Local Regulation Of Blood Flow Research Articles

Perivascular tissue inhibits rho-kinase-dependent smooth muscle Ca(2+) sensitivity and endothelium-dependent H2 S signalling in rat coronary arteries.

Interactions between perivascular tissue (PVT) and the vascular wall modify artery tone and contribute to local blood flow regulation. Using isometric myography, fluorescence microscopy, membrane potential recordings and phosphospecific immunoblotting, we investigated the cellular mechanisms by which PVT affects constriction and relaxation of rat coronary septal arteries. PVT inhibited vasoconstriction to thromboxane, serotonin and α1 -adrenergic stimulation but not to depolarization with elevated extracellular [K(+) ]. When PVT was wrapped around isolated arteries or placed at the bottom of the myograph chamber, a smaller yet significant inhibition of vasoconstriction was observed. Resting membrane potential, depolarization to serotonin or thromboxane stimulation, and resting and serotonin-stimulated vascular smooth muscle [Ca(2+) ]-levels were unaffected by PVT. Serotonin-induced vasoconstriction was almost abolished by rho-kinase inhibitor Y-27632 and modestly reduced by protein kinase C inhibitor bisindolylmaleimide X. PVT reduced phosphorylation of myosin phosphatase targeting subunit (MYPT) at Thr850 by ∼40% in serotonin-stimulated arteries but had no effect on MYPT-phosphorylation in arteries depolarized with elevated extracellular [K(+) ]. The net anti-contractile effect of PVT was accentuated after endothelial denudation. PVT also impaired vasorelaxation and endothelial Ca(2+) responses to cholinergic stimulation. Methacholine-induced vasorelaxation was mediated by NO and H2 S, and particularly the H2 S-dependent (dl-propargylglycine- and XE991-sensitive) component was attenuated by PVT. Vasorelaxation to NO- and H2 S-donors was maintained in arteries with PVT. In conclusion, cardiomyocyte-rich PVT surrounding coronary arteries releases diffusible factors that reduce rho-kinase-dependent smooth muscle Ca(2+) sensitivity and endothelial Ca(2+) responses. These mechanisms inhibit agonist-induced vasoconstriction and endothelium-dependent vasorelaxation and suggest new signalling pathways for metabolic regulation of blood flow.

α5-Integrin-mediated cellular signaling contributes to the myogenic response of cerebral resistance arteries

The myogenic response of resistance arterioles and small arteries involving constriction in response to intraluminal pressure elevation and dilation on pressure reduction is fundamental to local blood flow regulation in the microcirculation. Integrins have garnered considerable attention in the context of initiating the myogenic response, but evidence indicative of mechanotransduction by integrin adhesions, for example established changes in tyrosine phosphorylation of key adhesion proteins, has not been obtained to substantiate this interpretation. Here, we evaluated the role of integrin adhesions and associated cellular signaling in the rat cerebral arterial myogenic response using function-blocking antibodies against α5β1-integrins, pharmacological inhibitors of focal adhesion kinase (FAK) and Src family kinase (SFK), an ultra-high-sensitivity western blotting technique, site-specific phosphoprotein antibodies to quantify adhesion and contractile filament protein phosphorylation, and differential centrifugation to determine G-actin levels in rat cerebral arteries at varied intraluminal pressures. Pressure-dependent increases in the levels of phosphorylation of FAK (FAK-Y397, Y576/Y577), SFK (SFK-Y416; Y527 phosphorylation was reduced), vinculin-Y1065, paxillin-Y118 and phosphoinositide-specific phospholipase C-γ1 (PLCγ1)-Y783 were detected. Treatment with α5-integrin function-blocking antibodies, FAK inhibitor FI-14 or SFK inhibitor SU6656 suppressed the changes in adhesion protein phosphorylation, and prevented pressure-dependent phosphorylation of the myosin targeting subunit of myosin light chain phosphatase (MYPT1) at T855 and 20kDa myosin regulatory light chains (LC20) at S19, as well as actin polymerization that are necessary for myogenic constriction. We conclude that mechanotransduction by integrin adhesions and subsequent cellular signaling play a fundamental role in the cerebral arterial myogenic response.

