EGFP oligomers as natural fluorescence and hydrodynamic standards

EGFP oligomers are convenient standards for experiments on fluorescent protein-tagged biomolecules. In this study, we characterized their hydrodynamic and fluorescence properties. Diffusion coefficients D of EGFP1–4 were determined by analytical ultracentrifugation with fluorescence detection and by fluorescence correlation spectroscopy (FCS), yielding 83.4…48.2 μm2/s and 97.3…54.8 μm2/s from monomer to tetramer. A “barrels standing in a row” model agreed best with the sedimentation data. Oligomerization red-shifted EGFP emission spectra without any shift in absorption. Fluorescence anisotropy decreased, indicating homoFRET between the subunits. Fluorescence lifetime decreased only slightly (4%) indicating insignificant quenching by FRET to subunits in non-emitting states. FCS-measured D, particle number and molecular brightness depended on dark states and light-induced processes in distinct subunits, resulting in a dependence on illumination power different for monomers and oligomers. Since subunits may be in “on” (bright) or “off” (dark) states, FCS-determined apparent brightness is not proportional to that of the monomer. From its dependence on the number of subunits, the probability of the “on” state for a subunit was determined to be 96% at pH 8 and 77% at pH 6.38, i.e., protonation increases the dark state. These fluorescence properties of EGFP oligomeric standards can assist interpreting results from oligomerized EGFP fusion proteins of biological interest.


Chapter 1. Simulation of photophysical effects on the autocorrelation curves
Simulations were performed with a home-built FCS simulation software, available as open-source software from https://github.com/jkriege2/FCSSimulator. In brief, this software simulates a simple 3D random walk for several particles in a spherical box with a diameter of 8 µm. The singledirection jump length Δx in each time step Δtsim=1 µs is distributed normally around Δx=0 with an s.d. of 2 sim D t ∆ , where D is the diffusion coefficient fixed to 90, 70, 60, 50 µm²/s for EGFP1, EGFP2, EGFP3 and EGFP4. These values are approximately equal to Dcalc given in Table 1 in the main text. The particle concentration was set to 80 nM. To keep this concentration constant over time, a particle is deleted, when it leaves the simulation box, and a new particle is introduced at a random position at the surface of the box. Depending on the simulated molecule, 1-4 independent fluorophores are assigned to each random walker. Each of these fluorophores can bleach irreversibly and independently with a probability pbleach = Δtsim / τbleach, where τbleach is the 1/e bleach-lifetime at the center of the illumination focus, where the laser intensity is maximal. τbleach is inversely proportional to the laser intensity, so it remains unbleached longer at the borders of the illumination focus. If a bleached (or unbleached) fluorophore leaves the simulation box, the newly created particle that replaces it is in a non-bleached state again. This keeps the average particle number in the simulation box constant, and models an infinite reservoir of intact fluorophores outside the confocal observation volume. This is a good model for a small laser focus (femtoliter volume) in a reservoir (a few hundred microliters of sample in a sample chamber), which is several orders of magnitude larger. Finally, in each step, the detection of fluorescence from all particles in the simulation box is simulated. To this end, a Gaussian detection volume ( ) Here Nabs~6.4 is the number of photons that is absorbed on average by a single fluorophore during Δtsim=1 µs, the fluorescence quantum yield is qfluor = 0.92 and the detection efficiency is qdet = 1. The quantity

( )
Photons N t is accumulated over two subsequent time steps Δtsim, and then the number of detected photons Nphot,det(t) is drawn as a random number from a Poissonian distribution with the accumulated ( ) Photons N t as mean. From this random sequence of detected photons the simulation software then calculates the FCS correlation function: which is then evaluated just as the experimental curves using the software QuickFit 3.0 1 .

