A model of NO/O2 transport in capillary-perfused tissue containing an arteriole and venule pair

Violet LED induces vasodilation in rat aortic rings by soluble guanylate cyclase-dependent mechanism and increases SOD activity

We found several studies that have used the aortic rings as an experimental model, mainly for the testing of new drugs or new therapies that try to reverse or prevent endothelial dysfunction or characterize its mechanism of action in a biological system, creating the knowledge necessary to obtain the treatment of those several diseases, where many of these treatments involve photobiomodulation therapies. We also found numerous wavelengths represented by different colors of LASER or LED in which frequently, the mechanism of action in biological systems is unknown. This study has as main objective to investigate the effects of the Violet LED Light (405 nm) by using isolated aortic rings, looking for nitric oxide (NO) release, and evaluating if Violet LED Light can modulate the superoxide dismutase (SOD) activity. We performed a vascular reactivity study in isolated aortic rings from normotensive rats with a single LED application. Besides it, the rings were pre-incubated with soluble guanylate cyclase (sGC) inhibitor or endothelial NO synthase inhibitor and subsequently underwent the application of the Violet LED. The cell viability and nitric oxide release in cell culture of human umbilical codon vein cells (HUVEC) were analyzed. In the vascular reactivity experiment, we observed a peak of vasodilation when applying light to the aortic rings. The soluble guanylate cyclase inhibitor abolished the relaxation induced by the Violet LED Light. However, the NO synthase inhibitor did not modify the Violet LED effect. In an isolated system, we verified that the Violet LED Light can increase SOD activity. Our results suggest that Violet LED Light induces vasodilation by a mechanism dependent on sGC activation, and not by NOS activation, and part of this effect could be due to the increase of SOD activity.

Spatial and temporal patterns of nitric oxide diffusion and degradation drive emergent cerebrovascular dynamics

Nitric oxide (NO) is a gaseous signaling molecule that plays an important role in neurovascular coupling. NO produced by neurons diffuses into the smooth muscle surrounding cerebral arterioles, driving vasodilation. However, the rate of NO degradation in hemoglobin is orders of magnitude higher than in brain tissue, though how this might impact NO signaling dynamics is not completely understood. We used simulations to investigate how the spatial and temporal patterns of NO generation and degradation impacted dilation of a penetrating arteriole in cortex. We found that the spatial location of NO production and the size of the vessel both played an important role in determining its responsiveness to NO. The much higher rate of NO degradation and scavenging of NO in the blood relative to the tissue drove emergent vascular dynamics. Large vasodilation events could be followed by post-stimulus constrictions driven by the increased degradation of NO by the blood, and vasomotion-like 0.1-0.3 Hz oscillations could also be generated. We found that these dynamics could be enhanced by elevation of free hemoglobin in the plasma, which occurs in diseases such as malaria and sickle cell anemia, or following blood transfusions. Finally, we show that changes in blood flow during hypoxia or hyperoxia could be explained by altered NO degradation in the parenchyma. Our simulations suggest that many common vascular dynamics may be emergent phenomena generated by NO degradation by the blood or parenchyma.

A dynamic computational network model for the role of nitric oxide and the myogenic response in microvascular flow regulation

OBJECTIVES

The effect of NO on smooth muscle cell contractility is crucial in regulating vascular tone, blood flow, and O₂ delivery. Quantitative predictions for interactions between the NO production rate and the myogenic response for microcirculatory blood vessels are lacking.

METHODS

We developed a computational model of a branching microcirculatory network with four representative classes of resistance vessels to predict the effect of endothelium-derived NO on the microvascular pressure-flow response. Our model links vessel scale biotransport simulations of NO and O₂ delivery to a mechanistic model of autoregulation and myogenic tone in a simplified microcirculatory network.

RESULTS

The model predicts that smooth muscle cell NO bioavailability significantly contributes to resting vascular tone of resistance vessels. Deficiencies in NO seen during hypoxia or ischemia lead to a decreased vessel diameter for all classes at a given intravascular pressure. At the network level, NO deficiencies lead to an increase in pressure drop across the vessels studied, a downward shift in the pressure-flow curve, and a decrease in the effective range of the autoregulatory response.

CONCLUSIONS

Our model predicts the steady state and transient behavior of resistance vessels to perturbations in blood pressure, including effects of NO bioavailability on vascular regulation.

