#DeepLearning predicts protein flexibility with intricate atomic structures #ProteinFlexibility

Overview of RMSF-net procedure

We propose a deep learning approach named RMSF-net to analyze protein dynamics based on cryo-electron microscopy (cryo-EM) maps. The primary objective of this method is to predict the RMSF of local structures (residue, atoms) within proteins. RMSF is a widely used measure to assess the flexibility of molecular structures in MD analysis and defined by the following equation:

where \(x\) represents the real-time position of atoms or residues, \(t\) represents time and \(\widetilde{x}\) represents the mean position over a period of time \({T}\). In addition to the experimental cryo-EM maps, RMSF-net incorporates fitted PDB models, which represent the mean structures of fluctuating proteins. A schematic overview of RMSF-net is depicted in Fig. 1a. The cryo-EM map and PDB model are initially combined to create a dual feature pair. The PDB models are converted into voxelized density maps using the “MOLMAP” tool in UCSF Chimera²³ to facilitate seamless integration with cryo-EM maps. Subsequently, both the density grids of the cryo-EM maps and the PDB simulated maps are divided into uniform-sized density boxes (40 × 40 × 40) with a stride of 10. The corresponding density boxes from the mapping pair are concatenated to form a two-channel feature input for the neural network (RMSF-net) to predict the RMSF of atoms within the central subbox (10 × 10 × 10). RMSF-net is a three-dimensional convolutional neural network comprising two interconnected modules. The primary module employs a Unet + +(L3) architecture²⁴ for feature encoding and decoding on the input density boxes. The other module utilizes 1-kernel convolutions for regression on the channels of the feature map generated by the Unet + + backbone. A center crop is then applied to the regression module output to obtain the central RMSF subboxes, where the voxel values correspond to the RMSF of the atoms contained within them. Finally, the RMSF sub-boxes are spatially merged into an RMSF map using a merging algorithm.

RMSF-net incorporates several data processing strategies for maps, as illustrated in Fig. 1b. First, to ensure a consistent spatial scale, all the cryo-EM maps were resampled using the “ndimage.zoom” module from SciPy²⁵ to obtain a uniform voxel size of 1.5 Å, which is approximately the size of a Cα atom. Second, a screening algorithm is applied to retain only those boxes that encompass atoms within the central subbox to avoid processing unnecessary boxes located in structure-free regions. This strategy significantly improves the efficiency of RMSF-net when dealing with large cryo-EM maps. The retained box indices are recorded for the subsequent merging algorithm. In addition, the voxel densities within the boxes are normalized to a range of [0, 1] before being input into the network, thus mitigating density distribution variations across cryo-EM maps. Voxel density normalization is achieved through the following process: within each box, any density values less than 0 are set to 0, and then divided by the maximum density value within the box, thus scaling the voxel density to a range from 0 to 1.

Dataset construction

We created a high-quality protein dataset with 335 entries for training and evaluating RMSF-net. The dataset was constructed by selecting data from EMDB²⁶ and PDB²⁷. As of November 2022, EMDB contained over 23,593 deposited entries, with more than half being high-resolution maps with resolutions ranging from 2–4 Å. We focused on maps within this range. Initially, we included a high-resolution cryo-EM map dataset from EMNUSS¹² which underwent rigorous screening in EMDB and PDB prior to October 2020 and consisted of 468 entries. In addition, we performed data selection on deposited cryo-EM maps and PDB models from October 2020 to November 2022 to incorporate newly deposited data. The selected data had to meet specific criteria, including a well-fitting cryo-EM map and PDB model with a fitness above 0.7 (measured by the correlation between the PDB simulated map and cryo-EM map); the proteins had to contain at least one alpha helix or beta-strand, with no missing chains or nucleic acids. We further filtered these data by applying a clustering procedure to remove redundancy. Using the K-Medoids²⁸ algorithm with a k value of 50, we defined the distance between two proteins as the maximum distance between any two chains from each protein, where chain distances were determined by sequence identity. After clustering, we selected the 50 medoids and added them to the dataset. Finally, out of the remaining 518 entries, 335 were successfully subjected to MD simulations, resulting in the RMSF-net dataset.