Assessing Myogenic Response and Vasoactivity In Resistance Mesenteric Arteries Using Pressure Myography.

Small resistance arteries constrict and dilate respectively in response to increased or decreased intraluminal pressure; this phenomenon known as myogenic response is a key regulator of local blood flow. In isobaric conditions small resistance arteries develop sustained constriction known as myogenic tone (MT), which is a major determinant of systemic vascular resistance (SVR). Hence, ex vivo pressurized preparations of small resistance arteries are major tools to study microvascular function in near-physiological states. To achieve this, a freshly isolated intact segment of a small resistance artery (diameter ~260 μm) is mounted onto two small glass cannulas and pressurized. These arterial preparations retain most in vivo characteristics and permit assessment of vascular tone in real-time. Here we provide a detailed protocol for assessing vasoactivity in pressurized small resistance mesenteric arteries from rats; these arteries develop sustained vasoconstriction - approximately 25% of maximal diameter - when pressurized at 70 mmHg. These arterial preparations may be used to study the effect of investigational compounds on relationship between intra-arterial pressure and vasoactivity and determine changes in microvascular function in animal models of various diseases.

Near-infrared spectroscopy (NIRS) in functional research of prefrontal cortex.

Near-infrared spectroscopy (NIRS) in functional research of prefrontal cortex.

Effects of Myoendothelial Interactions on Arteriolar Myogenic and Agonist‐mediated Vascular Control

Local regulation of blood flow to tissue is governed by contraction and relaxation of circumferential vascular smooth muscle in resistance vessels. Interaction between endothelial cells (EC) and smooth muscle cells (SMC) play a critical role in regulating vascular tone. Although ion flux, IP3 and nitric oxide (NO) transport between cells are known to be involved in regulation of SMC activity, little is known about their relative contributions to myogenic and agonist-mediated vascular tone. To quantify their contributions we have assembled an isolated vessel model of a resistance artery by integrating models of vessel wall mechanics, smooth muscle force generation, and SMC and EC Ca2+ dynamics and electrophysiology. Steady-state pressure-diameter and agonist response data from pressure and isovolumic myography studies are analyzed to determine contributions of ionic, IP3 and NO transport between ECs and SMCs on isolated vessel tone. The model predicts levels of SMC and EC Ca2+ at a given vascular tone and can also show how the presence/absence of endothelial layers influences pressure/agonist-induced contraction response, under isobaric and isovolumic conditions. In order to replicate experimentally observed vasoconstriction response to the smooth muscle agonist phenylephrine, the model analysis shows there is a limit to ionic and IP3 coupling allowed between cells. Below these limits, the NO-cGMP pathway has a minimal effect on vasoconstriction response to pressure but yet still has a significant effect on endothelial agonist-induced vasodilatory response. Supported by NIH U01 HL118738, NSF CBET 1133260 and NIH P50-GM094503.

Endothelial cells and human cerebral small vessel disease.

Brain endothelial cells have unique properties in terms of barrier function, local molecular signaling, regulation of local cerebral blood flow (CBF) and interactions with other members of the neurovascular unit. In cerebral small vessel disease (arteriolosclerosis; SVD), the endothelial cells in small arteries survive, even when mural pathology is advanced and myocytes are severely depleted. Here, we review aspects of altered endothelial functions that have been implicated in SVD: local CBF dysregulation, endothelial activation and blood-brain barrier (BBB) dysfunction. Reduced CBF is reported in the diffuse white matter lesions that are a neuroradiological signature of SVD. This may reflect an underlying deficit in local CBF regulation (possibly via the nitric oxide/cGMP signaling pathway). While many laboratories have observed an association of symptomatic SVD with serum markers of endothelial activation, it is apparent that the origin of these circulating markers need not be brain endothelium. Our own neuropathology studies did not confirm local endothelial activation in small vessels exhibiting SVD. Local BBB failure has been proposed as a cause of SVD and associated parenchymal lesions. Some groups find that computational analyses of magnetic resonance imaging (MRI) scans, following systemic injection of a gadolinium-based contrast agent, suggest that extravasation into brain parenchyma is heightened in people with SVD. Our recent histochemical studies of donated brain tissue, using immunolabeling for large plasma proteins [fibrinogen, immunoglobulin G (IgG)], do not support an association of SVD with recent plasma protein extravasation. It is possible that a trigger leakage episode, or a size-selective loosening of the BBB, participates in SVD pathology.