Nitrite-Mediated Hypoxic Vasodilation Predicted from Mathematical Modeling and Quantified from in Vivo Studies in Rat Mesentery

Nitric oxide (NO) generated from nitrite through nitrite reductase activity in red blood cells has been proposed to play a major role in hypoxic vasodilation. However, we have previously predicted from mathematical modeling that much more NO can be derived from tissue nitrite reductase activity than from red blood cell nitrite reductase activity. Evidence in the literature suggests that tissue nitrite reductase activity is associated with xanthine oxidoreductase (XOR) and/or aldehyde oxidoreductase (AOR). We investigated the role of XOR and AOR in nitrite-mediated vasodilation from computer simulations and from in vivo exteriorized rat mesentery experiments. Vasodilation responses to nitrite in the superfusion medium bathing the mesentery equilibrated with 5% O₂ (normoxia) or zero O₂ (hypoxia) at either normal or acidic pH were quantified. Experiments were also conducted following intraperitoneal (IP) injection of nitrite before and after inhibiting XOR with allopurinol or inhibiting AOR with raloxifene. Computer simulations for NO and O₂ transport using reaction parameters reported in the literature were also conducted to predict nitrite-dependent NO production from XOR and AOR activity as a function of nitrite concentration, PO₂ and pH. Experimentally, the largest arteriolar responses were found with nitrite >10 mM in the superfusate, but no statistically significant differences were found with hypoxic and acidic conditions in the superfusate. Nitrite-mediated vasodilation with IP nitrite injections was reduced or abolished after inhibiting XOR with allopurinol (p < 0.001). Responses to IP nitrite before and after inhibiting AOR with raloxifene were not as consistent. Our mathematical model predicts that under certain conditions, XOR and AOR nitrite reductase activity in tissue can significantly elevate smooth muscle cell NO and can serve as a compensatory pathway when endothelial NO production is limited by hypoxic conditions. Our theoretical and experimental results provide further evidence for a role of tissue nitrite reductases to contribute additional NO to compensate for reduced NO production by endothelial nitric oxide synthase during hypoxia. Our mathematical model demonstrates that under extreme hypoxic conditions with acidic pH, endogenous nitrite levels alone can be sufficient for a functionally significant increase in NO bioavailability. However, these conditions are difficult to achieve experimentally.

Modeling of pulsatile flow-dependent nitric oxide regulation in a realistic microvascular network

Hemodynamic pulsatility has been reported to regulate microcirculatory function. To quantitatively assess the impact of flow pulsatility on the microvasculature, a mathematical model was first developed to simulate the regulation of NO production by pulsatile flow in the microcirculation. Shear stress and pressure pulsatility were selected as regulators of endothelial NO production and NO-dependent vessel dilation as feedback to control microvascular hemodynamics. The model was then applied to a real microvascular network of the rat mesentery consisting of 546 microvessels. As compared to steady flow conditions, pulsatile flow increased the average NO concentration in arterioles from 256.8±93.1nM to 274.8±101.1nM (P<0.001), with a corresponding increase in vessel dilation by approximately 7% from 27.5±10.6% to 29.4±11.4% (P<0.001). In contrast, NO concentration and vessel size showed a far lesser increase (about 1.7%) in venules under pulsatile flow as compared to steady flow conditions. Network perfusion and flow heterogeneity were improved under pulsatile flow conditions, and vasodilation within the network was more sensitive to heart rate changes than pulse pressure amplitude. The proposed model simulates the role of flow pulsatility in the regulation of a complex microvascular network in terms of NO concentration and hemodynamics under varied physiological conditions.

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.

Diffusive shunting of gases and other molecules in the renal vasculature: physiological and evolutionary significance

Countercurrent systems have evolved in a variety of biological systems that allow transfer of heat, gases, and solutes. For example, in the renal medulla, the countercurrent arrangement of vascular and tubular elements facilitates the trapping of urea and other solutes in the inner medulla, which in turn enables the formation of concentrated urine. Arteries and veins in the cortex are also arranged in a countercurrent fashion, as are descending and ascending vasa recta in the medulla. For countercurrent diffusion to occur, barriers to diffusion must be small. This appears to be characteristic of larger vessels in the renal cortex. There must also be gradients in the concentration of molecules between afferent and efferent vessels, with the transport of molecules possible in either direction. Such gradients exist for oxygen in both the cortex and medulla, but there is little evidence that large gradients exist for other molecules such as carbon dioxide, nitric oxide, superoxide, hydrogen sulfide, and ammonia. There is some experimental evidence for arterial-to-venous (AV) oxygen shunting. Mathematical models also provide evidence for oxygen shunting in both the cortex and medulla. However, the quantitative significance of AV oxygen shunting remains a matter of controversy. Thus, whereas the countercurrent arrangement of vasa recta in the medulla appears to have evolved as a consequence of the evolution of Henle’s loop, the evolutionary significance of the intimate countercurrent arrangement of blood vessels in the renal cortex remains an enigma.

