Langmuir 2003, 19, 9387-9394
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Thermodynamic Analysis of Polycation-DNA Interaction Applying Titration Microcalorimetry Touraj Ehtezazi,† Uracha Rungsardthong, and Snjezana Stolnik* School of Pharmaceutical Sciences, University of Nottingham, University Park Nottingham, NG7 2RD, United Kingdom Received November 20, 2002. In Final Form: July 30, 2003 Nonviral gene delivery systems based on DNA complexes with polycations have recently been extensively studied. An important consideration in the design of such therapeutic systems is the understanding of forces governing the DNA-polycation interaction and the complex stabilization. In this work, the interaction of a cationic polymer from the poly(amidoamine) family (poly(bis-acryloylpiperazine-2-methyl-piperazine), p(BAP-2MP)) with DNA at different salt concentrations and pHs and in different buffers was studied using isothermal titration microcalorimetry as a principal tool. The binding isotherms were analyzed using a proposed complexation-condensation model, to calculate the observed binding constant, Kobs, enthalpies of the complex formation and condensation process, ∆H°com and ∆H°con, and complexation site and condensation site exclusion sizes, ncom and ncon, respectively. Kobs, ∆H°com, and ∆H°con decreased with increasing salt concentration, indicating involvement of electrostatic interactions. However, ncom was rather independent of salt concentration and nearly equal to the average number of ionized charges at the polycation, indicating that the ratio of nucleotide to p(BAP-2MP) monomer units is close to 1. Dissection of the free energy of interaction showed that electrostatic contributions dominate the p(BAP-2MP)-DNA interaction. The use of buffers with different protonation enthalpies demonstrated that the p(BAP-2MP) interaction with DNA is coupled with a proton extraction from the buffer resulting in an enthalpy change and enabling the polymer ionization and interaction at a stoichiometric ratio. Obtained intrinsic binding parameters (in a buffer with ∆Hion ) 0) reveal that p(BAP-2MP) interaction with DNA is nonspecific with a moderate binding constant and that it contains the enthalpic contribution (probably due to the formation of hydrogen bonding). The values for the condensation process, ncon and ∆H°con, indicate that there is no further ionization of the p(BAP-2MP) polymer to interact with DNA and that the stoichiometric ratio is preserved.
1. Introduction DNA complexes with polycations have been extensively studied for their potential for introduction of functional genes into recipient cells and hence applications in the gene therapy field.1-4 Hence, the understanding of forces governing the DNA-polycation interaction and the complex stabilization will allow a correlation to be established between structural properties of polymeric materials, their condensation properties with DNA, and the resulting biological performance of the complexes. The interaction of ligands with DNA can be generally either specific or nonspecific.5 The most distinguished characteristic of a specific binding is a high binding constant, Ka (usually larger than 109 M-1), and the binding is usually accompanied by the release of water molecules at the ligand-DNA interface.6-9 Therefore, the avidity of the ligand to DNA increases by decreasing the water activity in aqueous solutions, the situation which happens * Corresponding author. Tel: 44 (0) 115 846 6074. Fax: 44 (0) 115 951 5102. E-mail:
[email protected]. † Present address: Faculty of Pharmacy and Chemistry, Liverpool John Moores University, Liverpool, L3 3AF, U.K. (1) Perales, J. C.; Grossmann, G. A.; Molas, M.; Ferkol, G. L.; Harpst, J.; Oda, H.; Hanson, R. W. J. Biol. Chem. 1997, 272, 7398. (2) Perales, J. C.; Ferkol, T.; Molas, M.; Hanson, R. W. Eur. J. Biochem. 1994, 266, 255. (3) Wu, G. Y.; Wu, C. H. J. Biol. Chem. 1992, 267, 12436. (4) Wilson, J. M.; Grossman, M.; Wu, C. H.; Chowdhry, N. R.; Wu, G. Y.; Chowdhury, J. R. J. Biol. Chem. 1992, 267, 963. (5) Lohman, T. M.; Mascotti, D. P. Methods Enzymol. 1992, 221, 400. (6) Garner, M. M.; Rau, D. C. EMBO J. 1995, 14, 1257. (7) Parsegian, V. A.; Rand, R. P.; Rau, D. C. Methods Enzymol. 1995, 259, 43. (8) Lundback, T.; Hansson, H.; Knapp, S.; Ladenstein, R.; Hard, T. J. Mol. Biol. 1998, 276, 775. (9) Sidorova, N. Y.; Rau, D. C. Proc. Natl. Acad. Sci. U.S.A. 1996, 93, 12272.
