Enhanced Sampling of Protein Conformations in AlphaFold3 with Repulsive Bias in the Diffusion Generative Model

Abstract

Conformational changes in proteins are vital to their function yet remain challenging for state-of-the-art artificial intelligence, such as AlphaFold3 (AF3), to predict. It has been observed that AF3 sometimes fails to capture ligand-induced conformational changes, even though it explicitly includes ligand molecules that induce such changes. To address this challenge, we develop an enhanced sampling scheme that leverages the diffusion-based generative model used in AF3 to predict protein structures. Interpreting the diffusion generative model as a stochastic sampling process analogous to molecular dynamics (MD) simulations, we introduce here a repulsive biasing potential between predicted structures to explore wider conformational space. We demonstrate that the developed sampling scheme, AF3-ReD, successfully samples multiple conformational states in the AF3 distribution, including ligand-bound conformations of motor, kinase, and transporter proteins, which are rarely captured by the default AF3 settings. Consistency with experimentally determined structures not only at the global structural level but also in local ligand-binding poses confirms reliable conformational sampling with AF3-ReD. Notably, AF3-ReD succeeded in sampling conformational states of transporters that were unresolved at the AF3 training cutoff. Compared to another strategy based on multiple sequence alignment (MSA), AF3-ReD predicted intermediate conformations that are relatively closer to the stable states. Thus, AF3-ReD provides a promising approach to predicting dynamic conformational changes of proteins associated with ligand binding, which could be further extended to other diffusion-based generative models, such as those for protein design, potentially expanding their accessible design space.

Introduction

Proteins change their conformation when they function. For example, motor proteins change their conformation in nucleotide-state-dependent manners to achieve the unidirectional motions. − Transporter proteins change conformation between inward-open and outward-open states to carry their substrates across the cell membrane. , Such conformational changes are vital to the function of these proteins, yet have been difficult for the state-of-the-art protein structure prediction artificial intelligence (AI), AlphaFold, , to predict. This posed a major challenge for AlphaFold2 (AF2) and led to the development of several pipelines to enable it to predict a wide range of conformations beyond a single conformational state, , including multiple-sequence-alignment (MSA)-related approaches, − template-related approaches, , and integrations of AF2 with experimental information , and other machine learning techniques. , The issue still persists in the latest version, AlphaFold3 (AF3), even though it explicitly includes ligand molecules that induce conformational changes.

AF3 employs diffusion-based generative models, − a powerful class of generative AI methods, to predict protein structures. Diffusion-based generative models have been utilized to generate protein structures, ,− protein–ligand complexes, ,− sequences, , and to back-map atomic structures from coarse-grained models. − The diffusion model in AF3 is based on a score-based generative model using stochastic differential equations, , in which the score, optimized in training, corresponds to the learned gradient of the log probability density (see eq ). Given that the score is equal to the gradient of an effective energy landscape defined as the negative log probability density (see eq ), the denoising process of the diffusion model in AF3 can be seen as simulating the formation of a protein conformation along an energy landscape (Figure A). Therefore, the limited prediction ability of AF3 to a single conformational state is somewhat similar to the sampling problem of rare events in MD simulations. In MD simulations, a system is typically trapped in a metastable state and unable to visit other metastable states due to the time scale of barrier crossing events. Various enhanced sampling techniques have been developed to overcome this problem, including umbrella sampling, − replica exchange, − steered MD, − transition path sampling, − accelerated MD, ,− and metadynamics. − Some of these methods apply an artificial force to enhance sampling of a wider region in conformational space. Considering that the presence of multiple conformational basins has been well-supported by MSA-related and alternative sampling strategies, − , such enhanced sampling techniques would also help AF3 overcome its limitations.

1.

Repulsive biasing potential introduced in the denoising process of the AlphaFold3 diffusion model (AF3-ReD). (A) Stochastic sampling of protein conformations with the denoising process of the AlphaFold3 diffusion model. (B) Architecture of AlphaFold3 diffusion model with repulsive biasing potential. The red box and arrows indicate the introduced biasing potential. (C) Stochastic conformational sampling with the denoising process in the presence of repulsive bias.

Enhanced sampling in diffusion-based generative models is an emerging research area. Based on AF3-related diffusion models, inference-time guidance of protein structure prediction has attracted significant attention over the past few years. − These existing methods typically utilize experimental information, such as cryo-electron microscopy density maps or NMR distance restraints, to guide structure inference. Instead, one can think of applying an artificial force to enhance sampling, inspired by enhanced-sampling techniques in MD simulations described above, without requiring external experimental data. Several independent works, including our current work, explore this direction. −

In this work, we introduce AlphaFold3 with a repulsive biasing potential applied to the diffusion model (AF3-ReD) to enhance conformational sampling of proteins. Inspired by the metadynamics method, , the structure generation in AF3-ReD is guided by repulsive biasing forces from previously predicted structures during the denoising process, enabling the diffusion model to avoid generating redundant structures within the same conformational basin. We also implemented one of the most widely used MSA-related methods, MSA subsampling, in AF3, and compared its performance to that of AF3-ReD. Application of AF3-ReD to motor, kinase, and transporter proteins in ligand-bound conditions demonstrated that it successfully predicts multiple conformational states, including ligand-bound conformations, which are rarely captured by the default AF3 or AF3 with MSA subsampling. AF3-ReD achieved conformational diversity without large deviation from stable states, representing plausible intermediate conformations. It can also be applied to multimer complexes, although capturing large-scale conformational changes in protein complexes remains challenging. AF3-ReD, together with previous studies, − , underscores the effectiveness of enhanced and guided sampling schemes in diffusion generative models and provides a foundation for predicting dynamic conformational changes in proteins.

Results

Repulsive Biasing Potential in AlphaFold3 Diffusion Model (AF3-ReD)

