In the Laboratory
Quantitative Determination of DNA–Ligand Binding Using Fluorescence Spectroscopy
W
An Undergraduate Biochemistry Experiment Eamonn F. Healy Department of Chemistry, St. Edward’s University, Austin, TX 78704;
[email protected] DAPI, 4´,6-diamidino-2-phenylindole (Figure 1), binds to double-stranded DNA forming a complex that fluoresces up to twenty times more than DAPI alone (1). The complex is stable for hours at room temperature and is unchanged over pH 4–11. The experiment described here measures the DAPI binding constant, Kf, for calf-thymus DNA using fluorescence measurements and a modified Scatchard analysis. This experiment also allows the student to estimate the occupancy of the minor groove by calculating the number of nucleotides per bound ligand. Previous experiments published in this Journal have illustrated the principles of ligand–protein binding using 8-anilino-1-naphthalenesulfonic acid and bovine serum albumin (2), caffeine and human serum albumin (3), and methyl orange and bovine serum albumin (4). The first two studies utilized spectrofluorometry, while the experiments detailed in ref 4 were done using UV–vis spectroscopy. Experiments utilizing other dyes and a wide array of proteins have also been described (5, 6). The use of fluorescence to measure the binding of the intercalating agent ethidium bromide to DNA has also been described (7), and a recent paper has adapted this procedure to illustrate polyelectrolyte effects on binding strength (8). Modern pharmaceutical studies, such as the one detailing the DNA binding and biodistribution of the bis(benzimidazole) anti-tumor agents Hoechst 33342 and IodoHoechst 33342, involve the generation of fluorescence titration curves by the addition of aliquots of DNA to a fixed quantity of the therapeutic agent or ligand. A Scatchard plot of the binding data is then calculated by plotting the ratio of bound兾free ligand versus the bound fraction and calculating the slope (9). Such a calculation requires knowledge of the fluorescence maximum observed at a DNA concentration where 100% of the ligand is bound. This experiment utilizes the same one-cuvette-type procedure, but employs a modified Scatchard analysis that has the student calculate a fraction, f , that represents the fraction of ligand bound varying from zero to one. In addition the analysis presented here does not require the concentration of free ligand to be known,
Figure 1. The structure of DAPI.
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but instead requires only [L]total, the total concentration of bound and unbound ligand. The modified Scatchard plot then involves a reciprocal plot of [DNA]兾f versus 1兾(1 − f ), where the slope yields the binding constant Kf and the intercept gives a value for the number of base-pairs involved in binding a ligand. The experimental procedure mirrors that employed in modern studies, and the results obtained are in good agreement with the values estimated in earlier work (10, 11). Thus this experiment exposes the student to the highly sensitive and widely used technique of fluorescence spectroscopy. Though the analysis can be viewed as somewhat complex, it utilizes measurements easily conceptualized by the student, making this experiment a useful introduction to the use of fluorescence titration to determine binding constants. Finally it is hoped that the derivation and discussion of the Scatchard analysis might serve to impart to the student an appreciation of the challenges and pitfalls associated with a quantitative treatment of ligand binding. Experimental
Preparation of Buffer and Reagents Phosphate buffer (0.01 mol L᎑1, pH = 7.4) is prepared from stock. Two solutions of calf-thymus DNA (SigmaAldrich) in buffer are prepared: a 400 µg兾mL DNA solution and a solution of 50 µg兾mL DNA in phosphate buffer. A 1 × 10᎑4 mol L᎑1 DAPI (Sigma-Aldrich) stock solution in ethanol is prepared by dissolving 1 mg of DAPI in 30 mL of EtOH. Working DAPI solutions of concentration 1 × 10᎑6 mol L᎑1 and 2 × 10᎑6 mol L᎑1 are prepared from stock. Fluorimetry: Determination of the Fmax and FL Fluorescence spectra were generated using a RF-5301 PC Shimadzu. Settings appropriate to this experiment are given in the Supplemental Material.W The excitation wavelength is 360 nm, which in turn gives an emission spectrum with a maximum at 450 nm. A cuvette containing 3 mL of the 1 × 10᎑6 mol L᎑1 DAPI solution in phosphate buffer is prepared and a fluorescence spectrum is run, generating a value for the fluorescence of the free ligand, FL. A cuvette containing 1.5 mL of the 2 × 10᎑6 mol L᎑1 DAPI solution in phosphate buffer and 1.5 mL of the 50 µg兾mL DNA solution in phosphate buffer is vortex stirred for 30 seconds and a fluorescence spectrum is run. This generates a value for the maximum fluorescence observed at 450 nm, Fmax, corresponding to the state where all possible DAPI is bound to the DNA under the experimental conditions.
