Active Growth Layer Induced by Micromechanical Feedback Shapes Proliferating Cell Collectives

Abstract

Proliferating cell collectives often develop an active growth layer near their boundary that regulates expansion and morphology, as observed in systems ranging from bacterial biofilms to epithelial tissues and tumor spheroids. While such layers have been attributed to diverse mechanisms, their microscopic origin remains unclear in many situations. Here, we show that micromechanical feedback alone provides a minimal mechanism for their emergence. We introduce a particle-based model of non-motile proliferating cells in which growth is locally inhibited by compressive stress, coupling division to mechanical interactions and generating an active growth layer without biochemical regulation. An emergent mechanical length scale sets the extent of the proliferative region and controls the system's behavior across scales, governing growth dynamics, morphology and organizing internal stress and velocity fields. Coarse-graining the model yields a continuum description with no adjustable parameters, providing a microscopic foundation for existing approaches. When the colony expands into a passive environment, we observe and characterize fingering instabilities driven purely by mechanical feedback. We further establish a correspondence with nutrient-depletion models, providing a route to study the statistical properties of expanding fronts within a minimal microscopic framework.

Figures (4)

• Figure 1: Results from discrete simulations of proliferating colonies with different $\Theta_1$ and $\Theta_2$ in the free-boundary configuration. (a) Morphological phase diagram with a particle-size color map. (b,c) Rescaled growth $R(t)/\chi$ and front velocity $\dot{R}(t)/u_0$ curves (dashed line in (b): $\sim e^{t/t^*}$; dashed line in (c): $\dot{R}/u_0=1$; insets: raw curves). (d) Radial distribution of cell sizes; shaded region indicates an interval of size $1-1/\sqrt{2}$. Radial profiles of overlap (e,f) and velocity (h,i): (e,h) temporal evolution for $\Theta_1=10^{-4}$, $\Theta_2=10$; (f,i) comparison of different parameter sets at $t=5t^*$. (g,j) Collapse of radial profiles onto continuum theory predictions (black lines) at $R=\chi$ and $R=8\chi$.
• Figure 2: Morphology of interfacial instabilities in a freely expanding colony as a function of $\chi$ and $\beta$, shown for $\Theta_2=\{0.1,10\}$.
• Figure 3: Growth dynamics in a confined channel geometry. (a) Snapshot of the expanding colony in the channel-constrained configuration. (b,c) Collapse of longitudinal profiles onto continuum theory predictions (black lines) at $L=\chi$ and $L=8\chi$. (d,e) Rescaled growth $L(\tau)/\chi$ and front velocity $\dot{L}(\tau)/u_0$ curves compared to continuum theory predictions (black lines). Inset shows zoom in the exponential-linear growth transition
• Figure 4: (a) Dispersion relation \ref{['eq:DispersionRelation']} for $\beta=\{0.02,0.1,0.75\}$ with $\chi=10a$ and $w=250a$. Shaded regions indicate the wavelengths accessible in the discrete model $\lambda' \in (\lambda'_{\min},\lambda'_{\max})$; stars mark the most unstable accessible modes. (b) Snapshots of colony fronts under the same conditions; superimposed sinusoidal profiles highlighting the dominant unstable wavelengths.(c) Normalized population size $N(t)$ (top) and growth rate $\dot{N}(t)$ (bottom) for stable ($w=4\chi$) and unstable ($w=40\chi$) configurations at $\beta=0.3$. (d) Time evolution of the colony front for both cases, corresponding to the shaded intervals in (c).