International Multiconference “Bioinformatics of Genome Regulation and Structure\Systems Biology”

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gene networks models

2 RESULTS
Systems computational biology: analysis, mathematical modeling and information technologies symposiumPhase Portraits of Gene Networks Models

Phase Portraits of Gene Networks Models

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Natalia Ayupova1, Vladimir Golubyatnikov2, Vyacheslav Gradov3, Liliya Minushkina4
1Lab. of inverse problems of mathematical physics. Sobolev Institute of Mathematics SB RAS, ayupova@math.nsc.ru
2Lab. of inverse problems of mathematical physics. Sobolev Institute of Mathematics SB RAS, Novosibirsk, Russia, vpgolubyatn@gmail.com
3Mechanical and mathematical department Novosibirsk State University Novosibirsk, Russia, v.gradov@g.nsu.ru
4Mechanical and mathematical department Novosibirsk State University Novosibirsk, Russia, l.minushkina@g.nsu.ru

We investigate geometric and combinatorial structures of phase portraits of dynamical systems considered as models of functioning of some circular gene networks. Invariant 2-dimensional piecewise linear surfaces constructed here allow to give full description of phase portraits of these models and to control their trajectories

Systems computational biology: analysis, mathematical modeling and information technologies symposiumA Model of one Central Regulatory Circuit

A Model of one Central Regulatory Circuit

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Tatyana Bukharina1, Andrey Akinshin2, Vladimir Golubyatnikov3, Dagmara Furman4
1Institute of Cytology and Genetics SB RAS, bukharina@bionet.nsc.ru
2Sobolev Institute of Mathematics SB RAS, Andrey.akinshin@gmail.com
3Sobolev Institute of Mathematics SB RAS, vpgolubyatn@gmail.com
4Institute of Cytology and Genetics SB RAS, furman@bionet.nsc.ru

Macrochaetes are sensor organs of the drosophila with a function of mechanoreceptors. An adult mechanoreceptor comprises four specialized cells. All these cells originate from the sensory organ precursor (SOP) cell. A characteristic feature of the SOP cell is the highest content of the proneural proteins ASC as compared with the surrounding cells. The accumulation of these proteins and maintenance of their amount in the SOP cell at a necessary level is provided by the gene network with the achaete-scute gene complex (AS-C) as its key component. The central regulatory circuit (CRC) controls the activity of this complex. The CRC activity comprises two phases differing in the time when they act. A specific feature of the second phase is the presence of PHYL protein, involved in degradation of proneural proteins. We propose a mathematical model for the CRC functioning as a regulator of the content of ASC proteins in the sensory organ precursor cell.