==== GMVAE Clustering of Protein Contacts ====
(author: Drs. Min-Kang Hsieh and Mahdi Ghorbani)
This is based off Dr. Ghorbani's GMVAE code available on [[https://github.com/ghorbanimahdi73/GMVAE-MD|Github]]. This has been updated to work with newer versions of python and Zaratan's architecture. Use on other HPC will likely need tweaking from the instructions below.
Tar file for all code: {{ :gmvae_tf1_v2.tgz |}}
The detailed instructions were added by Dr. Min-Kang Hsieh.
This instruction includes a complete workflow for unsupervised clustering of protein conformations using pairwise Cα (alpha-carbon) distance matrices (or BB atoms in CG modeling) as the input representation for a Gaussian Mixture Variational Autoencoder (GMVAE). The workflow covers dataset preparation, model hyperparameter optimization, systematic grid search over the number of Gaussian mixture components (K) and latent-space dimensions (z), and latent-space evaluation to identify the optimal (K, z) configuration for conformational clustering.
In addition to GMVAE training and evaluation, the package provides utilities for generating cluster-wise contact maps, representative conformations, and summary statistics for structural analysis and visualization.
The workflow can be executed on either GPU or CPU systems. The following hardware configurations are recommended:
* **Dataset preparation**: CPU
* **Single-model training (for Hyperparameter optimization)**: One NVIDIA V100 GPU (recommended) or ≥64 CPU cores for small datasets
* **Grid search**: One NVIDIA V100 GPU for training; ≥64 CPU cores for post-training evaluation (CPU-only grid search is suitable only for small datasets)
* **Model evaluation**: ≥64 CPU cores (typically performed after training)
* **Cluster visualization (contact map and structural interpretation)**: CPU
**Python Environment**
Note: The current GMVAE workflow requires two independent Python environments. Separating the environments avoids dependency conflicts between PyEMMA (used for trajectory processing) and TensorFlow 1.15.4 (used for GMVAE training). This is recommended because PyEMMA depends on several compiled C/C++/Fortran libraries (e.g., MDTraj, NumPy, and SciPy), which may conflict with the TensorFlow environment.
//**Environment 1**: Dataset Preparation (PyEMMA) and Cluster Contact Map//
This environment is used for molecular dynamics trajectory processing and dataset generation.
Option 1: Create from the provided environment file (recommended)
conda env create -p ~/scratch/pyemma_env -f pyemma.yml
Option 2: Install manually
conda create -p ~/scratch/pyemma_env -c conda-forge python=3.9 pyemma mdtraj
Activate the environment:
conda activate ~/scratch/pyemma_env
//**Environment 2**: GMVAE Train/Grid/Eval (TensorFlow 1.15.4)//
This environment is used for GMVAE training, hyperparameter optimization, grid search, and model evaluation.
Create the environment from the provided environment file:
conda env create -p ~/scratch/tf1.15.4 -f tf1.15.4.yml
conda activate ~/scratch/tf1.15.4
**Package Layout Tree**
gmvae_tf1_v2/
├─ pyemma.yml
├─ tf1.15.4.yml
├─ src/
│ ├─ gmvae_test/
│ │ ├─gmvae_pipeline_v2.py
│ │ ├─real_conv_GMVAE_graph_mse.py
│ │ ├─real_Conv_GMVAE_gumbel.py
│ │ ├─load_data.py
│ │ ├─logger.py
│ │ ├─base_graph.py
│ │ └─base_model.py
│ └─ utils/
│ ├─data_collection_v4.py
│ └─contact_heatmap_top_structures.py
└─ scripts/
├─run_datacoll.csh
├─run_datacoll_list.csh
├─run_train.csh
├─run_grid.csh
├─run_grid_manually.csh
├─run_grid_manually.scr
├─run_eval.csh
└─run_contact_heatmap_top_structures.csh
**Usage note: copy the scripts folder as your project name to begin.**
Note: If the servers where no graphical user interface (GUI) or display server is available, add matplotlib.use("Agg") before importing pyplot to force Matplotlib to use a non-GUI backend, allowing you to generate and save plots without opening a visual window.
import matplotlib
matplotlib.use("Agg")
import matplotlib.pyplot as plt
**Input data preparation**
Modify //run_datacoll.csh// or //run_datacoll_list.csh// to suit your input trajectory files. Detailed instructions for using this data collection script are provided below.
usage: data_collection_v4.py [-h] --pdb PDB
[--traj_files TRAJ_FILES [TRAJ_FILES ...]]
