Generation of protein dynamics by machine learning

Abstract

Machine learning has advanced protein structure prediction to deliver accurate but mostly static models. Capturing protein dynamics as conformational ensembles remains a significant challenge. Recent developments, especially generative models, are enabling the prediction of structural ensembles beyond traditional simulations. This review examines emerging machine learning approaches for modeling protein dynamics, in terms of generating PDB-like ensembles, accelerating molecular simulations, modeling non-globular protein ensembles, and integrating experimental data. General-purpose and system-specific models are discussed, particularly in terms of conformational coverage, transferability, and responsiveness to environmental conditions. Hybrid models, which combine experimental and simulation data, represent a promising direction. Nonetheless, key challenges remain, including generating states with correct probabilities, modeling unseen conformations, and integrating experimental constraints rigorously.

Introduction

In recent years, machine learning (ML) has made significant progress in predicting 3D structures of proteins as mostly static conformations similar to what experiments provide. Thanks to the contribution of AlphaFold2 [1] (AF2) and related methods, structure prediction has now a direct impact in structural biology [2]. Despite this, the characterization of protein dynamics via computation is still a significant challenge. Proteins inherently exist as conformational ensembles that populate energy landscapes and understanding those is crucial for studying and designing protein function [3].

Driven by AF2 and innovations in generative deep learning [4], ML models for capturing protein dynamics are emerging as an alternative to traditional simulation techniques. Here, we review current approaches of this kind, describe the underlying methodologies, and focus on their structural biology objectives.

Modeling PDB-like ensembles

The Protein Data Bank (PDB) contains numerous examples of conformational heterogeneity [5], including proteins crystallized in alternative states or NMR ensembles. Part of these describe biologically meaningful structural variability, which we would ideally like to capture computationally when predicting structures that are not available from experiments (Figure 1a). Although trained on the PDB, canonical AF2 is not well-suited for capturing multiple states, for example holo-apo pairs [6] or active-inactive membrane receptors [7]. The limitation originates from AF2 training as a regression model: its learning objective was to map input to output (one sequence to one structure) without considering the probabilistic nature of protein ensembles (one sequence leading to a distribution of structures).

Figure 1.

Overview of structural biology objectives of ML methods for generating protein dynamical ensembles. Each panel shows a list of examples reported in literature and some of the main challenges. (a) Modeling PDB-like ensembles. The goal is to capture different biologically relevant conformations. (b) Accelerating molecular simulations. After generating a structural ensemble, an energy landscape can be built, and different structural states can potentially be identified. (c) Modeling non-globular protein ensembles. The goal is to provide an ensemble approximating experimental observables. (d) Integrative structural biology. Experimental restraints are incorporated either during training or inference stages of an ML-based ensemble generator, effectively guiding sampling.

Early empirical attempts to overcome this utilized AF2 by modifying its input, leading to numerous sampling methods. We highlight a few examples, for more details see this review [8]. AlphaFold-multistate [7] extended AF2 by selecting state-specific templates and predicted both active and inactive G protein-coupled receptors structures. Subsampled AlphaFold2 [9] modified input multiple sequence alignments (MSA) and modeled multiple states of the Abl1 kinase. More recently, AFsample2 [10] randomly masked MSA columns and was benchmarked on systems with open-closed states and membrane receptors. These different MSA modification strategies show comparable improvements over AF2 [10] and surpass other AF2 perturbation methods like dropout [11,12]. However, as studied with Cfold [12], they have a limited ability to capture larger conformational changes. For example, AF-cluster [13], a pipeline based on clustering MSAs, showed promise in predicting large rearrangements in fold-switching proteins, like the metamorphic protein KaiB. However, successive studies indicated this approach did not work well for several fold-switchers outside the AF2 training set [14].

A different strategy based on AF2 is to retrain the model on the PDB as a deep generative model (GM). GMs are methods that allow neural networks to generate samples from probability distributions learned from data [15]. This is a principled way to turn AF2 from a one-to-one into a one-to-many model. Currently, the most successful GMs for protein structures are diffusion models [4] and related flow matching models [16]. We refer to another review [17] for more details on their use in structural biology. Examples of AF2-based GMs include AlphaFlow [18] and UFConf [19]. In several benchmarks, they obtain better performance at capturing multiple PDB-like conformations with respect to AF2 sampling strategies from above. Notably, AlphaFold3 [20] is also trained as a diffusion model on the PDB and does not outperform AF2-based GMs [19]. This suggests that training data, not model architecture, is likely the most important bottleneck.

