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Mathematical Modeling, Numerical Methods and Software Complexes
Mathematical modelling of tissue formation on the basis of ordinary differential equations
M. N. Nazarov National Research University of Electronic Technology,
Moscow, 124498, Russian Federation
(published under the terms of the Creative Commons Attribution 4.0 International License)
Abstract:
A mathematical model is proposed for describing the population dynamics of cellular clusters on the basis of systems of the first-order ordinary differential equations. The main requirement for the construction of model equations was to obtain a formal biological justification for their derivation, as well as proof of their correctness. In addition, for all the parameters involved in the model equations, the presence of biological meaning was guaranteed, as well as the possibility of evaluating them either during the experiment or by using models of intracellular biochemistry. In the desired model the intercellular exchange of a special signal molecules was chosen as the main mechanism for coordination of the tissue growth and new types selection during cell division. For simplicity, all signalling molecules that can create cells of the same type were not considered separately in the model, but were instead combined in a single complex of molecules: a ‘generalized signal’. Such an approach allows us to eventually assign signals as a functions of cell types and introduce their effects in the form of matrices in the models, where the rows are responsible for the types of cells receiving the signals, and the columns for the types of cells emitting signals.
Keywords:
morphogenesis modeling, ordinary differential equations, system biology, hierarchical models.
Received: March 22, 2017 Revised: June 13, 2017 Accepted: September 18, 2017 First online: September 20, 2017
Citation:
M. N. Nazarov, “Mathematical modelling of tissue formation on the basis of ordinary differential equations”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 21:3 (2017), 581–594
Linking options:
https://www.mathnet.ru/eng/vsgtu1535 https://www.mathnet.ru/eng/vsgtu/v221/i3/p581
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