Experiment-based Structural Ensemble Construction of Linear Diubiquitin Using Multi-scale Simulation and Deep Generative Modeling
Yoshiki YUGAMI *1, Xue-Ni HOU3, Sotaro FUCHIGAMI2, Hidehito TOCHIO3, Kei MORITSUGU1
1Osaka Metropolitan University Graduate School of Science
2Graduate School of Pharmaceutical Sciences, Shizuoka University
3Graduate School of Science, Kyoto University
Polyubiquitin modification is involved in various functions including protein degradation, DNA repair, and signal transduction. Polyubiquitin chains can form diverse structures through the polymerization of ubiquitin via seven Lys residues and the N-terminal methionine (M1; linear). Understanding the structural ensemble of polyubiquitin chains is essential for revealing their linkage-specific molecular functions. In our previous work, pseudo contact shifts (PCS) using lanthanoids were applied to linear diubiquitin and was found to be reproduced by using a series of representative structures. This study aims to establish a method for deriving the structure ensemble and the associated free energy landscape of linear diubiquitin that is in good agreement with the PCS experiment by (1) all-atom molecular dynamics (MD) simulations, (2) coarse-grained MD simulation together with sidechain generation, and (3) deep generative modeling using a variational autoencoder (VAE).
In (1), the initial model of linear diubiquitin was taken from a crystal structure (PDB ID: 3b0a). Using eight replicas with varying interactions between two ubiquitins, structural sampling simulation was performed for 500 ns using gREST module of GENESIS. In (2), as a faster alternative to (1), coarse-grained MD simulation was carried out using CafeMol to generate an extensive structural ensemble by multiple basin model connecting extended (PDB ID: 2w9n) and compact (PDB ID: 3axc) structures. The obtained Cα-atom structures were converted to all-atom models using the library cg2all. In (3), VAE was adopted to generated diverse diubiquitin conformations. All available linear diubiquitin crystal structures were associated with elastic network model to increase the number of Cα-atom structures for training VAE.
In the three methods, the PCS and radius of gyration were calculated for each of the structural ensemble. A weight was assigned to each structure and optimized using the steepest descent method to match the experimental data, thus extracting the structure ensemble consistent with PCS and small-angle X-ray scattering data. Although the PCS using 400,000 structures obtained by gREST simulation did not explain the experimental data, the optimization of the weights drastically improved the agreement. The free energy landscape along the distance and the torsion angle of diubiquitin was also changed considerably, showing that combining experimental data can avoid the convergence problem of the structure sampling and can remove the artifacts from the MD force field. It was also demonstrated that combining coarse-grained MD simulation with reconstructing the all-atom model can also generate an accurate structure ensemble to match the experiment data with much less computational cost. Furthermore, the VAE approach efficiently generated experiment-consistent structural ensemble with lowest computational cost, which methodology will be applicable to other flexible proteins.