Spatiotemporal dynamics of the biological interface between cancer and the microenvironment: a fractal anomalous diffusion model with microenvironment plasticity.
BACKGROUND
The 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.


METHODS
A 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.


RESULTS
The 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.


CONCLUSIONS
The 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.
Center for Mathematical Biology; Division of Plastic Surgery, Department of Surgery, Taipei Medical University Hospital, Taipei Medical University, Taipei, Taiwan. biopattern@gmail.com
Feng-Chou
FC
Tsai
Mei-Chuan
MC
Wang
Jeng-Fan
JF
Lo
Chih-Ming
CM
Chou
Yi-Lu
YL
Lin
D000818:Animals; D015815:Cell Adhesion Molecules / Q000378:metabolism; D045744:Cell Line, Tumor; D003198:Computer Simulation; D004058:Diffusion; D005260:Female; D017709:Fractals; D015972:Gene Expression Regulation, Neoplastic; D006801:Humans; D039001:Integrin alpha Chains / Q000235:genetics / Q000378:metabolism; D007889:Leiomyoma / Q000235:genetics; D051379:Mice; D008810:Mice, Inbred C57BL; D008954:Models, Biological; D019042:Muscle Neoplasms / Q000378:metabolism / Q000473:pathology; D012333:RNA, Messenger / Q000235:genetics / Q000378:metabolism; D013997:Time Factors; D059016:Tumor Microenvironment; D014594:Uterine Neoplasms / Q000235:genetics; D014783:Viscosity
D015815:Cell Adhesion Molecules; D039001:Integrin alpha Chains; D012333:RNA, Messenger