Multiscale Modelling, Analysis and Simulation of Cancer Invasion Mediated by Bound and Soluble Enzymes

Area of Science:

• Mathematical Biology
• Biophysics
• Cancer Research

Background:

• Cancer cells degrade the extracellular matrix (ECM) to invade tissues.
• This degradation is mediated by matrix-degrading enzymes, which can be membrane-bound or soluble.
• Understanding the interplay of these enzymes is crucial for modeling cancer invasion.

Purpose of the Study:

• To formulate a cell-scale model for ECM degradation by cancer cell enzymes.
• To develop a macroscopic model for cancer invasion based on the cell-scale model and homogenization theory.
• To analyze the roles of bound and soluble enzymes in cancer invasion.

Main Methods:

• Formulation of a microscopic, cell-scale model for enzyme-mediated ECM degradation.
• Application of homogenization theory to derive a macroscopic invasion model.
• Mathematical proof of well-posedness for the macroscopic model with relevant initial data.
• Development and application of a finite element method for numerical simulations.

Main Results:

• A macroscopic model for cancer invasion mediated by bound and soluble matrix-degrading enzymes was successfully derived.
• The macroscopic model was proven to be well-posed for biologically relevant initial conditions.
• Simulations demonstrated the distinct and combined roles of bound and soluble enzymes in facilitating cancer cell invasion.

Conclusions:

• The developed mathematical models provide a framework for understanding enzyme-driven cancer invasion.
• Both bound and soluble enzymes play significant roles in the process of cancer cell invasion.
• The study highlights the importance of considering enzyme dynamics in cancer progression models.