Biomathematical enzyme kinetics model of prebiotic autocatalytic RNA networks: degenerating parasite-specific hyperparasite catalysts confer parasite resistance and herald the birth of molecular immunity
Authors: Pirovino Magnus , Iseli Christian , Curran Joseph A. , Conrad Bernard 
Published: May 2024

Catalysis and specifically autocatalysis are the quintessential building blocks of life. Yet, although autocatalytic networks are necessary, they are not sufficient for the emergence of life-like properties, such as self-propagation (replication) and adaptation. The ultimate and potentially fatal threat faced by molecular replicators is parasitism; if the polymerase error rate exceeds a critical threshold, even the fittest molecular species will disappear. Here we have developed an autocatalytic RNA early life mathematical network model based purely on enzyme kinetics, more specifically the steady-state approximation. We confirm previous models showing that these autocatalytic cycles are sustainable, provided there is a sufficient nucleotide pool. However, molecular parasites arise rapidly and become unsustainable unless they sequentially degenerate to hyperparasites (i.e. parasites of parasites). These hyperparasites acquire parasite binding specificity via two distinct temporal pathways. Our model is supported at three levels; firstly, ribozyme polymerases display Michaelis-Menten saturation kinetics and comply with the steady-state approximation. Secondly, ribozyme polymerases are capable of sustainable auto-amplification and of surmounting the fatal error threshold. Thirdly, with growing sequence divergence of host and parasite catalysts, the probability of self-binding increases and the trend towards cross-reactivity diminishes. Our model predicts that primordial host-RNA populations evolved via an arms race towards a host-parasite-hyperparasite catalyst trio that conferred parasite resistance within an RNA replicator niche. As such, it adds another mechanism – what’s more, with biochemical precision – by which parasitism can be tamed and offers an attractive explanation for the universal coexistence of catalyst trios within prokaryotes and the virosphere, heralding the birth of a primitive molecular immunity.Author SummaryThe quintessential components of life comprise a potent mixture of naturally occurring, but improbable chemical reactions (catalysis), and the arrangement of such accelerated chemical reactions into closed loops (autocatalytic sets). This is required, but is not sufficient for such networks to self-propagate (amplification of the information carrier = host polymerization) and adapt (Darwinian evolution). As soon as self-propagation is attained, the next hurdle is parasitism. This typically involves shorter molecules (the products of replicative errors) that hitchhike the replicative potential of the host. They will invariably outcompete the regular amplification process, unless a solution is found. We have addressed this problem using a new model based on the mathematics of catalysis. This model confirms previous studies demonstrating that autocatalytic sets become self-sustaining, assuming that a sufficient pool of molecular building blocks is available. However, molecular parasitism is pervasive and potentially fatal for both host and parasite. In our model, we allow these parasites to degenerate in a controlled fashion, giving rise to parasites of parasites (hyperparasites). As long as these hyperparasites acquire binding specificity for parasites, an attenuation of parasitism is observed. These parasite-hyperparasite cycles stabilize the host cycle, explaining why they are conserved, and why they are the likely reason behind the observation that all cellular hosts are associated with parasites (e.g. bacteria) and hyperparasites (e.g. viruses) across all kingdoms of life. Moreover, it provides a novel solution to the usually intractable problem of parasitism.