G.A. Bocharov, V.A. Chereshnev, T.B. Luzyanina, E.A. Chiglintsev, B. Ludewig

The dynamics and outcome of infectious diseases depend both on the ability of the pathogen to spread rapidly in the host and also on the intensity of the cytotoxic T cell responses. Therefore, the analysis of the kinetic parameters of virus replication and clonal dynamics is one of the major factors for understanding the pathogenesis of virus and bacterial infections such as human im-munodeficiency virus infection (HIV), viral hepatitis B and C, tuberculosis. This work presents a methodology for developing biologically relevant mathematical models and computational technol-ogies for efficient parameter estimation problems related to virus replication and T cell turnover using experimental data. The formulation of quantitatively consistent theoretical models of immune responses and the methodology of their application for the analysis of pathogenic mechanisms of unfavorable outcomes of virus infections is the central task of mathematical immunology. The formal description of virus and immune response dynamics using mathematical structures and the model calibration require the introduction of some fundamental notions and procedures, such as direct and inverse problems, maximum likelihood approach, a priori identifiability. These issues are consistently presented in the context of the analysis (1) of the kinetic regulation of T-cell responses during acute LCMV infection in mice and (2) the in vitro T cell proliferation experiments based upon the carboxyfluorescein succinimidyl ester (CFSE) labeling. The computations were performed using the MATLAB programming system for analysis and visualization. We show that the magnitude of T cell response depends on the rate of virus replication in a bell-shaped form. There exist two ranges of the virus growth rates in which the sensitivity of T cell responses appears to be positive and negative, respectively. In the first one, the maximum CTL number increases with the higher virus growth rate, whereas in the second one it decreases for faster replication viruses. Using the flow cytometry data coming from standard carboxyfluorescein succinimidyl ester (CFSE) based proliferation experiments in the form of the histograms of cell distributions with respect to CFSE expression, we identify the kinetic parameters (cell division and apoptosis rates), characterizing the proliferative status of stimulated T-cells. We showed that the mean cell division time depends significantly on the number of completed mitoses and decreases about three-fold for cells which have undergone two divisions as compared to naïve cells. The results of our research provide a mathematical basis in the form of problem-oriented computational technologies for an integrative analysis of HIV infection pathogenesis, and in particular the processes underlying the increasing imbalance between the production and death of CD4 cells with both the spatial organization of secondary lymphoid organs and virus evolution taken into account.