Pathway-resolved flux decomposition reveals hidden kinetic hierarchy in protein folding

Abstract

Proteins fold through ensembles of competing pathways, yet the kinetic contribution of each route remains difficult to quantify. Structure-prediction methods such as AlphaFold identify folded endpoints, but do not resolve folding kinetics, pathway heterogeneity, or how flux partitions among competing mechanisms. Here, we introduce a framework that directly decomposes folding flux into pathway-specific kinetic contributions by combining forward-flux sampling with trajectory-level unsupervised learning, avoiding millisecond-scale trajectories, biasing potentials, and a priori state discretization. Applied to 2,637 statistically representative folding events of the TC5b variant of Trp-cage, the framework recovers a folding time in near-quantitative agreement with experiments and identifies four pathways distinguished by the ordering of helix formation, hydrophobic collapse, and salt-bridge stabilization. The resulting decomposition shows that structural prevalence is a poor proxy for kinetic importance: the most populated pathways are not the fastest, whereas a rare helix- salt-bridge route is disproportionately efficient and a premature salt bridge produces a frustrated slow route. By assigning statistical weights to competing pathways, this framework links structural evolution to kinetic relevance in biomolecular rare events and reveals how folding landscapes select kinetically important routes from many plausible structural sequences.