Keywords

1 Introduction

In addition to Gregorio Weber’s seminal contributions to the field of biological fluorescence, his work in the area of protein interactions, cooperativity, and allostery remains a major legacy in biochemistry [1]. Given his dual expertise in fluorescence and bio-molecular interactions, it is not surprising that he was able to make great progress in both fields simultaneously. Since Weber’s early work on the polarization of fluorescent dyes bound to proteins [2, 3], fluorescence emerged and has remained one of the best methods for quantitative measurements of protein interactions. The widespread use of fluorescence in modern quantitative biology stems from several major advantages over alternative methods, advantages that Gregorio Weber recognized, developed and exploited over his illustrious career. One major advantage of fluorescence is its high sensitivity, which allows for equilibrium measurements of very high affinities between biomolecules. Indeed, with the development of instrumentation capable of single molecule detection, fluorescence has replaced most detection methods based on radioactivity. Another advantage of fluorescence for measuring protein interactions is the fact that binding is determined at equilibrium with no need to separate bound from free species. In addition, given its high sensitivity, fluorescence can be measured very quickly, allowing highly quantitative characterization of the kinetics of protein interactions, extending down to the microsecond range, which is useful for monitoring the intra-molecular protein interactions implicated in fast protein folding (e.g., [4, 5]). Fluorescence detection is easily coupled to instrumentation for perturbing equilibria such as stopped flow or titration devices and microfluidic systems, as well as temperature and pressure perturbation. Indeed, Weber pioneered the use of fluorescence coupled to pressure perturbation to monitor protein interactions, both intra- and inter-molecular [6].

Weber used the many fluorescence approaches he developed to probe a number of different types of protein interactions. These include ligand binding (cooperative and antagonistic) [7–14], homologous and heterologous protein subunit interactions [15–25], and the coupling between the two [1, 26]. These studies highlighted the energetic subtlety of the protein and ligand concentration dependencies of important regulatory circuits. I was a graduate student in Gregorio Weber’s group in the early 1980s at the time he was working on the subject of free energy couplings between ligand binding and protein oligomerization. During that period, Brian Matthews visited the University of Illinois and gave a seminar presenting the first 3-D structure of a transcriptional repressor, the lambda Cro Repressor dimer [27], which is necessary to induce the lytic cycle of lambda phage infection. It binds to two operator regions in the phage DNA in competition with the cI repressor, which is required to maintain the lysogenic state. Each of the operator regions contains three binding sites for the repressor dimers, which exhibit different affinities for the different target sites in the operators. Together these two repressors control the switch between lysogenic and lytic phases of infection [28, 29]. Inspired by Brian Matthews’ beautiful dimeric structure, the complexity of this apparently finely tuned biological switch and Weber’s work on free energy couplings between subunit oligomerization and target binding, I asked if and how protein subunit interactions might be coupled to operator DNA binding in such cases. Indeed, work in the group of Gary Ackers [30–34] and later Don Senear [35, 36] revealed the quantitatively exquisite control at work in lambda switch, and the complex oligomerization equilibria involved. In collaboration with Kathleen Matthews we carried out a study of the role of subunit interactions in the mechanism of lac repressor function, a major subject of her research group [37–41]. This set me on the path of over thirty years of work using fluorescence approaches to characterize the energetics and structure–function relationships for protein systems implicated in the regulation of gene expression. In this chapter, I will review the major applications of these techniques by my group, highlighting what sort of information they have provided concerning the systems under study.

2 The Lac Repressor

I began to work on the lac repressor system in collaboration with Kathleen Matthews at Rice University, although less was known from a structural point of view at the time [42, 43] than for the cI/cro system. The lac repressor is predominantly tetrameric. Each monomer is made up of a ligand binding domain, to which the inducer galactose binds in a deep cleft, a linker region and a DNA binding domain. The DNA binding domain forms a helix-turn-helix motif that presents the recognition helix to a half operator site. LacI binds to three operator regions separated by a long intervening loops. Each site can be bound with high affinity by a dimer of the repressor with one DBD interacting in each of two half-sites. High affinity operator interactions are observed for the unliganded protein, and inducer binding (the synthetic inducer iso-propyl-thio-galactoside or IPTG is typically used in vitro) leads to a decrease in affinity for the operator by about five orders of magnitude, depending upon the salt concentration used in the measurements [44].