in vivo due to the crowding of the other organelles and biological compounds.6 In contrast, the nonspecific interaction of a ligand with DNA is independent of a nucleotide sequence and has a smaller binding constant relative to a specific binding and the binding constant decreases by increasing salt concentration.10-14 However, the binding constant for nonspecific interactions is independent of the water activity.8 Hence, a determination of the mechanism of polycation interaction with DNA is very important in the formulation of gene delivery systems. The driving force for a polycation interaction with DNA in a low to moderate ionic strength environment is, according to Manning’s theory, a dilution of monovalent cations condensed on DNA.10,11 In the presence of a polycation, the degree of charge neutralization of DNA increases as the polycation condensation is increased and after a critical polycation concentration DNA condenses into a compact dense structure that precipitates from the solution.15-18 Due to the important prospect of polycationDNA complexes for gene delivery, the condensation process has attracted considerable interest and has been studied by applying techniques such as atomic force microscopy,19,20 fluorescence spectroscopy,21,22 electron microscopy,1,23 X-ray scattering,24,25 and light scattering.15,17,26 However, these methods are unable to provide reliable (10) Manning, G. S. J. Chem. Phys. 1969, 51, 924. (11) Manning, G. S. Q. Rev. Biophys. 1978, 11, 179. (12) Record, M. T.; Anderson, C. F.; Lohman, M. L. Q. Rev. Biophys. 1978, 11, 103. (13) Lundback, T.; Hard, T. J. Phys. Chem. 1996, 100, 17690. (14) Matulis, D.; Rouzina, I.; Bloomfield, V. A. J. Mol. Biol. 2000, 296, 1053. (15) Porschke, D. Biochemistry 1984, 23, 4821. (16) Shapiro, J. T.; Leng, M.; Felsenfeld, G. Biochemistry 1969, 8, 3219. (17) Wilson, R. W.; Bloomfield, V. A. Biochemistry 1979, 18, 2192. (18) Bloomfield, V. A. Curr. Opin. Struct. Biol. 1996, 6, 334.
10.1021/la0268799 CCC: $25.00 © 2003 American Chemical Society Published on Web 09/13/2003
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Figure 1. Poly(bis-acryloylpiperazine-2-methyl-piperazine) structure, p(BAP-2MP).
quantitative thermodynamic information about the complexation process and consequently condensed DNA. Studies applying isothermal titration microcalorimetry can provide quantitative information about thermodynamic parameters and forces that govern the interaction and stabilize the complex and can also predict the stability of the complex in different biological environments. Isothermal titration calorimetry has been successfully applied to assess thermodynamic parameters of small ligands (such as anticancer drugs) or protein interaction with DNA, but there has been a lack of studies focusing on polycation-DNA condensation. In this work, we applied the isothermal titration calorimetry technique to study the complex formation between DNA and a linear polyamidoamine polymer: poly(bis-acryloylpiperazine-2-methyl-piperazine) p(BAP-2MP) (Figure 1.).27,28 p(BAP-2MP) belongs to a poly(amidoamine) (PAA) family of promising polymeric vectors for nonviral gene delivery, as the polymers are biodegradable and have low cell cytotoxicity. We have recently demonstrated that PAAs with different molecular architecture form complexes with DNA with very different cell transfection efficiency, stability to enzymatic degradation, morphology, and colloidal properties.29,30 These observations have led to the present study aimed at determining the thermodynamics of PAA-DNA interaction and developing a mathematical model to describe calorimetric data. 2. Model and Experimental Section 2.1. Complexation-Condensation Model. To analyze thermodynamic data on polycation-DNA condensation, we propose the following complexation-condensation model. The model implies that two processes are occurring during polycation-DNA condensation: (i) complex formation between the polycation and DNA and (ii) condensation of DNA by the polycation. We assume that each phosphate group of DNA is a binding site and that each polycation molecule can interact with more than one binding site on DNA. To reduce the complexity of the modeling, we assume that the interaction of the polycation with DNA is nonspecific, which allows us to apply a nonspecific site size exclusion model.31 This model has been applied to calculate the binding constant of DNA-spermine15 and DNA-poly-L-lysine interaction.32 In the present model, we assume that the complex formation stage of p(BAP-2MP) interaction with DNA is a noncooperative process. This assumption can be supported by a (19) Hansma, H. G.; Golan, R.; Hsieh, W.; Lollo, C. P.; Mullen-Ley, P.; Kwoh, D. Nucleic Acids Res. 1998, 26, 2481. (20) Fang, Y.; Hoh, J. H. J. Am. Chem. Soc. 1998, 120, 8903. (21) Trubetskoy, V. S.; Slattum, P. M.; Hagstrom, J. E.; Wolff, J. A.; Budker, V. G. Anal. Biochem. 1999, 267, 309. (22) Kidoaki, S.; Yoshikawa, K. Biophys. Chem. 1999, 76, 133. (23) Hud, N. V.; Downing, K. H.; Balhorn, R. Proc. Natl. Acad. Sci. U.S.A. 1995, 92, 3581. (24) Rau, D. C.; Parsegian, V. A. Biophys. J. 1992, 61, 246. (25) Haynes, M.; Garrett, R. A.; Gratzer, W. B. Biochemistry 1970, 9, 4410. (26) Schnell, J. R.; Berman, J.; Bloomfield, V. A. Biophys. J. 1998, 74, 1484. (27) Ferruti, P.; Barbucci, R. Adv. Polym. Sci. 1984, 58, 55. (28) Ferruti, P. Polymeric Material Encyclopaedia; CRC Press: Boca Raton, FL, 1996; Vol. 5 (H-L), p 3334. (29) Hill, I. R. C.; Garnett, M. C.; Bignotti, F.; Davis, S. S. Biochem. Biophys. Acta 1999, 1427, 161. (30) Martin, A. L.; Rackstraw, B. J.; Robert, C. J.; Stolnik, S.; Tendler, S. J. B.; Williams, P. M. FEBS Lett. 2000, 480, 106. (31) McGhee, J. D.; von Hippel, P. H. J. Mol. Biol. 1974, 86, 469.