Pharmacological characterization of the vasodilating effect induced by the ruthenium complex cis-[Ru(NO)(NO2)(bpy)2].(PF6)2

Nitric oxide (NO) can be found in different species and is a potent vasodilator. The ruthenium compound cis-[Ru(NO)(NO2)(bpy)2].(PF6)2 (BPY) can generate NO. This study aimed to investigate the BPY stability at physiological pH, the cellular mechanisms involved in BPY effect, NO species originating from BPY, and to verify how BPY affects blood pressure. Our results has shown that at pH 7.4 and 9.4, the NO coordinated to ruthenium (Ru-NO) is converted to nitrite (Ru-NO2) and remains stable. In aortic rings, the stable configuration of BPY (Ru-NO2) induces vascular relaxation in a concentration-dependent manner. Thus, further experiments were made with stable configuration of BPY (Ru-NO2). The relaxation induced by BPY was abolished in the presence of guanylyl cyclase inhibitor and decreased in the presence of potassium channel blocker. By using radicalar (NO) and nitroxyl (NO) scavenger, our results suggest that the BPY mainly release the radicalar species. By using fluorescence probes to detect intracellular NO concentration ([NO]i) and cytosolic Ca concentration ([Ca]c), we verified that in smooth muscle cells, BPY induces an increase in [NO]i and a decrease in [Ca]c. The intravenous bolus injection of 1.25, 2.5, and 5.0 mg/kg from stable configuration of BPY results in a decrease on basal blood pressure values. Taken together, our results indicated that the stable configuration of the compound BPY induces vascular relaxation in aorta because of NO release and decrease of [Ca]c in vascular smooth muscle cells. Also, the stable configuration is able to reduce the blood pressure in a dose-dependent manner.

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.

Renal oxygenation: preglomerular vasculature is an unlikely contributor to renal oxygen shunting

The primary aim of this study was to assess the plausibility of preglomerular arterial-to-venous oxygen shunting in the kidney. To this end, we have developed a segment-wise three-dimensional computational model that takes into account transport processes in arteries, veins, cortical tissue, and capillaries. Our model suggests that the amount of preglomerular oxygen shunting is negligible. Consequently, it is improbable that preglomerular shunting contributes to the hypothesized regulation of renal oxygenation. Cortical tissue oxygenation is more likely determined by the interplay between oxygen supply, either from the preglomerular vasculature or from capillaries, and oxygen consumption. We show that reported differences in permeability to oxygen between perfused and unperfused tissue may be explained by what we refer to as advection-facilitated diffusion. We further show that the preglomerular vasculature is the primary source of oxygen for the tissue when cortical consumption is high or renal arterial blood is highly oxygenated, i.e., under hyperoxemic conditions. Conversely, when oxygen demand in the tissue is decreased, or under hypoxemic conditions, oxygen is supplied predominantly by capillaries.

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.

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.

Simulation of NO and O2 transport facilitated by polymerized hemoglobin solutions in an arteriole that takes into account wall shear stress-induced NO production

A mathematical model was developed to study nitric oxide (NO) and oxygen (O(2)) transport in an arteriole and surrounding tissues exposed to a mixture of red blood cells (RBCs) and hemoglobin (Hb)-based O(2) carriers (HBOCs). A unique feature of this model is the inclusion of blood vessel wall shear stress-induced production of endothelial-derived NO, which is very sensitive to the viscosity of the RBC and HBOC mixture traversing the blood vessel lumen. Therefore in this study, a series of polymerized bovine Hb (PolyHb) solutions with high viscosity, varying O(2) affinities, NO dioxygenation rate constants and O(2) dissociation rate constants that were previously synthesized and characterized by our group was evaluated via mathematical modeling, in order to investigate the effect of these biophysical properties on the transport of NO and O(2) in an arteriole and its surrounding tissues subjected to anemia with the commercial HBOC Oxyglobin® and cell-free bovine Hb (bHb) serving as appropriate controls. The computer simulation results indicated that transfusion of high viscosity PolyHb solutions promoted blood vessel wall shear stress dependent generation of the vasodilator NO, especially in the blood vessel wall and should transport enough NO inside the smooth muscle layer to activate vasodilation compared to the commercial HBOC Oxyglobin® and cell-free bHb. However, NO scavenging in the arteriole lumen was unavoidable due to the intrinsic high NO dioxygenation rate constant of the HBOCs being studied. This study also observed that all PolyHbs could potentially improve tissue oxygenation under hypoxic conditions, while low O(2) affinity PolyHbs were more effective in oxygenating tissues under normoxic conditions compared with high O(2) affinity PolyHbs. In addition, all ultrahigh molecular weight PolyHbs displayed higher O(2) transfer rates than the commercial HBOC Oxyglobin® and cell-free bHb. Therefore, these results suggest that ultrahigh molecular weight PolyHb solutions could be used as safe and efficacious O(2) carriers for use in transfusion medicine. It also suggests that future generations of PolyHb solutions should possess lower NO dioxygenation reaction rate constants in order to reduce NO scavenging, while maintaining high solution viscosity to take advantage of wall shear stress-induced NO production. Taken together, we suggest that this mathematical model can be used to predict the vasoactivity of HBOCs and help guide the design and optimization of the next generation of HBOCs for use in transfusion medicine.

