⚛️ biophysics

Modelling the formation of skin ulcers observed in Buruli ulcer disease

This study presents a mathematical model of Buruli ulcer pathogenesis that reveals how the interplay between *Mycobacterium ulcerans* diffusion, bacterial growth, and mycolactone dynamics governs the rate and shape of skin ulcer expansion, highlighting that while initial wound development is sensitive to toxin diffusion and degradation rates, long-term expansion speed remains relatively stable across varying parameters.

Original authors: Atuhaire, F., Simmonds, R. E., Hoyle, R. B.

Published 2026-10-09

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CC BY 4.0

Original authors: Atuhaire, F., Simmonds, R. E., Hoyle, R. B.

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ⚕️ This is an AI-generated explanation of a preprint that has not been peer-reviewed. It is not medical advice. Do not make health decisions based on this content. Read full disclaimer

Buruli ulcer is a devastating skin disease found in parts of West and Central Africa, Australia, and Japan. It is caused by a bacterium called Mycobacterium ulcerans, which lives in the environment and can enter the human body, possibly through insect bites or contact with contaminated water. Once inside, the bacteria do not just multiply; they secrete a powerful poison known as mycolactone. This toxin is the true engine of the disease, capable of killing skin cells and destroying tissue, leading to large, painful sores that can take months to heal and often require surgery. While doctors know the bacteria and the toxin are responsible, the exact sequence of events that turns a tiny infection into a massive, expanding ulcer has remained a mystery. Understanding how these lesions grow is critical, because the longer a wound goes untreated, the more severe the damage becomes, potentially leading to permanent disability.

To solve this puzzle, researchers built a mathematical model to simulate the invisible battle happening beneath the skin. Instead of working with petri dishes or patients, they created a virtual landscape representing a patch of skin. In this digital world, they tracked how the bacteria spread, how the toxin diffused through the tissue, and how different types of skin cells reacted to the poison. The scientists focused on two specific ways the toxin might kill tissue. The first is direct poisoning, where the toxin hits a cell and kills it immediately. The second is a more indirect route: the toxin attacks the delicate cells lining the blood vessels, causing them to malfunction. This failure allows blood components to leak out and form clots, which cuts off the oxygen supply to surrounding tissue, causing those cells to die from starvation even if the toxin never touched them directly.

The researchers programmed their model with real-world data, such as how fast the bacteria reproduce and the specific concentrations of toxin required to kill different cell types. They discovered that skin cells are not all equally vulnerable. The cells lining the blood vessels are extremely sensitive, dying when exposed to very low levels of the toxin, while other skin cells require much higher concentrations to be killed directly. The simulation showed that when the toxin levels are high enough to kill everything, the wound expands rapidly. However, when toxin levels are lower, the indirect mechanism becomes the key player. In these scenarios, the toxin kills the blood vessel cells first, which then triggers a chain reaction of tissue death in the surrounding area due to lack of oxygen. This finding suggests that even in areas where the toxin concentration is too weak to directly poison healthy skin cells, the damage can still spread because the blood supply has been compromised.

A major part of the study involved watching how fast the edge of the wound moved over time. The team found that the speed of the wound's expansion is largely determined by how fast the bacteria grow and how quickly they spread through the skin. Interestingly, the speed at which the toxin itself moves through the tissue has a surprising effect. If the toxin spreads much faster than the bacteria, the wound grows quickly at the very beginning, as the poison reaches healthy tissue before the bacteria do. However, once the wound is established, its long-term speed of expansion remains steady, regardless of how fast the toxin moves or how quickly it breaks down. The study also revealed that if the toxin degrades slowly, the initial damage happens faster, but the overall pace of the wound's growth eventually settles into a predictable rhythm driven by the bacteria.

The researchers acknowledge that their work is a simulation based on the best available data, and that real human skin is far more complex than their model. They did not include the body's immune system, which plays a role in fighting the infection, and some details about how the toxin behaves inside a living body are still unknown. Despite these limitations, the model provides a clear picture of the mechanics behind Buruli ulcer. It confirms that the toxin is the primary driver of tissue death and highlights the critical role of blood vessel damage in spreading the disease. By understanding that the wound's growth is a balance between bacterial spread and toxin diffusion, scientists can better predict how these lesions develop. This knowledge offers a new lens through which to view the disease, moving beyond just the presence of bacteria to understand the dynamic process of how a small infection transforms into a large, destructive ulcer.