We used a combination of pressure and tryptophan or dansyl fluorescence polarization and tryptophan emission energy to measure the tetramer–dimer dissociation and to probe the effect of IPTG binding on this equilibrium [45, 46]. We found that the tetramer–dimer dissociation constant was 14 nM at 21°C and that addition of IPTG stabilized the tetramer against dissociation by a factor of 4 at that temperature. We also found that pressure dissociated the IPTG, with a rather large volume change, ~−70 ml/mol. In addition to revealing a free energy coupling between ligand binding and subunit interactions which could be important in controlling DNA looping upon induction, determination of the affinity between LacI dimers has become somewhat useful in recent years, as the stochastic modeling of transcriptional control by lac and other repressors requires knowledge of these constants.

3 The Trp Repressor: Affinity and Cooperativity

I became interested in another bacterial transcription factor, the trp repressor (TrpR), because its function was more akin to a rheostat than the toggle switch of the lac repressor. Trp repressor represses transcription of genes in E. coli involved in the biosynthesis of tryptophan [47–49]. It also represses its own transcription [50]. Its affinity for the three (trp, aroh, and trpR) operator sites is controlled by the co-repressor, tryptophan, such that when tryptophan is plentiful, it binds to TrpR, increasing its affinity for the operator sites and shutting down transcription of the tryptophan biosynthesis genes. However, since it also shuts down its own transcription at the trpR site, this decreases gradually the repressor concentration, leading to a gradual relief of repression that is accentuated if, in addition, tryptophan levels drop.

Typically at that time, protein–DNA interaction affinities were measured using either nitrocellulose filter binding assays or electrophoretic mobility shift assays (EMSA), both relying on radiolabeled oligonucleotides. Neither of these techniques is an equilibrium technique, since they involve separation of the free from bound species. Moreover, it is difficult to implement studies of the effects of solution conditions or temperature because the conditions for the function of the assays themselves are rather stringent. Trained by Gregorio, it occurred to me that a fluorescence anisotropy-based assay would provide an attractive alternative to these techniques. The sensitivity could be nearly as good as the radioactive assays and the measurement is made in solution at equilibrium, with no need to separate the bound from the free species. In previous studies by us and others using dyes of rather low quantum yield and wavelength, high affinity interactions could not be measured [51–53]. To overcome this limitation, we chose to use an oligonucleotide labeled at the 5′ end via phosphoramidite chemistry with fluorescein via a six carbon linker. We chose fluorescein as a dye because it was the most sensitive at the time. At neutral pH, the quantum yield was sufficiently high and the wavelength sufficiently removed from UV contaminants, that we could detect quite well, with some modifications to the instrument, 200 pM concentrations of fluorescein. At the time it had become possible to purchase custom labeled oligonucleotides from Promega Corporation (Madison, WI), as such labeling was being explored for use in new fluorescence-based sequencing approaches that are the norm today. Using a solution containing 200 pM of this 5′ fluorescein labeled double-stranded 25mer oligonucleotide containing the sequence of the trp operator, also in collaboration with Kathleen Matthews, we carried out measurements of protein–DNA interactions based on anisotropy [54]. We found that TrpR bound to its operator cooperatively, and analyzed the binding with a model of coupled monomer–dimer and dimer DNA binding, which yielded dissociation constants of 4 and 0.1 nM, respectively. We were also able to directly measure the effect of tryptophan on the interaction (Fig. 1).

