How does machine learning augment alchemical binding free energy calculations?

Calculating binding affinities between small molecules and proteins has become routine in drug discovery. Advances in crystallography, electron microscopy, and protein structure prediction led to a growing number of drug targets with structures solved at atomic resolution, including membrane proteins and large multi-protein complexes. The majority of small molecule drug discovery efforts today are supported by protein structures, thereby spurring the desire to use powerful physics-based methods along with machine learning to assist in the identification and optimization of lead compounds and drug candidates.

Ever since the inception of binding free energy (BFE) calculation methods to predict the affinity of biomolecular interactions [1], generations of computational chemists tried to improve the accuracy, usability, speed, and applicability of these methods, especially in the context of drug discovery. While many different use cases have been established for BFE calculations [2], they remain slow, resource-intensive as well as limited by extent of applicability for relative BFEs (RBFE) and accuracy, especially for absolute BFEs (ABFE). A 1 kcal/mol accuracy boundary has been suggested for BFEs; however, there are cases where BFE calculations for protein-ligand complexes do not work well enough to be used prospectively [3].

Calculating binding free energies between biomolecules has long been considered the pinnacle of computational chemistry efforts, especially in the context of small molecule drug discovery. As the accuracy and confidence of the BFE prediction is often considered more important than speed, using physics-based methods such as free energy perturbation (FEP) for RBFE calculations has been a prominent choice despite the time and resources needed to run lengthy molecular dynamics (MD) calculations. On the other hand, machine learning (ML), especially deep learning (DL), and artificial intelligence (AI) methods have recently emerged to accelerate, automate, and augment slow processes. It is therefore not surprising that DL and AI applications have made inroads to augment BFEs in many relevant domains, including predicting protein structures, improving force fields and scoring functions, initial placement of ligands in the protein pocket, managing molecular perturbation size for RBFE, and optimizing BFE calculation protocols.

1. AI/ML methods to facilitate FEP setup

Setting up FEP calculations can be tedious and complicated if not guided by expensive commercial tools or bespoke expertise. Efforts have been made in the past to automate a standard FEP system setup [4]. Recently, an automated workflow was introduced to rapidly generate FEP protocols, especially in cases where standard settings do not afford good performance. An active learning protocol using genetic programming drives the search for parameter settings with limited human interference. It includes the optimal splitting of test and training sets to counteract overfitting [5].

Predicting the reliability of RBFE calculations as function of the perturbation size is challenging. Chances to obtain inaccurate RBFE calculation results usually increase with the size of the molecular perturbation. To address this concern, an open source DL model was recently introduced that assesses the reliability of the perturbation prediction and informs an optimized network generator how best to explore the relevant RBFE space [6].

BFE calculations for protein-ligand complexes rely on the accuracy and relevance of the protein structure as well as the ligand binding pose. AlphaFold2 (AF2) practically solved the protein folding problem and is making high quality in-silico models of protein structures available for the majority of proteins relevant for drug discovery [7]. FEP benchmark studies suggest that the accuracy of using FEP to predict ligands bound to AF2 models is comparable to that of experimental structures [8]. AlphaFold3 promises to predict even the binding pose of a ligand more accurately – a most relevant advancement as FEP calculations are sensitive to the initial placement of ligands in FEP calculations. However, this claim could not be broadly validated yet due to the limited access to AF3 [9].

Not only can ML methods help in making BFE calculations more efficient, ML methods themselves can also benefit from the rigor of physics-based methods, making the relationship truly synergistic. Paucity of data is an essential problem for ML when training a predictive algorithm. Alleviating this issue, Burger et al. recently showed for multiple data sets of proto-oncogene tyrosine-protein kinase Src inhibitors that FEP-augmentation yields prediction accuracies of ML models that approach those obtained from models derived from experimental data [10].

2. AI/ML increase efficiency of free energy calculations

ABFE calculations are significantly slower than RBFE calculations. As ABFE calculations are preferably used in virtual screening applications, ML methods have been devised to guide ABFE calculations through the deliberate explorations of chemical space using active learning Bayesian optimization and surrogate random forest and direct message-passing neural networks with average processing time per compound shrinking from 1 week to 1–2 hours [11]. Active learning has also been deployed to efficiently explore chemical space for lead optimization [12] and systematic exploration of large congeneric series with models derived from FEP data of only a few hundreds of compounds [13]. As FEP calculations can take eight GPU hours per compound, using active learning is essential to explore large compound spaces. In the example of a series of 10,000 congeneric TYK2 inhibitors alluded to above [13], only six percent of compounds were subjected to explicit FEP calculations, yet 75% of the top-scoring 100 compounds were retrieved using the active learning approach. With a cost of $2 per GPU hour, the overall price was thereby reduced from $160,000 (80,000 GPU hours) to $9,600 (4,800 GPU hours) illustrating the scalability and cost savings of active learning.

