Gaugefixer: overcoming parameter non-identifiability in models of sequence-function relationships

Mathematical models of sequence-function relationships are widely used in computational biology. A key challenge when interpreting these models is that many different choices for model parameters can encode the same sequence-function relationship. These ambiguities, called "gauge freedoms," must be removed before parameter values can be meaningfully interpreted. Doing this requires imposing additional mathematical constraints on parameter values, a process called "fixing the gauge." We recently developed mathematical methods for fixing the gauge of a large class of commonly used models. The most direct computational implementation of these methods is often impractical, however, because it requires a projection matrix whose size scales quadratically with the number of parameters.

Here we introduce GaugeFixer, a Python package that exploits the mathematical structure of gauge-fixing projections to achieve log-linear scaling in computation time and linear scaling in memory usage. GaugeFixer thus requires orders of magnitude less time and memory than standard matrix multiplication, and can fix the gauge of models having millions of parameters in seconds. To demonstrate its utility, we used GaugeFixer to analyze an empirical fitness landscape for translation initiation in bacteria. This analysis revealed striking similarities (but also fine-scale differences) in ribosome-binding preferences at different positions relative to the start codon, thereby aiding the interpretation of this otherwise unwieldy landscape.

GaugeFixer thus fills an important gap in the computational tools available for interpreting quantitative models of sequence-function relationships.