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In the Laboratory
Fluorimetry: Generating the Saturation Curve A cuvette is prepared containing 3 mL of the 1 × 10᎑6 mol L᎑1 DAPI solution in phosphate buffer and 10 µL of the 400 µg兾mL DNA solution is added to the cuvette, vortex stirred for at least 30 seconds and the spectrum recorded. This measurement represents the fluorescence observed at 450 nm for the DAPI–DNA complex formed, Fobs. This is repeated for a total of 18 additions.
tration of bound and unbound ligand and the total concentration of macromolecule M. Setting eq 3 equal to eq 5 gives
f [L ]total
[ M]total
[ M]total
Kf =
[ SL ] [ S ][[L ]
[ SL ] [ SL ] + [S]
Nocc = N
(2)
Substituting [ML], expressed in terms of Kf ,from eq 1 into eq 2 gives the following representation for Nocc: Nocc = N
K f [L] K f [L ] + 1
(3)
A plot of Nocc versus [L] would yield a hyperbolic curve and contains the term [L], which is not easily amenable to experimental determination. Conversion to a linear form involves the introduction of the term f, corresponding to the fraction of ligand bound during a titration of ligand to macromolecule. Using our previous terminology, where Fobs is the fluorescence observed after sequential addition of DNA aliquots, FL is the fluorescence of free ligand, and Fmax is the maximum fluorescence when all possible ligand is bound, then f =
Fobs − F L
[L ]total N K f [L ]
+
[ L ]total N
(7)
It can be easily seen that fraction of free ligand, measured experimentally as (1 − f ), can be represented as 1− f =
[L] [L ]total
(8)
Finally, substituting eq 8 into eq 7 gives the final form of a Scatchard equation for this process
[ M]total f
=
1 N K f (1 − f
)
+
[L ]total N
(9)
In this experiment [L]total represents the initial concentration of DAPI and [M]total represents the concentration of DNA over the course of the titration. Using an average weight for a nucleotide base-pair of 650 (New England Biologicals, NEB, 200506 Catalog and Technical Reference, page 280) the [DNA] for a 10 µL aliquot of a 400 mg兾mL solution in a 3 mL cuvette corresponds to 4.11 × 10᎑6 mol L᎑1 (nucleotide), and the [DNA] over the course of the titration ranges from 4.11 × 10᎑6 mol L᎑1 (nucleotide) to 7.40 × 10᎑5 mol L᎑1 (nucleotide), Expressing [DNA] in mol L᎑1 (nucleotide) rather than mol L᎑1 DNA means that a plot of 1兾(1 − f ) versus [M]total兾f yields an intercept of [L]total兾N where N represents the number of ligand binding sites per nucleotide. The value of more relevance here is the reciprocal of N, which is the number of nucleotides per ligand binding site. The slope yields 1兾(NKf) where the binding constant Kf is in units of L mol᎑1 (nucleotide). Because eq 5 is only valid for conditions under which the macromolecule is not saturated values of f and 1兾(1 − f) need to be truncated. The regression line plotted below uses values of 1兾(1 − f) less than 10, or conditions where less than 90% of all available binding sites are occupied. A comparable derivation of the Scatchard equation can be found in ref 12. Hazards
f [L ]total
(5)
[ M]total
where the concentrations in eq 5 represent the total concen-
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(6)
(4)
Fmax − FL
The spectroscopic determination of f allows for the experimental determination of Nocc by realizing that under pre-saturation concentrations of ligand and macromolecule Nocc =
=
f
(1)
where [SL] and [S] are the numer of occupied and unoccupied macromolecule binding sites per unit volume at equilibrium and [L] is the equilibrium concentration of free ligand. If Nocc represents the average number of sites per macromolecule M occupied by the ligand, and N represents the total number of binding sites available per macromolecule M, then the ratio of Nocc to N can be expressed as
N K f [L ] K f [L] + 1
Taking the reciprocal of each side in eq 6 and multiplying through by [L]total gives
Scatchard Analysis The binding affinity between a ligand L and a macromolecule binding site S is expressed as a formation constant for the complex SL, often termed a binding constant
=
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DAPI is available as the 4´,6-diamidino-2-phenylindole dihydrochloride hydrate from Sigma-Aldrich Company. It is identified as an irritant, capable of causing irritation to the eyes, respiratory system, and the skin. It has an NFPA health rating of 2 and appropriate protective equipment, such as gloves and safety glasses, should be worn when handling DAPI solutions. This chemical should be disposed of in a manner consistent with all applicable regulations.
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In the Laboratory
Figure 2. Fluorescence titration curve from a plot of Fobs versus [DNA].
Figure 3. A plot of 1/(1 − f ) versus [DNA]total for the data from Figure 2.