Technical Summary: Modelling the Formation of Skin Ulcers Observed in Buruli Ulcer Disease

Problem Statement
Buruli ulcer (BU), caused by Mycobacterium ulcerans, is a neglected tropical disease characterized by extensive skin necrosis. While the pathogen secretes a toxin, mycolactone, which drives tissue damage, the precise spatiotemporal dynamics governing the transition from bacterial infection to large-scale ulcer formation remain unclear. Specifically, the relative contributions of two proposed mechanisms—direct cytotoxicity of mycolactone on skin cells versus indirect tissue death via ischaemia (caused by mycolactone-induced endothelial dysfunction and subsequent fibrin deposition)—are not fully understood. Furthermore, the factors controlling the rate of wound expansion and the specific roles of toxin diffusion versus bacterial growth in lesion progression require quantitative investigation.

Methodology
The authors formulated a mathematical model to describe the space-time dynamics of M. ulcerans bacteria, mycolactone concentration, and skin cell densities (specifically endothelial and stromal cells) within a two-dimensional spatial domain. The model incorporates:

Bacterial Dynamics: Logistic growth with a constant birth rate and density-dependent death, coupled with diffusion.
Toxin Dynamics: Mycolactone production proportional to bacterial density, diffusion, and first-order degradation.
Cellular Response: Two distinct cell death mechanisms triggered when local mycolactone concentrations exceed specific thresholds:
1. Direct Cytotoxicity: Cell death occurring when mycolactone levels surpass cell-specific toxicity thresholds ( $c_e$ for endothelial cells, $c_s$ for stromal cells).
2. Ischaemia: Cell death occurring in both cell types when mycolactone exceeds the endothelial threshold, leading to loss of blood supply and fibrin deposition.
Parameterization: Parameters were derived from existing experimental data (e.g., bacterial doubling times, in vitro toxicity thresholds) or estimated based on scaling arguments and equilibrium conditions where experimental data was lacking.
Analysis: The system of partial differential equations was non-dimensionalized, reducing the dependency on physical parameters to two key dimensionless groups: $\alpha$ (ratio of mycolactone to bacterial diffusion coefficients) and $\beta$ (ratio of mycolactone degradation rate to bacterial net birth rate). Numerical simulations were performed using Python to track bacterial growth, toxin accumulation, and the resulting wound edge progression over time.

Key Contributions and Results

Mechanistic Insight into Cell Death: The simulations demonstrate that the differential sensitivity of cell types to mycolactone dictates lesion morphology. When mycolactone concentrations are sufficient to kill endothelial cells but remain below the higher threshold for stromal cells, stromal cells survive only if the ischaemic mechanism is inactive. However, when the ischaemic pathway is active, stromal cells die even at sub-lethal direct toxin concentrations, provided endothelial cells are compromised. This supports the hypothesis that indirect ischaemic damage is a critical driver of tissue necrosis, particularly at lesion margins where toxin concentrations are lower.
Wound Expansion Dynamics: The study identifies that the long-term speed of wound expansion is primarily governed by the diffusion and net birth rate of the bacteria, which set the overall scaling. The trajectory of the wound edge is defined by the dimensionless parameters $\alpha$ $α$ and $\beta$ $β$ .
- Effect of $\alpha$ (Diffusion Ratio): When mycolactone diffuses significantly faster than bacteria ( $\alpha \gg 1$ ), the initial wound expansion is accelerated because the toxin spreads ahead of the bacterial front, causing rapid tissue damage in uninfected regions. However, the steady-state expansion speed remains relatively unchanged across a wide range of $\alpha$ values.
- Effect of $\beta$ (Degradation vs. Growth): Lower values of $\beta$ (indicating slower toxin degradation relative to bacterial growth) lead to faster initial wound development due to transiently higher toxin accumulation. Like $\alpha$ , $\beta$ has minimal impact on the long-term steady-state expansion speed.
Quantitative Scaling: The model confirms that higher mycolactone concentrations accelerate cell death, consistent with existing biological evidence. The results suggest that the wound edge position against time follows a trajectory defined by the interplay of bacterial spread and toxin kinetics, rather than being solely dependent on the absolute magnitude of individual parameters.

Significance and Claims
The paper claims to provide a mathematical framework that unifies the understanding of direct and indirect mechanisms of tissue necrosis in Buruli ulcer. By isolating the roles of diffusion and degradation rates, the model offers insights into why lesions expand at specific rates and how toxin mobility influences the initial phase of wound formation. The authors assert that their results are consistent with existing biological evidence regarding cell sensitivity and toxin effects.

The study modestly positions its contribution as an analytical tool to "unravel BU pathogenesis" and "understand the drivers of cell death," rather than a definitive clinical predictor. The authors acknowledge significant limitations, including the lack of in vivo experimental data for mycolactone production rates and diffusion coefficients in skin, the assumption of equilibrium conditions which may not reflect early infection stages, and the exclusion of immune system components. Consequently, the paper frames its significance as a foundational step toward refining parameter values and developing more realistic models that could eventually aid in the management and control of this neglected tropical disease.

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