Infinite Average Lifetime of an Unstable Bright State in the Green Fluorescent Protein

The time evolution of the fluorescence intensity emitted by well-defined ensembles of green fluorescent proteins has been studied by using a standard confocal microscope. In contrast with previous results obtained in single-molecule experiments, the photobleaching of the ensemble is well described by a model based on Lévy statistics. By assuming the presence of thermally activated barriers, this simple model allows us to obtain information about their height distribution.

Figure 1

Normalized fluorescence intensity $F(t)/F(t\to 0)$ (solid line) emitted by a well-defined ensemble of GFPuv ($\sim 200000$ proteins) as a function of the total illumination time $t$. Experimental conditions: $I=0.96\mathrm{MW}/{\mathrm{cm}}^2$ and $T=290\mathrm{K}$. The dotted line shows the power law used to fit the long-time tail: $(\frac{{\tau }_A}{t}{)}^{\alpha }$ with ${\tau }_A=6.8\mathrm{s}$ and $\alpha =0.73$. For comparison we report also a thermal aging curve obtained at $T=353\mathrm{K}$ (circle) in a fluorimeter together with a dotted-line curve that represents its best exponential fit.

Figure 2

Scheme of the relevant energy levels and coupling constants used to model the aging mechanism of the GFPuv. $|g⟩$ and $|e⟩$ are the electronic ground and excited states of the protein, while $|D⟩$ represents a permanent dark state. $|e⟩$ and $|D⟩$ are separated by a thermally activated barrier of height $E$. $\Gamma$, ${\Gamma }^{\prime }$, and ${\Gamma }_1=\frac{1}{\tau }$ are, respectively, the spontaneous emission, the absorption (and stimulated emission), and the conversion towards the dark state rates.

Figure 3

Barrier height distribution (dotted line) deduced from the experimental signal of Fig. 1 by using the expression (6). The energy scale on the horizontal axis is deduced in the absence of any free parameter. The solid line represents the best exponential fit in the range $E>k_{B}T$.

Figure 4

Parameters (a) $\alpha$ and (b) ${\tau }_A$ as a function of the excitation intensity $I$. Data are obtained by several experimental runs on different GFPuv ensembles. While the logarithmic increase of $\alpha$ is not explained by the theory, the prefactor ${\tau }_A$ [solid circles in (b)] follows an inverse saturation law $A+B/I$ as expected from expression (3). The solid line represents the best fit to this law ($A=3.7\mathrm{s}$ and $B=0.24\mathrm{s}\mathrm{MW}{\mathrm{cm}}^{-2}$).