Far from equilibrium dynamics of tracer particles embedded in a growing multicellular spheroid

Abstract

Local stresses on the cancer cells (CCs) have been measured by embedding inert tracer particles (TPs) in a growing multicellular spheroid. The utility of the experiments requires that the TPs do not alter the CC microenvironment. We show, using theory and extensive simulations, that proliferation and apoptosis of the CCs, drive the dynamics of the TPs far from equilibrium. On times less than the CC division times, the TPs exhibit sub-diffusive behavior (the mean square displacement, with βTP < 1). Surprisingly, in the long-time limit, the motion of the TPs is hyper-diffusive ( with αTP > 2) due to persistent directed motion for a number of CC division times. In contrast, CC proliferation randomizes their motion resulting from jamming at short times to super-diffusive behavior, with αCC exceeding unity, at long times. Surprisingly, the effect of the TPs on CC dynamics and radial pressure is negligible, suggesting that the TPs are reliable reporters of the CC microenvironment.