3. Improving force fields with AI/ML

The accuracy of empirical force fields is a limitation of BFE calculations. Rigorous methods to calculate intermolecular interactions from electronic structure using methods derived from first principles grounded in quantum mechanics (QM) have been developed some time ago, e.g., by Car and Parrinello and others [14]. However, these methods are too slow to be applied in MD simulations. Hence, fast and simple molecular mechanics force field methods are used in MD approaches, with individual parameters being derived from QM methods for chemically diverse small molecules. To bridge the gap of speed and accuracy, transferable ML models that learn the potential energy of small molecules from limited QM calculations have been developed. These ML models avoid QM calculations for entire classes of molecules and are broadly applicable as they learn generalized molecular properties. The neural network-derived Accurate NeurAl networK engINe for Molecular Energies (ANI) method and its extension to ANI-2× are recent representatives of this approach [15]. Combining the ANI-2× neural network potential (NNP) with molecular mechanics (MM) resulted in the hybrid method NNP/MM [16] that was recently applied in BFE calculations for eight protein targets. Although somewhat limited in applicability (potentials for seven elements have been calculated covering ~90% of drug-like molecules), scope and speed, using the NNP/MM hybrid method outperformed BFE calculations compared to a standard GAFF2 force field illustrating the potential for deep learning methods to contribute to improved accuracy of BFE methods. Alternative ML methods such as Espaloma using graph neural network methods to train MM force fields on QM and experimental data exhibited promising performance for BFE calculations on protein-ligand test systems as well [17]. It is worth noting that constructing ML force fields scales well for large data sets. It was demonstrated for Espaloma that representing 17,000 compounds with more than 1 million forces and energies required less than one GPU-day.

ML force fields and potentials come with a number of challenges and limitations. While ML force field parameters are trained on QM parameters, non-bonded interactions need be fitted to condensed-phase properties, training against which has proven difficult. In addition, quantifying force field uncertainties and how they influence predictions of endpoints such as BFEs have been recognized as an area for improvement. The neural network potentials ANI-2× has limitations in supporting certain chemical elements and charge states limiting the coverage of chemical space. Also, there are opportunities to improve the speed of ANI potentials – which is about an order of magnitude slower than that of conventional MM potentials – perhaps by reducing the number of underlying neural networks, increasing the simulation time steps, and optimizing software components.

Making BFE methods available to the scientific community without barriers is essential to further develop the field of BFE and ensure broad applicability. OpenMM is a popular MD engine. Now, its newest version supports the use of ML potentials [18], which has been quickly adapted to accommodate a plugin for deep potential models [19]. The Open Force Field initiative [20] has provided the infrastructure and data pipeline that were used to develop open-source ML force field models such as Espaloma. Using OpenMM as the foundation for BFE calculations, the OpenFE package was developed by the Open Free Energy Consortium [21]. The first stable release was announced a few months ago. The long-term vision is to establish OpenFE as portable and robust standard for BFE calculations.

4. Summary

ML methods have made inroads in augmenting binding free energy (BFE) approaches in several areas. Hybrid quantum mechanics/ML models improve the rigor of molecular potential descriptions. Community initiatives such as OpenMM, OpenFF, and OpenFE provide a platform to develop ML force fields to cover more chemical space and reduce barriers for training. The robust use of evolving ML force fields in prospective drug discovery projects will help to establish ML methods more broadly. Transfer learning improves generalization of BFE predictions and assists with data curation. Error predictions and post-hoc adjustments of BFE calculations can be guided by ML. High accuracy predictions of protein structures with AlphaFold2 expanded the number of available structures and promise to optimize ligand placement. Active learning generates surrogate models that speed up BFE calculations. ML methods are used to optimize BFE protocols. Conversely, FEP methods can assist ML performance by relieving data paucity issues. The synergistic interconnectedness between physics-based and ML methods has just begun to bear fruit. We expect further exciting developments to emerge as the field develops.

Funding Statement

This work was not funded.

Disclosure statement

The authors have no relevant affiliations or financial involvement with any organization or entity with a financial interest in or financial conflict with the subject matter or materials discussed in the manuscript. This includes employment, consultancies, honoraria, stock ownership or options, expert testimony, grants or patents received or pending, or royalties.