Ehtezazi et al. good fit of the noncooperative model to the experimental data. Both noncooperative and positively cooperative interactions of a polycation with DNA have been reported.16,33 For instance, interaction of poly-L-lysine with a high degree of polymerization and DNA was found to be positively cooperative,16 whereas for the DNA interaction with spermine and poly-L-lysine with a low degree of polymerization, a noncooperative interaction was assumed.15,32 Recently, the interaction of polycations with DNA even with a high degree of polymerization has been found to be noncooperative.33 Also, if a cooperativity occurs in the interaction of a polycation with DNA, our model describes the whole condensation process by the enthalpy of condensation (∆H°con) and number of nucleotides covered by one polycation molecule (ncon), and therefore details of the condensation process (such as possible cooperativity) do not affect the evaluation of the binding parameters. Applying the above consideration, the interaction of a polycation with DNA can be evaluated as the following:31
[
ν 1 - nν ) K(1 - nν) [p(BAP-2MP)]free 1 - (n - 1)ν
]
n-1
(1)
where [p(BAP-2MP)]free is the p(BAP-2MP) unbound (free) concentration, ν (binding density) denotes [p(BAP-2MP)]bound/ [DNA phosphate groups], n represents the number of phosphate groups occupied by each p(BAP-2MP) molecule, and K denotes the association constant. The heat content of the p(BAP-2MP)-DNA after i injections, Qi, is given by
Qi ) [p(BAP-2MP)]bound ∆H°com Vi
(2)
where ∆H°com denotes the standard enthalpy of complex formation, and Vi represents the volume of the interaction solution (which is the volume in the cell of the microcalorimeter). In the model, we have assumed that binding density increases with increasing polycation concentration, and when the number of neutralized charges on DNA exceeds a critical number, which corresponds to a critical binding density, νc, DNA condenses and precipitates.15,24 Therefore, the system consists of DNA/polycation complexes with binding densities up to νc and condensed DNA with binding densities above νc. These two forms of DNA are in equilibrium.16,34 If in the condensed form of DNA each polycation molecule is interacting with a number ns of DNA nucleotides, then we have the following relation:
[DNA]con ) [p(BAP-2MP)]conns
(3)
where [DNA]con denotes the concentration of nucleotides that forms the DNA condensates, and [p(BAP-2MP)]con is the concentration of polycation that takes part in the condensation. The heat content for the condensation, Qcon, can be given by eq 4.
Qi,con ) [p(BAP-2MP)]i,con ∆H°con Vi
(4)
where subscript i denotes the corresponding values after i injections, and ∆H°con represents the standard enthalpy of condensation. The total heat content, Qi, for interaction of a polycation with DNA is the sum of heat of complexation and heat of condensation, Qi,com and Qi,con, and therefore by adding eqs 2 and 4 we obtain
Qi ) Vi([p(BAP-2MP)]i,com ∆H°com + [p(BAP-2MP)]i,con ∆H°con) (5) For the modeling, we have assumed that precipitation and condensation happen simultaneously when the concentration of the polymer exceeds a critical value, to reduce the number of calculating parameters. (The complexation-condensation model proposed involves calculation of five parameters, and introduction (32) Lohman, T. M.; DeHaseth, P. L.; Record, M. T., Jr. Biochemistry 1980, 19, 3522. (33) Pouton, C. W.; Lucas, P.; Thomas, B. J.; Uduehi, A. N.; Milory, D. A.; Moss, S. H. J. Controlled Release 1998, 53, 289. (34) Leng, M.; Felsenfeld, G. Proc. Natl. Acad. Sci. U.S.A. 1966, 56, 1325.
