Not sure about polynomials, but how about "Genetic Regulatory Networks that count to 3" [1]. One of the interesting, counter-intuitive highlights from the paper

Not sure about polynomials, but how about "Genetic Regulatory Networks that count to 3" [1]. One of the interesting, counter-intuitive highlights from the paper: "Counting to 2 requires very different network design than counting to 3." [1] https://pubmed.ncbi.nlm.nih.gov/23567648 https://pubmed.ncbi.nlm.nih.gov/23567648