Theory of FRET “Spectroscopic Ruler” for Short Distances: Application to Polyproline

Abstract

Förster resonance energy transfer (FRET) is an important mechanism for the estimation of intermolecular distances, e.g., in fluorescent labeled proteins. The interpretations of FRET experiments with standard Förster theory relies on the following approximations: (i) a point-dipole approximation (PDA) for the coupling between transition densities of the chromophores, (ii) a screening of this coupling by the inverse optical dielectric constant of the medium, and (iii) the assumption of fast isotropic sampling over the mutual orientations of the chromophores. These approximations become critical, in particular, at short intermolecular distances, where the PDA and the screening model become invalid and the variation of interchromophore distances, and not just orientations, has a critical influence on the excitation energy transfer. Here, we present a quantum chemical/electrostatic/molecular dynamics (MD) method that goes beyond all of the above approximations. The Poisson-TrEsp method for the ab initio/electrostatic calculation of excitonic couplings in a dielectric medium is combined with all-atom molecular dynamics (MD) simulations to calculate FRET efficiencies. The method is applied to analyze single-molecule experiments on a polyproline helix of variable length labeled with Alexa dyes. Our method provides a quantitative explanation of the overestimation of FRET efficiencies by the standard Förster theory for short interchromophore distances for this system. A detailed analysis of the different levels of approximation that connect the present Poisson-TrEsp/MD method with Förster theory reveals error compensation effects, between the PDA and the neglect of correlations in interchromophore distances and orientations on one hand and the neglect of static disorder in orientations and interchromophore distances on the other. Whereas the first two approximations are found to decrease the FRET efficiency, the latter two overcompensate this decrease and are responsible for the overestimation of the FRET efficiency by Förster theory.

Visualizing conformational dynamics of proteins in solution and at the cell membrane

“…We chose L-Anap, a derivative of prodan, because of its small size (about the same as the amino acid tryptophan) and useful spectral properties. By introducing a fluorophore as the side-chain of an amino acid, we eliminated the need for a linker whose distance from the protein backbone and flexibility reduces the accuracy and empirical sensitivity of FRET ( Best et al, 2007 ; Schuler et al, 2005 ; Taraska et al, 2009b ; Sobakinskaya et al, 2018 ). L-Anap is therefore useful as a tmFRET donor for distance measurements.…”

Exploring hydrophobicity limits of polyproline helix with oligomeric octahydroindole‐2‐carboxylic acid

“…The latter may be quite complex, as these may be described in terms of n→π* donation, 25 dipole-dipole interaction, 26 carbonyl-carbonyl interaction, 27 and the cascade effect. 28,29 The geometric simplicity of this secondary structure (1 turn = 3.0 residues ≈ 9.0 Å) is also well appreciated and has been used as a molecular ruler for spectroscopic distance measurements [30][31][32] and for a variety of other studies based on molecular distance control. 33 Polymeric and oligomeric proline sequences serve as good models for studying features of P II conformation, since the tertiary amide bond formed by this amino acid opposes formation of regular hydrogen bond-based structure.…”

Electronic energy transfer in biomacromolecules

“…Several groups have reported more elaborated approaches to describe EET in the intermediate averaging regime, in which Markov chain sampling techniques are used to model D (and eventually A) fluorescence decays in addition to FRET efficiencies from electronic coupling trajectories. 22,24,25,28,29,38 In Scheme 1, we illustrate as an example the approach proposed by Grubmüller and coworkers. 25 In this scheme, first a random donor excitation instance is chosen from the trajectory.…”