Analytical Harmonic Vibrational Frequencies for the Green Fluorescent Protein Computed with ONIOM: Chromophore Mode Character and Its Response to Environment

Abstract

A systematic comparison of different environmental effects on the vibrational modes of the 4-hydroxybenzylidene-2,3-dimethylimidazolinone (HBDI) chromophore using the ONIOM method allows us to model how the molecule's spectroscopic transitions are modified in the Green Fluorescent Protein (GFP). ONIOM(QM:MM) reduces the expense of normal mode calculations when computing the majority of second derivatives only at the MM level. New developments described here for the efficient solution of the CPHF equations, including contributions from electrostatic interactions with environment charges, mean that QM model systems of ∼100 atoms can be embedded within a much larger MM environment of ∼5000 atoms. The resulting vibrational normal modes, their associated frequencies, and dipole derivative vectors have been used to interpret experimental difference spectra (GFPI2-GFPA), chromophore vibrational Stark shifts, and changes in the difference between electronic and vibrational transition dipoles (mode angles) in the protein environment.

The mechanism of a green fluorescent protein proton shuttle unveiled in the time-resolved frequency domain by excited state ab initio dynamics

“…5 appear at around 1500 and 1550 cm –1 for the C–O and C–N distances, respectively. From our static harmonic frequency analysis on a GFP reduced model and from previous studies, 15 , 63 – 65 these bands are easily attributed to modes containing C–O and C–N stretching contributions, respectively. In particular, the C–O dynamics are mainly driven by a mode involving a collective bending and deformation motion of the phenolic ring.…”

Wide-dynamic-range kinetic investigations of deep proton tunnelling in proteins

“…The value found for ℓ = 0.78 ( =2.76 is within the error of both the X-ray structure 40 and the I-state density functional theory (DFT) energy minimization 37 , where ~2.7 . The D-A frequency ( 273 cm -1 ) falls well within the range found from the independent Einstein oscillator analysis of the GFP normal modes ( 264-289 cm -1 ).…”

“…The quantity is the mean square Cartesian displacement along the unit vector between the donor and acceptor that is derived from each normal mode ( ) of the protein-chromophore system. The normal modes of GFP in the -state, as determined using hybrid ONIOM(QM:MM) methods 37 , allow us to find the mode-specific value, , for each pair of oxygen atoms shown in red in Fig. 2 …”

Meta‐analysis of uniform scaling factors for harmonic frequency calculations

“…The harmonic approximation 36 is the preferred choice in most vibrational frequency calculations due to its relative computational simplicity, reliability, and affordable scaling with larger systems. 27,[37][38][39][40][41] However, it is well-known that the calculated harmonic frequencies tend to systematically overestimate the experimentally derived fundamental frequencies, limiting the accuracy in the predictions.…”