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Description of Software

System requirements for users of the software package:


1. On the personal computer must be installed version MATLAB R2016b (not lower).

2. On the personal computer must be installed 64-bit version of Windows 7(not lower).

The software will be available after registration on the site.


User interface description for modelling of the scanning amino acid residues excluding three-dimensional structure.

Algorithm 1.

We present algorithm which determining the detection of proteins active regions and detecting the stability of different regions of protein complexes (linear docking) by analysing the potential energy matrix of pairwise electrostatic interaction between different sites of the biological complex, such as the homodimer of the histone chaperone Nap1-Nap1, which are responsible for the entry of a whole protein molecule into biochemical reactions. Below in the attached file is a description of the user interface for scanning amino acid residues excluding three-dimensional structure. This algorithm has been developed to search for protein sites responsible for protein interactions. During the development of this algorithm we have made the following assumptions:we know the short amino acid sequence of one protein, which takes an active part in binding to another protein, with formation large numbers nearly located interacting amino acid residues, for example, the formation of homodimers Mdm2-Mdm2 and Nap1-Nap1, we do not know the active site of the whole protein responsible for binding to the short polypeptide sequence. Thus, using algorithm 1, we find the active site on the polypeptide sequence of the whole protein. In order to choose a more stable biochemical compound between proteins, we select the matrix of the potential energy of electrostatic interaction with the smallest value of the condition number.

Algorithm 2.

We developed a second algorithm for detecting interacting regions of protein molecules. After finding all the participating pairs of one-dimensional arrays, we build a matrix of potential energy electrostatic interactions. These matrices will have a square form. Further, for all matrices we calculate the values lg(cond(W))(the logarithm of the condition number of the matrix, elements of which are potential energies electrostatic interaction between pairwise taken amino acid residues of proteins) and construct a graph of the dependence of lg(cond(W)) on the order number of the amino acid residue of the participating one-dimensional arrays. The sequence number will be the same for the two considered one-dimensional arrays. In this case, the amino acid residues corresponding to the ordinal number can be different, if the interactions of different proteins are investigated. In order to choose a more stable biochemical compound between proteins, we select the matrix of the potential energy of electrostatic interaction with the smallest value of the condition number.

Algorithm 3.

Algorithm 3 is designed to determine the stability of the dimeric complex, be it formed by various variations of the domains of the protein sequence without taking into account the three-dimensional structure. We divide the entire amino acid sequence of the protein conditionally into domains with a length of 20 a.a. up to 70 a.a. at the discretion of the researcher, depending on the tasks and initial assumptions about the availability of domains. Then we check in pairs the interactions of various combinations of such domains. Each domain we pre-cut from a common polypeptide chain. After finding all the participating pairs of vectors, we build a matrix of potential energy electrostatic interaction between their amino acid residues. Further, from each of these matrices we calculate the value lg(cond(W)). In order to choose a more stable biochemical compound between proteins, we select the matrix of the potential energy of electrostatic interaction with the smallest value of the condition number.

Below in the attached file is a description of the user interface for modelling scanning amino acid residues excluding structure (algorithm 1, algorithm 2 and algorithm 3).

User interface description for modelling of the effect of phosphorylation.

To account for the phosphorylation effect, we made the following assumptions:the selected amino acid residues of serine20 and threonine 18 of the P53 protein were replaced by negatively charged phosphoric acid residues, which we represented in the form of spheres with a radius equal to 0.3 nm;

residues of phosphoric acid interact with five charged amino acids (aspartic acid, glutamic acid, arginine, histidine, lysine) with a charge of 0.09а C;

residues of phosphoric acid interact with selected hydrophobic amino acids (methionine, asparagine, leucine, tyrosine, valine) with a charge of 0.01а C;

the distance between the centers of the phosphoric acid residue and the amino acid residue is 1.76 nm.

To analyze the biochemical processes we use the notion of condition number matrix of the potential energy of the pair electrostatic interaction between peptides. In this physical formulation of the problem, it will characterize the degree of stability of the configuration of the biological complex. In order to choose a more stable biochemical compound between proteins, we select the matrix of potential energy of electrostatic interaction with the smallest value of the condition number.

