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From the perfect radial symmetries of radiolarian mineral skeletons to thebroken symmetry of homochirality, the logic of Nature's regularities hasfascinated scientists for centuries. Some of Nature's symmetries are clearlyvisible in morphology and physical structure, whereas others are hidden in thenetwork of interactions among system components. Just as visible symmetries andasymmetries contribute to the system's beauty, might hidden symmetriescontribute to the system's functional harmony? And if so, how? Here wedemonstrate that the interaction networks of biological systems from cellsignaling to cancer display a form of dynamical reflection symmetry that servesto expand their dynamical complexity. The expansion proceeds according toprecise rules regarding the lengths of dynamical cycles, made possible by apeculiar imbalance between excitation and inhibition. To probe the conditionsunder which this reflection symmetry evolves, we use a multi-objective geneticalgorithm to produce networks with long dynamical cycles. We find that localstructural motifs that break the reflection symmetry are deleted in theevolutionary process, providing evidence for symmetry's causal role indynamical complexity. Finally, we identify symmetries in real continuous-valuedscRNA-seq data of gene expression in drug-resistant cancer cells. Broadly, ourwork reveals a class of hidden symmetries in biology, present in the network ofinteractions among system components, and it underscores their functionalimportance. Mathematically simple and computational inexpensive, our approachis applicable to the types of biological data commonly acquired in modernexperiments.

Excitation and inhibition imbalance affects dynamical complexity through symmetries