Symmetry reduction from D2 tetramer to C2 dimer: group-theoretic and thermodynamic modeling of enzyme catalytic efficiency

A mathematical framework is presented to quantify the relationship between quaternary-structure symmetry, free energy, and catalytic efficiency during the transition from aD2-symmetric tetramer to aC2-symmetric dimer, exemplified with LDHA. The approach constructs explicitD2representations on subunit and interface feature spaces, derives projection operators to decompose operators and data into irreducible-representation components, and computes symmetry-resolved free-energy differences via Gaussian/statistical and harmonic/Hessian methods. Connections to kinetics are made through transition state theory with channel degeneracy. Reproducible algorithms and a workflow for mapping FoldX outputs into irrep-resolved diagnostics and efficiency predictions are provided.