# The Energetics of Molecular Adaptation in Transcriptional Regulation

## TL;DR

This study introduces a framework linking mutations in an allosteric transcriptional repressor to changes in free energy, enabling prediction of gene expression responses and epistatic interactions through a parameter-based model.

## Contribution

The paper presents a novel energetic framework that quantitatively connects mutations to functional responses in transcriptional regulation, validated with experimental data on LacI mutants.

## Key findings

- Mutations can be categorized by their energetic effects with characteristic curves.
- Single mutations alter specific model parameters, such as DNA affinity or allosteric response.
- Double mutant induction profiles can be accurately predicted from single mutant data.

## Abstract

Mutation is a critical mechanism by which evolution explores the functional landscape of proteins. Despite our ability to experimentally inflict mutations at will, it remains difficult to link sequence-level perturbations to systems-level responses. Here, we present a framework centered on measuring changes in the free energy of the system to link individual mutations in an allosteric transcriptional repressor to the parameters which govern its response. We find the energetic effects of the mutations can be categorized into several classes which have characteristic curves as a function of the inducer concentration. We experimentally test these diagnostic predictions using the well-characterized LacI repressor of Escherichia coli, probing several mutations in the DNA binding and inducer binding domains. We find that the change in gene expression due to a point mutation can be captured by modifying only a subset of the model parameters that describe the respective domain of the wild-type protein. These parameters appear to be insulated, with mutations in the DNA binding domain altering only the DNA affinity and those in the inducer binding domain altering only the allosteric parameters. Changing these subsets of parameters tunes the free energy of the system in a way that is concordant with theoretical expectations. Finally, we show that the induction profiles and resulting free energies associated with pairwise double mutants can be predicted with quantitative accuracy given knowledge of the single mutants, providing an avenue for identifying and quantifying epistatic interactions.