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.

A mathematical model of diffusional shunting of oxygen from arteries to veins in the kidney

To understand how arterial-to-venous (AV) oxygen shunting influences kidney oxygenation, a mathematical model of oxygen transport in the renal cortex was created. The model consists of a multiscale hierarchy of 11 countercurrent systems representing the various branch levels of the cortical vasculature. At each level, equations describing the reactive-advection-diffusion of oxygen are solved. Factors critical in renal oxygen transport incorporated into the model include the parallel geometry of arteries and veins and their respective sizes, variation in blood velocity in each vessel, oxygen transport (along the vessels, between the vessels and between vessel and parenchyma), nonlinear binding of oxygen to hemoglobin, and the consumption of oxygen by renal tissue. The model is calibrated using published measurements of cortical vascular geometry and microvascular Po2. The model predicts that AV oxygen shunting is quantitatively significant and estimates how much kidney V̇o2 must change, in the face of altered renal blood flow, to maintain cortical tissue Po2 at a stable level. It is demonstrated that oxygen shunting increases as renal V̇o2 or arterial Po2 increases. Oxygen shunting also increases as renal blood flow is reduced within the physiological range or during mild hemodilution. In severe ischemia or anemia, or when kidney V̇o2 increases, AV oxygen shunting in proximal vascular elements may reduce the oxygen content of blood destined for the medullary circulation, thereby exacerbating the development of tissue hypoxia. That is, cortical ischemia could cause medullary hypoxia even when medullary perfusion is maintained. Cortical AV oxygen shunting limits the change in oxygen delivery to cortical tissue and stabilizes tissue Po2 when arterial Po2 changes, but renders the cortex and perhaps also the medulla susceptible to hypoxia when oxygen delivery falls or consumption increases.

Influence of tissue metabolism and capillary oxygen supply on arteriolar oxygen transport: a computational model

We present a theoretical model for steady-state radial and longitudinal oxygen transport in arterioles containing flowing blood (plasma and red blood cells) and surrounded by living tissue. This model combines a detailed description of convective and diffusive oxygen transport inside the arteriole with a novel boundary condition at the arteriolar lumen surface, and the results provide new mass transfer coefficients for computing arteriolar O(2) losses based on far-field tissue O(2) tension and in the presence of spatially distributed capillaries. A numerical procedure is introduced for calculating O(2) diffusion from an arteriole to a continuous capillary-tissue matrix immediately adjacent to the arteriole. The tissue O(2) consumption rate is assumed to be constant and capillaries act as either O(2) sources or sinks depending on the local O(2) environment. Using the model, O(2) saturation (SO(2)) and tension (PO(2)) are determined for the intraluminal region of the arteriole, as well as for the extraluminal region in the neighbouring tissue. Our model gives results that are consistent with available experimental data and previous intraluminal transport models, including appreciable radial decreases in intraluminal PO(2) for all vessel diameters considered (12-100 μm) and slower longitudinal decreases in PO(2) for larger vessels than for smaller ones, and predicts substantially less diffusion of O(2) from arteriolar blood than do models with PO(2) specified at the edge of the lumen. The dependence of the new mass transfer coefficients on vessel diameter, SO(2) and far-field PO(2) is calculated allowing their application to a wide range of physiological situations. This novel arteriolar O(2) transport model will be a vital component of future integrated models of microvascular regulation of O(2) supply to capillary beds and the tissue regions they support.

3D network model of NO transport in tissue

We developed a mathematical model to simulate shear stress-dependent nitric oxide (NO) production and transport in a 3D microcirculatory network based on published data. The model consists of a 100 μm × 500 μm × 75 μm rectangular volume of tissue containing two arteriole-branching trees, and nine capillaries surrounding the vessels. Computed distributions for NO in blood, vascular walls, and surrounding tissue were affected by hematocrit (Hct) and wall shear stress (WSS) in the network. The model demonstrates that variations in the red blood cell (RBC) distribution and WSS in a branching network can have differential effects on computed NO concentrations due to NO consumption by RBCs and WSS-dependent changes in NO production. The model predicts heterogeneous distributions of WSS in the network. Vessel branches with unequal blood flow rates gave rise to a range of WSS values and therefore NO production rates. Despite increased NO production in a branch with higher blood flow and WSS, vascular wall NO was predicted to be lower due to greater NO consumption in blood, since the microvascular Hct increased with redistribution of RBCs at the vessel bifurcation. Within other regions, low WSS was combined with decreased NO consumption to enhance the NO concentration.

