Stability analysis of an autocatalytic protein model | Zendy

Julian Lee | Zendy

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Stability analysis of an autocatalytic protein model

Author(s) -

Julian Lee

Publication year - 2016

Publication title -

aip advances

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.421

H-Index - 58

ISSN - 2158-3226

DOI - 10.1063/1.4950702

Subject(s) - eigenvalues and eigenvectors , hessian matrix , component (thermodynamics) , fixed point , stability (learning theory) , saddle point , control theory (sociology) , regulator , mathematics , rna , topology (electrical circuits) , autocatalysis , biological system , physics , mathematical analysis , computer science , combinatorics , biology , genetics , gene , geometry , quantum mechanics , control (management) , machine learning , artificial intelligence , kinetics

A self-regulatory genetic circuit, where a protein acts as a positive regulator of its own production, is known to be the simplest biological network with a positive feedback loop. Although at least three components—DNA, RNA, and the protein—are required to form such a circuit, stability analysis of the fixed points of this self-regulatory circuit has been performed only after reducing the system to a two-component system, either by assuming a fast equilibration of the DNA component or by removing the RNA component. Here, stability of the fixed points of the three-component positive feedback loop is analyzed by obtaining eigenvalues of the full three-dimensional Hessian matrix. In addition to rigorously identifying the stable fixed points and saddle points, detailed information about the system can be obtained, such as the existence of complex eigenvalues near a fixed point

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