AF3 takes protein and DNA/RNA sequences, ligand chemical information, and template structures as input, and computes embeddings from these inputs as well as MSAs from the sequences. The resulting embeddings, C, are then used to condition the score function, which corresponds to the learned gradient of the log probability density:

$$\mathit{s}(\mathit{X}(t);{\sigma }_{\mathrm{d}}(t),C)={\mathrm{\nabla }}_{\mathit{X}}\log p(\mathit{X}(t);{\sigma }_{\mathrm{d}}(t),C)$$ 1

where X (t) is protein structure coordinates at time t and p( X ;σ_d,C) is the probability density at a given noise level σ_d(t) in the denoising process. The score can be also expressed as the gradient of an effective energy landscape defined as the negative log probability density, E( X (t);σ_d(t),C):

$$\mathit{s}(\mathit{X}(t);{\sigma }_{\mathrm{d}}(t),C)={\mathrm{\nabla }}_{\mathit{X}}\log [\exp \{-E(\mathit{X}(t);{\sigma }_{\mathrm{d}}(t),C)\}/Z]=-{\mathrm{\nabla }}_{\mathit{X}}E(\mathit{X}(t);{\sigma }_{\mathrm{d}}(t),C)$$ 2

where Z is the normalizing constant (i.e., partition function) unrelated to the score calculation. Therefore, the score provides information about the underlying energy landscape, although careful regularization during training is required to ensure consistency between the learned energy and the training distribution. It should be noted, however, that the AF effective energy merely reflects the distribution of protein structures in the training data and does not correspond to physical energy with a rigorous thermodynamic interpretation. Hence, we hereafter refer to E( X (t);σ_d(t),C) as the AF effective energy to clearly distinguish it from physical energy. The conditioned score function in eq is then applied to the denoising process in the diffusion module of AF3, where initial random noise is gradually denoised according to the time-dependent effective energy landscape to yield a final structure (Figure A). Although the AF3 diffusion model can sample protein conformations along the AF effective energy landscape during the denoising process, imbalances in the learned distributions arising from the training data make it difficult to sample alternative conformational states.

To avoid predicting similar structures within the same conformational state, in analogy to the history-dependent repulsive biasing potential used in widely used metadynamics simulations, we introduce a Gaussian repulsive potential during the denoising process of the AF3 diffusion model (Figure B,C). Root-mean-squared deviation (RMSD) is used as a collective variable for the repulsive potential. For the m-th prediction model with the s-th random seed (m = 1···5 since typically five models are generated per seed in AF3), we denote the Cα-atom coordinates of a predicted structure as ${\mathit{X̃}}^{(s,m)}(t)=({\mathit{x}}_1^{(s,m)}(t),...,{\mathit{x}}_N^{(s,m)}(t))$ , where x _i ^{( s , m )}(t) represents the position of the i-th Cα atom at time t and N is the number of Cα atoms. For conciseness, the set of the Cα coordinates of the current structure in the diffusion process is denoted as X ~(t) without the superscripts. As AF3 sequentially performs the denoising process for each random seed, RMSD is calculated between the current structure and all previously predicted structures:

$$R(\mathit{X̃}(t),{\mathit{X̃}}_{\mathrm{f}}^{(s,m)})=\sqrt{\frac{1}{N_{\mathrm{e}\mathrm{f}\mathrm{f}}}\sum _i{\parallel {\mathit{x}}_i(t)-{\mathit{x}}_{i,\mathrm{f}}^{(s,m)}\parallel }^2}$$ 3

where ${\mathit{X̃}}_{\mathrm{f}}^{(s,m)}{\equiv \mathit{X̃}}^{(s,m)}(t_{\max })$ is the Cα coordinates of a previously predicted model (the m-th prediction with the s-th random seed) with the final time t _max = 160 in AF3, meaning a final denoised structure. N _eff is the number of atoms included in the atom set A, which contains the indices of Cα atoms whose pLDDT scores predicted with the first random seed are greater than 60:

$$A=\{i|pLDDT(i)>60\}$$ 4

If there are multiple prediction models for the first random seed, the pLDDT scores are averaged over the models. This pLDDT-based selection helps exclude disordered regions, which typically have low pLDDT scores, from the RMSD calculation. The Gaussian repulsive potential is defined using the RMSD as a collective variable:

$$V(\mathit{X̃}(t))=w\sum _{(s,m)}\exp \{-\frac{R^2(\mathit{X̃}(t),{\mathit{X̃}}_{\mathrm{f}}^{(s,m)})}{2{[\sigma +(t_{\max }-t)]}^2}\}$$ 5

where w is the strength of the Gaussian potential. The width of the Gaussian potential decreases linearly over the denoising process from σ + t _max to σ. In the denoising process, the noise level is time-dependent: high noise at the initial stage facilitates global exploration, while lowering the noise over time enables the system to settle into a minimum of the AF effective energy landscape, analogous to simulated annealing. Accordingly, the wider Gaussian width at the initial stage promotes global sampling of alternative conformational states by exerting repulsive forces over a broad region around the previously predicted structures, whereas the narrowed width at the later stage localizes the repulsion so as not to hinder the refinement of the structure into stable conformations. The time dependence of the Gaussian width also keeps the repulsive forces weak at the initial stage, which is somewhat similar to the initial warm-up stage without guidance employed in the previous experiment-guided approach, so that the early formation of protein structure is not disturbed by the forces, while their weak but spatially broad bias still facilitates global exploration. To avoid applying the biasing potential to alternative conformations, the sum is taken only over structures that are close to the ones from the first random seed (see Methods for details).

By adding the bias potential, the denoising process experiences repulsive forces from previously predicted structures. Because the denoising process lacks constraints between adjacent atoms, such as covalent bonds, raw repulsive forces are not effective at facilitating concerted motions required for transitions to alternative conformations. Thus, the repulsive force acting on the i-th Cα atom is smoothed over the adjacent n _smooth Cα atoms on each side:

$${\mathit{F̃}}_i^{ReD}(\mathit{X̃}(t))=-\frac{1}{N_i}\sum _{|j-i|\le n_{\mathrm{s}\mathrm{m}\mathrm{o}\mathrm{o}\mathrm{t}\mathrm{h}}}{\mathrm{\nabla }}_{j}V(\mathit{X̃}(t))$$ 6

where N _i represents the number of Cα atoms used for smoothing. n _smooth was set to 10 in this study. In addition, the force acting on each Cα atom is applied to all atoms within the residue to which that Cα atom belongs. The obtained force is referred to as F ^ReD ( X (t)), and is added during the positional update in the denoising process as follows:

$$\mathit{X}(t+\mathrm{\Delta }t)=\mathit{X}(t)+\eta \{\mathit{F}(\mathit{X}(t);{\sigma }_{\mathrm{d}}(t),C)+{\mathit{F}}^{ReD}(\mathit{X}(t))\}\mathrm{\Delta }t$$ 7

where F (·) represents the effective force of the original AF3, which is proportional to the score function conditioned on the embeddings (C) at a given noise level σ_d(t), and η is a step-scale parameter, set to 1.5 in AF3. Equation was used during the denoising process except in the final stage $(t>{t_{\max }-t}_{\lim })$ where no biasing force is applied to refine the structures. t _lim was set to 2.0 in this study. Stochastic sampling with the denoising process proceeds by alternately repeating this position update and a noise-adding step. , Note that in AF3, Δt is defined as negative due to the reverse diffusion process, but we here treat Δt as positive for clarity, so that the forces act in the direction of decreasing affective energy, as in standard MD simulations.

