Competition and niche construction in a model of cancer metastasis

Abstract

Niche construction theory states that not only does the environment act on populations to generate Darwinian selection, but organisms reciprocally modify the environment and the sources of natural selection. Cancer cells participate in niche construction as they alter their microenvironments and create pre-metastatic niches; in fact, metastasis is a product of niche construction. Here, we present a mathematical model of niche construction and metastasis. Our model contains producers, which pay a cost to contribute to niche construction that benefits all tumor cells, and cheaters, which reap the benefits without paying the cost. We derive expressions for the conditions necessary for metastasis, showing that the establishment of a mutant lineage that promotes metastasis depends on niche construction specificity and strength of interclonal competition. We identify a tension between the arrival and invasion of metastasis-promoting mutants, where tumors composed only of cheaters remain small but are susceptible to invasion whereas larger tumors containing producers may be unable to facilitate metastasis depending on the level of niche construction specificity. Our results indicate that even if metastatic subclones arise through mutation, metastasis may be hindered by interclonal competition, providing a potential explanation for recent surprising findings that most metastases are derived from early mutants in primary tumors.

Fig 1. Schematic representation of the model.

The model considers a primary tumor with four cell types and a distant pre-metastatic niche. Cheaters are white, local producers are blue, secondary producers are red, and global producers are both red and blue. Niche construction occurs in the primary microenvironment through production of resource R, which benefits the tumor by increasing carrying capacity, represented as a dotted line. Construction of the pre-metastatic niche by primary tumor cells is represented by the red arrow.

Fig 2. Schematic representation of the different competition structures.

The strength of competition between each cell type is shown along connections in the lattice. Intraclonal competition is 1 for all cell types. ϕ, θ, and ψ are positive and less than 1. ν, μ, and ω are positive and less than or equal to 1. In competition structure III, the two distinct niches are represented by boxes. Cells that cheat in the primary tumor experience competition of magnitude θ due to, and compete with magnitude ϕ with, cells that produce the primary resource.

Fig 3. Simulation of tumors starting with cheaters.

Parameters used are r₀₀ = 0.07, r₁₀ = 0.05, r₀₁ = 0.045, r₁₁ = 0.02, k = 10⁵, β₀ = 1, β₁ = 1.2, θ = ϕ = 0.9, g = 0.004, l = 0.001, α = 10⁻⁶, some of which are estimated in S3 Appendix. Mutation rates are mentioned in the text. If successful invasion of producers occurs, cheaters become extinct rather than arrive at coexistence for these parameters. A: Simulation of a single tumor starting with cheaters only and a small amount of resource. Black tick marks represent mutations leading to arrival of secondary or global producers, though none of them lead to successful invasion. B: Simulation of 200 tumors starting with cheaters only. Each red triangle indicates a successful invasion of a cheater-only tumor by secondary or global producers. Each blue curve represents a tumor that has been invaded by local producers; none of these producer-only tumors experienced successful invasion by secondary or global producers despite the arrival of numerous mutants, plotted on the y-axis.

Fig 4. Schematic of possible tumor trajectories with their corresponding conditions.

The thicker the arrow, the easier the ecological conditions are met. Arrow colors correspond to the mutation rate according to the mutation gradient on the right. Crossed out arrows indicate resistance to invasion. Tumor size and population mutation rate increase going down the flowchart, as indicated by the graph on the right.