Interpreting Frequency Responses to Dose-Conserved Pulsatile Input Signals in Simple Cell Signaling Motifs
Patrick A. Fletcher, Frederique Clement, Alexandre Vidal, Joel Tabak, Richard Bertram
Many hormones are released in a pulsatile pattern. This pattern can be modified, for instance by changing pulse frequency or amplitude, to encode relevant physiological information. How do signaling pathways of cells targeted by these hormones respond to different input patters? In this study, we ask if a given dose of hormone can induce different outputs from the target system, depending on how this dose is distributed in time. We use simple mathematical models of feedforward signaling motifs to understand how the properties of the target system give rise to preferences in input pulse pattern. We frame these problems in terms of frequency responses to pulsatile inputs, where the amplitude or duration of the pulses is varied along with frequency to conserve input dose. We find that nonlinearity in the steady state input/output function of the system is the key factor that predicts the optimal input pattern. It does so by selecting an optimal amplitude of the input signal. Our results predict the behavior of common signaling motifs such as receptor binding with dimerization, and protein phosphorylation. The findings have implications for experiments aimed at studying the frequency response to pulsatile inputs, as well as for understanding how pulsatile patterns of input drive biological responses via feedforward signaling pathways.