Unified Model for Photophysical and Electro-Optical Properties of Green Fluorescent Proteins

Abstract

Green fluorescent proteins (GFPs) have become indispensable imaging and optogenetic tools. Their absorption and emission properties can be optimized for specific applications. Currently, no unified framework exists to comprehensively describe these photophysical properties, namely the absorption maxima, emission maxima, Stokes shifts, vibronic progressions, extinction coefficients, Stark tuning rates, and spontaneous emission rates, especially one that includes the effects of the protein environment. In this work, we study the correlations among these properties from systematically tuned GFP environmental mutants and chromophore variants. Correlation plots reveal monotonic trends, suggesting that all these properties are governed by one underlying factor dependent on the chromophore’s environment. By treating the anionic GFP chromophore as a mixed-valence compound existing as a superposition of two resonance forms, we argue that this underlying factor is defined as the difference in energy between the two forms, or the driving force, which is tuned by the environment. We then introduce a Marcus–Hush model with the bond length alternation vibrational mode, treating the GFP absorption band as an intervalence charge transfer band. This model explains all of the observed strong correlations among photophysical properties; related subtopics are extensively discussed in the Supporting Information. Finally, we demonstrate the model’s predictive power by utilizing the additivity of the driving force. The model described here elucidates the role of the protein environment in modulating the photophysical properties of the chromophore, providing insights and limitations for designing new GFPs with desired phenotypes. We argue that this model should also be generally applicable to both biological and nonbiological polymethine dyes.

Four resonance structures elucidate double-bond isomerisation of a biological chromophore

“…This energy difference was implicated to explain all strong correlations of properties among a large number of systematically tuned GFP variants. 69 We note that the chargetransfer GFP model of Boxer and co-workers 69 is consistent with our computational results for the anionic pCTM À except that it does not invoke the QnBR and PhBR structures of pHBDI À . By analogy to pCTM À , we suggest that the energies and properties of the QnBR and PhBR resonance forms should be considered when addressing the S 1 PES of pHBDI À in GFPs, in particular its photoactivation.…”

“…Comparison of our findings and conclusions to the previously published computational and theoretical results characterizing other biological chromophores identifies many common features. In particular, our model derived from the high-level quantumchemistry calculations in its essence is similar to a model proposed by Boxer and co-workers 69,76 explaining spectral properties of systematically mutated GFP proteins. Yet, our model extends Boxer's model to the twisted geometries and invokes BR structures to describe the S 1 state properties.…”

“…Similar to pCTM À , the anionic p-hydroxybenzylideneimidazolinole (pHBDI À ) chromophore of GFPs is described by resonance interactions of the PhCS and QnCS forms coupled along the BLA reaction coordinate. 68,69 Recently, Boxer and co-workers 69 suggested that the energy difference of the PhCS and QnCS forms can serve as a linear scale for quantitative prediction of the GFP photophysical properties using a small number of parameters intrinsic to the pHBDI À chromophore. This energy difference was implicated to explain all strong correlations of properties among a large number of systematically tuned GFP variants.…”

Devising Efficient Red‐Shifting Strategies for Bioimaging: A Generalizable Donor‐Acceptor Fluorophore Prototype

“…have applied Marcus‐Hush theory (generally treating charge‐transfer processes) to account for correlations between photophysical properties of chromophores in fluorescent protein environments, including the absorption and emission maxima, Stokes shifts, extinction coefficients, vibronic couplings, etc. . This adapted theory treats the anionic GFP chromophore as a mixing of two resonance forms (P form and I form, with the negative charge on the oxygen atoms at the opposite ends of the chromophore in Figure a) that are referred to as diabatic states (not energy eigenstates), such that the adiabatic states (S 0 and S 1 , energy eigenstates) and all the corresponding photophysical properties can be derived and compared with experimental observables (Figure ).…”

“…With such an effective two‐state model for characterization and rational design, attaching EDGs/EWGs to the P‐ring is predicted to destabilize/stabilize the charge on P‐ring and decrease/increase the driving force, which consequently red‐shifts/blue‐shifts the absorption. On the other hand, introduction of EWGs to the I‐ring stabilizes I form more than P form, leading to a decreased driving force and hence a red‐shifted absorption.…”