The results of the signal-response relationship classification for the 18 responsive topologies.

For each topology, we have sampled 1000 parameter sets (rate constants and total protein concentrations) from a biologically permissible range (Supporting Text S6), derived the signal-response curve for each parameter set and classified this curve as hyperbolic or sigmoidal (see Methods). The topologies are indicated with a binary identification code that indicates the presence (1) or absence (0) of reverse phosphotransfer reactions along the relay, and the presence (1) or absence (0) of hydrolysis reactions at layers 2 and 4 (see Supporting Text S1 for all possible topologies). The classification results are given as the fraction of parameter sets resulting in a sigmoidal signal-response curve (the rest being classified as hyperbolic) and assuming a monofunctional HK. Classifications are based on the second derivative of the signal-response curve at zero and from sampling all parameters (with equal total protein concentrations at different layers) (see Methods). For additional results using alternative classification and sampling schemes (different total protein concentrations at different layers) or assuming bifunctional HK, see Supporting Text S3.

针对每种信号转导拓扑结构，我们从生物学可允许范围内（详见补充文本S6）采样了1000组参数集（包含速率常数与总蛋白浓度），为每组参数集推导其信号响应曲线，并将该曲线归类为双曲线型或S型（具体流程参见方法部分）。该类拓扑结构通过二进制识别码进行标注：该编码分别标识级联通路上是否存在反向磷酸转移反应（1表示存在，0表示不存在），以及第2层与第4层是否存在水解反应；所有可能的拓扑结构详见补充文本S1。分类结果以产生S型信号响应曲线的参数集占比呈现（其余参数集归类为双曲线型），且分析默认组氨酸激酶（Histidine Kinase, HK）为单功能型。分类依据为零位点处信号响应曲线的二阶导数，并对所有参数进行全采样（各层总蛋白浓度保持一致），详细方法参见方法部分。若需了解采用替代分类与采样方案（即各层总蛋白浓度不相等）或假设组氨酸激酶为双功能型的额外研究结果，请参见补充文本S3。