One bead per residue can describe all-atom protein structures

Lim Heo; Michael Feig

doi:10.1016/j.str.2023.10.013

. Author manuscript; available in PMC: 2025 Jan 4.

Published in final edited form as: Structure. 2023 Nov 23;32(1):97–111.e6. doi: 10.1016/j.str.2023.10.013

One bead per residue can describe all-atom protein structures

Lim Heo ¹, Michael Feig ^1,^*

PMCID: PMC10872525 NIHMSID: NIHMS1944498 PMID: 38000367

SUMMARY

Atomistic resolution is the standard for high-resolution biomolecular structures, but experimental structural data is often at lower resolution. Coarse-grained models are also used extensively in computational studies to reach biologically relevant spatial and temporal scales. This study explores the use of advanced machine-learning networks for reconstructing atomistic models from reduced representations. The main finding is that a single bead per amino acid residue allows construction of accurate and stereochemically realistic all-atom structures with minimal loss of information. This suggests that lower-resolution representations of proteins may be sufficient for many applications when combined with a machine-learning framework that encodes knowledge from known structures. Practical applications include the rapid addition of atomistic detail to low-resolution structures from experiment or computational coarse-grained models. The application of rapid, deterministic all-atom reconstruction within multi-scale frameworks is further demonstrated with a rapid protocol for the generation of accurate models from cryoEM densities close to experimental structures.

Keywords: multi-scale, coarse-graining, protein structure, low-resolution, cryoEM, machine learning

eTOC Blurb

Heo and Feig describe a machine-learning based protocol for accurate recovery of atomistic detail from coarse-grained models of proteins. The method can be applied to add atomistic details to low-resolution experimental structures. It also facilitates rapid structure determination based on cryoEM maps.

Graphical Abstract

graphic file with name nihms-1944498-f0001.jpg

INTRODUCTION

Proteins play central roles in biological processes, and their behavior is often studied at the molecular level to understand biological function. Structural resolution at an atomistic level is the gold standard for experiments and computation alike. Experimental methods such as X-ray crystallography^1,2, nuclear magnetic resonance (NMR)³, and cryogenic electron microscopy (cryo-EM)⁴ allow the construction of structural models in atomistic detail, but achieving such high resolution requires significant effort^5,6. Computational modeling and simulations also typically require all-atom representations of the protein to achieve maximum accuracy and to gain detailed mechanistic insights^7,8. Atomistic modeling remains computationally expensive, though, limiting practical applications⁹, even with the latest high-performance computing platforms and simulation accelerators. (e.g., Anton or CUDA)¹⁰. Similarly, it is also very demanding to train machine-learning based methods for directly predicting atomistic models^11–13 and conformational ensembles^14,15.

Coarse-graining (CG) of protein structures is a common strategy to overcome the various challenges⁷. When interpreting experimental data, reduced representations may be a natural fit to match lower experimental resolutions. In computational applications, CG models greatly increase efficiency by reducing the number of particles. CG representations may range from single beads per protein^16,17 to residue-based models^18,19 and multiple sites per amino acid residue^20–24. Lower-resolution models of experimental data often default to $C α$ traces. In computational applications, the choice of resolution may depend on the questions that are being investigated as model accuracy and transferability depend on the degree of coarse-graining^7,25.

While the coordinate mapping from atomistic levels to CG representations is straightforward, the reverse mapping is in principle ill-defined because of dynamics in degrees of freedom that are not reflected in a reduced representation. For example, side chains may fluctuate for the same set of $C α$ coordinates. However, the reverse mapping is better defined when the goal is to map CG models to an atomistic coordinate representation of the ensemble-averaged dominant state, essentially akin to how most experimental structures of proteins are meant to be interpreted.

To recover atomistic information from CG models, all-atom reconstruction algorithms have been developed with different strategies depending on the CG representation. For a united-atom model, which omits only hydrogen atoms, missing hydrogens can be placed using their pre-defined local geometries²⁶. An all-atom structure can still be generated relatively accurately and quickly from higher-resolution CG models such as PRIMO or MARTINI, based on geometry-based reconstruction rules^21,27. The reconstruction of all-atom structures from coarser representations such as $C α$ -traces is more complex. Methods such as PULCHRA²⁸ and REMO²⁹ convert $C α$ -traces to all-atom structures by first rebuilding the backbone atoms before predicting side chain orientations. There is also an additional set of methods that focus only on rebuilding side chains given a protein backbone³⁰. These methods typically rely on pre-defined backbone fragment libraries, side chain rotamer libraries^30,31, or other empirical information derived from known structures. In most cases, extensive optimization is then required to avoid clashes and find energetically optimal structures³². Most recent methods also adopted machine-learning approaches for rebuilding side chains without rotamer libraries^33,34. Nevertheless, the resulting reconstructions may retain significant deviations from correct all-atom structures when only $C α$ atoms are available as input. The reconstructions may also vary from one run to another if they depend on stochastic optimization techniques. The relatively poor accuracy when reconstructing atomistic coordinates from lower resolutions has limited the full interpretation of experimental data that does not directly provide atomistic details and hindered effective implementations of multi-scale sampling methods that are both efficient and thermodynamically consistent with sampling at all-atom levels^8,35,36.

In the meantime, the recent success of accurate structure prediction via machine learning methods^11–13 has demonstrated that deep neural network models can effectively learn from the large amount of known structures how to generate atomistic models just from amino acid sequences. This suggests that it should also be possible using similar approaches to reconstruct atomistic coordinates at high resolution if lower-resolution structural information is available as additional input.

Inspired by AlphaFold2¹¹, we trained an SE(3)-equivariant graph neural network model for reconstructing all-atom detail from lower representations. Like AF2, the model utilizes rigid-body blocks for generating 3D structures from predicted features, but the model was extended to better describe hydrogen atoms and secondary structure-dependencies. The network learned structural features of backbone and sidechain atoms from known protein conformations, but also incorporates physical constraints necessary to produce realistic all-atom structures. The model is applicable to a range of CG models such as $C α$ -traces, traces of residue-center-of-mass model, and MARTINI models²⁰. It provides all-atom reconstructions at much higher accuracy than with previous methods, better than 1 Å for heavy atoms from only $C α$ atoms and better than 0.5 Å with a single site at residue centers of mass. This suggests that structural details of proteins at a resolution close to experimental accuracy can be captured essentially with a single site per residue if the current knowledge of protein structures is taken advantage of via machine learning.

The all-atom reconstruction via the machine-learning framework is fast and deterministic, and since gradients are available via back propagation, it is straightforward to map energies and constraints at the all-atom level directly to the CG representation. It is therefore possible to sample a residue-based model guided directly by all-atom forces via back-mapping through the all-atom reconstruction network. As a proof-of-principle we demonstrate practical value in the rapid refinement of all-atom coordinates against intermediate- and low-resolution cryo-EM densities. The protocol achieves comparable accuracy to traditional all-atom simulation-based approaches but with much reduced computational effort.

RESULTS

Accurate reconstruction of all-atom structures from coarse-grained representations

We trained SE(3)-equivariant machine learning models, called cg2all, to reconstruct all-atom structures of proteins from CG representations (cf. STAR Methods section). The network architecture is shown in Fig. 1. The initialization module processes input features (Fig. S1 and Table S1) to encode a protein structure in a CG representation and the corresponding residue type information. (Methods S1, Algorithm 1) An interaction module based on SE(3)-Transformers³⁷ exchanges scalar and vector encodings between residues to infer inter-residue relationships. (Methods S1, Algorithm 2) The model adopts a rigid-body block-based all-atom structure building method, analogous to the method used for AlphaFold2 structure building.¹¹ A structure module predicts values for the rigid-body block-based structure building method: translation and rotation of backbone rigid body blocks consisting of N, $C α$ , and C atoms and torsion angles to place the remaining atoms of residues. (Methods S1, Algorithm 3) The model was trained using 5,690 structures (PDB 6k set) or 28,914 structures (PDB 29k set) for 300 and 120 epochs, respectively, using an Adam optimizer with learning rates of 0.01 for parameters for torsion angle predictions and 0.001 for the others (cf. STAR Methods). The target loss function combines a target-dependent loss to minimize differences between the target structure and a reconstruction and a data-independent loss to reduce physically unrealistic structural features (e.g., atomic clashes and rotamer outliers) (cf. STAR Methods). Model variations with different hyperparameters were explored to determine the optimal model architecture (cf. STAR Methods). An ablation study was further carried out to determine optimal input features and loss function components. Only results with the optimized architecture are described subsequently.

The progress in learning protein structural features by the $C α$ -trace model proceeded in the order of distance from the $C α$ atom (Fig. S2). When progress in the recovery of structural features was tracked for every 10 epochs, we observed that backbone-related features such as the Ramachandran angle, the result of translation and three-dimensional rotation of backbone rigid-body blocks, were saturated during the earlier epochs of the training. At epoch 10, the Ramachandran map already resembled that from experimental structures, and it changed little afterwards. On the other hand, learning side chain torsion angles required many more epochs. At epoch 20, predictions of χ₁ angles became reasonably accurate, and the model started to learn χ₂ angles and a little bit of χ₃ angles. At epoch 60, more states of χ₂ angles were captured, and there was progress in χ₃ angle predictions. At the end of the training at epoch 120, learning of most structural features converged. Many structural features were learnt by the model, however, a few torsion angles such as those for Arg/Lys χ₄ angles could not be learnt in the end. Consequently, the loss in structural information upon the conversion from all-atom structure to $C α$ -trace was most significant for structural features that were far from the $C α$ atom. Consequently, backbone features could be learnt quickly, while torsion angles farther from the $C α$ atoms were slow and sometimes incomplete. In contrast, the learning progress with the residue-center-of-mass model, which contains richer input information, was much faster overall and more complete than that with the $C α$ -trace model (Fig. S2). Most structural features started to converge at epoch 20 and were almost completed at epoch 60.

Models were generated for the reconstruction from $C α$ atoms, from all backbone atoms, from a single particle at the center of mass of an amino acid residue or at the center of the side chain, from the MARTINI model with several beads per residue²⁰, and from the higher-resolution CG model PRIMO²¹. The generated all-atom models were evaluated on a test set in terms of root mean square deviations (RMSD) and side chain torsion accuracy with respect to the original reference structures as well as MolProbity³⁸ scores to check stereochemical quality (Table 1). Because the machine-learning model estimates internal parameters that are then used to reconstruct all-atom detail via rigid body reconstruction¹¹, using the parameters from the experimental all-atom structures as input for the rigid body reconstruction provides an upper limit on the accuracy that can be achieved theoretically. Because of the reduced degree of freedom using rigid body blocks, it was not possible to reproduce the exact distribution of the bonded geometries. (Fig. S3) Thus, this ideal rigid body reconstruction resulted in slight deviations of atomic coordinates (heavy atom RMSDs of 0.16 Å) and increase in MolProbity scores to 1.81 (Table 1), but both are still within experimental accuracy of about 0.2 Å RMSD for coordinates in X-ray structures of proteins whereas MolProbity scores below 2 are expected for structures derived from data at better than 2 Å resolution^38–41. The reconstruction from the highest-resolution CG model, PRIMO, reaches the theoretical maximum accuracy and even lower MolProbity scores are obtained with slightly fewer clashes (Table 1). That may be expected since PRIMO was designed to retain maximum information from all-atom representations. However, even with lower-resolution models, it is still possible to recover accurate all-atom structures. Reconstruction from MARTINI models resulted only in a slight loss of accuracy (0.31 Å RMSD) and only slightly increased MolProbity scores. Remarkably, even a single bead per residue, located at the center of a residue or at the side chain center, still allows accurate reconstruction of all-atom details (<0.5 Å RMSD) without significant compromise of stereochemical quality. If the CG site is located at the $C α$ position, as is common in many CG representations, the loss of accuracy is greater with the average heavy-atom RMSD approaching 1 Å RMSD. The reason is that it becomes more difficult to accurately position side chains if only backbone atoms are given, especially side chains on the surface that are inherently free to sample different rotamer states (Fig. 2A). On the other hand, residue center-of-mass models contain information about the location of the side chain position and therefore side chains can be placed more accurately, even on the surface (Fig. 2B). In our approach we allowed the coordinates of the input low-resolution model to vary during the all-atom reconstruction so that small errors at the CG level could be corrected automatically. For reduced models based on experimental structures this made little difference when compared to a protocol where initial CG coordinates remained fixed (Table 1).

Table 1. Performance of conversion to all-atom structures from CG models with cg2all.

Table 2. Comparison of all-atom reconstruction accuracies with different methods.

Table 3. Average timing for all-atom reconstruction with different methods.

Accurate all-atom reconstruction from simulation models

The reconstruction of all-atom detail from reduced representations of experimental structures, as described in the previous section, may be considered an ideal scenario. We further tested how well all-atom resolution can be recovered from models generated via simulations. Two sets of models were considered. The first set consisted of snapshots that were extracted from all-atom molecular dynamics (MD) simulations; in the second set, the MD-based snapshots were further energy-minimized structures using a residue-based CG model, COCOMO¹⁸. Here, the all-atom MD snapshots serve as the reference for determining accuracy of the reconstruction protocol. All-atom reconstruction from $C α$ -traces of MD simulation snapshots was still accurate, but the accuracy became slightly worse than for experimental structures, with higher RMSD values of 1.18 Å for heavy atoms and lower side chain torsion accuracies (Table 4). Once the snapshots were minimized with COCOMO at the CG level, the all-atom reconstruction RMSD further increased to 1.34 Å (Table 4) with respect to the initial all-atom MD snapshots. However, that may be expected because the CG minimization by itself resulted in deviations of 0.30 Å for the $C α$ positions from the initial all-atom MD snapshots. In either case, the reconstructed all-atom models had again low clash scores and very low rotamer outliers and were much closer to the reference atomistic structural models than those generated with other methods (Table 4 and Fig. 2C). Thermal fluctuations in the simulations led to broadened bond geometry distributions (Fig. S7) and more rotamer outliers compared to experimental structures. However, since cg2all was trained to generate experimental structure-like conformations, the broader distributions were not completely reproduced (Fig. S7). This explains at least in part the slightly lower reconstruction accuracy for simulation-based models.

Table 4. Performance of conversion to all-atom structures from Cα-traces of simulation snapshots.

Addition of all-atom structural details to low-resolution models

The analysis so far shows that all-atom details can be captured essentially within experimental uncertainties at much reduced representations, up to a single bead at the center of mass of an amino acid. This is possible by drawing on the vast knowledge about protein structures via state-of-the-art machine learning. In turn, this means that all-atom structural details can be provided with high confidence for models that are initially only available at a CG level. Examples where cg2all may be used in practice are shown in Fig. 2 and discussed more in the following.

Low-resolution cryo-EM structures are often reported only at the $C α$ level. All-atom detail can be reconstructed quickly via cg2all (Fig. 2E). For a cryo-EM experimental structure (PDB ID: 3iyg⁴³) with a resolution of 4.0 Å the all-atom structure with 4,134 residues or 64,192 atoms was generated within 11.9 seconds, fast enough to be done on-demand when working with such structures. The generated structure had a higher density map correlation of 0.723 than that of the original $C α$ -trace, 0.647, but there were some clashes in the atomistic model, presumably because $C α$ atoms for some residues were packed too tightly in the original structure. Therefore, it may be possible to use the all-atom reconstruction as an indicator of issues with the low-resolution model itself.

We note that low-resolution cryo-EM density maps may make it challenging to trace all residues correctly⁴⁴, especially at flexible regions.⁴⁵ If residues are missing, cg2all treats residues before and after chain breaks as C- and N-termini to produce reasonable reconstructions for the residues that are resolved since cg2all can only produce atomistic coordinates for residues for which coarse-grained beads are available as input. However, for short segments, initial coarse-grained bead positions could be guessed via interpolation and subsequently refined against the cryo-EM density using for example the rapid cryo-EM refinement protocol using cg2all. (refer to Multi-scale sampling for rapid cryo-EM refinement). On the other hand, if longer residue stretches are missing or if the connectivity is incorrect, additional modeling would be needed outside the scope of what cg2all is designed to do in order to generate at least correct coarse-grained models consistent with given experimental data.

