How it Works
The simulation uses a 2D grid where each cell contains a density value u(x,y,t) representing the local cell density (0 = empty wound, 1 = fully confluent). The Fisher-KPP equation is solved numerically: diffusion spreads cells into the wound, while logistic growth refills the monolayer.
Individual cell particles are rendered at the leading edge to visualize the active migration front. Lamellipodia protrusions are drawn as small extending arms on edge cells. The front position is tracked over time and compared to the theoretical Fisher-KPP wave speed v = 2√(D·k).
Wave speed: v = 2√(D·k)
Lamellipodia: actin polymerization rate ∝ (1 - u)·motility
Gap area(t) = ∫∫ [u(x,y,t) < 0.5] dx dy
Wound closure % = 1 - Gap(t)/Gap(0)
Frequently Asked Questions
What is collective cell migration?
Collective cell migration is the coordinated movement of groups of cells rather than individual cells. It is essential for wound healing, embryonic development, and cancer invasion. Cells maintain cell-cell contacts while moving as a cohesive sheet.
What are lamellipodia?
Lamellipodia are flat, sheet-like protrusions at the leading edge of migrating cells, driven by branched actin polymerization. They sense the environment, adhere to the substrate, and generate the traction forces needed for cell movement.
What is the Fisher-KPP equation?
The Fisher-KPP equation ∂u/∂t = D·∂²u/∂x² + ku(1-u) describes a traveling wave front where u is cell density, D is motility, and k is proliferation rate. The wave speed approaches v = 2√(Dk), predicting wound closure rate.
What drives cells to move into a wound?
Multiple signals drive wound-directed migration: free edge detection (loss of contact inhibition), chemoattractants (EGF, FGF), electrotaxis (wound electric fields), and mechanical signals transmitted through the epithelial sheet via cadherins.
What is contact inhibition of locomotion?
Contact inhibition of locomotion (CIL) is the phenomenon where migrating cells stop and change direction upon contact with another cell. It prevents cells from migrating over one another and coordinates collective directional movement toward the wound.
What is the role of actin in cell migration?
Actin polymerization at the leading edge pushes the cell membrane forward. Myosin II contraction at the rear retracts the cell body. Focal adhesions anchor actin to the substrate, transmitting forces that propel the cell forward.
What are the phases of wound healing?
Wound healing has four overlapping phases: hemostasis (blood clotting), inflammation (immune cell recruitment), proliferation (cell migration, collagen deposition, angiogenesis), and remodeling (matrix reorganization over months to years).
How does the scratch assay measure cell migration?
The scratch assay (wound healing assay) creates a cell-free gap in a confluent monolayer using a pipette tip. Time-lapse microscopy tracks how quickly cells close the gap. This simple method measures motility and is widely used in cancer research.
How do growth factors affect wound healing?
Growth factors such as EGF, PDGF, TGF-β, and VEGF are released at wound sites. They stimulate cell proliferation, migration, and angiogenesis. Topical growth factor therapies are used clinically to accelerate healing of chronic wounds.
What happens in impaired wound healing?
Impaired wound healing occurs in diabetes, venous insufficiency, and immunosuppression. High glucose levels impair cell migration and angiogenesis. Chronic wounds become stuck in the inflammatory phase, leading to non-healing ulcers.