Markovian Timescales of Intramolecular Disulfide Pairing in Cyclotides

Kinetics of intramolecular disulphide pairing in a six-cysteine containing plant toxin peptide cycloviolacin O1 (CyO1) having a cyclic backbone and a cyclic cystine knot (CCK) is studied using a Hidden Markov Model (HMM) created from molecular dynamics simulation trajectories. Starting from a fully reduced form of CyO1 (peptide-D), the kinetic model is created to track the peptide's evolution to a native-like state (peptide-N) where all three correct pairs of S-S linkages are most likely to be observed. The structural evolution and fluctuation of peptide-D through many partially folded S-S intermediates and the associated propensity, along with the timescale of formation of a single or simultaneously two or three S-S pairs, is studied using this Markov chain. The phenomenon of intramolecular S-S pairing, as observed in proteins and peptides, is fast, with a computed rate constant of ~10⁶ s^-1 in line with experimental observations in the bacterial disulphide bond redox protein DsbD. Rate networks and transition path theory analysis are used to find the most probable pathway for peptide-D to evolve into peptide-N.