SSB–DNA Binding Monitored by Fluorescence Intensity and Anisotropy

Abstract

Fluorescence methods have proven to be extremely useful tools for quantitative studies of the equilibria and kinetics of protein–DNA interactions. If the protein contains tryptophan (Trp), as is often the case, and there is a change in intrinsic Trp fluorescence of the protein, one can use this change in signal (quenching/enhancement) to monitor binding. One can also attach an extrinsic fluorophore to either the protein or the DNA and monitor binding due to a change in fluorescence intensity or a change in fluorescence anisotropy. Such equilibrium studies can provide important quantitative information on stoichiometries (occluded site size, number of binding sites) and energetics (affinities and cooperativities) of the interactions. This information is needed to understand the mechanisms of protein–DNA interactions. A critical aspect of such approaches for systems that have non-unity stoichiometries (e.g., a protein that binds multiple ligands) is knowledge of the relationship between the change in fluorescence signal (intensity or anisotropy) and the average extent of binding. Here we describe procedures for using fluorescence approaches to examine the stoichiometries and equilibrium binding affinities of Escherichia coli single-stranded DNA-binding protein (SSB) and Deinococcus radiodurans SSB with long polymeric ssDNA to determine an occluded site size. We also provide examples of studies of SSB binding to shorter oligonucleotides to demonstrate analysis and fitting of the data to an appropriate model (monitoring fluorescence intensity or anisotropy) to obtain quantitative estimates of equilibrium binding parameters. We emphasize that the solution conditions (especially salt concentration and type) can influence not only the binding affinity, but also the mode by which an SSB oligomer binds ssDNA.

1. Introduction

If a change in the fluorescence properties (e.g., intensity or anisotropy) accompanies the binding of two species, this can be used to quantitatively monitor the binding interaction and determine both the stoichiometry and energetics (affinity and thermodynamics) of binding using equilibrium titration methods. Such approaches have been used extensively to examine numerous protein–DNA interactions in solution including many SSB–ssDNA interacting systems. Generally, if the molecule undergoes a change in its intrinsic fluorescence (e.g., tryptophan (Trp) in a protein), then this species is titrated with the nonfluorescent molecule (e.g., DNA) and the change in fluorescence signal (intensity or anisotropy) is monitored as a function of total DNA concentration. Alternatively, if the changes in the intrinsic fluorescence of the protein are not sufficient to reliably monitor the interaction, an extrinsic fluorophore can be attached to one species (either protein or DNA) to study the interaction. However in this case, it is often observed that the modification affects the energetics of the interaction. Independent of the nature of the fluorescence signal that is monitored (intensity or anisotropy), one needs to know (or determine) how the change in fluorescence signal relates to <X>, namely, the average number of ligands (in this case, DNA) that bind to the macromolecule (in this case, protein). We emphasize this point since for macromolecules that bind multiple ligands, the average fractional fluorescence signal change is often not directly proportional to <X>. However, once this relationship is established, then one can obtain an equilibrium binding isotherm that can be analyzed to determine stoichiometries (number of binding sites), equilibrium binding constants (K), and cooperativities of protein–DNA interactions. Equilibrium experiments performed at different temperatures and different solution conditions (salt, pH) allow one to examine how the binding is thermodynamically linked to these variables (1). Such linkage analysis can yield information on the binding enthalpy (linkage to temperature) and whether ions or protons bind preferentially to the protein–DNA complex or the free protein and/or DNA (2–6). This provides information about the thermodynamic forces that drive the formation of the complex and more practically how solution conditions (pH, salt concentration and type, etc.) can influence these interactions. This information is needed to understand the energetics of the protein–DNA interaction and allows predictions of their behavior under conditions that either have not been examined or are not as easily accessed experimentally.

Fluorescence equilibrium titrations have been used extensively to study interactions of single-stranded DNA-binding proteins (SSBs) with ssDNA. The Escherichia coli SSB (EcoSSB) and the Deinococcus radiodurans SSB (DrSSB) are used as examples in this chapter and are also discussed in the chapter describing isothermal titration calorimetry (ITC) methods; hence the reader should refer to that chapter for more introductory comments about these protein–DNA systems.

Here we briefly review the equilibrium fluorescence titration studies that have been performed to examine the interactions of EcoSSB and DrSSB with ssDNA. We first remind the reader that in solution, EcoSSB and DrSSB are stable homotetramers and homodimers, respectively. As a result of the multiple ssDNA-binding sites (4 OB folds each), these SSB proteins can bind to long polymeric ssDNA in different binding modes in vitro that depend on solution conditions, particularly salt concentration and type (7). The EcoSSB tetramer shows dramatic changes in its mode of binding to ssDNA as a function of salt concentration, type, and valence. On poly(dT) EcoSSB binds in its fully wrapped (SSB)₆₅ mode at [NaCl] >0.2 M in which ssDNA interacts with all four subunits of the SSB tetramer with an occluded site size of 65 nts. However, at lower [NaCl] (≤10 mM) it binds in its highly cooperative (SSB)₃₅ mode, in which ssDNA binds to an average of only two subunits of the tetramer with an occluded site size of~35 nts (2, 3, 7). At intermediate salts (40–100 mM NaCl), EcoSSB forms its (SSB)56 binding mode on poly(dT). Equilibrium fluorescence titrations have been used extensively to study the effects of various solution conditions on its different binding modes with polynucleotides and on the energetics of ssDNA binding. Effects of salt concentration (2, 3), anion and cation type (4–6), pH (4, 6), polyamines (8), binding density (4), and base composition (5, 9) have been examined. Statistical thermodynamic models describing the binding of SSB tetramers to long ssDNA in its highly cooperative (SSB)₃₅ mode at low salt conditions (<0.02 M NaCl) (10) and in its low cooperativity (SSB)₆₅ mode at higher salt concentrations (>0.2 M NaCl) (11) have also been developed.

Oligodeoxynucleotides of different lengths have also been used to examine binding of ssDNA to the individual tetramer. Four molecules of (dX)₁₆, two molecules of (dX)₃₅, or one molecule of (dX)₇₀ can bind per SSB tetramer. However, the shorter oligodeoxynucleotides, (dX)₁₆ or (dX)₃₅, display negative cooperative binding to an individual SSB tetramer such that ssDNA binds with high affinity to the first two subunits of the tetramer and with much lower affinity to the second two subunits. In addition, this negative cooperativity is highly salt dependent, decreasing with increasing [NaCl] or [MgCl₂], although high salt does not eliminate the negative cooperativity (12). In fact, this salt-dependent negative cooperativity provides part of the explanation for the salt-dependent change in the SSB–ssDNA binding modes observed with poly(dT) (12–14). Studies of the EcoSSB binding to oligodeoxynucleotides of lengths close to the occluded site size (n = 65) have been used to estimate the binding enthalpies and have shown that the unusually high negative heat capacity change associated with the binding of (dA)₇₀ is due to the temperature-dependent stacking of adenine within the ssDNA and the loss of these stacking interactions upon binding SSB (15,16). The energetics of cooperative binding of two SSB tetramers to (dA)₇₀ has also been examined at low salt conditions (17). More limited fluorescence binding studies have been performed with the DrSSB dimer (18) and yeast scRPA hetero-trimer (19).

