Stochastic failure of signal transmission reduces the relative sensitivity to low intensity input signals. The lower (blue) lines show the probability p=a e-bx that an input signal fails to produce an output. The upper (red) lines show the expected equilibrium output for Michaelis-Menten type dynamics corrected for a probability p that the output is zero. Each panel (a – d) shows a cascade of n reactions, in which the output of each reaction forms the input for the next reaction, given an initial signal input of x for the first reaction. Each reaction follows Eq. (8). The number of reactions in the cascade increases from the left to the right panel as n=1,2,4,8. The other parameters for Eq. (8) are the gain per reaction, g=1.5, the maximum probability of reaction failure as the input declines to very low intensity, a=0.3, and the rate at which increasing signal intensity reduces reaction failure, b=10. The final output signal is normalized to 0.8 of the maximum output produced as the input become very large.