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This paper uses machine learning to discover the committor (reaction coordinate) for retinal isomerization from molecular dynamics trajectories. By parameterizing the logit of the committor, the neural network accurately resolves the reaction coordinate across the entire transition region. Symbolic regression then extracts a compact analytical expression revealing a nonlinear coupling of four dihedrals is crucial for reproducing the S-shaped pathway observed in the transition path ensemble, a feature missed by the minimum-free-energy path.
AI reveals that the true reaction pathway for retinal isomerization follows a surprising S-shaped trajectory driven by non-equilibrium dynamics, a feature invisible to traditional free-energy surface analysis.
The thermal cis-trans isomerization around the C$_{13}$=C$_{14}$ double bond of retinal is a prototypical high-barrier reaction whose mechanism hinges on subtle out-of-plane bending motions. We apply Artificial Intelligence for Molecular Mechanism Discovery (AIMMD) to N-retinylidene-lysine in vacuum, learning the committor from unbiased molecular dynamics trajectories generated by two-way shooting. Parametrizing the logit of the committor, rather than the committor itself, allows the neural network to resolve the reaction coordinate across the full transition region, not only at the isocommittor surface $p_B(\mathbf{x}) = 0.5$. Holdback input randomization identifies four proper dihedrals around the reactive bond as the informative coordinates, while the improper dihedrals at C$_{13}$ and C$_{14}$ prove unsuitable because reactant, transition, and product states share the same values. Symbolic regression then distills the network into compact analytical expressions and shows that a nonlinear coupling of all four dihedrals is required to reproduce the S-shaped, stepwise pathway seen in the transition path ensemble. This S-shape is absent from the minimum-free-energy path: it arises from the non-equilibrium dynamics of the short ($\sim 0.13$ ps) transition events combined with the mass asymmetry between heavy-atom and hydrogen-bearing dihedrals. An interpretable, machine-learned committor thus exposes dynamical features of the mechanism to which the free-energy surface is blind. The workflow requires no prior assumptions about the reaction coordinate and extends naturally to other isomerizations and to chemical reactions more broadly.