We note that in all of the studies mentioned above the intrinsic Trp fluorescence quenching of the protein has been used to monitor binding, although recent studies (20) have used EcoSSB that has been extrinsically labeled with fluorophores that undergo fluorescence intensity changes upon binding ssDNA. Generally these extrinsic fluorophores also change the binding affinities and properties and thus care should be taken to characterize these labeled proteins rather than assume that their behavior mirrors the unlabeled protein.

The energetics and kinetics of EcoSSB binding to single-stranded oligodeoxynucleotides have also been studied by monitoring the change in fluorescence intensity of fluorescently labeled nucleic acid (21–23) as well as SSB (20, 24). Although changes in the fluorescence anisotropy of a labeled ssDNA can also be utilized to monitor binding, these have not been extensively used to study SSB–ssDNA interactions. Changes in the fluorescence anisotropy of EcoSSB have been used to study the self-assembly of a His-55 to Tyr mutant of SSB (SSB-1) that destabilizes the tetramer to form monomers (25, 26).

In the following sections we describe procedures for performing and analyzing titration experiments monitoring changes in either fluorescence intensity or anisotropy. These experiments were performed using a PTI QM-2000 spectrofluorometer (Photon Technologies, Inc., Lawrenceville, NJ) in which the quenching of the intrinsic Trp fluorescence of the protein or the change in fluorescence intensity or anisotropy of an ssDNA labeled with an extrinsic fluorophore (fluorescein) was used to monitor binding.

2. Materials

2.1. Buffer Solutions

All solutions were prepared with reagent grade chemicals and glass distilled water that was subsequently treated with a Milli Q (Milli-pore, Bedford, MA) water purification system. The buffer used is Buffer T (10 mM Tris (tris(hydroxymethyl) aminomethane), pH 8.1, 0.1 mM EDTA) with different NaCl concentrations as indicated in the text for each particular experiment. Buffers were prepared as described in the ITC Chapter.

2.2. Proteins and ssDNA

1. EcoSSB (27) and DrSSB (28) proteins were expressed, purified, and stored as described in the ITC Chapter. Protein concentrations were determined spectrophotometrically in buffer T containing 0.20 M NaCl using the extinction coefficients, ɛ₂₈₀ = 1.13×10⁵ M⁻¹ (tetramer) cm⁻¹ for EcoSSB and ɛ₂₈₀ = 8.2×10⁴ M⁻¹ (dimer) cm⁻¹ for DrSSB (see ^{Note 1}).

2. The single-stranded oligodeoxythymidylates, (dT)₇₀, (dT)₅₀, (dT)₃₅, and F-(dT)₅₀ (labeled with fluorescein at the 5′ end), were synthesized and stored as described in the ITC Chapter of this book. Poly(dT) has an average length ~1,100 nucleotides and was purchased from Midland Certified Reagents Co. (Midland, TX). The concentration of poly(dT) is expressed in nucleotides and was determined spectrophotometrically in buffer T(pH 8.1), 0.1 M NaCl using the extinction coefficient, ɛ₂₆₀,dT = 8.1×10³ M⁻¹ cm⁻¹. Concentrations of oligodeoxythymidylates were determined using extinction coefficients (per mole of ssDNA molecule) at 260 nm calculated according to the expression ɛ₂₆₀ = N×ɛ₂₆₀,_dT + ɛ₂₆₀,_F, where N is the number of nucleotides and ɛ₂₆₀,_F = 2.096×10⁴ M⁻¹ cm⁻¹ is the extinction coefficient for fluorescein (Glen Research) (see ^{Note 1}).

3. Methods

3.1. Equilibrium Binding Models Used for Analysis of Titration Data

For the binding of a ligand (X) to a one-site macromolecule (M), the equilibrium can be defined as in Scheme 1,

$$M+X\stackrel{K_{\mathit{obs}}}{\rightleftarrows }\mathit{MX}$$ Scheme 1

where K_obs = [MX]/[X][M] is the equilibrium association constant and [MX], [X], [M] are the equilibrium concentrations of each species in solution. The expression for the average degree of binding <X> (average number of ligands bound per macromolecule) can be obtained using the mass conservation equation [M]_tot = [M] + [MX] and is given in Eq. 1

$$<X>=\frac{\left[MX\right]}{{\left[M\right]}_{\text{tot}}}=\frac{K_{\text{obs}}\left[X\right]}{1+K_{\text{obs}}[X]}$$ (1)

If the macromolecule has n identical, independent sites the expression for <X> is given in Eq. 1a (1)

$$<X>=\frac{\left[MX\right]}{{\left[M\right]}_{\text{tot}}}=\frac{n{K}_{\text{obs}}\left[X\right]}{1+K_{\text{obs}}[X]}$$ (1a)

The equilibrium binding model in Scheme 1 was used to fit the titration curves for DrSSB binding to (dT)₅₀ shown in Figs. 2a and 3a, b (see Subheading 10).

Fig. 2.

The analysis of titration isotherms of SSB binding to oligo(dT) using model-independent approach and fitting the data to a particular model. (a) The titration isotherms from Fig. 1c for (dT)₅₀ binding to DrSSB (0.2 M NaCl, pH 8.1, 25°C) at two protein concentrations, 0.1 μM dimer (squares) and 0.5 μM dimer (triangles), shown in the form of relative fluorescence quenching versus total concentration of the (dT)₅₀. The insert shows the results of MBDF analysis of the data (see text for details) indicative that relative change in fluorescence is directly proportional to the extent of DNA binding (binding density) and that the stoichiometry of the formed complex is 1 mol of (dT)₅₀ per mole of DrSSB dimer (the maximum quenching ~80% is reached when the binding density <X> = 1). Smooth curves through the data points represent a global fit of the two experimental data sets to the model of n-independent and identical sites (see Eqs. 5 and 5a and text for details) with the following parameters: Q_max = 0.80 ± 0.01; n = 0.94 ± 0.02; and K_obs = (8.09 ± 0.73) × 10⁷ M⁻¹. (b) Titration curves representing fluorescence titrations of the EcoSSB tetramer with (dT)₃₅ in buffer T (0.2 M NaCl, pH 8.1, 25°C) at two protein concentrations, 0.1 μM tetramer (closed circles) and 0.32 μM tetramer (open circles) (14). The insert shows the results of an MBDF analysis of the data (as described for Fig. 1a), which indicates that two molecules of (dT)₃₅ bind to EcoSSB tetramer upon saturation. The binding of the first one is characterized by the fluorescence quenching of ~50% and the second one by fluorescence quenching of ~40% (~90% quenching for the final complex having 2 mol of (dT)₃₅ bound per mole of EcoSSB tetramer).

