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Article information
2017 , Volume 22, ¹ 1, p.67-83
Fadeev S.I., Leskova N.E., Akberdin I.R.
An investigation of the model of functional state of mouse embryonic stem cells based on a method of solution continuation with respect to parameter
The method of solution continuation with respect to parameter is an effective approach to study the properties of a mathematical model used to describe the nonlinear problem, depending on the model parameters. In many cases, when there is no enough a priori information on the problem under investigation, the design of the computational experiment based on the solution continuation with respect to parameter provides the unique opportunity to identify key features of the model, indicating the compliance between theoretical predictions and experimental estimations or observations on underlying mechanisms of the process. In this study, we have presented an application of the solution continuation method with respect to parameter to numerical study of the properties of stationary solutions of a nonlinear autonomous system of differential equations. The system of ordinary differential equations describes a dynamical functioning of the “core gene network” regulating the functional state of mouse embryonic stem cells (ESCs). The model was initially developed at the Institute of Cytology and Genetics of SB RAS on the basis of recently published and experimental data on the regulation of the pluripotency maintenance and differentiation of mouse ESCs. Understanding the mechanisms of this process is the basis for the development of efficient methods to manage it in dealing with modern applications of developmental biology. The numerical study of the properties for stationary solutions of the autonomous system, including the determination of their stability, has allowed us to find patterns of the functional state of the cell depending on the model parameters. In particular, the diagrams of stationary solutions were constructed on basis of the method of solution continuation depending on the model parameter, which characterizes the level of the external signal activating the pluripotent state of the cell. As a result, the domains of multiple solutions (up to five) were found as well as domains, in which all stationary solutions are unstable. The last one is the cause of auto-oscillations in this domain. Description of the patterns with a certain functional cell state has provided the basis for the comparison of obtained theoretical results with the known insights on the genetic control of processes functioning in ESC.
[full text]
Keywords: mathematical model, solution continuation with respect to parameter, multiplicity of stationary solutions, stability, embryonic stem cells, differentiation, pluripotency
Author(s):
Fadeev Stanislav Ivanovich
Dr. , Professor
Position: General Scientist
Office: Sobolev Institute of Mathematics of SB RAS, Novosibirsk state university
Address: 630090, Russia, Novosibirsk, Prospekt Academika Koptyga, 4
Phone Office: (383) 329-76-80
E-mail: fadeev@math.nsc.ru
Leskova Nataliya Evgenyevna
Position: The master of mathematics
Office: Novosibirsk State University
Address: 630090, Russia, Novosibirsk, Pirogov st, 2
E-mail: tasha.lesk@gmail.com
Akberdin Ilya Rinatovich
PhD.
Position: Research Scientist
Office: Novosibirsk State University, Institute of Cytology and Genetics SB RAS
Address: 630090, Russia, Novosibirsk, Pirogov st, 2
Phone Office: (383) 363-49-63
E-mail: akberdin@bionet.nsc.ru
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Bibliography link:
Fadeev S.I., Leskova N.E., Akberdin I.R. An investigation of the model of functional state of mouse embryonic stem cells based on a method of solution continuation with respect to parameter // Computational technologies. 2017. V. 22. ¹ 1. P. 67-83
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