 Logic approximation for gene regulation

A threshold approximation in which a regulatory input permits or blocks production according to whether a transcription factor exceeds a specified concentration. With first-order removal, $\dot{y}=\beta g-\alpha y$ and $g\in \{0,1\}$. A zero-initialized rising response reaches $K<\beta /\alpha$ at $-{\alpha }^{-1}\ln (1-\alpha K/\beta )$. Boolean rules must specify how several inputs combine; equal rate constants do not determine thresholds.