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Review
.2013 Aug;20(6):455-83.
doi: 10.1111/micc.12051.

Bang-bang model for regulation of local blood flow

Affiliations
Review

Bang-bang model for regulation of local blood flow

Aleksander S Golub et al. Microcirculation.2013 Aug.

Abstract

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.

Keywords: metabolic regulation; nitric oxide; on/off regulation; oxygen; superoxide anion.

© 2013 John Wiley & Sons Ltd.

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Figures

Figure 1
Figure 1
Schematic diagram represents the principle of negative feedback regulation in a steam engine using the centrifugal governor. Reducing the steam flow through the valve reduces the speed of the flyballs and causes a proportional downward shift of the gate in the valve, thereby increasing the flow of steam and speed of rotation. The principle of proportional regulation via negative feedback has been transferred to physiology as a model of local blood flow regulation via metabolic vasodilators. In this metaphor, a parenchymal cell is the sensor of the oxygen delivery rate, acting as the flyballs unit, which produces the metabolic vasodilators in response to hypoxia, and the smooth muscle cells in the arteriolar wall act as the gate valve. In this model active regulation is initiated by the lack of oxygen delivery and realized by reducing the arteriolar tone. The disadvantage of this model of regulation is the permanent state of tissue hypoxia required to produce metabolites and the failure to find an elusive set of metabolic vasodilators to account for the observed vasodilation.
Figure 2
Figure 2
Bang-bang regulator of the fluid level is a system with negative feedback that closes the inflow when the set-point level is reached. When the level is low, the gate is passively opened by the weight (labeled NO), which provides a permanent opening force. When the liquid level rises to the set point, the float closes the gate valve, stopping the flow. We propose the concept of local control of blood flow, which is built on the interaction of three types of cells on a principle similar to the bang-bang liquid level controller. The role of the permanent weight is performed by microvascular endothelial cells continuously producing NO. The flux of nitric oxide to the smooth muscle cells relaxes them and keeps the arterioles (gate valve) in a normally open state. Under conditions of adequate oxygen and glucose supply the cytosolic level of NAD(P)H and oxygen (fluid level) in the parenchymal cells is sufficient for the production of superoxide by membrane NAD(P)H oxidases (the float). The superoxide is injected into the interstitial space to neutralize NO and evoke arteriolar vasoconstriction (closed gate valve). At the activation of mitochondrial respiration (sink valve “rest / work” is open) the cytosolic reducing agents are sequestered by mitochondria, and at the same time the PO2 on the cell surface is reduced. Because of these changes superoxide production goes down, the NO flux reaches VSMCs and dilates the arterioles (opens the gate valve). Thus, in this scenario dilation is the normal state for the arterioles, and the upper limit of the oxygen and glucose supply is actively regulated. Therefore, the cells are sufficiently supplied at rest and the upper limit of delivery for oxygen and glucose is controlled in order to avoid excessive tissue perfusion.
Figure 3
Figure 3
The flux of nitric oxide, continuously produced by microvascular endothelial cells, is transported by diffusion to smooth muscle cells in the walls of arterioles. The interstitial concentration and distance of NO propagation depends on the presence of superoxide injected into the extracellular space by NAD(P)H oxidase. Thus the interstitial space represents a chemical gate, which controls the NO flux to the smooth muscle cells of arterioles via emission of superoxide mainly by parenchymal cells. Graphically, this process can be presented as a kind of transistor where the source is endothelial eNOS, the drain is sGC of the VSMCs and the interstitium is a gate controlled by the concentration of superoxide. Similarly, the flow of superoxide to ecSOD is modulated by NO concentration in the interstitium, and the interstitium also can be represented as a gate for superoxide, controlled by the interstitial concentration of NO. This concept is based on the results of mathematical modeling for the propagation of NO and superoxide in a diffusion/reaction system (37, 40, 158).
Figure 4
Figure 4
Hypothetical logical network (cell circuit) controlling local blood flow has three levels: microvessels, cells and interstitial space. Three types of cells are involved in the regulation of the local supply of oxygen and substrates: vascular smooth muscle cells (VSMC), endothelial cells (EC) and skeletal muscle cells (Skeletal MC). Basically, the signaling involves four enzymes: eNOS, NAD(P)H oxidase, sGC and ecSOD. Under normal conditions in resting muscle, with enough glucose (Glu) and oxygen in the arterial blood, the endothelium gets these materials without limitation. The constitutive enzyme eNOS produces a constant NO flux using oxygen, cytosolic NADPH and L-arginine, which is recyclable. Thus, in this diagram eNOS is represented as a logical AND gate, which has a “High” output state if both input levels (Glu and O2) are “High.” When the level of oxygen or glucose in blood is “Low,” the NO output is “Low.” If the levels of the input signals (Glu and O2) are “High,” and the level of interstitial superoxide is “Low.” the flux of NO through interstitium reaches sGC in the VSMCs, the arteriolar gate is open, and local blood flow is “High.” The flux of glucose and oxygen from the blood to the muscle fibers is limited by the diffusion resistance of the vascular wall, interstitium and the cells. At rest, with an adequate supply of glucose and oxygen, the level of reducing agents in the sarcoplasm is high and also the oxygen tension on the surface of muscle fibers is high. In this case NAD(P)H oxidase, located in sarcolemma, also works as an AND gate, producing a “High” level of superoxide in the interstitial space. This leads to the closure of the left interstitial NO gate and, consequently, to the “Low” level of local blood flow, corresponding to the state of resting muscle. In this cell circuit the pool of ecSOD actively reduces the concentration of superoxide in the interstitium, setting the set-point for the upper level of oxygen and glucose supply in resting muscle. When the mitochondria in the muscle fibers are activated (switches at the mitochondria box are connected) the reducing agents are sequestered from the cytosol by mitochondria and oxygen tension on the cell surface is decreased due to increased consumption and diffusion limitations. “Low” levels of the input signals of NAD(P)H oxidase lead to “Low” levels of superoxide output. The activity of ecSOD in the interstitium and a “High” level of NO accelerate the transition process, so the left NO gate opens, while the right one (Superoxide gate) closes; the sGC output is “High,” dilating the arterioles and setting the blood flow “High.”
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