It should be noted that the introduced repulsive force modifies only the atomic coordinate update during the denoising process and does not alter the token representations used as the conditioning inputs, C. In AF3, these conditioning representations are not updated based on the generated atomic coordinates (i.e., no recycling), and thus the bias does not propagate back to them. It is also worth noting that our developed AF3-ReD requires no retraining and just adds the biasing potential to the AF effective energy landscape trained by the original AF3. Such a modification can be interpreted as a form of guided diffusion, where an additional force derived from an external potential is incorporated during sampling without retraining the model, and is therefore consistent with established diffusion-based sampling frameworks. Although the metadynamics approach allows the unbiased energy landscape or probability density distribution to be estimated from the sum of the biasing potentials, it is not addressed here since, as mentioned earlier, the AF effective energy has no physical meaning. For the same reason, we chose not to employ well-tempered metadynamics, which dynamically reduces the height of the biasing potential based on the sampling history, even though it has been shown to accelerate free-energy convergence in both MD simulations and recent diffusion generative models.

In the following sections, we investigated whether AF3-ReD enhances sampling of alternative conformations for target proteins. Table S1 lists the training cutoff date for AF3 and the deposition dates of the experimental structures for each target protein. Although multiple conformational states for most target proteins had been determined before the AF3 training cutoff, certain transporter proteins possess conformational states that were either released postcutoff or remain experimentally unresolved. Therefore, this diverse selection of targets serves as a benchmark to evaluate the performance and generalization capability of our sampling scheme.

Application of AF3-ReD to Motor Proteins

As a target of our new approach, AF3-ReD, we looked into the β subunit of the rotary motor F₁-ATPase from thermophilic Bacillus (TF₁β), which binds ATP and changes its conformation from the open to the closed conformation (Figure A). The three β subunits, the three noncatalytic α subunits, and the central shaft γ subunit constitute the F₁-ATPase complex, one of the best-studied biomolecular motors. ,,− The conformational change of the β subunit is a major driving force of the unidirectional rotation of the γ subunit. The nuclear magnetic resonance (NMR) experiment previously showed that the monomeric TF₁β by itself changes its conformation upon ATP binding.

2.

Structure prediction of F₁-ATPase β subunit with AF3-MSA-subsampling and AF3-ReD. (A) Structures of the β subunit of F₁-ATPase from thermophilic Bacillus (TF₁β) in the open (cyan) and closed (pink) states. Both TF₁β structures were extracted from the F₁-ATPase complex determined by cryo-electron microscopy (PDB ID: 7XKH). (B–D) Root-mean-square deviations (RMSD) plots of predicted structures in the ATP-bound condition with MSA-subsampled AF3 (B), AF3-ReD with σ = 1 Å (C), and AF3-ReD with σ = 2 Å (D). RMSDs were calculated using the Cα atoms of residues 1–470 with respect to the open and closed cryo-EM structures. (E) A predicted closed conformation indicated by an arrow in Figure 2D, with residues colored according to their pLDDT scores (blue: pLDDT ≥ 90; cyan: 70 ≤ pLDDT < 90; yellow: 50 ≤ pLDDT < 70; orange: pLDDT < 50). Magnified views of the substrate-binding site are also shown for the experimental structure (PDB ID: 7XKQ) and the AF3-ReD predicted structure.

First, the default AF3 predicted the TF₁β conformation solely in the open state even under the ATP-bound conditions (blue points with the MSA depth 16,384 in Figure B), a typical limitation of AF3. Then, we implemented the previously proposed shallow MSA subsampling approach in AF3 by treating the MSA depth as a variable, serving as a baseline for our new method (see Methods for details). In the apo condition, the AF3-MSA subsampling still predominantly predicted the open conformations consistent with results obtained using the AF2-MSA subsampling, which does not consider ligands (Figure S1A,B). In the ATP-bound condition, as the MSA depth was reduced, the AF3-MSA subsampling extended the conformational distribution and predicted closed conformations with root-mean-squared deviations (RMSDs) to the experimental closed structure near 2 Å (Figure B). The pLDDT scores for the predicted structures are also shown in Figure S2A.

Figure C,D shows the TF₁β structures in the ATP-bound condition predicted by AF3-ReD with varying strengths and widths of the Gaussian potential (the pLDDT scores are shown in Figure S2B,C, and results for the apo condition are shown in Figure S1C,D). As these parameters increase, AF3-ReD predicts a wider range of conformations, similar to the AF3-MSA subsampling, spanning from the open to the closed state, including the half-closed state. The predicted closed conformations exhibit high confidence scores and bind ATP in a pose similar to that of experimentally determined closed structures (Figure E and Table S2). This binding pose is also consistent with that obtained via the AF3-MSA subsampling and remains stable during a 20 ns MD relaxation (Figure S3 and Table S2). These results indicate that our AF3-ReD approach with the repulsive biasing force is effective at sampling diverse conformations beyond the most populated open conformation without compromising the local geometry of the ATP-binding site. The only discrepancy in the ATP-binding pose compared to the experimental structure is the displacement of E190 away from the magnesium ion (Figure E and Table S2). Given that E190 remains separated from the magnesium ion even after the MD relaxation (the simulation details are described in Supporting Information), intersubunit interactions between the α and β subunits within the F₁-ATPase complex, such as the arginine finger from the adjacent α subunit, may be indispensable for forming the exact coordination mode observed in the experimental structure.

Dependences of sampling efficiency on other AF3-ReD parameters, such as t _lim and n _smooth, are shown in Figure S4. While AF3-ReD retains its ability to enhance conformational sampling across a wide range of parameter choices, the sampling efficiency for the alternative conformation (i.e., the closed state) varies depending on the magnitude of each parameter. For the RMSD cutoff value from the first-random-seed predictions, r _cut, where only predicted structures falling within this cutoff serve as the centers of the Gaussian biasing potentials (see Methods for details), a clear trade-off is observed: a larger r _cut makes the sampled conformations more diverse but hinders the targeted search for the alternative conformational state due to an overly broad application of the biasing potential. Additionally, if t _lim is set too large, meaning that the repulsive biasing potential is switched off too early, the enhancement of conformational sampling diminishes. Meanwhile, the number of amino acid residues used for smoothing forces, n _smooth, has little effect on the sampled conformational space of TF₁β. Based on these sensitivity analyses, we found that the probability of capturing the closed conformation was optimized with the parameter set used in Figures C,D, r _cut = 0.5Å, t _lim = 2.0, and n _smooth = 10. It should be noted that the parameter dependence of a transporter protein was also factored into the selection of the n _smooth value (discussed later). Therefore, this parameter set was consistently used for subsequent target proteins. In addition, predictions using the AF3-MSA subsampling and AF3-ReD with different random seeds demonstrated that the sampled conformational space is insensitive to random seed selection (Figure S5).

