Dark energy, physical and evolutionary frustration in ankyrin repeat proteins

Federico Caamaño, Diego Ferreiro

Protein Physiology Lab, Departamento de Química Biológica, Universidad de Buenos Aires, Instituto de Química Biológica de la Facultad de Ciencias Exactas y Naturales (IQUIBICEN-CONICET), Buenos Aires, Argentina

Evolution shapes protein sequences by preserving mutations that maintain function, thereby creating evolutionary constraints. These constraints manifest as position-specific amino acid frequencies and correlations between contacting residues. Direct-Coupling Analysis (DCA) uses multiple sequence alignments to derive an evolutionary force field (comprising local fields and pairwise couplings) that assigns an effective energy to sequences.
According to energy landscape theory, proteins must minimize energetic frustration to fold efficiently. Nativefrustration correlates with function and can be measured experimentally or via force fields such as AWSEM. Similarly, evolutionary frustration can be computed using DCA derived energies.
We introduce “Dark Energy” as the difference between the mutational perturbations in the folding and evolutionary energy landscapes. This metric helps localize and quantify evolutionary constraints.
We analyzed 300 ankyrin repeat proteins, computing physical frustration, evolutionary frustration, and Dark Energy to map evolutionary constraints in this family, comparing the established local frustration method with the novel Dark Energy approach.