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The purpose is a system-determining factor. There is a purpose - there is a system, there is no purpose - there is no system. Any system is always designed for something one and specific, exists for any purpose. The purpose of hemoglobin is to capture oxygen in the lungs and return it to the tissues. But the same hemoglobin has no purpose, for example, to secrete adrenaline, to develop pressure, or to transfer urea, because it is created and built specifically for the transfer of oxygen and only for this purpose.
A system can only be a group of elements whose result of their common interaction is different from the results of each of these elements individually. It can differ both qualitatively and quantitatively. A pile of sand weighs more than the weight of a single grain of sand (the difference is quantitative). The room, whose walls are built of bricks, has the property to limit the volume of space, which is not the case with individual bricks (quality difference). Any system is always designed for some purpose, but always it has the same goal. Hemoglobin is always intended only for oxygen transport, a car for transportation, and a juicer for squeezing juice from fruit. This constancy of purpose obliges the systems to act always the same to achieve the same, but their intended goal.
For example, if the pulmonary alveolar-capillary bed will flow through all the alveolar capillaries, regardless of whether they envelop alveoli with pO2 below or above the critical, venous blood flowing into the lungs will not be saturated enough with oxygen and arterial hypoxemia (intrapulmonary shunt) , because in the part of the alveoli there can be air with a low O2 content. Hence, the purpose of precapillary sphincters is to allow blood flow only through those capillary nets that envelop the alveoli with pO2 above the critical one. And where pO2 is below critical, the blood flow should be closed. To do this, the sensory elements of the regulator of local pulmonary blood flow should react only to pO2, and not to temperature, pressure or flow of anything. And the reaction of this regulator should be only in the form of closure or opening of pre-capillary sphincters that squeeze the terminal artery or precapillary, but not the form of hormone secretion, urinary excretion, nerve impulse generation, luminescence, reproduction, etc. They should only perceive a specific type of external influence - a change in the content of O2, and only in the alveolar air, and not in the blood, and their reaction should be manifested only in the form of their specific result of action - regulation of the lumen of precapillary sphincters.
In this case, the goal of the system is to allow blood flow only through those capillaries that "wash" the alveoli with a high O2 content (above 60 mm Hg). If pO2 is below critical, then the blood flow should be closed. If higher, it is open. This is the logic of the mechanism.