FRET calculations

PT Pablo Trigo-Mourino TT Thomas Thestrup OG Oliver Griesbeck CG Christian Griesinger SB Stefan Becker

This protocol is extracted from research article:

Dynamic tuning of FRET in a green fluorescent protein biosensor

**
Sci Adv**,
Aug 7, 2019;
DOI:
10.1126/sciadv.aaw4988

Dynamic tuning of FRET in a green fluorescent protein biosensor

Procedure

The orientation factor, κ^{2}, can be extracted from structural information as follows$${\mathrm{\kappa}}^{2}={(\text{cos}{\mathrm{\theta}}_{\mathrm{T}}-3\text{cos}{\mathrm{\theta}}_{\mathrm{D}}\text{cos}{\mathrm{\theta}}_{\mathrm{A}})}^{2}$$(1)where θ_{T} is the angle between the emission transition dipole of the donor and the absorption transition dipole of the acceptor; θ_{D} and θ_{A} are the angles between these dipoles and the vector, *r*, joining the donor and the acceptor fluorophores (*27*). The orientation of the transition dipole moments relative to the *C* → *O* bond vector (ω) in degrees$${\mathrm{\omega}}_{\mathrm{D}}=73\xb0$$$${\mathrm{\omega}}_{\mathrm{A}}=76\xb0$$were taken from Ansbacher *et al.* (*15*), and the angular parameters were extracted from the crystallographic coordinates, in angular units$${\mathrm{\theta}}_{\mathrm{T}}=152.95\xb0$$$${\mathrm{\theta}}_{\mathrm{D}}=149.17\xb0$$$${\mathrm{\theta}}_{\mathrm{A}}=26.79\xb0$$

The detailed calculations are explained in data file S1. The overlap integral, *J*(λ), was calculated from the experimental absorbance and emission spectra of the isolated cpVenus and mCerulean3 domains, respectively (fig. S5), with a Python script included as supplementary information. The *J*(λ) was determined to be 2.052 × 10^{15} M^{−1} cm^{−1} nm^{4}, as follows$$J(\mathrm{\lambda})={\displaystyle \underset{0}{\overset{\infty}{\int}}}{F}_{\mathrm{D}}(\mathrm{\lambda}){\mathrm{\epsilon}}_{\mathrm{A}}(\mathrm{\lambda}){\mathrm{\lambda}}^{4}d\mathrm{\lambda}=\frac{{\displaystyle {\int}_{0}^{\infty}}{F}_{\mathrm{D}}(\mathrm{\lambda}){\mathrm{\epsilon}}_{\mathrm{A}}(\mathrm{\lambda}){\mathrm{\lambda}}^{4}d\mathrm{\lambda}}{{\displaystyle {\int}_{0}^{\infty}}{F}_{\mathrm{D}}(\mathrm{\lambda})d\mathrm{\lambda}}$$(2)where *F*_{D}(λ) is the normalized fluorescence intensity of the donor in the wavelength range λ to λ + Δλ. ε_{A}(λ) is the extinction coefficient of the acceptor at λ.

The Förster distance, *R*_{0}, can be calculated from the previously derived experimental parameters$${R}_{0}=0.211{({\mathrm{\kappa}}^{2}{n}^{-4}{Q}_{\mathrm{D}}J(\mathrm{\lambda}))}^{1/6}$$(3)where *Q*_{D} (0.87) is the quantum yield of the donor in the absence of acceptor (*4*) and *n*, (1.33) the refractive index of the aqueous medium.

Last, the efficiency of energy transfer, *E*, can be calculated as the ratio of the transfer rate to the total decay rate of the donor in the presence of acceptor$$E=\frac{{R}_{0}^{6}}{{R}_{0}^{6}+{r}^{6}}$$(4)

Following this procedure, the FRET efficiency was determined to be *E* = 0.979, from the crystallographic structure of Twitch-2B. The equivalent calculation performed with the structure of the mutant Twitch-6 gives an *E* = 0.983 (see data files S1 and S2).

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