[--traj_dirs TRAJ_DIRS [TRAJ_DIRS ...]]
[--traj_prefix TRAJ_PREFIX]
[--traj_ext {dcd,trr,xtc}] [--start START]
[--end END] [--single_chain] [--dimer]
[--selected_atom SELECTED_ATOM]
[--indices1 INDICES1 INDICES1]
[--indices2 INDICES2 INDICES2] [--skip SKIP]
[--skip_first_frame SKIP_FIRST_FRAME]
[--output_prefix OUTPUT_PREFIX]
optional arguments:
-h, --help show this help message and exit
--pdb PDB Path to topology/structure file, usually .pdb or .gro.
--traj_files TRAJ_FILES [TRAJ_FILES ...]
Explicit list of trajectory files, e.g. traj1.trr
traj2.trr.
--traj_dirs TRAJ_DIRS [TRAJ_DIRS ...]
List of directories containing trajectory files.
--traj_prefix TRAJ_PREFIX
Prefix for trajectory files when using traj_dirs.
--traj_ext {dcd,trr,xtc}
Trajectory extension when using traj_dirs.
--start START Starting trajectory index.
--end END Ending trajectory index.
--single_chain Use the same atom indices for both chains.
--dimer Use separate atom indices for two chains.
--selected_atom SELECTED_ATOM
Selected atom name for analysis.
--indices1 INDICES1 INDICES1
Range for chain 1 MDTraj atom indices, e.g. 0 99.
Range for chain 2 MDTraj atom indices, e.g. 100 220.
--skip SKIP Frame skip interval.
--skip_first_frame SKIP_FIRST_FRAME
Number of initial frames to discard after loading all
trajectories.
--output_prefix OUTPUT_PREFIX
Prefix for output .npy files.
**GMVAE Clustering Workflow**
The GMVAE workflow consists of three major stages:
- Hyperparameter optimization (excluding K and z)
- Grid search over the number of clusters (K) and latent dimensions (z)
- Latent-space evaluation to identify the optimal (K, z) configuration
**Quick start**
Activate the TensorFlow environment before running the GMVAE pipeline.
conda activate ~/ scratch/tf1.15.4
The default training hyperparameters are:
--temp 0.05
--dropout 0.3
--lr 0.001
--epochs 300
--batch-size 100
--dense-n 64
--filters 64 64 32
--kernel-sizes 3 3 3
--pool-sizes 2 2 1
--num-layers 3
The gmvae_pipeline_v2.py script provides a unified interface for GMVAE training, hyperparameter grid search, and evaluation of GMVAE for data clustering. The prepared scripts have been included.
The program supports three operating modes:
* **train** – Train a single GMVAE model. (run_train.csh)
* **grid** – Perform a grid search over multiple values of K and z. (run_grid.csh or run_grid_manually.scr)
* **eval** – Evaluate a trained model and generate clustering results. (run_eval.csh)
**Training Mode (train)**
Train a single GMVAE model using a specified set of hyperparameters.
**Example: Single Training**
python gmvae_pipeline_v2.py --mode train \
--pdb /home/mhsieh/scratch/bst2/orf7a-cov-2_bst2_short/aa/c2_r1_cg2aa/openmm/ca_dcd/ca.pdb \
--dataset-npy orf7a_bst2_short_data.npy \
--rmsd-npy orf7a_bst2_short_rmsd.npy \
--mode_chain dimer \
--indices1 0 99 \
--indices2 100 220 \
--K 6 --z-dim 8 \
--epochs 100 --batch-size 500 \
--output-dir outputs
**Example: Training with Automatic Evaluation**
python gmvae_pipeline_v2.py --mode train \
--pdb /home/mhsieh/scratch/bst2/orf7a-cov-2_bst2_short/aa/c2_r1_cg2aa/openmm/ca_dcd/ca.pdb \
--dataset-npy orf7a_bst2_short_data.npy \
--rmsd-npy orf7a_bst2_short_rmsd.npy \
--mode_chain dimer \
--indices1 0 99 \
--indices2 100 220 \
--K 6 --z-dim 4 \
--epochs 100 --batch-size 500 \
--output-dir outputs \
--evaluate_after_train
**Grid Search Mode (grid)**
Once a suitable set of training hyperparameters has been determined (excluding K and z), perform a systematic grid search to identify the optimal latent-space dimension and number of clusters.
