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

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.