title: ÐÐ¾Ð´ÐµÐ»Ð¸ ÐºÐ¾Ð»ÐµÐ±Ð°ÑÐµÐ»ÑÐ½Ð¾Ð¹ Ð´Ð¸Ð½Ð°Ð¼Ð¸ÐºÐ¸ ÑÐºÑÐ¿ÑÐµÑÑÐ¸Ð¸ Ð³ÐµÐ½Ð¾Ð²
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð±Ð°ÐºÐ°Ð»Ð°Ð²ÑÐ°
titleType: Subtitle
title: Models of oscillatory dynamics of gene expression
Creators: name: ÐÐ°ÑÐ¸Ð¼Ð¾Ð², ÐÑÐºÐ°Ñ
Publisher: name: Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³ÑÐºÐ¸Ð¹ Ð¿Ð¾Ð»Ð¸ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ð¹ ÑÐ½Ð¸Ð²ÐµÑÑÐ¸ÑÐµÑ ÐÐµÑÑÐ° ÐÐµÐ»Ð¸ÐºÐ¾Ð³Ð¾
Year: 2023
Subjects: ÑÐµÐ¿ÑÐµÑÑÐ¸Ð»ÑÑÐ¾Ñ
ÐºÐ¾Ð»ÐµÐ±Ð°ÑÐµÐ»ÑÐ½Ð°Ñ Ð´Ð¸Ð½Ð°Ð¼Ð¸ÐºÐ°
Ð»Ð¸Ð½ÐµÐ¹Ð½ÑÐ¹ Ð°Ð½Ð°Ð»Ð¸Ð· ÑÑÑÐ¾Ð¹ÑÐ¸Ð²Ð¾ÑÑÐ¸
Ð±Ð¸ÑÑÑÐºÐ°ÑÐ¸Ñ
repressilator
oscillatory dynamics
linear stability analysis
bifurcation

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description: This work is dedicated to studying the Â«repressilatorÂ» model, which describes the oscillatory dynamics of three mutually repressing genes activity. The classical version of the model and its modifications, including different mathematical representations for protein synthesis and decomposition rates, are examined. The modified models utilize the Michaelis--Menten kinetics formalism to record the rates of these processes. It has been demonstrated that the dynamics of gene activity in the modified models can differ significantly from those in the classical model. Specifically, modifying the rates of protein synthesis and decay can result in the absence of oscillatory dynamics in the modified models, whereas the classical model predicts the presence of oscillations with the same parameter values, which are common to all models. Parametric modes corresponding to similar or different solutions in all models are described. The dependence of characteristic oscillation parameters on cooperativity parameters in the models has been investigated, revealing the similarity of solutions between the classical model and the considered modifications. The obtained results demonstrate the significance of selecting an appropriate mathematical formalism when formulating models of gene regulation with oscillatory dynamics.