**Example**
python gmvae_pipeline_v2.py --mode grid \
--pdb /home/mhsieh/scratch/bst2/orf7a-cov-2_bst2_short/aa/c2_r1_cg2aa/openmm/ca_dcd/ca.pdb \
--dataset-npy orf7a_bst2_short_data.npy \
--rmsd-npy orf7a_bst2_short_rmsd.npy \
--mode_chain dimer \
--indices1 0 99 \
--indices2 100 220 \
--grid-ks 3 4 5 6 7 8 \
--grid-zs 5 6 7 \
--epochs 100 --batch-size 500 \
--output-dir grid_outputs
**Evaluation Mode (eval)**
Evaluation is performed after model training and is primarily CPU-based. The evaluation step generates latent-space statistics and clustering summaries for model selection.
**Example**
python gmvae_pipeline_V2.py --mode eval \
--pdb /home/mhsieh/scratch/bst2/orf7a-cov-2_bst2_short/aa/c2_r1_cg2aa/openmm/ca_dcd/ca.pdb \
--dataset-npy orf7a_bst2_short_data.npy \
--rmsd-npy orf7a_bst2_short_rmsd.npy \
--mode_chain dimer \
--indices1 0 99 \
--indices2 100 220 \
--K 6 --z-dim 8 \
--batch-size 500 \
--model-dir ./outputs/K6_z8 \
--num-cpus 64 > ./outputs/K6_z8/eval.log
**Output Directory Structure**
Training results are saved in the directory specified by --output-dir. The output directory contains model checkpoints, training logs, evaluation results, and summary statistics.
**Output Files**
**Training Outputs**
The following files/folders are generated during training:
* **checkpoint/** Saved GMVAE model checkpoints.
* **summary/**: Summary statistics and evaluation results (generated after evaluation).
* **train_dic.pickle**: Training loss history recorded for each epoch.
* **valid_dic.pickle**: Validation loss history recorded for each epoch.
* **train.png**: Training loss versus epoch.
* **validation.png**: Validation loss versus epoch.
**Latent Space Visualization**
To visualize the learned latent representation, the pipeline generates two-dimensional t-SNE embeddings.
* **learned_labels.png**: Two-dimensional t-SNE projection of the latent space, colored by GMVAE cluster assignments.
* **learned_rmsd.png**: Two-dimensional t-SNE projection of the latent space, colored by RMSD values.
* **var2d_zsel.npy**: Two-dimensional t-SNE coordinates used to generate the visualization.
**Clustering Results**
* **y_tot.npy**: Predicted cluster assignment for each input conformation.
* **Z_tot.npy**: Learned latent-space representation for each conformation.
**Evaluation Summary**
After running the evaluation step (--mode eval), additional summary files are generated in .//summary/
including:
* **latent_mean_corr_matrix.csv** Correlation matrix of the latent variables.
* **latent_mean_corr_matrix.png** Heatmap visualization of the latent-variable correlation matrix.
* **latent_mean_pca_explained.png** Principal component explained variance of the latent space.
**GMVAE Operation details**
Detailed instructions for using this gmvae script are provided below.
usage: gmvae_pipeline_v2.py [-h] --mode {train,grid,eval} --pdb PDB
--dataset-npy DATASET_NPY --rmsd-npy RMSD_NPY
[--mode_chain {single_chain,dimer}]
[--indices1 INDICES1 INDICES1]
[--indices2 INDICES2 INDICES2]
[--batch-size BATCH_SIZE] [--lr LR]
[--epochs EPOCHS] [--num-layers NUM_LAYERS]
[--z-dim Z_DIM] [--temp TEMP] [--K K]
[--restore RESTORE] [--dense-n DENSE_N]
[--filters FILTERS [FILTERS ...]]
[--kernel-sizes KERNEL_SIZES [KERNEL_SIZES ...]]
[--pool-sizes POOL_SIZES [POOL_SIZES ...]]
[--valid-ratio VALID_RATIO] [--dropout DROPOUT]
[--r-nent R_NENT] [--r-label R_LABEL]
[--output-dir OUTPUT_DIR]
[--grid-ks [GRID_KS [GRID_KS ...]]]
