Prediction of Protein pKa with Representation Learning

The behavior of proteins is closely related to the protonation states of the residues. Therefore, prediction and measurement of pKa are essential to understand the basic functions of proteins. In this work, we develop a new empirical scheme for protein pKa prediction that is based on deep representation learning. It combines machine learning with atomic environment vector (AEV) and learned quantum mechanical representation from ANI-2x neural network potential (J. Chem. Theory Comput. 2020, 16, 4192). The scheme requires only the coordinate information of a protein as the input and separately estimates the pKa for all five titratable amino acid types. The accuracy of the approach was analyzed with both cross-validation and an external test set of proteins. Obtained results were compared with the widely used empirical approach PROPKA. The new empirical model provides accuracy with MAEs below 0.5 for all amino acid types. It surpasses the accuracy of PROPKA and performs significantly better than the null model. Our model is also sensitive to the local conformational changes and molecular interactions.

Improved chemistry restraints for crystallographic refinement by integrating the Amber force field into Phenix

The refinement of biomolecular crystallographic models relies on geometric restraints to help to address the paucity of experimental data typical in these experiments. Limitations in these restraints can degrade the quality of the resulting atomic models. Here, an integration of the full all-atom Amber molecular-dynamics force field into Phenix crystallographic refinement is presented, which enables more complete modeling of biomolecular chemistry. The advantages of the force field include a carefully derived set of torsion-angle potentials, an extensive and flexible set of atom types, Lennard–Jones treatment of nonbonded interactions and a full treatment of crystalline electrostatics. The new combined method was tested against conventional geometry restraints for over 22 000 protein structures. Structures refined with the new method show substantially improved model quality. On average, Ramachandran and rotamer scores are somewhat better, clashscores and MolProbity scores are significantly improved, and the modeling of electrostatics leads to structures that exhibit more, and more correct, hydrogen bonds than those refined using traditional geometry restraints. In general it is found that model improvements are greatest at lower resolutions, prompting plans to add the Amber target function to real-space refinement for use in electron cryo-microscopy. This work opens the door to the future development of more advanced applications such as Amber-based ensemble refinement, quantum-mechanical representation of active sites and improved geometric restraints for simulated annealing.

Improved chemistry restraints for crystallographic refinement by integrating the Amber force field into Phenix

The refinement of biomolecular crystallographic models relies on geometric restraints to help address the paucity of experimental data typical in these experiments. Limitations in these restraints can degrade the quality of the resulting atomic models. Here we present an integration of the full all-atom Amber molecular dynamics force field into Phenix crystallographic refinement, which enables a more complete modeling of biomolecular chemistry. The advantages of the force field include a carefully derived set of torsion angle potentials, an extensive and flexible set of atom types, Lennard-Jones treatment of non-bonded interactions and a full treatment of crystalline electrostatics. The new combined method was tested against conventional geometry restraints for over twenty-two thousand protein structures. Structures refined with the new method show substantially improved model quality. On average, Ramachandran and rotamer scores are somewhat better; clash scores and MolProbity scores are significantly improved; and the modelling of electrostatics leads to structures that exhibit more, and more correct, hydrogen bonds than those refined with traditional geometry restraints. We find in general that model improvements are greatest at lower resolutions, prompting plans to add the Amber target function to real-space refinement for use in electron cryo-microscopy. This work opens the door to the future development of more advanced applications such as Amber-based ensemble refinement, quantum mechanical representation of active sites and improved geometric restraints for simulated annealing.IMPORTANTthis document contains embedded data - to preserve data integrity, please ensure where possible that the IUCr Word tools (available from http://journals.iucr.org/services/docxtemplate/) are installed when editing this document.SynopsisThe full Amber force field has been integrated into Phenix as an alternative refinement target. With a slight loss in speed, it achieves improved stereochemistry, fewer steric clashes and better hydrogen bonds.

Excitation Spectrum of the Néel Ensemble of Antiferromagnetic Nanoparticles as Revealed in Mössbauer Spectroscopy

The excitation spectrum of the Néel ensemble of antiferromagnetic nanoparticles with uncompensated magnetic moment is deduced in the two-sublattice approximation following the exact solution of equations of motion for magnetizations of sublattices. This excitation spectrum represents four excitation branches corresponding to the normal modes of self-consistent regular precession of magnetizations of sublattices and the continuous spectrum of nutations of magnetizations accompanying these normal modes. Nontrivial shape of the excitation spectrum as a function of the value of uncompensated magnetic moment corresponds completely to the quantum-mechanical calculations earlier performed. This approach allows one to describe also Mössbauer absorption spectra of slowly relaxing antiferromagnetic and ferrimagnetic nanoparticles and, in particular, to give a phenomenological interpretation of macroscopic quantum effects observed earlier in experimental absorption spectra and described within the quantum-mechanical representation.

THE APPLICATION AND CHARACTERISTICS OF THE COHERENT ENTANGLED STATE |β, x〉

The coherent entangled state |β, x〉 is proposed in Fock space, which exhibits both the properties of the coherent and entangled states. The |β, x〉 makes up a new quantum mechanical representation, and the completeness relation of |β, x〉 is proved by virtue of the technique of integral within an ordered product of operators. The corresponding Schmidt decomposition of |β, x〉 is investigated. Furthermore, a feasible experimental scheme of |β, x〉 is presented, and generalized P-representation is constructed in the coherent entangled state |β, x〉.

NEW REPRESENTATION FOR DESCRIBING LOWERING AND ASCENDING OF AN ELECTRON'S ANGULAR MOMENTUM IN A UNIFORM MAGNETIC FIELD

We construct a new quantum mechanical representation |l,r> for describing an electron's angular momentum in a uniform magnetic field, where l is the eigenvalue of the azimuthal angular momentum Lz and r is the orbit radius of the electron's motion. The ascending and lowering operators for |l,r>→|l± 1,r> are also obtained. Throughout our discussion the <λ| representation is fully employed (see Hong-Yi Fan and Yong Ren, Mod. Phys. Lett.B10, 523 (1996).