The origin of large molecules in primordial autocatalytic reaction networks

Large molecules such as proteins and nucleic acids are crucial for life, yet their primordial origin remains a major puzzle. The production of large molecules, as we know it today, requires good catalysts, and the only good catalysts we know that can accomplish this task consist of large molecules. Thus the origin of large molecules is a chicken and egg problem in chemistry. Here we present a mechanism, based on autocatalytic sets (ACSs), that is a possible solution to this problem. We discuss a mathematical model describing the population dynamics of molecules in a stylized but prebiotically plausible chemistry. Large molecules can be produced in this chemistry by the coalescing of smaller ones, with the smallest molecules, the food set', being buffered. Some of the reactions can be catalyzed by molecules within the chemistry with varying catalytic strengths. Normally the concentrations of large molecules in such a scenario are very small, diminishing exponentially with their size. ACSs, if present in the catalytic network, can focus the resources of the system into a sparse set of molecules. ACSs can produce a bistability in the population dynamics and, in particular, steady states wherein the ACS molecules dominate the population. However to reach these steady states from initial conditions that contain only the food set typically requires very large catalytic strengths, growing exponentially with the size of the catalyst molecule. We present a solution to this problem by studying nested ACSs’, a structure in which a small ACS is connected to a larger one and reinforces it. We show that when the network contains a cascade of nested ACSs with the catalytic strengths of molecules increasing gradually with their size (e.g., as a power law), a sparse subset of molecules including some very large molecules can come to dominate the system.

💡 Research Summary

The paper tackles the long‑standing “chicken‑and‑egg” problem of how large biopolymers such as proteins and nucleic acids could have arisen in a pre‑biotic world where good catalysts are themselves large molecules. The authors construct a stylized but chemically plausible model in which a small set of monomers (the “food set”) is buffered at constant concentration, and all possible ligation (A_i + A_j ⇌ A_{i+j}) and reverse cleavage reactions are allowed. Each reaction proceeds with a spontaneous forward rate k_f and reverse rate k_r, and molecules can be lost from the system at a rate φ. Catalysis is introduced by allowing any molecule A_m to enhance both forward and reverse rates of a reaction pair proportionally to its concentration, with a catalytic strength κ_{ij}^m. The resulting deterministic rate equations are solved numerically (with a finite cutoff N on polymer length) and, where possible, analytically.

In the absence of catalysis (κ = 0) the steady‑state concentrations decay exponentially with polymer length: x_n ≈ c Λ^n (Λ < 1), where Λ decreases as the loss rate φ increases. Thus, without special organization, large polymers are essentially absent. The authors then focus on autocatalytic sets (ACSs). An ACS is defined as a collection of one‑way reactions whose products include a catalyst for every reaction in the set, and whose reactants are themselves producible from the food set using only reactions within the set. When an ACS is embedded in the chemistry, the molecules belonging to the ACS can dominate the “background” of non‑ACS species, leading to bistability: a low‑concentration fixed point (background‑dominated) and a high‑concentration fixed point (ACS‑dominated). However, reaching the high‑concentration state from the standard initial condition (only food molecules present) requires catalytic strengths that grow exponentially with the size of the catalyst. This reproduces the “catalyst‑strength barrier” identified in earlier work (e.g., Ohtsuki & Nowak’s symmetric prelife model).

To overcome this barrier the authors introduce the concept of a “nested ACS.” In a nested architecture a smaller ACS (ACS A) produces molecules that act as catalysts for a larger ACS (ACS B). Because ACS A can be activated with relatively modest κ, it seeds the activation of ACS B, thereby reducing the catalytic strength required for the larger set. By arranging several such layers in a cascade—each layer providing catalysts for the next—one can achieve the emergence of very large polymers while the required catalytic strengths increase only polynomially (e.g., as a power law) with polymer length rather than exponentially. Numerical simulations of two‑ and three‑layer cascades demonstrate that polymers containing 50–100 monomers can reach high steady‑state concentrations even when reverse reactions (cleavage) are present, confirming that the mechanism is robust to realistic degradation processes.

The authors also provide analytical insight by showing that, for homogeneous and fully connected chemistries, the un‑catalyzed steady state has the exact solution x_n = A (k_f/k_r)^{n‑1} (when φ = 0). They then extend this analysis to the catalyzed case, deriving conditions under which an ACS dominates and explaining the origin of bistability. Importantly, they prove that adding the reverse reactions does not destroy the nested‑ACS advantage; the same power‑law scaling of required κ holds, indicating that the mechanism could operate in a genuine pre‑biotic milieu where both synthesis and degradation occur.

Key conclusions are: (1) without catalysis, large polymers are exponentially suppressed; (2) ACSs can concentrate resources into a sparse set of molecules but suffer from an exponential catalyst‑strength requirement for initiation; (3) nesting smaller ACSs within larger ones creates a “bootstrap” effect that lowers the initiation threshold to a polynomial scaling; (4) this bootstrap works even in the presence of cleavage and loss, making it a plausible route for the emergence of macromolecules on early Earth. The work therefore offers a new theoretical framework for the stepwise construction of biochemical complexity, bridging the gap between simple monomers and the first functional biopolymers.