Thermodynamics of Polycation-DNA Interaction
Figure 2. Calorimetric data for the titration of p(BAP-2MP) into DNA in 20 mM Tris-HCl, pH 7.4. The blank titration (i.e., titration of p(BAP-2MP) into 20 mM Tris-HCl, pH 7.4) is also shown. of more parameters will substantially increase the complexity of modeling and the possibility of interconnections between calculated parameters.) The assumption is based on experimental findings that condensation of DNA is difficult to distinguish rigorously from aggregation or precipitation.35 While the condensation of single DNA molecules has been observed, it is more commonly reported that several molecules will associate into a single condensed structure which usually leads to the formation of insoluble complexes that phase separate from the solution,36 especially in the concentration range used in our experiments (see Figures 9 and 10). 2.2. Analysis of Binding Isotherms. The equilibrium binding parameters, K, ∆H°, and n were determined by applying the nonlinear least-squares routines available within Origin 5.0 (MicroCal Software) to eqs 1-5. The applied numerical method was modified to include the complexation-condensation model condition: where ν > νc is valid, the condensation should occur until that condition is not anymore valid. The value of νc was altered and chosen so that the standard deviations of the calculated parameters were minimal and an optimum fitting was obtained. The integrated heats of binding were corrected for the enthalpy of dilution, ∆Hd, before calculation of binding parameters. For each binding isotherm, ∆Hd was determined from the average of released heats of the end injections, when the reaction was completed. However, for each experiment a blank titration (injection of p(BAP-2MP) solution into the buffer solution, which does not contain DNA) was also performed to ensure that ∆Hd was small and rather constant in comparison to the heat of interaction (Figure 2). To ensure the accuracy of determined binding parameters, the concentration of DNA was chosen so that [DNA]totalK > 1 (varied between 11 and 164).37 Since the concentration of the reactants rather than their activities was used, the subscript “obs” was affixed to the calculated binding parameter. The free energy of complex formation (∆G°obs) was calculated from ∆G°obs ) -RT ln(Kobs), and the entropy of binding was determined from ∆S°obs ) (∆H°obs ∆G°obs)/T. 2.3. Materials and Methods. 2.3.1. Materials. Calf thymus DNA was purchased from Sigma, U.K., and was cleaned by ethanol precipitation. p(BAP-2MP) polymer was obtained from Dr. F. Bignotti, University of Brescia, Italy.38 The polymer has a weight-average molecular weight Mw ) 25 300 Da and a number-average molecular weight Mn ) 15 000 with a polydispersity of 1.68. The average degree of polymerization was calculated to be n ) 51. Two pK values for the polymer are pKa1 ) 7.2 and pKa2 ) 3.3. The polymer was supplied as a freeze-dried solid. Sodium chloride (reagent grade) and ethidium bromide were obtained from Sigma. Water used for all experiments was ultrapure Elgastat Option 3 water (Elga Ltd., U.K.). All other chemicals used were of chromatographical grade. 2.3.2. Isothermal Titration Microcalorimetry. Calorimetric experiments were performed using a thermal activity monitor (TAM 2277, Thermometric AB, Sweden) operated at (35) Bloomfield, V. A. Biopolymers 1997, 44, 269. (36) Kabanov, V. A. Macromolecular Complexes in Chemistry and Biology; Spring-Verlag: Berlin, 1994. (37) Wiseman, T.; Williston, C.; Brandt, J. F.; Lin, L. N. Anal. Biochem. 1989, 17, 131. (38) Bignotti, F.; Sozzani, P.; Ranucci, E.; Ferruti, P. Macromolecules 1994, 27, 7171.