Fig. 3.

Titrations of fluorescein-labeled DNA (F-(dT)₅₀) with SSB monitoring (a) quenching of total fluorescence intensity or (b) fluorescein anisotropy. (a) Binding isotherm for the titration of 0.2 μM of F-(dT)₅₀ with DrSSB (buffer T, pH 8.1, 0.2 M NaCl, 25 °C) plotted as relative fluorescence quenching versus total concentration of DrSSB (dimer). The smooth curve through the data points represents a fit of the data to an n-independent and identical sites model (see Eqs. 5 and 5a and text for details) with the binding parameters indicated. The residuals forthe fit are shown as open squares. (b) Binding isotherm for the titration of 0.2 μM of F-(dT)₅₀ with DrSSB (buffer T, pH 8.1,0.2 M NaCl, 25 °C) plotted as anisotropy versus total concentration of DrSSB (dimer) (yellow triangles). The dashed red line shows the best nonlinear least squares fit of the data to a 1:1 binding model (Eq. 9), assuming no fluorescence change between the bound and free states of DNA (i.e., c = F_bound/F_free was constrained to equal 1) and demonstrates that the fit is not adequate. The solid red curve shows the best nonlinear least squares fit of the same data to Eq. 9 when c is allowed to float yielding c = 0.44 ± 0.01 and K_obs = (2.72 ± 0.19)×10⁸ MT⁻¹ (see insert), which are in excellent agreement with the binding parameters obtained for the same experiment when total fluorescence quenching is monitored (Fig. 3a) (see text for more details). The titration curves shown in solid black lines are simulations showing the effect of different values of c (different extents of fluorescence quenching/enhancement) on the shape and position of the titration curves. The simulations were performed using Eq. 9 with K_obs = 2.4 × 10⁸ MT⁻¹ and different values of c (c = 1, no fluorescence change), (c = 2, 100 % fluorescence enhancement), and (c = 0.2, 80 % fluorescence quenching).

Scheme 2 defines the equilibrium for the binding of two molecules of ligand to a macromolecule,

$$M+X\stackrel{K_{\mathit{1},\mathit{obs}}}{\rightleftarrows }MX+X\stackrel{K_{\mathit{2},\mathit{obs}}}{\rightleftarrows }M{X}_{\mathit{2}}$$ Scheme 2

where K_1,obs = [MX]/[X][M] and K_2,obs = [MX₂]/[X][MX] are the macroscopic (see ^{Note 2}) equilibrium binding constants for binding of the first and second ligands, respectively. The expression for <X> for this system is given in Eq. 2 (1):

$$<X>=\frac{\mathrm{d}\mathrm{ ln }P}{\mathrm{d}\mathrm{ ln }X}=\frac{K_{1,\text{obs}}[X]+2K_{1,\text{obs}}{K}_{2,\text{obs}}{[X]}^2}{1+K_{1,\text{obs}}[X]+K_{1,\text{obs}}{K}_{2,\text{obs}}{[X]}^2}$$ (2)

This model was used to fit the data in Fig. 2b for the binding of two molecules of (dT)₃₅ to EcoSSB (see Subheading 10).

3.2. Monitoring Binding by a Fluorescence Intensity Change

The total fluorescence intensity of a mixture of “i” fluorescent species can be defined as in Eq. 3:

$$F={\displaystyle \sum F_i{[X]}_i}$$ (3)

where F_i is the molar fluorescence intensity of species i and [X]_i is its concentration. For a macromolecule (M) with fluorescence intensity, F_M = F₀, that upon formation of a 1:1 complex (MX) undergoes a quenching of its fluorescence intensity, F_MX = F_min, the observed change in relative fluorescence quenching is described by Eq. 4:

$$Q_{\text{obs}}=Q_{\max }\frac{K_{\text{obs}}[X]}{1+K_{\text{obs}}[X]}$$ (4)

where Q_obs = (F₀ − F_obs)/F₀ is the observed fluorescence quenching and Q_max = (F₀ − F_min)/F₀ is the fluorescence quenching at saturation of the macromolecule with ligand, where <X> and K_obs are as defined above. The concentration of free ligand, [X], can be determined from the mass conservation Eq. 4a:

$${[X]}_{\text{tot}}=[X]+<X>{[M]}_{\text{tot}}=[X]+\frac{K_{\text{obs}}[X]}{1+K_{\text{obs}}[X]}{[M]}_{\text{tot}}$$ (4a)

For a macromolecule with n independent and identical sites, Eqs. 4 and 4a transform into Eqs. 5 and 5a:

$$Q_{\text{obs}}=Q_{\max }\frac{n{K}_{\text{obs}}[X]}{1+K_{\text{obs}}[X]}$$ (5)

$${[X]}_{\text{tot}}=[X]+<X>{[M]}_{\text{tot}}=[X]+\frac{n{K}_{\text{obs}}[X]}{1+K_{\text{obs}}[X]}{[M]}_{\text{tot}}$$ (5a)

The expression describing the binding of two ligands to a macromolecule according to Scheme 2 is given by Eq. 6:

$$Q_{\text{obs}}=\frac{Q_1{K}_{1,\text{obs}}[X]+Q_2{K}_{1,\text{obs}}{K}_{2,\text{obs}}{[X]}^2}{1+K_{\text{obs}}[X]+K_{1,\text{obs}}{K}_{2,\text{obs}}{[X]}^2}$$ (6)

where K_1,obs and K_2,obs are the macroscopic equilibrium binding constants (see ^{Note 2}) for binding of the first and the second ligands, X, to the macromolecule M, and Q₁ and Q₂ are the fluorescence quenching upon binding of one and two molecules of ligand, respectively. In Eq. 6 the concentration of free ligand ([X]) can be determined from the mass conservation Eq. 6a:

$${[X]}_{\text{tot}}=[X]+<X>{[M]}_{\text{tot}}$$ (6a)

where <X> is defined in Eq. 2.

