Surface-Accelerated String Method for Locating Minimum Free Energy Paths

Abstract

We present a surface-accelerated string method (SASM) to efficiently optimize low-dimensional reaction pathways from the sampling performed with expensive quantum mechanical/molecular mechanical (QM/MM) Hamiltonians. The SASM accelerates the convergence of the path using the aggregate sampling obtained from the current and previous string iterations, whereas approaches like the string method in collective variables (SMCV) or the modified string method in collective variables (MSMCV) update the path only from the sampling obtained from the current iteration. Furthermore, the SASM decouples the number of images used to perform sampling from the number of synthetic images used to represent the path. The path is optimized on the current best estimate of the free energy surface obtained from all available sampling, and the proposed set of new simulations is not restricted to being located along the optimized path. Instead, the umbrella potential placement is chosen to extend the range of the free energy surface and improve the quality of the free energy estimates near the path. In this manner, the SASM is shown to improve the exploration for a minimum free energy pathway in regions where the free energy surface is relatively flat. Furthermore, it improves the quality of the free energy profile when the string is discretized with too few images. We compare the SASM, SMCV, and MSMCV using 3 QM/MM applications: a ribozyme methyltransferase reaction using 2 reaction coordinates, the 2′-O-transphosphorylation reaction of Hammerhead ribozyme using 3 reaction coordinates, and a tautomeric reaction in B-DNA using 5 reaction coordinates. We show that SASM converges the paths using roughly 3 times less sampling than the SMCV and MSMCV methods. All three algorithms have been implemented in the FE-ToolKit package made freely available.

Electronic and Nuclear Quantum Effects on Proton Transfer Reactions of Guanine–Thymine (G-T) Mispairs Using Combined Quantum Mechanical/Molecular Mechanical and Machine Learning Potentials

“…The reactions are broken down into competing wGT→GT* and wGT→G*T pathways and, separately, the interconversion GT*→G*T. These reaction steps are shown schematically in Figure 3 , and representative structures for key stationary points along the reaction paths are shown in Figure 4 . The 1D profiles shown are the result of the minimum free energy path derived from the finite temperature string method [ 37 , 38 ], followed by additional production path refinement sampling (see Section 3 ).…”

“…The QM region consisted of 51 atoms (the nucleobase and sugar of G4 and T21), and it had a net neutral charge. The minimum free energy path of each step was optimized in the space of 5 reaction coordinates with the finite temperature string method [ 38 ] for every QM/MM model. The 5 reaction coordinates were distance differences meant to represent the transfer of H3 and H1 protons and the relative displacement of the hydrogen bond pattern: , , , , .…”

Software Infrastructure for Next-Generation QM/MM−ΔMLP Force Fields

“…The simulations were sampled for 1 ps with a 1 fs time step, and the active learning procedure incorporated approximately 10,000 PBE0/6-31G* samples into the training procedure, in total. After training, the minimum free energy path of the DFTB3/3ob−ΔMLP was found using the finite temperature string method, and production simulations were performed using the same protocol described for the GFN2-xTB US.…”

“…The MTR1 free energy surface was generated from GFN2-xTB QM/MM US involving 2 reaction coordinates: ξ 1 = R C10/N3 – H – R O6mG/N1 – H and ξ 2 = R O6mG/O6 – C – R A63/N1 – C . The minimum free energy path was determined from 50 iterations of the surface-accelerated string method . Each string was discretized with 32 windows, and each window was sampled for 4 ps in each iteration (6.4 ns of aggregate sampling).…”