Dmitriy E. Balandin

In this paper, we develop a non-Hermitian coupling method for integrating heterogeneous datasets. Using the completeness of the root-vector system of the operator associated with the coupled graph Laplacian, we construct a generalization of a bi-orthogonal basis. Decomposing the trace functional into regular and nilpotent parts, we elaborate an analogue of the gradient ascent and descent method for the extremal trace problem. The central point of the concept is that the extremal values coincide with the trace values and their difference yields an intrinsic characteristic of dataset heterogeneity. The results are illustrated by single-cell multi-omics integration, where the indicators distinguish stable systems from stratified populations.

Chronological age can be estimated from molecular profiles; however, predictive accuracy alone does not establish a biologically validated ageing clock. We therefore evaluated whether plasma protein intensities measured by data-independent acquisition mass spectrometry (DIA-MS) support chronological-age estimation in a cross-sectional cohort from Moscow, Russia, while explicitly examining acquisition-order and MS-batch confounding. Plasma samples from 350 adult participants aged 19.8 to 99.1 years were analyzed as single-shot, single-injection DIA-MS acquisitions on a Q Exactive HFX platform. The final matrix comprised 222 protein groups and was generated with DIA-NN version 1.8.1 using a two-pass predicted-library-assisted workflow, cross-run precursor-level normalization, normalized MaxLFQ-like protein–group quantification, and 1% precursor and protein–group false-discovery-rate thresholds. Descriptive associations were assessed using Spearman rank correlation with Bonferroni correction. Feature selection and missing-value imputation were confined to each training subset. Generalization was assessed primarily by holding out complete MS batches, with repeated, nested, and random five-fold analyses retained as internal comparators. Of the 222 proteins, 148 were associated with chronological age at the nominal threshold p < 0.05, and 98 remained significant after Bonferroni correction. The strongest descriptive associations involved fibrinogen beta chain (FGB; rs = 0.590), SERPINA3 (rs = 0.560), ITIH4 (rs = 0.542), complement C5 (rs = 0.538), and ceruloplasmin (rs = 0.518). In internal random-split analyses, a 50-feature Gradient Boosting strategy yielded MAE = 8.90 ± 1.06 years in repeated five-fold cross-validation and MAE = 9.10 ± 1.10 years in nested cross-validation. However, when complete MS batches were held out, aggregate MAE increased to 10.56 years (R² = 0.554) using a batch-stratified assignment and 11.87 years (R² = 0.461) using GroupKFold. These batch-held-out results constitute the primary estimate of generalization from the present dataset. To assess the trade-off between error and assay complexity, strategies using 5, 8, 10, 12, 15, 20, 30, and 50 proteins selected within each training fold were compared. The 8-feature strategy yielded MAE = 11.83 years in repeated random cross-validation, whereas the 50-feature strategy yielded MAE = 8.90 years. These estimates concern feature-number strategies, not fixed panels. The post hoc eight-protein list is reported only as an exploratory candidate set for future independent validation. Acquisition order was associated with chronological age (rs = 0.336, p = 1.03 × 10⁻¹⁰), and age and sex distributions differed strongly across 27 MS batches. Order alone predicted age with MAE = 3.98 years in a negative-control model, demonstrating that age information was encoded in the acquisition design. Accordingly, the present findings support only a proof-of-concept for plasma-proteomic prediction of chronological age within this dataset; they do not establish a batch-independent model, a clinical tool, or a biologically validated ageing clock.

This review is devoted to diagonal integration of multi-omics data, an approach enabling to combine data from different molecular modalities obtained in independent studies without pairwise measurements. Twenty-two diagonal integration methods classified by mathematical basis are analyzed. A comparative analysis of international and Russian platforms is presented. A concept of a biocentric approach based on coupled Laplacians and kernel methods in reproducing Hilbert space is substantiated.

