Unlimited multistability in multisite phosphorylation systems.
Unlimited multistability in multisite phosphorylation systems.
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DOI：
10.1038/nature08102
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发表时间：
2009-07-09
期刊：
影响因子：
64.8
通讯作者：
Gunawardena, Jeremy
中科院分区：
文献类型：
--
作者：
Thomson, Matthew;Gunawardena, Jeremy
丝氨酸、苏氨酸和酪氨酸的可逆磷酸化是研究最广泛的蛋白质翻译后修饰。蛋白质上磷酸化位点的数量 (n) 显示出从原核生物（n≤7 个位点）到真核生物（例如 n≥150 个位点）的显着增加。多位点磷酸化具有多种作用，位点保守表明位点数量的增加不能仅仅归因于混杂的磷酸化。具有 n 个位点的底物具有指数数量 (2n) 的磷酸形式，并且各个磷酸形式可能具有不同的生物效应。这些磷酸形式的分布以及如何调节这种分布仍然未知。在这里，我们表明，当激酶和磷酸酶在多位点底物上反向作用时，系统可以在稳态下表现出明显的稳定磷酸形式分布，并且这种分布的最大数量随着n的增加而增加。虽然一些稳定的分布集中在单一磷酸形式上，但其他分布则更加分散，这使得磷酸蛋白质组有可能充当流体调节网络，能够编码信息并灵活地响应不同的需求。这种可塑性可能是真核细胞中复杂信息处理的基础，并表明拥有多个位点具有功能优势。我们的结果来自稳态磷酸形式浓度的不寻常几何形状，我们证明它构成了一条合理的代数曲线，与 n 无关。因此，我们降低了计算稳态的复杂性，从模拟 3×2n 微分方程到求解两个代数方程，同时以符号方式处理参数。我们预计这些方法可以扩展到具有多种底物和多种酶催化不同修饰的系统，如在翻译后修饰“代码”（例如组蛋白代码）中发现的那样。虽然模拟与呈指数级增长的分子复杂性作斗争，但这里开发的数学方法可以提供一种新的语言来阐明细胞信息处理的原理。
Reversible phosphorylation on serine, threonine and tyrosine is the most widely studied posttranslational modification of proteins. The number of phosphorylated sites on a protein (n) shows a significant increase from prokaryotes, with n≤7 sites, to eukaryotes, with examples having n≥150 sites. Multisite phosphorylation has many roles and site conservation indicates that increasing numbers of sites cannot be due merely to promiscuous phosphorylation. A substrate with n sites has an exponential number (2n) of phospho-forms and individual phospho-forms may have distinct biological effects. The distribution of these phospho-forms and how this distribution is regulated have remained unknown. Here we show that, when kinase and phosphatase act in opposition on a multisite substrate, the system can exhibit distinct stable phospho-form distributions at steady state and that the maximum number of such distributions increases with n. Whereas some stable distributions are focused on a single phospho-form, others are more diffuse, giving the phosphoproteome the potential to behave as a fluid regulatory network able to encode information and flexibly respond to varying demands. Such plasticity may underlie complex information processing in eukaryotic cells and suggests a functional advantage in having many sites. Our results follow from the unusual geometry of the steady-state phospho-form concentrations, which we show to constitute a rational algebraic curve, irrespective of n. We thereby reduce the complexity of calculating steady states from simulating 3×2n differential equations to solving two algebraic equations, while treating parameters symbolically. We anticipate that these methods can be extended to systems with multiple substrates and multiple enzymes catalysing different modifications, as found in posttranslational modification ‘codes’ such as the histone code. Whereas simulations struggle with exponentially increasing molecular complexity, mathematical methods of the kind developed here can provide a new language in which to articulate the principles of cellular information processing.
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DOI：
10.1073/pnas.0710515105
发表时间：
2008-03-18
影响因子：
11.1
作者：
Phanstiel, Doug;Brumbaugh, Justin;Coon, Joshua J.
通讯作者：
Coon, Joshua J.
影响因子：
13.8
作者：
Holmberg, CI;Tran, SEF;Sistonen, L
通讯作者：
Sistonen, L
影响因子：
9.8
作者：
Cohen JE
通讯作者：
Cohen JE
DOI：
10.1073/pnas.0235349100
发表时间：
2003-02-04
影响因子：
11.1
作者：
Sha, W;Moore, J;Sible, JC
通讯作者：
Sible, JC
影响因子：
64.8
作者：
Ozbudak, EM;Thattai, M;van Oudenaarden, A
通讯作者：
van Oudenaarden, A