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Distributions of regions and hydrophobicity over proteins. Part A: Number of D regions, O regions, hydrophobic and hydrophilic AA Part B: Distributions of disorder regions over proteins. length ≥1, length ≥10, length ≥20, length ≥30, length ≥40, length ≥50, length ≥60, length ≥70, length ≥80, length ≥90 and length ≥100
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The paper describes a new method for the analysis of protein sequences - the method of analysis of the information structure (ANIS method). The method uses a new approach to describe amino acid sequences and identify hierarchically organized elements in the information structure of protein sequences. It was shown that the top-level information stru...
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Citations
... By allowing possible substitutions in the pentapeptide sequence when counting for its occurrence, we find variants with all possible mutations and increase its evolutionary depth. A special mathematical method could reveal a hierarchy in the pentapeptide frequency curve [7]. The entire ANIS method is described in detail below in the Materials and Methods section. ...
... This work continues the cycle of our works devoted to the analysis of protein sequences [6,7] based on the information estimates. Here we will consider the effect of the information unit size and the number of permissible substitutions on the quality of the information graph of the sequence. ...
... An analysis of the location of ADD+ and ADDsites in the spatial structure of proteins made it possible to propose a model for the functioning of hem-containing proteins [13]. In the heat shock protein sequence, ANIS method isolated a peptide that activates the production of normal killers (NK cells) [7]. These examples are discussed in more detail below. ...
Background:
Analyzing the local sequence content in proteins, earlier we found that amino acid residue frequencies differ on various distances between amino acid positions in the sequence, assuming the existence of structural units.
Methods:
We used informational entropy of protein sequences to find that the structural unit of proteins is a block of adjacent amino acid residues-"information unit". The ANIS (ANalysis of Informational Structure) method uses these information units for revealing hierarchically organized Elements of the Information Structure (ELIS) in amino acid sequences.
Results:
The developed mathematical apparatus gives stable results on the structural unit description even with a significant variation in the parameters. The optimal length of the information unit is five, and the number of allowed substitutions is one. Examples of the application of the method for the design of protein molecules, intermolecular interactions analysis, and the study of the mechanisms of functioning of protein molecular machines are given.
Conclusions:
ANIS method makes it possible not only to analyze native proteins but also to design artificial polypeptide chains with a given spatial organization and, possibly, function.
... Analyzing the evolutionary and entropy properties of protein sequences, we have developed a method for revealing the hierarchical structure in the protein sequence Nekrasov et al. 2014). Correlations between the hierarchical elements were studied. ...
As one of the twelve Councilors of the International Union of Pure and Applied Biophysics elected in summer 2021, I have been asked to provide this short biographical sketch for the journal readers. I am a new member of the IUPAB Council. I hold a specialist degree in Applied Physics and Mathematics from the Moscow Institute of Physics and Technology and PhD in Biophysics from Moscow State University. I have spent my entire professional career at Engelhardt Institute of Molecular Biology of the Russian Academy of Sciences in Moscow, where I am currently a senior researcher. I am Associate Professor at the Digital Health Institute of the I.M. Sechenov First Moscow State Medical University since 2018, and have trained undergraduate students in structural biology, biophysics, and bioinformatics. In addition, I serve as the Guest Editor of special journal issues of International Journal of Molecular Sciences and Frontiers in Genetics BMC genomics. Now I joined Biophysical Reviews Editorial Board as IUPAB Councilor. I am a Secretary of National Committee of Russian Biophysicists, and have helped to organize scientific conferences and workshops, such as the VI Congress of Russian Biophysicists.
... Obviously, such concepts do not correspond to the observed structural and functional properties of proteins as seen with the large number of approaches to predicting coding zones in genomes by Hidden Markov Model approaches [15]. To resolve this contradiction, we proposed a new paradigm [16][17][18]. We have shown [16] that a low level of Shannon informational entropy [19] is observed in a range of two to eight amino acid-fragment; the lowest level is observed for pentapeptides. ...
... We have shown [16] that a low level of Shannon informational entropy [19] is observed in a range of two to eight amino acid-fragment; the lowest level is observed for pentapeptides. Taking a fragment of five amino acid residues as a unit of protein sequence, we proposed the ANIS (ANalysis of Informational Structure) method for identifying hierarchically organized structures in protein sequences [17,18]. This method identifies tree-like hierarchical structures (graphs) in a protein sequence. ...
