A century-long effort to identify specific metabolites responsible for explaining active and reactive hyperemia has not been successful. Furthermore, the metabolic theory is not compatible with new knowledge on the role of physiological radicals (e.g., nitric oxide, NO, and superoxide anion, O2 (-) ) in the regulation of microvascular tone. We propose a model of regulation in which muscle contraction and active hyperemia are considered the physiologically normal state. We employ the "bang-bang" or "on/off" regulatory model which makes use of a threshold and hysteresis; a float valve to control the water level in a tank is a common example of this type of regulation. Active bang-bang regulation comes into effect when the supply of oxygen and glucose exceeds the demand, leading to activation of membrane NADPH oxidase, release of O2 (-) into the interstitial space and subsequent neutralization of the interstitial NO. Switching arterioles on/off when local blood flow crosses the threshold is realized by a local cell circuit with the properties of a bang-bang controller, determined by its threshold, hysteresis, and dead-band. This model provides a clear and unambiguous interpretation of the mechanism to balance tissue demand with a sufficient supply of nutrients and oxygen.

Endothelial NO and O₂·⁻ production rates differentially regulate oxidative, nitroxidative, and nitrosative stress in the microcirculation

Endothelial dysfunction causes an imbalance in endothelial NO and O₂·⁻ production rates and increased peroxynitrite formation. Peroxynitrite and its decomposition products cause multiple deleterious effects including tyrosine nitration of proteins, superoxide dismutase (SOD) inactivation, and tissue damage. Studies have shown that peroxynitrite formation during endothelial dysfunction is strongly dependent on the NO and O₂·⁻ production rates. Previous experimental and modeling studies examining the role of NO and O₂·⁻ production imbalance on peroxynitrite formation showed different results in biological and synthetic systems. However, there is a lack of quantitative information about the formation and biological relevance of peroxynitrite under oxidative, nitroxidative, and nitrosative stress conditions in the microcirculation. We developed a computational biotransport model to examine the role of endothelial NO and O₂·⁻ production on the complex biochemical NO and O₂·⁻ interactions in the microcirculation. We also modeled the effect of variability in SOD expression and activity during oxidative stress. The results showed that peroxynitrite concentration increased with increase in either O₂·⁻ to NO or NO to O₂·⁻ production rate ratio (QO₂·⁻/QNO or QNO/QO₂·⁻, respectively). The peroxynitrite concentrations were similar for both production rate ratios, indicating that peroxynitrite-related nitroxidative and nitrosative stresses may be similar in endothelial dysfunction or inducible NO synthase (iNOS)-induced NO production. The endothelial peroxynitrite concentration increased with increase in both QO₂·⁻/QNO and QNO/QO₂·⁻ ratios at SOD concentrations of 0.1-100 μM. The absence of SOD may not mitigate the extent of peroxynitrite-mediated toxicity, as we predicted an insignificant increase in peroxynitrite levels beyond QO₂·⁻/QNO and QNO/QO₂·⁻ ratios of 1. The results support the experimental observations of biological systems and show that peroxynitrite formation increases with increase in either NO or O₂·⁻ production, and excess NO production from iNOS or from NO donors during oxidative stress conditions does not reduce the extent of peroxynitrite mediated toxicity.

Oxygen transport in the microcirculation and its regulation

OBJECTIVE

Cells require energy to carry out their functions and they typically use oxidative phosphorylation to generate the needed ATP. Thus, cells have a continuous need for oxygen, which they receive by diffusion from the blood through the interstitial fluid. The circulatory system pumps oxygen-rich blood through a network of increasingly minute vessels, the microcirculation. The structure of the microcirculation is such that all cells have at least one nearby capillary for diffusive exchange of oxygen and red blood cells release the oxygen bound to hemoglobin as they traverse capillaries.

METHODS

This review focuses first on the historical development of techniques to measure oxygen at various sites in the microcirculation, including the blood, interstitium, and cells.

RESULTS

Next, approaches are described as to how these techniques have been employed to make discoveries about different aspects of oxygen transport. Finally, ways in which oxygen might participate in the regulation of blood flow toward matching oxygen supply to oxygen demand is discussed.

CONCLUSIONS

Overall, the transport of oxygen to the cells of the body is one of the most critical functions of the cardiovascular system and it is in the microcirculation where the final local determinants of oxygen supply, oxygen demand, and their regulation are decided.

Nitric oxide signaling in the microcirculation

Several apparent paradoxes are evident when one compares mathematical predictions from models of nitric oxide (NO) diffusion and convection in vasculature structures with experimental measurements of NO (or related metabolites) in animal and human studies. Values for NO predicted from mathematical models are generally much lower than in vivo NO values reported in the literature for experiments, specifically with NO microelectrodes positioned at perivascular locations next to different sizes of blood vessels in the microcirculation and NO electrodes inserted into a wide range of tissues supplied by the microcirculation of each specific organ system under investigation. There continues to be uncertainty about the roles of NO scavenging by hemoglobin versus a storage function that may conserve NO, and other signaling targets for NO need to be considered. This review describes model predictions and relevant experimental data with respect to several signaling pathways in the microcirculation that involve NO.

Modeling O₂-dependent effects of nitrite reductase activity in blood and tissue on coupled NO and O₂ transport around arterioles

Recent evidence in the literature suggests that tissues play a greater role than blood in reducing nitrite to NO under ischemic or hypoxic conditions. Our previous mathematical model for coupled NO and O(2) transport around an arteriole, modified to include superoxide generation from dysfunctional endothelium, was developed further to include nitrite reductase activity in blood and tissue. Steady-state radial and axial NO and pO(2) profiles in the arteriole and surrounding tissue were simulated for different blood flow rates and arterial blood pO(2) values. The resulting computer simulations demonstrate that nitrite reductase activity in blood is not a very effective mechanism for conserving NO due to the strong scavenging of NO by hemoglobin. In contrast, nitrite reductase activity in tissue is much more effective in increasing NO bioavailability in the vascular wall and contributes progressively more NO as tissue hypoxia becomes more severe.