K+ channels in biological processes: vascular K+ channels in the regulation of blood pressure

K+ channels in biological processes: vascular K+ channels in the regulation of blood pressure Matthias E Werner,1 Jonathan Ledoux2–41Institute of Cardiovascular Sciences, Faculty of Medical and Human Sciences, University of Manchester, Manchester, UK; 2Research Center, Montreal Heart Institute; 3Department of Molecular and Integrative Physiology, 4Department of Medicine, Université de Montréal, Montreal, QC, CanadaAbstract: Appropriate supply of blood to organs and tissues is highly dependent on arterial blood pressure and therein of the peripheral blood vessel resistance. Of the two main components of vessel resistance, the active resistance results from the modulation of the contractility level of vascular smooth muscle cells (VSMCs). The intracellular level of Ca2+ in VSMCs is an essential component of muscle contraction and is tightly regulated through modulation of the membrane potential. Since resting membrane potential of vascular cells is mainly dependent on K+ ions, ion channels permeable to K+ ions have a significant impact on contractility of smooth muscle cells and therefore on vascular diameter and blood pressure. Activation of K+ channels on both endothelial cells and VSMCs is generally associated to hyperpolarization and relaxation of vascular smooth muscle. Several types of K+ channels are expressed in VSMCs and endothelial cells, and they are classified based on their pharmacological and biophysical properties. Voltage-dependent K+ channels are activated by depolarization and are mainly involved in negative-feedback mechanisms. Ca2+-activated K+ channels can be divided into three groups, with BKCa being activated by both intracellular Ca2+ and depolarization. On the other hand, KCa2.x and KCa3.1 channels (small and intermediate Ca2+-activated K+ channels, respectively) are almost strictly dependent on rises in intracellular Ca2+ levels to increase their open probability. Kir and adenosine triphosphate (ATP)-sensitive K+ (KATP) channels, members of the same family, have a significant impact on VSMC membrane potential. The more recently studied two-pore K+ channels are thought to be metabolic sensors (like KATP channels) and would be involved in acute regulation of local blood flow. This review will summarize the main K+ channels expressed in vascular cells and their relevance in the control of vascular tone and blood pressure.Keywords: membrane potential, Ca2+, vascular tone

Determination of vessel cross-sectional area by thresholding in Radon space.

The cross-sectional area of a blood vessel determines its resistance, and thus is a regulator of local blood flow. However, the cross-sections of penetrating vessels in the cortex can be non-circular, and dilation and constriction can change the shape of the vessels. We show that observed vessel shape changes can introduce large errors in flux calculations when using a single diameter measurement. Because of these shape changes, typical diameter measurement approaches, such as the full-width at half-maximum (FWHM) that depend on a single diameter axis will generate erroneous results, especially when calculating flux. Here, we present an automated method--thresholding in Radon space (TiRS)--for determining the cross-sectional area of a convex object, such as a penetrating vessel observed with two-photon laser scanning microscopy (2PLSM). The thresholded image is transformed back to image space and contiguous pixels are segmented. The TiRS method is analogous to taking the FWHM across multiple axes and is more robust to noise and shape changes than FWHM and thresholding methods. We demonstrate the superior precision of the TiRS method with in vivo 2PLSM measurements of vessel diameter.