... over sequences J of length five with Hamming distance from A not larger than δ = 1. In our papers [17,18], Hamming distance δ equal to one was also used, i.e., we summarized over fragments which differ from the initial fragment at no more than one amino acid residue. We will put in correspondence to a protein sequence (as a sequence I = i 1 . . . ...
Most non-communicable diseases are associated with dysfunction of proteins or protein complexes. The relationship between sequence and structure has been analyzed for a long time, and the analysis of the sequences organization in domains and motifs remains an actual research area. Here, we propose a mathematical method for revealing the hierarchical organization of protein sequences. The method is based on the pentapeptide as a unit of protein sequences. Employing the frequency of occurrence of pentapeptides in sequences of natural proteins and a special mathematical approach, this method revealed a hierarchical structure in the protein sequence. The method was applied to 24,647 non-homologous protein sequences with sizes ranging from 50 to 400 residues from the NRDB90 database. Statistical analysis of the branching points of the graphs revealed 11 characteristic values of y (the width of the inscribed function), showing the relationship of these multiple fragments of the sequences. Several examples illustrate how fragments of the protein spatial structure correspond to the elements of the hierarchical structure of the protein sequence. This methodology provides a promising basis for a mathematically-based classification of the elements of the spatial organization of proteins. Elements of the hierarchical structure of different levels of the hierarchy can be used to solve biotechnological and medical problems.
... Obviously, such concepts do not correspond to the observed structural and functional properties of proteins as seen with the large number of approaches to predicting coding zones in genomes by Hidden Markov Model approaches [22]. To resolve this contradiction, a new paradigm was proposed by us in [23][24][25], which was confirmed in a number of experimental researches [26][27][28]. We showed [23] that the lowest level of Shannon entropy [29] is observed inside blocks of five amino acid residues in protein sequences. ...
Most non-infectious diseases are associated with dysfunction of proteins or protein complexes. Аssociation between sequence and structure is analyzed since a long time, and analysis of sequence organization in domains and motifs is actual research area. A mathematical method is proposed here to identify the hierarchical organization of protein sequences. The method is based on pentapeptide as a unit of protein sequences. This method was applied on a non-homologous dataset of protein sequences. The analysis revealed 11 hierarchical levels of protein sequence organization, showing the relationship of these multiple fragments of sequences. Using different examples, we illustrated how the fragments of the spatial structure of protein correspond to the elements of the hierarchical structure of the protein sequence. A hierarchical structure is observed in the protein sequence. This methodology is an interesting basis for mathematically based classification of elements of spatial organization of proteins. Elements of the hierarchical structure of different levels of the hierarchy can be used for biotechnological and medical problems.
... The hierarchical structure of proteins was discussed in [86,87,84]. This approach generalizes the construction of protein conformations as sequences of conformations of short fragments, see [70], by consideration of different levels of hierarchy in models of fragments. ...
The principal objective of this article is a brief overview of the main parts of p-adic mathematics, which have already had valuable applications and may have a significant impact in the near future on the further development of some fields of theoretical and mathematical biology. In particular, we present the basics of ultrametrics, p-adic numbers and p-adic analysis, as well as insight into their applications for modeling some cognitive processes, genetic code and protein dynamics. We also argue that ultrametric concepts and p-adic mathematics are natural tools for the viable description of biological systems and phenomena with a hierarchical structure.
... In this paper, in the framework of our approach [6,23], we proposed a method for searching for conformationally stable pentapeptides for protein folding. For each protein sequence, it is possible to determine conformationally stable sites of the sequence and to predict their spatial structure. ...
The aim of this work was to find a minimal set of structurally stable pentapeptides, which allows forming a polypeptide chain of a required 3D structure. To search for factors that ensure structural stability of the pentapeptide, we generated peptide sequences with no more than three functional groups, based on the alanine pentapeptide AAAAA. We analyzed 44,860 structures of peptides by the molecular dynamics method and found that 1,225 pentapeptides over 80% of the simulation time were in a stable conformation. Clustering of these conformations revealed 54 topological types of conformationally stable pentapeptides. These conformations relate to different combined elements of the protein secondary structure. So, we obtained a minimal set of amino acid structures of conformationally stable pentapeptides, creating a complete set of different topologies that ensure the formation of pre-folded conformation of protein structures.
