Cell Competition Driven by Secreted Ligands: Modeling Liver Metastasis of Colorectal Cancer

TL;DR

This work addresses how liver progenitor cells and colorectal cancer cells competitively interact during liver metastasis via secreted signaling ligands. It introduces a minimal mean-field framework that couples autocrine/paracrine growth-factor signaling to cell-cycle dynamics, with $v_{G1}$ proportional to ligand uptake and a constant $v_S$ for S/G2/M, plus differentiation of wild-type cells. Fitting the model to experimental data yields $\tilde{S}=19.6$ and $\tilde{v}_S=10.8$, reproducing exponential growth in pure populations and asymmetric growth in mixed organoids driven by a higher cancer uptake $\tilde{\mu}_C$ relative to $\tilde{\mu}_W$, and by G1 sensitivity to the growth factor. The results reveal three essential ingredients for competition: autocrine secretion, differential ligand uptake, and growth-stage–dependent responsiveness, offering a general framework for growth-stage–dependent competition in biological populations.

Abstract

Cell competition in multicellular organisms has been shown to play a critical role during the development of organisms, cancer progression, and in the establishment and maintenance of tissue homeostasis. Various mechanisms of cell competition have been identified, including active elimination via mechanical forces or induced apoptosis, as well as competition for nutrients and other beneficial factors. A recent experiment demonstrated hallmarks of cell competition, associated with cell cycle dynamics, between liver progenitor cells and colorectal cancer cells [Krotenberg Garcia et al., iScience 27, 109718 (2024)]. However, a mechanistic explanation for this form of competition remains lacking. Here, we present a mean-field model of competition for signaling ligands, coupled with cell cycle dynamics, to provide such an understanding. Our model captures the salient features of the experiment, including population dynamics and cell cycle variations. We demonstrate that secretion of a beneficial factor by cells, coupled with the enhanced uptake efficiency of cancer cells, suffices to reproduce the experimental outcome. Our model, reminiscent of competition for secreted growth factors, provides insight into the minimal level of complexity required to achieve the observed competitive outcome as well as its link to cell cycle dynamics. It can also serve as a general framework for studying biological populations with growth-stage-dependent competition over consumer-produced products.

Figures (8)

• Figure 1: Competition in terms of population growth. (a) Normalized population of wild-type and cancer cells are plotted. The curves are from the model, while the data points are the experimental data. (b) Progression speed in G1 phase, $\tilde{v}_{\mathrm{G1}}$, as a function of growth factor concentration, $\tilde{\alpha}$, for wild-type and cancer cells. The solid circular markers show the equilibrium points in the pure conditions. The open square markers show the initial values of $\tilde{v}_{\mathrm{G1}}$ for wild-type and cancer cells in an example mixed organoid with a 50 : 50 composition. The gray and blue dashed lines serve to guide the eye.
• Figure 2: Graphical summary of the modeling approach. (a) Schematic representation of the cell cycle used in our mean-field modeling. The G1 phase is shown in purple, and the rest of the cell cycle in yellow. The gray box indicates the wild-type cells that have exited their cycle to start the differentiation process. Differentiation can happen from any point in G1, as indicated using the blue arrow. The axis indicates how the cell phase $\phi$ changes as a cell progresses through G1 with speed $v_{\text{G1}}$; and through S, G2, and M phases with speed $v_{\text{S}}$. Each time a cell exits the M phase ($\phi = 2\pi$), it is doubled and both daughters reenter the G1 phase with $\phi = 0$. (b) Visualization of the assumptions underlying the secretion and the uptake rates in the mean-field model. The wild-type (magenta) and cancer cells (green) are shown as well as their secretion rates indicated by $S_\mathrm{W}$ and $S_\mathrm{C}$, respectively. The uptake rates are proportional to the total amount of growth factor per capita with proportionality factors $\mu_\mathrm{W}$ and $\mu_\mathrm{C}$ for wild-type and cancer cells where $\mu_\mathrm{C}$ is assumed to be greater than $\mu_\mathrm{W}$, as indicated using the width of the arrow.
• Figure 3: Normalized population growth of each cell type at $t=60$ h vs. their initial fraction in the mixture. The data are shown for (a) wild-type cells and (b) cancer cells. The stars show the data from the experiment, while the dots from the model. The number of organoids for the experimental data is $n=45$ and for the model, $n=500$.
• Figure 4: Comparison of experimental data and model predictions for the proportions of wild-type cells in (a) G1 phase, (b) S/G2/M phases, and (c) G0 phase of the cell cycle. The data are provided for pure and mixed organoids at $t=60\;\mathrm{h}$. The experimental data are taken from Ref. Ana2024. For the cells in S/G2/M phases, the two different experimental measurement methods are shown. Uncertainties for experimental data indicate SEM. For the model, a basic 1% uncertainty due to rounding was considered. The statistical SEM was smaller. The dashed lines connect the data of the model to guide the eye.
• Figure 5: Influence of uptake coefficient ratio on competition. (a) Normalized populations under pure conditions for both cell types at different values of $r_\mu = \tilde{\mu}_\mathrm{C} / \tilde{\mu}_\mathrm{W}$. (b, c) Ratios of normalized populations in mixed and pure conditions for (b) cancer and (c) wild-type cells as a function of time. (d) Fraction of differentiated wild-type cells (G0 phase) as a function of time for different values of $r_\mu$. Colors in all panels correspond to the color bar in panel a. The arrows show the direction along which $r_\mu$ increases. The legend applies to all panels.