Urticaria (hives) is a skin condition that affects about one in five people at some point in their lives. Despite how common it is, researchers have long struggled to fully understand the mechanisms behind it. Professor Sungrim Seirin-Lee of the Institute for the Advanced Study of Human Biology (WPI-ASHBi) at Kyoto University Institute for Advanced Study, has brought a mathematician's perspective to the study of this disease. By decoding the patterns of skin eruptions and translating the disease's underlying mechanisms into mathematical models, she has shown how mathematics can help reveal the biology of the condition and pave the way for more personalized care. JST News spoke with Professor Seirin-Lee to hear more about how she constructs mathematical models in her head to uncover the mechanisms of this intractable skin disease.
A disease without an animal model: An unsolved mystery ignites scientific curiosity
Although urticaria is a common skin condition, the biological mechanisms underlying its development remain poorly understood. One reason for this is that it only occurs in humans, horses and chimpanzees, making it difficult to study using conventional laboratory animal models such as mice. Chronic urticaria, in which symptoms persist for more than six weeks, is particularly difficult to treat, and some patients suffer from the disease for several years. As a result, uncovering the mechanisms that drive chronic urticaria has been a long-standing challenge for medical researchers.
Seirin-Lee approached this challenge from an entirely different angle. Her research originally focused on Turing patterns and the mechanisms through which biological patterns emerge. Using mathematical models, she studied developmental processes and how patterns emerge on the surfaces of animals. She viewed patterns appearing on human skin as visible reflections of the body's internal state. If a mathematical model could reproduce skin eruption patterns based on underlying physiological processes, she reasoned, it might also be possible to work backwards and infer those processes from the patterns themselves.
Seirin-Lee's entry into urticaria research began with a conversation with Professor Michihiro Hide of Hiroshima University, a leading authority on the disease. He posed a question: "Could the patterns of urticaria eruptions be understood mathematically?" For a mathematician, it was an extraordinarily difficult problem. Describing complex, seemingly irregular patterns in mathematical terms is challenging even within mathematics itself. Moreover, Seirin-Lee had no background in the biological mechanisms underlying urticaria. "My first reaction was, 'There's no way I can do that. I should probably turn it down,'" she recalls. Yet at the same time, the problem sparked her scientific curiosity. The fact that it seemed impossible only made it more compelling.
A mathematical model of eruption patterns and refinements for clinical use
Urticaria is thought to be primarily caused by the excessive release of histamine, a chemical messenger that plays a crucial role in the immune system. When mast cells, a type of immune cell found in the skin, are exposed to external stimuli such as allergens, they release histamine. This creates gaps in the walls of blood vessels (vascular endothelial cells), allowing plasma and other blood components to leak into the surrounding tissue and form the characteristic red, raised wheals of urticaria, which range in size from a few millimeters to several centimeters (Figure 1). The histamine released in this process also triggers further histamine release from mast cells, creating a positive feedback loop.
Histamine release alone, however, cannot explain the wide variety of eruption patterns seen in urticaria. If it were the only factor involved, eruptions would be expected to appear uniformly across the skin. Seirin-Lee therefore expanded the model to include not only the mechanisms responsible for histamine release but also those involved in its suppression. By translating these interacting processes into mathematical equations, she created a model capable of representing a patient's underlying physiological state (Figure 2).
This equation is based on a reaction-diffusion equation, a mathematical framework used to describe how substances spread through space over time. It includes terms representing histamine release from mast cells (the second term on the right-hand side of the equation) as well as mechanisms that suppress its release (the third term). Seirin-Lee describes it as "a mathematically elegant equation" because it captures the essence of the spatiotemporal diversity of eruption patterns in a single line.
Although the model demonstrated how diverse eruption patterns could arise, Seirin-Lee felt it was only a first step. While the model could reproduce a variety of skin eruption patterns, it could not capture the detailed physiological conditions observed in real patients or assess the effectiveness of medications. As such, its value in clinical practice remained limited. Therefore, she began a collaboration with researchers at the Graduate School of Biomedical and Health Sciences at Hiroshima University to create a new mathematical model specifically focused on chronic urticaria.
Five distinct eruption patterns: Using biology to guide treatment decisions
In this collaboration, the Hiroshima University team used cultured-cell experiments to infer the biological processes occurring in patients with chronic urticaria, while Seirin-Lee translated them into a mathematical model. The mechanism proposed by the Hiroshima University team was as follows (Figure 3).
First, basophils, a type of white blood cell that circulates through the bloodstream, and mast cells in the skin begin releasing histamine in response to external stimuli. Histamine released from basophils then stimulates endothelial cells, which form the walls of blood vessels, to express tissue factor, a protein that initiates the blood clotting process. In turn, blood coagulation factors activated by tissue factor further promote histamine release from basophils.
Meanwhile, some of the blood coagulation factors activated by tissue factor leak out of the blood vessels and stimulate mast cells. This stimulation causes the mast cells to release large amounts of histamine, causing the gaps between vascular endothelial cells to widen even further. As more blood coagulation factors leak out into the surrounding tissue, stimulation of the mast cells intensifies, resulting in an even greater release of histamine.
