Critical behavior of spatial networks as a model of paracrine signaling in tumorigenesis

Abstract

Recent work on the study of cell populations in mouse tumors has revealed much about the clonal evolution of cancers from the initiated cell to metastasis. Although most cancers are clonal in origin, genetic instability leads to the emergence of new cell clones, some of which show cooperative behavior during progression to metastasis. The nature of these cell-cell interactions is unclear, and in particular it is possible that their spatial distribution could influence the emergence of fully malignant behavior. The spatial distribution would indicate a subtle dependence of the distribution of these cells and the emergence of malignancy. In this paper we model tumor evolution using dynamically evolving spatially embedded random graphs. The dynamic evolution of Spatio-Temporal graphs is not widely studied analytically, particularly when distance based preferences are included. In this paper we present analysis and simulations of such graphs, and demonstrate that the distance function relative to the mixing of the nodes can combine to create phase transitions in connectivity. This result supports the hypothesis that cell to cell interaction is a critical feature of malignancy in tumors.