Thermodynamically Optimized Machine-learned Reaction Coordinates for Hydrophobic Ligand Dissociation (2310.03819v1)

Abstract: Ligand unbinding is mediated by the free energy change, which has intertwined contributions from both energy and entropy. It is important but not easy to quantify their individual contributions. We model hydrophobic ligand unbinding for two systems, a methane particle and a C60 fullerene, both unbinding from hydrophobic pockets in all-atom water. By using a modified deep learning framework, we learn a thermodynamically optimized reaction coordinate to describe hydrophobic ligand dissociation for both systems. Interpretation of these reaction coordinates reveals the roles of entropic and enthalpic forces as ligand and pocket sizes change. Irrespective of the contrasting roles of energy and entropy, we also find that for both the systems the transition from the bound to unbound states is driven primarily by solvation of the pocket and ligand, independent of ligand size. Our framework thus gives useful thermodynamic insight into hydrophobic ligand dissociation problems that are otherwise difficult to glean.

• The paper demonstrates that machine learning-enhanced reaction coordinates effectively capture the thermodynamics of hydrophobic ligand unbinding in MD simulations.
• It employs the state predictive information bottleneck method combined with well-tempered metadynamics to delineate metastable states by varying the hyperparameter gamma.
• Results reveal distinct hydration dynamics and entropy barrier characteristics between methane and fullerene systems, guiding future biomolecular studies.

Introduction

The paper "Thermodynamically Optimized Machine-learned Reaction Coordinates for Hydrophobic Ligand Dissociation" (2310.03819) investigates the use of machine learning to optimize reaction coordinates (RCs) within molecular dynamics (MD) simulations. The paper is focused on understanding hydrophobic ligand dissociation processes, specifically examining methane and fullerene systems. The authors employ state predictive information bottlenecks (SPIB) to derive low-dimensional RCs that capture the essential dynamics and thermodynamic characteristics of ligand unbinding.

Methodology

Molecular Dynamics Simulations

MD simulations provide the data foundation for this paper. The systems under scrutiny involve a methane ligand in a hydrophobic pocket and a fullerene in a similar configuration. Both systems use the TIP4P water model with varying number densities and employ periodic boundary conditions. Specifically, the methane system includes 1931 water molecules, while the fullerene system contains 3375, reflecting differences in hydration dynamics due to size and interaction differences.

State Predictive Information Bottleneck

The SPIB method forms the core of the methodological approach, allowing the extraction of RCs that encapsulate both kinetic and thermodynamic information. By varying the hyperparameter $\gamma$, the paper elucidates how metastable states of ligand-pocket interaction are categorized, highlighting its role in adjusting the granularity of the state space.

Enhanced Sampling Techniques

Well-tempered metadynamics (WTMetaD) is utilized to enhance the sampling of simulation trajectories, thus accelerating the convergence of free energy landscapes and the detection of metastable states. The selection of adequate biasing parameters—such as the Gaussian height ($\omega$), bias factor ($\gamma$), and standard deviations ($\sigma_z$)—is critical in defining the reaction coordinate's landscape.

Results

Pocket Solvation Dynamics

The paper reveals distinct solvation behaviors for methane versus fullerene dissociation from the hydrophobic pocket. Pocket hydration is shown to influence ligand unbinding kinetics significantly. For methane, the pocket undergoes minimal hydration at intermediate ligand positions due to a void formation, while in the fullerene case, hydration monotonically increases as the ligand exits, reflecting persistent water penetration based on ligand size and shape.

Entropy Barrier Characteristics

The entropy barrier, a key thermodynamic barrier to ligand dissociation, is characterized through SPA derived RCs. The authors observe that the crossing of this entropy barrier chiefly occurs when the ligand reaches the threshold of the pocket, a configuration effectively captured by the SPIB.

Influence of $\gamma$ on Metastable States

Figures illustrating changes in metastable states as a function of $\gamma$ highlight SPIB's efficacy in systematically resolving the RC landscape. Increasing $\gamma$ consolidates metastable states into predominantly bound-unbound classifications, while smaller values explore finer subdivisions, adding interpretability to the RC landscape interpretation.

Implications and Future Work

The paper's insights into ligand unbinding kinetics provide a richer understanding of hydrophobic interactions underpinned by water dynamics within the solvation shell. The successful application of SPIB and WTMetaD opens pathways for further explorations into more complex molecular systems, including protein-ligand interactions where solvation and entropic effects play significant roles. Future work could aim to extend these methods to broader classes of biomolecular systems, potentially integrating with experimental techniques that validate and refine computational predictions.

Conclusion

The paper intricately combines state-of-the-art machine learning techniques with enhanced sampling methods to craft an efficient framework for understanding ligand dissociation in hydrophobic environments. The successful determination and optimization of reaction coordinates leverage the minimal yet informative representations of complex molecular dynamics, demonstrating the utility of SPIB in thermodynamic studies and offering a blueprint for future investigations into ligand-receptor interactions.