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All-or-None Principle

A receptor will either elicit a maximal response or none at all, reflecting the binary nature of signal transduction events.
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The statement of the theorem

The output signal RR resulting from an input stimulus II is modeled by a threshold function Θ\Theta: \n\nR(I)={Rmaxif I≥Ithreshold0if I<IthresholdR(I) = \begin{cases} R_{max} & \text{if } I \ge I_{threshold} \\ 0 & \text{if } I < I_{threshold} \end{cases} \n\nAlternatively, using a continuous approximation for mathematical analysis, the response can be modeled by a steep sigmoidal function, such as the Fermi function, centered at the threshold IthresholdI_{threshold}: \n\nR(I)=Rmax1+e−k(I−Ithreshold)R(I) = \frac{R_{max}}{1 + e^{-k(I - I_{threshold})}} \n\nwhere kk controls the steepness of the transition.