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

Posfai, A, McCandlish, DM, Kinney, JB (April 2025) Symmetry, gauge freedoms, and the interpretability of sequence-function relationships. Physical Review Research, 7 (2). ISSN 2643-1564

PDF 10.1103.PhysRevResearch.7.023005.pdf - Published Version Available under License Creative Commons Attribution. Download (1MB)

Abstract

Quantitative models that describe how biological sequences encode functional activities are ubiquitous in modern biology. One important aspect of these models is that they commonly exhibit gauge freedoms, i.e., directions in parameter space that do not affect model predictions. In physics, gauge freedoms arise when physical theories are formulated in ways that respect fundamental symmetries. However, the connections that gauge freedoms in models of sequence-function relationships have to the symmetries of sequence space have yet to be systematically studied. In this work we study the gauge freedoms of models that respect a specific symmetry of sequence space: the group of position-specific character permutations. We find that gauge freedoms arise when model parameters transform under redundant irreducible matrix representations of this group. Based on this finding, we describe an "embedding distillation"procedure that enables both analytic calculation of the number of independent gauge freedoms and efficient computation of a sparse basis for the space of gauge freedoms. We also study how parameter transformation behavior affects parameter interpretability. We find that in many (and possibly all) nontrivial models, the ability to interpret individual model parameters as quantifying intrinsic allelic effects requires that gauge freedoms be present. This finding establishes an incompatibility between two distinct notions of parameter interpretability. Our work thus advances the understanding of symmetries, gauge freedoms, and parameter interpretability in models of sequence-function relationships.

Item Type:	Paper
Subjects:	bioinformatics bioinformatics > genomics and proteomics bioinformatics > computational biology
CSHL Authors:	Posfai, Anna McCandlish, David Kinney, Justin B.
Communities:	CSHL labs > Kinney lab CSHL labs > McCandlish lab
SWORD Depositor:	CSHL Elements
Depositing User:	CSHL Elements
Date:	1 April 2025
Date Deposited:	14 Apr 2025 12:42
Last Modified:	14 Apr 2025 12:42
Related URLs:	Publisher
URI:	https://repository.cshl.edu/id/eprint/41849

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