# Nucleation of antagonistic organisms and cellular competitions on curved, inflating substrates

## TL;DR

This paper investigates how curvature, inflation, and cellular interactions influence the survival and nucleation of antagonistic organisms on curved, inflating substrates, revealing critical sizes and the impact of motility.

## Contribution

It introduces a model for the nucleation and survival of antagonistic organisms on curved, inflating surfaces, highlighting the effects of spatial diffusion, line tension, and curvature.

## Key findings

- Critical cluster size depends on selective advantage and interaction strength.
- Higher motility reduces survival probability when antagonistic interactions are present.
- Curvature and inflation increase the survival chances of mutant cells at the frontier.

## Abstract

We consider the dynamics of spatially-distributed, diffusing populations of organisms with antagonistic interactions. These interactions are found on many length scales, ranging from kilometer-scale animal range dynamics with selection against hybrids to micron-scale interactions between poison-secreting microbial populations. We find that the dynamical line tension at the interface between antagonistic organisms suppresses survival probabilities of small clonal clusters: the line tension introduces a critical cluster size that an organism with a selective advantage must achieve before deterministically spreading through the population. We calculate the survival probability as a function of selective advantage $\delta$ and antagonistic interaction strength $\sigma$. Unlike a simple Darwinian selective advantage, the survival probability depends strongly on the spatial diffusion constant $D_s$ of the strains when $\sigma>0$, with suppressed survival when both species are more motile. Finally, we study the survival probability of a single mutant cell at the frontier of a growing spherical cluster of cells, such as the surface of an avascular spherical tumor. Both the inflation and curvature of the frontier significantly enhance the survival probability by changing the critical size of the nucleating cell cluster.