... In this paper, in the framework of our approach [6,23], we proposed a method for searching for conformationally stable pentapeptides for protein folding. For each protein sequence, it is possible to determine conformationally stable sites of the sequence and to predict their spatial structure. ...
... Peptides from clusters 1, 22, 31, 44, 46 and 50 can link a-helix with [Yb-structure. Peptides from clusters 10,16,20,23,39,42 and 47 forming the link from the [Yb -structure to the a-helix. ...
... In this paper, in the framework of our approach [6,23], we proposed a method for searching for conformationally stable pentapeptides for protein folding. For each protein sequence, it is possible to determine conformationally stable sites of the sequence and to predict their spatial structure. ...
The aim of this work was to find a minimal set of structurally stable pentapeptides, which allows forming a polypeptide chain of a required 3D structure. To search for factors that ensure structural stability of the pentapeptide, we generated peptide sequences with no more than three functional groups, based on the alanine pentapeptide AAAAA. We analyzed 44,860 structures of peptides by the molecular dynamics method and found that 1,225 pentapeptides over 80% of the simulation time were in a stable conformation. Clustering of these conformations revealed 54 topological types of conformationally stable pentapeptides. These conformations relate to different combined elements of the protein secondary structure. So, we obtained a minimal set of amino acid structures of conformationally stable pentapeptides, creating a complete set of different topologies that ensure the formation of pre-folded conformation of protein structures. © 2019 Elsevier B.V. and Société Française de Biochimie et Biologie Moléculaire (SFBBM)
... The informational structure of cytochrome c was calculated according to the algorithm described in details in Ref. [21]. The problems of structural and functional ELIS-first ranking role were discussed in Ref. [20]. ...
We investigate functional role of the P⁷⁶GTKMIFA⁸³ fragment of the primary structure of cytochrome c. Based on the data obtained by the analysis of informational structure (ANIS), we propose a model of functioning of cytochrome c. According to this model, conformational rearrangements of the P⁷⁶GTKMIFA⁸³ loop fragment have a significant effect on conformational mobility of the heme. It is suggested that the conformational mobility of cytochrome c heme is responsible for its optimal orientation with respect to electron donor and acceptor within ubiquinol–cytochrome c oxidoreductase (complex III) and cytochrome c oxidase (complex IV), respectively, thus, ensuring electron transfer from complex III to complex IV. To validate the model, we design several mutant variants of horse cytochrome c with multiple substitutions of amino acid residues in the P⁷⁶GTKMIFA⁸³ sequence that reduce its ability to undergo conformational rearrangements. With this, we study the succinate–cytochrome c reductase and cytochrome c oxidase activities of rat liver mitoplasts in the presence of mutant variants of cytochrome c. The electron transport activity of the mutant variants decreases to different extent. Resonance Raman spectroscopy (RRS) and surface-enhanced Raman spectroscopy (SERS) data demonstrate, that all mutant cytochromes possess heme with the higher degree of ruffling deformation, than that of the wild-type (WT) cytochrome c. The increase in the ruffled deformation of the heme of oxidized cytochromes correlated with the decrease in the electron transport rate of ubiquinol–cytochrome c reductase (complex III). Besides, all mutant cytochromes have lower mobility of the pyrrol rings and methine bridges, than WT cytochrome c. We show that a decrease in electron transport activity in the mutant variants correlates with conformational changes and reduced mobility of heme porphyrin. This points to a significant role of the P⁷⁶GTKMIFA⁸³ fragment in the electron transport function of cytochrome c.
... In [215,216] an approach for description of hierarchical structure of proteins was proposed. It was shown that the domain structure of proteins is one of the levels of the described hierarchy. ...
p$-Adic mathematical physics is a branch of modern mathematical physics based on the application of $p$-adic mathematical methods in modeling physical and related phenomena. It emerged in 1987 as a result of efforts to find a non-Archimedean approach to the spacetime and string dynamics at the Planck scale, but then was extended to many other areas including biology. This paper contains a brief review of main achievements in some selected topics of $p$-adic mathematical physics and its applications, especially in the last decade. Attention is mainly paid to developments with promising future prospects.
