A single reaction-diffusion equation for the multifarious eruptions of urticaria

PLoS Comput Biol. 2020 Jan 15;16(1):e1007590. doi: 10.1371/journal.pcbi.1007590. eCollection 2020 Jan.

Abstract

Urticaria is a common skin disorder characterized by the rapid appearance and disappearance of local skin edema and flares with itching. It is characterized by various macroscopic skin eruptions unique to patients and/or subtypes of urticaria with respect to shape, size, color, and/or duration of eruptions. Nevertheless, the mechanism underlying multifarious eruptions in urticaria is largely unknown. The eruptions are believed to be evoked by histamine release from mast cells in the skin. However, the majority of visible characteristics of urticaria cannot be explained by a simple injection of histamine to the skin. To explain the multifarious eruptions of urticaria, we developed a single reaction-diffusion model suggesting the self-activation and self-inhibition regulation of histamine release from mast cells. Using the model, we found that various geometrical shapes of eruptions typically observed in patients can be explained by the model parameters and randomness or strength of the initial stimuli to mast cells. Furthermore, we verified that the wheal-expanding speed of urticaria, which is shown to be much smaller than that of the intradermal injection experimental system may be explained by our model and a simple diffusion equation. Our study suggests that the simple reaction-diffusion dynamics, including the independent self-activating and -inhibitory regulation of histamine release, may account for the essential mechanism underlying the formation of multifarious eruptions in urticaria.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Computational Biology
  • Histamine / metabolism
  • Histamine Release / physiology
  • Humans
  • Mast Cells / metabolism
  • Models, Biological*
  • Skin / metabolism
  • Skin / pathology
  • Skin / physiopathology
  • Urticaria* / metabolism
  • Urticaria* / pathology
  • Urticaria* / physiopathology

Substances

  • Histamine

Grants and funding

This work was supported by Grants-in-Aid for Scientific Research from the Ministry of Education, Culture, Sports, Science and Technology (JSPS), Japan (JP16K17643, JP19H01805, and JP17KK0094 to SSL; https://www.jsps.go.jp) and by the JST PRESTO program, Japan to SSL (JPMJPR16E2; https://www.jst.go.jp). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.