Fig. 1
figure 1

Anisotropy titration of 5′ fluorescein labeled 25mer oligonucleotide bearing the trp operator sequence at 21°C pH 7.6 10 mM phosphate buffer with purified trp repressor. (Left) 300 pM 25mer; (Right) 30 nM 25mer with 0 (closed circles), 0.04 (open diamonds), 0.4 (open triangles), and 4.0 (open circles) mM l-tryptophan. Figures reworked from [54]

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The thermodynamic binding model used to fit the data in Fig. 1 was based on the crystal structure of the trp repressor bound to a target oligonucleotide, the first repressor-operator co-complex ever published [55]. It revealed a dimer of the repressor with the recognition helix of the helix-turn-helix motif interacting with at CTAG palindromic sequence. However, the actual stoichiometry of binding and the true recognition sequence came into question. Uncertainty concerning stoichiometry and target sequence is rather typical in the case of protein–DNA interactions. Using a variety of techniques, fluorescence anisotropy, but also analytical ultracentrifugation, we and our collaborators had demonstrated that the repressor itself, in solution formed higher order oligomers that could be disrupted by the addition of the co-repressor, tryptophan or salt [51, 56]. Jannette Carey and colleagues published a crystal structure of an oligomeric form of trp repressor bound to a target sequence in which an alternative recognition mode was evident via a GNACT palindrome [57]. We went on to use fluorescence anisotropy, fitting the high affinity binding event as a cooperative dimer–tetramer equilibrium and demonstrated that the stoichiometry and affinity of the trp repressor-operator interactions depended on the length and sequence of the target oligonucleotide, with the different natural targets exhibiting different stoichiometry and cooperativity [58, 59].

We also examined the effect of super-repressor mutations on DNA binding [60]. Using a variety of fluorescence techniques and isothermal titration calorimetry we demonstrated that the super-repressor phenotype of the AV77 super-repressor discovered by Yanofsky and coworkers [61] was due to the fact that the free WT protein is partially unfolded in the DNA binding domain and that substitution of alanine by valine at the N-cap position of the recognition helix stabilized it in its folded form such that the binding of tryptophan, which also stabilizes the recognition helix, had little further effect in the super-repressor mutant [62]. It has recently come to my attention (Harish Subramanian and Jannette Carey, personal communication) that the TrpR DBD is not unfolded in absence of tryptophan, but in equilibrium between multiple conformations. In addition to a large number of studies by the Yanofsky, Carey, Sigler, Hurlburt, Matthews, Jardetsky, and other groups that will not be covered here, this ensemble of fluorescence studies on a transcriptional regulator, augmented by crystallography, calorimetry, analytical ultracentrifugation, and circular dichroism, allowed a highly quantitative and thorough characterization of the molecular mechanisms and thermodynamics in this highly complex regulatory system involving coupled folding, oligomerization, ligand binding, and DNA target recognition, all exquisitely tuned to achieve the appropriate level of tryptophan synthesis and energy usage for E. coli under varying nutrient conditions.

4 Nuclear Receptor Ligand Modulated Heterologous Protein Interactions

Nuclear receptors (NR) comprise a large family of ligand modulated transcription factors responsible for many important aspects of differentiation, growth, and homeostasis in metazoans [63]. There are two major subfamilies of NRs, the homo-dimeric NRs, which include the hormone receptors, estrogen receptors (ER), glucocorticoid receptors (GR), and androgen receptors (AR), and which bind to palindromic DNA target sites and the hetero-dimeric NRs, such as the retinoid receptors, RXR/RAR, thyroid hormone receptors, TR, peroxisome proliferator receptors, PPARs, etc., which bind to direct repeats. The NRs harbor structurally homologous C-terminal ligand binding domains, generally endowed with a ligand-dependent activation domain in the C-terminal helix, a DNA binding domain, and a highly variable N-terminal domain that can also exhibit activation functions. NRs interact with ligands (agonists, antagonists, partial agonists, and inverse agonists), which are generally hydrophobic in nature, although some NRs are thought to respond to gases such as NO via a bound heme moiety. Ligand binding modulates NR interactions with co-repressors and coactivators of transcription, which themselves exhibit chromatin remodeling activity and recruit other transcription factors. The stoichiometries, affinities, and cooperativity of the multiple linked interactions implicated in NR function are finely tuned to the proper level of control of these important physiological functions. Indeed, NRs represent an important class of targets for development of therapeutic agents, many of which have long been on the market, for the treatment of human disease states including many forms of cancer, heart disease, diabetes, and inflammation. Not surprisingly, the literature on NR structure function relationships is vast, and will not be reviewed here. However, few groups have been interested in deciphering the complex energetic relationships between ligand binding, both homologous and heterologous protein interactions and nucleic acid interactions. One exception is the work of David Bain’s group [64, 65]. For our part, often in collaboration with the structural group of William Bourguet, we have used fluorescence anisotropy to investigate ligand-dependent NR-DNA interactions [66–69] and NR-coregulator interactions [70–75].