In this paper, we consider the extremal trace problem for the coupled Laplacian on the sets homeomorphic to the Stiefel manifold defined on the complex Euclidean space. The study is implemented via various mathematical methods, including topological and probabilistic approaches. A detailed, comprehensive classification of the stationary points is given, which itself deserves to be considered as a general method in the framework of the optimization theory. Finally, an application to biologically meaningful integration of heterogeneous datasets, in which the structure of molecular interactions serves as a significant constraint for the mathematical model, is proposed. The main advantage of the elaborated method in comparison with the previously used ones is the absence of any conditions on the structure of the initial heterogeneous datasets. This paper is a continuation of a series of papers by our research group devoted to the development of new mathematical methods for integrating multi-omics data.

Background/Objectives : Understanding metabolic adaptations in long-livers provides critical insights into the biochemical mechanisms underlying extreme longevity. While many long-livers maintain metabolic stability, others exhibit significant metabolic alterations, potentially linked to age-related diseases. This study aims to identify distinct metabolic signatures in long-livers and their associations with clinical outcomes, particularly cardiovascular disease. Methods: We analyzed serum samples from 53 oldest long-livers (mean age 98.2 ± 2 years) using liquid chromatography–tandem mass spectrometry (LC-MS/MS) to identify metabolic alterations and gathered clinical data to link the detected metabolic changes with phenotypes. Results: Using Welch’s t-test with Benjamini–Hochberg FDR correction (q < 0.01, |log2FC| > 2), we identified 15 significantly altered metabolites distinguishing a subgroup of 6 long-livers from 47 metabolically stable individuals. This metabolically altered subgroup exhibited striking elevations in key metabolites, including L-serine (log2FC = 8.05, >250-fold increase, q = 1.26 × 10⁻⁸), D-galactose (log2FC = 6.86, 116-fold, q = 8.87 × 10⁻⁷), butyric acid (log2FC = 6.24, 75-fold, q = 9.79 × 10⁻⁵), and choline (log2FC = 6.11, ~69-fold, q = 5.45 × 10⁻⁷), with enrichment in the butyric acid metabolism pathway. Post hoc power analysis confirmed >80% power for all significant metabolites with very large effect sizes (Cohen’s d > 2.0). Conclusions: Our findings reveal substantial metabolic heterogeneity among long-livers, with a distinct subgroup exhibiting profound metabolic alterations and clinical features associated with cardiovascular and systemic disease. These results highlight that the butyric acid pathway may contribute to age-related disease survival in extreme aging.

In the paper, we present a comparison analysis of the methods of the topological alignment and extract the main mathematical principles forming the base of the concept. The main narrative is devoted to the so-called coupled methods dealing with the data sets of various natures. As a main theoretical result, we obtain harmonious generalizations of the graph Laplacian and kernel-based methods with the central idea to find a natural structure coupling data sets of various natures. Finally, we discuss prospective applications and consider far-reaching generalizations related to the hypercomplex numbers.

Background: The search for reliable aging biomarkers using proteomic databases and large-scale proteomic studies presents a significant challenge in biogerontology. Existing proteomic databases and studies contain valuable information; however, there is inconsistency in approaches to biomarker selection and data integration. This creates barriers to translating existing knowledge into clinical practice and use in biomedical research. This work analyzed experimental proteomic studies, the content of proteomic databases, and proposed recommendations for optimization and improvement of proteomic database formation and enrichment. Methods: The study utilized publications devoted to proteomic data acquisition methods, proteomic databases, and experimental studies. Results: Methods for obtaining proteomic data were analyzed (Protein Pathway Array (PPA), Tissue Microarray (TMA), Luminex (Bead Array), MSD (Meso Scale Discovery), Simoa (Quanterix), SOMAscan (SomaLogic), Olink (PEA), Alamar NULISA (PEA+), and Oxford Nanopore. A total of 16 proteomic databases were investigated (HAGR, KEGG, STRING, Aging Atlas, HALL, Human Protein Atlas, UniProt, AgeAnnoMO, AgeFactDB, AgingBank, iProX, jMorp, jPOSTrepo, MassIVE, MetaboAge DB, PRIDE Archive). Additionally, 22 proteomic studies devoted to aging and age-associated diseases were analyzed. Conclusions: Proteomic databases and experimental studies individually contain valuable information about aging biomarkers. Using data from different sources within biomedical research poses challenges for improving and optimizing methodological solutions for publication selection, database formation, and marker development.