Besides general-purpose PDB ensemble generators, specialized GMs have been introduced for specific systems. Examples include GMs for classes of membrane proteins capable of large conformational changes [21] or GMs for proteins interacting with small molecules that aim to capture ligand-induced changes [22]. While the latter models achieve state-of-the-art performance in docking benchmarks, there are still limits, such as modeling allosteric conformational changes [23].

Accelerating molecular simulations

Molecular dynamics (MD) is a fundamental technique in biophysics [24]. Its goal is to sample molecular conformations, and it is often used to characterize protein structural ensembles. However, MD is computationally expensive, motivating the development of ML models as an alternative.

Various ML approaches have been explored to achieve this goal, almost all of them effectively leveraging MD methodology. Here, we highlight four prominent directions: (i) GMs that are directly trained on MD datasets [25]. Since GMs can efficiently generate statistically independent samples, they can greatly speed up the construction of MD structural ensembles (Figure 1b); (ii) neural networks that are trained as effective coarse-grained (CG) force fields that can replicate all-atom MD [26] with reduced degrees of freedom. The insight that diffusion models trained on MD data can approximate forces learned by neural force fields [27] has recently provided a framework unifying these data-driven methods; (iii) using ML to “jump” over multiple timesteps of MD [28,29]. The idea is to train a GM that, given an input configuration, can propose another configuration at a significantly later time than the MD integration timestep. By iteratively taking such jumps, the models can eventually propagate stochastic dynamics; (iv) in a hybrid strategy ML can be used to drive enhanced MD sampling [30]. For example, AlphaFold2-RAVE [31] employs MSA subsampling via AF2 to generate a pool of conformations that are used to learn with an autoencoder the reaction coordinates for enhancing sampling.

In addition, other novel ideas have emerged. For example, the concept of modeling entire segments of MD trajectories [32], inspired by video generation models, blends concepts from the strategies above.

Currently, a common limit for all methods is transferability beyond training data. Transferability is challenging at different levels, including at the chemical [28,33] (e.g.: modeling new protein sequences), conformational [34] (e.g.: identification of structural states absent in the training data) and environmental [35] ones (e.g.: new temperatures). Because of these challenges, universal ML surrogates for MD are not yet available. Nevertheless, progress has been made toward transferable models for monomeric proteins, mainly using GMs. A spearheading example is AlphaFlow [18], which has also been trained as a GM on the ATLAS dataset [36] of MD simulations of PDB protein chains, inspiring similar approaches [37]. More recently, the aSAM diffusion model [34] was trained on the larger mdCATH [38] dataset. mdCATH contains simulations of proteins at multiple temperatures, allowing aSAM to be trained as the first GM capable of modeling ensembles of different proteins at multiple temperatures.

The four strategies discussed above each have strengths and limitations. For instance, GMs for statistically independent sampling yield only thermodynamic information [39], while time-step “jumping” methods can also recover kinetics [29]. So far, none of the first three has shown clear advantages in transferability, as training data remains the bottleneck. Many sequence-transferable methods are implemented as GMs [18,34,37,39], but also neural CG potentials have started to obtain transferability [40]. While all these methods can often approximate MD behavior of test systems, they struggle with complex landscapes involving multiple metastable states [33,39]. ML-driven enhanced MD can recover multiple states via sampling grounded in statistical mechanics [30], but this approach is currently non-transferable and requires training for new system.

Jointly learning from experiments and simulations

The recently introduced BioEmu model [39] implements ideas illustrated above and represents a crucial contribution to the field. By building upon AF2, BioEmu is a diffusion model that achieved unprecedented performance in modeling both PDB and MD ensembles. The key advance is that it consistently captures large and biologically significant conformational changes observed in PDB structures outside its training data. For MD data, BioEmu samples conformational spaces with coverage approaching long simulations. The advancements stem from its hybrid training strategy using multiple, large training sets combining data from experiments and simulations. The model was initially trained on a subset of the AlphaFold database [41], learning a robust prior on protein structures. It was then fine-tuned on a massive dataset of MD simulations to expand its sampling capabilities. Additionally, experimental folding free energy data were used during fine-tuning, to steer the model toward learning distributions of conformations that approximate experimental equilibria. BioEmu exemplifies how ML can pragmatically leverage different data sources to obtain a model useful for addressing biological problems.