Molecular dynamics simulation

RMSF-net employs a supervised training approach, requiring labeled RMSF values derived from MD simulations¹⁹. We conducted MD simulations on the PDB models of the dataset following a standardized procedure using Assisted Model Building with Energy Refinement (AMBER)²⁰, which consists of four stages: energy minimization, heating, equilibration, and production runs. To focus on local structure fluctuations around specific protein conformations, we configured the production run for 30 nanoseconds. Specifically, the initial atomic coordinates of the proteins were set to the original PDB model coordinates. Small molecule ligands in all complexes were removed to purely study the characteristics of proteins. Each system was immersed in a truncated octahedron box filled with TIP3P²⁹ water molecules (at least a 12 Å buffer distance between the solute and edge of the periodic box). Based on the charge carried by the protein, Na⁺ or Cl⁻ ions were placed randomly in the simulation box to keep each system neutral. An additional 150 mM NaCl solution was added to all systems according to the screening layer tally by the container average potential method³⁰ to match the experimental conditions better. All MD simulations were performed using the AMBER 20 software package^20,31 on NVIDIA Tesla A100 graphics cards. The parameters for Na⁺ and Cl^– ions were derived from the previous work by Joung et al.³². The parameters used for the protein structure were AMBER ff14SB force field³³. Each system was energy minimized using the conjugate gradient method for 6000 steps. Then, the systems were heated using the Langevin thermostat³⁴ from 0 to 300 K in 400 ps using position restraints with a force constant of 1000 kcal · mol⁻¹ · Å⁻² to the protein structure (NVT ensemble, T = 300 K). Subsequently, each system was gradually released in 5 ns (spending 1 ns each with position restraints of 1000, 100, 10, 1, and 0 kcal · mol⁻¹ · Å⁻²) using the NPT ensemble (P = 1 bar, T = 300 K) before a production run. Afterward, the final structure of each system was subjected to a 30 ns MD simulation at constant temperature (300 K) and pressure (1 bar) with periodic boundary conditions and the particle mesh Ewald (PME) method³⁵ We used the isotropic Berendsen barostat³⁶ with a time constant of 2 ps to control constant pressure. The protein structure was completely free in the solutions during the equilibration and production process. Simulations were run with an integration step of 2 fs, and bond lengths for hydrogen atoms were fixed using the SHAKE algorithm³⁷. PME electrostatics were calculated with an Ewald radius of 10 Å, and the cutoff distance was also set to 10 Å for the van der Waals potential.

Model training and validation

After simulation, the trajectories were processed and analyzed using the built-in Cpptraj module of AMBER Tools package³⁸. We first removed the translational and rotational motion of all protein molecules to ensure a rigorous comparison between different trajectories. Then, the average structure of each protein (only heavy atoms) was calculated as a reference structure. Afterward, each conformation in the trajectory was aligned to the reference structure and RMSF of the protein molecule was output. These computed RMSF values were subsequently mapped onto voxels of cryo-EM maps to serve as the ground truth for training and evaluating RMSF-net.

For the training of RMSF-net, we utilized a masked mean squared error (MSE) loss function to compute the loss between the predicted RMSF and ground truth RMSF on labeled voxels of the output subboxes. The training spanned 100 epochs with a batch size of 32, and we employed the Adam optimizer³⁹ with a learning rate of 0.004. Several techniques were implemented to mitigate overfitting, including Kaiming weight initialization⁴⁰, learning rate decay, and early stopping. If the validation loss did not decrease for 10 consecutive epochs, the learning rate was halved. If it did not decrease for 30 epochs, training was terminated, and the model with the minimum validation loss was saved. We applied rotation and mirroring augmentation to the training set to account for the lack of rotational and mirror symmetry in convolutional networks, increasing the training data eightfold. The training of RMSF-net was conducted on two NVIDIA Tesla A100 graphics cards, typically lasting 5–8 h. Following training, we conducted RMSF predictions on the test set to evaluate the performance of RMSF-net.