[--grid-zs [GRID_ZS [GRID_ZS ...]]]
[--evaluate-after-train] [--num-cpus NUM_CPUS]
[--model-dir MODEL_DIR]
GMVAE training & grid testing pipeline
optional arguments:
-h, --help show this help message and exit
--mode {train,grid,eval}
Mode to run: train | grid | eval
--pdb PDB Path to pdb file
--dataset-npy DATASET_NPY
Path to dataset .npy file
--rmsd-npy RMSD_NPY Path to RMSD .npy file
--mode_chain {single_chain,dimer}
Single chain or dimer analysis (affects indices_range2
selection)
--indices1 INDICES1 INDICES1
Range for chain 1 indices, e.g., 0 99.
--indices2 INDICES2 INDICES2
Range for chain 2 indices, e.g., 100 220.
--batch-size BATCH_SIZE
--lr LR
--epochs EPOCHS
--num-layers NUM_LAYERS
--z-dim Z_DIM
--temp TEMP
--K K
--restore RESTORE
--dense-n DENSE_N
--filters FILTERS [FILTERS ...]
--kernel-sizes KERNEL_SIZES [KERNEL_SIZES ...]
--pool-sizes POOL_SIZES [POOL_SIZES ...]
--valid-ratio VALID_RATIO
--dropout DROPOUT
--r-nent R_NENT
--r-label R_LABEL
--output-dir OUTPUT_DIR
Base output directory
--grid-ks [GRID_KS [GRID_KS ...]]
List of K values for grid
--grid-zs [GRID_ZS [GRID_ZS ...]]
List of z-dim values for grid
--evaluate-after-train
Run evaluation after each training run (CPU)
--num-cpus NUM_CPUS Number of CPU cores to pass to evaluation
--model-dir MODEL_DIR
Model output dir to evaluate (used in eval mode)
**1. Hyperparameter Optimization (excluding K and z)**
Optimize the network architecture and training parameters before performing the grid search.
**Recommended Network Architecture**
As a general guideline:
* 2 convolutional layers are recommended for small single-chain proteins (e.g., Trp-cage, BBA, and proteins with fewer than approximately 50 residues).
* 3 convolutional layers are recommended for larger proteins or protein dimers.
**1.1. Published Hyperparameter Sets**
Systems # of # of Latent # of Batch Kernel Learning # of Pooling
layers neurons dim. clusters size Temp. size rate filters sizes Ref
Trp-cage 2 64 5 8 5000 0.1 [3,3] 0.001 [64,64] [1,1] J. Chem. Phys. (2021) 155, 194108 doi: 10.1063/5.0069708
BBA 2 64 6 9 5000 0.1 [3,3] 0.001 [64,64] [2,2] J. Chem. Phys. (2021) 155, 194108 doi: 10.1063/5.0069708
villin 3 64 5 6 2500 0.05 [3,3,3] 0.001 [64,64,32] [2,2,1] J. Chem. Phys. (2021) 155, 194108 doi: 10.1063/5.0069708
BST-2/ORF7a 3 64 5 9 2500 0.05 [3,3,3] 0.001 [64,64,32] [2,2,1] BBA Biomembranes (2023) 1865(6), 184174. doi: 10.1016/j.bbamem.2023.184174
BST-2/ORF7a 3 64 5 13 2500 0.05 [3,3,3] 0.001 [64,64,32] [2,2,1] BBA Biomembranes (2023) 1865(6), 184174. doi: 10.1016/j.bbamem.2023.184174
ORF7b dimer 3 64 6 10 2500 0.05 [3,3,3] 0.001 [64,64,32] [2,2,1] J. Phys. Chem. B (2024) 128(1), 150-162. doi: 10.1021/acs.jpcb.3c07105
ORF7b dimer 3 64 6 8 2500 0.05 [3,3,3] 0.001 [64,64,32] [2,2,1] J. Phys. Chem. B (2024) 128(1), 150-162. doi: 10.1021/acs.jpcb.3c07105
BST-2/ORF7a 3 64 4 11 1000 0.05 [3,3,3] 0.001 [64,64,32] [2,2,1] J. Phys. Chem. B (2026) 130(5), 1553–1567. doi: 10.1021/acs.jpcb.5c07529
**1.2. Batch Size Recommendations**
GPU memory limits the maximum batch size during training. For single-channel, three-layer GMVAE models trained on an NVIDIA V100 GPU (32 GB), the recommended batch sizes are summarized below.:
chain A chain A matrix batch size
25 25 [25x25] 5000
50 50 [50x50] 2500
100 100 [100x100] 1000
150 150 [150x150] 200
**1.3. Dataset Size Considerations**
The current implementation processes only complete batches during training and evaluation. If the total number of samples is not divisible by the batch size, the remaining samples in the final incomplete batch are ignored.