Modeling non-globular protein ensembles

ML has also been applied for modeling the ensembles of non-globular proteins with significant dynamics and/or scarce structural data. Examples include amyloids [42,43], coiled coil proteins [44], and intrinsically disordered regions (IDRs) of proteins. Sampling of IDRs has received the most attention so far (Figure 1c). IDRs have fundamental biological roles which depend on their conformational ensembles and their interactions [45]. Characterizing IDR properties is challenging and ML can be applied in different ways in this task, as described in this recent review [46]. Here we focus on ML methods to model IDR structural ensembles.

It is well documented that AF2 produces unrealistic conformations of IDRs [47]. However, AF2 still effectively identifies IDRs in its 3D models by assigning them low confidence values [48] and it can model IDR interactions with globular proteins [49] and their folding upon binding [50]. Additionally, distance predictions from AF2 have been used to drive enhanced MD simulations of IDRs that recapitulate experimental observables like distance distributions [51]. The fact that AF2 can provide such information is remarkable since it was trained mostly on globular proteins.

Several ML methods (typically GMs) have been developed to explicitly model IDR structural ensembles. Here, we will describe transferable GMs for arbitrary sequences, but there are also examples of system-specific models [52]. Transferable generators are attractive since they can help unravel the rules for relating sequence to ensemble and function in IDRs, as exemplified in computationally efficient CG MD studies with CALVADOS [53].

A crucial aspect for ML models targeting IDR ensembles is the origin of the training data. Highly dynamic proteins are underrepresented on the PDB, with few NMR ensembles [54]. An alternative is to train based on simulations, but atomistic explicit solvent MD simulations of IDRs are also scarce. Instead, simulations with lower-resolution models may be used for training. For example, idpGAN [55], among the first transferable IDR generators, was trained on a large dataset of CG MD data performed using the COCOMO model [56]. This strategy can be problematic when the IDR behavior in the simulations is not close to experiments, because ML will inherit simulation inaccuracies [33]. The IDPFold [57] diffusion model instead introduced a different approach. It was pretrained on PDB structures, enriched with NMR ensembles, and then fine-tuned on CALVADOS simulations [53]. The model was shown to capture experimental observables of IDRs, such as Cα chemical shifts and radius-of-gyration, which were probably learned from high-resolution PDB backbones and CG simulations, respectively. Notably, BioEmu was also evaluated on IDRs, obtaining zero-shot ensembles approximating experimental radius-of-gyrations, despite not being trained on IDR data. This further suggests that heterogeneous training using both simulation and experimental data might be a promising approach for developing IDR generators.

A remaining challenge is the extrapolation to IDR sequences significantly longer than what was used for training [33]. Collecting data for long IDR sequences (> 200 residues) is essentially feasible only with CG simulation methods, due to challenges in structurally characterizing longer IDRs in vitro and in silico and further innovations are needed to scale IDP ensemble generation to arbitrary sequence lengths. Approaches like the hierarchical chain growth method [58] might help overcome this limit for GMs trained with short IDRs.

Integrating experimental data

The integration with experimental data is a cornerstone of exploring protein dynamics via computation [59]. Specifically, many impactful studies reshape computational models to match experimental observations, e.g. by using experimental data as restraints or for reweighting generated ensembles. A natural question is how ML methods can be used in this manner as an alternative to classical modeling methods. An approach similar to classical reweighting methods consists in building pools of conformations via ML (e.g.: with AF2-based sampling) followed by a post-processing step to reweight and refine based on experimental data and simulations, as recently exemplified with CryoEM data [60]. However, an alternative, likely more powerful approach is to directly incorporate experimental data during the generative process, which can currently be realized with two main strategies (Figure 1d).

In the first approach experimental data may be incorporated at training time. For example, DynamICE [61] is a system-specific model for IDR ensembles that pioneered a training procedure using a variety of NMR measurements. DEERFold [62] fine-tunes AlphaFold with double electron-electron resonance spectroscopy data. Other experimental sources that have been integrated in this type of models include two-dimensional infrared spectroscopy data [63] and large-scale NMR relaxation data by the recent Dyna-1 model [64].