A computational model for nitric oxide, nitrite and nitrate biotransport in the microcirculation: effect of reduced nitric oxide consumption by red blood cells and blood velocity

Bioavailability of vasoactive endothelium-derived nitric oxide (NO) in vasculature is a critical factor in regulation of many physiological processes. Consumption of NO by RBC plays a crucial role in maintaining NO bioavailability. Recently, Deonikar and Kavdia (2009b) reported an effective NO-RBC reaction rate constant of 0.2×10(5)M(-1)s(-1) that is ~7 times lower than the commonly used NO-RBC reaction rate constant of 1.4×10(5)M(-1)s(-1). To study the effect of lower NO-RBC reaction rate constant and nitrite and nitrate formation (products of NO metabolism in blood), we developed a 2D mathematical model of NO biotransport in 50 and 200μm ID arterioles to calculate NO concentration in radial and axial directions in the vascular lumen and vascular wall of the arterioles. We also simulated the effect of blood velocity on NO distribution in the arterioles to determine whether NO can be transported to downstream locations in the arteriolar lumen. The results indicate that lowering the NO-RBC reaction rate constant increased the NO concentration in the vascular lumen as well as the vascular wall. Increasing the velocity also led to increase in NO concentration. We predict increased NO concentration gradient along the axial direction with an increase in the velocity. The predicted NO concentration was 281-1163nM in the smooth muscle cell layer for 50μm arteriole over the blood velocity range of 0.5-4cms(-1) for k(NO-RBC) of 0.2×10(5)M(-1)s(-1), which is much higher than the reported values from earlier mathematical modeling studies. The NO concentrations are similar to the experimentally measured vascular wall NO concentration range of 300-1000nM in several different vascular beds. The results are significant from the perspective that the downstream transport of NO is possible under the right circumstances.

Extracellular diffusion and permeability effects on NO-RBCs interactions using an experimental and theoretical model

Nitric oxide (NO) is a potent vasodilator and its homeostasis depends on interaction with RBCs. A key factor in understanding NO-RBC interactions in vascular lumen is a comprehensive analysis of product identification and quantification. In this context, administration of NO during in vitro NO-RBC interactions becomes a crucial variable. In this study, we designed a bioreactor that maintains a precise NO concentration in the headspace that diffuses to RBCs suspension to study the quantitative effect of NO concentration and hematocrit (Hct) on NO-RBC interactions. The products of NO-RBC reaction (nitrite and total nitrogen species (total NOx)) were measured by chemiluminescence assay. A mathematical model simulating NO biotransport to a single RBC was developed to (1) estimate NO-RBC reaction rate constant; (2) predict the NO concentrations in the bulk RBC suspension and at the RBC membrane for RBC membrane NO permeability (P(m)) values of 0.0415-40 cm/s. Measured nitrite and total NOx concentrations increased with increase in headspace NO concentration whereas nitrite concentrations decreased with hematocrit and total NOx concentrations increased with hematocrit. This indicates that the extracellular resistance is a controlling factor for RBC uptake of NO. Modeling results showed that the effective reaction rate constant (k(eff)) for NO-RBC interactions was 2.32 x 10(4)-1.08 x 10(6) M(-1) s(-1). Results also predict that the membrane permeability in the range of 0.0415-0.4 cm/s is required to maintain physiologically relevant levels of NO at the smooth muscle cell layer. The effective reaction rate constant increased with increase in P(m) and magnitude of increase was higher at 45% Hct. For all P(m) values, the k(hb)/k(eff) ratios were lower for 45% Hct as compared to 5% Hct indicating extracellular resistance is important for RBC NO uptake. Our experimental and mathematical analyses of NO-RBC interactions indicate that both unstirred layer and RBC membrane have a significant effect on NO transport to RBCs. In addition, the membrane permeability in the range of 0.0415-0.4 cm/s is required to maintain sufficient NO concentrations at the smooth muscle cell layer.

Comparing the chemical biology of NO and HNO

For the past couple of decades nitric oxide (NO) and nitroxyl (HNO) have been extensively studied due to the important role they play in many physiological and/or pharmacological processes. Many researchers have reported important signaling pathways as well as mechanisms of action of these species, showing direct and indirect effects depending on the environment. Both NO and HNO can react with, among others, metals, proteins, thiols and heme proteins via unique and distinct chemistry leading to improvement of some clinical conditions. Understanding the basic chemistry of NO and HNO and distinguishing their mechanisms of action as well as methods of detection are crucial for understanding the current and potential clinical applications. In this review, we summarize some of the most important findings regarding NO and HNO chemistry, revealing some of the possible mechanisms of their beneficial actions.

