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

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 selfgenerated (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, ∆T P (t) ∼ t β T P with βT P < 1), similar to glass-forming systems. Surprisingly, in the long-time limit, the motion of the TPs is hyper-diffusive (∆T P (t) ∼ t α T P with αT P > 2) due to persistent directed motion for long times. In comparison, proliferation of the CCs randomizes their motion leading to superdiffusive behavior with αCC exceeding unity. Most importantly, αCC is not significantly affected by the TPs. Our predictions could be tested using in vitro imaging methods where the motion of the TPs and the CCs can be tracked. PACS numbers:The interplay of systematic short-range forces and nonequilibrium processes arising from cell division and apoptosis give rise to unexpected dynamics in the collective migration of cancer cells [1][2][3][4][5][6][7]. An example of relevance here is the invasion of cancer cells (CCs) in a growing multicellular spheroid (MCS), which is relevant in cancer metastasis [6,7]. Imaging experiments show that the cell dynamics, characterized by a group of cells that remain in contact for a long period, is complex manifesting far from equilibrium characteristics [7][8][9][10][11]. Simulations and theory of minimal models have been used to describe some of the unexpected features observed in the experiments [12][13][14][15]. These studies have also established that the dynamics of a growing tumor embedded in an extracellular matrix are spatially highly heterogeneous. The cells in the interior of the solid tumor spheroid undergo sluggish glass-like dynamics whereas those far from the center of the tumor undergo directed faster than diffusive motion [15]. It should be pointed out that explicit introduction of stochastic active forces could also give rise to unusual dynamics in abiotic systems [16][17][18].The dynamics of CCs in a growing tumor is determined by the effects of the CC microenvironment on the long time collective migration. The advent of new experimental techniques that probe the local stresses or pressure on the CCs [19][20][21][22][23][24] have provided insights into the mechanism by which the CCs invade the extracellular matrix. In a recent article, Dolega et. al.[24] developed a method to measure the mechanical stress within MCSs by embedding micron-sized inert deformable polyacrylamide beads (elastic and compressible hydrogel micro-beads) as local stress sensors. The local pressure profiles in the MCS were extracted from the volume c...

Statistical Mechanical theory for spatio-temporal evolution of Intra-tumor heterogeneity in cancers: Analysis of Multiregion sequencing data

“…Recent advancements in imaging modalities have helped unearth heterogeneous physical characteristics at the single cell resolution in three-dimensional cell collectives [66][67][68]. Our previous studies have shown that cell-division and apoptosis induced self-generated forces give rise to phenotypic diversity within a tumor [69][70][71][72][73][74][75]. In principle, the current theoretical framework, could be extended to estimate the ITH for both genetic and phenotypic heterogeneity of evolving tumors.…”

Statistical Mechanical theory for spatio-temporal evolution of Intra-tumor heterogeneity in cancers: Analysis of Multiregion sequencing data

“…Recent advancements in imaging modalities have helped unearth heterogeneous physical characteristics at the single cell resolution in three-dimensional cell collectives [66][67][68]. Our previous studies have shown that cell-division and apoptosis induced self-generated forces give rise to phenotypic diversity within a tumor [69][70][71][72][73][74][75]. In principle, the current theoretical framework, could be extended to estimate the ITH for both genetic and phenotypic heterogeneity of evolving tumors.…”

Inter-particle adhesion regulates the surface roughness of growing dense three-dimensional active particle aggregates

“…We briefly describe the simulation scheme adapted from our previous work on 3D tumor growth. [19][20][21][22][23] In the present study, we performed an off-lattice simulation of a growing 3D dense active particle aggregate. 25,26 In the growing aggregate (see Appendix, Movies 1-3), individual particles are modeled as soft deformable spherical agents.…”

“…18 described the out-of-equilibrium surface fluctuations of cell collectives in the homeostatic state when cell birth and death are balanced. Building on our prior work [19][20][21][22][23] where we modeled biological cells with pairwise elastic and adhesive interaction in addition to rules for size growth, division and death of particles, we study the surface roughness of a dense and fast expanding three dimensional (3D) collection of active particles. We focus on investigating 3D aggregate expansion at varying inter-particle adhesion strengths, known to critically tune collective properties in active matter systems.…”