Drift-diffusion (DrDiff) framework determines kinetics and thermodynamics of two-state folding trajectory and tunes diffusion models

The stochastic drift-diffusion (DrDiff) theory is an approach used to characterize the dynamical properties of simulation data. With new features in transition times analyses, the framework characterized the thermodynamic free-energy profile [F(Q)], the folding time (τ_f), and transition path time (τ_TP) by determining the coordinate-dependent drift-velocity [$v$(Q)] and diffusion [D(Q)] coefficients from trajectory time traces. In order to explore the DrDiff approach and to tune it with two other methods (Bayesian analysis and fep1D algorithm), a numerical integration of the Langevin equation with known D(Q) and F(Q) was performed and the inputted coefficients were recovered with success by the diffusion models. DrDiff was also applied to investigate the prion protein (PrP) kinetics and thermodynamics by analyzing folding/unfolding simulations. The protein structure-based model, the well-known G$o¯$-model, was employed in a coarse-grained C_α level to generate long constant-temperature time series. PrP was chosen due to recent experimental single-molecule studies in D and τ_TP that stressed the importance and the difficulty of probing these quantities and the rare transition state events related to prion misfolding and aggregation. The PrP thermodynamic double-well F(Q) profile, the “X” shape of τ_f(T), and the linear shape of τ_TP(T) were predicted with $v$(Q) and D(Q) obtained by the DrDiff algorithm. With the advance of single-molecule techniques, the DrDiff framework might be a useful ally for determining kinetic and thermodynamic properties by analyzing time observables of biomolecular systems. The code is freely available at https://github.com/ronaldolab/DrDiff.