Residue-level CG models, such as COCOMO, are increasingly being used to simulate very large systems over long time scales, for example to study protein-protein interactions or liquid-liquid phase separation. Again, cg2all can provide atomistic coordinates from the CG models (Figs. 2C, 2D, and 2F). Using this approach, we could obtain an all-atom structure from a snapshot of a CG model of a condensate formed by IDPs. In the example, a 14,112-residue CG system was converted to an all-atom structure with 183,624 atoms in just 33.5 seconds. This rendered detailed atomic interactions between peptides (e.g., salt bridges between charged side chains) inside the condensate. We note that a fully atomistic simulation of the condensation process is so far impossible to carry out.

Machine-learning based conformational ensemble generators such as FoldingDiff⁴⁶ or idpGAN¹⁴ may be limited to output consisting of $C α$ traces due to resource constraints, but all-atom models can be obtained rapidly via post-processing by cg2all (Fig. 2G). Using a GPU with a large batch size allowed us to convert 25,000 IDP conformations generated via idpGAN to all-atom detail in just 64.6 seconds. Consequently, a practical strategy for the rapid generation of conformational ensemble via machine-learning may be to focus on generating ensembles only at the CG level and leave it up to an all-atom reconstruction scheme as presented here to obtain atomistic ensembles.

Finally, since cg2all can efficiently parallelize all-atom reconstructions on GPUs, entire CG MD simulation trajectories could be rapidly converted to atomistic detail. For example, the conversion of 10,000 frames of a 1,824-residue system takes 1,774 seconds on a GPU with a batch size of 4 (Video S1). This allows not just the consideration of all-atom detail when sampling with CG models, but also, vice versa, suggests that CG models could be used for lossy data compression. This has been proposed before based on the higher-resolution CG model PRIMO⁴⁷, but much greater compression can be achieved if only a single particle per residue is used. For example, a 3.4 GB all-atom trajectory in the DCD format could be compressed into a 210 MB trajectory with single beads, such as $C α$ or center-of-mass, resulting in a 94% compression ratio. Such high degree of compression could greatly facilitate the public sharing of extensive atomistic trajectories that otherwise remains a significant resource challenge^48,49.

Multi-scale sampling for rapid cryo-EM refinement

To further demonstrate the potential of cg2all, we turn to the refinement of models against cryo-EM densities. A typical challenge involves the flexible fitting of initial models from crystallography or structure prediction to intermediate- to low-resolution density maps, for which direct atomistic model building is difficult due to insufficient information⁵⁰. A number of protocols are commonly used such as Coot⁵¹, Isolde⁵², and Direx⁵³. The most effective methods to date employ sampling via atomistic simulations, such as the MDFF protocol⁵⁴. This approach is successful but may take on the order of hours to days because of the computational cost of the simulations. Here we explore the sampling of CG models guided by a density map correlation energy function based on reconstructed all-atom representations that is possible with cg2all. Sampling at the CG level avoids the kinetic barriers that hinder sampling at the atomistic level, whereas using an energy penalty based on atomistic coordinate reconstructions ensures that the optimized CG model is maximally compatible with the experimental data.

The multi-scale approach based on cg2all outperformed local optimization protocols such as energy minimization at the all-atom representation using an atomistic energy function or energy minimization at the CG level using a CG energy function alone across the entire range of map resolutions (Fig. 4). With a high-resolution (3 Å) electron density map, local energy minimization of an all-atom model or a CG model is trapped in a local energy minimum because of a rugged energy landscape. Furthermore, local energy minimization of a CG model cannot exploit the high-resolution information from the electron density map. However, our multi-scale approach effectively optimizes structures by minimizing at the CG level where kinetic barriers are low or absent while still targeting the high-resolution data via all-atom reconstruction. During the minimization process, the gradient resulting from the discrepancy between an all-atom model and the target electron density map is backpropagated to the CG level through the cg2all network. This enables the utilization of high-resolution information from the electron density map at the CG level. Because all-atom models are compared with the high-resolution map, CG beads are less likely to become trapped in a local minimum where a correct all-atom structure could not be generated, as the gradient arising from the discrepancy at the all-atom resolution would guide the CG beads away from such a local minimum toward the correct positions. We believe that this multi-scale approach conceptually retains the accuracy of all-atom representation while achieving better performance by moving on a smooth landscape during minimization at the CG-level. Here, accuracy refers to comparisons of the generated models with the experimental reference structures and agreement with EM maps. The optimized structures obtained via the cg2all-based multi-scale approach reached comparable C⍺-RMSD values to the full MDFF protocol (0.36 vs. 0.35 Å), slightly lower cross-correlation coefficients (CCC, 0.866 vs. 0.881) and slightly larger heavy atom-RMSD values (0.88 vs. 0.74 Å). Importantly, the similar accuracy with cg2all vs. MDFF is achieved in much shorter time (minutes vs. hours). An example for the high model accuracy that can be achieved with cg2all is shown in Fig. 5. In the example, several regions in the initial AlphaFold2 model located outside of the 5 Å resolution electron density (indicated by red arrows) with a heavy-atom RMSD of 2.26 Å and a CCC of 0.829. Using the MDFF protocol with the electron density map, the model was optimized to a heavy-atom RMSD of 0.80 Å and has a higher CCC of 0.941. Our multi-scale approach optimized the model to a comparable accuracy, a heavy-atom RMSD of 0.85 Å and a CCC of 0.936, even though it performed the actual optimization at the CG-level. We note that our multi-scale approach achieved the comparable accuracy in 8.9 minutes, while the MDFF protocol took 8.8 hours.

Figure 4. — Initial models were obtained via AlphaFold2 (A) or ESM-Fold (B). Model quality in terms of cross correlation coefficient (CCC) against target cryo-EM density maps, $C α$ and heavy atom RMSDs were analyzed as a function of computation time for several protocols: (1) optimizations using cg2all models for residue center-of-mass model (blue circles) and $C α$ -trace (cyan circles) followed by all-atom energy minimization, (2) optimization at the residue center-of-mass (brown triangles) or $C α$ -trace representation (orange triangles) followed by all-atom energy minimization, (3) all-atom energy minimization only (red star), and (4) MDFF samplings (magenta ‘+’). The initial model qualities are shown as black dashed lines. The average values (n=9 for AlphaFold2 models and n=6 for ESM-Fold models) for each metric and computation time are shown. Shaded background indicates standard errors of the mean.

Figure 5. — The target tetrameric structure (PDB ID: 3isr ⁶⁴) is shown in green cartoon representation. Its synthetic electron density map was created at 5 Å resolution using “molmap” command in UCSC Chimera⁶⁵, which is based on EMAN2’s pdb2mrc program⁶⁶, and depicted as transparent grey surface at a density level of 0.3. The initial model structure generated by AlphaFold-Multimer⁶⁷ (A), its optimized structure using cg2all model for $C α$ -trace and followed by all-atom minimization (B), and another optimized model via all-atom minimization using MDFF (C) are shown in black, blue, and red. Overall tetrameric structures are shown in the top panels, and they are gradually zoomed in (red boxes) to highlight a region where significant deviations (indicated by red arrows) were optimized in the middle and bottom panels.

When the electron density map has much lower resolution, such as 10 Å, optimization at the all-atom level becomes less effective, even using MDFF, whereas the CG-based optimized refinement, via cg2all, still allows structure refinement, and still within minutes. This opens up the possibility for high-throughput model refinement of many lower-resolution maps, for example to fit models to maps of dynamics conformational ensembles captured via cryo-EM.

In this proof-of-concept demonstration, we employed a naïve CG energy function that only prevents severe clashes between CG beads. Distance restraints between CG beads were applied to keep the protein structure folded, however, this also limited the potential for improvement as it prohibited partial structure unfolding and refolding^55,56. In future work, this will be addressed by introducing a more sophisticated CG energy function that is capable of not only maintaining folded structures but also allowing significant structural changes.

DISCUSSION

The results presented here show that all-atom details of proteins can be captured essentially within experimental uncertainties with only a single bead per amino acid, especially when placed at the residue center of mass, but perhaps also with a more traditional $C α$ -trace representation. This is possible now because of advances in machine learning that allow vast information from known structures in the PDB, to be applied towards different objectives, in this case, the accurate reconstruction of all-atom features from low-resolution models. We focus here on reconstructions from widely used low-resolution representations as they are of significant practical relevance, but note that the correspondence between reduced and atomistic coordinate representations could also be improved by optimizing the CG representation itself⁵⁷.

It should be reiterated, that the all-atom reconstructions obtained here focus on finding a chemically realistic representative structure for the most likely time- and ensemble-averaged conformation. Conformational dynamics in degrees of freedoms that are not captured in the reduced representation are effectively averaged out. The resulting structures are therefore experiment-like structures where dynamics may be described only in the form of B-factors. We do not predict B-factors here for the reconstructed structures, but note that other methods are available for estimating B-factors from given atomistic structures⁵⁸.

The approach taken here was initially motivated by recent advances in protein structure prediction methods, but it is different in terms of input as well as the final objective. Sequence alignments or template libraries are not used here, instead a lower-resolution model serves as input. On the other hand, even although the ultimate goal of providing physically realistic, accurate atomistic structures is essentially the same, structure prediction methods aim at providing the best model for the likely native state whereas the method introduced here aims at generating atomistic coordinates for any conformation, whether energetically favorable or not. This suggests that recent advances in machine learning have broad implications for structural biology that reach far beyond just the prediction of native structures from sequence.

There are immediate applications in adding accurate atomistic coordinates to CG representations Low-resolution protein structure models based on experiments as well as CG models from simulations can thus be interpreted in atomistic detail. This is especially relevant for the generation of structures and ensembles via machine learning where the addition of atomistic detail often presents a significant burden during model training.

An important feature is that deterministic neural network architectures are not just very efficient but allow gradients to be back-propagated all the way from the final output (i.e. atomistic conformations) to the input (i.e. CG conformations). In essence, this provides an avenue for tightly coupled bidirectional multi-scaling. This approach again neglects the full dynamics at the atomistic level and instead emphasizes ensemble-averaged conformations as the representative atomistic states. Therefore, this framework is most suitable for interpreting time- and ensembled-averaged experimental data, especially data at lower resolutions. As one important application we highlight the refinement of models against cryo-EM densities based on sampling at a CG level but with energy penalty functions evaluated at the atomistic level from reconstructed all-atom conformations. Finally, we recognize that it is necessary to consider conformational sampling of all degrees of freedom, e.g. via traditional simulations^59,60 or machine-learning approaches^57,61 to achieve full thermodynamic consistency across different levels of resolution. Therefore, it will be ultimately necessary to learn how to generate not just a single ensemble-averaged structure, but entire conformational ensembles that are consistent with a given CG representation⁵⁷.

STAR METHODS

RESOURCE AVAILABILITY

Lead contact

Further information and requests for resources should be directed to and will be fulfilled by the lead contact, Michael Feig (mfeiglab@gmail.com)

Materials availability

This study did not generate any reagents.

Data and code availability

No new data has been generated in this study.

The source code and model parameter files of the cg2all method are available at https://github.com/huhlim/cg2all⁶⁸. It can be locally installed using a PIP command, “pip install git+http://github.com/huhlim/cg2all”. The list of PDB IDs and the corresponding PDB files (both cleaned up and side chain conformation augmented structure files) are available at https://zenodo.org/record/8273739 ⁶⁹.

Any additional information required to reanalyze the data reported in this paper is available from the lead contact upon request.

METHOD DETAILS

Experimental datasets

Two sets of experimental structures were clustered with a maximum mutual sequence identity of 70%, and one structure for each cluster was left. The original Top8000 ⁷⁰ and the PISCES ⁷¹ sets consisted of a single chain per Protein Data Bank (PDB) entry, however, we used all protein chains in each PDB entry instead. PDB entries with more than 1,200 residues were excluded. As a result, there were 7,130 and 30,354 entries in PDB 6k and 29k sets, respectively. To have common subsets for model validation and test, 720 entries were randomly selected among the common entries for each validation and test sets. The remaining 5,690 and 28,914 structures were used as PDB 6k and 29k training sets, respectively.

The Top8000 structures were further analyzed to obtain statistics of bonded geometries for building secondary structure-dependent rigid body (SS-dep) blocks. Three-state secondary structure for every residue was assigned by the DSSP algorithm ⁷² using the MDTraj Python library package ⁷³. Bond lengths, angles, and improper dihedral angles defined by amino acid topologies of the CHARMM36m force field ⁷⁴ were calculated. Their averaged values for each secondary structure type were then used to build SS-dep blocks.

Simulation datasets

We sampled an ensemble of structures by performing all-atom molecular dynamics (MD) simulations using OpenMM ⁷⁵. A protein structure was placed at the center of a periodic rectangular box with at least 10 Å distance from any protein atom to any dimension of the box edges. The remaining space in the simulation box was filled with the CHARMM version of TIP3P water molecules ⁷⁶. Some water molecules were randomly replaced with sodium or chloride ions to neutralize the system and achieve a total ion concentration of 0.015 M. The CHARMM36m force field ⁷⁴ was applied to describe the system throughout the series of simulations. The system was locally minimized with the l-BFGS-b algorithm ⁷⁷ in the presence of harmonic positional restraints on every $C α$ atom with a force constant of 0.5 kcal/mol/Å². Then, the systems were gradually heated to 298.15 K and equilibrated via Langevin dynamics simulations for 1 ns with a friction coefficient of 0.01/ps and a 2-fs integration time step. The NVT ensemble and the NpT ensemble at 1 bar with a Monte Carlo barostat were applied during the heating and equilibration steps, respectively. An ensemble of protein conformations was sampled from a 50 ns-long Langevin dynamics simulation with a friction coefficient of 1/ps and a 2-fs integration time step at 298.15 K and 1 bar. Five snapshots of protein conformations were picked up for further tests by selecting frames for every 10 ns. In total, 3,600 all-atom conformations were generated for 720 test set structures for further tests.

During minimization with COCOMO ¹⁸, harmonic positional restraints were applied to every bead of the CG model with a force constant of 1.0 kcal/mol/Å² to keep the original all-atom conformations as the respective ground truth conformations. Upon minimization, the conformations were distorted from their all-atom structures by 0.30 Å on average.

Input features

Input features extracted from a CG model are summarized in Table S1. In total, 57 (17 from the local geometries and 40 from the residue type embedding) scalar and four (or more for multiple site CG models) vector node features and three scalar edge features were used as input features. Pseudo-bond angles and -torsion angles were encoded using cosine and sine functions to account for periodicity. The number of neighboring nodes (e.g., < 10 Å) and the presence of a previous or next residue (to distinguish terminal residues and chain breaks) were added as scalar features. The residue type was converted to 40 scalars via a trainable embedding layer and concatenated with the scalar features. For vector features, unit bond vectors as illustrated in Fig. S1 were used for conversion from multiple site coarse-grained models such as a MARTINI model ²⁰, vectors from a BB bead to SC beads were additionally used to incorporate side chain information. The edge connection type (connection via a peptide bond, an inter-residue contact through space, or a disulfide bond) were used via one-hot encoding as edge features.

Neural network model

At the core of SE(3)-equivalent neural network model, the SE(3)-Transformers architecture ³⁷ was adopted. The input node features were processed via N (=4 for the baseline model) linear layer blocks to produce hidden features of 64 scalar and 32 vector values. (Methods S1, Algorithm 1) A LayerNorm ⁷⁸ and an exponential linear unit (ELU) activation function ⁷⁹ were used to normalize the norm of features for each degree, while keeping their phase. (<monospace>NormSE3</monospace>) The first linear layer without bias terms (<monospace>LinearNoBias</monospace>) projects the input features to hidden features with the numbers of channels of 64 and 32 for scalars and vectors, respectively. The linear layer blocks consisting of a LayerNorm, an ELU activation function, and a linear layer without bias terms are repeated N-1 times, while the numbers of channels for each degree of features are maintained. Until this step, interactions between nodes are not considered yet, and features are processed for each node and each degree. In the interaction module, we facilitated the original SE(3)-Transformers architecture with M (=4 for the baseline model) SE(3)-Transformers blocks with a LayerNorm and an ELU activation function for radial profiles (<monospace>AttentionBlockSE3</monospace>) to communicate between nodes through edges and evaluate tensor products between different degrees of hidden features. (Methods S1, Algorithm 2) For an <monospace>AttentionBlockSE3</monospace>, we used eight attention heads and 32 hidden channels of scalars (l=0), vectors (l=1), and rank-two tensors (l=2). A normalization layer (<monospace>NormSE3</monospace>) was followed by to stabilize the training. At the end of the interaction module, a SE(3)-equivariant convolutional layer with a LayerNorm and an ELU activation function for radial profiles (<monospace>ConvSE3</monospace>) was used to produce the output of the module. Throughout the module, the number of channels for each degree of hidden features were maintained between blocks: 64 for scalars and 32 for vectors. Finally, the input representations of the module were added to the output representations for a skip connection.⁸⁰

We used four linear layers and four SE(3)-Transformers blocks for the baseline model. Alternatively, fewer and greater numbers of blocks were examined to evaluate performance dependencies in the model size. We adopted ELU activation functions as replacements of rectified linear unit (ReLU) functions ⁸¹, which were used for the original SE(3)-Transformers work ³⁷. For hidden features of the SE(3)-Transformers blocks, features up to the degree of 2 were passed within a block, and a lower value (1) was also tested. For a protein structure, we used a subgraph with a crop size of 256 residues as the baseline and tested if a larger crop (384 residues) could improve the performance. Secondary structure-dependent rigid-body blocks were not used for the baseline, but they were adopted as optional features.