3.3. Monitoring Binding by Fluorescence Anisotropy Changes

SSB–DNA binding can also be monitored by the change in fluorescence anisotropy of an extrinsic fluorophore attached to either the SSB or the DNA. Fluorescence anisotropy (r) reflects the extent of depolarization of the fluorescence emission of a species in solution when excited with polarized light. It is directly related to the rotational diffusion of the species and is low for small and flexible molecules (higher depolarization), and increases when larger complexes are formed (slower rotational movement, smaller depolarization). Therefore, the change in fluorescence anisotropy can generally be used to monitor a binding event (see ^{Note 3}). This is particularly convenient for systems where no change in fluorescence intensity is observed between the free and bound states. For one-channel spectrofluorometers (L-format) the anisotropy is defined in Eq. 7 (29):

$$r=\frac{I_{\text{VV}}-G{I}_{\text{VH}}}{I_{\text{VV}}+2G{I}_{\text{VH}}}$$ (7)

where I_VV is the fluorescence emission intensity measured for vertically polarized excitation and vertically polarized emission. I_VH is the intensity measured for vertically polarized excitation and horizontally polarized emission, and G is the correction factor (see ^{Note 4}). We note that in many studies polarization (p) changes have been used directly to quantitatively analyze interacting systems rather than anisotropy (r). This will result in an incorrect binding isotherm and incorrect binding constant and should be avoided (see ^{Note 5}).

The anisotropy of a mixture of “i” fluorescent species is given by Eq. 8:

$$\overline{r}={\displaystyle \sum r_i{f}_i}$$ (8)

where f_i = X_iF_i/ΣX_iF_i is the fractional contribution to the observed fluorescence intensity of component i. It is important to note the differences in the weighting factors in Eq. 3 versus Eq. 8. In Eq. 3, the observed fluorescence intensity is the sum of the fluorescence intensities of each species weighted by their concentrations, whereas in Eq. 8, the observed anisotropy is the sum of the anisotropies of each species weighted by the fractional contribution of each species to the total fluorescence. Based on Eq. 8 the expression for r for a 1:1 binding system is given by Eq. 9:

$$r=r_0+(r_{\max }-r_0)\frac{K_{\text{obs}}{[X]}_c}{1+K_{\text{obs}}{[X]}_c}$$ (9)

where r₀ and r_max are the limiting values of the anisotropy for (M) and (MX), respectively, [X] is the free protein concentration, and K_obs is as defined above. The factor c = F_bound/F_free = F_MX/F_M is the ratio of the fluorescence of the bound and free macromolecule (DNA) (assuming that it is labeled with fluorophore).

3.4. Amounts of SSB and ssDNA Required for Fluorescence Titrations and the Design of the Experiment

In general, preliminary information on the system (such as the oligomerization state of the protein and its stability) should be obtained prior to performing titration experiments (see ^{Note 6}). EcoSSB (7) is a stable tetramer and DrSSB (28) is a stable dimer under the conditions of the experiments presented here. Any preliminary information on the value of binding affinities (if available from literature) can also be useful in designing the experiments and to estimate the amounts of SSB and DNA needed. For example, for most of the experiments presented in Fig. 1 (except the titrations with DrSSB in 1.0 M NaCl) the affinity of the SSB for ssDNA is so high that binding is “stoichiometric” (i.e., all DNA added is bound until the “stoichiometric” point n is achieved) and the reaction is completed at a total DNA-to-protein ratio, R = 1 (mole (dT)_L/mole SSB) in the case of oligonucleotides (Fig. 1c, d, 0.2 M NaCl) or R ≈ n for poly(dT) (Fig. 1a, b, 0.2 M NaCl), where n is the occluded site size in nucleotides (poly(dT) concentration is expressed in moles of nucleotides and not molecules). For such experiments the spectroscopic signal changes linearly with titrant concentration until the stoichiometric point is reached and does not change further upon addition of more titrant. A two- to threefold excess of [DNA]_tot over [SSB]_tot is usually sufficient for these titrations while generally obtaining 20–25 points in the titration. The amounts of SSB and DNA required for a single titration can be estimated using the formula in Eq. 10:

$$R\cdot V_{\text{SSB},\text{cell}}\cdot C_{\text{SSB},\text{cell}}=V_{\text{DNA}}\cdot C_{\text{DNA}}$$ (10)

where R is the final total DNA-to-total protein ratio desired in the spectrophotometric cell at the end of titration, V_SSB,cell is the minimum volume of protein solution in the cell (usually ~2 mL), C_SSB,cell is the concentration of SSB in the cell (usually varying from 0.1 to 1 μM), and V_DNA is the volume of the titrant (DNA solution, usually ~100 μl), which generally does not exceed 5% of the solution volume in the cell (see Subheading 7). The concentration of the titrant (C_DNA) required for the experiment can then be determined from Eq. 10. For example, in the stoichiometric titrations shown in Fig. 1b (C_SSB,_cell = 0.14 μM, R ≈ 160) and in Fig. 1d (C_SSB,_cell = 0.10 μM, R ≈ 4) the suggested titrant concentrations of poly(dT) and (dT)₇₀ are ~450 μM and ~8μM, respectively. These experiments are performed by adding equal-volume aliquots of the titrant to the protein solution as shown in Table 1 (see ^{Note 7}) for the titration of EcoSSB (0.14 μM) with poly(dT) (Fig. 1b). Since the only information that can be obtained from such a titration is the occluded site size on poly(dT) (or the stoichiometry of SSB binding to a (dT)_L) and the maximum fluorescence change at saturation (Q_max) these data are generally plotted in the form of relative fluorescence quenching (Q= (F₀ − F_i)/F₀) versus the ratio of total DNA concentration to total protein concentration as shown in Fig. 1, where F₀ is the initial protein fluorescence before the addition of DNA and F_i is the fluorescence for the ith addition of DNA (see Subheading 5 for more details).

Fig. 1.

Determination of the occluded site size of DrSSB (a) and EcoSSB (b) on poly(dT) under stoichiometric conditions monitoring change in intrinsic Trp fluorescence. (a) Fluorescence titrations of DrSSB (0.2 μM) with poly(dT) (829 μM (nucleotides)) under stoichiometric conditions (0.2 M NaCl, buffer T, pH 8.1, 25°C) are shown in green circles. The results are presented as a change in the extent of fluorescent quenching relative to free protein fluorescence versus the ratio of total poly(dT) concentration (nucleotides) to total concentration of the DrSSB dimer in the cell. The linear increase in relative quenching indicates stoichiometric binding of the protein to poly(dT) until the point of saturation (plateau value) is reached (~83% quenching). The occluded site size (≈52 nucleotides per DrSSB dimer) was determined by extrapolation of the linear part of the titration curve to the point of intersection with the corresponding plateau value after saturation (shown in red). For 1.0 M NaCl (yellow triangles) the titration is not stoichiometric, so a determination of occluded site size is not possible (in this case the concentrations used in the experiment were 0.2 μM DrSSB and 817 μM of poly(dT)). (b) Fluorescence titration of EcoSSB (0.14 μM) with Poly(dT) (495 μM (nucleotides)) under stoichiometric conditions (0.2 M NaCl, buffer T, pH 8.1, 25°C). For this titration the occluded site size determined from the intersection point (as described in panel A) is ~65 and maximum quenching is ~90%. (c) Fluorescence titrations of DrSSB with (dT)₅₀ in buffer T (pH 8.1, 25°C) under stoichiometric (0.2 M NaCl, green circles) and nonstoichiometric conditions (1.0 M NaCl, yellow squares and triangles). The titration isotherms are presented in the form of the dependence of relative fluorescence quenching versus the ratio of total (dT)₅₀ to total protein concentration. The concentrations of DrSSB (dimer) used in the titrations are shown under corresponding plots. (d) Fluorescence titration of EcoSSB (0.1 μM tetramer) with (dT)₇₀ in buffer T (0.2 M NaCl, pH 8.1, 25°C) is indicative of 1:1 stoichiometric binding of EcoSSB tetramer to ssDNA.

