Open AccessPositive And Negative Feedback Loops Coupled By Common Transcription Activator And Repressor
Author(s) -
Jan Sielewiesiuk,
Agata Łopaciuk
Publication year - 2015
Publication title -
annales universitatis mariae curie-skłodowska. sectio aaa, physica
Language(s) - English
Resource type - Journals
eISSN - 2300-7559
pISSN - 0137-6861
DOI - 10.1515/physica-2015-0006
Subject(s) - negative feedback , positive feedback , control theory (sociology) , feedback loop , hopf bifurcation , feedback regulation , physics , bifurcation , loop (graph theory) , repressor , amplitude , psychological repression , mathematics , computer science , chemistry , transcription factor , quantum mechanics , nonlinear system , combinatorics , engineering , control (management) , computer security , voltage , artificial intelligence , gene expression , biochemistry , mathematics education , electrical engineering , gene
Dynamical systems consisting of two interlocked loops with negative and positive feedback have been studied using the linear analysis of stability and numerical solutions. Conditions for saddle-node bifurcation were formulated in a general form. Conditions for Hopf bifurcations were found in a few symmetrical cases. Auto-oscillations, when they exist, are generated by the negative feedback repressive loop. This loop determines the frequency and amplitude of oscillations. The positive feedback loop of activation slightly modifies the oscillations. Oscillations are possible when the difference between Hilll’s coefficients of the repression and activation is sufficiently high. The highly cooperative activation loop with a fast turnover slows down or even makes the oscillations impossible. The system under consideration can constitute a component of epigenetic or enzymatic regulation network.