The orientation factor, κ2, can be extracted from structural information as followsκ2=(cos θT  3 cos θD cos θA)2(1)where θT is the angle between the emission transition dipole of the donor and the absorption transition dipole of the acceptor; θD and θA 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 CO bond vector (ω) in degreesωD=73°ωA=76°were taken from Ansbacher et al. (15), and the angular parameters were extracted from the crystallographic coordinates, in angular unitsθT=152.95°θD=149.17°θA=26.79°

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 × 1015 M−1 cm−1 nm4, as followsJ(λ)=0FD(λ)εA(λ)λ4dλ=0FD(λ)εA(λ)λ4dλ0FD(λ)dλ(2)where FD(λ) is the normalized fluorescence intensity of the donor in the wavelength range λ to λ + Δλ. εA(λ) is the extinction coefficient of the acceptor at λ.

The Förster distance, R0, can be calculated from the previously derived experimental parametersR0=0.211(κ2n4QDJ(λ))1/6(3)where QD (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 acceptorE=R06R06+r6(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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