Results
Note of Caution with Computer-Generated Solutions
A typical student plot of Fobs versus [DNA] generates a fluorescence titration curve such as the one shown in Figure 2, where the quantity of complex formed increases until all the available ligand is bound. The sequential addition of DNA aliquots represent changes in DNA concentration from 1.33 µg兾mL to a final value of 24.0 µg兾mL. These represent concentrations in the cuvette of 4.11 × 10᎑6 mol L᎑1 (nucleotide) to 7.40 × 10᎑5 mol L᎑1 (nucleotide). The dilution effect due to the added DNA aliquots is neglected in the calculation of the DNA and ligand concentrations. Plotting 1兾(1 − f ) versus [M]total兾f yields the plot shown in Figure 3, and values for Kf of 10.01 × 106 L mol᎑1 (nucleotide), and a value for 1兾N of 26. Because eq 9 is a reciprocal plot the largest errors are found with small values of f : this corresponds to the first two measurements for this experiment. These data points are omitted in the regression plot shown, giving a coefficient of regression of 0.995. As mentioned previously the regression line uses values of 1兾(1 − f ) less than 10 or conditions where less than 90% of all available binding sites are occupied.
Scatchard analysis remains one of the most popular methods for linearizing data from a saturation binding experiment to determine the binding constant. As is the case for any plot of this kind, such as the Eadie–Hofstee plot for analyzing kinetic data, care must be taken to ensure that the computergenerated solution is justified by the underlying assumptions and is not contravened by common sense. In an analysis of faulty graphical treatments in both Scatchard and Eadie– Hofstee plots it has been observed that the most common error found was the tendency to draw a straight line through points that obviously demanded a curve (14). Thus any degradation, or loss of activity, of either ligand or protein during the course of the experiment would obviously lead to results not amenable to any linearized treatment. Environmental factors affecting the homogeneity of the solution or systematic trends introduced by poor experimental design would also yield data incapable of being treated in such a manner. Special care must be taken with those systems that exhibit cooperativity of binding. In such a system a Scatchard analysis of the binding data would yield a plot that would be clearly nonlinear, and while it is not unusual to see such a curvilinear plot resolved into separate straight lines, such analysis must be undertaken with great caution. Presenting the primary experimental data in conjunction with any analysis of this kind probably provides the simplest defense against unwarranted computer-generated mechanization of experimental data. Residual plots, where the difference between the observed values for the dependent variable minus the value predicted by the regression fit is plotted against the independent variable or other convenient variable, represent a very effective and immediate technique for inspecting the validity of the linear fit. While the plot in Figure 3 does not indicate obvious curvature, in accordance with suggested practice a plot of residuals versus 1兾(1 − f ) was also generated and is included in the Supplemental Material.W A curved pattern in this residual plot would indicate a nonlinear correlation in the original data, but no such pattern is observed.
Discussion Table 1 summarizes the experimental values of Kf, in units of L mol᎑1 (nucleotide), and 1兾N obtained for the most recent group of ten students. Statistical analysis of these data yields a mean value for Kf of 10.79 × 106 L mol᎑1 (nucleotide) with a standard deviation of 7.51 × 106, giving a 95% confidence interval for the mean of 5.42 × 106 to 16.16 × 106. This allows us to eliminate the results for students 2, 3, and 7, giving a revised mean of 11 × 106 with a standard deviation of 2.45 × 106. This compares favorably with the values estimated by Manzini et al. (11) and Kubista et al. (13) of 5 × 106 to 10 × 106. Finally the revised mean value for 1兾N, representing the number of base pairs per bound ligand, for the data in Table 1 is 31. This number compares favorably with the nucleotide兾ligand ratio of 36 measured in the IodoHoechst 33342 study (9). 1306
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In the Laboratory
Literature Cited
Table 1. Student Results for Kf and 1/N Variable
Student 1
2
3
4
5
6
7
8
9
10
Kf
14
0.9
02
10
09
15
28
10
09
10
1/N
33
13
29
29
32
34
33
38
26
26
NOTE: The units of Kf are L mol−1 (nucleotide).
Acknowledgments This experiment was supported by an NSF grant awarded for the purchase of a RF-5301 PC Shimadzu spectrofluorophotometer. The author also wishes to thank the Welch Foundation for its continuing support of the Chemistry Department at St. Edward's University. For their helpful comments and insightful suggestions in the revision of the manuscript thanks is due to the reviewers and especially Randall J. Wildman, JCE Graphics Editor. Finally the author gratefully acknowledges the students of CHEM 4245: Jon Steuernagle, Gloria Martinez, Kevin Condel, Dulce Ibarra, Pedro Garza, Robert Guerra, Johanna Perkins, Emigdio Reyes, Jeanine Traag, and Ada Powers. Supplemental Material Detailed instructions for students, instructor notes, and sample experimental data are available in this issue of JCE Online. W
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