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7References
1. Klyucharyov A.A., Fomenkova A.A. Mathematical model of an anaerobic bioreactor with fixed biomass as a control
object. Information control systems. 2019. No. 2. P. 44-51. (in Russian).
2. Kolesnikov A.A. Synergetics and problems of control theory. Moscow: Fismatlit. 2004. (in Russian).
3. Kolesnikova S. I. Synthesis of the Control System for a Second Order Non-Linear Object with an Incomplete
Description. Autom. and Remote Control. V. 79. P. 1556�1566.
Mathematical models for dynamics of HIV infection acute phase
I. A. Gainova
Sobolev Institute of Mathematics SB RAS
Email: gajnova@math.nsc.ru
DOI 10.24412/cl-35065-2021-1-02-41
There are considered mathematical models for dynamics of HIV infection acute phase. The first mathe-
matical models describing the dynamics of HIV infection appeared as early as 1986 [1], three years after the
discovery of HIV. The basic mathematical model of the dynamics of HIV infection includes three key cell popu-
lations: uninfected target cells, infected target cells, and free virus particles. This basic model allowed to obtain
such important quantitative characteristics of the infectious disease as the virus replication rate and an aver-
age half-life of a virus particle, the rate of decrease of the viral load, a life span of infected T-lymphocytes and
the rate of virus production by a single infected cell (basic reproduction number, R0). The next generation of
dynamic models is an extension of the basic model by considering various types of cells in the immune system,
types of infection (acute, latent), localization in the compartments (blood, lymphatic system), mutated strains
of the virus, etc. [2, 3].
This work was supported by the Russian Foundation for Basic Research (grant 20-01-00352) and the state contract of
the Sobolev Institute of Mathematics (Project No. 0314-2019-0013).
References
1. Covert D.L., Kirschner D. Revisiting early models of the host-pathogen interactions in HIV infection // Comm.
Theor. Biol. 2000. V. 5(6), P. 383-411.
2. Bocharov G., Chereshnev V., Gainova I., Bazhan S., Bachmetyev B., Argilaguet J., Martinez J., Meyerhans A. Human
Immunodeficiency Virus Infection: from Biological Observations to Mechanistic Mathematical Modelling // Mathematical
Modelling of Natural Phenomena. 2012. V. 7 (5), P. 78�104.
3. Chereshnev V. A., Bocharov G. A., Kim A. V., Bazhan S. I., Gainova I. A., Krasovskii A.N., Shmagel N. G., Ivanov A. V.,
Safronov M. A., Tretyakova R. M. Introduction to modeling and control of HIV infection dynamics. Institute for Computer
Research, Moscow � Izhevsk, 2016.
Random graphs as structural models of biological networks
D. A. Gavrilov1, N. L. Podkolodnyy2,3
1Novosibirsk State University
2Institute of Computational Mathematics and Mathematical Geophysics SB RAS
3The Federal Research Center Institute of Cytology and Genetics SB RAS
Email: dgavrilov14@gmail.com
DOI 10.24412/cl-35065-2021-1-02-42
Modern methods of experimental research allow reconstruction of biological networks of various types,
including gene, metabolic, interatomic networks, gene co-expression networks, disease networks, etc.
Structural models as a random graphs can be used for testing various statistical hypotheses on networks,
searching for network biomarkers, studying the influence of structural patterns in biological networks on their
function.
In this paper, we use the method for generating a random graph with restrictions in the form of frequen-
cies of structural motives of various sizes. The process corresponds to a Markov chain, at each step of which
two non-adjacent edges of a graph are swapped in a random way. A computational experiment was carried
out to analyze the process of the Markov chain convergence to a stationary distribution when generating a
random graph from a set of starting positions. In addition, in order to estimate the optimal number of steps of
the Markov chain, methods of �multiple short runs� and �one long run� were applied. A computational exper-
iment was carried out to verify these estimates on mouse liver PPI network.
This work was supported by the grants No 0259-2021-0009 and No 0315-2021-0005 from the Russian Government
Budget.
Computer analysis of the gene network that controls appetite in human
E. V. Ignatieva1,2, E. A. Matrosova1,2
1 The Federal Research Center Institute of Cytology and Genetics SB RAS
2Novosibirsk State University
Email: eignat@bionet.nsc.ru
DOI 10.24412/cl-35065-2021-1-02-43
The drive to consume food is one of the most primitive of instincts promoting survival. Appetite disorders
can lead to human diseases (anorexia nervosa, hyperphagia, obesity). Gene network involving 120 human
genes and proteins that control appetite was built. This network also included miRNAs that regulated the ex-
pression of proteins, as well as diseases associated with network objects. It was found that the subsystem of
anorexigenic genes included more elements, had an additional mechanism of expression regulation involving
miRNA, and, on average, was associated with a greater number of diseases compared to the subsystem of
orexigenic genes. The study of the evolution of the genes based on PAI [1] showed that "middle-aged" genes
predominated in the network. An evolutionary stage was identified, corresponding to the moment of the
emergence of placental organisms, at which more genes "arose" than could be expected for random reasons.
The number of cases when the gene encoding the cell surface receptor was older than the gene encoding the
corresponding ligand (signaling molecule - hormone, neuropeptide, etc.) significantly exceeded the number of
cases when the opposite situation was observed. It turned out that most of the genes of the network undergo
stabilizing selection, but the genes encoding signaling molecules are less susceptible to it.
This work was supported by the budget project No.0259-2021-0009.
References
1. Mustafin Z. S., Lashin S. A., Matushkin Y. G., Gunbin K. V., Afonnikov D. A. Orthoscape: a cytoscape application for
grouping and visualization KEGG based gene networks by taxonomy and homology principles // BMC Bioinformatics.
2017. V. 18. P. 1�9.
