Feng Song, Sáez Meritxell, Wiuf Carsten, Feliu Elisenda, Soyer Orkun S
School of Life Sciences, University of Warwick, Coventry, UK.
Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark.
J R Soc Interface. 2016 Oct;13(123). doi: 10.1098/rsif.2016.0524.
Bistability, and more generally multistability, is a key system dynamics feature enabling decision-making and memory in cells. Deciphering the molecular determinants of multistability is thus crucial for a better understanding of cellular pathways and their (re)engineering in synthetic biology. Here, we show that a key motif found predominantly in eukaryotic signalling systems, namely a futile signalling cycle, can display bistability when featuring a two-state kinase. We provide necessary and sufficient mathematical conditions on the kinetic parameters of this motif that guarantee the existence of multiple steady states. These conditions foster the intuition that bistability arises as a consequence of competition between the two states of the kinase. Extending from this result, we find that increasing the number of kinase states linearly translates into an increase in the number of steady states in the system. These findings reveal, to our knowledge, a new mechanism for the generation of bistability and multistability in cellular signalling systems. Further the futile cycle featuring a two-state kinase is among the smallest bistable signalling motifs. We show that multi-state kinases and the described competition-based motif are part of several natural signalling systems and thereby could enable them to implement complex information processing through multistability. These results indicate that multi-state kinases in signalling systems are readily exploited by natural evolution and could equally be used by synthetic approaches for the generation of multistable information processing systems at the cellular level.
双稳态，更普遍地说是多稳态，是细胞中实现决策和记忆的关键系统动力学特征。因此，破译多稳态的分子决定因素对于更好地理解细胞通路及其在合成生物学中的（重新）工程设计至关重要。在这里，我们表明，一个主要在真核信号系统中发现的关键基序，即无效信号循环，当具有双态激酶时可以表现出双稳态。我们为该基序的动力学参数提供了必要且充分的数学条件，以保证多个稳态的存在。这些条件强化了这样一种直觉，即双稳态是激酶两种状态之间竞争的结果。从这个结果扩展来看，我们发现增加激酶状态的数量会线性地转化为系统中稳态数量的增加。据我们所知，这些发现揭示了细胞信号系统中产生双稳态和多稳态的一种新机制。此外，具有双态激酶的无效循环是最小的双稳态信号基序之一。我们表明，多态激酶和所描述的基于竞争的基序是几种天然信号系统的一部分，因此可以使它们通过多稳态实现复杂的信息处理。这些结果表明，信号系统中的多态激酶很容易被自然进化所利用，并且同样可以被合成方法用于在细胞水平上生成多稳态信息处理系统。
