Field theory of molecular cooperators

Jordi Piñero; Ricard Solé

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arXiv · 1508.01422

Field theory of molecular cooperators

Jordi Piñero·Ricard Solé

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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.

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Jordi Piñero, Ricard Solé. 2015-08-06. Field theory of molecular cooperators. https://arxiv.org/abs/1508.01422

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