We employed a five-fold cross-validation approach to assess the performance of this method. The dataset was randomly divided into five equal partitions, with one partition used as the test set each time, and the remaining four partitions served as the training and validation sets. In particular, the division was based on the maps rather than the segmented boxes in order to ensure independence between these sets. The training and testing process was repeated five times, and every data entry was tested once to obtain the method’s performance on the entire dataset. To prevent overfitting during model training, the training and validation sets were set at a ratio of 3:1. During testing, the correlation coefficients between the predicted RMSF and the ground truth (RMSF values derived from MD simulations) were computed as the evaluation metric. The correlation coefficients were computed at two levels: voxel level, corresponding to RMSF on the map voxels, and residue level, corresponding to RMSF on the PDB model residues (obtained by averaging RMSF on the corresponding atoms). We defaulted to using the correlation coefficient at the voxel level when analyzing and comparing model performance unless otherwise specified. In addition, we employed the correlation coefficient at the residue level when discussing the protein test cases.

Baselines

As a baseline, we initially used only the cryo-EM map intensity as the single-channel input to the neural network, referred to as RMSF-net_cryo. Cross-validation using RMSF-net_cryo on the dataset revealed an average correlation coefficient of 0.649 and a bias of 0.156. We also performed cross-validation using the prior method DEFMap method for comparison. DEFMap reported a test correlation of approximately 0.7 on its dataset. However, its dataset includes only 34 proteins and the dataset used in our study is more diverse and significantly larger. Therefore, we applied the DEFMap pipeline to our dataset to ensure fair comparisons. Notably, DEFMap employed different data preprocessing strategies and neural networks. During its preprocessing, a low-pass filter was adopted to standardize the resolution of the cryo-EM maps. In addition, the neural network it used took 10-cubic subvoxels as input and outputted the RMSF of the central voxel. We strictly followed DEFMap’s procedures and network for training and testing. The results showed an average correlation coefficient of 0.6 and a bias of 0.171. Through comparison, it is evident that RMSF-net_cryo exhibits superior performance compared to DEFMap.

Enhancing interpretability of dynamics inferred from cryo-EM intensity

Although RMSF-net_cryo performed better than DEFMap with our designed network and data processing strategies, it still relies on neural networks to directly establish patterns between cryo-EM maps and flexibility. What role the structural information plays in this process remains unknown. This prompted us to divide dynamic prediction via cryo-EM maps into two sequential steps: first, structural information extraction, and second, dynamic prediction based on the extracted structural information.

To accomplish the extraction of structural information, as depicted in Fig. 2a, we introduced an Occ-net module. This module predicts the probabilities of structural occupancy on cryo-EM map voxels using a 3D convolutional network. Both input and output dimensions were set to 40³. For training and evaluating Occ-net, we utilized PDB models to generate structure annotation maps as the ground truth, where voxels were categorized into two classes: occupied by structure and unoccupied by structure. The details of this network and data annotation process are provided in the Supplementary Information (section “Structure of Occ-net and the data annotation process”). Cross-entropy loss function was employed during training, with class weights set to 0.05:0.95 to address class imbalance. Once this training stage was completed, Occ-net parameters were fixed, and the second stage of training commenced. In the second stage, the two-channel classification probabilities output by Occ-net were input into the dynamics extraction module to predict the RMSF for the central 10³ voxels, which is consistent with the RMSF-net approach.

This model is referred to as Occ2RMSF-net, and cross-validation was conducted on it. After training, we first assessed the performance of Occ-net by calculating the precision, recall, and F1-score at the voxel level for the positive class (structure class) on the test set. This evaluation involves six classification thresholds, ranging from 0.3 to 0.8. As depicted in Fig. 2b, achieving high precision and recall simultaneously was challenging due to severe class imbalance and noise. A relative balance was achieved at the threshold of 0.7, where the F1 score reached its highest value of 0.581. Regarding the final output RMSF, the correlation between the Occ2RMSF-net predictions and the ground truth on the dataset is 0.662 ± 0.158, showing a slight improvement compared to RMSF-net cryo. Figure 2c displays the scatter plot of the test correlation of data for Occ2RMSF-net and RMSF-net cryo. The two models exhibited similar performance on most of the data points, with Occ2RMSF-net slightly outperforming RMSF-net_cryo overall. This highlights the critical role of structure information from cryo-EM maps for predicting the RMSF in the network and enhances the interpretability of methods like DEFMap and RMSF-net_cryo.

