# Tuning transcriptional regulation through signaling: A predictive theory of allosteric induction

## TL;DR

This paper develops a predictive theoretical framework for allosteric transcriptional regulation using the Monod-Wyman-Changeux model, validated through bacterial repression experiments, enabling precise predictions of gene regulation responses.

## Contribution

The paper introduces a general, predictive theory of allosteric transcriptional regulation that links tunable parameters to input-output responses, validated with experimental data.

## Key findings

- Accurately predicts induction profiles across diverse strains.
- Provides analytic expressions for dynamic range and EC50.
- Derives a free energy expression collapsing data onto a master curve.

## Abstract

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 $[EC_{50}]$. 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.