Ferroptosis is a regulated cell death process characterized by iron ion catalysis and reactive oxygen species, leading to lipid peroxidation. This mechanism plays a crucial role in age-related diseases, including cancer and cardiovascular and neurological disorders. To better mimic iron-induced cell death, predict the effects of various elements, and identify drugs capable of regulating ferroptosis, it is essential to develop precise models of this process. Such drugs can be tested on cellular models. Systems biology offers a powerful approach to studying biological processes through modeling, which involves accumulating and analyzing comprehensive research data. Once a model is created, it allows for examining the system’s response to various stimuli. Our goal is to develop a modular framework for ferroptosis, enabling the prediction and screening of compounds with geroprotective and antiferroptotic effects. For modeling and analysis, we utilized BioUML (Biological Universal Modeling Language), which supports key standards in systems biology, modular and visual modeling, rapid simulation, parameter estimation, and a variety of numerical methods. This combination fulfills the requirements for modeling complex biological systems. The integrated modular model was validated on diverse datasets, including original experimental data. This framework encompasses essential molecular genetic processes such as the Fenton reaction, iron metabolism, lipid synthesis, and the antioxidant system. We identified structural relationships between molecular agents within each module and compared them to our proposed system for regulating the initiation and progression of ferroptosis. Our research highlights that no current models comprehensively cover all regulatory mechanisms of ferroptosis. By integrating data on ferroptosis modules into an integrated modular model, we can enhance our understanding of its mechanisms and assist in the discovery of new treatment targets for age-related diseases. A computational model of ferroptosis was developed based on a modular modeling approach and included 73 differential equations and 93 species.

The investigation into cellular and replicative aging is crucial for both biology and medicine, particularly in light of the increasing percentage of the older population. Gaining a deeper understanding of the mechanisms of these forms of aging can help develop strategies aimed at prolonging active longevity. By comparing the processes of cellular and replicative aging, researchers can reveal both common and distinct molecular mechanisms, thus opening innovative approaches for diagnosing and treating age-related diseases. The identified aging markers can contribute to personalized medicine, improving the diagnosis and treatment of aging cells. Thus, these studies enhance developing methods for combating age-related diseases.AIM. The study aims to analyze cellular and replicative aging in order to identify common mechanisms underlying the aging process. The goal is to understand the relationship between these processes and their influence on age-related changes. Specific objectives include identifying aspects of aging and identifying molecular markers that can be used for the diagnosis and monitoring of age-related disorders. The findings from this study will contribute to the prevention and management of age-related conditions, thereby improving overall population health.MATERIALS AND METHODS. The public datasets E-MTAB-4879 (cellular senescence) and GSE130727 (replicative senescence) were analysed. Quality control was carried out using the FastQC program. Adapter removal was performed by sequencing using the cutadapt 2.3 and Trimmomatic-0.38 programs. Mapping was done using the bowtie2-2.4.0 program. Re-verification of the mapping results was performed using the kallisto-v0.45.0 pseudo-alignment algorithm. Quantification was done using featureCounts. RPKM (Read Per Kilobase per Million) normalization was applied (to the average total reads, coverage depth, and gene length). The mirnet.ca online service was used to search for regulatory miRNAs.RESULTS. For groups of genes that showed decreased (7,275) and increased (5,059) expression levels in the E-MTAB-4879 and GSE130727 datasets after filtering, we identified the biological processes they are involved in. For lists of the top 15 genes, we provided information on their role in the aging process. Additionally, for a group of commonly expressed genes, functional groups were determined using GO. The study compared two aging-related gene datasets and identified a total of 7,275 genes with decreased expression. Of these, 1,342 showed significant decreases in expression, with processes related to G-protein signaling, cholesterol metabolism, and cytokine signaling standing out. Some genes affect aging through inflammatory responses, membrane potential control, neurodegeneration, and cell differentiation. Further analyses identified 143 non-coding RNAs associated with aging and cancer. In a separate group, 1,673 genes exhibited increased expression, involving processes such as glycerolipid biosynthesis and actin filament regulation, as well as wound healing. Among these, 194 non-coding RNAs were linked to oncogenesis and osteogenesis.CONCLUSION. In conclusion, our study has identified key differences and similarities between cellular and replicative aging. This has allowed us to gain a deeper understanding of these aging processes and their roles in age-related changes. The analysis revealed that common molecular mechanisms such as decreased gene expression related to G-protein signaling and cholesterol metabolism significantly influence both forms of aging. Additionally, unique features have been identified, including differences in gene and non-coding RNA expression, which opens up possibilities for the development of personalized diagnostic and treatment strategies. These identified markers and mechanisms have the potential to contribute not only to diagnosis but also to monitoring of age-related changes and improving approaches to age-associated disease treatment. Therefore, our research significantly contributes to the development of techniques to combat age-associated illnesses by emphasizing the significance of investigating both the common and distinctive features of cellular and replicative aging processes.