Performance of RMSF-net that incorporates PDB information

Inspired by the above results, we incorporated PDB models representing precise structural information and integrated them into our method in a density map-like manner, i.e., simulated density maps generated based on PDB models. We employed two approaches to input the PDB simulated maps into the network. First, the PDB simulated map was taken as a single-channel feature input into the neural network, referred to as RMSF-net_pdb. Second, the PDB simulated map was transformed into a binary encoding map representing occupancy of the structure to highlight tertiary structural features: a threshold of 3 σ(σ represents r.m.s.d of the PDB simulated map density) was chosen, where voxels with densities above the threshold were encoded as 1 and the others as 0. This encoding map was then converted into a two-channel one-hot input to the network, known as RMSF-net_pdb01. The same cross-validation was applied to these two models. Results showed that RMSF-net_pdb achieved a test correlation coefficient of 0.723 ± 0.117, and RMSF-net_pdb01 achieved 0.712 ± 0.112. These two approaches demonstrated significantly better performance than the above cryo-EM map-based methods, further demonstrating the strong correlation between protein structure topology and flexibility.

We further combined the information from the PDB structure and cryo-EM map and input them into the network, which is the main method proposed in this work. We refer to this method, along with the neural network it employs, simply as RMSF-net. As outlined in the “Overview of RMSF-net procedure” section, RMSF-net takes the dual-channel feature of density from the cryo-EM map and PDB simulated map at the same spatial position as input, while the main part of the network remains the same as RMSF-net_cryo and RMSF-net_pdb. Conducting the same cross-validation on RMSF-net, the results revealed an average correlation coefficient of 0.746, with a median of 0.767 and a standard deviation of 0.127.

RMSF-net demonstrated an approximate 10% improvement compared to the baseline of RMSF-net_cryo, and a 15% enhancement over DEFMap. Figure 2d presents a comparison of the distribution of data quantities at different test correlation levels for the three methods. Overall, the two cryo-EM map-based methods (DEFMap and RMSF- net_cryo) exhibit similar distribution shapes, while the distribution of RMSF-net is more concentrated, focusing on the range between 0.6 and 0.9. Nearly half of the data points cluster around 0.7 to 0.8, and close to one-third fall between 0.8 and 0.9. In comparison, the two PDB-based methods in Fig. 2f exhibit similar distributions with RMSF-net. This suggests that the structure information from PDB models plays a primary role in the ability of RMSF-net to predict flexibility. On the other hand, RMSF-net further outforms the PDB-based methods through combination with information from cryo-EM maps, indicating image features related to structural flexibility in the cryo-EM map make an effective auxiliary. Regarding the robustness of these approaches, Table 1 demonstrates that RMSF-net_pdb and RMSF-net_pdb01 exhibited less deviation on the test set compared to RMSF-net, while RMSF-net_cryo displayed the highest deviation. This indicates the flexibility-related information in cryo-EM maps is unstable compared to that in PDB models, which might be caused by noise and alignment errors in cryo-EM maps.

Anomalies

The experimental results above prove that the combination of cryo-EM map and PDB model results in the superior performance of RMSF-net. As shown in Fig. 2e, the prediction of RMSF-net is better in most cases, comparing models utilizing only the cryo-EM map or only the PDB model. Because the PDB models are built from the corresponding cryo-EM maps, their spatial coordinates are naturally aligned, and their structural information is consistent. Moreover, the PDB model built from the cryo-EM map corresponds precisely to the average position of the structure, and the cryo-EM map reconstructed from multiple particles in the sample corresponds to the information of multiple instantaneous conformations. By combining the ‘expectation’ and conformational ‘variance’ from the two sources, we believe that this structural consistency and complementarity create an alignment effect, and promote the superior performance of RMSF-net. However, structural deviations may exist between the PDB model and the cryo-EM map in some instances, or the PDB model may only partially occupy the cryo-EM map. These anomalies might lead to subpar performance of RMSF-net_cryo compared to RMSF-net and RMSF-net_pdb. To exclude the influence of these factors, we performed dataset filtering by excluding data points with test correlations below 0.4 for RMSF-net_cryo and compared the three models on the filtered dataset. Figure 2g shows that RMSF-net and RMSF-net_pdb still demonstrated better performance overall compared to RMSF-net_cryo on the filtered dataset. The test correlations for the three models were 0.760 ± 0.084, 0.733 ± 0.083, and 0.684 ± 0.1, respectively. When the filtering threshold was increased to 0.5, the correlations for the three models were 0.761 ± 0.08, 0.734 ± 0.08, and 0.698 ± 0.084, respectively, showing consistent results.

