| Complex networks are studied across many fields of science. To discover design principles that underlie these networks, network motifs are introduced, as sub-graphs of interconnections occurring in complex networks much more often then expected at random. A distinct set of network motifs were identified in many types of biological networks, such as gene transcriptional networks, neuronal networks, and enzymatic networks, but only a small fraction of them have been well described. By connecting recurrent motifs with a particular cellular function, it is hoped that one can understand the dynamics of the entire network based on the dynamics of its core motifs.;Two biologically important functions were introduced and motivated through examples from biology, namely, exact adaptation, which represents a system's ability to respond to a change in the input signal and return to its pre-stimulated state even when the change in input persists, and Fold Change Detection, which is a special property of adapting systems, where the output is invariant under the scaling of inputs.;In this thesis, the study of network motifs was used as a motivation to further explore the dynamics of all 3-node enzymatic networks capable of achieving Fold Change Detection property. A search through 16,038 topologies sampled with 10,000 parameters each, led to the conclusion that despite the diversity of enzymatic circuits, only small number of them is capable of achieving the FCD property, and the mechanism for achieving it can be understood through a theoretical and computational analysis. |
