Committors without Descriptors

TL;DR

This work advances rare-event sampling by replacing descriptor-based inputs with a descriptor-free graph neural network that directly processes atomic coordinates to learn the committor function. Built on the Kolmogorov variational principle, the method uses a biased sampling scheme and a stabilized transformation to efficiently sample transition-state ensembles, while a truncated graph strategy significantly reduces computational cost in solvent environments. The approach is demonstrated on alanine dipeptide, calixarene-ligand binding, NaCl dissociation, and CaCO3 dissolution, revealing multiple transition-state ensembles and elucidating solvent roles through attention and node-sensitivity analyses. The results show accurate free-energy landscapes and mechanistic insights across complex aqueous systems, highlighting the method’s potential for broad application in solvent-mediated rare events and offering accessible code and data for reuse.

Abstract

The study of rare events is one of the major challenges in atomistic simulations, and several enhanced sampling methods towards its solution have been proposed. Recently, it has been suggested that the use of the committor, which provides a precise formal description of rare events, could be of use in this context. We have recently followed up on this suggestion and proposed a committor-based method that promotes frequent transitions between the metastable states of the system and allows extensive sampling of the process transition state ensemble. One of the strengths of our approach is being self-consistent and semi-automatic, exploiting a variational criterion to iteratively optimize a neural-network-based parametrization of the committor, which uses a set of physical descriptors as input. Here, we further automate this procedure by combining our previous method with the expressive power of graph neural networks, which can directly process atomic coordinates rather than descriptors. Besides applications on benchmark systems, we highlight the advantages of a graph-based approach in describing the role of solvent molecules in systems, such as ion pair dissociation or ligand binding.

Figures (13)

• Figure 1: Truncated graph. Schematic representation, using the dissociation of NaCl as an example, of the truncated graph construction to reduce the computational cost of using GNN-based methods when a few reacting atoms (NaCl) interact with a large number of environment atoms (H$_2$O). Only the atoms belonging to the neighborhood defined by the cutoff radius $R_t$ from reacting atoms are associated with graph nodes, whereas the other are neglected (A and C). Such nodes are then connected with edges based on the cutoff $R_c < R_t$ (B and C). To avoid having reacting atoms in disconnected graphs, edges between reacting atoms can be enforced regardless of the distance (D). The whole truncated graph is processed through the GNN model, but only the reacting atoms are considered in the readout function to obtain the final CV output.
• Figure 2: Alanine dipeptide. A) Relevant torsional angles of alanine dipeptide. B) Relative relevance, given by the color scale, to the GNN-based committor model of the graph nodes associated with the heavy atoms. C) Free energy surface (FES) projected along the $\varphi$ torsional angle obtained with the GNN-based setup proposed in this work (blue solid curve) and a reference OPES simulation using $\varphi$ and $\psi$ as CVs (red dashed curve).
• Figure 3: Calixarene. Snapshots of representative configurations along the dominant reaction pathway of $B_w$ to $B_d$ in the binding process of the G2 ligand (orange) to the OAMe host molecule (grey) in water, grouped according to the $z$ value. The water molecules are represented as blue sticks, depicted in transparency when outside the binding cavity and in solid color when inside.
• Figure 4: NaCl dissociation. A) Computed free energy surface (FES), indicated by the color map, in the space defined by the number of water molecules bridging the ions $n_b$ and by the inter-ionic distance $d_{NaCl}$. The two reactive pathways from the associated states are indicated by dashed lines. B) Distribution of the Kolmogorov probability $p_{\mathcal{K}}$, indicated by the color map, in the $n_b$ and $d_{NaCl}$ plane. The isolines of the free energy of A are superimposed in white as a reference. The insets show representative configurations of the transition states that characterize the two reaction pathways.
• Figure 5: CaCO3 dissociation. A) Free energy surface (FES), indicated by the color map, in the plane defined by the inter-ionic distance $d_{Ca-C}$ and the number of solvating water molecules around the Ca^2+ ion $n_w$. The metastable states are indicated on the FES, and representative snapshots are provided in the insets. The position of the transition states is indicated by a star. B) Medoid configurations for the two transition state ensemble clusters TS$_1$ and TS$_2$. C) Average attention scores $Att(r)$ of messages from water oxygen nodes to the Ca^2+ node as a function of the interatomic distance $d_{Ca-O_w}$ (red line). The radial distribution function of water oxygens with respect to Ca^2+ is reported as a reference (blue line). The two curves are both normalized to be in the range (0,1).