I. Yu. Torshin

The study of the solvability of the genome annotation problem on sets of elementary motifs

The problem of genome annotation (i.e., the establishment of the biological roles of proteins and corresponding genes) is one of the major tasks of postgenomic bioinformatics. This paper reports the development of the previously proposed formalism for the study of the local solvability of the genome annotation problem. Here, we introduce the concepts of elementary motifs, positional independence of motifs, heuristic evaluation of informativeness, and solvability on the sets of elementary motifs. We show that introduction of a linear order in a set of elementary motifs allows us to calculate the irreducible motif sets. The formalism was used in experiments to compute the sets of the most informative motifs for several protein functions.

On solvability, regularity, and locality of the problem of genome annotation

Determination of the nucleotide sequences of hundreds of organisms (in the first place, the human genome) is a significant technical achievement of modern biology. The next stage of studying the genome is to determine the functions of each gene and the corresponding protein: the so-called genome annotation. The existing methods of classifying the biological roles of proteins on the basis of the amino acid sequence are restricted to searching for similar sequences in a database and, as a result, have limited applicability. In this paper, a formalism is introduced for studying this problem in the framework of the algebraic approach and the solvability, locality, and regularity of the problem and monotonicity of the condition of solvability are considered. The proposed formalism enables one to study systematically the hypothesis of locality of various biological roles of proteins.

On the application of the combinatorial theory of solvability to the analysis of chemographs: Part 2. Local completeness of invariants of chemographs in view of the combinatorial theory of solvability

This paper presents a novel formalism for the application of the combinatorial theory of solvability to graph-theoretical problems in chemoinformatics. In the second part, it is shown that the binary relations of membership of χ-chains and χ-nodes in chemographs are invariants and the criteria for the completeness of these invariants are obtained. In the framework of the combinatorial theory of solvability, χ-graphs are treated as objects and their invariants (sets of invariants), as feature descriptions. We obtain criteria of the local completeness for the considered sets of invariants with respect to a given set of precedents. It is shown that combinatorial testing of the criteria for the local regularity of the corresponding problem of recognition allows one to make a quantitative assessment of the local completeness of the invariants under study. The formalism developed for the analysis of the local completeness of the invariants of chemographs provides considerable opportunities for substantiated generation and testing of various metrics on the sets of chemographs. Finally, the results of the practical application of the proposed formalism to one of the problems of chemoinformatics, i.e., finding structurally similar chemical compounds, are presented.

On the application of the combinatorial theory of solvability to the analysis of chemographs. Part 1: Fundamentals of modern chemical bonding theory and the concept of the chemograph

The combinatorial theory of solvability, which stems from the algebraic approach to recognition problems, is a modern tool for studying feature descriptions of objects. In this paper, we formulate the basics of a formalism for applying methods of combinatorial theory of solvability to applications of graph theory in chemoinformatics. In the first part of the paper it is shown that, in light of the fundamental physicochemical features of the molecular structure, in order to describe the chemical structure of molecules it is appropriate to introduce a special concept of a χ-graph (chemograph): a special kind of a labeled graph. The fundamental properties of chemographs are considered, and special types of labeling of χ-subgraphs are introduced: χ-chains (chains of labeled vertices) and χ-nodes (subgraphs of the neighborhoods of labeled vertices). An axiomatic is suggested for introducing chemograph labeling functions on the basis of the fundamental postulates of chemical bonding theory. The basics of a theoretical apparatus for representing chemographs as labeling sets are presented.

On metric spaces arising during formalization of recognition and classification problems. Part 1: Properties of compactness

In the context of the algebraic approach to recognition of Yu.I. Zhuravlev’s scientific school, metric analysis of feature descriptions is necessary to obtain adequate formulations for poorly formalized recognition/classification problems. Formalization of recognition problems is a cross-disciplinary issue between supervised machine learning and unsupervised machine learning. This work presents the results of the analysis of compact metric spaces arising during the formalization of recognition problems. Necessary and sufficient conditions of compactness of metric spaces over lattices of the sets of feature descriptions are analyzed, and approaches to the completion of the discrete metric spaces (completion by lattice expansion or completion by variation of estimate) are formulated. It is shown that the analysis of compactness of metric spaces may lead to some heuristic cluster criteria commonly used in cluster analysis. During the analysis of the properties of compactness, a key concept of a ρ-network arises as a subset of points that allows one to estimate an arbitrary distance in an arbitrary metric configuration. The analysis of compactness properties and the conceptual apparatus introduced (ρ-networks, their quality functionals, the metric range condition, i- and ρ-spectra, ε-neighborhood in a metric cone, ε-isomorphism of complete weighted graphs, etc.) allow one to apply the methods of functional analysis, probability theory, metric geometry, and graph theory to the analysis of poorly formalized problems of recognition and classification.