Examples and case study

Figure 3a showcases RMSF-net predictions for three relatively small proteins: the bluetongue virus membrane-penetration protein VP5 (EMD-6240/PDB 3J9E)⁴¹, African swine fever virus major capsid protein p72 (EMD-0776/PDB 6KU9)⁴² and C-terminal truncated human Pannexin1 (EMD-0975/PDB 6LTN)⁴³. Among these, 3J9E displays an irregular shape composed of loops and alpha helices, while 6KU9 and 6LTN exhibit good structural symmetry with beta sheets and alpha helices, respectively. The predictions by RMSF-net exhibit strong agreement with the ground truth for these proteins, yielding correlation coefficients of 0.887, 0.731, and 0.757, respectively, as depicted in Fig. 3b. Predictions by RMSF-net_cryo and RMSF-net_pdb are supplied in Supplementary Figs. S1–S3. On 3J9E and 6KU9, both RMSF-net_cryo and RMSF- net_pdb perform well, achieving correlations of 0.82, 0.69, and 0.881, 0.7, respectively. However, on 6LTN, RMSF- net_cryo only exhibits a correlation of 0.3 with the ground truth, possibly due to ring noise in the intermediate region of EMD-0975, leading to model misjudgment. In contrast, RMSF-net_pdb achieves a higher correlation of 0.767 on this protein, even surpassing RMSF-net, suggesting that instability factors in cryo-EM maps have a slight impact on RMSF-net’s inference.

In addition to small proteins, Fig. 3c presents test examples of large protein complexes, including Mycobacterium tuberculosis RNA polymerase with Fidaxomicin⁴⁴ (EMD-4230/PDB 6FBV), RSC complex⁴⁵ (EMD-9905/PDB 6K15), and coronavirus spike glycoprotein trimer⁴⁶ (EMD-6516/PDB 3JCL). RMSF-net also excels on these complex structures, achieving correlation coefficients of 0.902, 0.819, and 0.804, respectively. Remarkably, these proteins are associated with human diseases and drug development, emphasizing the potential value of RMSF-net in facilitating drug development efforts. Predictions by RMSF-net_cryo and RMSF-net_pdb for these proteins are provided in Supplementary Figs. S4–S6, with correlation coefficients of 0.759 and 0.859 for 6FBV, 0.661 and 0.774 for 6K15, and 0.635 and 0.784 for 3JCL, respectively. Comparing model predictions in the Supplementary Figs. shows that RMSF-net aligns more closely with RMSF-net_pdb, supporting the previous argument that information from the PDB model plays a primary role in RMSF-net’s feature processing.

We further applied RMSF-net to investigate dynamic changes in the NTCP protein during its involvement in biochemical processes. NTCP (Na + /taurocholate co-transporting polypeptide)⁴⁷ is a vital membrane transport protein predominantly located on the cell membrane of liver cells in the human body. It is responsible for transporting bile acids from the bloodstream into liver cells and plays a crucial role in the invasion and infection processes of liver viruses such as the hepatitis B virus. Therefore, structural and functional analysis of NTCP is crucial for liver disease treatment. In a previous study, two NTCP conformations, the inward-facing conformation (EMD-13593/PDB 7PQG) and the open pore conformation (EMD-13596/PDB 7PQQ), were resolved using cryo-electron microscopy. We performed dynamic predictions using RMSF-Net on these two conformations and revealed dynamic changes during the transition from the inward-facing to the open pore state, as shown in Fig. 3d. Compared to the inward-facing state, the open pore conformation displayed increased dynamics in the TM1 and TM6 regions of the panel domain, the TM7 and TM9 regions of the core domain, and the X motif in the center. Other regions maintained stability or exhibited enhanced stability. We hypothesize that the increased flexibility in these regions is associated with the relative motion between the panel and core domain in the open pore state, facilitating the transport of bile acids and the binding of preS1 of HBV in this conformation.

