The Numerical Simulations of Ligand Diffusion Towards Invadopodia Formation - Hanis Nasir; Mohd Rashid Admon; Suzarina Sukri; Mohd Ariff Admon; Sharidan Shafie; Noorehan Yaacob (Jambura Journal of Biomathematics (JJBM), 2026)
Metastasis refers to the spread of a primary tumor to a different location through the invasion of nearby tissues or organs. This process is aided by the formation of invadopodia, a subcellular structure. Invadopodia are formed through a biological process that involves ligands, signals, receptors, actin, extracellular matrix (ECM), and matrix metalloproteinases (MMPs). In the literature, several studies of the invadopodia model have considered the ligand and signal in their mathematical model. However, for most of the work done, the diffusion rate of the ligands is not considered. Hence, this study aimed to explore the ligand diffusion rate to investigate the influence of the diffusion rate on the behavior of the invadopodia. Since invadopodia are formed as a result of the movement of the plasma membrane, the zero-level set method is applied to detect the movement. In addition, the invadopodia model is solved numerically using a finite difference coupled with the ghost fluid with a linear extrapolation approach for regular and neighboring points, respectively. In this research, different rates of ligand diffusion are applied, and the profiles of the ligand and interface (plasma membrane) are analyzed. The results show that the diffusion rate of the ligand can influence the availability of the invadopodia on the plasma membrane.