## Section: New Results

### Coarse-Grained Protein Scoring Based on Geometrical Features

Participants : Mikhail Karasikov, Sergei Grudinin.

We learnt a scoring function to score protein structures with application to highly important problems in structural biology, namely, protein design, side-chain prediction, and selection of mutations increasing protein stability. For each native structure ${P}_{0}$ a set of ordered decoy structures $\mathcal{D}$ is given:

The problem is to train protein scoring function

such that

We proposed a residue-based scoring function, which uses not the positions of protein's atoms separately, but configurations of the entire residues. The proposed method requires artificially generated decoy structures for the training process and provides high quality scoring functions, which are efficient to compute. Several types of scoring functions are considered according to restrictions imposed by the specific application. For the prediction problems where the whole domain should be searched for the best prediction, we use functions that allow the reduction of emerging optimization problem

$\sum _{k=1}^{m}\sum _{l=1}^{m}{E}_{kl}({a}_{k},{a}_{l})\to \underset{({a}_{1},\cdots ,{a}_{m})\in {\mathcal{A}}^{m}}{min}$ | (1) |

to quadratic binary constrained optimization

$\begin{array}{cccc}& \underset{\overrightarrow{x}\in {\{0,1\}}^{n}}{\text{minimize}}\hfill & & {\overrightarrow{x}}^{\U0001d5b3}\mathbf{Q}\overrightarrow{x}\hfill \\ & \text{subject}\phantom{\rule{4.pt}{0ex}}\text{to}\hfill & & \mathbf{A}\overrightarrow{x}={\overrightarrow{1}}_{m}.\hfill \end{array}$ | (2) |