Below in the attached file is a description of the user interface for modelling of the effect of phosphorylation.

Results of a numerical calculation of the formation of biological complexes by different sites of the p53, Mdm2 and p300 proteins, taking into account the effect of phosphorylation of the flexible N-terminus of the p53 protein are described.

User interface description for modelling scanning amino acid residues including three-dimensional structure (static algorithm and algorithm rotation).

Static algorithm.

An algorithm and software package was developed for analyzing protein interactions, taking into account their three-dimensional structure from the PDB database. It consisted of the fact that the protein Bcl-2-BH3-Bax (the
name of the file in the PDB-«2XA0.pdb») was taken from
[Protein data bank. https://www.rcsb.org] and was split into two files: Bcl-2.pdb and BH3-Bax.pdb. Moreover, for each protein (Bcl-2.pdb and BH3-Bax.pdb) we saved the file with its atomic coordinates. Next, a line vector was formed consisting of the coordinates of the center of mass for  each i-th amino acid protein residue (Bcl-2.pdb). Similarly, a vector line was formed consisting of the coordinates of the center of mass  for each j-th  amino acid residue protein(BH3-Bax.pdb) and the corresponding distance was found between the centres of mass of the i-th and j-th amino acid residue of proteins (Bcl-2.pdb and BH3-Bax.pdb). Note that earlier experiments  [Fenley A.T., Adams D.A., Onufriev A.V. Charge state of the globular histone core controls the stability of the nucleosome. Biophys.//Biophys. J. 2010. V.99. V.5. Pp. 1577-1585] revealed that the interaction of protein molecules is determined by the potential energy of the electrostatic interaction. For this reason, this study is devoted to a theoretical analysis of the electrostatic interactions between protein molecules. Thus, we have calculated the potential energy of the electrostatic interaction between  pairwise amino acid residues of the proteins examined. The values obtained were recorded in the matrix. For analysis of the biochemical processes, we use the concept of the condition number For the calculation of the condition number we have used Kogbetliantz’s algorithm.  In this physical formulation of the problem, the degree of stability in the configuration of the biological complex will be characterized. In order to choose a more stable biochemical  compound between proteins, we select the matrix of the potential energy of electrostatic  interaction with the  smallest value of the condition number.

Algorithm rotation.

This algorithm, taking into account the rotation of one amino acid residue allows you to find the stability of protein-protein complexes, peptide-peptide complex, peptide-protein complex with a known amino acid sequence and with the known three-dimensional
structure from x-ray analysis. Rotation algorithm suggests rotation of the center of mass of one amino acid residue in some a small specified range indicating the initial radius of the sphere and the final radius of the sphere, which is achieved with a certain step. In order to choose a more stable biochemical compound between proteins, we select the matrix of the potential energy of electrostatic interaction with the smallest value of the condition number.

Below in the attached file is a description of the user interface for modelling scanning amino acid residues including three- dimensional structure (static algorithm and algorithm rotation).

Results of a numerical calculation of a map of protein interactions are given, the location of key amino acid residues in peptides are described, and the procedure for finding the range of Kd values for point mutations in the polypeptide chain of a peptide, when it is bound to a protein, are described.

User interface description for calculation of differential entropy change.

The entropy of is measure absence of pattern of molecular system. In this case, absence of pattern states correspond to a large value of entropy, and the ordered states correspond to low entropy value. Thus, if the process goes in the direction of increasing absence of pattern of the system, then the quantity ΔH >0 (ΔH is differential entropy change) ), indicates that the degree orderliness decreases relative to the wild-type peptide, if ΔH <0, then in this case the degree of ordering increases relative to the wild-type peptide.

Below in the attached file is a description of the user interface for modelling of entropy change multidimensional case.

Results of a numerical calculation of the change in entropy by the formula for multidimensional differential entropy in the interaction of two amyloid wild-type peptides from 11th amino acid residue to 42th amino acid residue are described.

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