Information Integration and Energy Expenditure in Gene Regulation.

The quantitative concepts used to reason about gene regulation largely derive from bacterial studies. We show that this bacterial paradigm cannot explain the sharp expression of a canonical developmental gene in response to a regulating transcription factor (TF). In the absence of energy expenditure, with regulatory DNA at thermodynamic equilibrium, information integration across multiple TF binding sites can generate the required sharpness, but with strong constraints on the resultant "higher-order cooperativities." Even with such integration, there is a "Hopfield barrier" to sharpness; for n TF binding sites, this barrier is represented by the Hill function with the Hill coefficient n. If, however, energy is expended to maintain regulatory DNA away from thermodynamic equilibrium, as in kinetic proofreading, this barrier can be breached and greater sharpness achieved. Our approach is grounded in fundamental physics, leads to testable experimental predictions, and suggests how a quantitative paradigm for eukaryotic gene regulation can be formulated.