Parameter Dependency of Faithful Responses. (A) To investigate the faithfulness of the response (red curve), we re-analysed those parameter sets that had produced sustained responses to a sustained input (red parameter sets in Additional file 3, Fig. S5) with time-varying inputs (linearly increasing and then decreasing TGF-β input concentration, black curve). Based on the squared residuals (grey area) between the normalized inputs (black line) and outputs (red line) we defined faithful and unfaithful responses as those in the first and last 10-quantile respectively. (B) An inefficient activation of the TGF-β receptor and a weak negative feedback favours faithful (light red to yellow) over unfaithful (black to salmon-pink) responses.