AlphaFold-RandomWalk and AlphaFold-Ensemble: sampling alternative protein conformations with perturbed versions of AlphaFold

Abstract

The ability of proteins to adopt multiple conformations is fundamental to their biological function. With the advent of AlphaFold, machine learning (ML)-based methods have extended their capabilities to more broadly sample this intrinsic conformational diversity. However, the extent to which ML approaches can independently generate ensembles of diverse and biologically relevant conformations remains an open question. We sought to tackle this challenge by developing AlphaFold-RandomWalk (AF-RW) and AlphaFold-Ensemble (AF-Ensemble), novel ML-based methods to generate diverse protein conformations. As opposed to traditional approaches which rely on modifying the input multiple sequence alignment, AF-RW systematically adds noise to the weights of the model on a per-target basis, significantly increasing the conformational diversity of predicted models compared to conventional methods. AF-Ensemble takes the complementary approach fine-tuning an ensemble of models to produce diversity from a set of two-state systems. Additionally, both methods were incorporated into an automated, multistage computational pipeline that seeds unbiased molecular dynamics simulations from ML-generated conformations to efficiently sample alternative conformations. When evaluated on a diverse set of ten proteins, our pipeline provided useful, MD-guided hypotheses for determining biologically meaningful alternative conformations. Moreover, simulations seeded from diverse ML-generated conformations provided a reasonable approximation to the free energy landscape of two challenging protein targets, K-Ras and ribose-binding protein. Overall, our work highlights the potential of combining diverse conformations generated by perturbing the weights of AF with molecular dynamics simulations to efficiently probe protein conformational heterogeneity.

Graphical Abstract

INTRODUCTION

Predicting the three-dimensional (3D) structure of a protein has been a defining challenge of computational biology for decades. Leveraging the latest advances in machine learning (ML), methods such as AlphaFold2 (AF2)¹ and AlphaFold3² have demonstrated that monomeric protein structures can be predicted with very high accuracy given evolutionary sequence information encoded in a multiple sequence alignment (MSA). While remarkable, proteins are dynamic, flexible, and can adopt different 3D configurations (i.e., conformations) depending on their biological context^3,4. It is natural to ask if ML-based approaches can aid in predicting different conformations a protein is likely to adopt.

Various methods building upon AF2 have been proposed to increase the conformational diversity of model predictions^5–7. One category of methods is based upon subsampling the input MSA. AFSample2 randomly masks columns of the MSA to diminish the constraints encoded by co-evolutionary signals⁵. Another method, AFCluster, relies on clustering sequences by sequence similarity to partition the MSA into discrete subgroups⁶. A second category of methods leverages Dropout⁸, a regularization method used to train neural networks that can be applied at inference time to induce stochasticity in the model’s output by randomly setting a proportion of the network’s weights to zero. This approach has been explored both in the context of monomer and multimer prediction^5,9. In general, these methods generate more diverse conformations than standard AF2, but the degree of diversity can be lacking for certain systems.

While potentially useful as standalone predictions, leveraging them with physics-based approaches such molecular dynamics (MD) simulations may supplement their utility^10,11. This can be especially important due to potentially aphysical or high energy conformations generated when AF2 is modified. Compared to machine learning approaches, MD simulations have the potential to sample conformations in a manner whose probabilities are distributed according to the true data-generating Boltzmann distribution¹². Indeed, multiple works have explored seeding unbiased MD simulations from AF2-based conformations and then constructing Markov state models to accelerate sampling of their free energy landscape^13,14. Complementary to this approach, works have also explored seeding short MD simulations from AF2-based conformations and then using them as input to train ML models to identify collective variables for enhanced sampling^15–17. In this work, we sought to further explore whether seeding unbiased MD simulations from AF2-based conformations can 1) adequately sample the free energy landscape of proteins whose landscapes have been previously well-characterized and 2) provide MD-guided hypotheses of relevant alternative conformations for proteins without known landscapes. These two evaluations are complementary: the first serves as a more rigorous thermodynamic benchmark, while the latter addresses the typical scenario where a free energy landscape has not been previously well-characterized. We also investigated to what extent the diversity of ML-generated conformations influences the quality of the resulting free energy landscape and hypotheses of potential alternative conformations.

We make two specific contributions towards these overarching objectives. Firstly, we developed an automated, multistage computational pipeline that seeds unbiased MD simulations from ML-generated conformations. Briefly, the pipeline extracts a representative subset of ML-generated conformations, programmatically corrects for a broad set of structural violations, runs unbiased MD simulations for each of them, and finally clusters the aggregate set of MD frames into a reduced set of states. Towards investigating the effect of conformational diversity, we developed two AF2-based methods (AlphaFold-RandomWalk and AlphaFold-Ensemble) to generate significantly more diverse conformations compared to conventional methods that rely on modifying the input MSA. AlphaFold-RandomWalk accomplishes this by systematically adding noise to the weights of the model while AlphaFold-Ensemble accomplishes this via an ensemble of fine-tuned versions of AF2 trained to predict a specific protein’s alternative conformation. Overall, our end-to-end computational pipeline reasonably approximates the free energy landscape of proteins whose landscapes have been previously well-characterized. In addition, when evaluated on a diverse set of ten proteins without known landscapes, our pipeline aids in reliably identifying biologically meaningful conformations as well as potentially relevant intermediate states. Overall, our work highlights the potential of combining diverse, ML-generated conformations with MD simulations to efficiently probe protein conformational heterogeneity.

RESULTS

Our computational pipeline consists of five stages (Fig.1): 1) An AF2-based method generates a large number of candidate conformations (300 were generated for the purposes of this study). We explored two methodologies: 1a) AlphaFold-RandomWalk (AF-RW), our approach based on systematically adding noise to the weights of the model (Supp. Fig. 1A) and 1b) AFSample2, a thoroughly validated MSA column masking approach⁵. 2) Agglomerative clustering is used to select a representative set of 10 conformations as starting structures for MD simulations. 3) Each structure is then refined to correct structural violations. 4) Unbiased MD simulations are run with OpenMM for each conformation for at least 100 ns. 5) A density-based clustering algorithm is finally applied to group the aggregate set of MD frames into a reduced set of macrostates. Macrostates are then characterized by their relative population and deviation from the initial AF2 prediction to facilitate further structural investigation. For reference, we refer to the entire computational pipeline as PAF-MD (Perturbed versions of AlphaFold with Molecular Dynamics).

Figure 1. Overview of the computational pipeline (PAF-MD).

An AF2-based method first generates hundreds of candidate conformations. Here, we highlight AlphaFold-RandomWalk, which systematically adds noise to the weights of the model. Agglomerative clustering is then used to select a representative set of conformations as starting structures for MD simulations. Each structure is then refined to correct structural violations followed by running unbiased MD simulations. A density-based clustering algorithm is finally applied to group the aggregate set of MD frames into a reduced set of macrostates.

