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

<p>For each topology, we have sampled 1000 parameter sets (rate constants and total protein concentrations) from a biologically permissible range (<i>Supporting <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003322#pcbi.1003322.s010" target="_blank">Text S6</a></i>), derived the signal-response curve for each parameter set and classified this curve as hyperbolic or sigmoidal (see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003322#s4" target="_blank"><i>Methods</i></a>). 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 <i>Supporting <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003322#pcbi.1003322.s005" target="_blank">Text S1</a></i> 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 <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003322#s4" target="_blank"><i>Methods</i></a>). For additional results using alternative classification and sampling schemes (different total protein concentrations at different layers) or assuming bifunctional HK, see <i>Supporting <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003322#pcbi.1003322.s007" target="_blank">Text S3</a></i>.