Scale-free correlations and criticality in an experimental model of brain cancer

Abstract

Collective behavior spans several orders of magnitudes of biological organization, ranging from cell colonies, to flocks of birds, to herds of wildebeests. In this work, we investigate collective motion of glioblastoma cells in an ex-vivo experimental model of malignant brain tumors. Using time-resolved tracking of individual glioma cells, we observed collective motion characterized by weak polarization in the (directional) velocities of single cells, with fluctuations correlated over many cell lengths. The correlation length of these fluctuations scales approximately linearly with the total population size, and these scale-free correlations suggest that the system is poised near a critical point. To further investigate the source of this scale-free behavior, we used a data-driven maximum entropy model to estimate the effective length scale (nc) and strength (J) of local interactions between tumor cells. The model captures statistical features of the experimental data, including the shape of the velocity distributions and the existence of long range correlations, and suggests that nc and J vary substantially across different populations. However, the scale and strength of the interactions do not vary randomly, but instead occur on the boundary separating ordered and disordered motion, where the model exhibits classical signs of criticality, including divergences in generalized susceptibility and heat capacity. Our results suggest that brain tumor assemblies are poised near a critical point characterized by scale-free correlations in the absence of strong polarization.