Table 1.

Experimental Excel spreadsheet design for the titration of EcoSSB (0.14 μM, 1,800 μL total volume) with 495 M of poly(dT) in buffer T, 0.2 M NaCl (see Fig. 1b)

#	Titrant conc. (μM)	Titrant aliquot (μL)	Total titrant volume (μL)	Titrant conc. in cell (μM)	[Poly(dT)]tot per [EcoSSB]tot
1	495	2	2	0.55	4
2	495	2	4	1.10	8
3	495	2	6	1.64	12
4	495	2	8	2.19	16
5	495	2	10	2.73	20
6	495	2	12	3.28	24
7	495	2	14	3.82	28
8	495	2	16	4.36	31
9	495	2	18	4.90	35
10	495	2	20	5.44	39
11	495	2	22	5.98	43
12	495	2	24	6.51	47
13	495	2	26	7.05	51
14	495	2	28	7.58	55
15	495	2	30	8.11	59
16	495	2	32	8.65	63
17	495	2	34	9.18	67
18	495	4	38	10.23	75
19	495	4	42	11.29	83
20	495	4	46	12.33	90
21	495	4	50	13.38	98
22	495	10	60	15.97	118
23	495	10	70	18.53	138
24	495	10	80	21.06	157

The results presented in Fig. 1a, c for DrSSB binding to poly (dT) and (dT)₅₀ in the presence of 1.0 M NaCl indicate that the binding affinity is not high enough to be stoichiometric under these conditions (see ^{Note 8}) and therefore larger ratios of DNA to protein are required to achieve saturation, R = [poly(dT)]_tot/[DrSSB]_tot > n (Fig. 1a) and R = [(dT)₅₀]_tot/[DrSSB]_tot ≫1 (Fig. 1c). In this case, it is better to plot the data as (Q= (F₀ − F_i)/F₀) versus log [DNA] (see Fig. 2) since for accurate analysis (see Subheadings 9 and 10) more experimental points should be obtained at low and high DNA concentrations. For example, in the titrations presented in Fig. 2a the concentration range of [(dT)₅₀]tot is varied from 1 nM to ~4 μM. In designing these experiments four different titrant stock concentrations with varying volumes of added titrant were used to achieve an even distribution of the experimental points over a logarithmic scale of titrant concentration in the cell. This is exemplified in Table 2 (see ^{Note 7}) for the particular titration of 0.5 μM of DrSSB with (dT)₅₀ (see Fig. 2a). In general, for this type of experiment we recommend preparing a concentrated stock of the titrant (~200 μM) (see ^{Note 9}), which can be diluted to the desired concentrations to perform the experiments.

Table 2.

Experimental Excel spreadsheet design for the titration of DrSSB (0.5 μM, 1,900 μL total volume) with (dT)₅₀ in buffer T, 1.0 M NaCl (see Figs. 1c and 2a)

#	Titrant conc. (μM)a	Titrant aliquot (μL)b	Total titrant volume (μL)	Titrant conc. in cell (M)	[(dT)50]tot per [DrSSB]tot
1	1	2	2	1.1 × 10−9	0.002
2	1	2	4	2.1 × 10−9	0.004
1	1	2	6	3.1 × 10−9	0.006
4	1	6	12	6.3 × 10−9	0.013
5	10	1	13	1.2 × 10−8	0.023
6	10	2	15	2.2 × 10−8	0.044
7	10	5	20	4.8 × 10−8	0.097
8	100	1	21	1.0 × 10−7	0.202
9	100	2	23	2.0 × 10−7	0.413
10	100	2	25	3.1 × 10−7	0.623
11	100	2	27	4.1 × 10−7	0.834
12	100	2	29	5.1 × 10−7	1.044
13	100	2	31	6.2 × 10×7	1.255
14	100	3	34	7.7 × 10−7	1.571
15	190	2	36	9.7 × 10−7	1.971
16	190	6	42	1.6 × 10−6	3.171
17	190	10	52	2.5 × 10−6	5.171
18	190	10	62	3.5 × 10−6	7.171
19	190	10	72	4.4 × 10−6	9.171

^aConcentrations and

^baliquots of titrant ([(dT)₅₀]_tot) are varied in a way that results in even distribution of experimental points over the logarithm of concentrations of the titrant in the cell

The following procedures describe the preparation of SSB and DNA samples used in performing 2–10 fluorescent titration experiments with 0.1–0.5 μM of SSB or F-(dT)₅₀ in the cell.

3.5. Dialysis of Proteins and ssDNA

We recommend dialyzing protein and DNA samples prior to performing titration experiments since the storage conditions for DNA (water or Tris buffer) and SSB (20 mM Tris (pH 8.3), 50% (V/V) glycerol, 0.50 M NaCl, 1 mM EDTA, and 1 mM BME) are very different from the typical experimental conditions.

1. Prepare ~1–1.5 mL of an approximately 2 μM solution of either DrSSB or EcoSSB by diluting an aliquot of the concentrated SSB stocks into the buffer to be used for dialysis. For titrations of fluorescein-labeled DNA (e.g., F-(dT)₅₀) make 500 μL of an ~15 μM DrSSB solution.

2. Prepare ~100–200 μL of an approximately 200 μM solution of (dT)_L or a 500–800 μM solution of poly(dT) by adding the appropriate volume of a concentrated DNA stock solution to dialysis buffer.

3. Place the SSB and DNA solutions in dialysis bags of appropriate size (MWCO: 10,000 Spectra/Por) and proceed with the dialysis as described in ITC Chapter.

4. After dialysis equilibrium has been reached (3 changes of 300 mL volume), remove the contents from the dialysis bag and determine the concentrations of protein and ssDNA (see ^{Note 1}).

3.6. Titration Protocol

Here we describe the experimental procedure for titration of the fluorescent species in the cell (SSB) with nonfluorescent ssDNA in which binding is monitored by quenching of the intrinsic Trp fluorescence of SSB. The procedure is essentially the same if the fluorescent species in the cell is DNA (e.g., (dT)₅₀ labeled with fluorescein) that is titrated with SSB while monitoring the change in fluorescein intensity or anisotropy (see Subheadings 10 and 11). We assume that the experimenter is familiar with the principles of operation of the fluorometer.

