Emerging patterns in tumor systems: Simulating the dynamics of multicellular clusters with an agent-based spatial agglomeration model

Brain cancer cells invade early on surrounding parenchyma, which makes it impossible to surgically remove all tumor cells and thus significantly worsens the prognosis of the patient. Specific structural elements such as multicellular clusters have been seen in experimental settings to emerge within the invasive cell system and are believed to express the systems' guidance toward nutritive sites in a heterogeneous environment. Based on these observations, we developed a novel agent-based model of spatio-temporal search and agglomeration to investigate the dynamics of cell motility and aggregation with the assumption that tumors behave as complex dynamic self-organizing biosystems. In this model, virtual cells migrate because they are attracted by higher nutrient concentrations and to avoid overpopulated areas with high levels of toxic metabolites. A specific feature of our model is the capability of cells to search both globally and locally. This concept is applied to simulate cell-surface receptor-mediated information processing of tumor cells such that a cell searching for a more growth-permissive place "learns" the information content of a brain tissue region within a two-dimensional lattice in two stages, processing first the global and then the local input. In both stages, differences in microenvironment characteristics define distinctions in energy expenditure for a moving cell and thus influence cell migration, proliferation, agglomeration, and cell death. Numerical results of our model show a phase transition leading to the emergence of two distinct spatio-temporal patterns depending on the dominant search mechanism. If global search is dominant, the result is a small number of large clusters exhibiting rapid spatial expansion but shorter lifetime of the tumor system. By contrast, if local search is dominant, the trade-off is many small clusters with longer lifetime but much slower velocity of expansion. Furthermore, in the case of such dominant local search, the model reveals an expansive advantage for tumor cell populations with a lower nutrient- depletion rate. Important implications of these results for cancer research are discussed.