The impact of "search precision" in an agent-based tumor model

Several cell surface receptors are overexpressed in malignant brain tumors and reportedly involved in tumor progression and invasion. It is unclear, however, whether such an improvement of cellular signal reception leads to a monotonic increase in the tumor system's average velocity during invasion or whether there is a maximum threshold beyond which the average velocity starts to decelerate. To gain more insight into the systemic effects of such cellular search precision modulations, this study proposes a two-dimensional agent-based model in which the spatio-temporal expansion of malignant brain tumor cells is guided by environmental heterogeneities in mechanical confinement, toxic metabolites and nutrient sources. Here, the spatial field of action is represented by an adaptive grid lattice, which corresponds to the experimental finding that tumor cells are more likely to follow each other along preformed pathways. Another prominent feature is the dual threshold concept for both nutrient level and toxicity, which determine whether cells proliferate, migrate, remain quiescent or die in the next period. The numerical results from varying the key parameters encoding the capability of tumor cells to invade and their ability to proliferate indicate an emergent behavior. Specifically, increasing invasiveness not only leads to an increase in maximum expansion velocity, but also requires a more precise spatial search process, corresponding to an improved cell signal reception, in order to obtain maximum velocity. To increase cellular invasiveness beyond the maximum that can be achieved by exclusively tuning the motility parameter, it requires an additional reduction in the cells' proliferation rate and prompts an even more biased search process. Most interestingly, however, a prominent phase transition suggests that tumor cells do not employ a 100 percent search precision to attain maximum spatial velocity. These findings argue for a selection advantage conferred by limited randomness in processing spatial search and indicate that our computational platform may prove valuable in investigating emergent, multicellular tumor patterns caused by alterations on the molecular level.