Cell Growth Rate Dictates the Onset of Glass to Fluidlike Transition and Long Time Superdiffusion in an Evolving Cell Colony

Abstract

Collective migration dominates many phenomena, from cell movement in living systems to abiotic selfpropelling particles. Focusing on the early stages of tumor evolution, we enunciate the principles involved in cell dynamics and highlight their implications in understanding similar behavior in seemingly unrelated soft glassy materials and possibly chemokine-induced migration of CD8 þ T cells. We performed simulations of tumor invasion using a minimal three-dimensional model, accounting for cell elasticity and adhesive cell-cell interactions, as well as cell birth and death, to establish that cell-growth-ratedependent tumor expansion results in the emergence of distinct topological niches. Cells at the periphery move with higher velocity perpendicular to the tumor boundary, while the motion of interior cells is slower and isotropic. The mean-square displacement ΔðtÞ of cells exhibits glassy behavior at times comparable to the cell cycle time, while exhibiting superdiffusive behavior, ΔðtÞ ≈ t α (α > 1), at longer times. We derive the value of α ≈ 1.33 using a field theoretic approach based on stochastic quantization. In the process, we establish the universality of superdiffusion in a class of seemingly unrelated nonequilibrium systems. Superdiffusion at long times arises only if there is an imbalance between cell birth and death rates. Our findings for the collective migration, which also suggest that tumor evolution occurs in a polarized manner, are in quantitative agreement with in vitro experiments. Although set in the context of tumor invasion, the findings should also hold in describing the collective motion in growing cells and in active systems, where creation and annihilation of particles play a role.

Spatially heterogeneous dynamics of cells in a growing tumor spheroid: Comparison between Theory and Experiments

“…We have used simulations of a minimal model [23] to analyze the experimental results [15], The sluggish cell dynamics in the core is reminiscent of relaxation in supercooled liquids as they undergo a transition to a glassy state [31]. Using concepts from glass transition theory, we showed that higher order susceptibility for cells near the tumor periphery in experiments, which are fully accounted for in the simulations, shows a peak at t ≈ 5.6…”

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

“…Simulations: In order to test the theoretical predictions, we simulated a three dimensional MCS with embedded, mobile TPs. As in our previous studies, [12,14,15], we used an agent-based model to simulate To study the dynamics of TPs, we account for the CC-CC, CC-TP and TP-TP interactions. We model the interactions using two potentials (Gaussian and Hertz scheme) to ensure that the qualitative results are independent of the nature of the potential (See the details in the SI).…”

“…We model the interactions using two potentials (Gaussian and Hertz scheme) to ensure that the qualitative results are independent of the nature of the potential (See the details in the SI). The equation of motion governing the dynamics of TP and CCs is taken to be,˙ r i = Fi γi , where˙ r i is the velocity of i th CC or TP, F i is the force on i th CC/TP, and γ i represents the damping term (for details see reference [12]). The simulations are performed in the over-damped limit (see [12] and the SI for details).…”

“…We used a pressure inhibition mechanism (see the details in SI) to model the observed growth dynamics [12] of the MCS. The CCs can be either dormant or in the growth phase depending on the local microenvironment, which in our model is taken to be the pressure on the i th cell.…”

“…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.…”