Langmuir, Vol. 19, No. 22, 2003 9389 298 K. Samples of calf thymus DNA and p(BAP-2MP) were prepared in buffers (1 mM phosphate buffer, Tris-HCl 20 mM or citrate monosodium 20 mM), and specified concentrations of NaCl were added to form final NaCl concentrations of 0.014, 0.024, 0.039, and 0.064 mM. The samples were adjusted to pH 7.4 or 5.0 using dilute HCl and NaOH. In each experiment, a 2.5 mL sample of a 125 µg/mL solution of DNA was placed in a sample cell and inserted into the instrument. Once the thermal equilibrium was reached, the titration was performed by consecutive injections of a 2.25 mg/mL solution of p(BAP-2MP). The titrant was added by means of a Hamilton microlab syringe mounted in a computer-operated syringe drive (Lund 6100 syringe pump). Heats of dilution/mixing were determined in blank titrations by injecting aliquots (20 µL) of p(BAP-2MP) (2.25 mg/ mL) into the appropriate buffer solution (the same NaCl concentration as the experiment) (2.5 mL). The experimental method setup via the Digitam 3 software allowed for data collection over a 15 min period for the injection and a 5 min baseline period before the next injection. This was found to be adequate for the interaction to proceed to completion at each injection point and reach baseline before the next injection. Data presented are the mean of a minimum of two replicate titrations at each NaCl concentration. The signs of the released heat values were reversed for data analysis since the output from the instrument employed in this study is from the perspective of the equipment and not the system under study. The pH change of all samples after the experiment did not exceed (0.2. 2.3.3. Scattering Intensity Studies. The scattering intensity of p(BAP-2MP)-DNA complexes was measured by a Malvern S4700 PCS system (Malvern Instruments, Malvern, U.K.). The study was undertaken by the titration of polymers into 10 µg of calf thymus DNA prepared in 500 µL of 1 mM phosphate buffer containing various concentrations of NaCl (0.014, 0.024, 0.039, and 0.064 mM). Following addition of polymer aliquots, the samples were mixed by gentle agitation and measurements were performed at 25 °C using a 40.7 mW laser and a scattering angle of 90°. The scattering intensity of each sample was obtained as the mean of 10 determinations. The data presented are the mean of a minimum of two replicate titrations at each NaCl concentration. 2.3.4. Quantification of Soluble/Complexed DNA. To quantify free and complexed DNA at various polymer concentrations, aliquots of p(BAP-2MP) solution were added into separate test tubes containing 40 µg of calf thymus DNA (1 mg/mL). (The samples were prepared with 1 mL of 1 mM phosphate buffer, pH 7.4.) The contents of the test tubes were centrifuged at 3600 rpm for 15 min. From each test tube, 0.5 mL of the supernatant was removed and quantified in duplicate at varying polymer concentrations by UV at 260 and 280 nm (Beckman spectrophotometer, Beckman Instruments, USA). 2.3.5. Ethidium Bromide Displacement Assay. Ethidium bromide (2 µg of 1 mg/mL) was added to 1 mM phosphate buffer in cuvettes and mixed by gentle agitation. Fluorescence was recorded in triplicate at λex ) 560 nm and λem ) 605 nm in a Hitashi F-4500 fluorescence spectrophotometer. Calf thymus DNA (10 µg) was added, and fluorescence was measured again. Following the aliquot, a volume of polymer was then titrated into the solution. Samples were mixed gently, and readings were taken after 1-2 min. Readings were estimated in duplicate, and separate tubes were used for each measurement. The relative fluorescence was calculated as below:
% relative fluorescence ) fluorescence(obs) - fluorescence(EtBr) fluorescence(DNA+EtBr) - fluorescence(EtBr) fluorescence(DNA+EtBr) ) fluorescence of observed DNA + ethidium bromide fluorescence(obs) ) fluorescence of observed measure fluorescence(EtBr) ) fluorescence of observed ethidium bromide alone
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Figure 3. (a) Integrated heats of interaction corrected for heats of dilution from the titrations of p(BAP-2MP) into DNA at varying concentrations of monovalent salt. Solid lines represent the fit of binding isotherms to the experimental data applying the proposed complexation-condensation model. (b) Integrated heats of interaction corrected for heats of dilution from the titrations of p(BAP-2MP) into DNA at varying concentrations of monovalent salt. Solid lines represent the fit of binding isotherms to the experimental data applying only the noncooperative McGhee-von Hippel model.
3. Results and Discussion 3.1. Salt Dependence of Complex Formation between p(BAP-2MP) and DNA. 3.1.1. Salt Dependence of Kobs. The experimental binding isotherms at different salt concentrations of phosphate buffer and the curves generated by applying the proposed complexationcondensation model to fit the experimental data are shown in Figure 3a. The graph illustrates that the generated curves fit the experimental data in good agreement (with a high value for the data fitting parameter). The experimentally released heats were also analyzed by applying only the noncooperative McGhee-von Hippel model,31 and the generated curves are illustrated in Figure 3b. Although the generated curves describe the experimental data well at lower polymer concentrations, there is a deviation at higher polymer concentrations (with the data fitting parameter significantly lower than for the former model). These curves therefore suggest that during the interaction of p(BAP-2MP) with DNA more than just complex formation occurs. This can be considered to be a condensation of DNA at higher polymer concentrations, when the critical neutralization of phosphate groups of DNA had occurred, as previously described.35 However, when the noncooperative McGhee-von Hippel model was applied, a good fit of the initial part of the experimental data was gained, which strongly suggests that during the first stage of the DNA interaction with p(BAP-2MP) the only process occurring is complex formation. Good fitting of the experimental data by applying the proposed complexation-condensation model and also a good fitting of the initial part of Figure 3b by applying only the McGhee-von Hippel model both indicate that the complex formation between DNA and p(BAP-2MP) is
Ehtezazi et al.