AF-RW induces more conformational diversity than AFSample2

To evaluate our pipeline’s ability to provide useful hypotheses of alternative conformations, we curated a refined dataset of ten proteins adopting at least two distinct conformations from existing datasets benchmarking MSA subsampling methods^5,18. Structures in this dataset span diverse protein families with lengths ranging from 221 to 715 amino acids. In addition, five out of the ten proteins have at least one experimentally determined structure corresponding to either the open or closed state released after AF2 training date cutoff. For reference, we refer to this dataset as the “Conformational states dataset”, with further details provided in the Methods section.

To assess and compare the conformational diversity of conformations generated via AF-RW and AFSample2, we generated two-dimensional Principal Component Analysis (PCA) plots of 50 representative conformations’ C-alpha pairwise distances for proteins from the conformational states dataset (Fig. 2). Residues corresponding to predicted N or C-terminal disordered tails were excluded from the C-alpha pairwise distance calculation (see Methods for further details). Overall, the larger spread of AF-RW derived points in the PCA plots suggests that AF-RW generates more diverse conformations compared to AFSample2. This observation is more apparent when superimposing representative structures derived from each method (Supp. Fig. 2). Interestingly, for proteins where AFSample2 yields discrete clusters of points (P30878, P43005, and P62495), AF-RW appears to sample conformations in a more continuous manner (Fig. 2).

Figure 2. PCA plots of representative conformations generated by AF-RW and AFSample2.

Each facet corresponds to a unique protein in the conformational states dataset and is specified by its UniProt ID. The corresponding percentage of explained variance attributed to the first two components is specified next to each UniProt ID in parentheses. Each point represents a specific conformation’s C-alpha pairwise distances projected onto its first two principal components. For reference, each conformation underwent our refinement procedure to correct structural violations. Red points correspond to conformations generated by AFSample2 and blue points correspond to conformations generated by AF-RW. The “X”/“+” refers to the initial AF2 prediction made by either AF-RW or AFSample2.

MD simulations initiated from AF-RW or AFSample2 derived conformations can approximate the free energy landscapes of RBP and K-Ras

To assess how well MD simulations seeded from conformations derived from AF-RW or AFSample2 can sample a protein free energy landscape (FEL), we applied the first four stages of our pipeline to two proteins that exhibit at least two well-defined and biologically relevant states: ribose-binding Protein (RBP, UniProt ID: P02925) and Kirsten rat sarcoma virus (K-Ras, UniProt ID: P01116). The FELs of both proteins have been previously characterized and can be described by pairs of physical and easy-to-interpret collective variables (CVs) simplifying the subsequent analysis and interpretation of results^19–22. For RBP, the CVs correspond to a hinge angle (the angle between the center-of-mass of three groups of residues) and a twist angle (the dihedral angle between the center-of mass of four groups of residues). For KRAS, the CVs correspond to the C-alpha distance between G12/T35 and T35/G60. The reference landscapes were generated via well-tempered metadynamics simulations, using these previously defined CVs, as described in the Methods section.

For RBP, the metadynamics-derived landscape reveals a broad minimum spanning a hinge/twist angle ranging from 120–150/75–125 degrees. The closed conformation lies outside this minimum and within the next lowest free energy contour. Conformations from both AF-RW (magenta circles) and AFSample2 (white crosses) sample regions in the landscape within vicinity of the experimentally-determined open and closed structures. Qualitatively, unbiased MD simulations seeded from AF-RW more accurately approximates the minimum than simulations seeded from AFSample2. Interestingly, both sets of simulations reveal a second minimum adjacent to the closed structure that is not captured in the metadynamics-derived landscape.

For K-Ras, the metadynamics-derived landscape reveals two distinct minima located approximately at a G12 and T35 C-alpha distance/T35 and G60 C-alpha distance of 1.1/0.75 nm, and 2.4/1.75 nm (Fig. 3B). Conformations from both AF-RW (magenta circles) and AFSample2 (white crosses) are distributed across both minima. The AF-RW derived landscape reveals one of the minima that spans a subset of the metadynamics-derived minimum located at 1.1/0.75 nm. Although simulations seeded from AFSample2 do not reveal this minimum, they do partially reveal the other minimum located at 2.4/1.75 nm. Notably, simulations seeded from both AF-RW and AFSample2 conformations capture both minima and provide the best approximation to the metadynamics-derived landscape.

Figure 3. Free energy landscape analysis for RBP and K-Ras.

A) FELs for RBP projected onto hinge and twist angles. B) FELs for K-Ras projected onto two key distances (G12–T35 and T35–G60). Columns from left to right correspond to FELs computed using: (1) metadynamics simulations, (2) unbiased MD simulations seeded from a combined ensemble from AF-RW and AFSample2, (3) unbiased MD simulations seeded from AF-RW and the default AF prediction, (4) unbiased MD simulations seeded from AFSample2 and the default AF prediction, and 5) unbiased MD simulations seeded from the default AF prediction alone. Conformational ensembles generated with AF-RW and AFSample2 are shown as magenta circles and white crosses, respectively. Experimentally determined structures corresponding to functionally relevant states are shown as black markers. The free energy is shown in kcal/mol, with lower-energy states in blue indicating more favorable conformations.

For reference, unbiased MD simulations seeded from the default AF prediction were also run for the cumulative amount of time as the simulations seeded from the AF-RW/AFSample2 conformations (Fig. 3, Supp. Fig. 3). This would represent a typical real-life scenario where a researcher predicts a single structure with AlphaFold and then performs unbiased MD simulations to refine the initial prediction and/or to explore the conformational landscape around the starting conformation. Overall, these landscapes are confined to a specific subregion and qualitatively perform the worst at reproducing the overall FEL.

MD simulations initiated from AF-RW or AFSample2 derived conformations can preferentially sample both the ground-truth open and closed conformation

After generating conformations via AF-RW or AFSample2, agglomerative clustering was applied to select a representative set of 10 conformations (one from each cluster) to be used as starting structures for MD simulations. The initial AF2 prediction was also included, resulting in 11 unique simulations run for each method. Conformations from each cluster superimposed with respect to their corresponding ground-truth states are provided in Supp. Figs 5–14 for each system/method. After refining each starting structure to correct structural violations, unbiased MD simulations were run with OpenMM for 250 ns (except for M1VAN7 and P62495 which were run for only 100 ns due to their larger size). We analyzed the results of each MD simulation by quantifying their structural similarity via the TM-score to either the open or closed state. This was done for both conformations generated via AF-RW (Fig. 4) and AFSample2 (Fig. 5).

Figure 4. TM-Score distributions by cluster for conformations generated by AF-RW.

Each facet corresponds to a unique protein in the conformational states dataset and is specified by its UniProt ID. The x-axis corresponds to the conformation used to seed each MD simulation (clusters 0–9 or the initial AF2 prediction). For each frame in each simulation, the TM-score was calculated with respect to the open or closed conformation. Clusters that are underlined in yellow or pink correspond to ones that are biased towards the open or closed conformation, respectively. Figures in the top row correspond to proteins where at least one macrostate was biased towards the open or closed state and at least another macrostate was biased towards the corresponding alternative state. Figures in the bottom row correspond to proteins where this was not the case.

