Resonance Assignment of the NMR Spectra of Disordered Proteins Using a Multi-objective Non-dominated Sorting Genetic Algorithm

A multi-objective genetic algorithm is introduced to predict the assignment of protein solid-state NMR (SSNMR) spectra with partial resonance overlap and missing peaks due to broad linewidths, molecular motion, and low sensitivity. This non-dominated sorting genetic algorithm II (NSGA-II) aims to identify all possible assignments that are consistent with the spectra and to compare the relative merit of these assignments. Our approach is modeled after the recently introduced Monte-Carlo simulated-annealing (MC/SA) protocol, with the key difference that NSGA-II simultaneously optimizes multiple assignment objectives instead of searching for possible assignments based on a single composite score. The multiple objectives include maximizing the number of consistently assigned peaks between multiple spectra ("good connections"), maximizing the number of used peaks, minimizing the number of inconsistently assigned peaks between spectra ("bad connections"), and minimizing the number of assigned peaks that have no matching peaks in the other spectra ("edges"). Using six SSNMR protein chemical shift datasets with varying levels of imperfection that was introduced by peak deletion, random chemical shift changes, and manual peak picking of spectra with moderately broad linewidths, we show that the NSGA-II algorithm produces a large number of valid and good assignments rapidly. For high-quality chemical shift peak lists, NSGA-II and MC/SA perform similarly well. However, when the peak lists contain many missing peaks that are uncorrelated between different spectra and have chemical shift deviations between spectra, the modified NSGA-II produces a larger number of valid solutions than MC/SA, and is more effective at distinguishing good from mediocre assignments by avoiding the hazard of suboptimal weighting factors for the various objectives. These two advantages, namely diversity and better evaluation, lead to a higher probability of predicting the correct assignment for a larger number of residues. On the other hand, when there are multiple equally good assignments that are significantly different from each other, the modified NSGA-II is less efficient than MC/SA in finding all the solutions. This problem is solved by a combined NSGA-II/MC algorithm, which appears to have the advantages of both NSGA-II and MC/SA. This combination algorithm is robust for the three most difficult chemical shift datasets examined here and is expected to give the highest-quality de novo assignment of challenging protein NMR spectra.