Metadynamics (MetaD) and Path Collective Variables (PCVs)

The central idea of the metadynamics method^19,30 is to bias the system along a set of CVs using a history-dependent potential. To achieve this, a Gaussian-shaped potential is added to bias the system at the current position of the CVs, at regular time intervals. This allows the system to escape from any local minimum and to visit new regions in the CVs space. In metadynamics, to push the system to visit even high free-energy regions, the Gaussian-shaped potential has constant height. On the contrary, in the well-tempered metadynamics⁸² approach, used in this work, the height of the Gaussian is decreased with the amount of bias already deposited according to

where w₀ is an initial Gaussian height, ΔT an input parameter with the dimension of a temperature, k_B is the Boltzmann constant, and τ_G is the time interval at which Gaussians are deposited.⁸²

The path CV formalism^32,83 has been widely used to investigate biological processes, to compute their free-energy surfaces, and to characterize their kinetic behavior.^39,34 In this work, PCVs were used to study the transition between the bound and the unbound states in the unbinding process of some HIF2-α ligands. We described the transition pathway with a set of frames derived from the SMD simulations: 12 frames were used for the THS-020 ligand and 11 frames for the KG-721 ligand. For the first part of the path, the frames (from 1 to 7 for THS-020 and from 1 to 6 for KG-721) were obtained from the SMD simulations with the lowest value of external work performed on the system. Frames were selected to be equally spaced (2 Å). For the second part of the path, the frames were obtained with linear interpolation (see the Supporting Information, Supplementary Text for the details). Following the procedure proposed by Branduardi et al.,³² we introduced two collective variables: s(R), the progress along the reference path, and z(R), the distance orthogonal to the reference path. The λ value was set to 33.0 nm². The distance between the instantaneous conformational state during the simulation and the reference coordinates in the path was evaluated by the RMSD metric.⁸⁴ In particular, the RMSD along the entry/exit pathway was calculated between a selection of protein atoms and all the ligand heavy atoms (see Figure S3). In all simulations, the Gaussian-shaped potentials were deposited every 500 simulation steps, the initial height was set to 1 kJ/mol, and the decay corresponding to a bias factor of 10 was chosen. The Gaussian widths (σ) for the s(R) and z(R) variables were set to 0.05 and 0.007, respectively. Widths were set so that they are about 1/3 of the CV standard deviations observed in the unbiased MD simulation. The two variables, s(R) and z(R), were constrained to be less than 12 and 0.2 nm², respectively.