A second strategy involves general-purpose models that are trained initially without explicitly considering experimental restraints, but restraints are then added as biases at inference time. This allows greater flexibility and mitigates training data requirements. The idea is to guide GM sampling with experimental restraints, similar to how protein design models are steered towards desired structures or functions [65]. This strategy has been mainly implemented in diffusion models of IDR ensembles. Examples include idpSAM [33], which included radius-of-gyrations, and PepFlow [66], which incorporated distance restraints to sample macrocycle structures. Recently, the IDPForge model [67] expanded on this idea, allowing to include NMR restraints, radius-of-gyration values, and structural information from folded domains.

Recently, integrative techniques have been implemented into AlphaFold and applied to globular proteins. The ROCKET algorithm [68] optimizes AF2 prediction to better match X-ray crystallography or CryoEM data, aiding model building of flexible regions. The experiment-guided AlphaFold3 protocol [69] integrates crystallographic electron densities or NMR restraints into the diffusion process of AF3, similarly refining dynamic regions to match experiments.

Outlook and challenges

ML methods for modeling protein dynamics and ensembles have rapidly evolved and are turning into useful tools beyond proof-of-principle implementations. Thanks to increased transferability, broader applications are now foreseeable. Despite these advances, PDB- and simulation-based models still face challenges.

As data-driven methods, their assessment requires careful train/test splits, yet consensus criteria are lacking. Sequence-transferable models often rely on splits based on sequence similarity, with reported thresholds of 20% [34] to 40% [39]. However, even distant homologs may share dynamics [70]. Since the goal is to explore novel structural states, we suggest that future studies should directly compare training and test ensembles [12] to exclude overlapping states, with application-dependent stringency. Another challenge is the scarcity and non-uniformity of training data. Currently, three major sources are used: experimental structures [5], predicted structures [41] and simulations [36,38]. Multi-source methods have shown promise [38,57]. Going forward, building larger datasets will be crucial, but universal transferability may have unfeasible data requirements. Thus, algorithms that reduce data dependence, such as neural networks with better inductive biases [71] and hybrid physics-ML strategies[72] are equally essential. This is crucial for modeling larger systems, as existing methods have been tested for monomeric sequences from 10 [33] to ~700 residues [18], while there is no evidence yet of extrapolation to significantly larger proteins or multimeric complexes.

There are also task-specific challenges. For models generating PDB-like structures, a significant unsolved issue is how to reliably generate different states with correct relative probabilities [10,12]. Without this capability, it remains difficult to determine which novel alternative states not already known in the PDB are biologically relevant: important states may not be captured by the model, while some of the generated states may have very low probability and may thus be irrelevant for biological function.

For MD approximators, enhancing conformational transferability is one of the main challenges. Current GMs do not yet capture full energy landscapes observable in long MD simulations and do not learn correct free energies, even for small proteins [34,39]. The scarcity of long simulation datasets is a bottleneck. Available datasets are valuable for developing novel proof-of-principle techniques [27,29], but the limited number of proteins prevents training transferable models [39]. Recently, MD datasets with thousands of systems have been released [36,38], but their trajectories cover only sub-microsecond time scales, insufficient for learning long timescale dynamics. Differences in protocols (e.g.: force field) also complicate integration when training. Developing larger MD databases will be crucial to further advance ML methods.

Furthermore, the problem of incorporating environmental factors has only recently started to be addressed [34,35]. Modeling the effect of the environment, such as temperature or molecular crowding effects, is straightforward for classical simulation methods, but presents significant challenges for ML. Additionally, ensuring consistency with experimental behavior while training on approximate simulation methods remains problematic. One approach could be to apply ML quantum potentials for sampling training data to reach better experimental agreement [73]. The alternative is to integrate experimental data during training or inference. A challenge for the latter, is the lack of a rigorous theoretical framework that puts biased ML sampling on a similar footing with frameworks developed for integrative structural biology and classical simulations such as those based on probability and Bayesian inference [59].

As ML approaches for generating structural ensembles of proteins have developed rapidly in recent years, we envisage further advances and broader applications of ML in protein biomolecular dynamics research.

Highlights.

• Emerging ML methods extend protein structure prediction to the generation of structure ensembles.

• ML methods can accelerate and substitute traditional simulations.

• ML sampling is attractive for the rapid generation of ensembles for disordered peptides.

• Applications of ML sampling within integrative modeling frameworks remain challenging.