Structure module

The structure module further processed the output of the interaction module to predict values for building all-atom structures via N (=4 for the baseline model) linear layer blocks. (Methods S1, Algorithm 3) It was analogous to the initialization module but projected hidden features with greater numbers of channels to predict 16 scalar (or 20 if SS-dependent rigid body blocks were used) and 3 vector values for the followed all-atom structure building. An all-atom structure was built using the predicted values. For this process, a similar procedure that is used by AlphaFold2 was adopted ¹¹. AlphaFold2 used rigid-body blocks of backbone atoms (N, $C α$ , and C atoms), the backbone oxygen atom, and side chain heavy atoms that were segmented by rotatable torsion angles. During the step of structure building, backbone rigid-body blocks for residues were oriented first using predicted translations $(t)$ and three-dimensional rotations $(R)$ . The remaining blocks were placed in the order of the bond connectivity from the backbone block to the tip of each side chain by rotating them by predicted torsion angles ( $ϕ, ψ$ , and $χ s$ ). In our work, we extended the procedure to build all-atoms including hydrogen atoms. Thus, 16 predicted scalar values were used as sine and cosine values of the torsion angles ( $ϕ, ψ$ , 4 $χ s$ , and 2 hydrogen atom-only torsion angles) to construct rotation matrices. In addition, secondary structure-dependent rigid body blocks were used as we found that some blocks have distinguished bonded geometries (bond lengths and angles and improper dihedrals) depending on the secondary structure. Thus, secondary structure prediction (SS) was also made by the module. Four predicted scalar values determined which rigid body blocks to use among blocks for helix, sheet, coil, or SS-independent blocks. One output vector predicted a translation vector $(t)$ , which places the $C α$ atom from the representative bead for a residue. We note that we used a 6D representation ⁸² using the remaining two predicted vectors, which describes three-dimensional rotation using two unit vectors and the Gram-Schmidt process, instead of the quaternion-based approach used by AlphaFold2, as it gave better performance in terms of accuracy and convergence during training for many SO(3) prediction tasks because of continuity in the rotation representations ⁸². For the final step, both N- and C-termini were patched by replacing backbone hydrogen (HN) and oxygen (O) with the terminal amino (NH₃-) and carboxyl (-COO⁻) groups, respectively, using the predicted position of the atoms.

Model training

Each model was trained for 300 and 120 epochs with the PDB 6k and 29k training sets, respectively, using a batch size of 4. This corresponds to 426,600 and 867,360 total training steps. An input data graph with more than 256 nodes for training was randomly cropped to a consecutive 256 residue graph by obtaining its subgraph. An Adam optimizer was used with learning rates of 0.01 for parameters for scalar features of the structure module and 0.001 for the others. The learning rates were linearly increased for the first ten epochs and then exponentially decreased with a multiplicative factor of 0.995. Clipping was used to prevent extreme gradients, and gradient checkpointing reduced memory consumption. Models were implemented in PyTorch, and they were trained using PyTorch Lightning ⁸³. The training of models was carried out on two NVIDIA GeForce RTX 2080 Ti GPU cards (11 GB of VRAM) with Distributed Data Parallel (DDP) to use multiple GPUs and eight CPU threads. We trained three models for each model variant to obtain statistics.

We fine-tuned the trained models for an additional 10 epochs to obtain variants where coordinates of the input coarse-grained structures are forced to remain unchanged. This allowed us to compare with other methods that maintain coordinates in the input structures. For example, sidechain prediction methods such as SCWRL4 ³⁰ and AttnPacker ³³ only predict sidechain conformations, leaving the backbone structures unchanged. It also allowed us to test to what degree cg2all may be able to correct for slight errors in the reduced representations.

Loss function

Models were trained with a loss function (Eq. 1) that consisted of training data-dependent loss functions and data-independent (physics-based) loss functions:

L = \begin{matrix} 5.0 L_{F A P E, C α} + 1.0 L_{B B} + 1.0 L_{R} + 1.0 L_{b a c k b o n e g e o m e t r y} (+ 0.1 L_{S S}) (D a t a - d e p e n d e n t) \\ + 5.0 L_{t o r s i o n} + 1.0 L_{v_{c n t r}} \\ + 5.0 L_{a t o m i c c l a s h} + 0.1 L_{t o r s i o n e n e r g y} + 1.0 L_{s i d e c h a i n g e o m e t r y} (P h y s i c s - b a s e d) \end{matrix}

(1)

The FAPE, $C α$ loss $(L_{F A P E, C α})$ was first introduced by AlphaFold2 ¹¹, and we used a variant that uses only $C α$ atoms for its evaluation with a distance clamp value of 10 Å. (Methods S1, Algorithm 4) The backbone loss $(L_{B B})$ also contributed to correctly placing backbone rigid bodies (Eq. 2).

L_{B B} (r_{B B}^{t r u t h}) = |r_{B B} - r_{B B}^{t r u t h}| + |1 - \vec{u_{C α \to N}} \cdot \vec{u_{C α \to N}^{t r u t h}}| + |1 - \vec{u_{C α \to C}} \cdot \vec{u_{C α \to C}^{t r u t h}}|

(2)

where $\vec{u}$ represents a unit vector. The loss function for three-dimensional rotation representation consisted of the similarity of two vectors for the 6D representation ⁸² against their truths and an auxiliary term that ensures their vector sizes close to 1. (Eq. 3)

L_{R} (\vec{R_{0}}, \vec{R_{1}} ∣ \vec{R_{0}^{t r u t h}}, \vec{R_{1}^{t r u t h}}) = |(\vec{R_{0}} - \vec{R_{0}^{t r u t h}}) + (\vec{R_{1}} - \vec{R_{1}^{t r u t h}})| + 0.01 (| ∥\vec{R_{1}}∥ - 1 | + |∥\vec{R_{1}}∥ - 1|)

(3)

where $\vec{R_{0}}$ and $\vec{R_{1}}$ are vectors for the 6D representation. A loss function helped the model having correct bonded geometries for backbone atoms (Eq. 4). It penalized deviations of peptide bond distances $(b_{C, + N})$ and peptide bond including bond angles ( $θ_{C α, C, + N}$ and $θ_{C, + N, + C α}$ ).

L_{b a c k b o n e g e o m e t r y} (b_{C, + N}, θ_{C α, C, + N}, θ_{C, + N, + C α} ∣ b_{C, + N}^{t r u t h}, θ_{C α, C, + N}^{t r u t h}, θ_{C, + N, + C α}^{t r u t h}) = |b_{C, + N} - b_{C, + N}^{t r u t h}| + \frac{1}{2} (|θ_{C α, C, + N} - θ_{C α, C, + N}^{t r u t h}| + |θ_{C, + N, + C α} - θ_{C, + N, + C α}^{t r u t h}|)

(4)

When the secondary structure-dependent rigid body blocks were used, a cross entropy loss for secondary structure prediction was additionally used.

Moreover, there were two loss functions for correctly reconstructing side chain atoms. The torsion angle loss tried to reduce discrepancies between the predicted torsion angles $(\{θ_{k}\})$ and their truth values $({θ_{k}^{t r u t h}})$ (Eq. 5).

L_{t o r s i o n} (\{θ_{k}\} ∣ {θ_{k}^{t r u t h}, θ_{k}^{t r u t h, a l t s}}) = \sum_{θ_{k} is d e f i n e d} (1 - m a x (c o s (θ_{k} - θ_{k}^{t r u t h}), c o s (θ_{k} - (θ_{k}^{t r u t h, a l t s})))

(5)

Some side chain torsion angles that have periodicity: χ₂ angles of Phe and Tyr, methyl groups in Ala, Ile, Leu, Met, Thr, and Val, the side chain amino group in Lys, and the side chain carboxyl groups in Asp and Glu. For those torsion angles, alternative truth values $({θ_{k}^{t r u t h, a l t s}})$ due to their periodicity were considered for the calculation. Furthermore, solvent-exposed side chains can have multiple valid conformations, while their experimental structures usually presented only one of them. For the training of models that convert from a $C α$ -based model, putative side chain conformations were generated prior to the training and used as additional ${θ_{k}^{t r u t h, a l t s}}$ . The procedure for putative side chain conformation generation is described in more detail below. The other loss function for side chain atoms depended on vectors from the $C α$ atom to the center of mass of a residue $(\vec{v_{c n t r}})$ . Their deviation in their vector size to their truth values and their cosine similarity was used to learn side chain orientations at a lower resolution.

L_{v_{c n t r}} (\vec{v_{c n t r}^{t r u t h}}) = |‖ \vec{v_{c n t r}} ‖ - ∥\vec{v_{c n t r}^{t r u t h}}∥| + |1 - \vec{u_{c n t r}} \cdot \vec{u_{c n t r}^{t r u t h}}|

(6)

In addition to these data-dependent loss functions, three physics-based terms were introduced to improve the geometric properties of the reconstructed models. These terms relied on the CHARMM36m force field ⁷⁴. As two atoms rarely overlapped within the sum of their atomic radii, atomic clashes were penalized (Eq. 7).

L_{a t o m i c c l a s h} (r) = \sum_{i < j, r_{i j} < 14 Å} \sum_{a \in i} \sum_{b \in j e x c l u d e 1 - 2,3, 4 p a i r s} \sqrt{ε_{a} ε_{b}} \times {(m i n (0, d_{a b} - σ_{a} - σ_{b}))}^{2}

(7)

where $ε$ and $σ$ are the depth of the potential and the distance at which the potential becomes zero in the Lennard-Jones potential. Torsion energy terms ( $L_{t o r s i o n e n e r g y}$ ) of the force field was applied to penalize disfavored torsion angles (Eq. 8). Torsion angles that can be defined within a residue were considered for evaluation, thus, torsion angles that span two consecutive residues (e.g., $ψ, ϕ$ , and $ω$ angles) were not subjected to the loss functions. In order to preserve torsion angle distributions, a torsion energy clamp $(E_{t o r s i o n e n e r g y}^{c l a m p})$ was used with a value of 0.6 kcal/mol.

L_{t o r s i o n e n e r g y} (\{θ_{k}\}) = \sum_{θ_{k} i s d e f i n e d} m a x (0, E_{t o r s i o n e n e r g y} (θ_{k}) - E_{t o r s i o n e n e r g y}^{m i n} (θ_{k}) - E_{t o r s i o n e n e r g y}^{c l a m p})

(8)

The final physical loss term was applied for two types of bonds that connect rigid body blocks in special ways, namely for proline ring closure and disulfide bonds. For these bonds, equilibrium bond lengths of 1.455 and 2.029 Å, respectively, were targeted (Eq. 9).

L_{S i d e c h a i n g e o m e t r y} (b_{P r o, N, C D}, b_{S S B O N D}) = |b_{P r o, N, C D} - b_{P r o, N, C D}^{o}| + |b_{S S B O N D} - b_{S S B O N D}^{o}|

(9)

Augmentation of putative side chain conformations

Alternative possible side chain conformations were generated prior to the training using first SCWRL4 ³⁰, followed by REDUCE ²⁶ and local energy minimization using the CHARMM36m force field ⁷⁴. Experimental structures, especially those determined by X-ray crystallography, have only one conformation in PDB in most of the entries even though there can be alternative coordinates. However, as proteins are not static molecules, they can have diverse conformation especially for solvent-exposed side chains. As such, reconstruction to those alternative conformations should not be penalized unless they are unfavorable. Because we aimed to reconstruct an all-atom conformation including side chains for a given $C α$ -trace of a protein, we generated putative side chain conformation. For a protein structure, side chain structures were predicted on the protein’s backbone using SCWRL4, which uses a rotamer library and optimizes combinations of rotamer states. Then, all hydrogens were attached to the predicted structure with an optimization of torsion angles for the side chain amide groups in Asn and Gln and the imidazole ring in His. Finally, the structures were subjected to energy minimization using the l-BFGS-b algorithm for up to 1,000 steps with the CHARMM36m force field using OpenMM ⁷⁵. To prevent extensive deviation of backbone positions, harmonic positional restraints were applied on every N, $C α$ , C, O, and $C β$ atoms with a force constant of 1.0 kcal/mol/Å². Torsion angles from the energy minimized structure were used as an additional set of ${θ_{k}^{t r u t h, a l t s}}$ for the torsion angle loss (Eq. 5).

Hyperparameter optimization and ablation studies

Several features were introduced in our neural network models and their training, and their contributions were evaluated via ablation studies. (Fig. S8) First of all, we used a hybrid loss function that consisted of data-dependent and -independent (or physics-based) loss functions (Eq. 1). The physics-based loss functions were introduced to learn the characteristics of a protein molecule more efficiently and to complement insufficient data points. The atomic clash loss penalized inter-atomic clashes and effectively lowered the clash score. Side chain modeling as rotamer outliers could be suppressed by introducing the torsion energy loss function (Fig. S9). Without the torsion energy loss function, side chain rotamer states could not be clearly separated, and some inferences resulted in rotamer outliers. Average MolProbity scores ³⁸ by models with and without those physics-based loss functions were different by 0.254 (2.292 vs. 2.546). Furthermore, side chain conformations were augmented prior to the model training to account for their putative heterogenic conformations due to their conformational flexibility. Because some side chains (especially solvent-exposed ones) can have alternative conformations in addition to the experimentally resolved one, both conformations should not be penalized unless there are atomic clashes. This side chain augmentation additionally helped suppress generating rotamer outliers (Fig. S9). If there were side chains with very similar input features but in different rotamer states in the training set, models could be trained to predict in the average of the rotamer states unless the side chain augmentation was used, and this could result in the inference of rotamer outliers. For example, for a homodimer with pseudo-C₂ symmetry, some side chain conformations may vary in different monomers, while overall $C α$ -traces were almost identical. As illustrated in Fig. S9B, if an Arginine from a monomer has a χ₁ angle of −180 degree, while the other Arginine in the symmetry has a χ₁ angle of −60 degree, training with these data would result in predicting their averaged value, −120 degree, which is a rotamer outlier. It is because the averaged torsion angle loss has a minimum at the value. With the consideration of both possible conformations in the torsion angle loss function via the side chain augmentation, the loss function has multiple minima (e.g., −180 and −60 degrees in this example), and the inference of rotamer outliers is diminished.

We tested two neural network parameters that were related to the amount of information passed between layers: 1) the choice of the activation function (ELU vs. ReLU); and 2) the maximum degree for the SE(3)-Transformers (l=2 vs. 1). When the ELU activation function was replaced with the ReLU function, which was originally used in SE(3)-Transformers, the overall quality of reconstructed models dropped slightly. It was probably because the use of ReLU function deactivated some neurons, which is known as the “dying ReLU problem” ⁸⁴, and the neurons could not be efficiently utilized. Regarding the maximum degree for the SE(3)-Transformers ³⁷, it was beneficial to use up to the degree of 2 features, even although the input and output features utilized only features up to a degree of 1 (scalars and vectors). Fuchs et al. observed that there was big improvement when they switched the maximum degree from 1 to 2 ³⁷. We observed a similar trend especially in features for which relationships between other residues were important such as atomic clashes or side chain angle accuracies. On the other hand, Ramachandran angles and rotamer outlier ratios were not affected as much since they could be predicted well with only localized information. Presumably, the use of higher degree hidden features provided inter-residue information, and this resulted in better predictions.

