Hamiltonian replica exchange augmented with diffusion-based generative models and importance sampling to assess biomolecular conformational basins and barriers

TL;DR

This study introduces a framework that combines Hamiltonian replica exchange with solute tempering (REST2) with denoising diffusion probabilistic models (DDPMs) and importance sampling to enhance the mapping of conformational free-energy landscapes and expands the utility of generative models in enhanced sampling simulations.

Abstract

Enhanced sampling techniques are essential for exploring biomolecular conformational dynamics that occur on timescales inaccessible to conventional molecular dynamics (MD) simulations. This study introduces a framework that combines Hamiltonian replica exchange with solute tempering (REST2) with denoising diffusion probabilistic models (DDPMs) and importance sampling to enhance the mapping of conformational free-energy landscapes. Building on previous applications of DDPMs to temperature replica exchange (TREM), we propose two key improvements. First, we adapt the method to REST2 by treating potential energy as a fluctuating variable. This adaptation allows for more efficient sampling in large biomolecular systems. Second, to further improve resolution in high-barrier regions, we develop an iterative scheme combining replica exchange, DDPM, and importance sampling along known collective variables. Benchmarking on the mini-protein CLN025 demonstrates that DDPM-refined REST2 achieves comparable accuracy to TREM while requiring fewer replicas. Application to the enzyme PTP1B reveals a loop transition pathway consistent with prior complex biased simulations, showcasing the approach's ability to uncover high-barrier transitions with minimal computational overhead with respect to conventional replica exchange approaches. Overall, this hybrid strategy enables more efficient exploration of free-energy landscapes, expanding the utility of generative models in enhanced sampling simulations.

Figures (9)

• Figure 1: Principles of DDPM. From left to right, the forward diffusion process progressively adds noise, transforming the original data into Gaussian white noise. From right to left, deep neural networks approximate the reverse diffusion process, which maps Gaussian white noise back into meaningful data.
• Figure 2: Comparison of different energy terms considered for DDPM. (A) Distributions of the total potential energy for the different replicas. (B) Distribution of $E_{rescaled,i}(\mathbf{X})=\lambda_{i}E_{pp}(\mathbf{X}) + \sqrt{\lambda_{i}}E_{pw}(\mathbf{X})$ for the different replicas. (C) Value of the free-energy surface taken along the minimum free-energy path from the prediction of DDPM trained on the total potential energy and on $E_{rescaled,i}$.
• Figure 3: Comparison of two-dimensional free-energy surfaces computed along RMSD and $R_{g}$, obtained from TREM (A), TREM refined by DDPM (B), REST2 (C), and REST2 refined by DDPM (D), as well as the free-energy values along the minimum free-energy path as predicted by DDPM (E). White lines on (B) and (D) show the minimum free-energy path. (F) One-dimensional free energy profile computed along the RMSD direction, comparing the training data from TREM and REST2 (dashed lines, orange and blue, respectively) with the DDPM predictions (solid lines, orange and blue, respectively), and Umbrella Sampling as a benchmark (solid green line). Representative structures of basins $\alpha$, $\beta$, $\gamma$, and $\delta$ are shown in Figure S1.
• Figure 4: Melting curves showing the fraction of folded protein computed from TREM simulations (in orange) (A) with exchanges between replicas, (B) without exchange between replicas, with the same folded initial structure for all replicas, (C) without exchange between replicas, with the same unfolded initial structure for all replicas. The prediction of DDPM trained using these TREM simulations is shown in blue.
• Figure 5: Superimposed closed and open conformations of PTP1B. A focus on the WPD loop is shown on the right, for the closed (blue) and the open (orange) conformations. The two dihedral angles used to distinguish the closed and open conformation are highlighted (A). The four collective variables used to train the DDPM, represented on the superimposed closed and open conformations of PTP1B. The two dihedral angles $\Psi_{181}$ and $\Phi_{182}$ are shown with an arrow, the distance between residue 181 and residue 221 is drawn in green, and the distance between residue 181 and residue 112 is drawn in red (B).