The investigation into cellular and replicative senescence is crucial for both biology and medicine, particularly in light of the increasing percentage of the elderly population. Gaining a deeper understanding of the mechanisms of these forms of aging can help develop strategies aimed at prolonging active longevity. By comparing the processes of cellular and replicative senescence, researchers can reveal both common and distinct molecular mechanisms, thus opening up innovative approaches to diagnosing and treating age-related diseases. The identified aging markers can contribute to personalized medicine and improving the diagnosis and treatment of aging cells. Thus, these studies greatly facilitate the development of methods for combating age-related diseases. The study aims to analyze cellular and replicative senescence in order to identify common mechanisms underlying the aging process. The goal is to understand the relationship between these processes and their influence on age-related changes. The specific objectives of this work include identifying aspects of aging and molecular markers that can be used for the diagnosis and monitoring of age-related disorders. The findings from this study will contribute to the prevention and treatment of age-related conditions, thereby improving overall population health. The public datasets E-MTAB-4879 (cellular senescence) and GSE130727 (replicative senescence) are analyzed. Quality control is carried out using the FastQC program. Adapter removal is performed by sequencing using the cutadapt 2.3 and Trimmomatic-0.38 programs. Mapping is carried out using the bowtie2-2.4.0 program. Reverification of the mapping results is performed using the kallisto-v0.45.0 pseudo-alignment algorithm. Quantification is carried out using featureCounts. RPKM (Read Per Kilobase per Million) normalization is applied (to average the total reads, coverage depth, and gene length). The mirnet.ca online service is used to search for regulatory miRNAs. For groups of genes that showed decreased (7275) and increased (5059) expression levels in the E-MTAB-4879 and GSE130727 datasets after filtering, we identify the biological processes they are involved in. For lists of the top 15 genes, we provide information on their role in the aging process. Additionally, for a group of commonly expressed genes, functional groups are determined using GO. The study compares two aging-related gene datasets and a total of 7275 genes with decreased expression are identified. Of these, 1342 show significant decreases in expression, with processes related to G-protein signaling, cholesterol metabolism, and cytokine signaling standing out. Some genes affect aging through inflammatory responses, membrane potential control, neurodegeneration, and cell differentiation. 143 noncoding RNAs associated with aging and cancer are identified upon further analysis. In a separate group, 1673 genes exhibit increased expression, involving processes such as glycerolipid biosynthesis and actin filament regulation, as well as wound healing. Among these, 194 noncoding RNAs are linked to oncogenesis and osteogenesis. In conclusion, our study has identified key differences and similarities between cellular and replicative senescence. This has allowed us to gain a deeper understanding of these aging processes and their roles in age-related changes. The analysis has revealed that common molecular mechanisms such as decreased gene expression related to G-protein signaling and cholesterol metabolism significantly influence both forms of senescence. Additionally, unique features have been identified, including differences in gene and noncoding RNA expression, which opens up possibilities for the development of personalized diagnostic and treatment strategies. These identified markers and mechanisms have the potential to contribute not only to diagnosis but also to the monitoring of age-related changes and improving approaches to age-associated disease treatment. Therefore, our research significantly contributes to the development of techniques to combat age-associated diseases by emphasizing the significance of investigating both the common and distinctive features of cellular and replicative senescence.