To maximize data utilization, select a batch size that minimizes the number of discarded samples.
# of start end data batch # of data
input data frame frame included size batch leftovers
15000 0 14999 15000 1000 15 0
5739 0 5699 5700 100 57 39
5739 0 5631 5632 128 44 107
5739 0 5695 5696 64 89 43
**My suggestion is to adjust the number of input data points to an appropriate batch size to ensure 0 leftover.**
**Note: The cluster label (in neither y tot.npy nor z tot.npy) would not be assigned to the leftovers. If the entire dataset is not used, please specify --start and --end in eval mode. **
**1.4. Recommended Optimization Strategy**
Optimize the hyperparameters in the following order:
- Batch size
- Number of convolutional layers
- Remaining network hyperparameters
- Number of clusters (K)
Based on our experience, z ≥ 4 generally provides sufficient latent-space capacity, with z = 6 serving as a good starting point for many protein systems. An initial K value between 6 and 13 is recommended, consistent with previously published GMVAE studies.
After selecting an initial configuration, perform several single-model training runs to refine the hyperparameters before proceeding to the grid search.
**2. Grid Search**
After optimizing the training hyperparameters (excluding K and z), perform a systematic grid search over candidate values of K and z. Compare the resulting models using reconstruction loss, clustering confidence, latent-space independence, and structural interpretability to identify the optimal (K, z) configuration.
**3. Evaluate the Latent Space and Select an Optimal (K, z)**
After completing the grid search, evaluate each model using multiple complementary metrics. The goal is to identify the lowest-complexity model that accurately represents the conformational landscape while producing confident, interpretable, and non-redundant clusters.
Optimal Model Selection Criteria
**3.1 An optimal GMVAE model should satisfy the following criteria:**
* Low reconstruction loss: Accurately reconstructs the input distance matrices while preserving conformational variability.
* Low cluster assignment entropy: Produces confident, well-separated Gaussian mixture assignments.
* Low latent multicollinearity (VIF): Latent variables are approximately independent and encode complementary structural information.
* Meaningful PCA contributions: Each latent dimension contributes measurable variance, with minimal redundancy.
* Balanced cluster populations: Avoids excessive empty or very small clusters while capturing dominant conformational states.
* Structural interpretability: Clusters correspond to physically meaningful and biologically relevant conformations.
**3.2 Practical Recommendations**
* Choose the smallest latent dimension (z) after reconstruction loss and cluster entropy have converged.
* Select the number of clusters (K) that balances structural diversity with sufficient samples per cluster.
* Verify that latent variables have low VIF and weak inter-latent correlations.
* Use PCA to confirm that each latent dimension contributes unique information.
* Inspect representative structures from each cluster to ensure biological interpretability.
* Prefer the smallest (K, z) configuration that meets all evaluation criteria, balancing reconstruction quality, clustering confidence, latent-space independence, cluster population, and structural interpretability. [the smallest (K, z) configuration]
**Cluster Visualization and Structural Interpretation**
After selecting an optimal (K, z) configuration, representative conformations from each cluster can be extracted for structural analysis and visualization. The contact_heatmap_top_structures.py script generates cluster-wise contact maps and identifies representative structures based on their cluster assignment probabilities.
usage: contact_heatmap_top_structures.py [-h] --mode {dataset,trajectory}
--mode_chain {single_chain,dimer}
[--A_dataset A_DATASET]
[--B_dataset B_DATASET]
[--AB_dataset AB_DATASET]
[--A_size A_SIZE] [--B_size B_SIZE]
[--pdb PDB]
[--traj_files TRAJ_FILES [TRAJ_FILES ...]]
[--traj_dirs TRAJ_DIRS [TRAJ_DIRS ...]]
