In the Laboratory
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Experimental Design and Polyelectrolyte Effects on Ligand Binding to Nucleic Acids An Undergraduate Biochemistry Lab Matthew A. Fisher,* Danielle Johnston, and Daniel A. Ritt Department of Chemistry, Saint Vincent College, Latrobe, PA 15650; *
[email protected] Ligand binding to biological macromolecules such as nucleic acids and the dependence of binding on solution variables such as pH or temperature is a central concern in biochemistry. Often, these binding equilibria are complicated functions of variables such as pH, salt concentration, temperature, and the presence of other potential ligands. Consequently, the use of experimental design approaches is particularly appropriate for understanding how these equilibria respond to changes in solution variables. Yet there are few experiments appropriate for use in the undergraduate biochemistry lab which provide students with direct experience in this area. The binding of ethidium bromide to DNA has long been a part of undergraduate biochemistry lab activities. In many cases this experiment is used simply to demonstrate the fluorescence increase upon intercalation and estimate the equilibrium constant for binding. By utilizing a procedure for monitoring ethidium binding published in this Journal (1), we have developed a new experiment that allows undergraduate students to explore the binding of the polyamine spermine to DNA. The binding of spermine, a cationic ligand, is influenced by the polyelectrolyte nature of DNA. As a result, the observed equilibrium binding constant is a function of the concentrations of both monovalent and divalent cations in solution. The interaction between these two variables provides a situation where students can develop a better understanding of how two or more variables may interact and therefore alter how the system of interest responds to changes in one variable. In addition, students are exposed to DNA–ligand interactions that involve two different modes of binding—intercalative and electrostatic. Completion of this experiment gives students a better understanding of experimental design and the polyelectrolyte nature of DNA.
The binding of any charged ligand involves the displacement of cations from the surface of the DNA. Generally the ligand binding equilibrium is written as DNA + Lz+ → complex
(1)
yet the actual equilibrium is given by DNA
(aM+,
+
bH2O)
᎑
Lz+
→
(cX , d H2O)
complex + (z)aM+ + cX ᎑ + (b + d )H2O
(2)
The equilibrium constant for eq 1 is normally written as
K obs =
c complex DNA Lz+
where ccomplex is the concentration of the ligand–DNA complex formed. Since Kobs does not explicitly include cations, anions, and water, it becomes a function of those variables. The cations displaced by ligand binding in eq 2 give rise to a favorable free entropy of dilution that is a significant source of the stability of the complex. As the bulk salt concentration is increased, the magnitude of the favorable entropy of dilution decreases and the complex becomes less stable. This approach has been used to examine the electrostatic contribution to the stability of various protein–DNA complexes (4). The entire analysis is more complicated in solutions containing both monovalent and divalent cations (5). In this case, divalent cations compete for association with the surface of the DNA. As a result, the dependence of Kobs on changes in monovalent salt concentration is reduced. Experimental Design
DNA as a Polyelectrolyte DNA is a highly charged polymer; in fact, with one negative charge every 1.7 Å, it is one of the most highly charged natural polymers known. The significant charge density and accompanying repulsive interaction result in cation accumulation near the DNA surface (2), which reduces the unfavorable interaction between adjacent phosphates. The degree of cation accumulation is relatively insensitive to bulk salt concentration, reaching the equivalent of 1–2 M in the vicinity of the DNA surface. Consequently, in solution DNA behaves thermodynamically as a weakly dissociated polyelectrolyte with a certain fraction of counterions “thermodynamically bound” per phosphate (3). In solutions containing only monovalent cations, DNA behaves as if there were 0.88 M+ cations bound per phosphate.