1. After starting the instrument allow the lamp to warm up for at least 15 min. Fluorescence intensity is temperature sensitive, as are the equilibrium binding constants for protein-DNA interactions (see ^{Note 10}). Hence, the temperature of the sample cell should always be controlled precisely when performing fluorescence experiments. Turn on the water bath or peltier block that controls the temperature of the cuvette holder, and set to the desired temperature, in this case, 25°C.

2. Place a magnetic stir bar in a 3 mL (10 mm pathway) quartz cuvette and dilute SSB directly in the cell to the desired concentration with dialysis buffer such that the total volume is 1.9–2 mL (see ^{Note 11}). Make certain that no bubbles are stuck to the stir bar. Prepare a reference cell by adding the same volume of dialysis buffer into another cuvette (also with a stir bar). Prepare solutions of the appropriate concentrations and volumes of the titrant by diluting the DNA stock with dialysis buffer.

3. Place cuvettes with protein and buffer into the cuvette holder of the instrument (see ^{Note 12}) and open the “Time base” mode in the software, which allows one to monitor the fluorescence emission at a particular wavelength (for a given excitation wavelength) as a function of time. Set the excitation (296 nm) and emission (350 nm) wavelengths (see ^{Note 13}) and slit widths (usually corresponding to a 2 nm bandpass for excitation and a 4–8 nm bandpass for emission, depending on SSB concentration (see ^{Note 14})). Specify a number of acquisition points and the averaging time for each point (we usually set 8 points with an averaging time of 1 s and then take average of these 8 points to obtain a single data point for the fluorescence intensity, F_obs,i).

4. Take the first measurement for the protein solution (F_obs,0) and then for the buffer (F_ref,0). Repeat the measurements a few times waiting 2–3 min between measurements to make sure that the signal is stable (see ^{Note 15}) and record the observed intensity values for the sample and the buffer.

5. Begin the titration by adding the same-volume aliquots of the titrant (DNA) into the sample cell and the reference cell containing buffer using a micropipette (see ^{Note 16}). Wait for 2–3 min for equilibration and take measurements (F_obs,1 and F_ref,1). Repeat acquisition after 2–3 min to make sure that the signal intensity is no longer changing indicating that the system has reached equilibrium (if a slow change in fluorescence is observed a separate kinetic experiment should be performed to determine the equilibration times required between additions of titrant). Record the fluorescence intensity values for both cuvettes.

6. Proceed with the serial addition of aliquots of the titrant as described in the previous step while recording F_obs,i and F_ref,i for each addition until saturation is reached (i.e., the fluorescence intensity is no longer changing). Further additions of the titrant (DNA) may still be needed (see ^{Note 17}).

7. After finishing the titration redetermine the concentration of the DNA solution used as the titrant (see ^{Note 18}).

3.7. Correction of Experimental Data for Background Signal, Dilution, Inner Filter Effects, and Photobleaching

Prior to analysis of the data it is necessary to correct the observed fluorescence intensities and concentrations for dilution, photo-bleaching, and inner filter effects (30, 31).

1. First the concentrations of the species in the cell need to be corrected for dilution. The total concentration of the SSB in the cell (P) after addition of the ith aliquot of titrant DNA (D) solution can be calculated using Eq. 11:

   $$P_{\text{tot},i}=\frac{P_0\cdot V_0}{(V_0+V_i)}$$ (11)

   where P₀ is the initial concentration in the cell, V₀ is the initial sample volume, and V_i is the total volume of titrant added up to the point i in titration. The total concentration of the titrant in the cell at each point i in the titration is calculated using Eq. 12:

   $$D_{\text{tot},\mathrm{i}}=\frac{D_0\cdot V_i}{(V_0+V_i)}$$ (12)

   where D₀ is the concentration of the titrant (see ^{Note 19}).
2. The first correction to obtain the true fluorescence intensities, F_i, is to subtract the background contribution to the signal due to any light scattering or impurities in the DNA or buffer. This background signal, F_ref,i, is obtained from the titration with DNA of the reference cuvette containing buffer, yielding F_i = F_obs,i – F_ref,i. Next, the experimentally observed intensities, F_i, must be further corrected for dilution, photobleaching, and inner filter effects (31). Photobleaching is the excitation-dependent loss of fluorescence intensity, whereas inner filter effects can result when the absorbance spectrum of the sample overlaps either the fluorescence excitation or emission wavelength, such that some of the excitation or emission intensity is re-absorbed (“filtered”) by the sample, resulting in attenuation of the fluorescence signal (30). These factors are multiplicative, so the corrected fluorescence for each titration point can be expressed as in Eq. 13:

   $$F_{i,\text{corr}}=\left(\frac{(V_0+V_i)}{(V_0)}\right)\left(\frac{1}{C_i}\right)\left(\frac{f_0}{f_i}\right)$$ (13)

   where the first term accounts for dilution, the second term is for inner filter effects (see ^{Note 20}), and the third term is for photobleaching, where f₀ and f_i are the fluorescence intensities measured before and during the experiment for a sample which was not titrated, but exposed to the excitation light for the same periods of time as a titrated sample (see ^{Note 15}).

3. The actual fluorescence signal depends on the concentration of the fluorescent species and will vary in different experiments. Hence, the change in fluorescence is usually expressed as a quenching (Q_i) or an enhancement (En_i), which normalizes the signal relative to the initial fluorescence of the sample before the start of the titration, i.e., Q_i = (F_corr,0 − F_corr,i)/F_corr,0 or En_i = (F_corr,_i − F_corr,₀)/F_corr,0.

3.8. Determination of the Occluded Site Size of SSB on Poly(dT) Under Stoichiometric Conditions

Titration of SSB proteins with polynucleotides under stoichiometric conditions can be used to determine the occluded site size of the protein on the DNA. The occluded site size is defined as the average number of nucleotides made inaccessible to other proteins by the binding of one protein (32). This differs from the number of nucleotides that are physically contacted by the protein, which is usually a lower number. Figure 1a, b shows the results of titrations of DrSSB and EcoSSB with poly(dT) at 0.2 M NaCl, a condition under which binding of these proteins to ssDNA is stoichiometric. Under these conditions, an accurate determination of the equilibrium binding constant (affinity) is not possible; however, this allows for an accurate determination of the occluded site size. In these titrations the intrinsic Trp fluorescence of the protein in the cell is monitored as a function of total added ssDNA. The data are plotted as the relative fluorescence change versus the ratio of the total poly(dT) concentration (in nucleotides) to total protein concentration. Such a plot allows one to determine the occluded site size as the point of intersection of a linear extrapolation of the linear part of the titration curve with the plateau value of the fluorescence at saturation. The occluded site sizes, n, and maximum fluorescence quenching, Q_max, differ for DrSSB (n ~ 52 nucleotides, Q_max = 82%) and EcoSSB (n ~ 65 nucleotides, Q_max = 90%). To ensure that binding is stoichiometric, multiple titrations should be performed at a few different SSB concentrations. If binding is stoichiometric, then plots of the type shown in Fig. 1a obtained for different SSB concentrations should overlay.

