In a college laboratory experiment, students added collagen to platelet-rich serum to observe platelet aggregation. When aspirin was introduced to inhibit one of the key positive feedback signals (specifically through the thromboxane A₂ pathway), the overall level of aggregation dropped significantly—suggesting that most platelets are activated by the positive feedback loop rather than by their initial interaction with collagen alone.
Yet an intriguing observation emerged: varying the concentration of collagen produced a logarithmic increase in platelet aggregation. If the feedback loop were entirely efficient, the initial collagen concentration should theoretically be irrelevant—once a few platelets activate, they should eventually recruit all available platelets.
My hypothesize is that when the first platelets are activated by collagen, they emit signaling molecules that spread outward in three dimensions to activate nearby platelets. Each newly activated “layer” of platelets then signals outward to activate the next layer, and so on. However, because this outward signal disperses into an increasing size volume with each layer (4/3 A = π r cubed), the signal becomes diluted. Past a certain dilution threshold, it can no longer activate additional platelets. Thus, aggregation remains localized rather than expanding to involve every platelet in the system.
As the collagen concentration increases, more initial foci of platelet activation form. Each focus launches its own positive feedback loop, which stops once the signal can no longer propagate effectively. Consequently, higher concentrations of collagen lead to more localized aggregation events—and thus, a logarithmic increase in total platelet aggregation.
Below is a simplified mathematical model employing differential equations to describe how platelet aggregation proceeds and how signal dilution arises with an expanding volume of activation factors:
