Gennady Bocharov

• Researcher at Institute of Numerical Mathematics, Russian Academy of Sciences

In this work, we search for the conditions for the occurrence of long COVID using the recently developed COVID-19 disease dynamics model which is a system of delay differential equations. To do so, we search for stable stationary or periodic solutions of this model with low viral load that can be interpreted as long COVID using our recently develop...

This paper presents a novel approach to modeling the repertoire of the immune system and its adaptation in response to the evolutionary dynamics of pathogens associated with their genetic variability. It is based on application of a dynamic programming-based framework to model the antigen-driven immune repertoire synthesis. The processes of formati...

SARS-CoV-2 still presents a global threat to human health due to the continued emergence of new strains and waning immunity among vaccinated populations. Therefore, it is still relevant to investigate potential therapeutics, such as therapeutic interfering particles (TIPs). Mathematical and computational modeling are valuable tools to study viral i...

EFFECT OF HIGHLY-ACTIVE ANTIRETROVIRAL THERAPY ON NEUROENDOCRINE REGULATION OF IMMUNOGENESIS IN HIV-INFECTED CHILDREN Bakhmetyev B.A.a, Bocharov G.A.b, c, Zverev S.Ya.d, Kalashnikova N.S.d a Institute of Ecology and Genetic of Microorganisms, Perm Federal Research Center, Ural Branch, Russian Academy of Sciences, Perm, Russian Federation b G. March...

Immunotherapy with checkpoint inhibitors, albeit commonly used against tumors, is still at its infancy against chronic virus infections. It relies on the reinvigoration of exhausted T lymphocytes to eliminate virus-infected cells. Since T cell exhaustion is a physiological process to reduce immunopathology, the reinvigoration of these cells might b...

Acute infection and chronic infection are the two most common fates of pathogenic virus infections. While several factors that contribute to these fates are described, the critical control points and the mechanisms that underlie infection fate regulation are incompletely understood. Using the acute and chronic lymphocytic choriomeningitis virus (LC...

The lymphocytic choriomeningitis virus (LCMV) is a non-cytopathic virus broadly used in fundamental immunology as a mouse model for acute and chronic virus infections. LCMV remains a cause of meningitis in humans, in particular the fatal LCMV infection in organ transplant recipients, which highlights the pathogenic potential and clinical significan...

Objective: Population screening for aneurysms in patients with risk factors and preventive surgical treatment are beneficial according to numerous studies. One of the most significant risk factors is heredity, namely, the presence of first-degree relatives (FDR) with aneurysmal subarachnoid hemorrhage (aSAH). Nevertheless, there are still no gener...

Virus plaque assays are conventionally used for the assessment of viral infections, including their virulence, and vaccine efficacy. These experiments can be modeled with reaction–diffusion equations, allowing the estimation of the speed of infection spread (related to virus virulence) and viral load (related to virus infectivity). In this work, we...

Animal models of diseases, particularly mice, are considered to be the cornerstone for translational research in immunology. The aim of the present study is to model the geometry and analyze the network structure of the murine lymphatic system (LS). The algorithm for building the graph model of the LS makes use of anatomical data. To identify the e...

Animal models of diseases in particular, the mice, are considered to be the cornerstone for translational research in immunology. The aim of the present study is to model the geometry and analyze the network structure of murine lymphatic system (LS). The algorithm for building the graph model of the LS makes use of anatomical data. To identify the...

A successful vaccination implies the induction of effective specific immune responses. We intend to find biomarkers among various immune cell subpopulations, cytokines and antibodies that could be used to predict the levels of specific antibody- and cell-mediated responses after measles–mumps–rubella vaccination. We measured 59 baseline immune stat...

The contribution of cross-presenting XCR1+ dendritic cells (DCs) and SIRPα+ DCs in maintaining T cell function during exhaustion and immunotherapeutic interventions of chronic infections remains poorly characterized. Using the mouse model of chronic LCMV infection, we found that XCR1+ DCs are more resistant to infection and highly activated compare...

In this work, we briefly describe our technology developed for computing periodic solutions of time-delay systems and discuss the results of computing periodic solutions for the Marchuk-Petrov model with parameter values, corresponding to hepatitis B infection. We identified the regions in the model parameter space in which an oscillatory dynamics...

The systemic bio-organization of humans and other mammals is essentially “preprogrammed”, and the basic interacting units, the cells, can be crudely mapped into discrete sets of developmental lineages and maturation states. Over several decades, however, and focusing on the immune system, we and others invoked evidence – now overwhelming – suggesti...

A mathematical model of the human immunodeficiency virus Type 1 (HIV-1) life cycle in CD4 T cells was constructed and calibrated. It describes the activation of the intracellular Type I interferon (IFN-I) response and the IFN-induced suppression of viral replication. The model includes viral replication inhibition by interferon-induced antiviral fa...

The successful vaccination implies the induction of effective specific immune responses. We intend to find biomarkers among various immune cell subpopulations, cytokines and antibodies which could be used to predict the levels of specific antibody- and cell-mediated responses after measles-mumps-rubella vaccination. We measured 59 baseline immune s...

Pancreatic cancer represents one of the difficult problems of contemporary medicine. The development of the illness evolves very slowly, happens in a specific place (stroma), and manifests clinically close to a final stage. Another feature of this pathology is a coexistence (symbiotic) effect between cancer cells and normal cells inside stroma. All...

A calibrated mathematical model of antiviral immune response to SARS-CoV-2 infection is developed. The model considers the innate and antigen-specific responses to SARS-CoV-2 infection. Recently published data sets from human challenge studies with SARS-CoV-2 were used for parameter evaluation. The calibration of the mathematical model of SARS-CoV-...

The clinical handling of chronic virus infections remains a challenge. Here we describe recent progress in the understanding of virus - host interaction dynamics. Based on the systems biology concept of multi-stability and the prediction of multiplicative cooperativity between virus-specific cytotoxic T cells and neutralising antibodies, we argue f...

A calibrated mathematical model of antiviral immune response to SARS-CoV-2 infection is developed. The model considers the innate and antigen-specific responses to SARS-CoV-2 infection. Recently published data sets from human challenge studies with SARS-CoV-2 were used for parameter estimation. Understanding the regulation of multiple intertwined r...

Mathematical modelling of infection processes in cells is of fundamental interest. It helps to understand the SARS-CoV-2 dynamics in detail and can be useful to define the vulnerability steps targeted by antiviral treatments. We previously developed a deterministic mathematical model of the SARS-CoV-2 life cycle in a single cell. Despite answering...

The paper is devoted to a nonlocal reaction-diffusion equation describing the development of viral infection in tissue, taking into account virus distribution in the space of genotypes, the antiviral immune response, and natural genotype-dependent virus death. It is shown that infection propagates as a reaction-diffusion wave. In some particular ca...

The lymph node (LN) represents a key structural component of the lymphatic system network responsible for the fluid balance in tissues and the immune system functioning. Playing an important role in providing the immune defense of the host organism, LNs can also contribute to the progression of pathological processes, e.g., the spreading of cancer...

A fundamental unsolved issue in vaccine design is how neutralizing antibodies and cytotoxic CD8+ T cells cooperate numerically in controlling virus infections. We hypothesize on a viewpoint for the multiplicative cooperativity between neutralizing antibodies and CD8+ T cells and propose how this might be exploited for improving vaccine-induced prot...

SARS-CoV-2 infection represents a global threat to human health. Various approaches were employed to reveal the pathogenetic mechanisms of COVID-19. Mathematical and computational modelling is a powerful tool to describe and analyze the infection dynamics in relation to a plethora of processes contributing to the observed disease phenotypes. In our...

Replication of Human Immunodeficiency Virus type 1 (HIV) in infected CD4+ T cells represents a key driver of HIV infection. The HIV life cycle is characterised by the heterogeneity of infected cells with respect to multiplicity of infection and the variability in viral progeny. This heterogeneity can result from the phenotypic diversity of infected...

The human lymphatic system (HLS) is a complex network of lymphatic organs linked through the lymphatic vessels. We present a graph theory-based approach to model and analyze the human lymphatic network. Two different methods of building a graph are considered: the method using anatomical data directly and the method based on a system of rules deriv...

Many human virus infections including those with the human immunodeficiency virus type 1 (HIV) are initiated by low numbers of founder viruses. Therefore, random effects have a strong influence on the initial infection dynamics, e.g., extinction versus spread. In this study, we considered the simplest (so-called, `consensus’) virus dynamics model a...

Type I interferons (IFN-I) play a critical role in shaping the antiviral immune response early after an infection. However, the dynamics by which different immune cell subsets regulate the IFN-I response during the early stages of acute and chronic infections is not completely understood. Here we used the Lymphocytic Choriomeningitis Virus (LCMV)-i...

There are many studies that model the within-host population dynamics of Human Immunodeficiency Virus Type 1 (HIV-1) infection. However, the within-infected-cell replication of HIV-1 remains to be not comprehensively addressed. There exist rather few quantitative models describing the regulation of the HIV-1 life cycle at the intracellular level. I...

Fibroblastic reticular cells (FRCs) form a road-like cellular network in lymph nodes (LNs) that provides essential chemotactic, survival, and regulatory signals for immune cells. While the topological characteristics of the FRC network have been elaborated, the network properties of the micro-tubular conduit system generated by FRCs, which drains l...

This work is devoted to the investigation of virus quasi-species evolution and diversification due to mutations, competition for host cells, and cross-reactive immune responses. The model consists of a nonlocal reaction–diffusion equation for the virus density depending on the genotype considered to be a continuous variable and on time. This equati...

The work is devoted to the investigation of virus quasispecies evolution and diversification due to mutations, competition for host cells, and cross-reactive immune responses. The model consists of a nonlocal reaction-diffusion equation for the virus density depending on the genotype considered as a continuous variable and on time. This equation co...

The novel therapies with immune checkpoint inhibitors hold great promises for patients with chronic virus infections and cancers. This is based mainly on the partial reversal of the exhausted phenotype of antigen-specific cytotoxic CD8 T cells (CTL). Recently, we have shown that the restoration of HIV-specific T cell function depends on the HIV inf...

[This corrects the article DOI: 10.3389/fimmu.2019.01213.].

The surveillance of host body tissues by immune cells is central for mediating their defense function. In vivo imaging technologies have been used to quantitatively characterize target cell scanning and migration of lymphocytes within lymph nodes (LNs). The translation of these quantitative insights into a predictive understanding of immune system...

The processes and mechanisms of virus infection fate decisions that are the result of a dynamic virus-immune system interaction with either an efficient effector response and virus elimination or an alleviated immune response and chronic infection are poorly understood. Here, we characterized the host response to acute and chronic lymphocytic chori...

The host immune response against infection requires the coordinated action of many diverse cell subsets that dynamically adapt to a pathogen threat. Due to the complexity of such a response, most immunological studies have focused on a few genes, proteins, or cell types. With the development of “omic”-technologies and computational analysis methods...

Nonlinear dynamics of a reaction-diffusion equation with delay is studied with numerical simulations in 1D and 2D cases. Homogeneous in space solutions can manifest time oscillations with period doubling bifurcations and transition to chaos. Transition between two regions with homogeneous oscillations is provided by quasi-waves, propagating solutio...

Upon a viral infection, the host immune system attempts to eradicate the virus. However, once the infection threat seems overwhelming, the infected host actively shuts down effector responses to reduce immunopathology. The price to pay for this is the establishment of a chronic infection that is only partially controlled by a lower level immune res...

Adaptive immune responses develop in secondary lymphoid organs such as lymph nodes (LNs) in a well-coordinated series of interactions between migrating immune cells and resident stromal cells. Although many processes that occur in LNs are well understood from an immunological point of view, our understanding of the fundamental organization and mech...

In this chapter, we illustrate the application of mathematical models and computational analyses tools of various complexities to the description and explanation of some observed phenotypes of viral infections in humans, such as HIV and HBV infections. Specifically, we try to gain a deeper understanding of the sensitivity of infection dynamics to g...

This chapter introduces a modular approach to the formulation of mathematical models of immune responses to virus infections. It presents a methodological basis for mathematical immunology of virus infections.

In this chapter, we illustrate a data-driven methodology to formulation and calibration of mathematical models of immune responses. The maximum likelihood approach to parameter estimation, Tikhonov regularization method and information-theoretic criteria for model ranking and selection are presented for models formulated with ODEs, DDEs and PDEs. E...

Mathematical immunology is dealing with increasingly complex models of immune phenomena formulated with ODEs or DDEs. Except for few studies, mathematical models of the immune response against virus infections conventionally consider the infected whole organism as a single homogenous compartment.

This chapter presents a brief overview of basic immunological concepts and ideas necessary for the development of mathematical models of immune processes during virus infections.

The term multi-scale models is used with different meanings in different sciences. In mathematics, it implies the presence of one or several small parameters, homogenization and averaging techniques. In physics, it is understood in the sense of microscopic–macroscopic scales (e.g. molecular dynamics versus continuum mechanics).

The outcome of a viral infection is determined by the race between an expanding virus and the respective antiviral immune response of the infected host. This dynamic interaction lends itself to a quantitative description inherent in mathematical modelling.

This chapter aims to give a clear idea of how mathematical analysis for experimental systems could help in the process of data assimilation, parameter estimation and hypothesis testing.

This monograph concisely but thoroughly introduces the reader to the field of mathematical immunology. The book covers first basic principles of formulating a mathematical model, and an outline on data-driven parameter estimation and model selection. The authors then introduce the modeling of experimental and human infections and provide the reader...

The lymphatic system is a body-wide network of lymphatic vessels and lymphoid organs. The complexity of the structural and functional organization of the lymphatic system implies the necessity of using computational modeling approaches to unravel the mechanisms of its regulation in quantitative terms. Although it is a vital part of the circulatory...

Background Moving from the molecular and cellular level to a multi-scale systems understanding of immune responses requires the development of novel approaches to integrate knowledge and data from different biological levels into mechanism-based integrative mathematical models. The aim of our study is to present a methodology for a hybrid modelling...

Secondary lymphoid organs have developed segregated niches that are able to initiate and maintain effective immune responses. Such global organization requires tight control of diverse cellular components, specifically those that regulate lymphocyte trafficking. Fibroblastic reticular cells (FRCs) form a densely interconnected network in lymph node...

In this study, we discuss critical issues in modelling the structure and function of lymph nodes (LNs), with emphasis on how LN physiology is related to its multi-scale structural organization. In addition to macroscopic domains such as B-cell follicles and the T cell zone, there are vascular networks which play a key role in the delivery of inform...

Virus spreading in tissues is determined by virus transport, virus multiplication in host cells and the virus-induced immune response. Cytotoxic T cells remove infected cells with a rate determined by the infection level. The intensity of the immune response has a bell-shaped dependence on the concentration of virus, i.e., it increases at low and d...

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In this study we discuss critical issues in modelling the structure and function of lymph nodes (LNs), with emphasis on how LN physiology is related to its multi-scale structural organization. In addition to macroscopic domains such as B-cell follicles and the T cell zone, there are vascular networks which play a key role in the delivery of informa...

The human immune system is characterized by enormous cellular and anatomical complexity. Lymph nodes are key centers of immune reactivity, organized into distinct structural and functional modules including the T-cell zone, fibroblastic reticular cell (FRC) network and the conduit system. A thorough understanding of the modular organization is a pr...

Impact of DT-graded ablation of the FRC network on LN architecture. (A) Representative 2-D overview images of whole LN sections of Ccl19eyfp/idtr mice injected twice IP with indicated doses of DT stained against the indicated markers from 2–5 mice per group. Scale bars represent 300 μm. The star indicates a partially ablated FRC network in one LN l...

Impact of DT-graded FRC ablation on LN cellularity and intranodal migration. Flow cytometric analysis of total numbers of CD4+ T cells (A) and B220+ B cells (B) in LNs of Ccl19idtr mice injected twice IP with indicated doses of DT. (C) Two-photon microscopy analysis of meandering index of adoptively transferred CD8+ T cells into Ccl19idtr mice inje...

Numerical data and statistical tests of all figures. (XLS)

FRC network restoration kinetics following complete ablation. (A) Two IP injections of 8 ng DT per gram mouse weight were given to Ccl19eyfp/idtr at the indicated time points, and the analysis was performed on day 0 (complete ablation), day 14 (partial restoration), and day 28 (complete restoration). (B) Confocal microscopy Z-stack images of the T...

Global multiparameter correlational analysis. (A) Heat map of Pearson correlation coefficients between the following parameters in four readouts: (1) functional biology—number of FRCs in the T cell zone determined by microscopy, total numbers of CD45+, CD4+, CD8+, B220+ cells, and CD11c+ DCs per LN by flow cytometry, total number of Thy1.1+CD8+ T c...

Impaired T cell movement in LN T cell zone. Intravital two-photon microscopy analysis of T cell movement in LN T cell zone from 8 ng/g DT-treated mice. Three-dimensional reconstructions of T cells (cyan) and high endothelial venules (grey) in a representative T cell zone 200 x 200 x 64 μm. T cell tracking displayed with time color coding indicating...

FRC network fragmentation kinetics under random node removal. Topological model of the 3-D-reconstructed FRC network (0 ng/g) under random node removal for one simulation (left panel). Fraction of nodes removed f and number of remaining nodes / initial number of nodes are displayed in the bottom left. Green nodes denote the largest connected cluste...

Normal T cell movement in LN T cell zone. Intravital two-photon microscopy analysis of T cell movement in LN T cell zone from PBS-treated control mice. Three-dimensional reconstructions of T cells (cyan) and high endothelial venules (grey) in a representative T cell zone 300 x 300 x 64 μm. T cell tracking displayed with time color coding indicating...

Description of the morphological, topological and migration parameters. * Dimensionless unit. ** Integer number. (DOCX)

FRC network 3-D reconstruction and analysis pipeline. Confocal microscopy analysis was performed on whole LN histological sections of naive adult Ccl19eyfp mice stained for EYFP, PDPN, and DAPI. One to two T cell zones (approximately 300 x 300 x 30 μm) per LN were acquired in high resolution in order to generate the representative T cell zone FRC n...

Virus infections represent complex biological systems governed by multiple-level regulatory processes of virus replication and host immune responses. Understanding of the infection means an ability to predict the systems behaviour under various conditions. Such predictions can only rely upon quantitative mathematical models. The model formulations...

The life cycle of human immunodeficiency virus type-1 (HIV-1) makes possible the realization of regulatory strategies that can lead to complex dynamical behavior of the system. We analyze the strategy which is based on two feedback mechanisms, one mediating a positive regulation of the virus replication by Tat protein via the antitermination of the...

Since their invention in 1994, fluorescent dyes such as carboxyfluorescein diacetate succinimidyl ester (CSFE) are used for cell proliferation analysis in flow cytometry. Importantly, the interpretation of such assays relies on the assumption that the label is divided equally between the daughter cells upon cell division. However, recent experiment...

Models of phenomena that evolve with time, notably those in bioscience, may be more realistic as scientific models if they incorporate a memory or time-lag rather than assume instantaneous effects. The differences and similarities between the two types ...

Since their invention in 1994, fluorescent dyes such as carboxyfluorescein diacetate succinimidyl ester (CFSE) are used for cell proliferation analysis in flow cytometry. Importantly, the interpretation of such assays relies on the assumption that the label is divided equally between the daughter cells upon cell division. However, recent experiment...

Flow cytometry-based analysis of lymphocyte division using carboxyfluorescein succinimidyl ester (CFSE) dye dilution permits acquisition of data describing cellular proliferation and differentiation. For example, CFSE histogram data enable quantitative insight into cellular turnover rates by applying mathematical models and parameter estimation tec...

Although multiple biological phenomena are related to temperature (e.g. elevation of body temperature due to an illness, adaptation to environmental temperature conditions, biology of coldblooded versus warm-blooded organisms), the molecular mechanisms of these processes remain to be understood. Perturbations of secondary RNA structures may play an...

Infections with HIV represent a great challenge for the development of strategies for an effective cure. The spectrum of diseases associated with HIV ranges from opportunistic infections and cancers to systemic physiological disorders like encephalopathy and neurocognitive impairment. A major progress in controlling HIV infection has been achieved...

The immune system exhibits an enormous complexity. High throughput methods such as the "-omic'' technologies generate vast amounts of data that facilitate dissection of immunological processes at ever finer resolution. Using high-resolution data-driven systems analysis, causal relationships between complex molecular processes and particular immunol...

A robust and reliable parameter estimation is a critical issue for modeling in immunology. We developed a computational methodology for analysis of the best-fit parameter estimates and the information-theoretic assessment of the mathematical models formulated with ODEs. The core element of the methodology is a robust evaluation of the first and sec...

HIV infection is multi-faceted and a multi-step process. The virus-induced pathogenic mechanisms are manifold and mediated through a range of positive and negative feedback regulations of immune and physiological processes engaged in virus-host interactions. The fundamental questions towards understanding the pathogenesis of HIV infection are now s...

Burst-like proliferation is in the first place a hallmark of antigen-specific immune responses. In unperturbed mice, clonal proliferation bursts, representing a significant minority of all dividing CD4 T cells, have recently been identified by sequencing analysis. Of interest, mice maintained under sterile and non-sterile conditions showed similar...