Art by Luna Aguilar
The moment a paper cut penetrates the skin, a cascade of biological events aimed at healing the wound is set into motion. Wound healing is essential for the survival of a wide range of organisms, from the tiniest insects to the most complex mammals. Despite its fundamental nature, wound healing varies considerably among different species and even within different developmental stages of the same organism.
In a recent article published in Physical Review Research, a team of Yale researchers introduced the deformable particle (DP) model, which factors in the physical properties of cells—such as mobility, stiffness, and cell shape—to understand how wounds close. Using this model, the team investigated wound closure dynamics in Drosophila, commonly known as fruit flies. They focused specifically on the differences in wound healing at the embryo and larval stages, which mark the two initial stages of development in the Drosophila life cycle.
How Epithelial Wounds Close
Imagine your epithelial cells—which form the protective layer covering your internal organs and outer skin—as the construction workers responsible for building and repairing structures within your body. They use a unique tool to close gaps or wounds: the actomyosin purse string. This mechanism involves assembling actin filaments and myosin motor proteins into a ring-shaped structure around the wound’s edges, similar to a drawstring on a bag. In a coordinated effort, cells contract the myosin proteins, shortening the actin filaments and effectively cinching the wound edges together, much like tightening a purse string.
The actomyosin purse string, along with changes in cell motility and morphology, is the physical mechanism that controls epithelial wound closure and encourages the healing and repair of damaged tissue. As a result, variations in the cell’s physical properties can contribute to the different wound closure phenotypes observed across different developmental stages of Drosophila. Wound closure phenotypes refer to the observable physical properties of a healed wound, such as the shapes of the cells after closure and whether the wounds form raised or compressed scars.
Past research has largely focused on computational models of wound closure. These models assume that cell membranes respond to wounds primarily through elastic deformation—stretching or bending in response to external forces but returning to their original shape afterward, like a rubber band. However, comparisons to experimental data show that this perspective doesn’t capture the entire picture.
So, what then constitutes the best model for epithelial wound closure? “The difficulty is developing a model that is simple enough to explain the [experimental] data,” said Corey O’Hern, a professor of mechanical engineering, materials science, and applied physics at Yale and senior author of the study. “You can build a model that is so complicated that […] you can overfit the model to the experimental data.”
In this study, the researchers sought to develop a simple yet versatile model to accurately mirror the properties and behaviors of the cells themselves, without unnecessary complexity.
The Deformable Particle Model
The DP model was developed using experimental data previously published by Yanlan Mao, a professor of developmental biophysics at University College London. In Mao’s experiments, wounds were created in Drosophila embryos using a laser, and the subsequent wound-healing process was observed.
“This model is trying to quantitatively capture some of the key features, such as wound closure time and rate and the shapes of cells near the wound,” said Arthur MacKeith, a graduate student in Yale’s Department of Mechanical Engineering and Materials Science and co-author of the study. MacKeith and his coauthors believe that the DP model may be suitable for representing the wound closure process.
At the heart of the DP model lies a simple yet powerful idea: cells are represented as deformable particles that are connected to each other by springs. This approach allows researchers to simulate the intricate alterations in cell shape and the cell-cell interactions that drive wound closure. By adjusting model parameters like cell stiffness (the resistance to deformation) and membrane plasticity (the ability to change shape or properties), researchers can use the DP model to measure how these physical traits affect the process of wound healing.
“We started off with the basic DP model […] and added in the ingredients of, for example, cell-cell adhesion, cell deformability, and collective pursestring motion. The exciting part was getting to the conclusion of plastic shape change and testing it through our simulations,” said Andrew Ton, a physics graduate student at Yale and first author of the study.
The researchers focused on simulating two specific body parts and developmental stages of Drosophila: the embryonic ectoderm, which forms the outermost layer of cells in early embryos, and the larval wing disc epithelium, a flat tissue structure present during the larval stage that originates from the embryonic ectoderm and serves as the starting point for the formation of the adult wing.
Numerical simulations of the DP model were carried out to investigate actomyosin purse string-based wound closure in the embryonic ectoderm and larval wing disk. The results were then analyzed, and predictions about real-world phenomena were made.
The results of the study showed that the wound area decreases more rapidly in embryos while the cell shape parameter rapidly increases. This rapid wound shrinking during the embryonic stage is especially important, as many critical organs and tissues develop during this period. The researchers also examined the overall healing rates of simulated wing disc wounds compared to simulated embryonic wounds. They observed that the wounds on the wing discs took over four hours to fully close, while in the simulated embryo, it closed in just forty-eight minutes. In other words, wounds heal fast for larvae, but they heal even faster for embryos.
“Healing wounds quickly in embryonic cells would help avoid delaying development if any damage occurs,” Ton said. “We think [embryos] are a little more inclined to support orchestrated cell movements earlier in development. Whenever it sees a wound, the embryo is ready to close […] whether it comes from development or an artificial wound.”
The researchers validated the DP model’s results by comparing them with experimental results to ensure the model’s accuracy, consistency, and relevance to real-world applications. The experimental systems were visualized using confocal microscopy, a technique in which high-resolution images are captured by scanning a focused beam of light onto a specimen, resulting in an exceptionally clear and detailed image. They found that the experimental results were similar to the simulated results, noting a rapid elongation of the cell shape, alongside a swift decrease in wound area over time in both sets of data.
Evaluating the DP Model
The current DP model has many strengths that set it apart from previous computational models used to simulate wound healing. The DP model is versatile; it can reliably help researchers understand and characterize how cells behave, irrespective of how densely packed together they are. The model also accommodates cells of various shapes, ranging from flat and angular to more rounded cells, and can account for push-and-pull interactions among cells, where cells repel each other or tightly adhere to one another. Another strength of the DP model is its inclusion of irreversible cell shape changes, a feature lacking in previous models limited to elastic deformation. This enables researchers to investigate the significance of these changes for effective tissue repair.
While the DP model has many strengths, it also comes with certain limitations. One key drawback is its restriction to the two-dimensional aspects of wound healing. “[Wound healing] is a three-dimensional problem, whereas we are only considering one layer of cells in the current work,” MacKeith said. He explained that wounds involve not only the surface epithelial layer, but also underlying tissues, blood vessels, nerves, and other components. Although the DP model can provide valuable insights into a two-dimensional slice of the problem, it simply cannot account for some aspects of the complex three-dimensional nature of wound healing.
Nonetheless, focusing on a single layer of cells can yield valuable insights into how cells behave during wound healing in epithelial tissues. For example, studying how cell deformability influences wound healing can provide important clues to developing new treatments for congenital defects.
The researchers hope that someday, the DP model can be applied to human wound healing or development—though this will take much more work. Computational models like the DP model allow for detailed simulations and hypothesis testing, complementing experimental approaches. They enable researchers to explore hypothetical scenarios, integrate diverse datasets, and advance personalized medicine by predicting individual responses to treatments.
“One way that this [research] could be translated into treatment for humans could be in telling researchers where to focus their efforts […] when we are considering ways to accelerate healing,” Ton said. Thus, further studies using the DP model hold promise for accelerating our understanding of cell biology and its relevance to human health.