Finally, we examined if more training data, larger model, and secondary structure-dependent rigid body blocks (SS-dep blocks) could improve the performance. When we increased the training dataset size from 5,690 (6k) to 28,914 (29k) with the baseline model, there was marginal improvement. Presumably, the baseline model did not have enough capacity for learning with the bigger training data. Larger models with more layers showed comparable results to the baseline model with the smaller training data set. (Fig. S8) However, the performance with smaller models dropped significantly. We observed that training of models with eight linear layer blocks was unstable and occasionally resulted in poor performance. When larger models were trained using the bigger training dataset, the bigger data could be learned by larger models as they had enough capacity to learn them. They outperformed in terms of clash score and side chain torsion accuracies. Similarly, the use of larger crops (384 residues) slightly improved the MolProbity score. The use of SS-dep blocks contributed to accurately model backbone bonded geometries including bond lengths, angles, and Ramachandran angles. The best performance was achieved by aggregating all these components.

Structure refinement against cryo-EM density map via the cg2all network

The cg2all network enabled local optimization of a CG representation using scoring functions at both the CG and atomistic representations. (Methods S1, Algorithm 5) In the algorithm, an atomistic structure is generated from a CG structure via a cg2all network for the CG representation. An objective function can be defined as a function of both atomistic and the CG representation. Once the objective function is evaluated, the score is backpropagated to get derivatives of the CG structure. Then, the CG structure is updated using the derivative. We applied this algorithm to optimize incorrect protein model structures against cryo-EM density maps as an example usage. Nine protein structures were arbitrarily selected from the test set, and their biological assemblies were set as target structures: 1kq1 ⁸⁵ (369 residues, 6-mer), 1vim ⁸⁶ (760 residues, 4-mer), 1g2o ⁸⁷ (786 residues, 3-mer), 2ibp ⁸⁸ (814 residues, 2-mer), 1a2z ⁸⁹ (880 residues, 4-mer), 1s57 ⁹⁰ (906 residues, 6-mer), 3isr ⁶⁴ (1,149 residues, 4-mer), 1j0h ⁹¹ (1,176 residues, 2-mer), and 1wur ⁹² (1,848 residues, 10-mer). For those experimental structures, synthetic electron density maps were generated using “molmap” command in UCSF Chimera ⁶⁵ that employs EMAN2’s “pdb2mrc” program ⁶⁶ at resolutions of 3, 4, 5, 6, 8, and 10 Å. Initial models for local optimization against the electron density maps were predicted by AlphaFold-Multimer ⁶⁷ with multiple sequence alignments from the ColabFold API ⁹³ and without structural templates using ESMFold ¹³. We tested our local optimization protocol that utilized an objective function based on both CG and atomistic representations and compared with alternative protocols, including local optimizations at either CG or atomistic representations and molecular dynamics flexible fitting (MDFF) protocol ⁵⁴.

The objective function for local optimization against electron density map consisted of four objective functions in either atomistic or the CG representation. The first one was the electron density map potential taken from MDFF (Eq. 10):

U ({\vec{x}}) = \sum_{i} w_{i} m a x (1,1 - \frac{Φ ({\vec{x}}_{i}) - Φ_{t h r}}{Φ_{m a x} - Φ_{t h r}})

(10)

where $Φ (x_{i})$ refers to the values of the density map.

For this test, we set $Φ_{thr}$ to zero and $w_{i}$ to corresponding atom’s atomic mass. The potential was evaluated at the atomistic representation using predicted coordinates from a $C α$ -trace using the cg2all model network. The second one was backbone bonded potential at the atomistic representation (Eq. 4) The third one was a simple CG potential that evaluated pseudo-bond length and angle potential energies (Eq. 11) and soft-core van der Waals potential energy (Eq. 12).

U_{b o n d e d} = {(\frac{b_{C α - C α} - \bar{b_{C α - C α}}}{σ (b_{C α - C α})})}^{2} + {(\frac{θ_{C α - C α - C α} - \bar{θ_{C α - C α - C α}}}{σ (θ_{C α - C α - C α})})}^{2}

(11)

U_{v d W} = \sum_{i j} {(m i n (0, d_{i j} - d_{i j, m i n}))}^{2}

(12)

Parameters for the potential functions were obtained from a statistical analysis on the Top8000 structure. As the final one, $C α - C α$ distance restraints were applied to residue pairs for which the distances in the initial model were closer than 10 Å. For this experiment, we set relative weights to 1:1:0.1:100.

Initial protein model structures were locally optimized at either residue center-of-mass or $C α$ -trace representations using a cg2all network-based optimization algorithm (Methods S1, Algorithm 1). For this test, we superposed the initial structures onto their target experimental structures using MM-align ⁹⁴ as initial fits to electron density maps, and the superposition was iteratively updated as well by optimizing the overall structural translation and rotation against the density maps. A structure was optimized using the Adam optimizer ⁹⁵ for 1,000 or 2,500 steps for AlphaFold and ESMFold models, respectively, and intermediate snapshots were recorded for every 100 steps. The learning rate was updated every step using a cosine annealing scheduler ⁹⁶, which changed the learning rate from 0.005 to 0.0005 for 200 steps. From the snapshots, a structure with the highest cross-correlation coefficients (CCC) to the target density map was selected as an optimized structure. As alternatives, we performed local optimization with a CG representation using only CG-level objective functions. For the electron density map potential, we used the total mass of a residue as 𝑤_𝑖 instead. Optimization at a CG representation was carried out in the same way. Then, atomistic structures were generated from $C α$ -traces using the cg2all network, and the highest CCC structure was selected as an optimized structure using the CG representation. For the local optimization protocol at atomistic resolution, we took the initial minimization step of MDFF protocol implemented by CHARMM-GUI ⁹⁷ and modified it not to use positional restraints. It performed local energy minimization for 1,000 steps in vacuum using the CHARMM36m force field using NAMD ⁹⁸, the MDFF electron density map potential, and restraints for secondary structure elements, chirality, and for fixing cis-peptide bonds. We also applied the local optimization protocol at atomistic representation to optimized structures from cg2all network-based optimization and optimization at the CG representations for better agreement of solvent exposed sidechains. As the final option, we carried out the full MDFF protocol implemented by CHARMM-GUI ⁹⁷.

QUANTIFICATION AND STATISTICAL ANALYSIS

The performance of the machine-learning model was assessed by analyzing its performance on independent test sets that are distinct from training and validation sets as described in the Method Details section. Performance metrics reported in Tables 1–4 as well as additional results shown in Figures S2–S5 and S7–S9 were averaged over test sets consisting of 720 structures. Standard deviations are reported in Tables 1–4 to indicate the statistical variation of each metric. In addition, the results from the ablation study in Figure S8 are averaged over three independent training runs. CryoEM refinement results were averaged over nine and six different structures for AlphaFold2 and ESMFold models, respectively. To assess uncertainties, standard errors of the mean were calculated are indicated in Figure 4. We did not perform optimization of ESMFold models for 1wur (ESMFold could not model a structure due to its large size), 1j0h and 1s57 (very poor initial model quality; Cɑ-RMSDs of 56.1 and 46.0 Å, respectively). We performed statistical analysis using in-house Python scripts based on functions from the NumPy package. Details of the experiments can be found in the figure legends and table footnotes.

Supplementary Material

Video S1, Related to Figure 2. Reconstructed all-atom trajectory from CG representations. An example of conversion of simulation trajectory from a $C α$ -level CG model to the all-atom model as described in Figure 2D. A periodic simulation box is shown as a blue box. $C α$ -traces of proteins are presented as traces on the left side. Their converted all-atom models are shown as cartoon representation on the right side with additional side chain structures as sticks. Each chain has different colors but used the same colors for both representations.

Download video file^{(21.5MB, mp4)}

NIHMS1944498-supplement-2.pdf^{(4.6MB, pdf)}

KEY RESOURCES TABLE.

REAGENT or RESOURCE	SOURCE	IDENTIFIER
Deposited data
List of PDB IDs and corresponding PDB files	This paper	10.5281/zenodo.10011305




Software and algorithms
Cg2all source code and model parameter files	This paper	10.5281/zenodo.8273738
		https://github.com/huhlim/cg2all

Open in a new tab

Highlights.

Accurate all-atom reconstruction from coarse-grained representations of proteins
Addition of atomistic detail to lower-resolution protein models
Rapid refinement against cryoEM maps via multiscale protocol

ACKNOWLEDGMENTS

Funding was provided by the National Institute of Health (NIGMS) grant R35 GM126948.

Footnotes

DECLARATION OF INTERESTS

The authors declare no competing interests.

ADDITIONAL RESOURCES

cg2all is demonstrated at https://huggingface.co/spaces/huhlim/cg2all and https://colab.research.google.com/github/huhlim/cg2all/blob/main/cg2all.ipynb. A Google Colab notebook for local optimization with cryo-EM density map is available at https://colab.research.google.com/github/huhlim/cg2all/blob/main/cryo_em_minimizer.ipynb.

Publisher's Disclaimer: This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