a noncooperative process, and if cooperation occurs, it takes place after a critical binding density is achieved and during the condensation process. Similarly, the cooperative nature of an interaction of polycations (such as poly-Llysine) and DNA reported previously1,16 has been attributed to the entropically favorable precipitation of DNA when electrostatic neutralization is achieved. In fact, the binding isotherms in Figure 3b indicate that there is cooperativity in the interaction, in the way that the total reaction heat content, Q, reaches a plateau earlier than the generated curves by applying only the noncooperative McGhee-von Hippel model, especially when the ionic strength of the medium is low. This reveals that all available binding sites on DNA are occupied at low concentrations of p(BAP-2MP) rather than in very high (or mathematically at infinite) concentrations of p(BAP2MP). Actually, our proposed complexation-condensation model considers the cooperativity of interaction between p(BAP-2MP) and DNA implicitly. The model assumes that above a critical binding density, νc, DNA condenses and precipitates in a way that the ratio of bound nucleotides to each p(BAP-2MP) molecule is ns and that the precipitation continues until the binding density, ν, falls below νc. Therefore, condensed DNA has a certain degree of coverage by p(BAP-2MP), which reflects the cooperativity of interaction. In other words, binding of molecules of p(BAP-2MP) to DNA (above νc) leads to precipitation until available polymer molecules are used up and ν falls below ν c. The binding parameters resulting from the analysis of binding isotherms by applying the proposed complexation-condensation model at different salt concentrations (total monovalent cation concentration [M+], pH ) 7.4, and 1 mM phosphate buffer) are given in Table 1. The calculated values for ∆Hcom, ∆Scom, and ∆Hcon do not represent the intrinsic binding values and they are buffer dependent, as explained in the following sections. The results of the analysis of binding isotherms by applying only the noncooperative McGhee-von Hippel model are given in Table 2. A comparison between these two sets of data (Tables 1 and 2) demonstrates that when only the McGhee-von Hippel model is applied there is no trend between Kobs and salt concentration (Table 2), whereas according to Manning’s counterion-condensation theory,10-12 Kobs should decrease with increasing salt concentration. On the contrary, when the proposed complexation-condensation model is applied the trend between Kobs and increasing salt concentration is established and the fit to experimental data is better (Table 1). However, using only the noncooperative McGhee-von Hippel model, one can obtain a good approximation of the parameters (ncon and ∆Hcom are in good agreement, Tables 1 and 2), which are useful as initial values in calculating binding parameters by applying the complexationcondensation model. The results in Table 1 clearly show an ionic strength (salt) dependence of Kobs, which decreases by increasing the salt concentration. Figure 4 shows the plot of log(Kobs) versus log(M+) and demonstrates that log(Kobs) decreases linearly by increasing log(M+). By application of linear regression to the experimental data, a best-fit line was obtained with a slope of -2.61 and an intercept of 0.61. The slope value demonstrates the high sensitivity of Kobs to the salt concentration of the solution and thus indicates that electrostatic interactions are an important part of the interaction forces in the complex formation. The small value of the intercept further indicates that electrostatic forces are indeed dominant forces for p(BAP-2MP)-DNA interaction. Dissection of the total free energy of interac-
Thermodynamics of Polycation-DNA Interaction
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Table 1. Calculated Parameters of Interaction of DNA with p(BAP-2MP) in 1 mM Phosphate Buffer (with Varied Total Monovalent Salt Concentration) by Applying the Complexation-Condensation Model [M+] (M)
νc
νmax
ncom
Kobs (M-1 × 105)
∆H°com (kJ/mol)
∆G°com (kJ/mol)
∆S°com (kJ/(mol K))
ncon
∆H°con (kJ/mol)
0.014 0.024 0.039 0.064
0.010 0.010 0.011 0.009
0.017 0.020 0.020 0.018
58 ( 3 50 ( 6 50 ( 2 54 ( 8
3.40 ( 0.87 0.46 ( 0.14 0.24 ( 0.08 0.25 ( 0.10
-459.9 ( 3.82 -273.9 ( 15.67 -307.9 ( 13.89 -197.1 ( 7.10
-31.6 ( 0.07 -26.6 ( 0.78 -24.9 ( 0.79 -25.1 ( 0.91
-1.4 ( 0.01 -0.8 ( 0.03 -0.9 ( 0.04 -0.6 ( 0.02
59 ( 1 54 ( 6 58 ( 8 73 ( 11
