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

TL;DR

This study investigates the non-equilibrium dynamics of inert tracer particles in a growing multicellular spheroid, revealing complex sub-diffusive and hyper-diffusive behaviors driven by cellular proliferation and apoptosis.

Contribution

The paper provides a theoretical and simulation-based analysis of tracer particle dynamics in spheroids, highlighting the effects of cellular activities on particle motion.

Findings

Tracer particles exhibit sub-diffusive behavior at short times.

At long times, tracer particles show hyper-diffusive motion.

Cell proliferation causes superdiffusive behavior in cancer cells.

Abstract

By embedding inert tracer particles (TPs) in a growing multicellular spheroid the local stresses on the cancer cells (CCs) can be measured. In order for this technique to be effective the unknown effect of the dynamics of the TPs on the CCs has to be elucidated to ensure that the TPs do not greatly alter the local stresses on the CCs. We show, using theory and simulations, that the self-generated (active) forces arising from proliferation and apoptosis of the CCs drive the dynamics of the TPs far from equilibrium. On time scales less than the division times of the CCs, the TPs exhibit sub-diffusive dynamics (the mean square displacement, $\Delta_{TP}(t) \sim t^{\beta_{TP}}$ with $\beta_{TP}<1$), similar to glass-forming systems. Surprisingly, in the long-time limit, the motion of the TPs is hyper-diffusive ($\Delta_{TP}(t) \sim t^{\alpha_{TP}}$ with $\alpha_{TP}>2$) due to persistent directed motion for long times. In comparison, proliferation of the CCs randomizes their motion leading to superdiffusive behavior with $\alpha_{CC}$ exceeding unity. Most importantly, $\alpha_{CC}$ is not significantly affected by the TPs. Our predictions could be tested using \textit{in vitro} imaging methods where the motion of the TPs and the CCs can be tracked.