Nakabayashi Jun, Sasaki Akira
Department of Biology, Faculty of Sciences, Kyushu University, Fukuoka 812-8581, Japan.
J Theor Biol. 2005 Apr 7;233(3):413-21. doi: 10.1016/j.jtbi.2004.10.022. Epub 2004 Dec 15.
Eukaryotic cells use signal-transduction network to respond in specific ways to external signals from their environment. Several signal-transduction pathway are composed of multi-step chemical reactions. We here theoretically study what determines the number of kinase phosphorylation steps composing of the intracellular signal-transduction cascade. We examine a simple mathematical model for the association and phosphorylation process of kinases in the signal-transduction cascade. We focus on the speed of signal transduction as the criterion for determining the optimal response. The present model first reveals that the initial expression level of kinase in each step of the cascade must be the same in the optimal response under the constraint of the constant total kinase concentration. The second conclusion is that the optimal step number of kinase cascade is primarily determined by the ratio of the target concentration of the final phosphorylated kinase in the cascade to that of input signal molecule, C/S. A multi-step cascade is optimum if the amplification of the final product concentration C relative to the input signal S is sufficiently large; whereas, a single-step reaction is optimum if C/S is small. This suggests that multi-step phosphorylation would have evolved to accelerate the speed of transduction of weak signals.
真核细胞利用信号转导网络以特定方式响应来自其环境的外部信号。几种信号转导途径由多步化学反应组成。我们在此从理论上研究是什么决定了构成细胞内信号转导级联的激酶磷酸化步骤的数量。我们研究了信号转导级联中激酶的结合和磷酸化过程的一个简单数学模型。我们将信号转导速度作为确定最佳响应的标准。本模型首先揭示，在总激酶浓度恒定的约束下，级联每一步中激酶的初始表达水平在最佳响应中必须相同。第二个结论是，激酶级联的最佳步数主要由级联中最终磷酸化激酶的靶浓度与输入信号分子浓度的比值C/S决定。如果最终产物浓度C相对于输入信号S的放大倍数足够大，多步级联是最佳的；而如果C/S较小，单步反应是最佳的。这表明多步磷酸化可能已经进化以加速弱信号的转导速度。
