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A recurring set of small sub-networks have been identified as the building blocks of biological networks across diverse organisms. These network motifs are associated with certain dynamic behaviors and define key modules that are important for understanding complex biological programs. Besides studying the properties of motifs in isolation, current algorithms typically evaluate the occurrence frequency of a specific motif in a given biological network compared to that in random networks of similar structure. However, it remains challenging to relate the structure of motifs to the observed and expected behavior of the larger, more complex network they are contained within. This problem is compounded as even the precise structure of most biological networks remains largely unknown. Previously, we developed a formal reasoning approach enabling the synthesis of biological networks capable of reproducing some experimentally observed behavior. Here, we extend this approach to allow reasoning over the requirement for specific network motifs as a way of explaining how these behaviors arise. We illustrate the approach by analyzing the motifs involved in sign-sensitive delay and pulse generation. We demonstrate the scalability and biological relevance of the approach by studying the previously defined networks governing myeloid differentiation, the yeast cell cycle, and na&#x00EF;ve pluripotency in mouse embryonic stem cells, revealing the requirement for certain motifs in these systems.

Formal Analysis of Network Motifs Links Structure to Function in Biological Programs