Symmetry, gauge freedoms, and the interpretability of sequence-function relationships.

Gauge freedoms-diections in parameter space that do not affect model predictions-are ubiquitous in mathematical models of biological sequence-function relationships. But in contrast to theoretical physics, where gauge freedoms play a central role, little is understood about the mathematical properties of gauge freedoms in models of sequence-function relationships. Here we identify a connection between specific symmetries of sequence space and the gauge freedoms present in a large class of commonly used models for sequence-function relationships. We show that this connection can be used to perform useful mathematical computations, and we discuss the impact of model transformation properties on parameter interpretability. The results fill a major gap in the understanding of quantitative sequence-function relationships.