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Experimental design is a strategy by which deliberate changes are made in the factors that contribute to a process in order to observe the corresponding changes in the responses (6 ). This approach can be used for (i) identifying key input factors, (ii) understanding the relationship between input factors and response, (iii) developing mathematical models relating response to input, and (iv) determining optimal settings. The goal is to map out the “response surface” for a process as a function of several key variables. In recent years the suggestion that undergraduates should be familiar with experimental design has been made with increasing frequency (7). The experiment that we describe in this paper uses a full factorial design, in which all possible combinations of the selected factors are examined at various levels in same experimental series. Since only two factors are being varied in this
Journal of Chemical Education • Vol. 79 No. 3 March 2002 • JChemEd.chem.wisc.edu
In the Laboratory 16 8
(1/Kobs) / 10−6
(ν/[L]) / 104
12
8
6
4
2
4 0 0
0 0.0
0.1
ν
4
8
12
Spermine Concentration / mM
0.2
Figure 1. Scatchard plot of ethidium binding at various spermine concentrations. ν/[L] represents the ratio of bound to free ethidium and ν represents bound ethidium. Spermine concentrations used were (䊉) 0 mM, (䉬) 4.5 mM, (䉱) 9 mM, and (䊏) 13.5 mM.
Figure 2. Plot of the reciprocal of Kobs, the ethidium binding constant, as a function of the spermine concentration. The slope of this line divided by the intercept gives K ′, the binding constant for spermine. Data shown were obtained at 0.2 M NaCl and K ′ was determined to be 338 M᎑1.
experiment, a full factorial design requires only four sets of data. While it is possible to examine more variables than the ones selected here, focusing on how spermine binding is affected by changes in both Na+ and Mg2+ concentrations allows students to develop a clearer sense of how these variables are linked.
To examine the effect of changing either Na+ or Mg2+ concentration on spermine binding, complete sets of titrations (fluorescent intensity constants and ethidium binding constants) were carried out under four solution conditions:
Procedure The procedure that we used was essentially the one described by Strothkamp and Strothkamp (1). All spectra were recorded on a Perkin Elmer LS-50B spectrofluorometer. Exact concentrations of ethidium and DNA solutions were determined by UV–vis spectroscopy. The buffer used throughout was 0.05 M Hepes, pH 7.5, with the NaCl and MgCl2 concentrations listed below. The intensity constant for free ethidium was determined by recording fluorescence spectra after each addition of a small aliquot of 3 × 10᎑4 M ethidium to a cuvette that initially contained 3 × 10᎑6 M ethidium. Titrations of 3 x 10-6 M ethidium solutions with small aliquots of 3 × 10᎑3 M DNA were used for the determination of the fluorescence intensity constants for ethidium bound to DNA. Binding titrations were carried out by the addition of small aliquots of 3 × 10᎑4 M ethidium to a 3 × 10᎑6 M solution of DNA. The degree of ethidium binding to DNA was determined by the relationship Iobs = Ib + If where Iobs is the observed fluorescence intensity, Ib is the fluorescence intensity of the bound dye, and If is the fluorescence intensity of the dye still free in solution. The intensities of both bound and free dye are a function of the concentration of the relevant form of the dye and a fluorescence intensity constant. Titrations were carried out at several spermine concentrations and Kobs for ethidium binding was determined. Replotting the reciprocal of this observed equilibrium constant as a function of spermine concentration allowed determination of K ′, the equilibrium constant for spermine binding.
0.2 M Na+, 0 mM Mg2+ 0.2 M Na+, 10 mM Mg2+ 0.3 M Na+, 0 mM Mg2+ 0.3 M Na+, 10 mM Mg2+
(low Na+/low Mg2+) (low Na+/high Mg2+) (high Na+/low Mg2+) (high Na+/high Mg2+)
All reagents used in a particular titration set (ethidium bromide solution, DNA, spermine) were prepared in buffer that contained the appropriate Na+ and Mg2+ concentration for that set. Each group of students was responsible for one complete titration set. Data collection was spread out over two 3-hour lab periods; students determined the fluorescence intensity constants for free and bound ethidium during the first lab period and completed the actual binding titrations during the second lab period. Hazards Ethidium bromide (CAS Registry 1239-45-8) is a mutagen that may cause skin and eye irritation. Appropriate protective equipment (goggles, gloves) should be worn when working with ethidium bromide solutions. The chemical should be disposed of in a manner consistent with federal, state, and local regulations. Ethidium-contaminated materials must not be disposed of with household garbage and should not be allowed to reach the sewage system. Results and Discussion Figure 1 shows typical student results for the Scatchard plot that allows determination of Kobs, the equilibrium constant for ethidium binding to DNA. As the concentration of spermine increases, the slope of the line (equal to ᎑Kobs) becomes less steep. By replotting these values as a function of spermine concentration (as shown in Fig. 2), the spermine–DNA binding constant can be determined.
