Allosteric regulation is found across all domains of life, yet we still lack
simple, predictive theories that directly link the experimentally tunable
parameters of a system to its input-output response. To that end, we present a
general theory of allosteric transcriptional regulation using the
Monod-Wyman-Changeux model. We rigorously test this model using the ubiquitous
simple repression motif in bacteria by first predicting the behavior of strains
that span a large range of repressor copy numbers and DNA binding strengths and
then constructing and measuring their response. Our model not only accurately
captures the induction profiles of these strains but also enables us to derive
analytic expressions for key properties such as the dynamic range and
[EC50​]. Finally, we derive an expression for the free energy of allosteric
repressors which enables us to collapse our experimental data onto a single
master curve that captures the diverse phenomenology of the induction profiles.Comment: Substantial revisions for resubmission (3 new figures, significantly
elaborated discussion); added Professor Mitchell Lewis as another author for
his continuing contributions to the projec