Figure 5. TM-Score distributions by cluster for conformations generated by AFSample2.

Each facet corresponds to a unique protein in the conformational states dataset and is specified by its UniProt ID. The x-axis corresponds to the conformation used to seed each MD simulation (clusters 0–9 or the initial AF2 prediction). For each frame in each simulation, the TM-score was calculated with respect to the open or closed conformation. Clusters that are underlined in yellow or pink correspond to ones that are biased towards the open or closed conformation, respectively. Figures in the top row correspond to proteins where at least one macrostate was biased towards the open or closed state and at least another macrostate was biased towards the corresponding alternative state. Figures in the bottom row correspond to proteins where this was not the case.

Results for a given system were considered successful if at least one simulation was biased towards sampling the open state and at least one simulation was biased towards sampling the closed state. A simulation was biased towards sampling a given state if 1) the median TM-score corresponding to that state was greater than 80 and 2) the interquartile range of its TM-score distribution did not overlap with that of the other state. Given this criterion, conformations derived from both AF-RW and AFSample2 achieved success for half of the proteins. For the five failures, three were consistently biased towards the closed state, while for the remaining two, there did not appear to be a consistent bias towards either state.

Results on this benchmark were also compared to BioEmu²³, a generative deep learning model trained on structural and MD simulation data, that was shown to be capable of sampling relevant protein conformational changes and emulate equilibrium distributions generated by high-throughput MD. While BioEmu generated a diverse set of conformations comparable to AF-RW (Supp. Fig. 15), they were generally biased towards a specific state (Supp. Fig. 16 and 17). We also extended our comparison to a specific target (Angiopoietin-1 receptor, UniProt ID: Q02763) with a cryptic pocket that was previously benchmarked by BioEmu but posed a challenge for the model to sample. While the initial AF2 prediction was biased towards the holo state, AF-RW preferentially sampled an ensemble of relevant conformations around the pocket that more faithfully reproduced its geometry (Supp. Fig. 18).

Macrostates derived from MD simulations can provide useful hypotheses for determining relevant alternative conformations

After running the unbiased MD simulations, a previously validated methodology to cluster MD frames was adapted and applied to group the aggregate set of MD frames into a reduced set of macrostates. The macrostate relationships are summarized in a dendrogram, in which similar macrostates are grouped together according to their respective transition probabilities (see Methods for details). We note that we are not making any thermodynamically-based claims regarding the relative probabilities of these macrostates. Rather, we view the dendrogram-based representation as an efficient way to probe potentially relevant alternative conformations in an MD-guided manner when the ground-truth is not known.

Our results can be summarized in two categories. The first category consists of proteins where medium to highly populated macrostates preferentially sample conformations biased towards at least two of either open, closed or intermediate conformations (i.e. ranging between open and closed). The second category consists of proteins where medium to highly populated macrostates are uniformly biased towards either the open or closed conformation.

The proteins that can be grouped into the first category include: ABC1 family protein (A0QTT2) (Fig. 6), PotF (P31133), beta-phosphoglucomutase (P71447), sugar ABC transporter (Q53W80), excitatory amino acid transporter 3 (P43005), and prolyl endopeptidase (O76728) (Supp. Figs. 19–23, respectively). For ABC1 family protein (A0QTT2), PotF (P31133), and beta-phosphoglucomutase (P71447), conformations were biased towards either the open, closed, or intermediate conformations. For sugar ABC transporter (Q53W80) and excitatory amino acid transporter 3 (P43005), conformations were biased towards either the open/outward or closed/inward conformation. For prolyl endopeptidase (O76728), conformations were biased towards either the closed or intermediate conformations. Proteins in the second category include ycf16 (M1VAN7), peptide chain release factor subunit 1 (P62495), melibiose permease (P30878), and 5’-nucleotidase (P21589) (Supp. Figs. 24–27, respectively). For ycf16 (M1VAN7) and peptide chain release factor subunit 1 (P62495), conformations were biased towards intermediate conformations. For melibiose permease (P30878) and 5’-nucleotidase (P21589), the conformations were exclusively biased towards the inward/closed conformation.

Figure 6. Dendrogram-based representation of AF-RW derived macrostates for A0QTT2.

In the top-left of the figure, the ground-truth open and closed conformation are superimposed alongside TM-Score distributions with respect the open/closed conformation as a function of macrostate. The dendrogram summarizes macrostate relationships, in which similar macrostates are grouped together according to their respective transition probabilities. Each node (i.e., macrostate) in the dendrogram is colored according to its average RMSD with respect to the initial AF2 prediction and its edge thickness is weighted according to the relative percentage of MD frames grouped in that macrostate. The percentage of non-excluded MD frames represented in the dendrogram is specified in the title of the dendrogram (see Methods for further details regarding the criteria used to exclude a macrostate). Below the dendrogram, the initial AF2 prediction is superimposed with respect to the open and closed conformation. Residues from the initial AF2 prediction are colored by their corresponding pLDDT score. For relevant macrostates in the dendrogram (i.e., medium to high population states that span the dendrogram), a representative MD conformation is highlighted and colored by its corresponding root-mean square fluctuation (RMSF). The cluster from which the MD frame was sourced from (0–9 or initial) is specified below the conformation. For A0QTT2, conformations were biased towards either the open, closed, or pseudo intermediate conformations.

Overall, distributional biases in the structural similarity towards the open or closed conformation as a function of macrostate were similar between AF-RW and AFSample2 (Supplementary Figs. 29 and 30). Prolyl endopeptidase (O76728) was the notable exception, where we observed that simulations seeded from AF-RW conformations were more strongly biased towards the open state compared to simulations seeded from AFSample2 (Supplementary Fig. 31).

Using an ensemble of fine-tuned AlphaFold models to generate further conformational diversity and probe elusive conformations

For three out of five systems neither AF-RW or AFSample2 were able to fully recover the alternative conformation. To address this, we explored the capabilities of a hybrid approach (termed AF-Ensemble) to generate alternative conformations. Briefly, we constructed a carefully curated dataset of 566 proteins adopting two different, experimentally-determined conformations and created 566 unique fine-tuned AF2 models (Supp. Fig. 1B). For each protein in this dataset, each model was fine-tuned to predict the conformation that the default AF2 model predicted with lower accuracy (determined via the default AF2 prediction’s RMSD with respect to each reference conformation). For each model, we then generated five unique predictions with column masking applied to the input MSA. The intuition behind this approach is that each fine-tuned model can potentially make larger ‘jumps’ in conformational space while MSA column masking can augment each prediction by inducing more local perturbations. Further details regarding AF-Ensemble are provided in Methods.

