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.
Highlights
In previous work we introduced and investigated a mathematical model of catalytic reaction systems and autocatalytic sets [1,2]
In [2], we showed through computer simulations that a linear growth rate in the level of catalysis appears to be sufficient for Reflexively autocatalytic and F-generated (RAF) sets to occur with high probability in the binary polymer model with ligation and cleavage reactions and random catalysis
Notice that P (n) can be chosen as close to 1 as we wish by selecting λ large enough. This result justifies the statement that the average number of reactions each molecule catalyzes needs to grow only linearly with n in order for there to be a given probability of generating an RAF. We describe how this result modifies if catalysis is required to be template-based, as described above
Summary
In previous work we introduced and investigated a mathematical model of catalytic reaction systems and autocatalytic sets [1,2]. We introduce a small modification to our mathematical definition of autocatalytic sets and the corresponding algorithm for finding them in general catalytic reaction systems (Section 3). We show that there is a discrepancy between the theoretical and simulation results (Section 4) Both results show that a linear growth rate in level of catalysis is sufficient for the emergence of autocatalytic sets. We show how more chemical realism can be included in our model, for example by considering template-based catalysis (Section 6) Even though this makes the model harder to analyze, it still generates interesting and useful results.
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