The AF3-MSA subsampling with shallower MSA depth predicts conformations that are far apart (RMSD > 3 Å) from both the open and closed experimental conformations, probably due to reduced coevolutional signals from MSA. This structural degradation is particularly evident in predictions with an MSA depth of 16 or 32, where the TF₁β fold completely collapses, accompanied by a significant drop in pLDDT scores (Figure S2D). In contrast, AF3-ReD with the refined parameters predicted conformations that are close to either the open or the closed experimental conformations. Although an excessively high bias-potential weight occasionally generates conformations that deviate from the experimental references, this failure mode stems from the localized displacement of specific peripheral helices rather than a global collapse (Figure S2E). It should also be noted that although AF3-ReD introduces additional biasing forces in the diffusion process, its computational cost remained almost unchanged. Generation of 100 protein structures (excluding MSA generation) for the TF₁β took 12 min 13 s with AF3 and 12 min 24 s with AF3-ReD using an AMD EPYC 7763 (16 cores) and an NVIDIA A100 GPU.

AF3-ReD was further applied to other motor and motor-related proteins. Figures S6 and S7 show the structure predictions for the N-terminal domain of skeletal troponin C (TnC) and dynamin 1, respectively. TnC is a motor-related protein that regulates muscle contraction and undergoes a conformational transition from the closed to the open state upon binding of two calcium ions to its N-terminal domain, thereby activating the unidirectional movement of myosin motor proteins along actin filaments (Figure S6A). While the default AF3 predominantly predicted the open state even in the apo conditions, both AF3-MSA subsampling and AF3-ReD enhanced conformational sampling, capturing the closed and intermediate conformations (Figure S6B–G). Furthermore, we also observed the structures along the positive-slope diagonal lines, corresponding to even more open or more closed conformations relative to the experimental structures. Highly open or closed conformations of TnC can emerge due to thermal fluctuations around the stable open or closed structures, although future studies are needed to clarify whether the predicted conformational ensemble is aligned with these thermally driven motions. Dynamin 1 is a motor protein that undergoes a conformational transition from the open GTP-bound state to the closed apo or GDP-bound state, thereby catalyzing membrane fission (Figure S7A). We found that, although the default AF3 correctly captures the open conformation in the GTP-bound condition and the closed conformation in the apo condition, AF3-ReD remains useful for sampling intermediate conformations between the open and closed states (Figure S7B–G).

Application of AF3-ReD to Kinase Proteins

We also investigated the ability of AF3-ReD to explore alternative conformations of kinase proteins. As the first target, phosphoglycerate kinase (PGK) was selected. PGK catalyzes the transfer of a phosphate group from 1,3-bisphosphoglycerate (BPG) to ADP, generating ATP and 3-phosphoglycerate (3PG). Ligand binding (BPG or 3PG at one site and ADP or ATP at the other site) induces a conformational transition from the open to the closed state, which is responsible for phosphoryl transfer (Figure A). As with TF₁β, the biasing potential of AF3-ReD enables AF3 to predict the half-closed and closed conformations in the ligand-bound condition, without the generation of structures far from stable states, in contrast to the AF3-MSA subsampling (Figure B–D; results for the apo condition are shown in Figure S8). The pLDDT scores for the predicted structures are also shown in Figure S9. The ligand-binding poses in the closed structures predicted with AF3-ReD are consistent with those of experimentally determined structures (Figure E and Table S3). In contrast, a displacement of D374 away from the magnesium ion is observed in the closed state predicted by the AF3-MSA subsampling (Figure S10 and Table S3). Although both the AF3-MSA subsampling and AF3-ReD occasionally predict conformations along the positive-slope diagonal line starting from the experimental open state, these structures retain high pLDDT scores and feature a substrate-binding site that is even more open than that of the experimental open structure (Figure S9). Interestingly, solution SAXS measurements for PGK have previously suggested the existence of such an highly open state, implying that these outlier predictions may still correspond to biologically relevant alternative conformations rather than unphysical artifacts. These results, together with those of motor proteins described in the previous section, collectively demonstrate that AF3-ReD overcomes the limitation of AF3 in sampling open–closed conformational changes upon ligand binding.

3.

Structure prediction of phosphoglycerate kinase with AF3-MSA-subsampling and AF3-ReD. (A) Structures of phosphoglycerate kinase (PGK) in the open (cyan; PDB ID: 2XE6) and closed (pink; PDB ID: 2WZB) states. (B–D) RMSD plots of predicted structures in the ADP/3PG-bound condition with MSA-subsampled AF3 (B), AF3-ReD with σ = 1 Å (C), and AF3-ReD with σ = 2 Å (D). RMSDs were calculated using the Cα atoms of residues 4–131, 142–372 and 386–416 with respect to the open and closed X-ray structures. (E) A predicted closed conformation indicated by an arrow in Figure 3D. Magnified views of the substrate-binding site are also shown for the experimental structure (PDB ID: 2WZB) and the AF3-ReD predicted structure.

We then predicted conformations of another kinase protein, cyclin-dependent kinase 2 (CDK2). CDK2 is activated by phosphorylation of the activation loop (A-loop) and binding of a cognate cyclin subunit, where its conformation changes from the inactive DFG-out state with the A-loop folded to the active DFG-in state with the A-loop extended (Figure S11). While monomeric CDK2 is stable in the inactive state, a previous study using double electron–electron resonance spectroscopy revealed that the A-loop can take the active-like extended form even without phosphorylation. Bhakat and Strauch recently showed that BioEmu succeeded in sampling both the active DFG-in and inactive DFG-out conformational states in monomeric CDK2, while AF2-MSA subsampling predicted only the DFG-in conformations. We found that AF3-MSA subsampling also sampled only the active DFG-in conformations, where Phe146 is far away from Lys33 and close to Glu51 (Figure S11B). In contrast, the biasing potential of AF3-ReD allowed AF3 to sample, in addition to the active DFG-in conformation, the inactive DFG-out conformation, where Phe146 gets closer to Lys33 and moves away from Glu51 (Figure S11C,D). However, the A-loop remains extended in the observed conformation (Figure S11E–H), indicating that AF3-ReD facilitates the conformational sampling of CDK2 but is still insufficient.

Application of AF3-ReD to Transporter Proteins

We next apply AF3-ReD to transporter proteins that change conformation between outward-open and inward-open states to carry their substrates across the membrane. They typically have an intermediate occluded state in which the binding site is occupied with the substrate and not accessible from either side of the membrane. Previous studies using AF2 showed that it predicts either the inward or outward state with the default MSA depth, and as the MSA depth decreases, predicted conformations extend to the occluded and finally reach the alternative conformation. , The major limitation of AF2 here is that the occluded conformation lacks the bound substrate, a problem addressed by AF3.

