Solvable model for template coexistence in protocells

¹ Instituto de Física de São Carlos, Universidade de São Paulo - Caixa Postal 369, 13560-970 São Carlos, SP, Brazil
² Departamento de Biofísica e Farmacologia, Universidade Federal do Rio Grande do Norte 59072-970 Natal, RN, Brazil

Received: 11 October 2012
Accepted: 24 January 2013

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.