Seirin-Lee expressed this series of mechanisms as a mathematical model consisting of four equations (Figure 4). Using this model, she repeatedly ran in silico simulations while varying factors such as the rate of histamine release and its ability to diffuse. As a result, the distribution patterns of histamine could be classified into five categories. Two of these annular and broken annular patterns, are characterized by swelling along their boundaries, while the remaining three, geographic, circular, and dotted patterns are characterized by swelling across broader areas (Figure 5, top).
Based on these results, the team developed a set of classification criteria for eruption patterns that could be used in clinical practice. They then asked dermatologists to classify images of skin eruptions collected from 105 chronic urticaria patients according to these criteria. As a result, 87.6% of the patients could be classified into one of the five patterns. Clinicians had long recognized that skin eruptions tend to exhibit distinct patterns. However, they had never imagined that those patterns, and the underlying physiological conditions they reflect, could be described mathematically. They welcomed the findings enthusiastically.
Further analysis of the mathematical model revealed that each individual eruption pattern is generated by a different balance between tissue factor expression in vascular endothelial cells and histamine release from mast cells (Figure 5, bottom). The team also investigated the respective roles of basophils and mast cells in shaping eruption patterns and in the various phases of eruption development, from their onset to resolution. Antihistamines are the current standard treatment for urticaria, but approximately 30% of patients do not respond adequately to them. If the patient's underlying physiological state can be inferred from the shape of skin eruptions using a mathematical model, it may be possible to make more informed treatment decisions. For example, patients with dotted-pattern wheals may benefit particularly from therapies that target basophils.
Returning to research through mathematical biology — A perspective beyond traditional academic boundaries
Despite her success in using mathematics to shed light on the mechanisms of urticaria, Seirin-Lee did not originally set out to become a mathematician. Born and raised in Busan, South Korea, she initially hoped to study architecture. However, at a time when engineering was widely considered unsuitable for women, by process of elimination, she entered the College of Natural Science and chose to major in mathematics. Her training in pure mathematics would become the foundation of her research career. With a laugh, she recalls, "I eventually learned how to work through mathematical equations and structures in my head without relying on pen and paper."
A major turning point in her life came after she completed her master's degree in South Korea and moved to Japan. She lived as a full-time homemaker while learning Japanese from scratch until one day, she happened to pick up a book that captured her imagination. The book explained the processes of biological invasion and dispersal using mathematical models. She was struck by the realization that mathematics, which she had believed to be a world of symbols and logic, could be deeply connected to biology.
She was also captivated by the beauty of Turing patterns, a theory proposed by the mathematician Alan Turing that explains how biological patterns emerge through mathematical principles. Inspired by this idea, she enrolled in graduate school at Okayama University to study mathematical biology, returning to research for the first time in four years. During her doctoral studies, she spent a year abroad at the University of Oxford in the UK, where she deepened her understanding of mathematical approaches to pattern formation. Although her stay lasted only a year, she devoted herself to research and earned the respect of leading researchers in the field. The connections she made there have grown into a worldwide network of mathematical biologists that still continues today.
Although her career looks like it took an unconventional path, it gave Seirin-Lee a perspective unconstrained by traditional academic boundaries. While conducting her research at the University of Oxford, she came to realize that building a mathematical model requires careful observation of the biological phenomena it is intended to describe. With the belief that "life itself holds the clues to its mysteries," she approaches biological phenomena as they are, viewing them through the lens of a mathematician. This mindset, she says, is her greatest strength and the driving force behind her efforts to unravel the mysteries of skin diseases that had long resisted explanation.
Personalized care through mathematical modeling: Building a new field of mathematical dermatology
In mathematical modeling, researchers construct equations from the ground up, guided by the question of which phenomena they want to understand and what underlying mechanisms they hope to uncover. "When developing a mathematical model, you start from an infinite number of combinations and decide what it is you want to see," says Seirin-Lee. "This requires a kind of intuition and craftsmanship that is unique to mathematicians. At the same time, if we rely solely on mathematical models, mathematics research will remain confined to basic research. The future of mathematical science requires even greater innovation than we've seen so far."
Seirin-Lee's interests extend beyond basic research. Inspired by the dedication of physicians who work directly with patients, her focus has shifted from pursuing elegant mathematical equations to finding ways to improve patient care. She is currently developing a system that can estimate a patient's underlying physiological state from the shape of skin eruptions using only a photo of the affected area taken with a smartphone. This research integrates mathematical models with cutting-edge data science and AI. If successful, this could help advance personalized medicine by identifying optimal treatment without the need for burdensome diagnostic tests. In the field of drug discovery, the ability to develop therapies based on physiological states inferred from eruption patterns could potentially shorten treatment periods and help prevent conditions from becoming chronic.
There remains much to learn about skin diseases. "I don't want to pursue only research that seems achievable," says Seirin-Lee. "I want to pursue research ambitious enough to feel like a dream. Ultimately, I hope to establish an entirely new field: mathematical dermatology."
Large scale projects such as CREST bring not only a sense of purpose but also great responsibility. To motivate herself to take on such ambitious goals, Seirin-Lee deliberately took up running, despite never particularly enjoying it. She is building up both her mental and physical strength to see this big project through to the end. Bringing together mathematics and medicine through a perspective unconstrained by traditional academic boundaries, Seirin-Lee continues her pursuit of new possibilities for the future of healthcare.
(Article: Mari Ando, Photography: Hiroyuki Obayashi)