For prolyl endopeptidase (O76728), 5’-nucleotidase (P21589), and ycf16 (M1VAN7), distinct clusters of conformations emerged that were significantly biased towards the conformation not fully captured by AF-RW or AFSample2 (Fig. 7, Supp. Figs. 6–8 and 32). Melibiose permease (P30878) and peptide chain release factor subunit 1 (P62495) remained challenging targets where AF-Ensemble was unable to recover the alternative conformation (Supp Figs. 9 and 10). However, for melibiose permease, we observed a cluster of conformations featuring a distinctive domain movement positioned in an intermediate state between inward and outward orientations (Supp. Fig. 9). Finally, we note that while AF-Ensemble did produce diverse sets of conformations, some of the clusters that emerged may correspond to physically unlikely states (e.g cluster 3 for P21589 (Supp. Fig. 7), cluster 0 for M1VAN7 (Supp. Fig. 8), cluster 4 for P62495 (Supp. Fig. 10)).

Figure 7. AF-Ensemble predictions for challenging proteins.

In the first row, the initial AF2 prediction is superimposed with the state that it does not predict. This corresponds to the open state for prolyl endopeptidase (O76728) and 5’-nucleotidase (P21589), and the closed state for ycf16 (M1VAN7). In the second row, this state is superimposed with conformation(s) from AF-Ensemble that are significantly biased towards it. Black boxes highlight regions in each protein where the initial AF2 prediction favors the alternative state whereas AF-Ensemble does not. For P21589, corresponding residues in the open and closed state are colored black to highlight the dramatic conformational change.

A case study showcasing the ability of PAF-MD to aid in structure-based drug discovery

Traditional molecular docking approaches treat the target receptor as rigid, so selecting a representative structure or ensemble of structures for docking is an important factor influencing docking success. We reasoned that a targeted application of PAF-MD would be to generate an ensemble of conformations with varying druggability properties spanning the apo, holo, and potentially relevant intermediate states. To assess pocket druggability, we leveraged Fpocket, a protein pocket detection tool, that calculates a druggability score reflecting the likelihood a pocket will bind drug-like molecules²⁴. From the APOBind dataset, we found an enzyme (UDP-N-acetylmuramoyl-L-alanine—D-glutamate ligase, UniProt ID: P14900) where the default prediction of AF2 is biased towards the holo conformation (RMSD of 1.1 angstroms), yet has a low druggability score (.01) relative to that of the native, ligand-binding pocket (druggability score of .70). Given the low druggability score of the default AF2 prediction, we applied PAF-MD to generate an ensemble of conformations and assessed if a relevant subset of these conformations contains native-like pockets with higher druggability scores. Starting structures used for MD simulations generated by AF-RW span a diverse set of states between the apo and holo conformation (Supp. Fig. 33). Overall, PAF-MD yielded macrostates that were generally biased towards the holo conformation, except for macrostate 11 which was biased towards the apo conformation (Fig. 8, Supp. Fig. 34). From a druggability standpoint, we observe that select conformations from the six most populated macrostates (1–5 and 11) contain native-like pockets that are predicted to be at least or more druggable than the native, ligand-binding pocket according to Fpocket’s computed druggability score (Fig. 8B). Importantly, conformations with favorable druggabilty profiles were sourced from a diverse set of AF-RW conformations (i.e., clusters 0, 3, 5, 6, and 8) and grouped across multiple macrostates that varied in terms of their degree of bias towards the holo state.

Figure 8. Assessing the ability of PAF-MD to generate relevant conformations for structure-based discovery.

A) TM-Score distributions with respect to the apo/holo conformation as a function of macrostate. Below the macrostate number on the x-axis, the percentage of frames that were assigned to it are specified. B) For conformations in the six most populated macrostates (1–5 and 11), Fpocket’s computed druggability score is plotted as a function of each cluster each conformation is sourced from. The top dotted line corresponds to Fpocket’s computed druggabilty score for the native, ligand-binding pocket from the holo conformation while the bottom dotted line corresponds to Fpocket’s computed druggability score for the default AF2 prediction. For reference, the numerical druggability score is notated next to relevant points. Our results are restricted to pockets who shared at least 35% of the residue vertices defining the holo pocket.

DISCUSSION

Using ML-based approaches to probe protein conformational heterogeneity is an exciting research frontier. However, it remains an open question to what extent machine learning approaches can independently generate ensembles of diverse conformations that capture biologically relevant conformations¹⁰. Furthermore, it remains unclear if machine learning approaches can independently and reliably assess which conformations among the ones generated actually correspond to biologically relevant conformations. To the best of our knowledge, there is no strong evidence suggesting that confidence metrics such as the pLDDT score are able to distinguish relevant conformations among an ensemble of predictions^6,25. Leveraging ML-generated conformations with physics-based simulations may be a fruitful direction to address this gap. Indeed, a result supported by our work is that seeding unbiased MD simulations from ML-generated conformations can aid in approximating a protein’s FEL when the CVs are well-defined and provide useful MD-guided hypotheses for determining relevant alternative conformations when the CVs are not well-defined.

An important methodological advancement of this work are approaches to induce conformational diversity by modifying the weights of AF as opposed to modifying the MSA. AF-RW accomplishes this by systematically adding noise to the weights of the model and AF-Ensemble accomplishes this by generating hundreds of fine-tuned versions of AF2 trained to predict a specific protein’s alternative conformation. AF-RW can be viewed as a complementary approach to MSA subsampling: while MSA subsampling effectively adds noise to the input, AF-RW holds the input fixed and adds noise to the model. We note that while AF-Ensemble seems like an orthogonal approach to AF-RW, theoretical work in modeling the dynamics of stochastic gradient descent trajectories often approximates the gradient of a single data point as the full batch gradient plus Gaussian noise²⁶. Hence, in some sense, each model in AF-Ensemble, which is fine-tuned with respect to a single datapoint, can be viewed as adding noise to the base AF2 model but in a more structured manner.

Our results demonstrated that AF-RW generated a significantly more diverse set of conformations compared to AFSample2 for the majority of proteins we evaluated. For K-Ras and RBP, conformations from AF-RW were consistently distributed across each protein’s respective minima. Both methods resulted in a coarse approximation of the metadynamics derived FEL, and seeding simulations from both AF-RW and AFSample2 appears to provide the most comprehensive representation of the overall landscape. Testing AF-RW and AFSample2 across more proteins with known CVs and running MD simulations from a larger number of starting structures can help provide a more definitive assessment of each method’s ability to sample FELs and suggest directions for further improvements.

Importantly, we evaluated our overall pipeline (PAF-MD) on proteins without known CVs. For half of the evaluated proteins, there was at least one macrostate biased towards either the open or closed state and at least another macrostate biased towards the respective alternative state. While more challenging to validate the thermodynamic relevance of our pipeline in a prospective scenario, our results suggest inspecting conformations from macrostates hierarchically grouped by their metastability criterion is a meaningful approach to probe biologically relevant conformations. Future work could evaluate our pipeline on proteins whose relative populations of different functional states have been experimentally characterized through techniques such as NMR and smFRET^27,28. This would enable one to correlate macrostate populations with experimentally determined fractions and thus assess the thermodynamic relevance of our macrostate population distribution.

