Dimensionality and confinement reshape competition in cellular renewing active matter

TL;DR

This study asks how dimensionality and spatial confinement shape clonal competition in renewing active matter composed of proliferating and apoptotic cells. Using a 2D agent-based dumbbell-cell model where competing clones differ solely in the dead-cell degradation parameter $E$, the authors compare 1D and 2D dynamics under periodic boundaries and then impose a circular confinement to probe boundary effects, analyzing outcomes via active-density and homeostatic-pressure metrics and a partial-information decomposition (PID). They find that 1D systems are dominated by opportunistic competition tied to $ riangle ho^h$, while 2D systems exhibit a mixed influence of $ riangle ho^h$ and $ riangle P^h$ that can shift over time; confinement introduces spatial heterogeneity, with wall regions showing quasi-1D dynamics where opportunistic effects can dominate early, before pressure effects reemerge due to slow radial mixing. Overall, the work links dimensionality and geometry to tissue-like competitive outcomes and provides a framework (PID) to quantify when each mechanism controls clonal success, with implications for understanding tumor growth, tissue development, and renewal dynamics in heterogeneous cellular populations.

Abstract

Cellular renewing active matter - assemblies of proliferating and apoptotic cells - underlies tissue homeostasis, morphogenesis, and clonal competition. Previous work in one-dimensional periodic systems identified a fitness advantage associated with rapid dead-cell clearance, an "opportunistic" competition mechanism. Extending this framework, we study two-dimensional cellular aggregates and show that dimensionality modifies the interplay between competition mechanisms for clones with different clearance rates: in 2D, opportunistic and homeostatic-pressure-based competition jointly shape clonal selection, to varying degrees. We then introduce an explicit circular confinement to probe how boundaries modulate this interplay. While opportunistic competition persists, distinct timescale-dependent behaviors emerge through weakened homeostatic-pressure-based competition near boundaries. Structural analysis reveals that confinement promotes tangential alignment and spatially heterogeneous homeostatic pressure, thereby reshaping competitive outcomes at tissue edges. Our study connects newly discovered competition mechanisms with more realistic biological contexts, highlighting how dimensionality and spatial constraints influence tissue structures and modulate competition in heterogeneous cell populations, with implications for tumor growth dynamics and tissue development.

Figures (6)

• Figure 1: 2D Agent-based model. (a) Stages in the lifecycle of a dumbbell-shaped cell. Starting from a living cell (green), which can grow and divide for multiple cycles, until the cell dies eventually, stopping all growth. Dead cells degrade until they are removed. Duration of active and passive phase are not to scale. (b) Cell nodes repel each other on contact through Hertzian forces $F$. Forces increase with overlap distance $d$. (c) Cell growth can be inhibited when the population is crowded locally, which is implemented by the monotonically decreasing function $G(F^\text{int})$. A cell's probability to die is unaffected by its environment. Cross-section (green) marks a theoretical homeostasis point, at which growth and death balance for a stable homeostasis. (d) The scaling factor $S$ linearly affects interaction forces of dead cells with their neighbors during their degradation. The degradation factor $E$ modulates the force scaling. At high negative $E$ (red), dead cells stay structually intact during degradation, while cells with high positive $E$ (purple) lose their repellent force quickly. For small $|E|$ (green), the degradation is gradual. Low scaling factors allow for higher overlap to neighboring cells. Alive cells have $S=1$.
• Figure 2: Cellular competition in two dimensions (2D) (a) Simulation snapshots in systems with two clones, one with fast dead matter elimination (cyan, $E=20$) and the other with slower and gradual degradation (magenta, $E=0$). Initially well mixed ($t=0\,$gen.) populations in periodic boundary conditions (“PBC”, left) and circular confinement (“CC”, right). The dynamics favor a specific clone over time, having a visibly larger population at the end of the simulation ($t\approx72\,$gen.). (b) Time series of global population numbers $N$ in total (black) and of either clone (magenta/cyan). The type of environment is indicated by solid or dashed line for confined population or in periodic system, respectively.
• Figure 3: Quantification of competition outcomes. (a) Competition matrix summarizes results for global fitness $N_\text{H}/N^\text{t}$ at the end of the simulation for 1D periodic (PBC) systems. Each data point corresponds to a specific mixture of H and L clones. Global fitness is color-coded, where blue/red means that the H clone increases/decreases in population size. (b) The same visualization for the 2D PBC system. (c) Prediction of homeostatic active density $\rho^h$ according to \ref{['eq:activedensity']} (green line) and measurements in homeostasis for a set of degradation factors $E$. (d) Homeostatic pressure $P^\text{h}$ in the same two systems. (e) Correlation between global fitness and difference in homeostatic active density $\Delta\rho^\text{h}$ (normalized) of competing clones. (f) Correlation of global fitness to normalized difference in homeostatic pressure $\Delta P^\text{h}$.
• Figure 4: Spatially resolved competition dynamics and fitness; illustrative pairings (a) Time series of population fraction of clone $E=2$ in competition against a clone with $E=-20$, measured in the center of the population (bulk, orange) and near the confining border (wall, cyan). Global behavior in 2D PBC as a reference (black). (b) Same measurements for clone $E=20$ in competition against $E=5$. (c) Spatial measurement of fitness of clone $E=2$ in competition scenarios against all other clones (see color bar for adversary clone color). Neutral competition case indicated by a dashed line (examples discussed in text: red: $E=2$ vs $E=-20$, ink blue + dashed black: $E=2$ vs $E=2$). (d) Same measurements for the clone $E=20$ (with the ink-blue curve corresponding to the same competition scenario as the purple curve in panel c, only viewed from the winner's side).
• Figure 5: Spatial homeostasis measurements in annuli of equal area. (a) Snapshot of homeostasis simulation with $E=-20$, highlighting polar cell orientation (radial: red, tangential: blue). Cells form highly ordered layers near the confining wall. (b) A nematic order parameter captures local structures of the cell populations, showing tangential alignment at the wall, which propagates into the bulk. (c) Spatial measurement of active density $\rho^\text{h}$ captures the global monotonic increase across the range of degradation factors $E$, but no significant dependence along the spatial coordinate can be observed. (d) The homeostatic pressure shows a non-monotonic behavior approaching the confining wall while also reducing relative differences between populations (see Supp. Note 3). Below is a zoom in to the previous panel at the region close to the wall.