REFERENCES

1.Shi Y (2014). A glimpse of structural biology through X-ray crystallography. Cell 159, 995–1014. 10.1016/j.cell.2014.10.051. [DOI] [PubMed] [Google Scholar]
2.Jones N (2014). Crystallography: Atomic secrets. Nature 505, 602–603. 10.1038/505602a. [DOI] [PubMed] [Google Scholar]
3.Wüthrich K (1990). Protein structure determination in solution by NMR spectroscopy. J Biol Chem 265, 22059–22062. 10.1016/S0021-9258(18)45665-7. [DOI] [PubMed] [Google Scholar]
4.Cheng Y (2015). Single-Particle Cryo-EM at Crystallographic Resolution. Cell 161, 450–457. 10.1016/j.cell.2015.03.049. [DOI] [PMC free article] [PubMed] [Google Scholar]
5.Nogales E (2016). The development of cryo-EM into a mainstream structural biology technique. Nat Methods 13, 24–27. 10.1038/nmeth.3694. [DOI] [PMC free article] [PubMed] [Google Scholar]
6.Garman EF (2014). Developments in x-ray crystallographic structure determination of biological macromolecules. Science 343, 1102–1108. 10.1126/science.1247829. [DOI] [PubMed] [Google Scholar]
7.Kmiecik S, Gront D, Kolinski M, Wieteska L, Dawid AE, and Kolinski A (2016). Coarse-Grained Protein Models and Their Applications. Chem Rev 116, 7898–7936. 10.1021/acs.chemrev.6b00163. [DOI] [PubMed] [Google Scholar]
8.Saunders MG, and Voth GA (2013). Coarse-graining methods for computational biology. Annu Rev Biophys 42, 73–93. 10.1146/annurev-biophys-083012-130348. [DOI] [PubMed] [Google Scholar]
9.Feig M, Chocholoušová J, and Tanizaki S (2006). Extending the horizon: towards the efficient modeling of large biomolecular complexes in atomic detail. Theor Chem Acc 116, 194–205. 10.1007/s00214-005-0062-4. [DOI] [Google Scholar]
10.Lane TJ, Shukla D, Beauchamp KA, and Pande VS (2013). To milliseconds and beyond: challenges in the simulation of protein folding. Curr Opin Struct Biol 23, 58–65. 10.1016/j.sbi.2012.11.002. [DOI] [PMC free article] [PubMed] [Google Scholar]
11.Jumper J, Evans R, Pritzel A, Green T, Figurnov M, Ronneberger O, Tunyasuvunakool K, Bates R, Zidek A, Potapenko A, et al. (2021). Highly accurate protein structure prediction with AlphaFold. Nature 596, 583–589. 10.1038/s41586-021-03819-2. [DOI] [PMC free article] [PubMed] [Google Scholar]
12.Baek M, DiMaio F, Anishchenko I, Dauparas J, Ovchinnikov S, Lee GR, Wang J, Cong Q, Kinch LN, Schaeffer RD, et al. (2021). Accurate prediction of protein structures and interactions using a three-track neural network. Science 373, 871–876. 10.1126/science.abj8754. [DOI] [PMC free article] [PubMed] [Google Scholar]
13.Lin Z, Akin H, Rao R, Hie B, Zhu Z, Lu W, Smetanin N, Verkuil R, Kabeli O, Shmueli Y, et al. (2023). Evolutionary-scale prediction of atomic-level protein structure with a language model. Science 379, 1123–1130. 10.1126/science.ade2574. [DOI] [PubMed] [Google Scholar]
14.Janson G, Valdes-Garcia G, Heo L, and Feig M (2023). Direct generation of protein conformational ensembles via machine learning. Nat Commun 14, 774. 10.1038/s41467-023-36443-x. [DOI] [PMC free article] [PubMed] [Google Scholar]
15.Noé F, Olsson S, Kohler J, and Wu H (2019). Boltzmann generators: Sampling equilibrium states of many-body systems with deep learning. Science 365, eaaw1147. 10.1126/science.aaw1147. [DOI] [PubMed] [Google Scholar]
16.Dutagaci B, Nawrocki G, Goodluck J, Ashkarran AA, Hoogstraten CG, Lapidus LJ, and Feig M (2021). Charge-driven condensation of RNA and proteins suggests broad role of phase separation in cytoplasmic environments. Elife 10, e64004. 10.7554/eLife.64004. [DOI] [PMC free article] [PubMed] [Google Scholar]
17.Yu I, Mori T, Ando T, Harada R, Jung J, Sugita Y, and Feig M (2016). Biomolecular interactions modulate macromolecular structure and dynamics in atomistic model of a bacterial cytoplasm. Elife 5, e19274. 10.7554/eLife.19274. [DOI] [PMC free article] [PubMed] [Google Scholar]
18.Valdes-Garcia G, Heo L, Lapidus LJ, and Feig M (2023). Modeling Concentration-dependent Phase Separation Processes Involving Peptides and RNA via Residue-Based Coarse-Graining. J Chem Theory Comput 19, 669–678. 10.1021/acs.jctc.2c00856. [DOI] [PMC free article] [PubMed] [Google Scholar]
19.Dignon GL, Zheng W, Kim YC, Best RB, and Mittal J (2018). Sequence determinants of protein phase behavior from a coarse-grained model. PLoS Comput Biol 14, e1005941. 10.1371/journal.pcbi.1005941. [DOI] [PMC free article] [PubMed] [Google Scholar]
20.Monticelli L, Kandasamy SK, Periole X, Larson RG, Tieleman DP, and Marrink SJ (2008). The MARTINI Coarse-Grained Force Field: Extension to Proteins. J Chem Theory Comput 4, 819–834. 10.1021/ct700324x. [DOI] [PubMed] [Google Scholar]
21.Gopal SM, Mukherjee S, Cheng YM, and Feig M (2010). PRIMO/PRIMONA: a coarse-grained model for proteins and nucleic acids that preserves near-atomistic accuracy. Proteins 78, 1266–1281. 10.1002/prot.22645. [DOI] [PMC free article] [PubMed] [Google Scholar]
22.Gray JJ, Moughon S, Wang C, Schueler-Furman O, Kuhlman B, Rohl CA, and Baker D (2003). Protein-protein docking with simultaneous optimization of rigid-body displacement and side-chain conformations. J Mol Biol 331, 281–299. 10.1016/s0022-2836(03)00670-3. [DOI] [PubMed] [Google Scholar]
23.Kolinski A (2004). Protein modeling and structure prediction with a reduced representation. Acta Biochim Pol 51, 349–371. [PubMed] [Google Scholar]
24.Yang J, Yan R, Roy A, Xu D, Poisson J, and Zhang Y (2015). The I-TASSER Suite: protein structure and function prediction. Nat Methods 12, 7–8. 10.1038/nmeth.3213. [DOI] [PMC free article] [PubMed] [Google Scholar]
25.Kar P, and Feig M (2014). Recent advances in transferable coarse-grained modeling of proteins. Adv Protein Chem Struct Biol 96, 143–180. 10.1016/bs.apcsb.2014.06.005. [DOI] [PMC free article] [PubMed] [Google Scholar]
26.Word JM, Lovell SC, Richardson JS, and Richardson DC (1999). Asparagine and glutamine: using hydrogen atom contacts in the choice of side-chain amide orientation. J Mol Biol 285, 1735–1747. 10.1006/jmbi.1998.2401. [DOI] [PubMed] [Google Scholar]
27.Wassenaar TA, Pluhackova K, Bockmann RA, Marrink SJ, and Tieleman DP (2014). Going Backward: A Flexible Geometric Approach to Reverse Transformation from Coarse Grained to Atomistic Models. J Chem Theory Comput 10, 676–690. 10.1021/ct400617g. [DOI] [PubMed] [Google Scholar]
28.Rotkiewicz P, and Skolnick J (2008). Fast procedure for reconstruction of full-atom protein models from reduced representations. J Comput Chem 29, 1460–1465. 10.1002/jcc.20906. [DOI] [PMC free article] [PubMed] [Google Scholar]
29.Li Y, and Zhang Y (2009). REMO: A new protocol to refine full atomic protein models from C-alpha traces by optimizing hydrogen-bonding networks. Proteins 76, 665–676. 10.1002/prot.22380. [DOI] [PMC free article] [PubMed] [Google Scholar]
30.Krivov GG, Shapovalov MV, and Dunbrack RL Jr. (2009). Improved prediction of protein side-chain conformations with SCWRL4. Proteins 77, 778–795. 10.1002/prot.22488. [DOI] [PMC free article] [PubMed] [Google Scholar]
31.Alford RF, Leaver-Fay A, Jeliazkov JR, O’Meara MJ, DiMaio FP, Park H, Shapovalov MV, Renfrew PD, Mulligan VK, Kappel K, et al. (2017). The Rosetta All-Atom Energy Function for Macromolecular Modeling and Design. J Chem Theory Comput 13, 3031–3048. 10.1021/acs.jctc.7b00125. [DOI] [PMC free article] [PubMed] [Google Scholar]
32.Xu D, and Zhang Y (2011). Improving the physical realism and structural accuracy of protein models by a two-step atomic-level energy minimization. Biophys J 101, 2525–2534. 10.1016/j.bpj.2011.10.024. [DOI] [PMC free article] [PubMed] [Google Scholar]
33.McPartlon M, and Xu J (2023). An end-to-end deep learning method for protein side-chain packing and inverse folding. Proc Natl Acad Sci U S A 120, e2216438120. 10.1073/pnas.2216438120. [DOI] [PMC free article] [PubMed] [Google Scholar]
34.Misiura M, Shroff R, Thyer R, and Kolomeisky AB (2022). DLPacker: Deep learning for prediction of amino acid side chain conformations in proteins. Proteins 90, 1278–1290. 10.1002/prot.26311. [DOI] [PubMed] [Google Scholar]
35.Flores SC, Bernauer J, Shin S, Zhou R, and Huang X (2012). Multiscale modeling of macromolecular biosystems. Brief Bioinform 13, 395–405. 10.1093/bib/bbr077. [DOI] [PubMed] [Google Scholar]
36.Predeus AV, Gul S, Gopal SM, and Feig M (2012). Conformational sampling of peptides in the presence of protein crowders from AA/CG-multiscale simulations. J Phys Chem B 116, 8610–8620. 10.1021/jp300129u. [DOI] [PMC free article] [PubMed] [Google Scholar]
37.Fuchs FB, Worrall DE, Fischer V, and Welling M (2020). SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networks. arXiv, 2006.10503. 10.48550/arXiv.2006.10503. [DOI] [Google Scholar]
38.Chen VB, Arendall WB 3rd, Headd JJ, Keedy DA, Immormino RM, Kapral GJ, Murray LW, Richardson JS, and Richardson DC (2010). MolProbity: all-atom structure validation for macromolecular crystallography. Acta Crystallogr D Biol Crystallogr 66, 12–21. 10.1107/S0907444909042073. [DOI] [PMC free article] [PubMed] [Google Scholar]
39.Daopin S, Davies DR, Schlunegger MP, and Grutter MG (1994). Comparison of two crystal structures of TGF-beta2: the accuracy of refined protein structures. Acta Crystallogr D Biol Crystallogr 50, 85–92. 10.1107/S090744499300808X. [DOI] [PubMed] [Google Scholar]
40.Chen VB, Wedell JR, Wenger RK, Ulrich EL, and Markley JL (2015). MolProbity for the masses–of data. J Biomol NMR 63, 77–83. 10.1007/s10858-015-9969-9. [DOI] [PMC free article] [PubMed] [Google Scholar]
41.Paxman JJ, and Heras B (2017). Bioinformatics Tools and Resources for Analyzing Protein Structures. In Proteome Bioinformatics, Keerthikumar S, and Mathivanan S, eds. (Springer; New York: ), pp. 209–220. 10.1007/978-1-4939-6740-7_16. [DOI] [PubMed] [Google Scholar]
42.Berkholz DS, Shapovalov MV, Dunbrack RL Jr., and Karplus PA (2009). Conformation dependence of backbone geometry in proteins. Structure 17, 1316–1325. 10.1016/j.str.2009.08.012. [DOI] [PMC free article] [PubMed] [Google Scholar]
43.Cong Y, Baker ML, Jakana J, Woolford D, Miller EJ, Reissmann S, Kumar RN, Redding-Johanson AM, Batth TS, Mukhopadhyay A, et al. (2010). 4.0-Å resolution cryo-EM structure of the mammalian chaperonin TRiC/CCT reveals its unique subunit arrangement. Proc Natl Acad Sci U S A 107, 4967–4972. 10.1073/pnas.0913774107. [DOI] [PMC free article] [PubMed] [Google Scholar]
44.Terashi G, and Kihara D (2018). De novo main-chain modeling for EM maps using MAINMAST. Nat Commun 9, 1618. 10.1038/s41467-018-04053-7. [DOI] [PMC free article] [PubMed] [Google Scholar]
45.Benjin X, and Ling L (2020). Developments, applications, and prospects of cryo-electron microscopy. Protein Sci 29, 872–882. 10.1002/pro.3805. [DOI] [PMC free article] [PubMed] [Google Scholar]
46.Wu KE, Yang KK, Berg R.v.d., Zou JY, Lu AX, and Amini AP (2022). Protein structure generation via folding diffusion. arXiv, 2209.15611. 10.48550/arXiv.2209.15611. [DOI] [PMC free article] [PubMed] [Google Scholar]
47.Cheng YM, Gopal SM, Law SM, and Feig M (2012). Molecular dynamics trajectory compression with a coarse-grained model. IEEE/ACM Trans Comput Biol Bioinform 9, 476–486. 10.1109/TCBB.2011.141. [DOI] [PMC free article] [PubMed] [Google Scholar]
48.Tiemann JKS, Szczuka M, Bouarroudj L, Oussaren M, Garcia S, Howard RJ, Delemotte L, Lindahl E, Baaden M, Lindorff-Larsen K, et al. (2023). MDverse: Shedding Light on the Dark Matter of Molecular Dynamics Simulations. bioRxiv, 2023.2005.2002.538537. 10.1101/2023.05.02.538537. [DOI] [PMC free article] [PubMed] [Google Scholar]
49.Feig M, Abdullah M, Johnsson L, and Pettitt BM (1999). Large Scale Distributed Data Repository: Design of a Molecular Dynamics Trajectory Database. Fut Gen Comput Sys 16, 101–110. 10.1016/S0167-739X(99)00039-4. [DOI] [Google Scholar]
50.Malhotra S, Trager S, Dal Peraro M, and Topf M (2019). Modelling structures in cryo-EM maps. Curr Opin Struct Biol 58, 105–114. 10.1016/j.sbi.2019.05.024. [DOI] [PubMed] [Google Scholar]
51.Casañal A, Lohkamp B, and Emsley P (2020). Current developments in Coot for macromolecular model building of Electron Cryo-microscopy and Crystallographic Data. Protein Sci 29, 1055–1064. 10.1002/pro.3791. [DOI] [PMC free article] [PubMed] [Google Scholar]
52.Croll T (2018). ISOLDE: a physically realistic environment for model building into low-resolution electron-density maps. Acta Crystallogr D Biol Crystallogr 74, 519–530. doi: 10.1107/S2059798318002425. [DOI] [PMC free article] [PubMed] [Google Scholar]
53.Wang Z, and Schröder GF (2012). Real-space refinement with DireX: From global fitting to side-chain improvements. Biopolymers 97, 687–697. 10.1002/bip.22046. [DOI] [PubMed] [Google Scholar]
54.Trabuco LG, Villa E, Schreiner E, Harrison CB, and Schulten K (2009). Molecular dynamics flexible fitting: a practical guide to combine cryo-electron microscopy and X-ray crystallography. Methods 49, 174–180. 10.1016/j.ymeth.2009.04.005. [DOI] [PMC free article] [PubMed] [Google Scholar]
55.Heo L, and Feig M (2018). What makes it difficult to refine protein models further via molecular dynamics simulations? Proteins 86, 177–188. 10.1002/prot.25393. [DOI] [PMC free article] [PubMed] [Google Scholar]
56.Heo L, and Feig M (2018). Experimental accuracy in protein structure refinement via molecular dynamics simulations. Proc Natl Acad Sci U S A 115, 13276–13281. 10.1073/pnas.1811364115. [DOI] [PMC free article] [PubMed] [Google Scholar]
57.Chennakesavalu S, Toomer DJ, and Rotskoff GM (2023). Ensuring thermodynamic consistency with invertible coarse-graining. J Chem Phys 158, 124126. 10.1063/5.0141888. [DOI] [PubMed] [Google Scholar]
58.Bramer D, and Wei GW (2018). Blind prediction of protein B-factor and flexibility. J Chem Phys 149, 134107. 10.1063/1.5048469. [DOI] [PMC free article] [PubMed] [Google Scholar]
59.Tozzini V (2010). Multiscale modeling of proteins. Acc Chem Res 43, 220–230. 10.1021/ar9001476. [DOI] [PubMed] [Google Scholar]
60.Ayton GS, Noid WG, and Voth GA (2007). Multiscale modeling of biomolecular systems: in serial and in parallel. Curr Opin Struct Biol 17, 192–198. 10.1016/j.sbi.2007.03.004. [DOI] [PubMed] [Google Scholar]
61.Durumeric AEP, Charron NE, Templeton C, Musil F, Bonneau K, Pasos-Trejo AS, Chen Y, Kelkar A, Noé F, and Clementi C (2023). Machine learned coarse-grained protein force-fields: Are we there yet? Curr Opin Struct Biol 79, 102533. 10.1016/j.sbi.2023.102533. [DOI] [PMC free article] [PubMed] [Google Scholar]
62.Macedo-Ribeiro S, Darimont B, Sterner R, and Huber R (1996). Small structural changes account for the high thermostability of 1[4Fe-4S] ferredoxin from the hyperthermophilic bacterium Thermotoga maritima. Structure 4, 1291–1301. 10.1016/s0969-2126(96)00137-2. [DOI] [PubMed] [Google Scholar]
63.Elbaum-Garfinkle S, Kim Y, Szczepaniak K, Chen CC, Eckmann CR, Myong S, and Brangwynne CP (2015). The disordered P granule protein LAF-1 drives phase separation into droplets with tunable viscosity and dynamics. Proc Natl Acad Sci U S A 112, 7189–7194. 10.1073/pnas.1504822112. [DOI] [PMC free article] [PubMed] [Google Scholar]
64.Stein AJ, Bigelow L, Trevino D, Buck K, and Joachimiak A (2009). The Crystal Structure of a Putative Cysteine Protease from Cytophaga hutchinsonii to 1.9Å. Protein Data Bank. 10.2210/pdb3ISR/pdb. [DOI] [Google Scholar]
65.Pettersen EF, Goddard TD, Huang CC, Couch GS, Greenblatt DM, Meng EC, and Ferrin TE (2004). UCSF Chimera--a visualization system for exploratory research and analysis. J Comput Chem 25, 1605–1612. 10.1002/jcc.20084. [DOI] [PubMed] [Google Scholar]
66.Tang G, Peng L, Baldwin PR, Mann DS, Jiang W, Rees I, and Ludtke SJ (2007). EMAN2: an extensible image processing suite for electron microscopy. J Struct Biol 157, 38–46. 10.1016/j.jsb.2006.05.009. [DOI] [PubMed] [Google Scholar]
67.Evans R, O’Neill M, Pritzel A, Antropova N, Senior A, Green T, Žídek A, Bates R, Blackwell S, Yim J, et al. (2022). Protein complex prediction with AlphaFold-Multimer. bioRxiv, 2021.2010.2004.463034. 10.1101/2021.10.04.463034. [DOI] [Google Scholar]
68.Heo L, and Feig M (2023). github.com/huhlim/cg2all. 10.5281/zenodo.10011305. [DOI] [Google Scholar]
69.Heo L, and Feig M (2023). cg2all data set. 10.5281/zenodo.8273738. [DOI] [Google Scholar]
70.Hintze BJ, Lewis SM, Richardson JS, and Richardson DC (2016). Molprobity’s ultimate rotamer-library distributions for model validation. Proteins 84, 1177–1189. 10.1002/prot.25039. [DOI] [PMC free article] [PubMed] [Google Scholar]
71.Wang G, and Dunbrack RL Jr. (2003). PISCES: a protein sequence culling server. Bioinformatics 19, 1589–1591. 10.1093/bioinformatics/btg224. [DOI] [PubMed] [Google Scholar]
72.Kabsch W, and Sander C (1983). Dictionary of protein secondary structure: pattern recognition of hydrogen-bonded and geometrical features. Biopolymers 22, 2577–2637. 10.1002/bip.360221211. [DOI] [PubMed] [Google Scholar]
73.McGibbon RT, Beauchamp KA, Harrigan MP, Klein C, Swails JM, Hernandez CX, Schwantes CR, Wang LP, Lane TJ, and Pande VS (2015). MDTraj: A Modern Open Library for the Analysis of Molecular Dynamics Trajectories. Biophys J 109, 1528–1532. 10.1016/j.bpj.2015.08.015. [DOI] [PMC free article] [PubMed] [Google Scholar]
74.Huang J, Rauscher S, Nawrocki G, Ran T, Feig M, de Groot BL, Grubmuller H, and MacKerell AD Jr. (2017). CHARMM36m: an improved force field for folded and intrinsically disordered proteins. Nat Methods 14, 71–73. 10.1038/nmeth.4067. [DOI] [PMC free article] [PubMed] [Google Scholar]
75.Eastman P, Swails J, Chodera JD, McGibbon RT, Zhao Y, Beauchamp KA, Wang LP, Simmonett AC, Harrigan MP, Stern CD, et al. (2017). OpenMM 7: Rapid development of high performance algorithms for molecular dynamics. PLoS Comput Biol 13, e1005659. 10.1371/journal.pcbi.1005659. [DOI] [PMC free article] [PubMed] [Google Scholar]
76.Jorgensen WL, Chandrasekhar J, Madura JD, Impey RW, and Klein ML (1983). Comparison of simple potential functions for simulating liquid water. J Chem Phys 79, 926–935. 10.1063/1.445869. [DOI] [Google Scholar]
77.Liu DC, and Nocedal J (1989). On the limited memory BFGS method for large scale optimization. Math Program 45, 503–528. 10.1007/bf01589116. [DOI] [Google Scholar]
78.Ba JL, Kiros JR, and Hinton GE (2016). Layer Normalization. arXiv, 1607.06450. 10.48550/arXiv.1607.06450. [DOI] [Google Scholar]
79.Clevert D-A, Unterthiner T, and Hochreiter S (2016). Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs). arXiv, 1511.07289. 10.48550/arXiv.1511.07289. [DOI] [Google Scholar]
80.He K, Zhang X, Ren S, and Sun J (2015). Deep Residual Learning for Image Recognition. arXiv, 1512.03385. 10.48550/arXiv.1512.03385. [DOI] [Google Scholar]
81.Nair V, and Hinton GE (2010). Rectified Linear Units Improve Restricted Boltzmann Machines. Proceedings of the 27th International Conference on Machine Learning (ICML10), 807–814. https://icml.cc/Conferences/2010/papers/432.pdf. [Google Scholar]
82.Zhou Y, Barnes C, Lu J, Yang J, and H Li. (2020). On the Continuity of Rotation Representations in Neural Networks. arXiv, 1812.07035. 10.48550/arXiv.1812.07035. [DOI] [Google Scholar]
83.Falcon W, and The_PyTorch_Lightning_team (2022). PyTorch Lightning Zenodo. 10.5281/zenodo.7859091. [DOI] [Google Scholar]
84.Lu L (2020). Dying ReLU and Initialization: Theory and Numerical Examples. Comm Comp Phys 28, 1671–1706. 10.4208/cicp.OA-2020-0165. [DOI] [Google Scholar]
85.Schumacher MA, Pearson RF, Moller T, Valentin-Hansen P, and Brennan RG (2002). Structures of the pleiotropic translational regulator Hfq and an Hfq-RNA complex: a bacterial Sm-like protein. EMBO J 21, 3546–3556. 10.1093/emboj/cdf322. [DOI] [PMC free article] [PubMed] [Google Scholar]
86.Badger J, Sauder JM, Adams JM, Antonysamy S, Bain K, Bergseid MG, Buchanan SG, Buchanan MD, Batiyenko Y, Christopher JA, et al. (2005). Structural analysis of a set of proteins resulting from a bacterial genomics project. Proteins 60, 787–796. 10.1002/prot.20541. [DOI] [PubMed] [Google Scholar]
87.Shi W, Basso LA, Santos DS, Tyler PC, Furneaux RH, Blanchard JS, Almo SC, and Schramm VL (2001). Structures of purine nucleoside phosphorylase from Mycobacterium tuberculosis in complexes with immucillin-H and its pieces. Biochemistry 40, 8204–8215. 10.1021/bi010585p. [DOI] [PubMed] [Google Scholar]
88.Boutz DR, Cascio D, Whitelegge J, Perry LJ, and Yeates TO (2007). Discovery of a thermophilic protein complex stabilized by topologically interlinked chains. J Mol Biol 368, 1332–1344. 10.1016/j.jmb.2007.02.078. [DOI] [PMC free article] [PubMed] [Google Scholar]
89.Singleton M, Isupov M, and Littlechild J (1999). X-ray structure of pyrrolidone carboxyl peptidase from the hyperthermophilic archaeon Thermococcus litoralis. Structure 7, 237–244. 10.1016/s0969-2126(99)80034-3. [DOI] [PubMed] [Google Scholar]
90.Im YJ, Kim JI, Shen Y, Na Y, Han YJ, Kim SH, Song PS, and Eom SH (2004). Structural analysis of Arabidopsis thaliana nucleoside diphosphate kinase-2 for phytochrome-mediated light signaling. J Mol Biol 343, 659–670. 10.1016/j.jmb.2004.08.054. [DOI] [PubMed] [Google Scholar]
91.Hondoh H, Kuriki T, and Matsuura Y (2003). Three-dimensional structure and substrate binding of Bacillus stearothermophilus neopullulanase. J Mol Biol 326, 177–188. 10.1016/s0022-2836(02)01402-x. [DOI] [PubMed] [Google Scholar]
92.Tanaka Y, Nakagawa N, Kuramitsu S, Yokoyama S, and Masui R (2005). Novel reaction mechanism of GTP cyclohydrolase I. High-resolution X-ray crystallography of Thermus thermophilus HB8 enzyme complexed with a transition state analogue, the 8-oxoguanine derivative. J Biochem 138, 263–275. 10.1093/jb/mvi120. [DOI] [PubMed] [Google Scholar]
93.Mirdita M, Schutze K, Moriwaki Y, Heo L, Ovchinnikov S, and Steinegger M (2022). ColabFold: making protein folding accessible to all. Nat Methods 19, 679–682. 10.1038/s41592-022-01488-1. [DOI] [PMC free article] [PubMed] [Google Scholar]
94.Mukherjee S, and Zhang Y (2009). MM-align: a quick algorithm for aligning multiple-chain protein complex structures using iterative dynamic programming. Nucleic Acids Res 37, e83. 10.1093/nar/gkp318. [DOI] [PMC free article] [PubMed] [Google Scholar]
95.Kingma DP, and Ba J (2017). Adam: A Method for Stochastic Optimization. arXiv, 1412.6980. 10.48550/arXiv.1412.6980. [DOI] [Google Scholar]
96.Loshchilov I, and Hutter F (2017). SGDR: Stochastic Gradient Descent with Warm Restarts. arXiv, 1608.03983. 10.48550/arXiv.1608.03983. [DOI] [Google Scholar]
97.Qi Y, Lee J, Singharoy A, McGreevy R, Schulten K, and Im W (2017). CHARMM-GUI MDFF/xMDFF Utilizer for Molecular Dynamics Flexible Fitting Simulations in Various Environments. J Phys Chem B 121, 3718–3723. 10.1021/acs.jpcb.6b10568. [DOI] [PMC free article] [PubMed] [Google Scholar]
98.Phillips JC, Hardy DJ, Maia JDC, Stone JE, Ribeiro JV, Bernardi RC, Buch R, Fiorin G, Henin J, Jiang W, et al. (2020). Scalable molecular dynamics on CPU and GPU architectures with NAMD. J Chem Phys 153, 044130. 10.1063/5.0014475. [DOI] [PMC free article] [PubMed] [Google Scholar]