Upon increasing the [NaCl], the binding isotherm for DrSSB becomes non-stoichiometric (less sharp) (see Fig. 1a) indicating a decrease in affinity (lowering of the equilibrium binding constant, K_obs). In contrast, the binding of EcoSSB to poly(dT) remains stoichiometric up to 3 M NaCl (14). This does not mean that increasing [NaCl] does not reduce the value of K_obs for the EcoSSB-DNA interaction, but rather that K_obs remains above the value (generally ~10⁹ M⁻¹) needed for binding to appear “stoichiometric”. In each case an increase in [NaCl] does not affect the maximum quenching suggesting no change in the mode of DNA binding. On the other hand, as the [NaCl] decreases to ~0.010 M NaCl, the occluded site size and maximum fluorescence quenching change for both EcoSSB (2, 7) and DrSSB (18). For EcoSSB this change is more dramatic (n = 35 and Q= 50%) and indicates a transition from its (SSB)₆₅ mode to its (SSB)₃₅ mode of DNA binding in which on average only two instead of four subunits of SSB tetramer are bound to ssDNA (7,33). For DrSSB the change is less dramatic (n = 45 and Q= 76%) (18) but still represents a change in ssDNA binding mode (18). For this reason one should always examine the effects of solution conditions on the occluded site size, rather than assume that a site size measured under one condition is applicable to all conditions.

3.9. Model-Independent Analysis of Titration Data Using the Macromolecule Binding Density Function Method

A model-independent analysis of two or more titrations performed at different macromolecule concentrations can be used to determine the stoichiometry of binding and to construct a true binding isotherm (34–36). This is most useful for systems in which one species binds multiple copies of the other. For this discussion, the macromolecule is defined as the species that binds multiple ligands. This analysis is also needed when the relationship between the average extent of ligand binding (<X> = ligands bound per total macromolecule) and the spectroscopic signal change (in this case fluorescence intensity or anisotropy) is not known a priori. Application of the following analysis to two or more titrations performed at different SSB concentrations as shown in Fig. 2a, b results in a true isotherm, i.e., a plot of <X> versus free or total ligand concentration (34–36). The two titrations need to be performed under conditions such that the total protein concentration is high so that the free ligand and total ligand concentrations differ significantly throughout the titrations.

The basis for this analysis is the thermodynamic constraint that for a macromolecule that does not undergo self-association, the average number of ligands bound per macromolecule, <X>, is determined solely by the free ligand concentration (strictly the chemical potential of the ligand) (34–36). Moreover, it is important to recognize that for a given set of solution conditions the relative fluorescence change (Q_i = (F_corr,0 − F_corr,i)/F_corr,0) is an intrinsic property of the system and is determined by the average degree of saturation of the binding sites, which in turn is determined solely by the free ligand concentration. Therefore, if two titrations are performed at two different total macromolecule (SSB) concentrations, [M₁]_tot and [M₂]tot, and plotted as a function of the total ligand concentration [X]_tot (DNA), then whenever the fluorescence quenching is the same for the two titrations (e.g., for the horizontal line in Fig. 2a, where Q= 0.18), it follows that the free ligand concentration must be the same at that same fluorescence quenching value (e.g., Q= 0.18) (34–36). As such, one can calculate the value of <X> and the free ligand concentration, [X], from knowing the pair of [M₁]_tot and [M₂]_tot and [X₁]_tot and [X₂]_tot that are needed to attain the same value of Q as indicated in Eqs. 14 and 15:

$$<X>=\frac{{[X_2]}_{\text{tot}}-{[X_1]}_{\text{tot}}}{{[M_2]}_{\text{tot}}-{[M_1]}_{\text{tot}}}$$ (14)

$$[X]=\frac{{[M_1]}_{\text{tot}}{[X_2]}_{\text{tot}}-{[M_2]}_{\text{tot}}{[X_1]}_{\text{tot}}}{{[M_1]}_{\text{tot}}-{[M_2]}_{\text{tot}}}$$ (15)

By repeating this calculation at multiple values of the observed Q for the two titrations, the titration curves can be analyzed as shown in Fig. 2a to obtain the dependence of Q_obs on <X> ([(dT)₅₀]_bound/[DrSSB]_tot or [(dT)₃₅]_bound/[EcoSSB]_tot; see inserts in Fig. 2a, b, respectively) and to construct true binding isotherm of <X> versus [X] or [X]_tot (not shown).

The model-independent analysis of multiple titrations of a fluorescent ligand at different concentrations with a nonfluorescent macromolecule (“reverse titrations”) can also be performed to obtain the same information, although the analysis is a bit more complex (35, 36).

MBDF analysis of two titrations of DrSSB (at 0.1 and 0.5 μM) with (dT)₅₀ shown in the insert to Fig. 2a indicates that the observed fluorescence quenching is directly proportional to the average degree of binding (<X>), as expected for a 1:1 binding interaction, and that the binding stoichiometry for this system is 1:1 (as follows from linear extrapolation of the dependence of Q on <X> to the value of Q_max = 0.8). Another example of an MBDF analysis for a system where the macromolecule binds multiple ligands is shown in Fig. 2b for the binding of EcoSSB to (dT)₃₅ (14). Two titrations were performed at two protein concentrations, 0.10 and 0.32 μM (buffer T, pH 8.1,0.2 M NaCl, 25°C). The analysis (see insert in Fig. 2b) shows that two molecules of (dT)₃₅ can bind to an EcoSSB tetramer at saturation (~90% quenching); however binding of the first and the second molecule is characterized by different fluorescence quenching values of ~50% and ~40%.

3.10. Fitting the Data to a Particular Model to Obtain the Equilibrium Binding Parameters

Model-independent analysis of the titrations in Fig. 2a shows that a 1:1 complex is formed upon interaction of DrSSB with (dT)₅₀. The binding isotherm shown in Fig. 2a can be directly fit to the expression for an “n” site binding model given in Eqs. 5 and 5a (see Subheadings 1 and 2). A global fit of the data for two titrations performed at DrSSB concentrations of 0.1 and 0.5 μM (see Fig. 2a and see ^{Note 21}) is consistent with this model and yields the following binding parameters: n = 0.94 ± 0.02; Q_max = 0.80 ± 0.02; and K= (8.09 ± 0.73) × 10⁷ M⁻¹.

