Brown University, United States.
Math Biosci. 2018 Dec;306:56-59. doi: 10.1016/j.mbs.2018.10.008. Epub 2018 Oct 26.
Oscillations play a major role in a number of biological systems, from predator-prey models of ecology to circadian clocks. In this paper we focus on the question of whether oscillations exist within dual-site phosphorylation systems. Previously, Wang and Sontag showed, using monotone systems theory, that the Michaelis-Menten (MM) approximation of the distributive and sequential dual-site phosphorylation system lacks oscillations. However, biological systems are generally not purely distributive; there is generally some processive behavior as well. Accordingly, this paper focuses on the MM approximation of a general sequential dual-site phosphorylation system that contains both processive and distributive components, termed the composite system. Expanding on the methods of Bozeman and Morales, we preclude oscillations in the MM approximation of the composite system. This implies the lack of oscillations in the MM approximations of the processive and distributive systems, shown previously, as well as in the MM approximation of the partially processive and partially distributive mixed-mechanism system.
在许多生物系统中，如捕食者-猎物模型的生态学到生物钟，振荡起着重要的作用。在本文中，我们专注于在双位点磷酸化系统内是否存在振荡的问题。以前，Wang 和 Sontag 使用单调系统理论表明，分布和顺序双位点磷酸化系统的米氏-门捷列夫（MM）近似缺乏振荡。然而，生物系统通常不是纯粹的分布性的；通常也有一些连续性行为。因此，本文关注于包含连续性和分布性成分的一般顺序双位点磷酸化系统的 MM 近似，称为复合系统。在 Bozeman 和 Morales 方法的基础上，我们排除了复合系统 MM 近似中的振荡。这意味着先前显示的在 MM 近似中的连续性和分布性系统中没有振荡，以及在部分连续性和部分分布性混合机制系统的 MM 近似中没有振荡。
