A major ambition of systems biology is to uncover the building blocks of biological networks to shed light on how these networks are assembled from their constitutive units to regulate their function. In this regard, some simple network motifs have been shown to appear more often than they would by pure chance, a regularity that has been interpreted as evidence that these motifs are basic building blocks of biological networks. While the discovery of network motifs has had a major impact on systems biology, whether these motifs may have a functional role remains controversial. In this proposal we advance a different approach to identify the minimal building blocks of biological networks, by identifying, from a theoretical and principled approach through the theory of symmetry fibration and symmetry groups, what topological properties guarantee that a circuit will organize into minimal forms of coherent function. In the present project we will develop new theory to understand: (i) the basic building blocks of biological networks ranging from genetic networks to the connectome using the concept of network symmetry, and (ii) the funtional relation between these symmetric building blocks to neural synchronization and gene coexpression profiles. Intellectual Merit: Our strategy begins by 1) identifying a constructive procedure to build biological building blocks from principles (symmetry) considerations, 2) showing how these circuits have rich dynamics which are signatures of core biological computations, and 3) show that these symmetries can be investigated in a systematic way to understand and build circuits that are surprisingly close analogues to the more emblematic and founding developments of solid-state electronics and computer memory. We propose to follow three Specific Aims: Aim 1: Theory of fibration symmetry and symmetry groups to identify building blocks across species and biological networks. Aim 2: Validation of building blocks against experimental data. Aim 3: Validation of building blocks against all alternative network theories (from network motif, to modularity and clustering, to scale-free theory, to small worlds and all network centralities). Broader Impacts: This is an interdisciplinary project that synergistically combines a new collaboration with theoretical expertise in network theory (Makse), systems biology (Liebermeister) and neuroscience (Zimmer). The project will develop core concepts from mathematics, statistics, group theory and advanced graph theoretical methods to understand the fundamental building blocks of biological networks and how these building blocks are related to function. If confirmed, our falsifiable hypothesis will have broader scientific impacts at the interface of abstract algebra, systems biology and neuroscience. Further broader impacts will include training of STEM students and postdocs at the interface between math and biology through curriculum development and rotations of students across different specialized international labs ranging from theory, experimental validation and biology. The PI will emphasize recruiting underrepresented minorities from the large population of minorities in the CUNY system. Additional broader impacts include data sharing of a network toolbox to identify the building blocks of networks offered through a dedicated website that will offer a library of building blocks across all biological networks and species studied in the project.