Associated Data

This section collects any data citations, data availability statements, or supplementary materials included in this article.

Supplementary Materials

Download video file^{(21.5MB, mp4)}

NIHMS1944498-supplement-2.pdf^{(4.6MB, pdf)}

Data Availability Statement

No new data has been generated in this study.

Any additional information required to reanalyze the data reported in this paper is available from the lead contact upon request.

[R1] 1.Shi Y (2014). A glimpse of structural biology through X-ray crystallography. Cell 159, 995–1014. 10.1016/j.cell.2014.10.051. [DOI] [PubMed] [Google Scholar]

[R2] 2.Jones N (2014). Crystallography: Atomic secrets. Nature 505, 602–603. 10.1038/505602a. [DOI] [PubMed] [Google Scholar]

[R3] 3.Wüthrich K (1990). Protein structure determination in solution by NMR spectroscopy. J Biol Chem 265, 22059–22062. 10.1016/S0021-9258(18)45665-7. [DOI] [PubMed] [Google Scholar]

[R4] 4.Cheng Y (2015). Single-Particle Cryo-EM at Crystallographic Resolution. Cell 161, 450–457. 10.1016/j.cell.2015.03.049. [DOI] [PMC free article] [PubMed] [Google Scholar]

[R5] 5.Nogales E (2016). The development of cryo-EM into a mainstream structural biology technique. Nat Methods 13, 24–27. 10.1038/nmeth.3694. [DOI] [PMC free article] [PubMed] [Google Scholar]

[R6] 6.Garman EF (2014). Developments in x-ray crystallographic structure determination of biological macromolecules. Science 343, 1102–1108. 10.1126/science.1247829. [DOI] [PubMed] [Google Scholar]

[R7] 7.Kmiecik S, Gront D, Kolinski M, Wieteska L, Dawid AE, and Kolinski A (2016). Coarse-Grained Protein Models and Their Applications. Chem Rev 116, 7898–7936. 10.1021/acs.chemrev.6b00163. [DOI] [PubMed] [Google Scholar]

[R8] 8.Saunders MG, and Voth GA (2013). Coarse-graining methods for computational biology. Annu Rev Biophys 42, 73–93. 10.1146/annurev-biophys-083012-130348. [DOI] [PubMed] [Google Scholar]

[R9] 9.Feig M, Chocholoušová J, and Tanizaki S (2006). Extending the horizon: towards the efficient modeling of large biomolecular complexes in atomic detail. Theor Chem Acc 116, 194–205. 10.1007/s00214-005-0062-4. [DOI] [Google Scholar]

[R10] 10.Lane TJ, Shukla D, Beauchamp KA, and Pande VS (2013). To milliseconds and beyond: challenges in the simulation of protein folding. Curr Opin Struct Biol 23, 58–65. 10.1016/j.sbi.2012.11.002. [DOI] [PMC free article] [PubMed] [Google Scholar]

[R11] 11.Jumper J, Evans R, Pritzel A, Green T, Figurnov M, Ronneberger O, Tunyasuvunakool K, Bates R, Zidek A, Potapenko A, et al. (2021). Highly accurate protein structure prediction with AlphaFold. Nature 596, 583–589. 10.1038/s41586-021-03819-2. [DOI] [PMC free article] [PubMed] [Google Scholar]

[R12] 12.Baek M, DiMaio F, Anishchenko I, Dauparas J, Ovchinnikov S, Lee GR, Wang J, Cong Q, Kinch LN, Schaeffer RD, et al. (2021). Accurate prediction of protein structures and interactions using a three-track neural network. Science 373, 871–876. 10.1126/science.abj8754. [DOI] [PMC free article] [PubMed] [Google Scholar]

[R13] 13.Lin Z, Akin H, Rao R, Hie B, Zhu Z, Lu W, Smetanin N, Verkuil R, Kabeli O, Shmueli Y, et al. (2023). Evolutionary-scale prediction of atomic-level protein structure with a language model. Science 379, 1123–1130. 10.1126/science.ade2574. [DOI] [PubMed] [Google Scholar]

[R14] 14.Janson G, Valdes-Garcia G, Heo L, and Feig M (2023). Direct generation of protein conformational ensembles via machine learning. Nat Commun 14, 774. 10.1038/s41467-023-36443-x. [DOI] [PMC free article] [PubMed] [Google Scholar]

[R15] 15.Noé F, Olsson S, Kohler J, and Wu H (2019). Boltzmann generators: Sampling equilibrium states of many-body systems with deep learning. Science 365, eaaw1147. 10.1126/science.aaw1147. [DOI] [PubMed] [Google Scholar]

[R16] 16.Dutagaci B, Nawrocki G, Goodluck J, Ashkarran AA, Hoogstraten CG, Lapidus LJ, and Feig M (2021). Charge-driven condensation of RNA and proteins suggests broad role of phase separation in cytoplasmic environments. Elife 10, e64004. 10.7554/eLife.64004. [DOI] [PMC free article] [PubMed] [Google Scholar]

[R17] 17.Yu I, Mori T, Ando T, Harada R, Jung J, Sugita Y, and Feig M (2016). Biomolecular interactions modulate macromolecular structure and dynamics in atomistic model of a bacterial cytoplasm. Elife 5, e19274. 10.7554/eLife.19274. [DOI] [PMC free article] [PubMed] [Google Scholar]

[R18] 18.Valdes-Garcia G, Heo L, Lapidus LJ, and Feig M (2023). Modeling Concentration-dependent Phase Separation Processes Involving Peptides and RNA via Residue-Based Coarse-Graining. J Chem Theory Comput 19, 669–678. 10.1021/acs.jctc.2c00856. [DOI] [PMC free article] [PubMed] [Google Scholar]

[R19] 19.Dignon GL, Zheng W, Kim YC, Best RB, and Mittal J (2018). Sequence determinants of protein phase behavior from a coarse-grained model. PLoS Comput Biol 14, e1005941. 10.1371/journal.pcbi.1005941. [DOI] [PMC free article] [PubMed] [Google Scholar]

[R20] 20.Monticelli L, Kandasamy SK, Periole X, Larson RG, Tieleman DP, and Marrink SJ (2008). The MARTINI Coarse-Grained Force Field: Extension to Proteins. J Chem Theory Comput 4, 819–834. 10.1021/ct700324x. [DOI] [PubMed] [Google Scholar]

[R21] 21.Gopal SM, Mukherjee S, Cheng YM, and Feig M (2010). PRIMO/PRIMONA: a coarse-grained model for proteins and nucleic acids that preserves near-atomistic accuracy. Proteins 78, 1266–1281. 10.1002/prot.22645. [DOI] [PMC free article] [PubMed] [Google Scholar]

[R22] 22.Gray JJ, Moughon S, Wang C, Schueler-Furman O, Kuhlman B, Rohl CA, and Baker D (2003). Protein-protein docking with simultaneous optimization of rigid-body displacement and side-chain conformations. J Mol Biol 331, 281–299. 10.1016/s0022-2836(03)00670-3. [DOI] [PubMed] [Google Scholar]

[R23] 23.Kolinski A (2004). Protein modeling and structure prediction with a reduced representation. Acta Biochim Pol 51, 349–371. [PubMed] [Google Scholar]

[R24] 24.Yang J, Yan R, Roy A, Xu D, Poisson J, and Zhang Y (2015). The I-TASSER Suite: protein structure and function prediction. Nat Methods 12, 7–8. 10.1038/nmeth.3213. [DOI] [PMC free article] [PubMed] [Google Scholar]

[R25] 25.Kar P, and Feig M (2014). Recent advances in transferable coarse-grained modeling of proteins. Adv Protein Chem Struct Biol 96, 143–180. 10.1016/bs.apcsb.2014.06.005. [DOI] [PMC free article] [PubMed] [Google Scholar]

[R26] 26.Word JM, Lovell SC, Richardson JS, and Richardson DC (1999). Asparagine and glutamine: using hydrogen atom contacts in the choice of side-chain amide orientation. J Mol Biol 285, 1735–1747. 10.1006/jmbi.1998.2401. [DOI] [PubMed] [Google Scholar]

[R27] 27.Wassenaar TA, Pluhackova K, Bockmann RA, Marrink SJ, and Tieleman DP (2014). Going Backward: A Flexible Geometric Approach to Reverse Transformation from Coarse Grained to Atomistic Models. J Chem Theory Comput 10, 676–690. 10.1021/ct400617g. [DOI] [PubMed] [Google Scholar]

[R28] 28.Rotkiewicz P, and Skolnick J (2008). Fast procedure for reconstruction of full-atom protein models from reduced representations. J Comput Chem 29, 1460–1465. 10.1002/jcc.20906. [DOI] [PMC free article] [PubMed] [Google Scholar]

[R29] 29.Li Y, and Zhang Y (2009). REMO: A new protocol to refine full atomic protein models from C-alpha traces by optimizing hydrogen-bonding networks. Proteins 76, 665–676. 10.1002/prot.22380. [DOI] [PMC free article] [PubMed] [Google Scholar]

[R30] 30.Krivov GG, Shapovalov MV, and Dunbrack RL Jr. (2009). Improved prediction of protein side-chain conformations with SCWRL4. Proteins 77, 778–795. 10.1002/prot.22488. [DOI] [PMC free article] [PubMed] [Google Scholar]

[R31] 31.Alford RF, Leaver-Fay A, Jeliazkov JR, O’Meara MJ, DiMaio FP, Park H, Shapovalov MV, Renfrew PD, Mulligan VK, Kappel K, et al. (2017). The Rosetta All-Atom Energy Function for Macromolecular Modeling and Design. J Chem Theory Comput 13, 3031–3048. 10.1021/acs.jctc.7b00125. [DOI] [PMC free article] [PubMed] [Google Scholar]

[R32] 32.Xu D, and Zhang Y (2011). Improving the physical realism and structural accuracy of protein models by a two-step atomic-level energy minimization. Biophys J 101, 2525–2534. 10.1016/j.bpj.2011.10.024. [DOI] [PMC free article] [PubMed] [Google Scholar]

[R33] 33.McPartlon M, and Xu J (2023). An end-to-end deep learning method for protein side-chain packing and inverse folding. Proc Natl Acad Sci U S A 120, e2216438120. 10.1073/pnas.2216438120. [DOI] [PMC free article] [PubMed] [Google Scholar]

[R34] 34.Misiura M, Shroff R, Thyer R, and Kolomeisky AB (2022). DLPacker: Deep learning for prediction of amino acid side chain conformations in proteins. Proteins 90, 1278–1290. 10.1002/prot.26311. [DOI] [PubMed] [Google Scholar]

[R35] 35.Flores SC, Bernauer J, Shin S, Zhou R, and Huang X (2012). Multiscale modeling of macromolecular biosystems. Brief Bioinform 13, 395–405. 10.1093/bib/bbr077. [DOI] [PubMed] [Google Scholar]

[R36] 36.Predeus AV, Gul S, Gopal SM, and Feig M (2012). Conformational sampling of peptides in the presence of protein crowders from AA/CG-multiscale simulations. J Phys Chem B 116, 8610–8620. 10.1021/jp300129u. [DOI] [PMC free article] [PubMed] [Google Scholar]

[R37] 37.Fuchs FB, Worrall DE, Fischer V, and Welling M (2020). SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networks. arXiv, 2006.10503. 10.48550/arXiv.2006.10503. [DOI] [Google Scholar]

[R38] 38.Chen VB, Arendall WB 3rd, Headd JJ, Keedy DA, Immormino RM, Kapral GJ, Murray LW, Richardson JS, and Richardson DC (2010). MolProbity: all-atom structure validation for macromolecular crystallography. Acta Crystallogr D Biol Crystallogr 66, 12–21. 10.1107/S0907444909042073. [DOI] [PMC free article] [PubMed] [Google Scholar]

[R39] 39.Daopin S, Davies DR, Schlunegger MP, and Grutter MG (1994). Comparison of two crystal structures of TGF-beta2: the accuracy of refined protein structures. Acta Crystallogr D Biol Crystallogr 50, 85–92. 10.1107/S090744499300808X. [DOI] [PubMed] [Google Scholar]

