For examining Ste11 and Ste50 interaction, we constructed a yeast strain expressing Ste11-GFP and Ste50-mCherry from their respective chromosomal loci (). Fluorescence cross-correlation spectroscopy measurements were first performed as previously described 
to confirm the expected heterotypic interaction (). All of the fluorescence fluctuation measurements described in this study were made on the cytosolic pool by appropriately targeting the laser beam ( and Materials and Methods
). As expected, a high degree of cross-correlation was observed (), as demonstrated by the high amplitude of the cross-correlation curve relative to the autocorrelation curves of the individual channels. Results were quantified 
and showed over 60% of Ste50 bound with Ste11 (). The interaction of these proteins remained strong after activation of the pheromone response pathway or the osmotic stress pathway () (see Materials and Methods
). To test if the observed interaction relies on the SAM domain, two mutations, L73A and L75A, were introduced into the Ste50 SAM domain (). These mutations were previously shown to abolish the binding between Ste11 and Ste50 SAM domains in vitro 
-GFP was driven by the STE50
promoter from a centromeric plasmid and expressed in the ste50Δ
background. The cross correlation was diminished (), demonstrating as expected that the Ste50 SAM domain plays a role in Ste50's interaction with Ste11 in vivo
Yeast strains used in this study.
Cross-correlation analysis determines protein co-diffusion.
, the Ste11 and Ste50 SAM domains have been shown to mediate homo-oligomerization, but this has not been demonstrated in vivo
when proteins are expressed at the endogenous levels. PCH analyzes the probability distribution of detected photons from a small confocal volume to calculate particle concentration and brightness, usually reported as the average number of molecules in the focal volume (N) and counts per second per molecule (CPSM), respectively () 
. As a comparison technique, molecular brightness reflects the oligomeric state of the fluorescent species when compared to the brightness of a standard, for example, a known monomer or dimer of the same fluorescent molecule. For controls, yeast strains expressing monomeric, dimeric, and trimeric cytosolic GFP under the control of the BZZ1 promoter were constructed, as previously described () 
. The distribution of brightness values for 1dPCH measurements in live yeast cells were recorded using the Zeiss confocor 3 with 488 nm excitation and BP 505–540 nm emission collection (Materials and Methods
). Box plots, as well as example curves, are shown in . The brightness distributions of these GFP species were easily distinguishable, providing the basis of comparison for oligomeric status of mobile GFP-tagged proteins in yeast. In addition, the BAT2
locus was replaced by cytosolic mCherry and the BZZ1
locus was replaced by mCherry-mCherry (). At the low excitation powers that are necessary to minimize photobleaching in our experiments, the brightness of mCherry was less than that of eGFP () but, at over 2000 CPSM, still presented an improvement from other monomeric, red autofluorescent protein options 
, as expected based on improvements in photostability, and quantum yield 
1dPCH analysis of Ste50-GFP and Ste11-GFP probes homo-oligomerization.
Box plots of average brightness for individual 1dPCH measurements of Ste11 and Ste50 are presented in , with lines representing average brightness values of monomer, dimer, and trimer controls for a basis of comparison. Ste11 exhibited an average brightness close to that of dimeric cytosolic GFP, whereas Ste50 showed an average brightness in-between dimeric and trimeric cytosolic GFP. Interestingly, the SAM domain mutant, Ste50L73A-L75A-GFP, revealed a brightness much reduced relative to Ste50-GFP, near that of monomeric GFP, suggesting that these mutations also affect homo-oligomerization of Ste50. Surprisingly, PCH of Ste11-GFP in a yeast strain where the only form of Ste50 was untagged Ste50L73A-L75A revealed a decreased brightness, distinct from the distribution of Ste11-GFP in wild-type cells (p<0.05), suggesting that the SAM domain of Ste50 is also required for stabilization of Ste11 homo-oligomers.
To examine the effect of signals that normally activate MAP kinase cascade on Ste11-GFP and Ste50-GFP complexes, we activated the yeast mating response pathway by treatment of yeast cells with 50 µM α-factor or the osmotic stress pathway by treating the cells with 0.4 mM NaCl for 30 minutes 
(see Materials and Methods
). Average brightness values for PCH measurements are shown in . The average brightness of Ste11-GFP and Ste50-GFP were slightly decreased in response to both conditions.
The average brightness values of Ste11-GFP and Ste50-GFP, which were above the brightness of monomeric GFP, suggested an ability of these proteins to form homo-oligomeric structures, but the composition of the complexes was unclear. This represents a difficulty with 1dPCH. For example, the average brightness of Ste50-GFP could be explained by a distribution of dimers and trimers, but could also be explained by a distribution of monomers and high-order oligomers, or any other combination. In an ideal case, such as a solution measurement, sufficient statistics can be obtained to accurately distinguish a distribution of species freely from PCH data without a priori
knowledge. However, this is not the case in live yeast cells due to limits of laser exposure time to minimize photobleaching. Similarly, other live cell studies have also found it necessary to make certain reasonable assumptions and/or fix brightness values to fit fluctuation data to distributions to extract additional information 
To better examine the stoichiometry of the Ste11 and Ste50 complexes, 2dPCH was performed. As a proof of principle, we first applied 2dPCH to a yeast strain expressing GFP and mCherry physically linked to the cytosolic protein Bat2 
(). The 2dPCH histograms of Bat2-GFP-mCherry fit well to a 1 species model, with diffusing particles having coincidence brightness in the GFP and mCherry channels with values consistent with monomeric GFP and mCherry (, compare to ). As a negative control, 2dPCH was conducted for a yeast strain expressing unlinked, cytosolic GFP and cytosolic mCherry (). As expected, the data fit well with a two-species model (average chi2
0.9) but not with a one-specie model (average chi2
4.5). The resulting brightness values for the 2dPCH data sets were consistent with those expected for monomeric GFP and mCherry. In all two-species 2dPCH fits, an F test was used to validate the necessity of the second-component (F>97%).
