Invasiveness of a Growth-Migration System in a Two-dimensional Percolation cluster: A Stochastic Mathematical Approach.

We developed a framework based on the software Unstructured Reaction-Diffusion Master Equation (URDME) to address tumor cells' proliferation and migration in a heterogeneous space, herein a 2D percolation cluster. A mitogenic paracrine signaling pathway is utilized phenomenologically to reveal how cells cooperate with one another. We modeled the emerging Allee effect using low seeding density culture (LSDC) assays to fit the model parameters. A Finite time scaling (FTS) function has been formulated to quantitatively analyze invasiveness of a virtual Growth-Migration (GM) system in mimicking the cancer cell growth. Through such simulation, we analyzed the GM dynamics of virtual model in mimicking the growth of BT-474 cancer cell populations in vitro in a 2D percolation cluster and calculated the successful penetration rate (SPR). By analyzing the temporal trajectories of the SPR, we could determine the critical exponents of the critical SPR scaling relation. The SPR transition point ([Formula: see text]), which is a fundamentally different from a conventional percolation transition point, is found to be negatively correlated with the invasiveness of this cancer cell. The [Formula: see text] of the three variations of the virtual GM system distinctly designated by varying paracrine-regulated Allee (PAllee) model phenotypes is 0.3408, 0.3675, and 0.4454, respectively. FTS algorithm thereon may serve as an approach to quantify invasiveness of tumor cells. Through a phenomenological paracrine model, inter-cell cooperation and mutual mitogenic boosting are enabled to elicit the Allee effect in the GM systems. The rationale behind such computationally tunable virtual mechanism can be applied to other circumstances concerning emerging processes.