Dynamics of Growth and Signaling along Linear and Surface Structures in Very Early Tumors

Abstract

There exists evidence that in early stages tumors progress along linear, tubular, or irregular surface structures. This seems to be the case for atypical adenomatous hyperplasia (AAH), a precursor of adenocarcinoma of the lung. We previously published a simplified model, which showed that early structures had a potential towards spontaneous invasive growth following a latency phase. The transition was facilitated by diffusion of a growth factor and nonlinear cell cycle regulation in cancer cells. The mechanism is analogous to that in Turing pattern formation, although the patterns are irregular and unstable. We introduce more biologically justifiable signaling, in which only the free growth factor molecules diffuse. Flexible nonlinearities in the model accommodate several growth patterns of cells as well as internal versus external production of the growth factor. We show that the reaction-diffusion setup results in complicated spike-like solutions. We discuss these results in the light of published data on the AAH.