Regulatory networks are able to process complex signals and respond appropriately to the cellular context. Thus, an increasing effort by systems biology researchers is being focused on understanding which interactions are responsible for a given functional response. When translated into specific mathematical models, however, it has been repeatedly shown that this mapping between topology and function is not one-to-one, even for the simplest networks. Moreover, dynamical behavior may play an important role which is necessary to integrate in the general picture. We propose a unified theoretical/statistical approach to characterize the structure–function relationship in molecular networks when temporal features of both input signal and output response are important. The theory allows fast computation of network responses in terms of interaction strengths irrespective of molecular details, while statistical analysis identifies constraints between structural and dynamical features and network function. Investigating different feedback and feedforward loop architectures, we find that processing of temporal signals is strongly correlated to certain combinations of structural and dynamical characteristics, rather than to individual interactions. Our analysis offers new insight into the structure–function relationship in network motifs, quantifying how much the tuning of specific interactions affects network outcome, identifying key structural parameters for a given response and relating dynamics to network topology and function. This kind of analyses can be especially useful for synthetic biology approaches, where promoter libraries with a range of inputs and outputs can be engineered, and one has to choose the correct component needed to produce the desired network function.
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