We were the first to use anisotropy to investigate the impact of different types of ligands on NR interactions with fluorescently labeled peptides derived from co-activators (Fig. 2) [73]. We found differential effects of ligands for recruitment of the SRC-1 coactivator to two different subtypes of ER. Such differences can have significant impact on tissue specific therapeutic effects, since the ER subtypes are differentially expressed in different tissues. Indeed, this anisotropy assay for the effect of ligands on NR coregulator interactions has become a common practice in the pharmaceutical industries drug development programs targeting NRs. Following Schwabe and co-workers [76], we also used C-terminal labeling of the activation helix 12 on RAR to investigate by time-resolved anisotropy, the effects of ligation and peptide binding on the dynamics of this all important helix [71]. More recently, we have used FCS to measure the ER-Tif2 coactivator interaction K d as a function of ligand in live Cos7 cells, using transient transfection of cerulean and mCherry fusions of the two proteins [77].

Fig. 2
figure 2

Titrations of 2 nM Alexa488 labeled 26 kDa fragment of the SRC-1 NR coactivator with either ERα or ERβ in presence of saturating concentrations of agonist ligands, estradiol (open circles), genistein (open squares), estrone (closed circles), estriol (triangles), and ethylene estradiol (diamonds)

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5 Translational Control of Ribosomal Protein Production: L20 – Stoichiometry

As noted above, ascertaining the stoichiometry of protein–nucleic acid complexes under physiologically significant conditions of concentration, temperature, salt, etc., is often rather challenging. A lack of clarity as to the stoichiometry of the large ribosomal protein, L20, from E. coli and other bacterial species with a long and complex translational operator on its messenger RNA illustrates the issue [78–82]. The translational operator RNA sequence comprises hundreds of base pairs and forms a required long-range pseudoknot that is recognized by L20 and which overlaps the Shine-Dalgarno sequence of the mRNA. Another similar site also exists within this operator, and both sites mimic the site recognized by L20 in the 16S ribosomal RNA. Both sites are required for translational control in vivo. Anisotropy assays had indicated that perhaps the stoichiometry might not be 2:1, at least under the conditions of titrations. In this case we used fluorescence correlation spectroscopy (FCS) and fluorescence cross-correlation spectroscopy (FCCS), to ascertain whether two molecules of L20 could bind to the operator RNA. FCS first proposed by Magde et al. [83] uses the fluctuations in fluorescence intensity in a small confocal observation (or in our case 2-photon excitation) volume to characterize the concentration and diffusion properties of the molecules. If one uses molecules labeled with different colors in two different detection channels it is possible to deduce whether the two molecules form a complex. For a review of FCS and FCCS, see [84].

We labeled separately two solutions of a C-terminal construct of L20 known to be sufficient for translational control in vivo, with a green and red fluorescent dye (Alexa 488 and Atto647N) on the N-terminus of the protein via succinimidyl ester chemistry. First, we carried out FCS experiments observing only the fluorescence from the Alexa488 (green) labeled L20 (Fig. 3, left). Upon addition of the operator RNA at a concentration tenfold the K d [85] determined by anisotropy, the correlation profile shifted to longer lag times, indicating binding of the protein to the RNA (which was large, 660 base pairs). Then, still observing in the green channel, we added the red (Atto647N) labeled L20. If two or more molecules of L20 could bind to the RNA, then we would have expected (under the equimolar conditions used) that the curve would remain at the same lag time, since the L20 C-terminal construct is only 6 kDa, and would not be expected to make a significant difference to the diffusion time of the already large complex of the operator RNA bound by the green labeled L20. Instead, the curve was shifted back to faster diffusion times, indicating that the green L20 was competed off of the operator RNA by the red L20. To further demonstrate that two L20 proteins could not bind simultaneously to the operator RNA, we carried out cross-correlation measurements. Here we added equimolar amounts of L20 green and L20 red, with the RNA at a concentration tenfold above the K d [85]. If more than one L20 molecule could interact simultaneously with the RNA, then we would have expected to see some cross-correlation signal. Instead, absolutely no cross-correlation amplitude was observed (Fig. 3, right), indicating that the stoichiometry of the L20/operator RNA complex was 1:1, despite the existence of two possible sites. Further studies indicated anti-cooperative allosteric interaction between the two putative binding sites on the operator RNA [85].

