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Systems computational biology: From molecular genetic systems to populations and ecosystems
S. A. Lashin12, N. A. Kolchanov12
1Kurchatov Genomics Center, Institute of Cytology and Genetics, SB RAS
2Novosibirsk State University
Email: lashin@bionet.nsc.ru
DOI: 10.24412/cl-35065-2022-1-02-36
In the study, we formulate and solve new problems of mathematical and computer modeling of complex, hierarchically organized biological systems. The developed models take into account such levels of biological organization as metabolic, genetic, cellular, organismal, population and ecological. We present the modeling methods of the so-called "next-generations modeling", the principles of which were formulated in the last decade. Among the main principles are structural realism, emergent and predictive, model construction "from first principles", heterogeneity and dynamism of habitats, microevolution, interconnection of hierarchical levels and use of standardized submodels. The models presented in our work not only satisfy the properties described above, but also expand the range of their applications in biology, taking into account additional levels of systemic organization not mentioned by Grimm and Berger, in particular the molecular-genetic and social levels.
The developed modeling methods were implemented in the form of software packages "Haploid Evolutionary Constructor" (HEC), "Microcosm", "Diploid Evolutionary Constructor" (DEC), "Population Genetics of Deafness-Simulator" (PGD-S), and others. The methods of construction and numerical analysis of hierarchical multilayer models of biological systems developed in our study, as well as the software packages implemented on their basis are effective tools for solving meaningful biological problems of both fundamental and applied orientation.
This research was funded by the Russian state budget (project No FWNR-2022-0020) and the Kurchatov Genomic Centre of the Institute of Cytology and Genetics, SB RAS (project No 075-15-2019-1662).
Оптимизация численно-статистических проекционных оценок одномерных характеристик решений интегральных уравнений.
Г. А. Михайлов1, С. В. Рогазинский1,2, А. С. Корда1
1Институт вычислительной математики и математической геофизики СО РАН
2Новосибирский государственный университет
Email: svr@osmf.sscc.ru
DOI: 10.24412/cl-35065-2022-1-00-63
Строятся и оптимизируются численно-статистические проекционные оценки решений интегральных уравнений с использованием полиномов Лежандра в связи с вычислительной сложностью ортогональных разложений с адаптированным весом. С помощью специальных теоретических и численных оценок определяется параметр практически реализуемой степенной зависимости детерминированного слагаемого среднего квадрата погрешности, что позволяет минимизировать ее в целом. Предлагаемая методика успешно апробирована в тестовой задаче, близкой к проблеме Милна, причем она оказалась весьма эффективной сравнительно с использованием регуляризованного разложения по полиномам Лагерра.
