Correcting for spectral cross-talk in dual-color fluorescence cross-correlation spectroscopy

Abstract

Dual-color fluorescence cross-correlation spectroscopy (dcFCCS) allows one to quantitatively assess the interactions of mobile molecules labeled with distinct fluorophores. The technique is widely applied to both reconstituted and live-cell biological systems. A major drawback of dcFCCS is the risk of an artifactual false-positive or overestimated cross-correlation amplitude arising from spectral cross-talk. Cross-talk can be reduced or prevented by fast alternating excitation, but the technology is not easily implemented in standard commercial setups. An experimental strategy is devised that does not require specialized hardware and software for recognizing and correcting for cross-talk in standard dcFCCS. The dependence of the cross-talk on particle concentrations and brightnesses is quantitatively confirmed. Moreover, it is straightforward to quantitatively correct for cross-talk using quickly accessible parameters, that is, the measured (apparent) fluorescence count rates and correlation amplitudes. Only the bleed-through ratio needs to be determined in a calibration measurement. Finally, the limitations of cross-talk correction and its influence on experimental error are explored.

Figure 1

The extent of the cross-correlation artifact caused by spectral cross-talk depends on particle brightnesses and concentrations. A) Spectral bleed-through. The emission spectra of the dyes (filled gray: Alexa 488, hatched: Alexa 546) are not perfectly separated by the emission filters (—). The arrow points to the overlap of the green emission with the transmission of the filter in the red detection channel, which is the cause of the bleed-through. The bleed-through parameter κ for given spectral characteristics of the setup and dyes needs to be determined experimentally [Eq. (3)]. B) Simulation of the effect of the bleed-through parameter κ on the relative cross-correlation amplitude. The plots show the calculated amplitude of the cross-correlation relative to the green autocorrelation for a mixture of green and red molecules in the absence of truly double-labeled species. The entirely artifactual relative cross-correlation is depicted as a function of the brightness ratio and number ratio of the red and green species according to Equation (34c). The upper plot was calculated for a very small bleed-through ratio (κ=1.6 %, Alexa 488 and Cy5), the lower plot for a larger bleed-through ratio (κ=10.7 %, Alexa 488 and Alexa 546). C) Attempt to approximate the artifactual relative cross-correlation by substituting apparent brightnesses and numbers ( , ) for true brightnesses and numbers ( , ) in Equation (34c). The circles show the measured artifactual relative cross-correlations, the crosses the predictions of the cross-talk artifact. A rather large discrepancy between prediction and measurement is obtained. Equating true and apparent parameter values should hence be avoided.

Figure 2

Cross-talk artifact predictions using brightnesses and numbers obtained in a separate measurement. Artifactual relative cross-correlation obtained from mixtures of green and red dye molecules in the absence of double-labeled species. Theoretical values predicted as in Figure 1 B from brightness and number ratios and the indicated κ value are denoted by crosses; experimentally determined relative cross-correlations are denoted by open circles. Data points have been slightly shifted in the horizontal plane to allow visualization of both experimental and theoretical values in a single diagram. A, B) Relative cross-correlations as a function of real brightness and number ratios ( and ). To determine these, separate measurements were performed in which the 488 nm laser was switched off. The prediction using the bleed-through ratio κ_cal=1.6 % from the calibration measurement is mostly successful. At low red brightnesses, however, the artifactual cross-correlation is overestimated. The reason for this discrepancy is that the red brightness is underestimated from the separate measurements, in which the 488 nm laser does not contribute to the excitation of the red dye (Cy5), whereas it does so in the actual cross-correlation measurement. C, D) Relative cross-correlations as a function of real brightness and number ratios ( and ) for a dye and filter combination with larger spectral cross-talk (Alexa 488, Alexa 546; κ_cal=10.7 %).

Figure 3

Cross-talk artifact predictions using apparent brightnesses and numbers directly from the measurement. A, B) Relative cross-correlations as a function of apparent brightness and number ratios , determined directly from the count rates and amplitudes obtained in the cross-correlation experiment. The calculation (predicted values, crosses) provides a reliable estimate of the artifactual relative cross-correlation (open circles). The projection of the experimental values in (B) fits a hyperbolic function, which confirms that x_κ/r is independent of [Eq. (35b)]. The hyperbolic fit also allows an independent determination of the bleed-through ratio κ, yielding κ=1.5 %, which is close to the value of κ_cal=1.6 % that was determined in the initial calibration [Eq. (3)] and was used for the cross-talk prediction. C, D) Relative cross-correlations as a function of apparent brightness and number ratios ( and ) for a dye and filter combination with larger bleed-through (Alexa 488, Alexa 546; κ_cal=10.7 %). The calculation provides very good estimates for the expected artifactual relative cross-correlation. Projection: from fitting Equation (13a), a bleed-through ratio of κ=10.8 % is recovered, which is close to the value of 10.7 % obtained by the simple calibration.

Figure 4

Effectiveness of cross-talk correction in the presence of green excess. A) Two samples with different proportions of double-labeled species (488/633-DNA) and red-labeled species (633-DNA) were prepared (top and bottom graphs). The binding degree with respect to the total amount of red particles, θ=N^RG/N^R, is given by the amplitude of the cross-correlation relative to the green autocorrelation, x=X/G_g. Increasing amounts of extra green molecules (488-DNA) were added and dcFCCS measurements were performed after each addition. The apparent (i.e. measured) relative cross-correlation values were plotted versus the apparent green-to-red count-rate ratios. Error bars indicate single standard deviations of multiple measurements. The apparent relative cross-correlation increases solely due to cross-talk (open symbols). Each data point was independently cross-talk corrected by using Equation (38) and the bleed-through ratio from calibration, κ_cal=1.2 % (filled symbols). B) The same procedure was applied to two different mixtures of 488/543-DNA′ and 543-DNA′. Increasing amounts of 488-DNA′ were added. The relative cross-correlation increases due to increasing cross-talk (open symbols). Each data point was cross-talk corrected using the bleed-through ratio from calibration, κ_cal=17.3 % (filled symbols). Fitting a line to the apparent relative cross-correlation values provides an alternative way of obtaining the true relative cross-correlation, , by finding the intersection with the ordinate axis (Eq. (4); indicated by the dashed lines). In addition, the intersections with the x=1 line yield κ_fit⁻¹ which is in reasonable agreement with κ_cal⁻¹. The value κ_cal from the initial calibration is slightly smaller than the bleed-through values obtained by fitting the data sets, κ_fit, which is why the cross-correlation values corrected using κ_cal lie above the dashed lines. Errors increase with increasing κf. C) The data from (A) were plotted on a different scale, which allows the comparison of the values of κ_fit from the data sets with κ_cal from the initial calibration. They are in reasonably good agreement. For the 488/633 configuration, dcFCCS measurements tend to be limited by the usable range of count-rate ratios f. Errors remain rather small because of the small bleed-through ratio κ.

Figure 5

Simulation of the effect of bidirectional cross-talk on the relative cross-correlation amplitude using Equation (37a). The bleed-through of the Green dye into the red channel κ_Gr in this example is 10 %. In contrast to Figure 1 B, this example assumes that there is a significant amount of “reverse” bleed-through from the Red dye into the green channel (κ_Rg=0.5 %). With bidirectional bleed-through, the resulting cross-talk artifact becomes large not only when the green particles are in excess and brighter compared to the red, but also in the other extreme, when the red particles are in excess and brighter than the green particles. A relevant “reverse” bleed-through like in this simulation was not encountered in the experiments with Alexa 488/Alexa 546 and Alexa 488/Cy5 (Figure 2).