Required levels of catalysis for emergence of autocatalytic sets in models of chemical reaction systems

Abstract

The formation of a self-sustaining autocatalytic chemical network is a necessary but not sufficient condition for the origin of life. The question of whether such a network could form "by chance" within a sufficiently complex suite of molecules and reactions is one that we have investigated for a simple chemical reaction model based on polymer ligation and cleavage. In this paper, we extend this work in several further directions. In particular, we investigate in more detail the levels of catalysis required for a self-sustaining autocatalytic network to form. We study the size of chemical networks within which we might expect to find such an autocatalytic subset, and we extend the theoretical and computational analyses to models in which catalysis requires template matching.

Keywords: autocatalytic sets; chemical reaction networks; origin of life; template-based catalysis.

Figure 1.

A simple example of a catalytic reaction system (CRS) with seven molecule types {a, b, c, d, e, f, g} (solid nodes) and four reactions {r₁, r₂, r₃, r₄} (open nodes). The food set is F = {a, b}. Solid arrows indicate reactants going into and products coming out of a reaction, dashed arrows indicate catalysis. The subset ℛ = {r₁, r₂} (shown with bold arrows) is RAF.

Figure 2.

The linear relations for the three cases.

Figure 3.

The probability P_n of finding RAF sets for different (fixed) catalysis probabilities p and values of n.

Figure 4.

The level of catalysis f (n) required for the template-based catalysis case compared to the original (purely random) case, for different values of n.