We present a combined quantum mechanics/molecular mechanics (QM/MM) molecular dynamics–statistical approach for the interpretation of nuclear magnetic resonance (NMR) chemical shift patterns in phycocyanobilin (PCB). These were originally associated with colour tuning upon photoproduct formation in red/green-absorbing cyanobacteriochrome AnPixJg2 and red/far-red-absorbing phytochrome Cph1Δ2. We pursue an indirect approach without computation of the absorption frequencies since the molecular geometry of cofactor and protein are not accurately known. Instead, we resort to a heuristic determination of the conjugation length in PCB through the experimental NMR chemical shift patterns, supported by quantum chemical calculations. We have found a characteristic correlation pattern of 13C chemical shifts to specific bond orders within the π-conjugated system, which rests on the relative position of carbon atoms with respect to electron-withdrawing groups and the polarisation of covalent bonds. We propose the inversion of this regioselective relationship using multivariate statistics and to apply it to the known experimental NMR chemical shifts in order to predict changes in the bond alternation pattern. Therefrom the extent of electronic conjugation, and eventually the change in absorption frequency, can be derived. In the process, the consultation of explicit mesomeric formulae plays an important role to qualitatively account for possible conjugation scenarios of the chromophore. While we are able to consistently associate the NMR chemical shifts with hypsochromic and bathochromic shifts in the Pg and Pfr, our approach represents an alternative method to increase the explanatory power of NMR spectroscopic data in proteins.
Real-time Prediction of 1H and 13C Chemical Shifts with DFT accuracy using a 3D Graph Neural Network