Simulation of intensity-dependent bleaching:
According to the above model the bleach-process does not depend on the laser intensity at the position xi(t), yi(t), zi(t) of a fluorophore i. Because bleaching occurs in the excited state of the fluorophore, the above model needs to be modified to account for the number of photons absorbed by a fluorophore at its current position: Then the probability of bleaching, which was initially determined by the average lifetime τbleach of the on-state of a fluorophore, is modified as follows: where fbleach is a dimensionless scaling factor, which was set to 10 for all simulations. This factor simply adapts the range of values of the MDE ( ] ) to a reasonable probability for the simulation, as compared to the case of position-independent bleaching. The same effect could have been reached by altering the lifetime τbleach itself. As we do not interpret the absolute value of τbleach quantitatively, only its relative changes, this does not influence our interpretation of the data.
Simulation of the effect of excitation saturation: In order to simulate the saturation of the fluorescence excitation transition, the sum over all visible fluorophores is modified as follows with a relative saturation intensity αsat 2 : For real fluorophores, the saturation is usually described by the fluorophore's saturation intensity Isat. For the simulations, described herein, the absolute saturation intensity is not important and it is replaced by the dimensionless saturation parameter 0 sat sat I I α = , which determines Isat relative to the maximum illumination intensity I0 = 22 kW/cm 2 in the center of the MDE (corresponding to a laser power of 250 μW at the objective).
Note that all simulations shown in this paper were performed in order to separate the effects of bleaching and saturated excitation, i.e., we always simulated only one of the two effects exclusively. Therefore, there is no saturation-effect in the bleaching process and vice versa. Including such an effect would require the calibration of both the saturation intensity and the bleaching lifetime to real experimental values, which is out of the scope of this paper. Accordingly, we did not interpret the absolute values of the parameters τbleach and 0 sat sat I I α = , and did not relate them to each other quantitatively. However, the parameterization of the simulations was chosen in such a way that the relative changes in τbleach and 0 sat sat I I α = reflect the behavior expected from real experiments, and therefore allow for a comparison with them.

Chapter 2. Generalized calculation of the apparent molecular brightness of FP oligomers having longlived dark states
For a mixture of n different species in an FCS experiment, the mean fluorescence intensity is where Nk is the number of molecules and Ψk is the molecular brightness of the k-th species. The amplitude of the correlation function is ( ) where Napp is the apparent number of molecules in the detection volume, and γ is a factor depending on the geometry of the detection volume. For the sake of simplicity we set γ=1. The denominator of equation (S8) is the square of the mean fluorescence intensity. The apparent molecular brightness is where pk is the fraction of molecules in the k-th state.
For the calculation of the apparent brightness of an FP oligomer, we need the following parameters: 1-p: probability of an FP molecule to be in a non-fluorescent "off" state lasting longer than the diffusion time (τoff>>τdiff) p: probability of an FP molecule to be in the "on" state (involving the fluorescent state, the triplet state and other short-lived dark states having an off-time shorter than τdiff) N: mean number of particles in the detection volume F: mean total fluorescence Ψ: molecular brightness of a single FP (F/N) n: number of subunits in the FP oligomer k: number of FPs in the on state in a given oligomer In an FP n-mer 0, 1, …,n FP molecules can fluoresce. The probability that in an n-mer exactly k FPs are in the "on" state is given by a binomial formula: The brightness of a species with k FPs being in the "on" state is Ψk = kΨ. Example for n=3: Equation ( (S12) Using the relation and considering that the variance of the binomial variable X is we get the following expression for the apparent brightness: The effects of fast photophysical transitions such as triplet formation, which have shorter off-times (2-30 μs) than the diffusion time, average out during the diffusion time, therefore they do not affect the relation between the apparent mean brightness values of the different oligomers.

Calculation of the real number of particles Nreal from Napp and p:
Equation (S8) can also be written in the form: The total number real N of FP oligomers in the detection volume is: (S17)  162-165 (1994).

Supplementary Figure S1
Sedimentation equilibrium centrifugation using fluorescence detection.
The top panels show the radial concentration distributions. Centrifugation was carried out at 7000 (red), 11000 (green) and 18000 rpm (blue). The concentration of EGFP 1 was 150 nM, the concentrations of the other samples were set to yield the same fluorescence intensity. For each EGFP oligomer data recorded at different rotor speeds were globally fitted to single exponentials with fixed baselines (solid lines). The bottom panels present the residuals. M eq values were derived as described.