[--traj_prefix TRAJ_PREFIX]
[--traj_ext {dcd,trr,xtc}]
[--start START] [--end END]
[--skip SKIP]
[--skip_first_frame SKIP_FIRST_FRAME]
[--skip_after_frame SKIP_AFTER_FRAME]
[--selected_atom SELECTED_ATOM]
[--A_indices A_INDICES A_INDICES]
[--B_indices B_INDICES B_INDICES]
--cluster_folder CLUSTER_FOLDER
[--threshold THRESHOLD]
[--cutoff CUTOFF]
[--output_dir OUTPUT_DIR]
[--save_generated_dataset]
[--generate_top_structures]
[--top_n TOP_N]
[--mean_iterations MEAN_ITERATIONS]
[--representative_output_dir REPRESENTATIVE_OUTPUT_DIR]
The script performs the following tasks:
* Reads one or more molecular dynamics trajectories; it has to follow exactly the data_collection setting.
* Loads GMVAE clustering results (y_tot.npy) from the specified cluster_folder.
* Assigns each trajectory frame to its corresponding GMVAE cluster.
* Generates residue-residue contact probability heatmaps for each cluster.
* Identifies the top representative conformations (highest cluster assignment probability) from each cluster.
* Writes representative structures to individual trajectory files for downstream visualization and analysis.
**Example script**
#!/bin/bash
#Conda
source ~/.bashrc
conda init --all
#conda activate /scratch/zt1/project/energybio/user/dvan1/plexinA1/gmcave_tf1_update_copy/gmcave
conda activate /your/pyemma_env/
#Directories
dir_pdb="/scratch/zt1/project/energybio/user/mhsieh/bst2/orf7a-cov-2_bst2_short/aa/c2_r1_cg2aa/openmm/ca_dcd/ca.pdb"
dir1="/scratch/zt1/project/energybio/user/mhsieh/bst2/orf7a-cov-2_bst2_short/aa/c2_r1_cg2aa/openmm/ca_dcd/"
dir2="/scratch/zt1/project/energybio/user/mhsieh/bst2/orf7a-cov-2_bst2_short/aa/c2_r2_cg2aa/openmm/ca_dcd/"
dir3="/scratch/zt1/project/energybio/user/mhsieh/bst2/orf7a-cov-2_bst2_short/aa/c2_r3_cg2aa/openmm/ca_dcd/"
dir4="/scratch/zt1/project/energybio/user/mhsieh/bst2/orf7a-cov-2_bst2_short/aa/c4_r1_cg2aa/openmm/ca_dcd/"
dir5="/scratch/zt1/project/energybio/user/mhsieh/bst2/orf7a-cov-2_bst2_short/aa/c4_r2_cg2aa/openmm/ca_dcd/"
dir6="/scratch/zt1/project/energybio/user/mhsieh/bst2/orf7a-cov-2_bst2_short/aa/c4_r3_cg2aa/openmm/ca_dcd/"
out_prefix="orf7a_bst2_short"
#Files
file_traj1="ca_dyn301.dcd"
file_traj2="ca_dyn302.dcd"
file_traj3="ca_dyn303.dcd"
file_traj4="ca_dyn304.dcd"
file_traj5="ca_dyn305.dcd"
#Commands
python3 ../src/utils/data_collection_v4.py \
--pdb ${dir_pdb} \
--dimer --selected_atom CA --indices1 0 99 --indices2 100 220 --output_prefix ${out_prefix} \
--traj_files ${dir1}${file_traj1} ${dir1}${file_traj2} ${dir1}${file_traj3} ${dir1}${file_traj4} ${dir1}${file_traj5} \
${dir2}${file_traj1} ${dir2}${file_traj2} ${dir2}${file_traj3} ${dir2}${file_traj4} ${dir2}${file_traj5} \
${dir3}${file_traj1} ${dir3}${file_traj2} ${dir3}${file_traj3} ${dir3}${file_traj4} ${dir3}${file_traj5} \
${dir4}${file_traj1} ${dir4}${file_traj2} ${dir4}${file_traj3} ${dir4}${file_traj4} ${dir4}${file_traj5} \
${dir5}${file_traj1} ${dir5}${file_traj2} ${dir5}${file_traj3} ${dir5}${file_traj4} ${dir5}${file_traj5} \
${dir6}${file_traj1} ${dir6}${file_traj2} ${dir6}${file_traj3} ${dir6}${file_traj4} ${dir6}${file_traj5}