[R40] 40.Chen VB, Wedell JR, Wenger RK, Ulrich EL, and Markley JL (2015). MolProbity for the masses–of data. J Biomol NMR 63, 77–83. 10.1007/s10858-015-9969-9. [DOI] [PMC free article] [PubMed] [Google Scholar]

[R41] 41.Paxman JJ, and Heras B (2017). Bioinformatics Tools and Resources for Analyzing Protein Structures. In Proteome Bioinformatics, Keerthikumar S, and Mathivanan S, eds. (Springer; New York: ), pp. 209–220. 10.1007/978-1-4939-6740-7_16. [DOI] [PubMed] [Google Scholar]

[R42] 42.Berkholz DS, Shapovalov MV, Dunbrack RL Jr., and Karplus PA (2009). Conformation dependence of backbone geometry in proteins. Structure 17, 1316–1325. 10.1016/j.str.2009.08.012. [DOI] [PMC free article] [PubMed] [Google Scholar]

[R43] 43.Cong Y, Baker ML, Jakana J, Woolford D, Miller EJ, Reissmann S, Kumar RN, Redding-Johanson AM, Batth TS, Mukhopadhyay A, et al. (2010). 4.0-Å resolution cryo-EM structure of the mammalian chaperonin TRiC/CCT reveals its unique subunit arrangement. Proc Natl Acad Sci U S A 107, 4967–4972. 10.1073/pnas.0913774107. [DOI] [PMC free article] [PubMed] [Google Scholar]

[R44] 44.Terashi G, and Kihara D (2018). De novo main-chain modeling for EM maps using MAINMAST. Nat Commun 9, 1618. 10.1038/s41467-018-04053-7. [DOI] [PMC free article] [PubMed] [Google Scholar]

[R45] 45.Benjin X, and Ling L (2020). Developments, applications, and prospects of cryo-electron microscopy. Protein Sci 29, 872–882. 10.1002/pro.3805. [DOI] [PMC free article] [PubMed] [Google Scholar]

[R46] 46.Wu KE, Yang KK, Berg R.v.d., Zou JY, Lu AX, and Amini AP (2022). Protein structure generation via folding diffusion. arXiv, 2209.15611. 10.48550/arXiv.2209.15611. [DOI] [PMC free article] [PubMed] [Google Scholar]

[R47] 47.Cheng YM, Gopal SM, Law SM, and Feig M (2012). Molecular dynamics trajectory compression with a coarse-grained model. IEEE/ACM Trans Comput Biol Bioinform 9, 476–486. 10.1109/TCBB.2011.141. [DOI] [PMC free article] [PubMed] [Google Scholar]

[R48] 48.Tiemann JKS, Szczuka M, Bouarroudj L, Oussaren M, Garcia S, Howard RJ, Delemotte L, Lindahl E, Baaden M, Lindorff-Larsen K, et al. (2023). MDverse: Shedding Light on the Dark Matter of Molecular Dynamics Simulations. bioRxiv, 2023.2005.2002.538537. 10.1101/2023.05.02.538537. [DOI] [PMC free article] [PubMed] [Google Scholar]

[R49] 49.Feig M, Abdullah M, Johnsson L, and Pettitt BM (1999). Large Scale Distributed Data Repository: Design of a Molecular Dynamics Trajectory Database. Fut Gen Comput Sys 16, 101–110. 10.1016/S0167-739X(99)00039-4. [DOI] [Google Scholar]

[R50] 50.Malhotra S, Trager S, Dal Peraro M, and Topf M (2019). Modelling structures in cryo-EM maps. Curr Opin Struct Biol 58, 105–114. 10.1016/j.sbi.2019.05.024. [DOI] [PubMed] [Google Scholar]

[R51] 51.Casañal A, Lohkamp B, and Emsley P (2020). Current developments in Coot for macromolecular model building of Electron Cryo-microscopy and Crystallographic Data. Protein Sci 29, 1055–1064. 10.1002/pro.3791. [DOI] [PMC free article] [PubMed] [Google Scholar]

[R52] 52.Croll T (2018). ISOLDE: a physically realistic environment for model building into low-resolution electron-density maps. Acta Crystallogr D Biol Crystallogr 74, 519–530. doi: 10.1107/S2059798318002425. [DOI] [PMC free article] [PubMed] [Google Scholar]

[R53] 53.Wang Z, and Schröder GF (2012). Real-space refinement with DireX: From global fitting to side-chain improvements. Biopolymers 97, 687–697. 10.1002/bip.22046. [DOI] [PubMed] [Google Scholar]

[R54] 54.Trabuco LG, Villa E, Schreiner E, Harrison CB, and Schulten K (2009). Molecular dynamics flexible fitting: a practical guide to combine cryo-electron microscopy and X-ray crystallography. Methods 49, 174–180. 10.1016/j.ymeth.2009.04.005. [DOI] [PMC free article] [PubMed] [Google Scholar]

[R55] 55.Heo L, and Feig M (2018). What makes it difficult to refine protein models further via molecular dynamics simulations? Proteins 86, 177–188. 10.1002/prot.25393. [DOI] [PMC free article] [PubMed] [Google Scholar]

[R56] 56.Heo L, and Feig M (2018). Experimental accuracy in protein structure refinement via molecular dynamics simulations. Proc Natl Acad Sci U S A 115, 13276–13281. 10.1073/pnas.1811364115. [DOI] [PMC free article] [PubMed] [Google Scholar]

[R57] 57.Chennakesavalu S, Toomer DJ, and Rotskoff GM (2023). Ensuring thermodynamic consistency with invertible coarse-graining. J Chem Phys 158, 124126. 10.1063/5.0141888. [DOI] [PubMed] [Google Scholar]

[R58] 58.Bramer D, and Wei GW (2018). Blind prediction of protein B-factor and flexibility. J Chem Phys 149, 134107. 10.1063/1.5048469. [DOI] [PMC free article] [PubMed] [Google Scholar]

[R59] 59.Tozzini V (2010). Multiscale modeling of proteins. Acc Chem Res 43, 220–230. 10.1021/ar9001476. [DOI] [PubMed] [Google Scholar]

[R60] 60.Ayton GS, Noid WG, and Voth GA (2007). Multiscale modeling of biomolecular systems: in serial and in parallel. Curr Opin Struct Biol 17, 192–198. 10.1016/j.sbi.2007.03.004. [DOI] [PubMed] [Google Scholar]

[R61] 61.Durumeric AEP, Charron NE, Templeton C, Musil F, Bonneau K, Pasos-Trejo AS, Chen Y, Kelkar A, Noé F, and Clementi C (2023). Machine learned coarse-grained protein force-fields: Are we there yet? Curr Opin Struct Biol 79, 102533. 10.1016/j.sbi.2023.102533. [DOI] [PMC free article] [PubMed] [Google Scholar]

[R62] 62.Macedo-Ribeiro S, Darimont B, Sterner R, and Huber R (1996). Small structural changes account for the high thermostability of 1[4Fe-4S] ferredoxin from the hyperthermophilic bacterium Thermotoga maritima. Structure 4, 1291–1301. 10.1016/s0969-2126(96)00137-2. [DOI] [PubMed] [Google Scholar]

[R63] 63.Elbaum-Garfinkle S, Kim Y, Szczepaniak K, Chen CC, Eckmann CR, Myong S, and Brangwynne CP (2015). The disordered P granule protein LAF-1 drives phase separation into droplets with tunable viscosity and dynamics. Proc Natl Acad Sci U S A 112, 7189–7194. 10.1073/pnas.1504822112. [DOI] [PMC free article] [PubMed] [Google Scholar]

[R64] 64.Stein AJ, Bigelow L, Trevino D, Buck K, and Joachimiak A (2009). The Crystal Structure of a Putative Cysteine Protease from Cytophaga hutchinsonii to 1.9Å. Protein Data Bank. 10.2210/pdb3ISR/pdb. [DOI] [Google Scholar]

[R65] 65.Pettersen EF, Goddard TD, Huang CC, Couch GS, Greenblatt DM, Meng EC, and Ferrin TE (2004). UCSF Chimera--a visualization system for exploratory research and analysis. J Comput Chem 25, 1605–1612. 10.1002/jcc.20084. [DOI] [PubMed] [Google Scholar]

[R66] 66.Tang G, Peng L, Baldwin PR, Mann DS, Jiang W, Rees I, and Ludtke SJ (2007). EMAN2: an extensible image processing suite for electron microscopy. J Struct Biol 157, 38–46. 10.1016/j.jsb.2006.05.009. [DOI] [PubMed] [Google Scholar]

[R67] 67.Evans R, O’Neill M, Pritzel A, Antropova N, Senior A, Green T, Žídek A, Bates R, Blackwell S, Yim J, et al. (2022). Protein complex prediction with AlphaFold-Multimer. bioRxiv, 2021.2010.2004.463034. 10.1101/2021.10.04.463034. [DOI] [Google Scholar]

[R68] 68.Heo L, and Feig M (2023). github.com/huhlim/cg2all. 10.5281/zenodo.10011305. [DOI] [Google Scholar]

[R69] 69.Heo L, and Feig M (2023). cg2all data set. 10.5281/zenodo.8273738. [DOI] [Google Scholar]

[R70] 70.Hintze BJ, Lewis SM, Richardson JS, and Richardson DC (2016). Molprobity’s ultimate rotamer-library distributions for model validation. Proteins 84, 1177–1189. 10.1002/prot.25039. [DOI] [PMC free article] [PubMed] [Google Scholar]

[R71] 71.Wang G, and Dunbrack RL Jr. (2003). PISCES: a protein sequence culling server. Bioinformatics 19, 1589–1591. 10.1093/bioinformatics/btg224. [DOI] [PubMed] [Google Scholar]

[R72] 72.Kabsch W, and Sander C (1983). Dictionary of protein secondary structure: pattern recognition of hydrogen-bonded and geometrical features. Biopolymers 22, 2577–2637. 10.1002/bip.360221211. [DOI] [PubMed] [Google Scholar]

[R73] 73.McGibbon RT, Beauchamp KA, Harrigan MP, Klein C, Swails JM, Hernandez CX, Schwantes CR, Wang LP, Lane TJ, and Pande VS (2015). MDTraj: A Modern Open Library for the Analysis of Molecular Dynamics Trajectories. Biophys J 109, 1528–1532. 10.1016/j.bpj.2015.08.015. [DOI] [PMC free article] [PubMed] [Google Scholar]

[R74] 74.Huang J, Rauscher S, Nawrocki G, Ran T, Feig M, de Groot BL, Grubmuller H, and MacKerell AD Jr. (2017). CHARMM36m: an improved force field for folded and intrinsically disordered proteins. Nat Methods 14, 71–73. 10.1038/nmeth.4067. [DOI] [PMC free article] [PubMed] [Google Scholar]

[R75] 75.Eastman P, Swails J, Chodera JD, McGibbon RT, Zhao Y, Beauchamp KA, Wang LP, Simmonett AC, Harrigan MP, Stern CD, et al. (2017). OpenMM 7: Rapid development of high performance algorithms for molecular dynamics. PLoS Comput Biol 13, e1005659. 10.1371/journal.pcbi.1005659. [DOI] [PMC free article] [PubMed] [Google Scholar]

[R76] 76.Jorgensen WL, Chandrasekhar J, Madura JD, Impey RW, and Klein ML (1983). Comparison of simple potential functions for simulating liquid water. J Chem Phys 79, 926–935. 10.1063/1.445869. [DOI] [Google Scholar]

[R77] 77.Liu DC, and Nocedal J (1989). On the limited memory BFGS method for large scale optimization. Math Program 45, 503–528. 10.1007/bf01589116. [DOI] [Google Scholar]

[R78] 78.Ba JL, Kiros JR, and Hinton GE (2016). Layer Normalization. arXiv, 1607.06450. 10.48550/arXiv.1607.06450. [DOI] [Google Scholar]

[R79] 79.Clevert D-A, Unterthiner T, and Hochreiter S (2016). Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs). arXiv, 1511.07289. 10.48550/arXiv.1511.07289. [DOI] [Google Scholar]

[R80] 80.He K, Zhang X, Ren S, and Sun J (2015). Deep Residual Learning for Image Recognition. arXiv, 1512.03385. 10.48550/arXiv.1512.03385. [DOI] [Google Scholar]

[R81] 81.Nair V, and Hinton GE (2010). Rectified Linear Units Improve Restricted Boltzmann Machines. Proceedings of the 27th International Conference on Machine Learning (ICML10), 807–814. https://icml.cc/Conferences/2010/papers/432.pdf. [Google Scholar]

[R82] 82.Zhou Y, Barnes C, Lu J, Yang J, and H Li. (2020). On the Continuity of Rotation Representations in Neural Networks. arXiv, 1812.07035. 10.48550/arXiv.1812.07035. [DOI] [Google Scholar]

[R83] 83.Falcon W, and The_PyTorch_Lightning_team (2022). PyTorch Lightning Zenodo. 10.5281/zenodo.7859091. [DOI] [Google Scholar]

[R84] 84.Lu L (2020). Dying ReLU and Initialization: Theory and Numerical Examples. Comm Comp Phys 28, 1671–1706. 10.4208/cicp.OA-2020-0165. [DOI] [Google Scholar]

[R85] 85.Schumacher MA, Pearson RF, Moller T, Valentin-Hansen P, and Brennan RG (2002). Structures of the pleiotropic translational regulator Hfq and an Hfq-RNA complex: a bacterial Sm-like protein. EMBO J 21, 3546–3556. 10.1093/emboj/cdf322. [DOI] [PMC free article] [PubMed] [Google Scholar]

[R86] 86.Badger J, Sauder JM, Adams JM, Antonysamy S, Bain K, Bergseid MG, Buchanan SG, Buchanan MD, Batiyenko Y, Christopher JA, et al. (2005). Structural analysis of a set of proteins resulting from a bacterial genomics project. Proteins 60, 787–796. 10.1002/prot.20541. [DOI] [PubMed] [Google Scholar]

[R87] 87.Shi W, Basso LA, Santos DS, Tyler PC, Furneaux RH, Blanchard JS, Almo SC, and Schramm VL (2001). Structures of purine nucleoside phosphorylase from Mycobacterium tuberculosis in complexes with immucillin-H and its pieces. Biochemistry 40, 8204–8215. 10.1021/bi010585p. [DOI] [PubMed] [Google Scholar]

[R88] 88.Boutz DR, Cascio D, Whitelegge J, Perry LJ, and Yeates TO (2007). Discovery of a thermophilic protein complex stabilized by topologically interlinked chains. J Mol Biol 368, 1332–1344. 10.1016/j.jmb.2007.02.078. [DOI] [PMC free article] [PubMed] [Google Scholar]

[R89] 89.Singleton M, Isupov M, and Littlechild J (1999). X-ray structure of pyrrolidone carboxyl peptidase from the hyperthermophilic archaeon Thermococcus litoralis. Structure 7, 237–244. 10.1016/s0969-2126(99)80034-3. [DOI] [PubMed] [Google Scholar]

[R90] 90.Im YJ, Kim JI, Shen Y, Na Y, Han YJ, Kim SH, Song PS, and Eom SH (2004). Structural analysis of Arabidopsis thaliana nucleoside diphosphate kinase-2 for phytochrome-mediated light signaling. J Mol Biol 343, 659–670. 10.1016/j.jmb.2004.08.054. [DOI] [PubMed] [Google Scholar]

[R91] 91.Hondoh H, Kuriki T, and Matsuura Y (2003). Three-dimensional structure and substrate binding of Bacillus stearothermophilus neopullulanase. J Mol Biol 326, 177–188. 10.1016/s0022-2836(02)01402-x. [DOI] [PubMed] [Google Scholar]

[R92] 92.Tanaka Y, Nakagawa N, Kuramitsu S, Yokoyama S, and Masui R (2005). Novel reaction mechanism of GTP cyclohydrolase I. High-resolution X-ray crystallography of Thermus thermophilus HB8 enzyme complexed with a transition state analogue, the 8-oxoguanine derivative. J Biochem 138, 263–275. 10.1093/jb/mvi120. [DOI] [PubMed] [Google Scholar]

[R93] 93.Mirdita M, Schutze K, Moriwaki Y, Heo L, Ovchinnikov S, and Steinegger M (2022). ColabFold: making protein folding accessible to all. Nat Methods 19, 679–682. 10.1038/s41592-022-01488-1. [DOI] [PMC free article] [PubMed] [Google Scholar]