Overall, macrostates derived from MD simulations seeded from AF-RW and AFSample2 yielded similar distributional biases. With that said, results from prolyl endopeptidase (O76728) highlight a specific case where a significant increase in conformational diversity induced by AF-RW led to MD simulations sampling conformations more biased towards the otherwise unsampled alternative state. For challenging targets, where neither AF-RW nor AFSample2 sampled conformations biased towards the alternative conformation, AF-Ensemble represents a promising approach to explore such states. 5’-nucleotidase (P21589) highlights a specific case where a dramatic conformational rearrangement between the open and closed state is exclusively sampled by AF-Ensemble. More generally, both AF-RW and AF-Ensemble highlight that modifying the model’s weights is a useful alternative approach for instances where subsampling the MSA does not induce significant diversity.

Compared to AF2 and AF2-based models, generative models such as BioEmu generate predictions through a reverse denoising process modeled via a stochastic differential equation²³. Hence, stochasticity is embedded in the model framework itself. While BioEmu generated a diverse set of conformations on our benchmarks, it is difficult to make standardized comparisons with our methods as BioEmu was trained on both structural and MD simulation data while AlphaFold was trained on only structural data. Nonetheless, generative models provide an additional lever to induce stochasticity that can be combined with other approaches such as MSA subsampling or perturbing the model weights. In theory, each of these approaches can be applied to general purpose biomolecular interaction models like AlphaFold3², and using them to probe protein-protein and protein-ligand interactions represents an exciting avenue for future work. A potential interesting future extension of AF-RW would be to constrain the noise addition process to a subset of the network in order to selectively induce diversity (i.e., ligand only).

Regardless of the method used to generate conformations, work remains to robustly integrate these diverse conformational ensembles into an MD pipeline. The increased number of generated conformations can introduce low-quality or “junk” structures, a trend observed in certain AF-Ensemble outputs. Future work could address this by developing more sophisticated clustering or filtering techniques to exclude thermodynamically improbable states. Alternatively, training with additional data sources such as MD data and relevant experimental measurements may enable a model to directly encode thermodynamic information. This approach was implemented by BioEmu, but it remains unclear to what extent empirical approaches can sample from a Boltzmann or Boltzmann-like distribution²³. When evaluating BioEm on our conformational states dataset, we observed cases where its predictions were exclusively biased towards a specific state.

There are multiple considerations to interpreting results from our MD simulations. In the absence of well-defined CVs for a system, we used inter-residue distances and contacts as input PCA features for clustering our MD frames into macrostates. While we removed predicted N or C-terminal disordered tail residues that could exhibit large amplitude motions during a simulation and corrupt the signal-to-noise ratio, there could be other sources of irrelevant motions sampled during a simulation that could skew PCA features. In addition, the relative probabilities of our macrostates should be interpreted with caution, especially given the relatively short aggregate simulation times and the fact that specific conformations may be only stabilized in the presence of a relevant ligand, cofactor, or binding partner.

From an application standpoint, our pipeline could be used within numerous contexts spanning molecular dynamics, structural biology, and computational drug discovery. For instance, AlphaFold2-Rave is an MD protocol that uses an autoencoder to learn CVs from unbiased MD simulations seeded from AF2, MSA subsampled conformations¹⁵. Seeding MD simulations from a more diverse set of conformations derived from AF-RW or AF-Ensemble could facilitate the discovery of more informative CVs to improve the sampling of a protein’s FEL. In the context of cryogenic electron-microscopy (cryo-EM), our pipeline could aid computational methods such as DiffModeler that leverage predicted AF2 monomeric structures to model large protein complexes captured at intermediate resolutions²⁹. A candidate set of conformations derived from PAF-MD could help to account for the uncertainty within an intermediate resolution EM density map. Lastly, from a computational drug discovery perspective, conformations assigned to populated macrostates could be screened for distinct and diverse druggabilty properties. These conformations could be used to perform ensemble docking and potentially increase the likelihood of finding hits in a virtual screen³⁰.

METHODS

MSA generation

For each protein, we fetched an MSA from the OpenProteinSet, a database of precomputed MSAs encompassing all Protein Data Bank (PDB) chains used in AF2’s training set and more than 16 million MSAs for each cluster in Uniclust30³¹. This database was used to train OpenFold, a reproduction of AF2 implemented in PyTorch³².

Models used

We used the original AF2 model weights, specifically params_model_3_ptm. Templates were disabled during model inference.

AFSample2

As a reference method for generating ML-derived conformations, we use an MSA column masking approach with a masking probability of 15 percent (this method is referred to as AFSample2). Kalakoti et al. determined this masking percentage as optimal, and demonstrated AFSample2 outperforms AFCluster and standard AF2 with dropout in its ability to sample different conformational states⁵. For each protein in our evaluation dataset, we generated 300 conformations using this method. Timing information for running AFSample2 on an 80 gigabyte NVIDIA A100 GPU is summarized in Supplementary Fig. 35.

AF-RandomWalk

The basic idea behind our approach is to iteratively add noise to all layers in the Evoformer and ExtraMSAStack modules of AF2. We aimed to do this in a systematic manner such that the noise is large enough to induce significant conformational changes while not completely corrupting the model weights. The amount of noise added is partially governed by a fixed acceptance criterion, which determines whether to continue adding noise to the weights or to restart the noise addition process from scratch. A conceptual schematic of this method is highlighted in Supp. Fig. 1A.

Instead of generating a noise vector whose dimensionality corresponds to the number of weights in the model we want to perturb, we generate a noise-vector in a lower dimensional space that updates the weights from a given layer via: ${\theta }^D={\theta }_0^D+P({\theta }^d)$, where ${\theta }_0^D$ represents the original D-dimensional weights for a given layer of the model, ${\theta }^d$ is sampled from a multivariate normal distribution, and $P$ is a transformation that projects a parameter from a d-dimensional space into a D-dimensional space where d < D. In our case, P corresponds to a random linear projection computed via the Fastfood transform. Specifically, ${\theta }^D={\theta }_0^D+{(s*\theta }^d)M_{l_i}$, where $s$ is a scaling factor and $M=\mathit{\text{HG}}\Pi \mathit{\text{HB}}.H$ corresponds to a Hadamard matrix, $G$ corresponds to a random diagonal matrix with independent standard normal entries, $B$ corresponds to a random diagonal matrix with ±1 entries, and $\Pi$ corresponds to a random permutation matrix. The matrix multiplication with $H$ is computed in $D\mathit{\text{log}}(d)$ time via the Fast Walsh-Hadamard Transform. A random seed is used to generate $M$, and we generate a unique random seed for each layer of the model such that there is a unique $M$ per layer of the model. This overall approach was originally introduced by Aghajanyan et al. as a mechanism to finetune models in a lower dimensional space³³.

