Gains and optimal design in signaling pathways

Signal amplification and other input-to-output properties of signaling cascades are characterized by the H_∞ gain in the case of linear systems, or by the L₂ induced norm in the nonlinear case. The effect of the length of the cascade on the output signal is examined. In particular, for a fixed gain, there is an optimal length that generates "sharp" outputs (signals that simultaneously exhibit short duration and high amplitude).