-382.78 ( 0.70 -191.82 ( 1.33 -210.87 ( 2.17 -138.85 ( 1.52
Table 2. Calculated Parameters of Interaction of DNA with p(BAP-2MP) in 1 mM Phosphate Buffer (with Varied Total Monovalent Salt Concentration) by Applying Only the McGhee-von Hippel Model
Table 3. Dissecting of Total Free Energy of Interaction, ∆G°obs, into Electrostatic Free Energy, ∆G°es, and Nonelectrostatic Free Energy, ∆G°ns, of Interaction
[M+] (M)
n
Kobs (M-1 × 105)
∆H°obs (kJ/mol)
[M+] (M)
∆G°obs (kJ/mol)
∆G°es (kJ/mol)
∆G°ns (kJ/mol)
∆G°es/∆Gobs
0.014 0.024 0.039 0.064
57 ( 1 52 ( 1 56 ( 1 72 ( 1
17.65 ( 7.96 2.41 ( 0.88 5.33 ( 0.86 6.45 ( 1.51
-440.7 ( 6.47 -242.8 ( 0.60 -253.1 ( 4.38 -167.8 ( 3.14
0.014 0.024 0.039 0.064
-31.6 -26.6 -25.0 -25.1
-27.6 -24.1 -21.0 -17.8
-4.0 -2.5 -4.0 -7.3
0.9 0.9 0.8 0.7
Figure 4. Variation of the association constant (Kobs) for the interaction of p(BAP-2MP) with DNA as a function of monovalent salt concentration.
tion, ∆G°obs, to its nonelectrostatic free energy of interaction, ∆G°ns, and electrostatic free energy of interaction, ∆G°es, can be obtained from the following relations from Manning counterion-condensation theory:10,11
∆G°obs ) -RT ln Kobs
(6)
∆G°es ) -aRT ln [M+]
(7)
∆G°ns ) ∆G°obs - ∆G°es
(8)
where
a)
∂ log Kobs ∂ log [M+]
(9)
The values of ∆G°obs, ∆G°ns, and ∆G°es at different salt concentrations at pH 7.4 are given in Table 3. The data clearly show that electrostatic interactions constitute approximately 90% of the total binding energy at the low salt concentration and that the contribution of nonelectrostatic forces is increasing at higher salt concentration, where electrostatic interactions are reduced. Since a dominance of electrostatic interactions is a distinguished characteristic of a nonspecific binding of ligands with DNA,5 the results in Table 3 confirm our initial assumption on a nonspecific interaction of p(BAP-2MP) with DNA. However, this cannot be generalized and it is not the case for all polycationic DNA condensing agents. Poly-L-lysine has increased affinity to the A-T rich part of DNA.16 Initially we assumed that p(BAP-2MP)-DNA is a nonspecific interaction (for the complexation-condensation model) and that the results obtained demonstrate that this is indeed the case. If the interaction of p(BAP-2MP) with DNA was a specific interaction, then other forces
Figure 5. Ethidium bromide displacement from the titration of p(BAP-2MP) into DNA in 1 mM phosphate buffer adjusted to various pH values.
would be expected and their existence would have been reflected in the free energy of nonelectrostatic interaction between DNA and p(BAP-2MP). 3.1.2. Salt Dependence of ∆H°com. Results in Table 1 show that the interaction between p(BAP-2MP) and DNA is strongly salt dependent. Usually the enthalpy of interaction of positively charged ligands with DNA is not strongly salt dependent, although a mild variation can be seen.13 A plausible explanation is that during the interaction of p(BAP-2MP) with DNA other processes, which are strongly salt dependent, are also occurring (such as an ionization of the buffer). In fact, the following section shows that ∆H°com is not intrinsic enthalpy for p(BAP-2MP)DNA binding and that it contains the enthalpy of buffer ionization. 3.1.3. Buffer and pH Dependency of p(BAP-2MP) and DNA Interaction. The p(BAP-2MP) used in experiments has on average 51 monomeric units each containing one piperazine ring where two charges are possible. It has been previously determined that the polymer has pKa1 ) 7.2 and pKa2 ) 3.3.27,28 Hence, under experimental conditions of pH ) 7.4, pKa ) 3.3 groups from p(BAP2MP) are not ionized, whereas 39% (i.e., 20) of the possible charges from pKa ) 7.2 groups are protonated. Data from ncom in Table 1 show that the value of ncom, complexation site exclusion size, is between 50 ( 2 and 60 ( 2 and hence indicate that the polymer would require a buffer protonation to interact with DNA. Moreover, ethidium bromide displacement studies (Figure 5) and the titrations at different pH values of the buffer (Figure 6) clearly indicate strong buffer pH dependency of DNAp(BAP-2MP) interaction. At pH 5.0 (Figure 5) when almost all of the pKa ) 7.2 groups from the polymer are protonated and the pKa ) 3.3 groups are 2% ionized, the
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Figure 6. Integrated heats of interaction corrected for heats of dilution from the titrations of p(BAP-2MP) into DNA in 1 mM phosphate buffer adjusted to various pH values.