On metric spaces arising during formalization of problems of recognition and classification. Part 2: Density properties

In order to obtain tractable formal descriptions of poorly formalized problems within the context of the algebraic approach to pattern recognition, we develop methods for analyzing metric configurations. In this paper, using the concepts of σ-isomorphism and σ-completion of metric configurations, a system of criteria for assessing the properties of “generalized density” is obtained. The analysis of the density properties along the axes of a metric configuration allowed us to formulate methods for calculating the topological neighborhoods of points and for finding the “grains” of metric condensations. The theoretical results point to a new plethora of algorithms for searching metric condensations − methods based on the “restoration” of the set (the condensation searched) using the data on the components of the projection of the set on the axes of the metric configuration. The only mandatory parameters of any algorithm of this family of algorithms are the metric itself and the distribution of σ, which characterizes the accuracy of the values of the metric.

On the theoretical basis of metric analysis of poorly formalized problems of recognition and classification

In many fields of modern science, there are problems adequate formalization of which is indispensable for obtaining practically and theoretically important results. In the terminology of the scientific school of academician Yu.I. Zhuravlev, a formalized problem is uniquely defined by the matrix of information and the information matrix. In the present paper, a whole class of issues related to the formalization of recognition/classification problems is considered, and a universal formalism is proposed for carrying out a metric analysis of poorly formalized problems. Thus, the formalization of a problem can be represented as a successive transition from the set of original descriptions to a particular topology, then to a lattice, and then to a certain metric space. It is shown that the property of Zhuravlev’s regularity is sufficient for the existence of bijective mappings between these mathematical constructs. The possibilities of application of the apparatus developed are illustrated by several issues important for the formalization of the problems: introduction of metrics on the sets of the features and metrics on the sets of objects and analysis of “interactions” between dissimilar feature descriptions.

Optimal dictionaries of the final information on the basis of the solvability criterion and their applications in bioinformatics

Within the algebraic approach to the pattern recognition, the sets of the input (initial) and the output (final) information are defined on the basis of some additional expert information from the relevant subject area. Finding, in a sense, “optimal” definitions for the sets of the output information is crucial, for instance, for solving problems in bioinformatics. In this paper, we propose a formalism to establish optimal dictionaries for output information on the basis of the solvability criterion for the relevant problem. The formalism developed is applied to the problem of recognition of the secondary structure of proteins. The experiments have shown that the optimal dictionary to describe the secondary structure of proteins consists of four five-letter elements. The dictionary allows making a significant increase in the cross-validated recognition accuracy of the secondary structure.

Synergistic application of zinc and vitamin C to support memory, attention and the reduction of the risk of the neurological diseases

Zinc and vitamin C supplementation of the body is important for CNS functioning. Zinc ions are involved in the neurotransmission (signal transmission from acetylcholine, catecholamine, serotonin, prostaglandin receptors) and in ubiquitin-related protein degradation. Zinc deficits are associated with Alzheimers disease and depression. Zinc supplementation (10-30 mg daily) improves neurologic recovery rate in patients with stroke and brain injury, has a positive impact on memory and reduces hyperactivity in children. Vitamin C, a zinc synergist, maintains antioxidant resources of the brain, synaptic activity and detoxification. Vitamin C in dose 130-500 mg daily should be used to prevent dementia and neurodegenerative pathology.

The Adaptogenic and Neuroprotective Properties of Lithium Ascorbate

Objectives. To study the neuroprotective properties of lithium ascorbate (LA) in in vivo and in vitro stress models. Materials and methods. Neurocytological and behavioral studies were run in models of stress in nerve cell cultures and experimental animals. Results. LA was shown to have a marked neuroprotective effect in conditions of glutamate-induced cytotoxicity in vitro and an adaptogenic effect on induction of stress in vivo. Conclusions. The results obtained here demonstrated that LA has high neuroprotective potential in stress induced in vivo and in vitro.