Figure 8. Quantities (black) and parameters (blue) in the model for time-resolved transition metal ion fluorescence resonance energy transfer (tmFRET).

(A) Plot of fluorescence lifetimes in the time domain for a donor fluorophore with two exponential components with time constants (${\displaystyle {\tau }_{D_1}}$ and ${\displaystyle {\tau }_{D_2}}$) and relative amplitude (${\sigma }_1$). (B) Plot of the FRET efficiency (E) as a function of distance (${\displaystyle r}$) showing the characteristic distance for the donor-acceptor pair(${\displaystyle R_0}$). (C) Plot of a distribution of donor-acceptor distances ${\displaystyle P\left(r\right)}$ with two Gaussian components with means (${\displaystyle {\overline{r}}_1}$ and ${\displaystyle {\overline{r}}_2}$), standard deviations (${\displaystyle {\sigma }_1}$ and ${\displaystyle {\sigma }_2}$), and relative amplitude of the second component (${\displaystyle A_2}$). The fraction of donor only (${\displaystyle f_D}$) was modeled as a narrow Gaussian with a mean distance of 150 Å and a standard deviation of 0.1 Å, too far to exhibit any detectable FRET. (D) Plot of the imaginary (${\displaystyle N_{\omega }}$) and real (${\displaystyle D_{\omega }}$) components of the measured, corrected, and background fluorescence response as a function of the modulation frequency ($\omega$) where $f_B$ is the fraction of the fluorescence intensity due to background. (E) Plot of the phase delay ${\displaystyle ({\phi }_{\omega })}$ and modulation ratio ${\displaystyle (m_{\omega })}$ of the measured and corrected fluorescence response as a function of the modulation frequency ($\omega$) where $t_0$ is the time shift of the instrument response function.

Figure 8—figure supplement 1. Spectral overlap between donors and acceptors for Acd experiments.

Emission spectra in response to excitation at 370 nm normalized to the fluorescence intensity measured at 465 nm (left axis) and absorption spectra (right axis) are shown for donors and acceptors, respectively, in KBT. Each emission spectrum represents the mean of 5–6 experiments. The color scheme is as labeled in the figure.

Figure 8—figure supplement 2. Measuring fluorescence resonance energy transfer (FRET) in the time domain and frequency domain.

Simulated FRET depicted in the time and frequency domains for a donor with a τ = 15 ns lifetime in the absence of acceptor and a τ = 3 s lifetime in the presence of acceptor. (A) Simulated emission of a donor in the absence (blue) and presence (red) of acceptor in response to pulsed excitation (black). (B) Simulated emission of a donor in the absence (blue, D) and presence (red, DA) of acceptor in response to 50 MHz modulated excitation (black) shown in the time domain. The phase delay is given by φ, and the modulation ratio is given by m. (C) Simulated emission of a donor in the absence (blue) and presence (red) of acceptor in response to modulated excitation from 10 to 200 MHz shown in the frequency domain. The phase delay is given by φ, and the modulation ratio is given by m. The points indicate φ and m in response to 50 MHz modulated excitation.