Effects of multi-phase control mechanism on fibroblast dynamics: A segmented mathematical modeling approach

TL;DR

The paper develops a phase-segmented, size-structured framework to study how phase-specific control mechanisms across the G1, S, G2, and M phases govern fibroblast population size and size distributions. By combining a PDE-based description with Beta-distributed division kernels and agent-based stochastic simulations, it reveals a fundamental trade-off between extrinsic population-density feedback and intrinsic size-dependent growth, showing that nonlinear growth regulation yields robust size homeostasis and bounded population growth. The baseline S adder–G2 timer configuration best reconciles data fit with long-term stability, while large-cell retention accelerates population recovery after depletion. These insights advance understanding of tissue repair dynamics and offer a mechanistic basis for how growth, division, and death co-regulate fibroblast homeostasis in health and disease.

Abstract

Cell size is a fundamental determinant of cellular physiology, influencing processes such as growth, division, and function. In this study, we develop a segmented mathematical framework to investigate how different control mechanisms operating across multiple phases of the cell cycle affect fibroblast population dynamics. Building on our previous work modeling sizer, timer, and adder strategies, we extend the analysis by introducing phase-specific control schemes in the S and G2 phases, incorporating nonlinear growth dynamics and cell death. Using agent-based stochastic simulations, we examine how these mechanisms shape steady-state size distributions and respond to parameter variations. Our results reveal that the steady-state cell size distribution is primarily governed by division kernels and phase-specific control strategies, and appears remarkably robust to cell death modalities. We identify a fundamental trade-off between extrinsic and intrinsic growth feedbacks: while population-density-dependent regulation tightly limits total cell numbers, cell-size-dependent regulation acts as a proportional homeostatic mechanism, suppressing relative size variability. Furthermore, we demonstrate that population recovery is accelerated by the retention of proliferation-competent large cells. This study provides biologically relevant insights into the complex interplay between growth, division, and homeostasis, with implications for understanding tissue repair and disease progression.

Figures (13)

• Figure 1: Fibroblasts in the skin. The skin consists of the epidermis, dermis, and subcutaneous tissue. Fibroblasts are primarily located in the extracellular matrix of the dermis, where they exhibit stellate or spindle-shaped morphologies with multiple cytoplasmic protrusions that interact with surrounding collagen, elastin, and neighboring cells (e.g., immune cells and vascular endothelial cells). The right panel shows a schematic of the fibroblast cell cycle.
• Figure 2: Control mechanisms across cell cycle phases. (a) Phase progression regulated by control conditions $\phi_i$, where $i = 1, 2, 3, 4$ correspond to the G1, S, G2, and M phases, respectively. A cell advances to the next phase only when the corresponding $\phi_i$ condition is satisfied. (b) Specific regulatory mechanisms for each phase.
• Figure 3: Calibration of control mechanisms against experimental fibroblast size distributions. Scatter points represent experimental data from Russel et al. russell1976cell. Red solid lines denote simulation results at equilibrium ($t = 400$) using parameters from Table \ref{['table1']}. For clarity, the specific control strategies adopted for the S and G2 phases, along with the corresponding coefficient of determination ($R^2$), are explicitly labeled in each subplot.
• Figure 4: Steady-state size distributions under different combinations of S- and G2-phase control mechanisms with linear growth rates. Control strategies along with threshold parameters are shown in each subplot. The cells grow at rate $v_i(s, a) = c s$ with $c = 0.05$ or $0.1$. Unless otherwise specified, other parameters are consistent with row (h) in Table \ref{['table1']}.
• Figure 5: Steady-state size distributions under nonlinear growth rate (PD-GR). (a) Steady-state distribution with growth constants $c$ ranging from $0.05$ to $0.2$. (b) Phase-specific distributions.