Deciphering the Molecular Mechanisms of Phosphoester Bond Formation in Abiotic Conditions With Reactive Neural Network Potentials

Phosphoester bonds are fundamental components of both small molecules and polymeric biomolecules, most notably nucleic acids. Their formation from alcohol groups and phosphate is a significant challenge for living systems, as it involves substantial free-energy barriers. These barriers, while hindering bond formation, also ensure the kinetic stability of the resulting biomolecular structures. This duality presents a major obstacle in understanding the emergence of RNA-based systems at the origins of life, where protein enzymes capable of catalyzing such reactions were absent. Understanding the mechanisms underlying phosphoester formation is therefore essential for developing non-biological catalytic strategies. In a recent proof-of-concept study (Benayad et al. Proc. Natl. Acad. Sci. USA 121 e2322040121 (2024)), we demonstrated that machine-learned interatomic potentials (MLIPs) can be effectively trained and employed to sample the reactive pathways of the uncatalyzed reaction in water on microsecond timescales. In this work, we significantly expand upon our previous analysis to offer a detailed molecular characterization of two families of mechanisms, associative and dissociative, each associated with a variety in the order of proton exchange events. We focus on the two protonation states of phosphate prevalent under near-neutral conditions ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msub><mml:mi>H</mml:mi> <mml:mn>2</mml:mn></mml:msub> <mml:msubsup><mml:mi>PO</mml:mi> <mml:mn>4</mml:mn> <mml:mo>-</mml:mo></mml:msubsup> </mml:mrow> <mml:annotation>${\rm H}_2{\rm PO}_{4}^-$</mml:annotation></mml:semantics> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:msubsup><mml:mi>HPO</mml:mi> <mml:mn>4</mml:mn> <mml:mrow><mml:mn>2</mml:mn> <mml:mo>-</mml:mo></mml:mrow> </mml:msubsup> <mml:annotation>${\rm HPO}_{4}^{2-}$</mml:annotation></mml:semantics> </mml:math> ). We find that dissociative pathways are consistently lower in free-energy as compared to associative ones, and that <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msub><mml:mi>H</mml:mi> <mml:mn>2</mml:mn></mml:msub> <mml:msubsup><mml:mi>PO</mml:mi> <mml:mn>4</mml:mn> <mml:mo>-</mml:mo></mml:msubsup> </mml:mrow> <mml:annotation>${\rm H}_2{\rm PO}_{4}^-$</mml:annotation></mml:semantics> </mml:math> is much more reactive than <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:msubsup><mml:mi>HPO</mml:mi> <mml:mn>4</mml:mn> <mml:mrow><mml:mn>2</mml:mn> <mml:mo>-</mml:mo></mml:mrow> </mml:msubsup> <mml:annotation>${\rm HPO}_{4}^{2-}$</mml:annotation></mml:semantics> </mml:math> . Special attention is given to the role of the solvent, elucidating its involvement in the reaction process, as well as the contributions of proton transfer events and oxygen substitution at the phosphorus center. We conclude by proposing molecular-level explanations for the observed differences in reactivity between the two phosphate protonation states based on charge redistribution during the reaction.