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Section: New Results
Molecular Modeling
The CARBON method
Participants : Sergei Grudinin, Stephane Redon, Petr Popov.
In molecular docking, various refinement algorithms are implied either to take into account flexibility of molecular complexes or to get rid of the docking artefacts, e.g. steric clashes. To address the latter problem, one possibility is to continuously minimize the energy of the complex with respect to the affine transformations, i.e. rigid transformations. Petr Popov developed a fast and efficient method called CARBON, where one considers the rigid-body optimization problem as the calculation of quasi-static trajectories of rigid bodies influenced by the inverse-inertia-weighted energy gradient. In order to determine the appropriate step-size in the direction of the net generalized force, we introduce the concept of advancement region, which is the interval of step-sizes that provide movements of the rigid body within a certain range of root mean square deviation from the initial conformation. We tested and validated CARBON on several benchmarks using both a classical force-field and a knowledge-based scoring function and demonstrated that CARBON significantly improves the quality of docking pre- dictions an also remains stable when monomers of a molecular complex significantly overlap. CARBON will be made available as a SAMSON Element for the SAMSON software platform at http://www.samson-connect.net .
The KSENIA method
Participants : Petr Popov, Sergei Grudinin.
Molecular docking as an integral part of the drug discovery involves the scoring stage, where one selects the best binding candidates from the set of ligand poses. The scoring stage incorporates sophisticated scoring functions based on the empirical force-fields or the information derived from known structures of protein complexes. The latter type of scoring functions belongs to the family of the knowledge-based or statistical scoring functions. Typically, for the training of a knowledge-based scoring function, modern methods require an ensemble of generated non-native decoy structures and a computation of the reference state, which is challenging. Petr Popov developed a method that does not require neither the computation of the reference state nor the ensemble of non-native complexes. Furthermore, the developed approach fully relies on the structures of protein complexes in their native configurations. More precisely, Petr trained the knowledge-based scoring function based on sets of near-native conformations. These are composed using the fluctuations along the direction of low-frequency normal modes computed at the native configurations. The obtained scoring function is capable to distinguish the native and near-native protein-protein interactions from the non-native ones. The robustness of the method was verified on several protein-protein docking benchmarks. Our methodology can be easily adapted to the recognition of other types of molecular interactions, such as protein-ligand, protein-RNA, etc. KSENIA will be made publicly available as a part of the SAMSON software platform at http://www.samson-connect.net .
Optimization solvers
Participants : Petr Popov, Anatoli Juditsky, Sergei Grudinin.
To derive a knowledge-based scoring function, we map non-native and near-native molecular complexes to the vectors of descriptors in a high- dimensional space. In this space, we formulate an optimization problem to construct the scoring function in such a way, that the projection of a descriptor vector onto the scoring vector corresponds to the score of a molecular complex. The formulated problem contains the regularization term and the penalty term and might vary depending on the method applied to solve the optimization problem. Different methods provide different convergence rates and cost per operation. We implemented several modern first- and second- order optimization techniques and explored which one works the best on the given data. Namely, we tested the standard gradient descent method, the conjugate gradients method, the Nesterov method, the Fista and Fista-descent methods, and the proximal gradient method.
Novel Docking Criterion
Participants : Petr Popov, Sergei Grudinin.
Generally, to assess the prediction capabilities of a scoring function for protein- protein interactions, one evaluates the success rate of the scoring function on widely used protein-protein benchmarks. The percentage of correctly predicted complexes is taken as the characteristic of the scoring function. However, all existing benchmarks nowadays consists on many non-native and only few near- native conformations. However, the ability of the scoring function to distinguish a particular near-native conformation from the non-native decoys does not guarantee that the scoring function is able to distinguish another near-native conformation. The same is applied if the scoring function fails on a particular molecular complex. Thus, the success rate is not a robust criterion, since it depends on the near-native and non-native conformations presented in the benchmark. We proposed the new robust method to evaluate the predictive capability of a scoring function, which does not suffer from such drawback. The method uses the probability density function of the score computed from the set of the near-native conformations and complementary empirical distribution function of the score computed from the set on non-native conformations. We tested the criterion on the previously derived scoring functions and showed that the criterion also provides an insight on some limits and restrictions of the atom-atom distant- dependent knowledge-based scoring functions.