Characterization of vascular endothelial and smooth muscle cell pathways and their contributions to myogenic and agonist‐mediated control (677.16)

Vascular smooth muscle cell contraction and relaxation is central to the local regulation of blood flow to tissue. At the arteriolar level, interactions between vascular endothelial cells and smooth muscel cells play critical role in determining the level of vascular tone. During mechanical and/or agonist stimulations, vascular Ca2+ dynamics are finely adjusted via a number of signaling pathways and the Ca2+ levels in the smooth muscle cells determine the level of contraction. To quantify how cellular Ca2+ dynamics are transformed into changes in vascular tone, we have constructed a cellular‐based model of isolated resistance vessel by integrating models of vessel wall mechanics, smooth muscle force generation, smooth muscle Ca2+ handling and electrophysiology with an endothelial electrophysiology and Ca2+ handling model. The dose‐response vasodilation and vasoconstriction data of different sizes of vessels in response to pharmacological vasoconstrictors and vasodilators, measured using a novel isovolumic myograph developed by Lu and Kassab are analyzed. The model simulates how changes in intraluminal pressure are used to maintain a constant vessel diameter during application of phenylephrine and acetylcholine. In order to simulate these sets of experimental data the model captures integrated vessel behavior including ionic (Ca2+, K+, Na+, etc.), IP3 and nitric oxide myoendothelial transport. Model analysis shows that α‐adrenergic pathways in smooth muscle and NO pathways in endothelium are sufficient to capture the experimentally observed phenylephrine and acetylcholine mediated responses.Grant Funding Source: NIH U01 HL118738, NSF CBET 1133260 and NIH P50‐GM094503

Ageing differentially affects myogenic tone of coronary microcirculatory arteries according to vessel diameter (LB644)

Aging is the major cause of decline in cardiovascular function and for structural and functional alterations of coronary microvasculature. There is close association between cardiac function and coronary blood flow; hence, age‐associated impairment of cardiac function may be related to reduced coronary blood flow capacity. As myogenic tone has a major role in regulation of local blood flow, the aim of this study was to investigate changes in myogenic tone with aging and its heterogeneity based on resistance arteries size. Coronary resistance arteries from young (3 ‐ 4 months) and old (22 ‐ 24 months) males F344 rats were isolated and mounted on a pressure myograph system and changes in outer diameter in response to alteration of intravascular pressure (0‐100 mmHg) with a 20 mmHg increments under no flow condition were recorded. Myogenic tone calculated as a percentage of the difference between Active (in the presence of calcium) and Passive (in the absence of calcium) diameter over passive diameter for each pressure point. Vessel sizes determined as active outer diameter at 80 mmHg. Values calculated using Student t‐test and expressed as (mean ± s.e.m.). Myogneic tone calculated from arteries of young rats 115 µm ± 9 n= 12 (diameter range; 75 ‐ 167 µm) was significantly higher compared to old one 125 µm ± 9 n = 14 (diameter range; 72 ‐ 186 µm) (p蠄0.001). However, when subdividing vessel sizes into small arteries for young (88 µm ± 4) n= 6 and old (92 µm ± 5) n = 6; and large arteries for young (142 µm ± 6) n= 6 and old (149 µm ± 8) n = 8, the myogenic tone was highly significant when comparing small arteries from young and old (p<0.001) and there was no significant differences in myogenic tone between large arteries. Study findings stating that; Both myogenic tone and response decreased dramatically with aging in small resistance arteries, while increasing in young one. There is a very narrow range of myogenic tone drop, so care must be taken when selecting vessels sizes range for aging studies.Grant Funding Source: Supported by Sultan Qaboos University, Oman

A new model for metabolically‐linked regulation of local blood flow (674.5)

In skeletal muscle an increase in O2 consumption over a wide range evokes a proportional increase in LBF. The regulation of LBF ensures matching the delivery of materials with their rate of consumption. The mechanism by which this happens is thought to operate according to the metabolic hypothesis of LBF control, whereby an increase in tissue hypoxia (caused by an imbalance between O2 demand and supply) stimulates the production of metabolites by the hypoxic cells which further open blood vessels and lead to increased blood flow and O2 supply. The drawback of this model is the inevitable maintenance of tissue hypoxia. An alternative mechanism to explain the matching of LBF to demand in O2 and nutrients is proposed which depends on the interaction of two naturally occurring signaling radicals, nitric oxide (NO), constantly produced by endothelial cells, and superoxide (O2‐), produced primarily by the parenchymal cells. These two highly reactive molecules interact in the interstitium at a rate controlled by diffusion to determine the level of the vasodilator NO. The proposed mechanism is based on the concept that functional activity is the normal physiological state for a tissue; the corresponding normal state for its vasculature is dilation. The goal of regulation is maintaining a sufficient, but not excessive, supply of O2 and substrates to the cells. This mechanism explains why the vasodilation signal is generated by microvessels, and how the parenchymal cells block this signal when LBF provides a sufficient supply of O2 and substrates. Production of O2‐ by membrane NAD(P)H oxidase depends on the balance of glycolysis and oxidative phosphorylation via the availability of NADH and NAD(P)H in the cytosol and the interstitial PO2. Thus, the coupling of tissue metabolic activity with LBF is achieved.Grant Funding Source: Supported by NHLBI HL18292

