Fibration symmetries uncover the building blocks of biological networks

The success of symmetries in explaining the physical world, from general relativity to the standard model of particle physics and all phases of matter, raises the question of why the same concept could not be equally applied to explain emergent properties of biological systems.

We found that genetic networks exhibit fibration symmetry, which have never been observed in physical systems. We were able to deconstruct the network into synchronized parts, which gave us an opportunity to study genetic networks in a novel way and uncover their building blocks based on the function rather than the statistical significance. Further, we were able to classify the building blocks into topological classes of input trees characterized by integer branching ratios and complex topologies with golden ratios of Fibonacci sequences representing cycles in the network. From this idea we show that the core functional logic of discovered genetic circuits arises from a fundamental symmetry breaking of the interactions of the biological network. Observed genetic circuits, ubiquitous across species, are surprising analogues to the emblematic circuits of solid-state electronics: starting from the transistor and progressing to ring oscillators, current-mirror circuits to toggle switches and flip-flops.