First, we investigated the oxalate transporter OxlT. The apo outward-open and oxalate-bound occluded structures were previously solved by X-ray crystallography (left and center panels of Figure A). Notably, both of these structures were released after the AF3 training cutoff date. The Gaussian-accelerated MD simulation, one of the enhanced-sampling methods with external biasing potentials, revealed the remaining inward-open conformation (right panel of Figure A). AF3 with the default MSA depth in oxalate-bound conditions already predicted both the inward-open and outward-open conformations (Figure B). As the MSA depth decreases, the inward-open and outward-open conformations were slightly extended (the pLDDT scores are shown in Figure S12A). However, although oxalate binds in the correct pose within the substrate-binding site (Figure S13 and Table S4), the prediction does not overlap with either the occluded crystal structure or its corresponding MD ensemble (green and gray points in Figure B, respectively). This result indicates that the AF3-MSA subsampling is limited in predicting the substrate-bound occluded conformation of OxlT. In contrast, AF3-ReD efficiently predicted the occluded conformation with oxalate bound (Figure C,D), which was not predicted in the apo condition (Figure S14). The pLDDT scores for the AF3-ReD prediction are shown in Figure S12B,C. The predicted conformations overlapped with either the MD-sampled occluded region or transition pathway between the occluded and inward-open states. Furthermore, the bound oxalate was in a pose consistent with the experimental structure, which remained stable during a 20 ns MD relaxation simulation (Figures E and S13, and Table S4), demonstrating AF3-ReD’s improved ability to sample the substrate-bound occluded state. We note that, apart from the majority of the predictions, AF3-ReD’s outlier predictions with large w include highly open structures (Figure S12D). We also note that the parameter set refined for TF₁β also worked well for OxlT (Figure S15). In particular, the concerted motions toward the occluded conformation were most effectively facilitated when n _smooth = 10 was employed. Furthermore, consistent with the observations for TF₁β, the conformational space sampled for OxlT was also found to be insensitive to the random seed selection (Figure S16). The fact that these intermediate structures, such as those along the transition pathway between the occluded and inward-open states, are reproducibly sampled across different random seeds suggests that their prediction is due to the existence of metastable basins on the AF effective energy landscape rather than mere stochastic noise.

4.

Structure prediction of transporter proteins with AF3-MSA-subsampling and AF3-ReD. (A) Structures of OxlT. The outward-open and occluded structures were previously obtained by X-ray crystallography (PDB ID: 8HPJ and 8HPK, respectively). The inward-open structure was previously predicted by our molecular dynamics (MD) study. N-terminal and C-terminal domains are colored in cyan and orange, respectively. (B–D) RMSD plots of predicted structures in the oxalate-bound condition with MSA-subsampled AF3 (B), AF3-ReD with σ = 1 Å (C), and AF3-ReD with σ = 2 Å (D). RMSDs were calculated using the Cα atoms of residues 11–196 and 204–405 with respect to the outward-open crystal structure and the inward-open structure predicted with the default AF3. For the latter, the prediction with the highest pLDDT for the apo OxlT was used as the reference. The occluded crystal structure (green) and the MD simulation structures initiated from it (gray) are also plotted. (E) A predicted occluded conformation indicated by an arrow in Figure D. Magnified views of the substrate-binding site are also shown. (F) Structures of NarK. The inward-open and occluded structures were previously obtained by X-ray crystallography (PDB ID: 4U4V and 4U4W, respectively). The outward-open structure was previously predicted in our previous study using AF2. (G–I) RMSD plots of predicted structures in the nitrate-bound condition with MSA-subsampled AF3 (G), AF3-ReD with σ = 1 Å (H), and AF3-ReD with σ = 2 Å (I). RMSDs were calculated using the Cα atoms of residues 14–239, 252–342 and 344–457 with respect to the inward-open crystal structure (PDB ID: 4U4V) and the outward-open structure predicted with the default AF3. For the latter, the prediction with the highest pLDDT for the apo NarK was used as the reference. The occluded structures obtained from X-ray crystallography (green) and from MD simulations (gray) are also plotted. (J) A predicted occluded conformation indicated by an arrow in Figure H. Magnified views of the substrate-binding site are also shown.

Next, we applied our AF3-ReD to the nitrate transporter NarK. The apo/nitrate-bound inward-open and nitrate-bound occluded structures were previously solved by X-ray crystallography (Figure F). We previously showed that decreasing the MSA depth in AF2 successfully predicted broad conformations of NarK, including the experimentally unresolved outward-open state (Figure S17). Furthermore, MD simulations initiated from an AF2-predicted intermediate conformation found the occluded conformation with the inward (cytoplasmic) gate more closed than the occluded crystal structure, which is closer to the outward-open state (gray points in Figure G). As already seen with OxlT, the default AF3 and the AF3-MSA subsampling predicted both inward-open and outward-open conformations in the nitrate-bound conditions. A reduction in the MSA depth broadened the distribution (Figure G; results in the apo condition are shown in Figure S17). The pLDDT scores are shown in Figure S18A. However, we observed no overlap between the AF3-MSA subsampling distribution and either the occluded crystal or MD-generated structures although nitrate binds in the correct pose within the substrate-binding site (Figure S19 and Table S5). AF3-ReD, in contrast, predicted the occluded state close to the crystal or MD structures (Figure H,I; the pLDDT scores are shown in Figure S18B,C), where nitrate is in a binding pose consistent with the crystal structure (Figure J and Table S5). We note that, apart from the majority of the predictions, AF3-ReD’s outlier predictions with large w include occluded conformations in which helices clash sterically with low pLDDT scores (Figure S18D). These results indicate that AF3-ReD is more efficient in sampling substrate-bound occluded conformations of transporter proteins than the AF3-MSA subsampling.

AF3-ReD was also applied to the Lipid II flippase MurJ. MurJ is a member of the multidrug/oligo-saccharidyl-lipid/polysaccharide (MOP) superfamily, which is distinct from the major facilitator superfamily to which OxlT and NarK belong, and undergoes conformational transitions between outward-open and inward-open states to flip Lipid II (Figure S20A). The default AF3 and AF3-MSA subsampling predominantly predicted the inward-open conformation, with all predictions yielding the inward-open state except for a single instance of the outward-open conformation at an MSA depth of 16 (Figure S20B). In contrast, AF3-ReD sampled a broader range of conformations (Figure S20C,D), including outward-open and intermediate states, demonstrating its applicability across different transporter superfamilies.

