Traveling wave of inflammatory response to regulate the expansion or shrinkage of skin erythema.

Many skin diseases show circular red lesions on the skin, called erythema. Erythema is characterized by the expansion of its circular area solely from local stimulation. A pathological inflammatory response caused by the stimulation persistently increases inflammatory mediators in the dermis, whereas a normal inflammatory response transiently increases mediators, resulting in the shrinkage of the erythema. Although the diffusion of mediators theoretically reproduces the expansion, how the inflammatory response expands or shrinks the erythema remains unknown. A possibility is positive feedback, which affects mediator production and can generate two distinct stable states (i.e., inflamed and noninflamed), referred to as bistability. Bistability causes a state transition either from the noninflamed to inflamed state or the reverse direction by suprathreshold stimulation. Additionally, the diffusion selectively causes state transition in either direction, resulting in spatial spread of the transited state, known as the traveling wave. Therefore, we hypothesize that the traveling wave of the inflammatory response can account for both the expansion and shrinkage. Using a reaction-diffusion model with bistability, we theoretically show a possible mechanism in which the circular inflamed area expands via the traveling wave from the noninflamed to the inflamed state. During the expansion, the boundary between the inflamed and noninflamed areas moves at a constant velocity while maintaining its concentration gradient. Moreover, when the positive feedback is weak, the traveling wave selectively occurs from the inflamed to noninflamed state, shrinking the inflamed area. Whether the inflamed area expands or shrinks is mainly controlled by the balance of mediator concentration between the noninflamed and inflamed states, relative to the threshold. The traveling wave of the inflammatory response provides an experimentally testable framework for erythema expansion and shrinkage, thereby contributing to the development of effective treatments, including probiotics.