In order to modulate the magnitude of the noise added, we multiply ${\theta }^d$ by a scaling factor $s$. The scaling factor is an input-specific parameter algorithmically determined per protein. To optimally tune the scaling factor, we introduce the idea of a simple acceptance criterion, where we either accept or reject the proposed conformation given $s$ and ${\theta }^d$. Given an acceptance criterion, we can tune $s$ such that the percentage of accepted conformations lies within a given range after repeatedly sampling ${\theta }^d$ n times. More specifically, a simple and efficient binary search-like procedure was implemented that attempts to return a scaling factor that yields an acceptance rate between a and b percent. The initial value of s is then correspondingly either increased or decreased to satisfy the acceptance rate requirements. If multiple scaling factors satisfy the acceptance rate requirements, we picked the scaling factor nearest to (a+b)/2 percent. The default values of n, s, a, and b were set to 10, 10, 65, and 85 respectively. From a user standpoint, higher/lower values of a and b will result in smaller/larger noise levels added per iteration.

In general, we accept a conformation if its average pLDDT score is greater than or equal to 60 and its percentage of unstructured residues is less than or equal to 80 percent. A residue was classified as unstructured if the DSSP algorithm³⁴ assigned it a category of “-”, “T”, or “S”. During this check, we exclude any predicted N or C-terminal disordered tails. The first/last n consecutive residues of a protein are considered an N/C-terminal tail if each of them are predicted to be disordered. We consider a residue predicted to be disordered if its pLDDT score is less than 69. This threshold was sourced from prior work that demonstrated it accurately differentiates between disordered and ordered regions³⁵. From a user standpoint, higher/lower pLDDT score thresholds will result in smaller/larger cumulative amounts of noise added (i.e. the amount of noise added prior to restarting the process).

Our overall approach to generate different conformations consists of three phases, and we provide more algorithmic details below:

Phase 1 (bootstrap phase)

In the first phase, we generate a new conformation by sampling ${\theta }^d$ from a d-dimensional spherical gaussian (i.e., $N_d(0,I)$) and normalizing it to have unit length, and then applying the transformation ${\theta }^D={\theta }_0^D+(s*{\theta }^d)M_{l_i}$ to relevant layers of the model. The scaling factor $s$ is set to a value of 10. We generate a total of 50 conformations, where each model prediction corresponds to a new sample of ${\theta }^d$. Each conformation is either accepted or rejected according to the acceptance criterion outlined above.

Phase 2 (gradient descent phase)

In the second phase, we leverage gradient descent with the end goal of generating ${\theta }^d$ in a more sophisticated manner. The high-level idea is that we finetune the model with respect to ${\theta }^d$ to predict a conformation outputted by the bootstrap phase. The third phase then incorporates information derived from the update trajectory of ${\theta }^d$ induced by gradient descent to sample ${\theta }^d$.

To accomplish this, we first extract the top k conformations from the bootstrap phase with the highest root mean square deviation (RMSD) with respect to the initial AF2 prediction. For this work, k was set to 3. For each conformation, we then apply gradient descent to update ${\theta }^d$ to minimize the loss function (which we set to a linear combination of the AF2 distogram loss with a weight of .3 and AF2 backbone Frame-Aligned Point Error with a weight of 1) between the initial AF2 prediction and the conformation derived from the bootstrap phase. To bias the loss function towards relevant residues, we exclude residues from the FAPE calculation who were predicted to be disordered based upon the initial AF2 prediction or residues between the initial AF2 prediction and target conformation whose Euclidean distance between their corresponding C-alpha atoms was less than 1 angstrom. The extra MSA depth was capped at 1024, unless the sequence length was greater than 600, in which case it was capped at 512. We used Adam with ${\beta }_1=0.9$, ${\beta }_2=0.999$, and ϵ = 1e−5, a learning rate of 1e-2, and trained the model for 10 epochs³⁶. At the completion of this phase, we have k unique update trajectories of ${\theta }^d$ (i.e., ${{\theta }^d(t)}_1,{{\theta }^d(t)}_2,\dots {{\theta }^d(t)}_k$).

Phase 3 (random walk phase)

As opposed to sampling ${\theta }^d$ from a d-dimensional spherical gaussian, we sought to sample ${\theta }^d$ from a multivariate normal distribution of the form $N(0,{\Sigma }_k)$ informed by the update trajectories generated in the previous phase. We generated the covariance matrix ${\Sigma }_k$ via the following formula: $\mathit{\text{diag}}\left(S\right)*C*\mathit{\text{diag}}\left(S\right)$. $S$ corresponds to a diagonal matrix, where the i-th diagonal entry of $S$ corresponds to $\sum {({{\theta }_i^d(t)}_k-{{\theta }_i^d(t-1)}_k)}^2/(N-1)$ (i.e., the standard deviation of the first difference time series of i-th component of ${\theta }^d$). $C$ corresponds to a random correlation matrix generated via the standard angles parameterization method³⁷. We note that there is a unique covariance matrix for each of the k update trajectories of ${\theta }^d$ derived from the gradient descent phase.

To generate a given conformation, we first sample ${\theta }^d$ from $N(0,{\Sigma }_k)$ and apply the transformation ${\theta }^D={\theta }_0^D+(s*{\theta }^d)M_{l_i}$ to relevant layers of the model. If the conformation is rejected, we ‘reset’ and draw a new sample of ${\theta }^d$. Otherwise, we update ${\theta }^d$ in a manner dependent on the previous iteration such that ${\theta }^d(i)={\theta }^d(i-1)+ϵ$ where $ϵ~N(0,{\Sigma }_k)$. For each of the k conformations generated via the bootstrap phase, we sampled ${\theta }^d$ from $N(0,{\Sigma }_k)$ 125 times in order to generate ~100 accepted conformations (due to our target acceptance rate of 75 percent). Because k=3, we generated roughly 300 accepted conformations for each protein in our evaluation dataset.

Timing information for running this portion of the pipeline on an 80 gigabyte NVIDIA A100 GPU is summarized in Supplementary Fig. 36.

AF-Ensemble

We first curated a high-quality dataset of proteins in the PDB adopting two distinct conformations. We leveraged work by the Protein Data Bank in Europe - Knowledge Base (PDBe-KB), who developed an automated data pipeline to cluster proteins in the PDB archive into distinct conformational states³⁸. We used their provided API to find PDBs that 1) were grouped into two distinct clusters and 2) had a corresponding precomputed MSA available in the OpenProtein dataset. We then applied a filtering step to include PDBs whose length ranged between 150 to 500 residues and whose RMSD between their respective states was greater than 15 angstroms. This procedure yielded a dataset of 1096 proteins. From this dataset, we manually inspected each protein and removed a protein if conformational variability was primarily localized to loops or linkers where AF2 identified them as low confidence regions (i.e., pLDDT less than 70). Our overall process yielded a final dataset of 566 proteins with two distinct conformations.

