  From the perfect radial symmetries of radiolarian mineral skeletons to the
broken symmetry of homochirality, the logic of Nature's regularities has
fascinated scientists for centuries. Some of Nature's symmetries are clearly
visible in morphology and physical structure, whereas others are hidden in the
network of interactions among system components. Just as visible symmetries and
asymmetries contribute to the system's beauty, might hidden symmetries
contribute to the system's functional harmony? And if so, how? Here we
demonstrate that the interaction networks of biological systems from cell
signaling to cancer display a form of dynamical reflection symmetry that serves
to expand their dynamical complexity. The expansion proceeds according to
precise rules regarding the lengths of dynamical cycles, made possible by a
peculiar imbalance between excitation and inhibition. To probe the conditions
under which this reflection symmetry evolves, we use a multi-objective genetic
algorithm to produce networks with long dynamical cycles. We find that local
structural motifs that break the reflection symmetry are deleted in the
evolutionary process, providing evidence for symmetry's causal role in
dynamical complexity. Finally, we identify symmetries in real continuous-valued
scRNA-seq data of gene expression in drug-resistant cancer cells. Broadly, our
work reveals a class of hidden symmetries in biology, present in the network of
interactions among system components, and it underscores their functional
importance. Mathematically simple and computational inexpensive, our approach
is applicable to the types of biological data commonly acquired in modern
experiments.