Mathematical model of NO and O2 transport in an arteriole facilitated by hemoglobin based O2 carriers

The increasing demand for donated human blood has spurred research to develop hemoglobin-based O(2) carriers (HBOCs) that can be used as red blood cell (RBC) substitutes. However, in vivo studies of acellular HBOCs have shown an increase in mean arterial pressure following transfusion that has been attributed to the HBOC's ability to scavenge NO (an important vasodilator that is synthesized by endothelial cells in the blood vessel wall that signals neighboring smooth muscle cells to relax). In this study, a mathematical model was developed to describe NO and O(2) transport in an arteriole containing a mixture of acellular HBOCs and RBCs. The acellular HBOCs studied in this work possessed a wide range of O(2) affinities, O(2) dissociation rate constants and NO reactivities in order to evaluate their effect on O(2) tension and NO concentration in the arteriole tissue region. By focusing on the concentration of NO that is localized in the arteriole smooth muscle cell region, the model can predict the vasopressor response of HBOCs. The results of this study confirmed that acellular HBOCs scavenge large amounts of NO from the entire arteriole (approximately 50% or more NO compared to RBCs only). A recombinant Hb, rHb3011, displayed the least NO reactivity and consequently left the most NO remaining in the arteriole. The NO concentration in the arteriole with respect to the other HBOCs studied was proportional to their NO reactivity. Therefore, the results of this study demonstrate that NO scavenging is an unavoidable consequence of transfusing HBOCs. To prevent or reduce vasodilatation, we suggest administration of NO by either inhaling NO or transfusing nitrite into the blood stream followed by transfusion of HBOC.

Hemorrhagic shock and nitric oxide release from erythrocytic nitric oxide synthase: a quantitative analysis

A large loss of blood during hemorrhage can result in profound shock, a state of hypotension associated with hemodynamic abnormalities. One of the hypotheses to account for this collapse of homeostasis is that the production of nitric oxide (NO), a gas molecule that dilates blood vessels, is significantly impaired during hemorrhage, resulting in a mismatch between O(2) delivery and the metabolic activity in the tissues. NO can be released from multiple sources in the vasculature. Recent studies have shown that erythrocytes express functional endothelial nitric oxide synthase (NOS3), which potentially serves as an intraluminal NO source. NO delivery from this source is complex: erythrocytes are not only NO producers but also act as potent sinks because of the high affinity of NO for hemoglobin. To test our hypothesis that the loss of erythrocytic NOS3 during hemorrhage contributes to NO deficiency-related shock, we have constructed a multicellular computational model that simulates NO production and transport to allow us to quantify the loss of NO under different hemorrhagic conditions. Our model shows that: (1) during mild hemorrhage and subsequent hemodilution (hematocrit >30%), NO from this intraluminal source is only slightly decreased in the vascular smooth muscle, but the NO level is significantly reduced under severe hemorrhagic conditions (hematocrit <30%); (2) whether a significant amount of NO from this source can be delivered to vascular smooth muscle is strongly dependent on the existence of a protective mechanism for NO delivery; (3) if the expression level of NOS3 on erythrocytes is similar to that on endothelial cells, we estimate approximately 13 pM NO at the vascular smooth muscle from this source when such a protective mechanism is involved. This study provides a basis for detailed studies to characterize the impairment of NO release pathways during hemorrhage and yield important insights for the development of resuscitation methods.

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

Computer simulations were performed based on a multiple chemical species convection-diffusion model with coupled biochemical reactions for oxygen (O2), nitric oxide (NO), superoxide (O2*-), peroxynitrite (ONOO-), nitrite (NO2-) and nitrate (NO3-) in cylindrical geometry with blood flow through a 30 microm diameter arteriole. Steady state concentration gradients of all chemical species were predicted for different O2*- production rates, superoxide dismutase (SOD) concentrations, and blood flow rates. Effects of additional O2*- production from dysfunctional endothelial nitric oxide synthase (eNOS) were also simulated. The model predicts that convection is essential for characterizing O2 partial pressure gradients (PO2) in the bloodstream and surrounding tissue, but has little direct effect on NO gradients in blood and tissue.

Theoretical models of microvascular oxygen transport to tissue

To improve understanding of microvascular O(2) transport, theoretical modeling has been pursued for many years. The large number of studies in this area attests to the complexities (i.e., biochemical, structural, and hemodynamic) involved. This article focuses on theoretical studies from the last two decades and, in particular, on models of O(2) transport to tissue by discrete microvessels. A brief discussion of intravascular O(2) transport is first given, highlighting the physiological importance of intravascular resistance to blood-tissue O(2) transfer. This is followed by a description of the Krogh tissue cylinder model of O(2) transport by a single capillary, which is shown to remain relevant in modified forms that relax many of the original biophysical assumptions. However, there are many geometric and hemodynamic complexities that require the consideration of microvascular arrays and networks. Multivessel models are discussed that have shown the physiological importance of heterogeneities in vessel spacing, O(2) supply, red blood cell flow path, as well as interactions between capillaries and arterioles. These realistic models require sophisticated methods for solving the governing partial differential equations, and a range of solution techniques are described. Finally, the issue of experimental validation of microvascular O(2) delivery models is discussed, and new directions in O(2) transport modeling are outlined.