Fig. 3
figure 3

Stoichiometry of the L20-operator RNA complex investigated by fluorescence correlation spectroscopy. (Left) 150 nM L20-Alexa488 (circles), plus 150 nM operator RNA (triangles), and 150 nM L20-Alexa488, plus 150 nM operator RNA, plus 150 nM L20-Atto647N (crosses); (Right) 150 nM L20-Alexa488, plus 150 nM operator RNA plus 150 nM L20-Atto647N – Alexa488 channel (closed circles), Atto647N channel (open circles), cross-correlation (crosses). Figures reworked from [85]

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6 Control of the Switch Between Glycolysis and Gluconeogenesis in B. subtilis

In collaboration with Nathalie Declerck and Stephane Aymerich, we set out to use fluorescence approaches in the characterization of the molecular mechanisms of transcriptional regulators involved in the control of the central carbon metabolism in the soil bacterium, Bacillus subtilis. The switch between glycolysis and gluconeogenesis in B. subtilis is controlled at the level of the transformation of glyceraldehyde phosphate to 1,3-diphosphoglycerate (Fig. 4) [86–88]. The reaction in the glycolysis direction is catalyzed by the GapA enzyme, while the reverse reaction, unlike in E. coli, requires a second enzyme, GapB. Expression of GapA is controlled at the transcriptional level by the central glycolytic genes repressor or CggR. CggR is induced by fructose bis-phosphate (FBP) a product of glucose degradation. Expression of the GapB enzyme is very strongly catabolite repressed when cells are grown on a glycolytic carbon source by the control catabolite protein of gluconeogenic genes (CcpN). The mode of induction of CcpN upon a nutrient shift to gluconeogenic carbon sources, such as malate, is not known, but genetic evidence suggests that the co-transcribed YqfL protein is implicated [88].

Fig. 4
figure 4

Schematic diagram of the switch between glycolysis and gluconeogenesis in B. subtilis. In blue, operative interactions under gluconeogenesis and in red operative interactions under glycolysis. Repressor proteins and co-regulators are shown as black and grey ellipses

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6.1 In Vitro Biophysical Studies

The groups of Declerck and Aymerich had investigated in detail the structural and in vivo functional properties of this genetic metabolic switch. Our collaboration with these groups involved applying a variety of fluorescence approaches, coupled with other biophysical methodologies, to characterize the energetic couplings implicated in their function. In the case of CcpN, the repressor that strongly downregulates the gapB and pckA promoters on glucose, we showed by FCCS, using DNA oligonucleotides labeled with a red dye and the CcpN protein labeled with a green dye (Fig. 5) that the stoichiometry of binding was different on oligonucleotides bearing the proposed sequence recognition motifs for these two operator sites [89]. Plotting the ratio of the cross-correlation amplitude to that of the amplitude of the fluctuations in the green channel (that of the protein, tenfold more concentrated than the red-labeled target DNA oligonucleotides) provides a direct measure of binding, and the value of this ratio at the plateau of the binding curve depends upon the stoichiometry of the complex. Indeed it can be seen directly from the Gox/GoG ratios in Fig. 5, that the stoichiometry of one complex is approximately twice that of the other. Correcting for labeling ratios and CcpN oligomerization, we deduced stoichiometries of dimer and tetramer, respectively, for the gapB and pckA target oligonucleotides. Later it was shown that the target sequence for the gapB oligonucleotide was not complete, and that the protein bound as a tetramer to the full-length gapB target as well.

