On three genetic repressilator topologies

Masa Dukarić, Hassan Errami, Roman Jerala, Tina Lebar, Valery G. Romanovski, János Tóth, and Andreas Weber
In: Reaction Kinetics, Mechanisms and Catalysis (Dec. 2018):11144(1-28)
 

Abstract

Novel mathematical models of three different repressilator topologies are introduced. As designable transcription factors have been shown to bind to DNA non-cooperatively, we have chosen models containing non-cooperative elements. The extended topologies involve three additional transcription regulatory elements—which can be easily implemented by synthetic biology—forming positive feedback loops. This increases the number of variables to six, and extends the complexity of the equations in the model. To perform our analysis we had to use combinations of modern symbolic algorithms of computer algebra systems Mathematica and Singular. The study shows that all the three models have simple dynamics that can also be called regular behaviour: they have a single asymptotically stable steady state with small amplitude damping oscillations in the 3D case and no oscillation in one of the 6D cases and damping oscillation in the second 6D case. Using the program QeHopf we were able to exclude the presence of Hopf bifurcation in the 3D system.

Keywords: Repressilator models Genetic oscillator Steady states Computer algebra Mathematica Singular QeHopf Designable repressor

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Bibtex

@ARTICLE{DukaricErrami2018,
    author = {Dukarić, Masa and Errami, Hassan and Jerala, Roman and Lebar, Tina and Romanovski, Valery G. and
              T{\'o}th, J{\'a}nos and Weber, Andreas},
     pages = {1--28},
     title = {On three genetic repressilator topologies},
   journal = {Reaction Kinetics, Mechanisms and Catalysis},
    number = {11144},
      year = {2018},
     month = dec,
  keywords = {Repressilator models Genetic oscillator Steady states Computer algebra Mathematica Singular QeHopf
              Designable repressor},
  abstract = {Novel mathematical models of three different repressilator topologies are introduced. As designable
              transcription factors have been shown to bind to DNA non-cooperatively, we have chosen models
              containing non-cooperative elements. The extended topologies involve three additional transcription
              regulatory elements—which can be easily implemented by synthetic biology—forming positive
              feedback loops. This increases the number of variables to six, and extends the complexity of the
              equations in the model. To perform our analysis we had to use combinations of modern symbolic
              algorithms of computer algebra systems Mathematica and Singular. The study shows that all the three
              models have simple dynamics that can also be called regular behaviour: they have a single
              asymptotically stable steady state with small amplitude damping oscillations in the 3D case and no
              oscillation in one of the 6D cases and damping oscillation in the second 6D case. Using the program
              QeHopf we were able to exclude the presence of Hopf bifurcation in the 3D system.},
      issn = {1878-5190 // 1878-5204},
       url = {https://link.springer.com/article/10.1007%2Fs11144-018-1519-5#citeas},
       doi = {https://doi.org/10.1007/s11144-018-1519-5}
}