2dPCH analysis of Ste50-mCherry and Ste11-GFP detects binding stoichiometry.
2dPCH was applied to the Ste11-GFP, Ste50-mCherry fluctuation data, and revealed the in vivo
binding stoichiometry of the complexes (). Again, a one-specie model did not adequately fit the data (average chi2
4.1); a two-component fit was necessary (average chi2
1.2). The data reveal a dominant specie (N comprises approximately 65 to 75% of the total particles from the fit) with a mCherry average brightness (2400±150) consistent with that of a monomer (p
0.12) and a GFP average brightness of 4980±230, which is indistinguishable from the 1dPCH GFP-GFP dimer brightness (p
0.7). Thus, the data suggests a dominant complex in the yeast cytosol consisting of monomeric Ste50 and dimeric Ste11. A second abundant specie revealed by the 2dPCH consisted of a high order oligomer of Ste50 that is not associated with Ste11. This data reveals a mutual exclusiveness between Ste50 homo-oligomerization and Ste50 forming a complex that contains two molecules of Ste11. Based on 1dPCH data, we expected a small fraction of a third specie, consisting of monomeric Ste11, but a three-component fit cannot be confirmed with statistics provided by the live cell measurements. Consistent with the lack of cross-correlation reported in , 2dPCH of Ste11-GFP, Ste50L73A-L75A
-mCherry did not fit with a one-specie model (average chi2
6.8), but rather a two-species model (average chi2
1.2), with non-interacting, monomeric species. This result confirms the FCCS and 1dPCH results that the Ste50 SAM domain is required for homo-oligomerization of Ste50, interaction of Ste50 with Ste11, and it plays a role in stabilization of the Ste11 dimer.
The effects of activation of the mating pathway and osmotic stress pathway were subtle, with the dominant specie in either case still consisting of monomeric Ste50 interacting with Ste11. The average GFP brightness value of this dominant complex under these conditions were lower than that in cycling cells; this decrease was statistically significant at the 95% level for high salt conditions relative to wt (p
0.05) but not at the 95% confidence limit for α-factor treated cells (p
0.11). The trend is consistent with a lower average brightness of the Ste11 component of this complex, and perhaps a distribution of interacting species that varies between 2
1 and 1
Ste50. The average brightness of the Ste50 high-order oligomer observed by 2dPCH was significantly reduced upon activation of the pheromone pathway (p
0.02), while the average brightness of the oligomer upon activation of the osmotic stress pathway was not reduced at a statistically high confidence level (p
Thus, a possible effect of activation of these pathways is a trend toward a reduction in the size of the high-order Ste50 oligomer. This is consistent with change observed by 1dPCH as the decreased average brightness of Ste50-GFP upon activation of the signaling pathways. However, at this point we are uncertain how brightness of mCherry containing complexes scales with number of mCherry subunits at high stoichiometry. The brightness of GFP complexes scales well with GFP subunits, as demonstrated by the fit of the average brightness of the monomeric, dimer, and trimeric controls (). We revisited the 1dPCH data of Ste50-GFP to attempt to better quantify the stoichiometry of the high-order, Ste50 oligomer. The result that the dominant specie of Ste50 was a monomer, as shown by 2dPCH, provided an important constraint for fitting the 1dPCH data to a distribution. Therefore the 1dPCH data for Ste50-GFP was fit to a distribution consisting of a fixed monomer brightness and freely varied oligomer brightness. N for each species was also freely varied. The Ste50 1dPCH data was well fit (average chi2
0.9) to a distribution that consists of a large percentage of monomer and a small percentage of high order oligomer, in percentages roughly equivalent with those found using 2dPCH. The constrained fits revealed that the treatment with α-factor or high salt led to a slightly decreased percentage of oligomer, and also a decreased oligomer brightness (). Using this analysis, average brightness values of the Ste50 oligomer were approximately 12,500, 8900, and 7700 CPSM for cycling cells, α-factor treated cells, and cells at high salt, respectively (). Assuming that the linearity of GFP brightness continues to hold at a high number of subunits, we estimate the number of Ste50 subunits in this complex to be ~5 to 6 in cycling cells, ~4 in α-factor treated cells, and ~3 to 4 in high salt condition. While the slight decrease in brightness of the Ste50 oligomer was also observed with mCherry in the 2dPCH data, it was not nearly as pronounced as that observed with 1dPCH () or the global fit (), raising the possibility that mCherry brightness may not scale linearly with subunit number at high stoichiometry, perhaps due to a self-quenching mechanism or increased propensity for photobleaching or photoblinking relative to GFP.
Constrained fits of the 1dPCH data to two-species allows for the examination of monomer and oligomer populations.