The chemical biology of nitric oxide: implications in cellular signaling

Nitric oxide (NO) has earned the reputation of being a signaling mediator with many diverse and often opposing biological activities. The diversity in response to this simple diatomic molecule comes from the enormous variety of chemical reactions and biological properties associated with it. In the past few years, the importance of steady-state NO concentrations has emerged as a key determinant of its biological function. Precise cellular responses are differentially regulated by specific NO concentration. We propose five basic distinct concentration levels of NO activity: cGMP-mediated processes ([NO]<1-30 nM), Akt phosphorylation ([NO] = 30-100 nM), stabilization of HIF-1alpha ([NO] = 100-300 nM), phosphorylation of p53 ([NO]>400 nM), and nitrosative stress (1 microM). In general, lower NO concentrations promote cell survival and proliferation, whereas higher levels favor cell cycle arrest, apoptosis, and senescence. Free radical interactions will also influence NO signaling. One of the consequences of reactive oxygen species generation is to reduce NO concentrations. This antagonizes the signaling of nitric oxide and in some cases results in converting a cell-cycle arrest profile to a cell survival profile. The resulting reactive nitrogen species that are generated from these reactions can also have biological effects and increase oxidative and nitrosative stress responses. A number of factors determine the formation of NO and its concentration, such as diffusion, consumption, and substrate availability, which are referred to as kinetic determinants for molecular target interactions. These are the chemical and biochemical parameters that shape cellular responses to NO. Herein we discuss signal transduction and the chemical biology of NO in terms of the direct and indirect reactions.

Nitric oxide in the vasculature: where does it come from and where does it go? A quantitative perspective

Nitric oxide (NO) affects two key aspects of O2 supply and demand: It regulates vascular tone and blood flow by activating soluble guanylate cyclase (sGC) in the vascular smooth muscle, and it controls mitochondrial O2 consumption by inhibiting cytochrome c oxidase. However, significant gaps exist in our quantitative understanding of the regulation of NO production in the vascular region. Large apparent discrepancies exist among the published reports that have analyzed the various pathways in terms of the perivascular NO concentration, the efficacy of NO in causing vasodilation (EC50), its efficacy in tissue respiration (IC50), and the paracrine and endocrine NO release. In this study, we review the NO literature, analyzing NO levels on various scales, identifying and analyzing the discrepancies in the reported data, and proposing hypotheses that can potentially reconcile these discrepancies. Resolving these issues is highly relevant to improving our understanding of vascular biology and to developing pharmaceutical agents that target NO pathways, such as vasodilating drugs.

Intrarenal oxygenation: unique challenges and the biophysical basis of homeostasis

The kidney is faced with unique challenges for oxygen regulation, both because its function requires that perfusion greatly exceeds that required to meet metabolic demand and because vascular control in the kidney is dominated by mechanisms that regulate glomerular filtration and tubular reabsorption. Because tubular sodium reabsorption accounts for most oxygen consumption (Vo2) in the kidney, renal Vo2 varies with glomerular filtration rate. This provides an intrinsic mechanism to match changes in oxygen delivery due to changes in renal blood flow (RBF) with changes in oxygen demand. Renal Vo2 is low relative to supply of oxygen, but diffusional arterial-to-venous (AV) oxygen shunting provides a mechanism by which oxygen superfluous to metabolic demand can bypass the renal microcirculation. This mechanism prevents development of tissue hyperoxia and subsequent tissue oxidation that would otherwise result from the mismatch between renal Vo2 and RBF. Recent evidence suggests that RBF-dependent changes in AV oxygen shunting may also help maintain stable tissue oxygen tension when RBF changes within the physiological range. However, AV oxygen shunting also renders the kidney susceptible to hypoxia. Given that tissue hypoxia is a hallmark of both acute renal injury and chronic renal disease, understanding the causes of tissue hypoxia is of great clinical importance. The simplistic paradigm of oxygenation depending only on the balance between local perfusion and Vo2 is inadequate to achieve this goal. To fully understand the control of renal oxygenation, we must consider a triad of factors that regulate intrarenal oxygenation: local perfusion, local Vo2, and AV oxygen shunting.

Po2measurements in the microcirculation using phosphorescence quenching microscopy at high magnification

In phosphorescence quenching microscopy (PQM), the multiple excitation of a reference volume produces the integration of oxygen consumption artifacts caused by individual flashes. We analyzed the performance of two types of PQM instruments to explain reported data on Po2in the microcirculation. The combination of a large excitation area (LEA) and high flash rate produces a large oxygen photoconsumption artifact manifested differently in stationary and flowing fluids. A LEA instrument strongly depresses Po2in a motionless tissue, but less in flowing blood, creating an apparent transmural Po2drop in arterioles. The proposed model explains the mechanisms responsible for producing apparent transmural and longitudinal Po2gradients in arterioles, a Po2rise in venules, a hypothetical high respiration rate in the arteriolar wall and mesenteric tissue, a low Po2in lymphatic microvessels, and both low and uniform tissue Po2. This alternative explanation for reported paradoxical results of Po2distribution in the microcirculation obviates the need to revise the dominant role of capillaries in oxygen transport to tissue. Finding a way to eliminate the photoconsumption artifact is crucial for accurate microscopic oxygen measurements in microvascular networks and tissue. The PQM technique that employs a small excitation area (SEA) together with a low flash rate was specially designed to avoid accumulated oxygen photoconsumption in flowing blood and lymph. The related scanning SEA instrument provides artifact-free Po2measurements in stationary tissue and motionless fluids. Thus the SEA technique significantly improves the accuracy of microscopic Po2measurements in the microcirculation using the PQM.

