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 FRET Experiments |
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FRET Experiments
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Nicola Lima and
Helmut Grubmüller
Single-molecule Förster Resonance Energy Transfer (smFRET) measurements use the non-radiative transfer of energy from a donor to an acceptor dye. By monitoring the relative fluorescence intensities from the two dyes, the energy transfer efficiency can be evaluated for individual molecules. The transfer efficiency is commonly employed to determine the interdye distance. This method has emerged as a powerful biophysical tool providing a sensitive 10-100 Å distance reporter to investigate biological structures and functions. Moreover with the development of time-resolved (tr) experiments it is now possible to extract information on the dynamics of a system. Ligand-receptor interactions, conformational changes, protein folding kinetics, and translocations of genes are only some of the many issues that can be addressed.
However, the extraction of structural information from tr-smFRET experiments is not straightforward. Several assumptions founded on the isotropies of the dipoles and the uncorrelated motion of the dyes don’t help to shed light on these experiments. A first-principle Molecular Dynamics (MD) simulation with atomistic details and explicit solvent would enable to review these assumptions and to provide more accurate interpretations at the molecular level. To this end we developed a theoretical approach for the interpretation of FRET experiments: a series of steps to derive FRET efficiency values from MD simulations whose comparison with experimental results provides additional information on the tested system.
According to Förster theory [1] the FRET efficiency, E, depends on the inverse sixth power of the distance between the two chromophores, R, as described by
 (1)
where R0 is the Förster distance, i.e., the distance at which 50% of the excitation energy of the donor is transferred to the acceptor, and it is defined by
 (2)
where QD is quantum yield of the donor in the absence of the acceptor, J is the overlap integral, NAV is the Avogadro’s number, n is the index of refraction of the medium in which the donor and the acceptor are embedded, and κ2 is the orientation factor. κ2 is defined as
 (3)
where θDA is the angle between the emission transition dipole of the donor and the absorption transition dipole of the acceptor, and θD and θA are the angles between these dipoles and the line connecting the donor and the acceptor dyes. All the parameters but κ2 introduced in Eq. 2 can be considered constant during a FRET experiment, so that it’s the evaluation of κ2 the key step if we want to relate distances with FRET efficiencies.
As testing system we studied a series of polyproline chains with two dyes, one donor and one acceptor, attached to their ends. Polyproline chains in water solution are stable in a type II helix, that means all the peptide bonds are in the trans conformation. In Fig. 1 it is reported by way of example the structure containing a poly-20-proline chain.
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Fig. 1: Poly-20-proline molecular structure with Alexa 488 (green) and Alexa 594 (red) dyes and their linkers. Water molecules and ions have been omitted for clarity.
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We simulated the aforementioned systems with first-principle classical MD simulations with atomistic details, explicit solvent, and a customized OPLS-AA force field to obtain relative distances and orientations in time between the two dyes. With the values of the relative angles, and thanks to Eq. 3, it was possible to calculate the orientation factor κ2 and subsequently the Förster radius R0 (see Eq. 2). Including the knowledge of relative distances we can obtain FRET efficiency values through Eq. 1. In Fig. 2 we report the theoretical E values for a poly-15-proline systems compared with experimental results made by B. Schuler et al. [2].
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Fig. 2: Comparison between transfer efficiency values. Histograms: theoretical data obtained through MD simulations on a poly-15-proline chain. Black solid line: experimental data for a poly-14-proline chain.
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References
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- T. Förster. Zwischenmolekulare Energiewanderung und Fluoreszenz. Ann. Physik 2, 55-75 (1948)
- B. Schuler, E. A. Lipman, P. J. Steinbach, M. Kumke and W. A. Eaton. Polyproline and the “spectroscopic ruler” revisited with single molecule fluorescence. Proc. Natl. Acad. Sci. USA 102, 2754-2759 (2005)
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