Sampling Precision and Diversity

Thus far, our results demonstrate that AF3-ReD enhances conformational sampling efficiency in the presence of substrate molecules. To obtain quantitative insights, we compared the sampling precision and diversity of AF3-ReD with those obtained from the MSA-subsampling method and examined their dependence on sampling scheme parameters. The sampling precision was defined as the fraction of predicted structures with RMSD below a specified threshold from any biologically relevant state (the open/half-closed/closed states for the TF₁β and PGK, and the inward-open/occluded/outward-open states for the transporter proteins). The threshold was set to 50% of the RMSD between the two stable end point states. The sampling diversity was defined as the exponential of the Shannon entropy , estimated from the probability density of RMSDs with respect to the reference structures, and normalized by that obtained from the default AF3 (see Methods for details). For both the sampling precision and diversity, we used all structures obtained from MSA depths above a given depth or obtained from strengths of the Gaussian potential below a given strength, w. For example, the sampling precision and diversity for the MSA depth of 16 were calculated using all the depths tested here.

The sampling precision and diversity of the TF₁β in the ATP-bound condition are shown in Figure A for the MSA subsampling and in Figure B for AF3-ReD. Decreasing MSA depth for the ATP-bound TF₁β increased the diversity but markedly worsened the precision, which is consistent with the observation in Figure B. In contrast, AF3-ReD demonstrates that increasing the weight of the bias potential leads to a higher diversity and a larger σ leads to a further increase in the diversity while maintaining a relatively high level of precision (Figure B). We also estimated the average and standard error of the precision and diversity from four independent samplings, which were obtained by changing the random seeds for prediction as shown in Figure S5, and found a clear difference between AF3-MSA subsampling and AF3-ReD (Figure S21).

5.

Sampling precision and diversity of AF3-MSA-subsampling and AF3-ReD. (A–H) Sampling precision and diversity for TF₁β (A, B), PGK (C, D), OxlT (E, F), and NarK (G, H). For each protein, results are obtained in the presence of ligand using different methods and parameter settings: AF3 with MSA subsampling (A, C, E, G) and AF3-ReD (B, D, F, H) with σ = 1 Å (open squares) and σ = 2 Å (filled squares).

Figures C,D, E,F, and G,H show the sampling precision and diversity of PGK kinase, OxlT, and NarK transporter proteins obtained by the AF3-MSA subsampling and our AF3-ReD in the presence of ligand, respectively (the average and standard error for OxlT are shown in Figure S21). Compared to the TF₁β, the relative diversity in the MSA subsampling increases in a less effective manner as the MSA depth decreases (Figure C for PGK, 5E for OxlT and 5G for NarK). For all of these proteins, AF3-ReD achieves a higher diversity than the AF3-MSA subsampling while maintaining high precision values of over 0.9 (Figure D for PGK, 5F for OxlT and 5H for NarK). These results further support the conclusion that AF3-ReD efficiently enhances conformational sampling compared to the AF3-MSA subsampling.

Application of AF3-ReD to the E3 Ubiquitin Ligase Complex

We further tested our AF3-ReD with a larger multisubunit system, the E3 ubiquitin ligase complex. The E3 ubiquitin ligase complex, composed of cereblon (CRBN), the DNA damage-binding protein 1 (DDB1), Cullin-4, and the RING finger protein ROC1, transfers ubiquitin to substrate proteins. A previous cryo–electron microscopy (cryo-EM) study solved part of the complex, CRBN-DDB1, showing the open CRBN in the apo state and the closed CRBN in the mezigdomide-bound state. The observed structures reveal a substantial conformational change (RMSD > 10 Å) in the complex (Figure A). In the original AF3 paper, Abramson et al. reported that AF3 is unable to capture the conformational state of the CRBN-DDB1 complex, as the closed state is predicted even in the apo condition. Thus, the CRBN–DDB1 complex serves as a challenging target for testing the capability of AF3-ReD.

6.

Structure prediction of the E3 ubiquitin ligase complex with AF3-ReD. (A) Structures of the E3 ubiquitin ligase complex CRBN-DDB1 in the open and closed states (PDB ID: 8CVP and 8D7U, respectively). (B) RMSD plot of structures in the apo condition predicted by AF3-ReD with σ = 2 Å. RMSDs were calculated using the Cα atoms of CRBN residues 64–341 and 358–425 with respect to the open and closed cryo-EM structures. (C) A partially open conformation indicated by a black arrow in Figure B. The red arrow indicates the rotation required to complete the transition to the fully open conformation (transparent gray).

We here predicted the structures of the CRBN–DDB1 with the N-terminal region of CRBN (residues 1 to 63) deleted, because this region is reported to stabilize the closed conformation. First, the default AF3 predicted the apo CRBN–DDB1 complex exclusively in the closed conformation, even after deletion of the N-terminal region (Figure S22A). AF3 with MSA subsampling produced structures closer to the open state when the MSA depth was set to 256 and when the number of predicted structures was tripled (Figure S22B). However, these structures exhibited very low pLDDT scores (Figure S22C), and the relative orientation between CRBN and DDB1 deviated substantially from the experimental structure, though the BPB domain of DDB1 is known to be flexible (Figure S22D), highlighting the difficulty of predicting complex structures via the AF3-MSA subsampling. In contrast, AF3-ReD extended the conformational distribution toward the open state while maintaining high pLDDT scores (Figure B,C). Nevertheless, the predictions did not achieve an RMSD below 5 Å from the experimental open structure. Comparison with the experimental structure revealed that, although the two CRBN domains (Lon and TBD) were sufficiently separated, AF3-ReD failed to capture the additional rotational motion of the TBD (Figure C). We also tested whether combining AF3-ReD with MSA subsampling could overcome the sampling difficulty of the apo CRBN–DDB1 complex. However, conformations close to the experimental open structure were not observed in the combined approach at an MSA depth of either 256 or 512 (Figure S23). Taken together, these results indicate that predicting such large-scale conformational changes in protein complexes remains challenging even with individual or combined applications of the AF3-MSA subsampling and AF3-ReD, underscoring the need for further methodological improvements.

Discussion

We here developed AF3-ReD, where the repulsive biasing potential, inspired by the metadynamics technique, − was introduced to the AF3 diffusion model to enhance sampling of protein conformations. Applications of AF3-ReD to the motor, kinase, and transporter proteins demonstrated its ability to predict substrate-induced conformational changes of these proteins, which were rarely captured by the default AF3 settings. Notably, AF3-ReD succeeded in sampling specific conformational states of the transporters OxlT and NarK that were unresolved at the AF3 training cutoff date. This indicates that AF3-ReD biasing potentials applied on the AF effective energy landscape achieve enhanced sampling beyond the simple retrieval of memorized conformational states. Nevertheless, considering that OxlT and NarK belong to the major facilitator superfamily, for which many experimental structures have accumulated for each conformational state, testing the AF3-ReD scheme on targets with minimal homologous representation of alternative conformational states would be desirable to further validate its strength in future work.