From this dataset, we created 566 unique fine-tuned AF2 models, where each model was fine-tuned to predict the conformation that it was less biased towards. To fine-tune each model, we calculated the RMSD between the initial AF2 prediction and both conformations. Each model was then fine-tuned to predict the conformation with the larger RMSD with respect to the initial AF2 prediction. The loss function was a linear combination of the AF2 distogram loss with a weight of .3 and AF2 backbone Frame-Aligned Point Error with a weight of 1. To bias the loss function towards relevant residues, we exclude residues from the FAPE calculation who were predicted to be disordered based upon the initial AF2 prediction or residues between the initial AF2 prediction and target conformation whose Euclidean distance between their corresponding C-alpha atoms was less than 1 angstrom. We used Adam with ${\beta }_1=0.9$, ${\beta }_2=0.999$, and ϵ = 1e−5, a learning rate of 1e-3, and trained each model for 50 epochs³⁶. Weights were fine-tuned only for layers in the Evoformer module. For inference, we generated five unique predictions for each fine-tuned model with column masking applied to the input MSA. If a given fine-tuned model was trained to predict a conformation whose sequence had at least 80% sequence similarity to the input sequence, it was excluded from the set of models run. Sequence similarity distributions between each input sequence and each of the proteins for which AF-Ensemble was fine-tuned with respect to are presented in Supp. Fig. 37. A conceptual schematic of this method is highlighted in Supp. Fig. 1B.

Conformational states dataset

To evaluate our pipeline’s ability to provide useful hypotheses of alternative conformations, we curated a refined dataset of ten proteins adopting at least two distinct conformations from existing datasets benchmarking MSA subsampling methods. From an open/closed conformation dataset assembled by Kalakoti et al. (entitled OC23), we evaluated our pipeline on seven proteins⁵. From an outward or inward-facing conformation dataset of transporter proteins assembled by Xie et al. (entitled IOMemP), we evaluated our pipeline on three proteins¹⁸. The PDB ID sourced from the OpenProteinSet used to generate the MSA is specified in the third column and corresponds to the wild-type sequence.

UniProt ID	Protein	Source Dataset	PDB ID (MSA)	PDB ID (open)	PDB ID (closed)	AF2 prediction bias	# of residues
A0QTT2	ABC1 family protein	OC23	7cy2_A	7cy2_A*	7cyr_A*	7cy2_A	439
O76728	Prolyl endopetidase	OC23	4bp8_A	4bp8_A	4bp9_A	4bp9_A	715
P21589	5’-nucleotidase	OC23	6vc9_A	4h2f_A	4h2i_A	neither	553
P31133	Putrescine-binding periplasmic protein PotF	OC23	6ye0_A	6yed_B*	6ye0_A	6ye0_A	344
P62495	Eukaryotic peptide chain release factor subunit 1	OC23	1dt9_A	1dt9_A	3e1y_B	1dt9_A	437
P71447	Beta-phosphoglucomutase	OC23	5olw_A	5olw_A	1z4n_A	1z4n_A	221
Q53W80	Sugar ABC transporter, periplasmic sugar-binding protein	OC23	7c63_A	7c63_A*	7c67_A*	7c67_A	416
M1VAN7	Probable ATP-dependent transporter ycf16	IOMemP	3wme_A	3wme_A	6a6m_A	neither	604
P30878	Melibiose permease	IOMemP	4m64_A	4m64_A	7l16_A*	7l16_A	476
P43005	Excitatory amino acid transporter 3	IOMemP	6×2l_B	8cua_A*	6×2l_B*	neither	524

^*indicates that 1) the PDB ID corresponding to a given state was released after AF2’s training date cutoff (training cutoff date (28 August 2019)) and 2) no other PDB IDs corresponding to the same state were released before AF2’s training date cutoff. We made the second determination with PDB in Europe - Knowledge Base’s structural cluster viewer, which partitions all PDB entries corresponding to a given protein into distinct conformational states.

Preprocessing conformations derived from AF-RW or AFSample2

ML-generated conformations are preprocessed prior to running MD simulations. N or C-terminal disordered tails are first removed. The first/last n consecutive residues of a protein are considered an N/C-terminal tail if each of them are predicted to be disordered. We consider a residue predicted to be disordered if its pLDDT score is less than 69.

We then assign each ML-generated conformations to one of 10 unique clusters. Conformations were clustered via agglomerative clustering with a pairwise C-alpha absolute difference score. This approach was used by Ellaway et al. as part of an automated data pipeline to cluster proteins in the PDB archive into distinct conformational states³⁸. Specifically, for each conformation, a C-alpha pairwise distance vector ($C$) is calculated. Then, for each pair of conformations, an absolute difference vector $d^{\mathit{\text{mn}}}$ is computed as $\mathit{\text{abs}}(C_m-C_n)$. Each entry in this vector is set to 0 if $d_{\mathit{\text{ij}}}^{\mathit{\text{mn}}}<=1$. The final mn entry in the distance matrix used by agglomerative clustering corresponds to $\mathit{\text{sum}}\left(d^{\mathit{\text{mn}}}\right)$.

To get the representative conformations for the PCA plots in Fig. 2, conformations were sequentially extracted from each cluster in a repeated manner until there were 50 total conformations. If multiple conformations were assigned to the same cluster, the conformation with the highest pLDDT score was selected.

For the MD simulations, ten conformations (one from each cluster) plus the initial AF2 prediction were then used as starting structures. If multiple conformations were assigned to the same cluster, the conformation with the highest pLDDT score was selected. We refer to this source set of eleven conformations for which MD simulations were run as $C_{\mathit{\text{MD}}}$.

Prior to running MD simulations, we programmatically refined each structure with OpenMM such that there were no clashing atoms, strained side chain bonds, incorrect peptide bond lengths, cis peptide bonds, or amino acids in the D-configuration. We built upon an existing script developed by Quast et al., making it more robust and amenable to high-throughput usage³⁹. We also added functionality to add disulfide bonds, which can either be automatically detected based on if two cysteine residues are within a prespecified distance range or added between prespecified pairs of cysteine residues. In the initial version of our refinement procedure, we automatically detect pairs of cysteine residues with disulfide bonds that exist in the initial AF2 prediction, and then add disulfide bonds to these same pairs of cysteine residues in the ML-generated conformations.

Preprocessing conformations derived from AF-Ensemble

The preprocessing pipeline for conformations derived from AF-Ensemble was similar to that of conformations derived from AF-RW or AFSample2. There are two notable exceptions. Firstly, if a predicted conformation had a pLDDT score less than 70 or its percentage of unstructured residues was greater than 70%, it was excluded from the set of candidate conformations. A residue was classified as unstructured if the DSSP algorithm³⁴ assigned it a category of “-”, “T”, or “S”. Secondly, we assigned each ML-generated conformations to one of 25 unique clusters (as opposed to 10).

Unbiased MD simulations

Simulations were run with OpenMM 8.1⁴⁰. Proteins were parameterized with the AMBER FF14SB force field and solvated with the TIP3P water model⁴¹. Each system was neutralized with NaCl, adjusted to an ionic concentration of .15 M, and the box was extended 1.2 nm from protein atoms in all directions. Local energy minimization was then run for 200 steps while all protein atoms were subject to a restrained harmonic potential of 10 kcal/mol. This was followed by 500 steps of unrestrained local energy minimization applied to the whole system. Each system was then heated from 0 to 300 K using the NVT ensemble for 500 ps with a restrained harmonic potential of 10 kcal/mol applied to all protein heavy atoms. Next, each system was equilibrated at 300 K and 1 bar in an NPT ensemble for 1 ns without any restraints using a Monte Carlo barostat. Production runs were conducted in the NPT ensemble at 300 K and 1 bar with a 2 fs time step. Nonbonded interactions were cut off at 1.0 nm, and long-range electrostatic potentials were treated using the Particle Mesh Ewald (PME) method⁴². The SHAKE algorithm was used to constrain H-bonds during MD simulations⁴³.