Examples in more complex dynamic environments

Despite exhibiting high-performance, RMSF-net is trained and tested based on relatively short-term (30 ns) MD simulations. In order to determine whether the structural fluctuation patterns obtained through the 30 ns simulation are stable enough for the model training, we performed longer simulations on three proteins^46,48,49 (PDB 3JCL, 6QNT, and 6SXA). The detailed setup and results are provided in the Supplementary Information (section “MD simulations over longer time periods”). In these cases, the results from the previous 30 ns simulation showed strong correlations with the results up to 500 ns, indicating that the 30 ns simulation can effectively capture stable structural fluctuation mode, thus qualified to serve as the foundation for our model training. The RMSF-net predictions also maintain high correlations with the long-term MD simulations, proving that the trained model has effectively absorbed the structural fluctuation patterns in MD simulations.

In addition, to make large-scale simulations feasible, we removed small molecules and ionic ligands during MD simulations, but ligands are included in the input density of RMSF-net. Therefore, the simulation results may be inaccurate regarding the flexibility of the ligand-containing protein, especially the flexibility near the ligands. To assess the impact of this treatment, we performed MD simulations for two protein systems containing ligands: the structure of the cargo bound AP-1:Arf1:tetherin-Nef closed trimer monomeric subunit⁵⁰ (EMD-7537/PDB 6CM9) and spastin hexamer in complex with substrate⁵¹ (EMD-20226/PDB 6P07). Configurations of the MD simulations are provided in the Supplementary Information (section “MD simulation configurations for ligand-binding proteins and membrane proteins”). The simulations with and without ligands exhibited high correlations in terms of RMSF, with correlations of 0.748 and 0.859 for the two proteins, respectively (Table 2). The predictions of RMSF-net also maintain comparable correlations with the additional simulations, of 0.757 and 0.859 respectively. This indicates that, overall, small molecule ligands have little impact on protein structural flexibility. However, we observed that near the ligands, the RMSF obtained from simulations without ligands is indeed higher than that obtained from simulations with ligands, as shown in Fig. 4. In these regions, the predicted values of RMSF-net are even closer to simulations with ligands, i.e., the predicted RMSF is lower. Our understanding of this phenomenon is that on one hand, the structure of the ligands is relatively small compared to the protein structure, so the scope of influence is limited and does not greatly affect the global distribution of structural flexibility. On the other hand, the local structures near the ligands became relaxed without the ligands in the original simulations. The deep model utilizes the learned pattern between protein internal structures and flexibility to infer the dynamics of the protein structure binding to the ligands. Although this is only an approximation, it has some correction effect.

Another aspect of MD simulation is the simulation of membrane proteins. In the sample preparation of cryo-EM, membrane proteins are purified and separated from membrane structures (Van Heel et al., 2000), which means that the structure and dynamics of membrane proteins in cryo-EM reflect their free state in solution. Correspondingly, our dynamic simulations were also performed in the membrane-free state. Therefore, our model is applicable to proteins in their free state in solution. However, in vivo, membrane proteins are attached to the cell membrane, so considering the simulation environment of the membrane will more accurately simulate their dynamics in biological systems. To explore the differences brought by the membranes, we conducted MD simulations in a membrane environment on two membrane proteins, the cryo-EM structure of TRPV5 (1-660) in nanodisc⁵² (EMD-0593/PDB 6O1N) and cryo-EM structure of MscS channel, YnaI⁵³ (EMD-6805/PDB 5Y4O). The configurations of the MD simulations are provided in Supplementary Information (section “MD simulation configurations for ligand-binding proteins and membrane proteins”). The results, as shown in Table 3 and Fig. 5, demonstrate that the RMSF obtained from MD simulations with and without membranes maintain consistency overall, with correlations of 0.767 and 0.678 on 6O1N and 5Y4O respectively. The correlations between RMSF-net predictions and MD simulations with membranes are 0.804 and 0.675 respectively for these two proteins. As shown in Fig. 5b, the presence of the membrane leads to some changes in the flexibility of 5Y4O: in the upper region of 5Y4O, the RMSF obtained from MD simulations with the membrane is lower than that from MD simulations without membrane and RMSF-net. We speculate that this region may be influenced by membrane constraints, resulting in decreased flexibility, but the overall flexibility distribution remains largely unchanged. In addition, we observe that on these two highly symmetrical structures, the predictions of RMSF-net also maintain symmetry similar to MD simulations.