Fig. 5
figure 5

FCCS measurements of CcpN interaction with target oligonucleotides bearing recognitions sequences for the operators present in the pckA and gapB promoters. Red curves are the FCS profiles for the oligonucleotides labeled with the red dye, Atto-647N. Green curves are the FCS profiles for the CcpN protein labeled with fluorescein. The FCCS (cross-correlation) profiles are shown in yellow. (a) CcpN interactions with the pckA oligonucleotide. (b) CcpN interactions with the gapB oligonucleotide. (c) Gox/GoG ratio for the pckA and gapB targets as a function of CcpN concentration

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Co-variance analysis was used in the case of the CggR protein to investigate the coupled effects of ligand binding and oligomerization in the control of its operator interactions. CggR represses transcription of the gapA operon when the bacteria are grown on gluconeogenic carbon sources, such as malate (see schematic in Fig. 4). In addition to the genes coding for the glycolytic enzymes, the first gene in the gapA operon is that encoding CggR itself, such that this system includes an auto-repression loop. CggR is induced (i.e., dissociates from the operator) when the bacteria sense glucose in the environment. It had been thought that the inducer was FBP. Our work using fluorescence and other biophysical approaches confirmed this hypothesis and demonstrated that FBP played a structural role as well, with two binding sites per CggR monomer. The high affinity site was the structural stabilization site, while the low affinity site was responsible for allosteric induction of CggR [90]. In a classical Weber free energy coupling analogy, using fluorescence anisotropy and analytical ultracentrifugation, we showed how inducer binding was allosterically coupled to cooperative DNA binding by CggR [91].

A model based on these data by which FBP binding leads to CggR tetramer dissociation, and hence decreased affinity and cooperativity in operator binding was confirmed using a combination of FCCS, non-covalent mass spectrometry, and small angle X-ray scattering [92]. The effect of FBP on dimerization is most clearly shown in the FCCS profiles in Fig. 6. Two double-stranded DNA oligonucleotides containing CggR half-sites (able to bind one CggR dimer) were labeled with a red and a green dye, respectively, on the 5′-end of the sense and anti-sense strand. When annealed with their complementary unlabeled strand and mixed in absence of CggR, no interaction between the two double-stranded oligonucleotides is observed, as expected (Fig. 6a). When the two labeled complementary oligonucleotides are annealed, cross-correlation is observed (Fig. 6b). The cross-correlation amplitude is not 100% due to imperfect labeling ratios of the oligonucleotides. If the two separately labeled double-stranded oligonucleotides are mixed with the CggR protein in absence of FBP, cross-correlation is observed (Fig. 6c), and the amplitude under these concentrations conditions is maximal, with respect to that observed for the doubly labeled double-stranded oligonucleotide in Fig. 6b. This indicates that the CggR tetramer can non-covalently cross-link the two oligonucleotides into a single complex. However, this interaction is abolished when FBP is added (Fig. 6d), although mass spectrometry and fluorescence anisotropy demonstrated that the protein is still bound to DNA under these conditions. However, the CggR is dimeric in presence of FBP and can no longer cross-link the two oligonucleotides.

Fig. 6
figure 6

FCCS measurements of CggR interaction with target oligonucleotides bearing recognitions sequences for half-site operators. (a) Two singly labeled double-stranded oligonucleotides labeled, respectively, on the 5′-end of the sense strand for one with fluorescein and the 5′-end of the anti-sense strand for the other with Atto 647N. Green and red curves are FCS profiles for the red and green labeled oligonucleotides as depicted in the schematics. Black curves are cross-correlation profiles between the red and the green detected fluorescence. CggR protein is depicted as grey ellipses. (a) 60 nM each of separately labeled green and red double-stranded oligonucleotides with the CggR half-sites. (b) 60 nM doubly labeled double-stranded oligonucleotide with the CggR half-site. (c) 60 nM each of the two separately labeled double-stranded oligonucleotides in presence of saturating CggR protein. (d) 60 nM each of the two separately labeled double-stranded oligonucleotides in presence of saturating CggR protein (300 nM in monomer units) and 0.5 mM FBP

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6.2 In Vivo Fluctuation Microscopy

