Composition of Boolean functions restricts biologically permitted logics

    The bipartite nature of genetic regulatory networks means their logics are composed, which severely restricts which ones can show up in life.

    Submitted to Physical Review Letters (2021)

    T. Fink, R. Hannam

    Composition of Boolean functions restricts biologically permitted logics

    We show that composing Boolean functions severely restricts their range of computation. For bipartite systems, where two species depend on each other but not themselves, this heavily constrains the observed behaviour of each species. We apply our insights to gene regulation, where genes interact via transcription factors but only gene-gene interactions are observed. We derive an expression for the number of distinct Boolean functions under composition and show that the fraction of permitted biological logics tends to be very small. We confirm our results with computational enumeration.