Model performance across different resolutions

The experimental results also indicate that our method exhibits consistent performance across cryo-EM maps with varying resolutions. The resolution of cryo-EM maps signifies the minimum scale at which credible structures are discernible within the map. In our dataset, there are more maps in the resolution range of 3–4 Å compared to 2–3 Å, as shown in Fig. 6a. Considering that our method takes cryo-EM maps of various resolutions into network training, concerns arise regarding potential model bias towards specific map resolutions. To address this concern, we conducted an analysis of the test performance of RMSF-net_cryo, Occ2RMSF-net, and RMSF-net compared to RMSF- net_pdb on maps of different resolutions. Results demonstrate that these models exhibit no significant performance differences across different resolution ranges, as shown in Fig. 6b–d. Only a minor deviation is observed in the range of 2–2.5 Å, which is statistically insignificant due to the limited number of 7 data points. This underscores that neural networks can fit data indiscriminately within the high-resolution range of 2–4 Å, without the need to process the maps to a uniform resolution at the preprocessing stage. The similar distributions of RMSF-net and Occ2RMSF-net across different resolutions, shown in Fig. 6b, e, further support the conclusion that dynamic inference from cryo-EM maps relies on an intermediate process of structural resolution. Furthermore, Fig. 6d demonstrates that, on average, RMSF-net outperforms RMSF-net_pdb across different resolution ranges, indicating that cryo-EM maps have an auxiliary effect on PDB models for dynamic analysis across different resolutions.

Runtime assessment

In addition to its superior performance, RMSF-net demonstrates rapid inference capabilities and minimal storage overhead, whether running on high-performance GPUs or CPUs. Using a computer equipped with 10 CPU cores and 2 NVIDIA Tesla A100 GPUs, we conducted runtime assessments on the dataset, revealing a strong linear relationship between the execution time of RMSF-net and the data size. Moreover, compared to conventional MD simulations and DEFMap, this approach achieves substantial acceleration in processing speed.

As shown in Fig. 6e, Supplementary Figs. S11c and S12a, when executed on CPUs, RMSF-net’s runtime is directly proportional to the weighted summation of cryo-EM map size and PDB model size, with a weight ratio of map size to PDB size at 0.0015:0.9985, both measured in units of k voxels. For most data, the weighted sum of map size and PDB size is within 500 k voxels, and processing can be completed in under a minute. When executed on GPUs, since most of the time is spent on preprocessing, the total time is linearly related to the map size, as shown in Fig. 6f, Supplementary Figs. S11a and S12b. For most maps with sizes below 300³ voxels, computations can be completed within 30 s. Detailed information regarding the RMSF-net processing time is provided in the Supplementary Information (section “Details of the RMSF-net processing time”).

For comparative analysis, we selected ten relatively small maps from our dataset and performed runtime assessments using RMSF-net and DEFMap. As presented in Supplementary Tables S1–S3, across these ten data points, DEFMap exhibited processing times of 45.94 ± 31.84 minutes on CPUs and 37.51 ± 10.51 minutes on GPUs, concurrently generating data files of size 11.98 ± 8.30 GB. In contrast, RMSF-net showcased remarkable efficiency, with runtime durations of 16.66 ± 9.60 s and 3.09 ± 1.45 s on CPUs and GPUs, respectively, and yielding data files of 66.30 ± 31.06 MB. Both in terms of storage occupancy and time consumption, RMSF-net demonstrates significant improvements over DEFMap. Furthermore, in contrast to extended MD simulations, which often require hours or even days to perform simulations of 30 ns on individual proteins, RMSF-net delivers predictions with an average correlation of up to 0.75 and saves time and resources significantly, making it an ultra-fast means of performing protein dynamic analysis.