Förster Resonance Energy Transfer (FRET)

Dipole–dipole energy transfer rate ∝ 1/r⁶ — a molecular ruler for nanoscale distances

FRET efficiency E
Transfer rate k_T
Donor lifetime τ_DA
Acceptor emission

Physics

FRET efficiency: E = 1/(1 + (r/R₀)⁶)

Förster radius: R₀⁶ = (9000·κ²·Q_D·J·ln10)/(128π⁵n⁴N_A)

Transfer rate: k_T = (1/τ_D)·(R₀/r)⁶

The (R₀/r)⁶ dependence makes FRET exquisitely sensitive to distances in the 1–10 nm range — the scale of protein domains, nucleic acid structures, and molecular machines. κ² = ⅔ for freely rotating dipoles (isotropic average).

Applications: protein folding, DNA hybridisation, live-cell imaging, single-molecule experiments.