Local metabolic and feed forward regulation of coronary blood flow (1079.23)

When red blood cells reach a low oxygen environment they release a small amount of ATP into the plasma. The ATP and its breakdown products ADP and AMP act on capillary endothelial purinergic receptors to initiate a vasodilator response that is conducted upstream. This forms the basis of a local metabolic feedback control mechanism where the red blood cell is the sensor of the balance of oxygen delivery (flow) versus oxygen consumption by the heart. This is a paradigm shift from the previous idea that the myocardium acts as the sensor of oxygen balance. The existence of feed forward control of the coronary circulation by sympathetic beta adrenoceptor vasodilation, and a modest alpha adrenoceptor vasoconstriction adds complexity and redundancy. A mathematical computer model has been developed to understand the simultaneous action of feedback and feed forward control of coronary blood flow. Data from canine experiments during control exercise and with adrenergic and purinergic receptor blockade were analyzed to elucidate the simultaneous interplay between local metabolic feedback control, and feed forward coronary control. The results indicate that ~71% of coronary vasodilation is due to purinergic local metabolic control and ~27% is due to feed forward adrenergic control during exercise.Grant Funding Source: NIH U01 HL 118738

Commentaries on Viewpoint: A paradigm shift for local blood flow regulation

# COMMENT ON “A PARADIGM SHIFT FOR LOCAL BLOOD FLOW REGULATION” {#article-title-2} to the editor: The proposed role of O2− produced by NAD(P)H oxidase acting in concert with changes in mitochondrial O2 on regulating local blood flow hypothesized by Golub and Pittman ([5][1]) could very well

Last Word on Viewpoint: A paradigm shift for local blood flow regulation

to the editor: We are grateful to our colleagues for their comments (see Ref. [1][1]) about the proposed model of local blood flow regulation ([3][2]). The two main objections put forward are its simplicity and its incompatibility with conventional belief in the “highly complex nature” and “

Muscle contraction increases interstitial nitric oxide as predicted by a new model of local blood flow regulation

The prevailing metabolic theory of local blood flow regulation suggests the dilatation of arterioles in response to tissue hypoxia via the emission of multiple metabolic vasodilators by parenchymal cells. We have proposed a mechanism of regulation, built from well-known components, which assumes that arterioles are normally dilated in metabolically active tissues, due to the emission of NO by the endothelium of microvessels. Regulation of local blood flow aims at preventing an excessive supply of oxygen (O2) and glucose to the tissue and thus provides an adequate supply, in contrast to the metabolic regulation theory which requires permanent hypoxia to generate the metabolic vasodilators. The mediator of the restrictive signal is superoxide anion (O2(-)) released by membrane NAD(P)H oxidases into the interstitial space, where it neutralizes NO at a diffusion-limited rate. This model predicts that the onset of muscle contraction will lead to the cessation of O2(-) production, which will cause an elevation of interstitial NO concentration and an increase in fluorescence of the NO probe DAF-FM after its conversion to DAF-T. The time course of DAF-T fluorescence in contracting muscle is predicted by also considering the washout from the muscle of the interstitially loaded NO indicator. Experiments using pulse fluorimetry confirmed an increase in the interstitial concentration of NO available for reaction with DAF-FM during bouts of muscle contraction. The sharp increase in interstitial [NO] is consistent with the hypothesis that the termination of the neutralizing superoxide flow into the interstitium is associated with the activation of mitochondria and a reduction of the interstitial oxygen tension. The advantage of the new model is its ability to explain the interaction of metabolic activity and local blood flow through the adequate delivery of glucose and oxygen.

