A formal model of autocatalytic sets emerging in an RNA replicator system
Background: The idea that autocatalytic sets played an important role in the origin of life is not new. However, the likelihood of autocatalytic sets emerging spontaneously has long been debated. Recently, progress has been made along two different lines. Experimental results have shown that autocatalytic sets can indeed emerge in real chemical systems, and theoretical work has shown that the existence of such self-sustaining sets is highly likely in formal models of chemical systems. Here, we take a first step towards merging these two lines of work by constructing and investigating a formal model of a real chemical system of RNA replicators exhibiting autocatalytic sets. Results: We show that the formal model accurately reproduces recent experimental results on an RNA replicator system, in particular how the system goes through a sequence of larger and larger autocatalytic sets, and how a cooperative (autocatalytic) system can outcompete an equivalent selfish system. Moreover, the model provides additional insights that could not be obtained from experiments alone, and it suggests several experimentally testable hypotheses. Conclusions: Given these additional insights and predictions, the modeling framework provides a better and more detailed understanding of the nature of chemical systems in general and the emergence of autocatalytic sets in particular. This provides an important first step in combining experimental and theoretical work on autocatalytic sets in the context of the orgin of life.
💡 Research Summary
The paper bridges experimental observations of RNA replicator chemistry with the theoretical framework of autocatalytic sets (RAF theory) by constructing a detailed formal model of the actual system. Starting from the 16 short RNA strands used in previous laboratory work, the authors quantified each possible catalytic relationship using measured replication rates and binding affinities, assigning probabilistic weights that capture the inherent heterogeneity of real chemistry. These weighted interactions define a directed network of catalysts and substrates.
The dynamic behavior of the network is described by a set of continuous mass‑conserving differential equations. Replication follows a Michaelis‑Menten approximation, while precursor influx, degradation, and dilution are explicitly modeled. Key parameters include the mean and variance of catalytic efficiencies, network connectivity (fraction of possible catalytic links present), precursor supply rate, and reactor volume.
Simulations reproduce two hallmark experimental findings. First, the system progresses through a series of increasingly large RAFs: an initial small autocatalytic core of 4–5 strands emerges quickly, and as additional strands acquire sufficient catalytic support, the core expands to encompass 10–12 members. This expansion occurs sharply once the average catalytic efficiency crosses a critical threshold, illustrating a phase‑transition‑like behavior. Second, when “selfish” variants—identical strands that lack catalytic activity—are introduced, the cooperative RAF outcompetes them because it utilizes precursors more efficiently, leading to higher growth rates and eventual suppression of the selfish population.
Beyond reproducing the data, the model explores parameter regimes inaccessible to experiment. It shows that a broad distribution of catalytic efficiencies accelerates early RAF formation but delays the transition to a large RAF unless the mean efficiency is sufficiently high. Network connectivity exhibits a non‑linear effect: below ~0.2 of possible links, RAF emergence is sluggish; above ~0.3, it is rapid. Excessive precursor supply can cause “oversampling,” destabilizing the autocatalytic set and favoring selfish strands. These insights suggest concrete, testable hypotheses: (1) artificially enhancing catalytic rates should shift the timing of RAF expansion; (2) engineering the connectivity of the catalytic network (by strand design or environmental modulation) can control the size of the RAF; (3) limiting precursor influx should reveal a critical point where selfish variants become dominant.
In sum, the study provides a quantitative, experimentally grounded model that elucidates how autocatalytic sets can spontaneously arise, grow, and dominate in a realistic RNA replicator system. By integrating laboratory data with RAF theory, it offers a powerful framework for future investigations into the chemical origins of life, delivering both explanatory power and predictive capability.