Each MD simulation was run for 250 ns, except for P62495 and M1VAN7, which were run for 100 ns due to their larger size. 500 frames were saved for each simulation, yielding a total of 5500 frames per protein.

Clustering MD frames

We apply a previously validated pipeline to spatiotemporally coarse grain MD simulations^44–47. The pipeline can be summarized as follows: First, a suitable dimensionality reduction method is applied to map each conformation from each MD frame to a k-dimensional vector. We applied PCA to both the C-alpha pairwise distances and C-alpha contacts with k=3 to generate two separate representations⁴⁸. For each k-dimensional vector, a free energy is calculated for each conformation with a density-based clustering algorithm. Each conformation is then assigned to a microstate by iteratively assigning conformations to their respective geometrically closest neighbor with lower energy. Finally, each microstate is grouped into a relevant macrostate by applying the most probable path (MPP) algorithm. MPP first calculates a transition matrix between microstates assuming Markovian dynamics. Based on the transition probabilities, a dendrogram is constructed that reflects the hierarchical structure of the free energy landscape. Specifically, if the self-transition probability of a given microstate is lower than a certain metastability criterion Qmin, the state will be lumped with the state to which the transition probability is the highest. This procedure is iteratively repeated until there are no more transitions for a given Qmin. Microstates with a common parent node and below a Qmin threshold are then grouped into the same macrostate. We followed the guidelines of Nagel et al. and required macrostates to have a Qmin of at least 0.5 and a relative minimum population of 0.5%⁴⁶. This filtering criteria effectively excludes macrostates that are either rare or disjointed from the remaining macrostates. For each dendrogram, we also output a corresponding plot comparing the predicted self-transition probability of each macrostate as a function of lag time with respect to actual MD data to gauge the goodness of fit of the underlying Markov state model (Supp. Fig. 28).

We note that a given transition matrix can have multiple connected components (typically we observe only 1 connected component, though occasionally there may be 2 or 3). In this case, our pipeline will output a dendrogram per connected component. Because we generated macrostates using two feature sets (C-alpha pairwise distances and C-alpha contacts), we showed results for the feature set with a lower number of connected components. If both feature sets corresponded to the same number of connected components, we defaulted to showing results derived from the C-alpha pairwise distances.

To visualize the final output, a separate PyMOL session is generated for each macrostate. In each PyMOL session, a representative subset of MD frames corresponding to a given macrostate are superimposed with respect to the initial AF2 prediction, and each residue is colored based on its Root-Mean Square Fluctuation (RMSF). The RMSF is calculated for each unique MD simulation trajectory. Conformations are labelled by the source cluster from which an MD simulation originated (i.e., one of the conformations in $C_{\mathit{\text{MD}}}$).

Metadynamics simulations

The starting conformation for RBP was 1URP, which corresponds to the apo (ribose-free) wild type structure, and the G134R mutation was manually introduced. For K-Ras, the starting structure was 5W22, which corresponds to the WT GDP-bound conformation.

MD simulations were performed using OpenMM 8.1⁴⁰. The Amber FF14SB force field was used to parameterize the protein⁴¹. Ligands were parameterized using the graph neural network framework Espaloma 0.3.2⁴⁹. A dodecahedral box containing TIP3P-FB water molecules was constructed around the protein with a 1.5 nm padding. The system was neutralized with NaCl and adjusted to an ionic concentration of 0.15 M.

A Langevin Middle integrator was employed with a temperature of 300 K and a friction coefficient of 1/ps. The timestep was set to 4 fs using the hydrogen mass repartitioning (HMR) and SHAKE algorithms⁴³. Harmonic positional restraints were applied to all heavy atoms, and the systems were gradually heated to 300 K in the NVT ensemble. Subsequently, a Monte Carlo barostat was introduced, and 15 steps of NPT equilibration were performed, progressively releasing the restraints. Finally, 50 ns of unrestrained MD simulations were conducted to ensure proper equilibration.

Well-tempered metadynamics simulations were performed with PLUMED 2.9 using the OpenMM-plumed plugin⁵⁰. For K-Ras, five independent replicas of 100 ns were conducted, depositing gaussians of 0.01 nm width and 1.2 kcal/mol height every 2ps with a bias factor of 10. As anticipated in the results section, the CVs chosen where C-alpha distances between G12-T35 and T35-G60. For RBP, five replicas were run for 250ns, depositing gaussians of 0.05 nm width and 2 kcal/mol height every 2ps with a bias factor of 12. The hinge-angle CV was defined as the angle between the center of mass of residue groups (1–100, 236–259), (101–107, 232–235, 260–268), and (108–231, 269–271). The twist-angle CV was defined as a torsion between the following groups of residues: (1–100, 236–259), (99–100, 236–237, 258–259), (108–109, 230–231, 269–270) and (108–231, 269–271). A schematic representation of the CVs used for K-Ras and RBP is shown in Supp. Fig. 3.

Replicas were combined using the Mean Force Integration method⁵¹ to obtain the final Free Energy Landscape (FEL) and assess its convergence (Supp. Fig. 4)

For the corresponding unbiased MD simulations for RBP, the starting structures were derived from the same methodology used to generate the starting structures for proteins in the conformational states dataset. (i.e., ten conformations, one from each cluster, plus the initial AF2 prediction). If multiple conformations were assigned to the same cluster, the conformation with the highest pLDDT score was selected. For the corresponding unbiased MD simulations for K-Ras, because it was being simulated in the GDP and Mg bound state, we visually inspected 50 candidate structures and selected 10 representative, non-redundant structures that did not clash with either GDP or Mg.

Supplementary Material

Conceptual overview of AF-RW and AF-Ensemble; conformational diversity comparison of AF-RW and AFSample2 for all proteins; metadynamics convergence plots; conformational diversity comparison of AF-RW and AFSample2 per protein; conformational diversity comparison of AF-RW and BioEmu; analysis of macrostates generated by AF-RW coupled with MD simulations for each protein; Markov state model convergence plots; TM-score distributions as a function of macrostate for AF-RW and AFSample2; conformational diversity of AF-Ensemble for challenging proteins; AF-RW in the context of structure-based drug discovery; timing information for AF-RW and AFSample2; sequence similarity distributions for proteins used as training for AF-Ensemble.

DATA AND SOFTWARE AVAILABILITY

The code for running the PAF-MD pipeline is available on GitHub: https://github.com/forlilab/pafmd. Our work was built upon OpenFold, a reproduction of AF2 implemented in PyTorch³⁰.