A cellular automaton model for tumor dormancy: emergence of a proliferative switch

Abstract

Malignant cancers that lead to fatal outcomes for patients may remain dormant for very long periods of time. Although individual mechanisms such as cellular dormancy, angiogenic dormancy and immunosurveillance have been proposed, a comprehensive understanding of cancer dormancy and the "switch" from a dormant to a proliferative state still needs to be strengthened from both a basic and clinical point of view. Computational modeling enables one to explore a variety of scenarios for possible but realistic microscopic dormancy mechanisms and their predicted outcomes. The aim of this paper is to devise such a predictive computational model of dormancy with an emergent "switch" behavior. Specifically, we generalize a previous cellular automaton (CA) model for proliferative growth of solid tumor that now incorporates a variety of cell-level tumor-host interactions and different mechanisms for tumor dormancy, for example the effects of the immune system. Our new CA rules induce a natural "competition" between the tumor and tumor suppression factors in the microenvironment. This competition either results in a "stalemate" for a period of time in which the tumor either eventually wins (spontaneously emerges) or is eradicated; or it leads to a situation in which the tumor is eradicated before such a "stalemate" could ever develop. We also predict that if the number of actively dividing cells within the proliferative rim of the tumor reaches a critical, yet low level, the dormant tumor has a high probability to resume rapid growth. Our findings may shed light on the fundamental understanding of cancer dormancy.

Figure 1. Fluorescence micrograph of a breast tumor stained to visualize carcinoma cells (phospho-p53, green) surrounded by macrophages (CD11b, red) (a).

Nuclei appear blue (DAPI). Image courtesy of Michael Graham Espey, PhD, National Cancer Institute, NIH (private communication). (b) Representative pictures of dormant and fast-growing tumors and their vascular structure. Reprinted from Cancer Letters, 294, Almog N, Molecular mechanisms underlying tumor dormancy, 139–146, Copyright (2010), with permission from Elsevier.

Figure 2. Upper panel: statistics of a simulated noninvasive tumor growing in the ECM with and microenvironmental suppression factors, as predicted by the “CA dormancy model”.

(a) Tumor area A_T normalized by the area A ₀ of the growth permitting region. (b) Areas of different cell populations normalized by the area A ₀ of the growth permitting region. Lower panel: statistics of a simulated noninvasive tumor growing in the ECM with without suppression. (c) Tumor area A_T normalized by the area A ₀ of the growth permitting region. (d) Areas of different cell populations normalized by the area A ₀ of the growth permitting region.

Figure 3. Snapshots of a simulated noninvasive tumor growing in the ECM with on different days given by the CA dormancy model.

Upper panel: Dormancy period. Lower panel: Regrowth period.

Figure 4. The “critical” point at which the noninvasive tumor growing in the ECM with switches from a dormant state to a proliferative state as functions of α and (a).

A schematic phase diagram that characterizes the growth dynamics of a noninvasive tumor growing in the ECM with under different α and (b).

Figure 5. Simulated tumor area A_T normalized by the area A ₀ of the growth permitting region of a noninvasive tumor growing in the ECM with different .

Figure 6. Tumor area A_T normalized by the area A ₀ of the growth permitting region of a simulated noninvasive tumor growing in the ECM under different killing rates by microenvironmental suppression factors.

The parameter k ₀ is the fraction that the suppression factors from the microenvironment kill the actively dividing proliferative cells when the suppression factors counteract these cells.