[R94] 94.Mukherjee S, and Zhang Y (2009). MM-align: a quick algorithm for aligning multiple-chain protein complex structures using iterative dynamic programming. Nucleic Acids Res 37, e83. 10.1093/nar/gkp318. [DOI] [PMC free article] [PubMed] [Google Scholar]

[R95] 95.Kingma DP, and Ba J (2017). Adam: A Method for Stochastic Optimization. arXiv, 1412.6980. 10.48550/arXiv.1412.6980. [DOI] [Google Scholar]

[R96] 96.Loshchilov I, and Hutter F (2017). SGDR: Stochastic Gradient Descent with Warm Restarts. arXiv, 1608.03983. 10.48550/arXiv.1608.03983. [DOI] [Google Scholar]

[R97] 97.Qi Y, Lee J, Singharoy A, McGreevy R, Schulten K, and Im W (2017). CHARMM-GUI MDFF/xMDFF Utilizer for Molecular Dynamics Flexible Fitting Simulations in Various Environments. J Phys Chem B 121, 3718–3723. 10.1021/acs.jpcb.6b10568. [DOI] [PMC free article] [PubMed] [Google Scholar]

[R98] 98.Phillips JC, Hardy DJ, Maia JDC, Stone JE, Ribeiro JV, Bernardi RC, Buch R, Fiorin G, Henin J, Jiang W, et al. (2020). Scalable molecular dynamics on CPU and GPU architectures with NAMD. J Chem Phys 153, 044130. 10.1063/5.0014475. [DOI] [PMC free article] [PubMed] [Google Scholar]

CG representation	Maximum number of beads per residue	RMSD¹		χ-angle accuracy^1,2		MolProbity¹

		Backbone [Å]	Heavy atom [Å]	χ1 [%]	χ1+2 [%]	Score	Clash score	Rama favor [%]	Rotamer outlier [%]

Experimental structure	-	-	-	-	-	1.25 (0.34)	3.2 (2.4)	97.9 (1.2)	1.4 (1.2)

Rigid body reconstruction³	-	0.03 (0.01)	0.16 (0.03)	-	-	1.81 (0.29)	12.2 (4.8)	97.4 (1.3)	1.4 (1.2)

Cα	1	0.18 (0.05)	0.96 (0.12)	86.2 (3.0)	71.4 (4.8)	2.07 (0.21)	31.2 (9.5)	97.9 (1.1)	0.8 (0.7)
Cα (fixed)⁴	1	0.17 (0.05)	0.93 (0.12)	86.5 (3.0)	71.8 (4.7)	2.13 (0.21)	34.2 (10.3)	98.0 (1.1)	1.0 (0.7)
N, Cα, C	3	0.07 (0.02)	0.83 (0.11)	89.3 (2.8)	75.7 (4.5)	2.09 (0.23)	27.6 (8.5)	97.5 (1.3)	1.1 (0.7)
N, Cα, C (fixed)⁴	3	0.06 (0.02)	0.82 (0.11)	89.4 (2.7)	75.8 (4.5)	2.07 (0.22)	27.8 (8.6)	97.9 (1.2)	1.1 (0.7)
N, Cα, C, O	4	0.04 (0.01)	0.82 (0.11)	89.6 (2.8)	75.6 (4.7)	2.08 (0.22)	26.9 (8.3)	97.4 (1.3)	1.0 (0.8)
N, Cα, C, O (fixed) ⁴	4	0.00 (0.00)	0.82 (0.11)	89.7 (2.8)	75.7 (4.6)	2.05 (0.22)	27.3 (8.3)	97.9 (1.2)	1.1 (0.8)

CM⁵	1	0.22 (0.05)	0.46 (0.06)	95.4 (1.9)	85.9 (3.9)	2.00 (0.23)	20.6 (6.2)	97.3 (1.4)	1.1 (0.7)
SC⁶	1	0.29 (0.07)	0.49 (0.06)	92.8 (2.4)	85.6 (4.1)	2.13 (0.28)	22.9 (7.1)	97.0 (1.5)	1.5 (1.0)
Cα + CM⁵	2	0.11 (0.03)	0.39 (0.05)	98.0 (1.3)	88.7 (3.6)	1.97 (0.20)	22.7 (6.8)	97.7 (1.2)	0.8 (0.7)
Cα + CM⁵ (fixed) ⁴	2	0.10 (0.03)	0.39 (0.05)	98.0 (1.3)	88.8 (3.5)	1.99 (0.21)	23.6 (6.9)	97.7 (1.2)	0.8 (0.7)
Cα + SC⁶	2	0.13 (0.04)	0.40 (0.04)	95.2 (1.9)	88.9 (3.4)	1.93 (0.21)	20.1 (6.2)	97.7 (1.2)	0.9 (0.7)
Cα + SC⁶ (fixed) ⁴	2	0.12 (0.04)	0.39 (0.04)	95.1 (1.9)	89.1 (3.4)	1.96 (0.21)	21.4 (6.3)	97.6 (1.2)	0.9 (0.7)
MARTINI	5	0.08 (0.02)	0.31 (0.05)	98.8 (1.0)	93.1 (2.8)	1.88 (0.21)	17.2 (5.4)	97.5 (1.2)	0.9 (0.7)
PRIMO	8	0.04 (0.01)	0.18 (0.03)	99.9 (0.2)	99.7 (0.5)	1.72 (0.27)	10.7 (4.2)	97.5 (1.3)	1.1 (0.9)

Input	Method	RMSD¹		χ-angle accuracy^1,2		MolProbity¹

		Backbone [Å]	Heavy atom [Å]	χ1 [%]	χ1+2 [%]	Score	Clash score	Rama favor [%]	Rotamer outlier [%]

Cα	cg2all	0.18 (0.05)	0.96 (0.12)	86.2 (3.0)	71.4 (4.8)	2.07 (0.21)	31.2 (9.5)	97.9 (1.1)	0.8 (0.7)
	w/SCRWL³		1.06 (0.14)	83.2 (3.6)	70.1 (5.2)	2.00 (0.18)	28.6 (8.1)	97.9 (1.1)	0.0 (0.1)
	cg2all (fixed)⁴	0.17 (0.05)	0.93 (0.12)	86.5 (3.0)	71.8 (4.7)	2.13 (0.21)	34.2 (10.3)	98.0 (1.1)	1.0 (0.7)

	PULCHRA⁵	0.47 (0.11)	1.57 (0.14)	59.2 (4.0)	39.6 (4.5)	3.79 (0.23)	164.4 (28.5)	86.4 (3.9)	4.9 (1.7)
	w/SCWRL³		1.36 (0.14)	73.0 (4.3)	58.4 (5.6)	2.90 (0.20)	67.4 (17.8)	86.4 (3.9)	0.1 (0.2)

	REMO^5,6	0.81 (0.42)	2.09 (0.41)	43.6 (4.3)	28.5 (5.4)	4.37 (0.21)	200.2 (36.8)	78.4 (7.2)	14.8 (3.8)
	w/SCWRL³		1.74 (0.52)	68.5 (6.5)	53.8 (7.5)	3.15 (0.25)	95.7 (43.6)	78.4 (7.2)	0.2 (0.3)

	ModRefiner^5,6	0.66 (0.20)	1.51 (0.21)	71.8 (4.1)	55.1 (5.6)	2.38 (0.24)	56.5 (19.6)	97.0 (1.7)	0.6 (0.5)
	MODELLER	0.97 (0.88)	2.12 (0.76)	42.8 (4.0)	25.4 (4.0)	3.63 (0.19)	93.3 (15.7)	86.4 (3.4)	6.0 (1.8)

CM	cg2all	0.22 (0.05)	0.46 (0.06)	95.4 (1.9)	85.9 (3.9)	2.00 (0.23)	20.6 (6.2)	97.3 (1.4)	1.1 (0.7)
	w/SCWRL³		1.00 (0.14)	83.9 (3.6)	70.9 (5.2)	2.01 (0.20)	25.5 (7.3)	97.3 (1.4)	0.0 (0.1)

	PULCHRA⁵	1.08 (0.08)	1.91 (0.12)	46.6 (4.0)	29.0 (4.1)	4.49 (0.13)	291.6 (36.2)	72.9 (4.4)	10.5 (2.3)
	w/SCWRL³	1.08 (0.08)	1.84 (0.12)	55.3 (4.0)	36.3 (4.5)	3.51 (0.11)	176.2 (27.6)	72.9 (4.4)	0.2 (0.3)
	MODELLER⁵	1.63 (1.03)	2.38 (0.94)	43.7 (3.9)	25.5 (3.8)	3.80 (0.18)	123.6 (19.9)	81.8 (3.4)	5.5 (1.8)

N, Cα, C, O	cg2all	0.04 (0.01)	0.82 (0.11)	89.6 (2.8)	75.6 (4.7)	2.08 (0.22)	26.9 (8.3)	97.4 (1.3)	1.0 (0.8)
	cg2all (fixed)⁴	-	0.82 (0.11)	89.7 (2.8)	75.7 (4.6)	2.05 (0.22)	27.3 (8.3)	97.9 (1.2)	1.1 (0.8)

	SCWRL	-	0.97 (0.13)	85.6 (3.4)	73.0 (5.0)	1.97 (0.19)	26.7 (7.8)	97.9 (1.2)	0.0 (0.1)

	AttnPacker	-	0.61 (0.11)	90.9 (2.9)	73.3 (5.4)	2.32 (0.25)	22.8 (7.7)	97.9 (1.2)	3.8 (1.5)
	+local min.	-	0.67 (0.11)	92.4 (2.8)	80.6 (4.9)	1.86 (0.28)	11.9 (3.9)	97.9 (1.2)	2.0 (1.1)

MARTINI	cg2all	0.08 (0.02)	0.31 (0.05)	98.8 (1.0)	93.1 (2.8)	1.88 (0.21)	17.2 (5.4)	97.5 (1.2)	0.9 (0.7)
	w/SCWRL³		0.98 (0.13)	85.2 (3.6)	72.6 (5.2)	2.00 (0.19)	26.1 (7.5)	97.5 (1.2)	0.0 (0.1)

	Backward⁷	0.84 (0.07)	1.06 (0.08)	60.9 (5.8)	46.1 (7.2)	2.71 (0.29)	4.5 (1.7)	86.7 (4.5)	15.9 (3.8)
	w/SCWRL³		1.64 (016.	64.5 (55)	50.4 (66.	2.93 (0.22)	74.4 (2L4)	86.7 (4.5)	0.1 (02.

Input	Method	Device¹	Time [s]²

Cα	cg2all	CPU (1)	6.4 (3.6)
		CPU (4)	4.4 (1.6)
		CPU (16)	3.9 (1.1)
		CUDA	8.7 (1.7)
		Apple Silicon	3.2 (1.8)
	cg2all+SCWRL³	CPU (1)	13.0

	PULCHRA	CPU (1)	0.4

	REMO	CPU (1)	6.1

	ModRefiner	CPU (1)	5211

	MODELLER	CPU (1)	98.5

N, Cα, C, O	cg2all	CPU (1)	8.2 (4.4)

	SCWRL	CPU (1)	7.0

	AttnPacker	CPU (1)	197.5 (191.6)
	+local min.		231.4

MARTINI	cg2all	CPU (1)	7.4 (4.4)

	Backward	CPU (1)	33.8

Input	Method	RMSD¹		χ-angle accuracy^1,2		MolProbity¹

		Backbone [A]	Heavy atom [A]	χ1 [%]	χ1+2 [%]	Score	Clash score	Rama favor [%]	Rotamer outlier [%]

Cα from all-atom MD snapshots	MD snapshots					1.45 (0.23)	0.8 (0.5)	93.5 (2.1)	2.7 (1.2)

	cg2all	0.25 (0.04)	1.18 (0.12)	77.7 (3.4)	58.7 (4.6)	2.31 (0.23)	37.1 (9.8)	96.4 (1.5)	1.0 (0.7)
	w/SCRWL³		1.27 (0.14)	76.2 (3.6)	58.1 (4.8)	2.20 (0.19)	32.5 (8.0)	96.4 (1.5)	0.0 (0.1)
	cg2all (fixed)⁴	0.25 (0.04)	1.15 (0.12)	77.9 (3.4)	58.8 (4.6)	2.42 (0.24)	41.0 (10.1)	96.3 (1.5)	1.4 (0.8)

	PULCHRA⁵	0.52 (0.16)	1.70 (0.14)	54.2 (4.0)	32.1 (3.9)	3.84 (0.20)	162.7 (25.5)	85.1 (3.8)	5.2 (1.6)
	w/SCWRL³		1.51 (0.15)	68.0 (4.2)	49.7 (4.8)	2.93 (0.17)	67.1 (15.5)	85.1 (3.8)	0.1 (0.2)

	REMO^5,6	0.94 (0.47)	2.21 (0.46)	44.5 (4.5)	26.4 (4.8)	4.42 (0.21)	197.5 (37.2)	75.1 (7.9)	15.6 (3.9)
	w/SCWRL³		1.95 (0.53)	63.5 (5.9)	45.5 (6.5)	3.22 (0.24)	102.4 (45.0)	75.1 (7.9)	0.2 (0.3)

Cα after minimization with COCOMO⁷	cg2all	0.43 (0.13)	1.34 (0.19)	73.7 (4.2)	54.8 (5.1)	2.55 (0.23)	44.5 (12.5)	94.4 (1.9)	1.1 (0.8)
	w/SCWRL³		1.43 (0.19)	72.3 (4.1)	53.5 (5.2)	2.38 (0.18)	36.1 (10.2)	94.4 (1.9)	0.1 (0.1)
	cg2all (fixed)⁴	0.42 (0.13)	1.32 (0.19)	73.3 (4.3)	54.3 (5.0)	2.70 (0.24)	50.1 (13.3)	94.1 (2.0)	1.7 (0.9)

	PULCHRA⁵	0.61 (0.18)	1.79 (0.18)	52.5 (4.1)	31.0 (4.1)	3.87 (0.19)	156.8 (25.3)	83.5 (3.9)	5.6 (1.7)
	w/SCWRL³		1.62 (0.19)	65.8 (4.4)	47.1 (5.1)	2.95 (0.15)	65.1 (15.3)	83.5 (3.9)	0.1 (0.2)

	REMO^5,6	1.16 (0.49)	2.40 (0.53)	43.3 (4.7)	25.7 (4.8)	4.50 (0.22)	194.5 (40.1)	69.9 (9.5)	17.4 (4.3)
	w/SCWRL³		2.23 (0.59)	59.4 (6.1)	41.3 (6.6)	3.33 (0.25)	116.1 (48.2)	69.9 (9.5)	0.2 (0.3)

PERMALINK

One bead per residue can describe all-atom protein structures

Lim Heo

Michael Feig

SUMMARY

eTOC Blurb

Graphical Abstract

INTRODUCTION

RESULTS

Accurate reconstruction of all-atom structures from coarse-grained representations

Figure 1. Architecture of coarse-grained to all-atom structure conversion model.

Table 1. Performance of conversion to all-atom structures from CG models with cg2all.

Figure 2. Examples of conversion from CG models to all-atom models.

Table 2. Comparison of all-atom reconstruction accuracies with different methods.

Table 3. Average timing for all-atom reconstruction with different methods.

Accurate all-atom reconstruction from simulation models

Table 4. Performance of conversion to all-atom structures from Cα-traces of simulation snapshots.

Figure 3. Stability of all-atom MD simulations continued from reconstructed all-atom models.

Addition of all-atom structural details to low-resolution models

Multi-scale sampling for rapid cryo-EM refinement

Figure 4. Refinement of initial models against cryo-EM density maps.

Figure 5. Refinement against a cryo-EM density map for 3isr.

DISCUSSION

STAR METHODS

RESOURCE AVAILABILITY

Lead contact

Materials availability

Data and code availability

METHOD DETAILS

Experimental datasets

Simulation datasets

Input features

Neural network model

Structure module

Model training

Loss function

Augmentation of putative side chain conformations

Hyperparameter optimization and ablation studies

Structure refinement against cryo-EM density map via the cg2all network

QUANTIFICATION AND STATISTICAL ANALYSIS

Supplementary Material

KEY RESOURCES TABLE.

Highlights.

ACKNOWLEDGMENTS

Footnotes

REFERENCES

Associated Data

Supplementary Materials

Data Availability Statement

ACTIONS

PERMALINK

RESOURCES

Similar articles

Cited by other articles

Links to NCBI Databases