One can also examine binding by monitoring the fluorescence intensity or anisotropy of a DNA molecule if it is labeled with an extrinsic fluorophore. To demonstrate this we show in Fig. 3 the results of a titration of F-(dT)₅₀ ((dT)₅₀ labeled with fluorescein at its 5′ end) with DrSSB performed at the same solution conditions as for the experiment in which the DrSSB Trp fluorescence was monitored in Fig. 2a (buffer T, pH 8.1,1.0 M NaCl, 25°C). In this case, binding is accompanied by a quenching of the fluorescein fluorescence (0.2 μM F-(dT)₅₀ in the cell, λ_ex = 494 nm, λ_ex =520 nm) upon binding protein. The data have been corrected as described above for titrations of the SSB with DNA and the resulting binding isotherm shown in Fig. 3a was fitted to the expression for an “n” independent and identical sites model given in Eqs. 5 and 5a, where DrSSB is now considered the ligand (X) and F-(dT)50 is the macromolecule (M). The fit describes the data well and provides the following binding parameters: n = 0.98 ± 0.01; Q_max = 0.55 ± 0.01; and K= (2.42 ± 0.35) × 10⁸ M⁻¹. The results indicate that the affinity of (dT)₅₀ when labeled with fluorescein is increased threefold compared to the binding of an unlabeled (dT)₅₀. This is likely due to additional interactions of the fluorescein with the protein. Hence, although the use of extrinsically labeled protein or DNA is convenient, the extrinsic probes will generally influence the energetics of the interaction. In fact, this is common for SSB interactions with DNA labeled with different fluorescent dyes. For example, the affinity of EcoSSB binding to (dT)₇₀ (2.0 M NaBr) increases three- and tenfold, when the DNA is labeled with fluorescein or Cy3, respectively (22). However, one can always use the equilibrium of the SSB with the labeled DNA in a competition experiment to probe the interaction of SSB with an unlabeled DNA (37, 38).

The data in Fig. 2b (14) can be fit to the equilibrium model presented in Scheme 2 using Eqs. 6 and 6a. Under the conditions of this experiment (buffer T, 0.2 M NaCl) the following parameters were obtained (12): Q₁ = 0.50 ± 0.02; Q₂ = 0.90 ± 0.01; and K₂,_obs = (3.3 ± 0.3) × 10 M⁻¹. Determination of K_1,obs was not possible at this salt concentration due to the fact that the binding affinity is too high (K_1,obs >10¹⁰ M⁻¹). These data show that an EcoSSB tetramer can bind two (dT)35 molecules, but with negative cooperativity. Similar titrations performed over a range of salt concentrations (12) indicate that this negative cooperativity decreases as the salt concentration increases and contributes to the fact that SSB displays salt-dependent binding modes (12).

3.11. Analysis of Titration Data When Monitoring a Change in Fluorescence Anisotropy

If a change in fluorescence anisotropy of one species accompanies binding of a second species, then this can also be used to monitor binding. In fact, this approach has become increasingly popular due to the ease with which DNA can be labeled with an extrinsic fluorescence probe. However, there are some important caveats to be considered when using this approach. These include the likelihood that the binding energetics will be influenced by the addition of the extrinsic fluorophore, as shown above for F-(dT)₅₀. In addition, if there is also a change in fluorescence intensity of the probe, this must be considered in the analysis of the data.

As an example of a binding system that is accompanied by a fluorescence anisotropy change we show results for the binding of DrSSB to F-(dT)₅₀ (where F is fluorescein). This experiment is identical to that shown in Fig. 3a, in which the change in fluorescein fluorescence intensity of F-(dT)₅₀ was monitored. However, in Fig. 3b we plot the change in fluorescein fluorescence anisotropy as a function of added DrSSB (see ^{Note 22}). For this system, the fluorescence anisotropy for the free F-(dT)₅₀ is r = 0.039, whereas r = 0.218 for the SSB–DNA complex. (We note that the maximum fluorescence anisotropy for a system is r = 0.4; see also ^{Note 3}).

We have chosen this system as an example because it allows us to demonstrate the need for caution when using fluorescence anisotropy to analyze a binding equilibrium if there is also a change in fluorescence intensity that accompanies binding. For this system the fluorescence intensity of the bound F-(dT)₅₀ is quenched by 55% relative to the free F-(dT)₅₀ (F₀ − F_min/F₀ ≈ 0.55) as shown in Fig. 3a. Since the observed anisotropy is a sum of the individual species’ anisotropies weighted by the fractional fluorescence contribution (see Eq. 8), this will influence the measured values of the anisotropies (29, 39) and thus the shape of the titration curve, a problem that seems not to be widely appreciated. Indeed, a direct comparison of the titration curves monitoring fluorescence intensity (Fig. 3a) and fluorescence anisotropy (Fig. 3b) shows that the titration curve obtained by monitoring the anisotropy change is steeper and shifted to higher total protein concentrations compared to the titration curve obtained by monitoring the fluorescence intensity change. As a result, an attempt to fit the anisotropy titration curve to a simple 1:1 binding model without accounting for the fluorescence intensity change fails (red dashed curve in Fig. 3b) in the direction that would suggest some positive cooperativity, which is impossible for a simple 1:1 binding system such as this.

To analyze the anisotropy titration curve correctly, one must account for the change in fluorescence intensity of the free and bound DNA. This is taken into account in Eq. 9 by the factor c = F_bound/F_free = F_mx/F_m (in this case we consider the DNA as the macromolecule (M) and DrSSB as the ligand (X)).

The experimental data shown in Fig. 3b are well described by a simple 1:1 binding model Eq. 9 as long as the correction factor (c = 0.44 ± 0.01) is included and the resulting best fit equilibrium binding parameters (r₀ = 0.039 ± 0.001; r_max = 0.218 ± 0.00; K_obs = (2.72 ± 0.19) × 10 M⁻¹) are in excellent agreement with the parameters obtained by directly fitting the fluorescence intensity titration curve in Fig. 3a (n = 0.98 ± 0.01; K_obs = (2.42 ± 0.35) × 10⁸ M⁻¹; and Q_max = 0.55 ± 0.01) (recall that Q_max in Fig. 3a is related to c in Fig. 3b by c = 1 − Q_max).

In order to further illustrate the effect on the observed anisotropy titration curve when a fluorescence quenching/enhancement accompanies binding, we also show several simulations for a 1:1 binding system where K_obs = 2.4 × 10 M⁻¹ but with different values of c (c = 1, no fluorescence change), (c = 2,100% fluorescence enhancement), and (c = 0.2,80% fluorescence quenching). The solid lines in Fig. 3b show the resulting shifts in apparent binding affinity and shape of the isotherms. As a result, significant errors in binding parameters and even conclusions about cooperativity can result if these corrections are not considered. This also points out that if there is a significant change in fluorescence intensity of the labeled DNA it is simpler to use that signal directly to monitor binding rather than the anisotropy change.