Furthermore, our analysis revealed a notable contrast in the conformational exploration capabilities of AF3-ReD and MSA subsampling. While AF3 with MSA subsampling also succeeded in predicting the substrate-bound conformation of the F₁ β subunit and PGK, it failed to do so for the transporters. These results indicate that the effectiveness of MSA subsampling depends on the protein system. This is likely due to differences in the underlying biases in MSAs that prevent the default AF3 from exploring alternative conformations. For the F₁ β subunit and PGK, the increase in diversity upon decreasing the MSA depth indicates that the coevolutionary information in the MSA, used to condition the score function of the AF3 diffusion model, favors a specific conformational state. In contrast, the weaker MSA-depth dependence of sampling diversity for the transporter proteins suggests that the difficulty in sampling arises from other sources inherent in the AF3 diffusion model, such as biases in the AF3 training data and insufficient sampling time at high noise levels due to the noise schedule, as well as the lack of lipid molecules in the system. Unlike the MSA subsampling, AF3-ReD can mitigate both coevolution-derived and diffusion-model-derived sampling difficulties, as it directly modulates the AF effective energy landscape determined by the training data and the MSA-derived coevolution. Nevertheless, even AF3-ReD has yet to capture the large-scale conformational change observed in the E3 ubiquitin ligase complex, and conversely, it sometimes predicts structures that deviate from biologically relevant states, indicating that further improvements in conformational sampling are needed. Such improvements may include redefining the biasing potentials in AF3-ReD using different CVs, or refining the AF effective energy landscape itself (i.e., the neural network parameters).

Extending CVs, which are limited to Cα atoms in the current implementation, would also be helpful for side-chain and RNA/DNA conformational sampling. For example, the aspartic protease plasmepsin-II opens its cryptic pocket by flipping Trp41 (Figure S24A). Recent studies have shown that MSA subsampling allows AF2 to sample the Trp41 orientation observed in the cryptic-pocket open state. , Here, we applied AF3-MSA subsampling and AF3-ReD to plasmepsin-II. The AF3-MSA subsampling captured the flipping motion of Trp41, including the orientation observed in the cryptic-pocket open state (Figure S24B), which is consistent with the previous AF2-MSA subsampling. , In contrast, AF3-ReD could not enhance the conformational sampling of the Trp41 side chain, as expected from the application of biasing forces only to Cα atoms (Figure S24C,D). As is the case with the large-scale conformational change in the ubiquitin ligase complex, this result also indicates the need for further methodological improvements to AF3-ReD.

Although AlphaFold generates only static structural information, integrating its predictions with MD simulations can provide deeper insights into conformational dynamics and energetics. ,, We previously demonstrated that AF2 with MSA subsampling can generate transition-state-like conformations of NarK that lie between the stable conformational states. Such intermediate conformations were also observed in predictions by AF3-ReD. These structures can serve as starting points for rare-event MD sampling, such as Markov state modeling ,− or transition path sampling, − thereby enabling efficient characterization of conformational dynamics and thermodynamics in proteins. In fact, we recently developed an AlphaFold-facilitated Markov state modeling approach to identifying free energy landscapes and conformational transition pathways of a redox-driven transporter protein. Besides, MD simulations themselves may even be replaceable by generative AI methods. For example, recently developed BioEmu generates a conformational ensemble of proteins through a diffusion-based generative model that learned MD simulations and experimental stability data, although its use is currently limited to the apo condition. Therefore, generative AI methods and MD simulations can mutually reinforce each other, and such bidirectional integrations should provide fruitful insights into dynamic conformational changes associated with ligand binding, including drug molecules.

Diffusion models are powerful AI frameworks that have been widely applied to the prediction and design of biomolecules, as well as to the generation of ligands and drugs that bind to them. However, the quality of the generated samples often comes at the expense of their diversity, as also observed in AF3. To address this issue, AF3-ReD introduces repulsion between sampled structures during the denoising process. This history-dependent guidance for the denoising process should complement existing frameworks that rely on external experimental observables. − , The utility of such repulsive mechanisms in diffusion models has also been demonstrated in image generation and small-molecule conformation generation. , While AF3-ReD shares the idea of biasing the sampling dynamics, their approach operates on multiple structures generated simultaneously, where repulsive interactions are imposed between parallel diffusion trajectories with a fixed number of structures. A similar parallel-sampling strategy was recently applied to protein conformational sampling in Metadiffusion. In contrast, AF3-ReD generates structures sequentially and applies biasing forces based on previously generated structures, allowing the number of structures to be flexibly increased. This sequential and history-dependent formulation is expected to be advantageous for exploring a vast conformational space. Furthermore, as demonstrated in the prediction of TF₁β, the computational overhead associated with the bias calculation in AF3-ReD is negligible, allowing the overall prediction cost to increase linearly with the number of structures. This represents a distinct advantage over Metadiffusion, where the computational cost scales as O(N ²) due to the all-to-all interactions among parallel trajectories.

Concurrently with the release of our preprint, several independent studies have reported conformational sampling schemes for diffusion generative models, similarly inspired by enhanced sampling techniques developed for MD simulations. − Richman et al., Hori et al., and Xie et al. implemented umbrella-sampling-like harmonic potentials within diffusion-based structure inferences, such as Boltz-1, Boltz-2, or BioEmu. While applying such harmonic potentials along collective variables can facilitate the sampling of a broad conformational space, multiple umbrella windows needed for such sampling inevitably increases the computational cost. This limitation highlights the advantage of our metadynamics-like repulsive potential, which allows the system to bypass exhaustive exploration of intermediate conformations and instead discover alternative metastable states more efficiently by destabilizing previously predicted stable states. Furthermore, similarly to our method, Xie et al. also implemented a metadynamics-like repulsive potential in BioEmu, called MetaDiff, which enables the estimation of unbiased free energy by leveraging BioEmu-learned equilibrium distribution and a reweighting technique. However, the current implementations of BioEmu and MetaDiff do not support incorporating ligands into structure prediction, thereby limiting their applicability to ligand-induced conformational changes. This limitation underscores the unique advantage of AF3-ReD, which enables the conformational sampling of ligand–protein complexes with accurate binding poses by carefully applying the repulsive biasing forces through specific architectural choices, including residue-level force smoothing, first-seed anchoring, and inference-time-decaying potential widths. In AF3-ReD, the repulsive biasing potential is defined simply by the structural similarity (i.e., RMSD) between sampled structures, which facilitates diverse conformational sampling without retraining. This strategy could be further extended to other diffusion-based generative models for even protein structure design, such as RFdiffusion, potentially expanding their accessible design space.

Methods

Repulsive Biasing Potential in AlphaFold3 Diffusion Model (AF3-ReD)

The repulsive biasing potential was implemented in AF3 (code version as of Mar 17, 2025, commit ID: 8151373). Before calculating RMSDs according to eq , all previously predicted structures were superimposed onto the current structure during the denoising process of the diffusion module using the Kabsch algorithm. , In the case of protein complexes, either the entire complex or only specific subunits were used for the superposition; for example, in the CRBN–DDB1 complex, only CRBN was aligned here.

