Lateral diffusion coefficients in membranes measured by resonance energy transfer and a new algorithm for diffusion in two dimensions

We describe measurements of lateral diffusion in membranes using resonance energy transfer. The donor was a rhenium (Re) metal-ligand complex lipid, which displays a donor decay time near 3μs. The long donor lifetime resulted in an ability to measure lateral diffusion coefficient below 10^-8 cm²/S. The donor decay data were analyzed using a new numerical algorithm for calculation of resonance energy transfer for donors and acceptors randomly distributed in two dimensions. An analytical solution to the diffusion equation in two dimensions is not known, so the equation was solved by the relaxation method in Laplace space. This algorithm allows the donor decay in the absence cf energy transfer to be multiexponential. The simulations show that mutual lateral diffusion coefficients of the donor and acceptor on the order of 10^-8 cm²/S are readily recovered from the frequency-domain data with donor decay times on the microsecond timescale. Importantly, the lateral diffusion coefficients and acceptor concentrations can be recovered independently despite correlation between these parameters. This algorithm was tested and verified using the donor decays of a long lifetime rhenium lipid donor and a Texas red-lipid acceptor. Lateral diffusion coefficients ranged from 4.4 × 10^-9 cm²/S in 1,2-dimyristoyl-sn-glycero-3-[phospho-rac-(1-glycerol)] (DMPG) at 10°C to 1.7 × 10^-7 cm²/S in 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC) at 35°C. These results demonstrated the possibility of direct measurements of lateral diffusion coefficients using microsecond decay time luminophores.