JChemEd.chem.wisc.edu • Vol. 79 No. 3 March 2002 • Journal of Chemical Education
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In the Laboratory
Spermine Binding Constant
400
300
200
100
0 0.20
0.25
0.30
+
[Na ] / M Figure 3. Factor interaction plot showing the spermine binding constant as a function of Na+ concentration. The solid line represents data obtained in the absence of Mg2+; the dashed line represents data obtained in the presence of 10 mM Mg2+.
Figure 3 shows a “factor interaction” plot. This is a visual representation of how the system of interest responds to changes in one variable at different fixed levels of a second variable. In this graph, the dependence of the spermine binding constant is shown as a function of Na+ concentration at 0 and 10 mM Mg2+. In factor-interaction plots, parallel lines indicate that the two variables represented act independently on the system. Intersecting lines indicate that the two variables are linked and that changing one of them will alter how the system responds to changes in the other. As shown here, the presence of 10 mM Mg2+ has a significant effect on how sensitive the spermine binding constant is to changes in Na+ concentration. This can be explained by considering the higher affinity of Mg2+ for the highly charged DNA. In a mixed salt solution, spermine binding can displace either a Na+ or a Mg2+ ion, in contrast to the pure monovalent salt solution where only Na+ ions can be displaced by spermine. The contribution of the Mg2+ entropy of dilution to the binding free energy varies very little with changes in Na+ concentration. As a result, the spermine binding constant is much less sensitive to changes in Na+ concentration when Mg2+ is present in the reaction. Students carry out this experiment as part of our secondsemester biochemistry laboratory focused on nucleic acids and membranes. The values obtained in this experiment— approximately 340 M᎑1 at 0.2 M Na+ and no Mg2+—compare very well with values published in the research literature and obtained by equilibrium dialysis (8). Biochemistry majors take this course at the same time as the instrumental analysis lab, where the concepts of experimental design also are presented.
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Comments from students as they carry out this experiment indicate that they appreciate the connections between the two courses. Although we have described this experiment as being carried out within the context of an undergraduate biochemistry lab course, we believe that it can also be effectively incorporated into other upper-level lab courses where biophysical chemistry experiments would be appropriate. In addition, the experiment could be modified for use in larger lab sections where instrument access is limited. The students can work in groups, each group doing a different experiment during the same lab period and rotating experiments every week or every other week until each group has done every experiment. Instructors could have students experimentally determine the fluorescence intensity constant for free ethidium but provide them with previously collected data to be used in calculating the fluorescence intensity constant for bound ethidium, which is more time consuming to determine. These modifications would provide additional flexibility in terms of carrying out the experiment without sacrificing any pedagogical goals. Acknowledgment Purchase of the Perkin Elmer LS-50B was made possible in part by an ILI grant from the National Science Foundation. WSupplemental
Material
Detailed instructions for students and additional tips and resources for the instructor are available in this issue of JCE Online. Literature Cited 1. Strothkamp, K. G.; Strothkamp, R. E. J. Chem. Educ. 1994, 71, 77–79. 2. Record, M. T. Jr; Anderson, C. F.; Lohman, T. M. Q. Rev. Biophys. 1978, 11, 103–178 3. Record, M. T. Jr.; Lohman, T. M.; deHaseth, P. L. J. Mol. Biol. 1976, 107, 145–158 4. Record, M. T. Jr.; Ha, J. H.; Fisher, M. A. Methods Enzymol. 1991, 208, 291. 5. Record, M. T; deHaseth, P. L.; Lohman, T. M. Biochemistry 1977, 16, 4791–4795. 6. Schmidt, S. R.; Launsby, R. G. Understanding Industrial Designed Experiments, 4th ed.; Air Academy Press: Colorado Springs, CO, 1994. 7. Van Ryswyk, H.; Van Hecke, G. R. J. Chem. Educ. 1991, 68, 878. 8. Braunlin, W. H.; Strick, T. J.; Record, M. T. Jr. Biopolymers 1982, 21, 1301–1314.
Journal of Chemical Education • Vol. 79 No. 3 March 2002 • JChemEd.chem.wisc.edu
