Fig. 2.

Dose–response curves for signaling mechanisms through molecular switches. The response is measured in terms of fraction of active switches $Y^{*}/Y_T$ as the stimulus level varies. The receptor-occupancy curve denotes the fraction of active receptors $X^{*}/X_T$. The stimulus is normalized by its binding affinity to the receptor (${\mathrm{\Theta }}_{X^{*}}$). (A) For the activation mechanism, the half-maximal stimulus (${\mathrm{\Theta }}_{Y^{*}}$) of a dose–response curve is less than ${\mathrm{\Theta }}_{X^{*}}$. Each dose–response curve (solid line) is for a fixed activation strength (act. str.) $k_5{X}_T$. Increasing $k_5{X}_T$, depicted by the solid arrow, causes an upward expansion and leftward shift in dose–response. For these plots, the following values for parameters were used: $k_3=0,k_4=1$ and $k_6=0$. The activation strength ($k_5{X}_T$) was varied to take values from $\left(\mathrm{1,10,100}\right)$. (B) For the derepression mechanism, the dose–response of the switch for a given repression strength (rep. str.) ($k_6{X}_T$) has half-maximal stimulus (${\mathrm{\Theta }}_Y$) greater than ${\mathrm{\Theta }}_{X^{*}}$. Increasing $k_6{X}_T$, shown by the solid arrow, leads to a downward expansion and rightward shift in the dose–response curve. The repression strength $k_6{X}_T$ takes values from $\left(\mathrm{1,10,100}\right)$. The rest of the parameters were set as $k_3=1$, $k_4=0$, and $k_5=0$. (C) In the case of concerted mechanism, ${\mathrm{\Theta }}_{Y^{*}}$ may be greater than, equal to, or less than ${\mathrm{\Theta }}_{X^{*}}$, depending upon the relative (rel.) values of the activation strength and the derepression strength. Increasing the ratio $k_5/k_6$, depicted by the solid arrow, shifts the dose response (resp.) to the left. Dose–response alignment (${\mathrm{\Theta }}_{Y^{*}}={\mathrm{\Theta }}_{X^{*}}$) occurs when $k_5=k_6$. The parameters used for the plots are $k_3=0$ and $k_4=0$. The ratio $k_5/k_6$ was varied over $\left(0.1,\mathrm{1,10}\right)$.