Scale-free correlations and potential criticality in weakly ordered populations of brain cancer cells

Abstract

Collectivebeha vior spans severalorders ofmagnitude ofbiological organization, from cell colonies toflocks of birds. Weused time-resolved tracking ofindividual glioblastoma cells toinv estigatecollectiv emotion inan ex vivomodel ofglioblas toma. At the population level, glioblastoma cells displayweakly polarized motion inthe (directional) velocities ofsingle cells. Unexpectedly,fluctua tions invelocities arecorr elated overdis tances many times the size ofacell. Correlation lengths scale linearly with the maximum end-to-end length ofthe population, indicating thatthe yarescale-fr ee and lackachar acteristic decayscale other than the size ofthe system. Last,a data-driven maximum entropy model captures statistical features ofthe experimental datawith only two free parameters: the effectivelength scale (nc)and strength (J )oflocal pairwise interactions between tumor cells. These results showtha tglioblas toma assemblies exhibit scale-free correlations inthe absence ofpolariza tion, suggesting thatthe yma ybe poised near acritical point.