Angiotensin II Regulates Islet Microcirculation and Insulin Secretion in Mice

Angiotensin II causes potent increases in systemic and local pressure through its vasoconstrictive effect. Despite the importance of angiotensin II for local blood flow regulation, whether angiotensin II regulates the pancreatic islet microcirculation remains incompletely understood. We hypothesized that angiotensin II directly regulates the pancreatic islet microcirculation and thereby regulates insulin secretion. The aims of this study were to develop a new technique to visualize pancreatic islet hemodynamic changes in vivo and to analyze changes in islet circulation induced by angiotensin II or an angiotensin type 1 receptor blocker. Using an in vivo imaging method, we observed the pancreatic islet microcirculation. Various doses of angiotensin II or an angiotensin type 1 receptor blocker were injected intravenously, and changes in islet microcirculation were observed. Glucose-stimulated insulin secretion from the pancreas was measured from the hepatic portal vein. We identified islet microcirculation using a fluorescent dye. Angiotensin II significantly induced blood vessel contraction in the islets in a dose-dependent manner. In contrast, the angiotensin type 1 receptor blocker induced vasodilation. Glucose-stimulated insulin secretion was decreased by angiotensin II infusion. These results show that angiotensin II is involved in the regulation of pancreatic islet microcirculation and insulin secretion.

Enhancement of endothelial function inhibits left atrial thrombi development in an animal model of spontaneous left atrial thrombosis.

Left atrial (LA) thrombosis is an important cause of systemic embolization. The SPORTS rat model of LA thrombi (Spontaneously-Running Tokushima-Shikoku), which have a unique characteristic of high voluntary wheel running, was previously established. The aim of the present study was to investigate how SPORTS rats develop LA thrombi. Nitric oxide (NO) produced from cardiovascular endothelial cells plays an important protective role in the local regulation of blood flow, vascular tone, and platelet aggregation. No evidence of atrial fibrillation or hypercoagulability in SPORTS rats regardless of age was found; however, SPORTS rats demonstrated endothelial dysfunction and a decrease of NO production from a young age. In addition, endothelial NO synthase activity was significantly decreased in the LA and thoracic aorta endothelia of SPORTS rats. While voluntary wheel running was able to intermittently increase NO levels, running did not statistically decrease the incidence of LA thrombi at autopsy. However, L-arginine treatment significantly increased NO production and provided protection from the development of LA thrombi in SPORTS rats. They present study results indicate that NO has an important role in the development of LA thrombus, and endothelia pathways could provide new targets of therapy to prevent LA thrombosis.

A paradigm shift for local blood flow regulation

a remarkable example of physiological regulation is the coordination between metabolic rate and local blood flow in microscopic volumes of an organ. In skeletal muscle an increase in oxygen consumption (Vo2) over a wide range evokes a proportional (∼5 to 6 × Vo2) increase in blood flow ([29][

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.

Flow‐induced ATP release in patient‐specific arterial geometries – a comparative study of computational models

The importance of the endothelium in the local regulation of blood flow is reflected by its influence on vascular tone by means of vasodilatory responses to many physiological stimuli. Regulatory pathways are affected by mass transport and wall shear stress (WSS), via mechanotransduction mechanisms. In the present work, we review the most relevant computational models that have been proposed to date, and introduce a general framework for modelling the responses of the endothelium to alteration in the flow, with a view to understanding the biomechanical processes involved in the pathways to endothelial dysfunction. Simulations are performed on two different patient-specific stenosed carotid artery geometries to investigate the influence of WSS and mass transport phenomena upon the agonist coupling response at the endothelium. In particular, results presented for two different models of WSS-dependent adenosine-5'-triphosphate (ATP) release reveal that existing paradigms may not account for the conditions encountered in vivo and may therefore not be adequate to model the kinetics of ATP at the endothelium.