# Neural Upscaling from Residue-Level Protein Structure Networks to Atomistic Structures

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## Abstract

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## 1. Background

## 2. Methods

**Data Generation**Our data come from atomistic MD trajectories of A${\beta}_{1\u201340}$, a widely studied IDP implicated in the etiology of Alzheimer’s disease; the atomistic trajectories and associated PSN coarsenings, respectively, serve as ground truth and inputs for the upscaling model (Figure 2). Beginning with the lowest energy monomer of the PDB structure, 2LFM [34], one A${\beta}_{1\u201340}$ monomer was simulated in explicit solvent for 1 μs using NAMD [35] via the following protocol: the initial monomer structure was solvated in a cubic TIP3P [36] water box of minimum margin 25 Å, and neutralized with NaCl counter-ions. This assembly was minimized for 10,000 iterations, followed by velocity initialization and 250 simulation iterations before final adjustment of the water box. A trajectory of approximately 1.1 μs was then simulated. Simulation was performed under periodic boundary conditions in NAMD with the CHARMM36m forcefield [37], using an NPT ensemble at 300K and 1 atm pressure. Temperature control was maintained by Langevin dynamics with a period of 1/ps, with Nosé-Hoover Langevin piston pressure control [38,39]. Creation of initial conditions and related data processing were performed using VMD [40].

`statnet`[41,42] and

`bio3d`[43] libraries for

`R`[44]).

**Neural network architecture and hyperparameters**After generation of input and output data, a multi-layer perceptron (MLP) neural network was utilized for training as indicated in the pipeline (Figure 3). This neural network contains four hidden layers (structured as follows), and was implemented using the machine-learning libraries Keras [46] and tensorflow [47]. The first three hidden layers consist of 2000 neurons, the fourth layer contains 8000 neurons, and the last output layer predicts the flattened upper triangle of the pairwise interatomic distance matrix for a given frame from the MD simulation (46,665 neurons) (Figure 6). Hyperparameters were optimized using the Talos Keras tuning module [48]. A Nvidia P6000 Quadro GPU card was used to train the model with the following hyperparameters: nonlinearity = relu, dropout rate = 0.2, optimization = AMSGrad, loss = mean squared error, batch size = 50, epochs = 100. Predicted output data were initially assessed using three metrics: root-mean squared deviation/error (RMSD/RMSE), mean squared error (MSE), and mean absolute percentage error (MAPE).

**Post-prediction processing**The predicted output data (the flattened upper triangles of the pairwise interatomic distance matrices) were first transformed into symmetric pairwise interatomic distance matrices. These were then transformed into 3D coordinate data using the multi-dimensional scaling (MDS) function from the scikit-learn python module and MDtraj [49] to generate PDB structures (Figure 3). Chimera [50] was then used to add hydrogens to predicted PDB structures, which were then further processed to remove inaccurate chiral predictions. If more than half of C$\alpha $ centers were inaccurately predicted as R chiral centers (D-amino acids instead of L-amino acids), this indicated that the MDS procedure (which is reflection-invariant) predicted a reflection of the true coordinates. This was mitigated by reflecting all coordinates over the y-axis for predictions exhibiting an $\frac{R}{S}$ ratio greater than 1. If fewer than half of $\alpha $-carbons exhibited R chiral centers, reflecting coordinates was unnecessary. Instead, Chimera was used to switch side chain coordinates and the $\alpha $-hydrogen for all inaccurately predicted C$\alpha $ chiral centers. After checking for correct chirality for each residue, all conformations were further minimized for 75 conjugate gradient steps.

## 3. Results

#### 3.1. Multilayer Perceptron (MLP) Neural Network Reconstructs Aβ Conformations with Atomistic Detail

#### 3.2. Generation of 3D Structures and Subsequent Minimization

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**The ability to impute atomistic structures from network representations enables both compressive representation of structures from MD trajectories and the use of generative network models to predict distributions of atomistic structures.

**Figure 2.**Data generation of input (upper triangle of PSN adjacency matrices) and output (upper triangular of PIDs) data.

**Figure 4.**Distribution of the optimal number of CG steps for structure refinement, by metric, with green vertical lines representing means, and notches representing medians. Although exact optima vary by structure and metric, 50–100 steps are sufficient to provide good performance on most structures; extensive refinement beyond this point is rarely beneficial.

**Figure 5.**Boxplots of distributions for the following metrics (RMSE, MAE, MAPE) for the train, validation, and test datasets: Minimum, maximum, median, outliers (grey dots), average (yellow diamond) ± standard error, lower and upper quartiles.

**Figure 6.**A histogram of metrics for the combined validation and test set of the first cross validation fold. Metrics include RMSD/RMSE in angstroms, LDDT, TM-Score, and GDT_TS. Excluding RMSD, the other three metrics range from 0 (inaccurate) to 1 (accurate) prediction. Lower RMSD values indicate more accurate predictions.

**Figure 7.**Mean validation performance ± standard error on RMSE, MAE, and MAPE for each of five cross-validation splits. Performance is robust to choice of fold.

**Figure 8.**Comparison between original and predicted pairwise interatomic distances for frame 1133 (from the test set). (

**a**) Actual distances are shown for all heavy atoms. (

**b**) Heavy-atom predictions of all pairwise interatomic distance. (

**c**) Histogram of differences between original and predicted Euclidean distances. (

**d**) Binary plot displaying the absolute difference values between each actual and predicted distance for frame 1133.

**Figure 9.**Alignment between original and predicted and processed 3D structures for (

**a**) the best, (

**b**) median, and (

**c**) worst predictions based on RMSE values of PIDs.

**Figure 10.**Comparison of pre- and post-minimized structures of the best prediction in the test set, frame 1133.

**Figure 11.**Juxtaposition of 3D structural metrics of the combined validation-test set: TM score, LDDT, GDT_TS, and RMSD. In addition, best, median, and worst predictions are shown based on PIDs. (

**a**) LDDT vs. TM score metrics of the validation-test set. (

**b**) LDDT vs. GDT_TS score metrics of the validation-test set. (

**c**) RMSD vs. TM score metrics of the validation-test set. (

**d**) RMSD vs. GTD_TS score metrics of the validation-test set.

**Figure 12.**Barplot of average 3D accuracy metrics and corresponding 95% confidence intervals per score type.

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**MDPI and ACS Style**

Duong, V.T.; Diessner, E.M.; Grazioli, G.; Martin, R.W.; Butts, C.T. Neural Upscaling from Residue-Level Protein Structure Networks to Atomistic Structures. *Biomolecules* **2021**, *11*, 1788.
https://doi.org/10.3390/biom11121788

**AMA Style**

Duong VT, Diessner EM, Grazioli G, Martin RW, Butts CT. Neural Upscaling from Residue-Level Protein Structure Networks to Atomistic Structures. *Biomolecules*. 2021; 11(12):1788.
https://doi.org/10.3390/biom11121788

**Chicago/Turabian Style**

Duong, Vy T., Elizabeth M. Diessner, Gianmarc Grazioli, Rachel W. Martin, and Carter T. Butts. 2021. "Neural Upscaling from Residue-Level Protein Structure Networks to Atomistic Structures" *Biomolecules* 11, no. 12: 1788.
https://doi.org/10.3390/biom11121788