Chromophore–Protein Coupling beyond Nonpolarizable Models: Understanding Absorption in Green Fluorescent Protein

Abstract

The nature of the coupling of the photoexcited chromophore with the environment in a prototypical system like green fluorescent protein (GFP) is to date not understood, and its description still defies state-of-the-art multiscale approaches. To identify which theoretical framework of the chromophore-protein complex can realistically capture its essence, we employ here a variety of electronic-structure methods, namely, time-dependent density functional theory (TD-DFT), multireference perturbation theory (NEVPT2 and CASPT2), and quantum Monte Carlo (QMC) in combination with static point charges (QM/MM), DFT embedding (QM/DFT), and classical polarizable embedding through induced dipoles (QM/MMpol). Since structural modifications can significantly affect the photophysics of GFP, we also account for thermal fluctuations through extensive molecular dynamics simulations. We find that a treatment of the protein through static point charges leads to significantly blue-shifted excitation energies and that including thermal fluctuations does not cure the coarseness of the MM description. While TDDFT calculations on large cluster models indicate the need of a responsive protein, this response is not simply electrostatic: An improved description of the protein in the ground state or in response to the excitation of the chromophore via ground-state or state-specific DFT and MMpol embedding does not significantly modify the results obtained with static point charges. Through the use of QM/MMpol in a linear response formulation, a different picture in fact emerges in which the main environment response to the chromophore excitation is the one coupling the transition density and the corresponding induced dipoles. Such interaction leads to significant red-shifts and a satisfactory agreement with full QM cluster calculations at the same level of theory. Our findings demonstrate that, ultimately, faithfully capturing the effects of the environment in GFP requires a quantum treatment of large photoexcited regions but that a QM/classical model can be a useful approximation when extended beyond the electrostatic-only formulation.

A quantum-mechanical perspective on linear response theory within polarizable embedding

“…For a generalization beyond a few-state model, see Refs. 40,41. Regardless the debated interpretation of this term as a dispersion effect, 39,[42][43][44] a nonresonant excitonic coupling between subsystems 41,45 or a resonant coupling, 46 it is a manifestation of the mutual correlation of the electrons in the subsystems.…”

Introducing QMC/MMpol: Quantum Monte Carlo in Polarizable Force Fields for Excited States

“…26−29 Such a polarizable embedding (QM/MMpol) scheme has been combined with coupled cluster theory (CC), 23,26,30,31 the complete-active-space self-consistent field (CASSCF) method, 32 and time-dependent density functional theory (TDDFT) 27,28,33,34 and has provided a very effective description of excitation energies beyond static multipole models, 23,34−37 allowing the systematic study of different polarization effects induced in the ground state and in response to the excitation of the solute. 15,25 Here, we combine for the first time quantum Monte Carlo (QMC) methods with the reaction field of polarizable dipoles and investigate the performance of QMC/MMpol for the computation of the excitation energies of small solvated molecules, namely, methylenecyclopropene and acrolein in water. The use of QMC to compute electronic excitations has already been extensively validated in the gas phase 21,38−41 and also employed in combination with standard MM methods 17,21,25 and DFT embedding.…”

Exploring the Solvatochromism of Betaine 30 with Ab Initio Tools: From Accurate Gas‐Phase Calculations to Implicit and Explicit Solvation Models

“…Recently,D aday et al performed calculations of the absorption spectrumo ft he green fluorescentp rotein. [93] To reproduce the experimentally observed influenceo ft he environment on the excitation energies, these authors found it necessary not only to combine point charges and polarisable dipolesa tt he CASSCF/MMpol level in the ground-state and the excited-state, but also to add an estimated dispersion-correction term based on the LR TD-DFT results. This inspired us to address the disagreement by similarly adding an empirical dispersion term [Eq.…”