Field theory of molecular cooperators

TL;DR

This paper develops a field theoretical model of molecular hypercycles, analyzing how surface diffusion and spatial correlations influence the emergence and survival of cooperative molecular systems in prebiotic evolution.

Contribution

It introduces a many-body Hamiltonian approach to model hypercycle dynamics, highlighting the critical dimension and the impact of surface diffusion on molecular cooperation.

Findings

Critical dimension for hypercycle dynamics is d_c=2.

Surface diffusion provides a selective advantage.

Spatial correlations affect hypercycle stability.

Abstract

It has been suggested that major transitions in evolution require the emergence of novelties, often associated to the cooperative behaviour of previously existing objects or agents. A key innovation involves the first cooperative interactions among molecules in a prebiotic biosphere. One of the simplest scenarios includes two molecular species capable of helping each other forming a catalytic loop or hypercycle. The second order kinetics of the hypercycle implies a hyperbolic growth dynamics, capable of overcoming some selection barriers associated to non-cooperative molecular systems. Moreover, it has been suggested that molecular replicators might have benefited from a limited diffusion associated to their attachment to surfaces: evolution and escape from extinction might have been tied to living on a surface. In this paper we propose a field theoretical model of the hypercycle involving reaction and diffusion through the use of a many-body Hamiltonian. This treatment allows a characterisation of the spatially correlated dynamics of the system, where the critical dimension is found to be $d_c=2$. We discuss the role of surface dynamics as a selective advantage for the system's survival.