Protein structure prediction using the evolutionary algorithm USPEX.

Protein structure prediction is one of major problems of modern biophysics: current attempts to predict the tertiary protein structure from amino acid sequence are successful mostly when the use of big data and machine learning allows one to reduce the "prediction problem" to the "problem of recognition". Compared with recent successes of deep learning, classical predictive methods lag behind in their accuracy for the prediction of stable conformations. Therefore, in this work we extended the evolutionary algorithm USPEX to predict protein structure based on global optimization starting with the amino acid sequence. Moreover, we compared frequently used force fields for the task of protein structure prediction. Protein structure relaxation and energy calculations were performed using Tinker (with several different force fields) and Rosetta (with REF2015 force field) codes. To create new protein structure models in the USPEX algorithm, we developed novel variation operators. The test of the new method on seven proteins having (for simplicity) no cis-proline (with ω ≈ 0°) residues, and a length of up to 100 residues, revealed that our algorithm predicts tertiary structures of proteins with high accuracy. The comparison of the final potential energies of the predicted protein structures obtained using the USPEX and the Rosetta Abinitio approach showed that in most cases the developed algorithm found structures with close or even lower energy (Amber/Charmm/Oplsaal) and scoring function (REF2015). While USPEX has clearly demonstrated its ability to find very deep energy minima, our study showed that the existing force fields are not sufficiently accurate for accurate blind prediction of protein structures without further experimental verification.

The dual role of fragments in fragment-assembly methods for de novo protein structure prediction.

In fragment-assembly techniques for protein structure prediction, models of protein structure are assembled from fragments of known protein structures. This process is typically guided by a knowledge-based energy function and uses a heuristic optimization method. The fragments play two important roles in this process: they define the set of structural parameters available, and they also assume the role of the main variation operators that are used by the optimiser. Previous analysis has typically focused on the first of these roles. In particular, the relationship between local amino acid sequence and local protein structure has been studied by a range of authors. The correlation between the two has been shown to vary with the window length considered, and the results of these analyses have informed directly the choice of fragment length in state-of-the-art prediction techniques. Here, we focus on the second role of fragments and aim to determine the effect of fragment length from an optimization perspective. We use theoretical analyses to reveal how the size and structure of the search space changes as a function of insertion length. Furthermore, empirical analyses are used to explore additional ways in which the size of the fragment insertion influences the search both in a simulation model and for the fragment-assembly technique, Rosetta.

Variation and oscillation for the multilinear singular integrals satisfying Hörmander type conditions.

Suppose that the kernel K satisfies a certain Hörmander type condition. Let b be a function satisfying [Formula: see text] for [Formula: see text], and let [Formula: see text] be a family of multilinear singular integral operators, i.e., [Formula: see text] The main purpose of this paper is to establish the weighted [Formula: see text]-boundedness of the variation operator and the oscillation operator for [Formula: see text].

Oscillation and variation inequalities for the multilinear singular integrals related to Lipschitz functions.

The main purpose of this paper is to establish the weighted [Formula: see text] inequalities of the oscillation and variation operators for the multilinear Calderón-Zygmund singular integral with a Lipschitz function.