Temporal evolution of mediator concentrations in the fading or expanding patterns.

Blue and red lines represent the concentrations of the pro- and anti-inflammatory mediators, respectively. A high concentration of pro-inflammatory mediator was transiently applied at time = 10 to 11. Da = Di = 0; and the other parameter values for these simulations are listed in S2 Table. (TIF)</p

Modeling of the expansion of erythema.

(A) Process of the inflammatory response for erythema development. When keratinocytes in the epidermis and resident immune cells in the dermis are stimulated (i), they secrete inflammatory mediators that induce their own production from these mediator-secreting cells (ii). The mediators diffuse in the dermis and cause the dilation of local blood vessels (iii). The dilation appears as redness on the skin surface, forming erythema (iv). (B, C) Photographs of erythema expansion showing well-circumscribed lesion (B) and poorly circumscribed lesion (C) of mRNA COVID-19 vaccine. (D) Range (surrounded by black solid line) of a and b such that the model (Eq 3, d = 0) exhibits bistability. (E) Kinetics of bistability in Eq (3) represented by the production rate of mediators () as a function of the concentration (q). Two filled circles represent stable steady states (SNI, SI), whereas the hollow circle indicates an unstable steady state (ST). This system can switch between the stable states of low (SNI)- and high (SI)- concentration depending on the perturbation, such as initial stimulation or diffused mediators (a = 2.14, b = 0.05).</p

Balance of mediator concentration regulates expansion or shrinkage.

(A) Range of a and b for the velocity v > 0 (calculated from Eq 5), indicating the expansion (orange), v v = 0 (dashed line). d = 0.5. (B–D) Kinetics of bistability in Eq (3) represented by the production rate of mediators () as a function of the concentration (q) for a = 2.14 (B), a = 2.04 (C), a = 1.96 (D). b = 0.05 in B–D. Two filled circles (SNI, SI) represent stable steady states, whereas the hollow circle (ST) indicates an unstable steady state.</p

Parameter values used in the simulations.

Parameter values used to generate the fading patterns in Fig 2 (A) and the five types of expanding patterns in Fig 3 (B). (XLSX)</p

Erythema patterns observed in eleven diseases.

References for each case are listed in S1 Table [48–96].</p

Simulated time courses of the healthy fading patterns.

Spatiotemporal evolution of pro-inflammatory mediator levels (a) upon initial stimulation in linear (A), reticular (B), and circular areas (C and D). The parameter values for these simulations are listed in S2(A)Table.</p

Erythema pattern and modeling of erythema development.

(A) Process of the inflammatory response for erythema development. Upon stimulation, keratinocytes and resident immune cells secrete pro-inflammatory mediators that induce the production of pro- and anti-inflammatory mediators. Pro-inflammatory mediators dilate local blood vessels. The dilation appears as redness on the skin surface, developing erythema. (B–H) Photographs of erythema with linear [24] (B), reticular [25] (C), circular [26] (D), annular [27] (E), polycyclic [28] (F), arcuate [29](G), or gyrate patterns [30] (H). (I) A model for regulatory feedback between pro- and anti-inflammatory mediators. (J) A representation of simulation in the skin. The skin surface is partitioned into square regions. Erythema is initiated by keratinocytes and immune cells in the skin through secreting pro-inflammatory mediators. The area of microinflammation with a high concentration of pro-inflammatory mediators is considered as a “seed” region, and its projection to the surface is colored in red.</p

System parameters and their interpretations.

The spatiotemporal dynamics of inflammation provide vital insights into the understanding of skin inflammation. Skin inflammation primarily depends on the regulatory feedback between pro- and anti-inflammatory mediators. Healthy skin exhibits fading erythema. In contrast, diseased skin exhibits expanding erythema with diverse patterns, which are clinically classified into five types: circular, annular, arcuate, gyrate, and polycyclic. Inflammatory diseases with expanding erythema are speculated to result from the overproduction of pro-inflammatory mediators. However, the mechanism by which feedback selectively drives the transition from a healthy fading erythema to each of the five types of diseased expanding erythema remains unclear. This study theoretically elucidates the imbalanced production between pro- and anti-inflammatory mediators and prospective treatment strategies for each expanding pattern. Our literature survey showed that eleven diseases exhibit some of the five expanding erythema, thereby suggesting a common spatiotemporal regulation underlying different patterns and diseases. Accordingly, a reaction-diffusion model incorporating mediator feedback reproduced the five observed types of diseased expanding and healthy fading patterns. Importantly, the fading pattern transitioned to the arcuate, gyrate, and polycyclic patterns when the productions of anti-inflammatory and pro-inflammatory mediators were lower and higher, respectively than in the healthy condition. Further depletion of anti-inflammatory mediators caused a circular pattern, whereas further overproduction of pro-inflammatory mediators caused an annular pattern. Mechanistically, the bistability due to stabilization of the diseased state exhibits circular and annular patterns, whereas the excitability exhibits the gyrate, polycyclic, arcuate, and fading patterns as the threshold of pro-inflammatory mediator concentration relative to the healthy state increases. These dynamic regulations of diffusive mediator feedback provide effective treatment strategies for mediator production wherein skins recover from each expanding pattern toward a fading pattern. Thus, these strategies can estimate disease severity and risk based on erythema patterns, paving the way for developing noninvasive and personalized treatments for inflammatory skin diseases.</div

Examples of the positive-and-negative-feedback circuit (Eq. 4) in dynamical quorum sensing systems.

$<p>Negative regulator of autoinducer synthetase <i>x</i>.</p

Gene circuit design for group-level transitions.

<p>(<b>A–B</b>) Schematics of two types of group transition in response to changes in cell density. (<b>A</b>) A graded transition is seen when the fraction of cells in the ON state (red) gradually increases with cell density. (<b>B</b>) An all-or-none transition appears when the state change occurs simultaneously across the population. (<b>C–E</b>) Schematics of an autoinducing gene circuit model (<b>C</b>; <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003110#pcbi.1003110.e004" target="_blank">Eq. 1</a>), dual-positive feedback regulations (<b>D</b>; <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003110#pcbi.1003110.e012" target="_blank">Eq. 3</a>), and positive-and-negative feedback regulations (<b>E</b>; <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003110#pcbi.1003110.e013" target="_blank">Eq. 4</a>) in operation.</p