Figure 1. Regulatory cascades in signal transduction. (a) A generic signalling cascade. (b) The receptor tyrosine kinase cascade. This cascade transduces signals from various growth factor (GF) receptors to targets in the cytoplasm and nucleus in a variety of biological contexts. (c) The visual cascade. This cascade allows retinal rod outer segments to detect single photons. PDE, phosphodiesterase.

Figure 2. Responses of a Michaelian monocyclic cascade. (a) Reversible conversion of A to A* in response to an activating stimulus S and an inactivator I. (b) Steady-state response. A Michaelian response is very graded; an 81-fold increase in input stimulus (S) is required to drive the system from 10% to 90% maximal response. (c) Time course of the changes in A* in response to an increase in S. Increasing the rate of either the forward or the back reaction increases the speed with which the system attains its new steady state.

Figure 3. Michaelian sensitivity, ultrasensitivity and subsensitivity. The responses of signalling cascades are often well approximated by the Hill equation [A]*_ss = [A]_tot [S]ⁿ/(EC₅₀ⁿ + [S]ⁿ). If the Hill coefficient n = 1, the Hill equation is equivalent to eqn (4) in the text. The resulting curve is a hyperbola, and the response is termed Michaelian. If n > 1, the resulting curve is sigmoidal and the response is termed ultrasensitive. The higher the value of n, the more steeply sigmoidal the response. If n < 1, the response is termed subsensitive.

Figure 4. A cascade as a sensitivity amplifier. (a) If individual levels of a cascade exhibit Michaelian responses, the overall response of the cascade will be Michaelian. (b) If individual levels in a cascade exhibit sigmoidal responses, the overall response of the cascade becomes progressively more steeply sigmoidal as the cascade is descended.

Figure 5. Time course of a Michaelian signalling cascade with multiple rate-determining steps. Responses become more abrupt as the number of rate-determining steps increases. t₉₀ denotes the time it takes for the system to achieve a 90% maximal response.