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A proof of bistability for the dual futile cycle

机译：双无效周期的双稳态证明

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摘要

The multiple futile cycle is an important building block in networks of chemical reactions arising in molecular biology. A typical process which it describes is the addition of n phosphate groups to a protein. It can be modelled by a system of ordinary differential equations depending on parameters. The special case n = 2 is called the dual futile cycle. The main result of this paper is a proof that there are parameter values for which the system of ODE describing the dual futile cycle has two distinct stable stationary solutions. The proof is based on bifurcation theory and geometric singular perturbation theory. An important entity built of three coupled multiple futile cycles is the MAPK cascade. It is explained how the ideas used to prove bistability for the dual futile cycle might help to prove the existence of periodic solutions for the MAPK cascade. (C) 2015 Elsevier Ltd. All rights reserved.
机译：无效的多重循环是分子生物学中发生的化学反应网络的重要组成部分。它描述的典型过程是将n个磷酸基团添加到蛋白质上。它可以由常微分方程系统根据参数进行建模。 n = 2的特殊情况称为双重无效周期。本文的主要结果是证明存在一些参数值，描述双无效周期的ODE系统具有两个不同的稳定平稳解。该证明基于分岔理论和几何奇异摄动理论。由三个耦合的多个无效周期构成的重要实体是MAPK级联。解释了用来证明双无效周期的双稳态的思想如何有助于证明MAPK级联的周期解的存在。 （C）2015 Elsevier Ltd.保留所有权利。

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