Solvable model for template coexistence in protocells

TL;DR

This paper presents an analytical model explaining how coexistence of different templates within protocells can be maintained through group selection, highlighting a phase transition between coexistence and segregation.

Contribution

It introduces a solvable analytical model combining competition and genetic drift, revealing a continuous phase transition in protocell template coexistence.

Findings

Identifies a phase transition between coexistence and segregation regimes.

Provides explicit formulas for the critical steady-state protocell composition density.

Shows the order parameter vanishes linearly near the critical point.

Abstract

Compartmentalization of self-replicating molecules (templates) in protocells is a necessary step towards the evolution of modern cells. However, coexistence between distinct template types inside a protocell can be achieved only if there is a selective pressure favoring protocells with a mixed template composition. Here we study analytically a group selection model for the coexistence between two template types using the diffusion approximation of population genetics. The model combines competition at the template and protocell levels as well as genetic drift inside protocells. At the steady state, we find a continuous phase transition separating the coexistence and segregation regimes, with the order parameter vanishing linearly with the distance to the critical point. In addition, we derive explicit analytical expressions for the critical steady-state probability density of protocell compositions.