Stochastic Chemical Kinetics and Free-Energy Landscape Reconstruction in Non-Equilibrium Protein Folding Dynamics

We present a theoretical and numerical study of protein folding kinetics and conformational transitions in complex free-energy landscapes using generalized Langevin equations with memory kernels and Fokker-Planck formalisms. Moving beyond standard deterministic approaches, we investigate non-equilibrium folding dynamics, hydrodynamic solvent effects, and the reconstruction of multi-dimensional free-energy landscapes via collective reaction coordinates. Our analysis examines first-passage time distributions, transition rate constants between native and denatured states, and analytical expressions for anomalous diffusion coefficients within the intramolecular polymer chain space. Furthermore, we validate the theoretical predictions using Brownian dynamics numerical simulation protocols with noise smoothing and finite-size scaling.