The above in vitro biophysical studies on the CcpN/CggR control of the switch between glycolysis and gluconeogenesis provided models for how the proteins functioned in vivo. In the case of the CcpN protein, we hypothesized a “hold back” mechanism, by which the CcpN protein bound to the operator overlapping the gapB and pckA promoters, would interact directly with the RNA polymerase, preventing transcription initiation. In the case of the CggR repressor a “road-block” model proposed that CggR bound to the operator, downstream of the start site of the gapA promoter and blocked transcription elongation by RNA polymerase. We sought to verify these proposed models in vivo using an advanced microscopy technique based on fluorescence fluctuations introduced by Digman and Gratton in 2008 and called scanning Number and Brightness [93]. In scanning Number and Brightness, two-photon in our case, a field of view is imaged using rapid scanning of the excitation laser via galvanometric mirrors, such that the dwell-time at each pixel is shorter than the diffusion time (i.e., that one is sampling at a rate near the top of the FCS curves shown in Figs. 5 and 6, for example). Multiple (50–100) raster scans of the field of view (FOV) are carried out, such that at each pixel, one has 50–100 values for the fluorescence intensity. If the fluorescent molecules have diffused in the time between imaging of the same pixel (about 2–3 s for the frame time), then the fluorescence intensity values incorporate fluctuations due to diffusion. The average and variance of these values at each pixel can be used in a moment analysis to calculate the number of fluorescent molecules in the excitation volume at each pixel, and their molecular brightness. These values must be corrected for shot noise and where possible background auto-fluorescence contributions.

We adapted the two-photon scanning N&B approach to determine the level of gene expression from bacterial GFP promoter fusions [94]. Given the low photon statistics and small size of the bacteria, pixel averaging strategies were implemented in order to obtain robust values for single cell GFP concentrations. We then used this approach to measure and model stochastic expression form the gapA and gapB GFP promoter fusions in the natural chromosomal locus of B. subtilis grown on glycolytic (glucose) and gluconeogenic (malate) carbon sources (Fig. 7). This approach, which yields absolute protein concentrations for single cells, allows for stochastic modeling and absolute determination of the biological noise parameters (Fig. 8). Extremely strong catabolite repression with low noise for the CcpN repressor, and high noise repression for CggR support the “hold back” and “road block” mechanisms for CcpN and CggR, respectively. Stochastic modeling of the gapA/gapB promoter system under different nutrients yielded rate constants that were entirely consistent with the biophysical models.

Fig. 7
figure 7

Scanning 2-photon N&B measurements on B. subtilis live cells expressing GFP from promoter fusions of the gapA, gapB, pckA, and pccpN promoters. (a) Images of bacteria on pads in presence of G, glucose or M, malate for the gapA, gapB, and pccpN promoters as labeled. (b) Histograms of the number of GFP molecules in the excitation volume from the quantification of multiple FOV for the gapA, gapB, pckA, and pccpN promoters in presence of glucose (black) or malate (grey)

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Fig. 8
figure 8

Stochastic modeling based on the scanning 2-photon N&B measurements on B. subtilis live cells expressing GFP from promoter fusions of the gapA, gapB, pckA, and pccpN promoters. (a) The “hold back” and “road block” models for CcpN and CggR repression, respectively. (b) Stochastic model for repression. (c) Fits of the experimental distributions for GFP expression on glucose (red) and malate (blue) to the model in (b) for pccpN and pcggR promoters as labeled

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7 Conclusions

The above set of examples serves to illustrate how multiple fluorescence approaches can be used both in vitro and in vivo to reveal the very subtle mechanisms underlying the regulation of gene expression. These examples are by no means exhaustive, and our group as well as many others has applied such approaches to multiple protein systems involved in gene regulation. What is clear from these examples is the central role of protein oligomerization interactions, both homologous and heterologous, in the fine tuning of gene expression levels. This key role of protein interactions is a lesson learned from Gregorio Weber, whose insight continues to inspire all of the work of my group. Protein stoichiometry is often missing in the models proposed for biological regulation of gene expression, as well as many other important physiological processes. The work we have carried out over the years, some of which is presented here, underscores that quantitative determination of the coupling between protein–protein interactions and transcriptional regulation is absolutely required for the understanding of these systems, and eventually, the intelligent modulation of their activity in the context of therapeutic strategies to combat disease.