The String Method with Swarms of Trajectories: A Tutorial for Free-Energy Calculations Along a Zero-Drift Pathway

The objective of this tutorial is to provide a comprehensive overview of the string method and its usage to determine a detailed transition pathway and the free-energy difference between two conformational states of a system. The computational protocol is illustrated in detail by setting out to calculate the free-energy difference between the C7eq and C7ax conformations of the short, terminally blocked peptide, N–acetyl–N′–methylalaninamide. Starting from a rectilinear transition pathway connecting the two conformations in the backbone-torsional subspace, an optimal zero-drift pathway (ZDP) is determined using the string method with a swarm of trajectories. The free-energy change along this path is then estimated using the path-collective variables (PCV) coordinate in the framework of the adaptive biasing force (ABF) importance-sampling algorithm.