Abstract
BackgroundThe invasion-metastasis cascade of cancer involves a process of parallel progression. A biological interface (module) in which cells is linked with ECM (extracellular matrix) by CAMs (cell adhesion molecules) has been proposed as a tool for tracing cancer spatiotemporal dynamics.MethodsA mathematical model was established to simulate cancer cell migration. Human uterine leiomyoma specimens, in vitro cell migration assay, quantitative real-time PCR, western blotting, dynamic viscosity, and an in vivo C57BL6 mouse model were used to verify the predictive findings of our model.ResultsThe return to origin probability (RTOP) and its related CAM expression ratio in tumors, so-called "tumor self-seeding", gradually decreased with increased tumor size, and approached the 3D Pólya random walk constant (0.340537) in a periodic structure. The biphasic pattern of cancer cell migration revealed that cancer cells initially grew together and subsequently began spreading. A higher viscosity of fillers applied to the cancer surface was associated with a significantly greater inhibitory effect on cancer migration, in accordance with the Stokes-Einstein equation.ConclusionThe positional probability and cell-CAM-ECM interface (module) in the fractal framework helped us decipher cancer spatiotemporal dynamics; in addition we modeled the methods of cancer control by manipulating the microenvironment plasticity or inhibiting the CAM expression to the Pólya random walk, Pólya constant.
Highlights
The analysis of complex dynamic phenomena such as cancer cell migration through the cell-Cell adhesion molecule (CAM)-Extra-cellular matrix (ECM) interface requires a simple but efficient methodology
Cancer cells are thought to move by a continuous process of “diffusion” or “random walk”, their natural retractionprotrusion crawling motion is slower than molecular diffusion
The positional probability (CAM expression) of different cancer cells showed a biphasic pattern The simulated curve of positional probability and molecular expressions in Eq (1) revealed a biphasic pattern of an initial increase followed by later decline, known as Lévy flight (Figure 3)
Summary
The analysis of complex dynamic phenomena such as cancer cell migration through the cell-CAM-ECM interface (module) requires a simple but efficient methodology. A biological interface (module) in which cells is linked with ECM (extracellular matrix) by CAMs (cell adhesion molecules) has been proposed as a tool for tracing cancer spatiotemporal dynamics. An emerging paradigm shift challenges the traditional invasion-metastasis cascade model [2,3] and proposes instead a “parallel progression” cancer model. In this new concept, cancer cells are thought to move by a continuous process of “diffusion” or “random walk”, their natural retractionprotrusion crawling motion is slower than molecular diffusion. The tracking of single molecules has supported the notion that the sub-diffusion of biological matter in nonhomogeneous and anisotropic microenvironments is non-Fickian [4]
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