When calculating the repulsive biasing potential, the sum in eq is taken over the set S of previously predicted structures for which the RMSD from at least one model with the first random seed is less than the cutoff length r _cut:

$$S=\underset{n}{\cup }\{(s,m)|R({\mathit{X̃}}_{\mathrm{f}}^{(s,m)},{\mathit{X̃}}_{\mathrm{f}}^{(1,n)})<r_{\mathrm{c}\mathrm{u}\mathrm{t}}\}$$ 8

where s and m represent the indices for the random seed and prediction model, respectively. r _cut was set to 0.5 Å in this study. This restriction prevents us from applying the biasing potential to alternative conformations. In addition, the use of multiple structures from the first random seed as the reference enables applying the biasing potential to structures frequently observed in default AF3, even if outlier predictions are included in the reference structures.

MSA Subsampling in AlphaFold3

In AF3 (code version as of Mar 17, 2025, commit ID: 8151373), the maximum number of homologous sequences in the multiple sequence alignment (MSA), ‘max_msa’, referred to as the MSA depth, is hard-coded with a default value of 16,384. To enable control of this parameter, we modified the AF3 source code so that the MSA depth could be specified as a variable. For the proteins studied here, the MSA depth was varied in the range from 16,384 (default) to 16.

Structure Prediction of Proteins

The amino acid sequences of the target proteins used in this study (UniProt IDs) were as follows: P07677 for the β subunit of F₁-ATPase from thermophilic Bacillus (TF₁β), P00558 (excluding the initiator methionine) for PGK, P24941 for CDK2, Q51330 for OxlT, P10903 for NarK, B7IE18 for MurJ, Q96SW2 for CRBN, and Q16531 (excluding the initiator methionine) for DDB1. For TnC, dynamin 1, and Plasmepsin-II, we used the amino acid sequences corresponding to the experimental structures (PDB IDs: 1AVS for TnC; 2X2E for dynamin 1; 1LF4 for plasmepsin-II). For OxlT and NarK, the MSAs generated in our previous studies , were used. The N-terminal region of CRBN (residues 1–63) was truncated to facilitate sampling of the open conformation. The MSA depth in the AF3-MSA subsampling, as well as the strength and width of the Gaussian potential in AF3-ReD, were varied to investigate the effects of these parameters on conformational sampling. For each random seed, AF3 generated five model structures, and 20 seeds were used for each condition, yielding 100 structures (20 seeds × 5 models) per condition for the default AF3, each MSA subsampling depth, and each (σ, w) combination in AF3-ReD. For comparison, structure prediction with AlphaFold2 was performed using ColabFold version 1.5.2, which is compatible with AlphaFold 2.3. No templates were used in any of the structure predictions. Molecular graphics were prepared with UCSF Chimera and ChimeraX, and RMSD analysis was performed with MDAnalysis. ,

Sampling Precision and Diversity

The sampling precision was calculated to evaluate the ability of the AF3-MSA subsampling and AF3-ReD to predict conformations close to biologically relevant states. We first counted the number of predicted structures with RMSD below a specified threshold from any biologically relevant state. The threshold was set to 50% of the RMSD between the two stable end point states. As the biologically relevant states, the open, half-closed, and closed states were used for TF₁β and PGK, and the inward-open, occluded, and outward-open states were used for the transporter proteins. The precision was then obtained by dividing that number by the total number of predictions, yielding a value between 0 and 1.

The sampling diversity was calculated to evaluate the ability of the AF3-MSA subsampling and AF3-ReD to explore a broad range of conformations. It was defined as the exponential of the Shannon entropy S: ,

$$D=\exp (S)$$ 9

The Shannon entropy was estimated from the probability density of RMSDs with respect to the reference structures:

$$S=-\int p(x,y)\ln p(x,y)\mathrm{d}x\mathrm{d}y$$ 10

where x and y are the RMSDs from each of the two reference structures, and p(x,y) is the probability density estimated from a two-dimensional histogram with a bin width of 0.2 Å over a range of 0 to 50 Å for both axes. The Miller–Madow correction was applied to the estimated Shannon entropy to account for finite-sample bias, after which the diversity D was calculated. D has a desirable property as a measure of diversity: D doubles when the range of an equiprobable distribution doubles. The relative diversity was then obtained by dividing D by that from the default AF3, and compared between AF3-ReD and the AF3-MSA subsampling.

The source codes of AF3-ReD and theAF3-MSA subsampling are available at https://github.com/OkazakiLab/af3_red and https://github.com/OkazakiLab/af3_mmm, respectively. All prediction results to generate the figures are openly available in Zenodo at 10.5281/zenodo.19363619.

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/jacsau.6c00596.

• Additional MD simulation details, training cutoff date of AF3 and released date of experimental structures (Table S1), summary of predicted closed conformations of F₁-ATPase β subunit (Table S2), phosphoglycerate kinase (Table S3), OxlT (Table S4), and NarK (Table S5), structure prediction of F₁-ATPase β subunit in the apo condition (Figure S1), pLDDT scores and failure predictions of TF₁β in the ATP-bound condition (Figure S2), the substrate-binding site of F₁-ATPase β subunit (Figure S3), dependence of conformational sampling of TF₁β on AF3-ReD parameters (Figure S4), dependence of conformational sampling of TF₁β on initial random seeds (Figure S5), structure prediction of the N-terminal domain of TnC (Figure S6), structure prediction of dynamin 1 (Figure S7), structure prediction of PGK in the apo condition (Figure S8), pLDDT scores and failure predictions of PGK in the ADP/3PG-bound condition (Figure S9), the substrate-binding site of phosphoglycerate kinase (Figure S10), structure prediction of cyclin-dependent kinase 2 (Figure S11), pLDDT scores and failure predictions of OxlT in the oxalate-bound condition (Figure S12), the substrate-binding site of OxlT (Figure S13), structure prediction of OxlT in the apo condition (Figure S14), dependence of conformational sampling of OxlT on AF3-ReD parameters (Figure S15), dependence of conformational sampling of OxlT on initial random seeds (Figure S16), structure prediction of NarK in the apo condition (Figure S17), pLDDT scores and failure predictions of NarK in the nitrate-bound condition (Figure S18), the substrate-binding site of NarK (Figure S19), structure prediction of MurJ (Figure S20), averaged precision and diversity (Figure S21), the E3 ubiquitin ligase complex predicted with AF3-MSA subsampling (Figure S22), structure prediction of the E3 ubiquitin ligase complex using the combination of AF3-ReD with MSA subsampling (Figure S23), and structure prediction of plasmepsin-II (Figure S24) (PDF)

The authors declare no competing financial interest.