A dynamic model of nitric oxide inhibition of mitochondrial cytochrome c oxidase

Nitric oxide can inhibit mitochondrial cytochrome oxidase in both oxygen competitive and uncompetitive modes. A previous model described these interactions assuming equilibrium binding to the reduced and oxidised enzyme respectively (Mason, et al. Proc. Natl. Acad. Sci. U S A 103 (2006) 708-713). Here we demonstrate that the equilibrium assumption is inappropriate as it requires unfeasibly high association constants for NO to the oxidised enzyme. Instead we develop a model which explicitly includes NO binding and its enzyme-bound conversion to nitrite. Removal of the nitrite complex requires electron transfer to the binuclear centre from haem a. This revised model fits the inhibition constants at any value of substrate concentration (ferrocytochrome c or oxygen). It predicts that the inhibited steady state should be a mixture of the reduced haem nitrosyl complex and the oxidized-nitrite complex. Unlike the previous model, binding to the oxidase is always proportional to the degree of inhibition of oxygen consumption. The model is consistent with data and models from a recent paper suggesting that the primary effect of NO binding to the oxidised enzyme is to convert NO to nitrite, rather than to inhibit enzyme activity (Antunes et al. Antioxid. Redox Signal. 9 (2007) 1569-1579).

Nitric oxide from nitrite reduction by hemoglobin in the plasma and erythrocytes

Experimental evidence has shown that nitrite anion plays a key role in one of the proposed mechanisms for hypoxic vasodilation, in which the erythrocyte acts as a NO generator and deoxygenated hemoglobin in pre-capillary arterioles reduces nitrite to NO, which contributes to vascular smooth muscle relaxation. However, because of the complex reactions among nitrite, hemoglobin, and the NO that is formed, the amount of NO delivered by this mechanism under various conditions has not been quantified experimentally. Furthermore, paracrine NO is scavenged by cell-free hemoglobin, as shown by studies of diseases characterized by extensive hemolysis (e.g., sickle cell disease) and the administration of hemoglobin-based oxygen carriers. Taking into consideration the free access of cell-free hemoglobin to the vascular wall and its ability to act as a nitrite reductase, we have now examined the hypothesis that in hypoxia this cell-free hemoglobin could serve as an additional endocrine source of NO. In this study, we constructed a multicellular model to characterize the amount of NO delivered by the reaction of nitrite with both intraerythrocytic and cell-free hemoglobin, while intentionally neglecting all other possible sources of NO in the vasculature. We also examined the roles of hemoglobin molecules in each compartment as nitrite reductases and NO scavengers using the model. Our calculations show that: (1) approximately 0.04pM NO from erythrocytes could reach the smooth muscle if free diffusion were the sole export mechanism; however, this value could rise to approximately 43pM with a membrane-associated mechanism that facilitated NO release from erythrocytes; the results also strongly depend on the erythrocyte membrane permeability to NO; (2) despite the closer proximity of cell-free hemoglobin to the smooth muscle, cell-free hemoglobin reaction with nitrite generates approximately 0.02pM of free NO that can reach the vascular wall, because of a strong self-capture effect. However, it is worth noting that this value is in the same range as erythrocytic hemoglobin-generated NO that is able to diffuse freely out of the cell, despite the tremendous difference in hemoglobin concentration in both cases (microM hemoglobin in plasma vs. mM in erythrocyte); (3) intraerythrocytic hemoglobin encapsulated by a NO-resistant membrane is the major source of NO from nitrite reduction, and cell-free hemoglobin is a significant scavenger of both paracrine and endocrine NO.

Nitric oxide regulation of microvascular oxygen

The role of nitric oxide (NO) as a highly diffusible free radical gaseous vasodilator is intrinsically linked to the control of blood flow and oxygen (O(2)) delivery to tissue. NO also is involved in regulating mitochondrial O(2) metabolism, growth of new blood vessels, and blood oxygenation through control of respiratory ventilation. Hemoglobin and myoglobin may help to conserve NO for subsequent release of a NO-related vasoactive species under hypoxic conditions. NO has a major role in regulating microvascular O(2), and dysfunctional NO signaling is associated with the pathogenesis of metabolic and cardiovascular diseases.