Figure 7. Integrated heats of interaction corrected for heats of dilution from the titrations of p(BAP-2MP) into DNA in various buffers adjusted to pH 7.4.
curve profile indicates that the displacement of intercalating dye from its complex with DNA is occurring at lower monomer/nucleotide ratios. This is in agreement with microcalorimetry data in Figure 6 which illustrate that at pH ) 5.0 the total heat of interaction is significantly lower compared to that at pH ) 7.4. The data thus indicate that although the polymer has two ionizable groups in each monomer unit, it is effectively behaving as having one with an ionization level that is buffer dependent. Therefore, to bind with DNA at pH 7.4 as one monomer unit to one DNA base the polymer needs to abstract protons from the buffer to interact. 3.1.4. Intrinsic Binding Parameters for p(BAP2MP) and DNA Interaction. To assess the role of buffer protonation in p(BAP-2MP) and DNA interaction, the calorimetric results obtained in three buffers with different buffer ionization enthalpies were compared. The buffering components used were Tris-HCl (∆Hion ) 46.02 kJ/mol), phosphate buffer (∆Hion ) 4.18 kJ/mol), and citrate buffer (∆Hion ) 0 kJ/mol). The results (Figure 7) clearly confirm that the observed binding enthalpy is not intrinsic enthalpy for DNA-polycation interaction but also contains enthalpy of the buffer protonation. Binding parameters for p(BAP-2MP) interaction with DNA in these three buffers (calculated by applying the complexation-condensation model) are given in Table 4. The data show that values for ncom, ncon, and Kobs are close for all three buffers (for phosphate buffer, the corresponding salt concentration is 0.024 M). Conversely, ∆H°com, ∆H°con, and ∆S°com are buffer-dependent parameters and thus vary considerably by changing the buffer. The absolute value of ∆H°con is again smaller than the corre-
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sponding ∆H°com, which can be attributed to a smaller number of consumed protons in the condensation process in comparison to the complexation process. The measurements in citrate buffer, which has ∆Hion ) 0 kJ/mol, can be used to obtain intrinsic binding parameters at pH ) 7.4 and 25 °C. The results show that the interaction is exothermic with an intrinsic enthalpy of interaction of ∆Hint ) -448.9 kJ/mol and a moderate binding constant of Kint ) 0.63 × 105 M-1, with a corresponding ∆Gint ) -27.4 kJ/mol and ∆Sint ) -1.41 kJ/(mol K). These binding parameters demonstrate that p(BAP-2MP) and DNA binding contains an enthalpic contribution and that the interaction is nonspecific, as suggested by a relatively small negative entropy. The enthalpic contribution (negative values of ∆Hint) and a low value for ∆Sint are taken as an indication of formation of hydrogen bonding between DNA and the p(BAP-2MP). A precise identification of interaction forces would obviously require further studies and structural information. The values for intrinsic binding parameters were also confirmed from the intercept of a linear regression analysis of ∆Hcom as a function of buffer ionization enthalpies,40 shown in Figure 8. The analysis yields an intercept value of -421.5 kJ/mol as the intrinsic enthalpy of interaction, which confirmed the value obtained from citrate buffer. The slope of the curve, which indicates the number of protons released by the buffer, NH+, has a value of 28. This suggests that 28 protons were needed from the buffer per 1 polymer molecule to interact with DNA. Taking into account that at pH 7.4 only 20 out of 51 monomeric units of the polymer are ionized, these values would be in good agreement. It is however interesting that the intrinsic binding parameters indicate a substantial contribution of nonelectrostatic interactions, which are not apparent from the dissection of the total free energy, as discussed above. However, the polymer used in the experiment has on average 51 monomeric units and per 1 polymer molecule a number of proton extractions from the buffer are occurring all contributing to the intrinsic enthalpy (expressed in kJ per mol of polymer). 3.1.5. Salt Dependence of ∆S°com. The entropy of complex formation between p(BAP-2MP) and DNA, ∆S°com, at different salt concentrations is given in Table 1. It can be seen that ∆S°com increases with increasing salt concentration. On the contrary, when the interaction between two species is mostly electrostatic in nature, then according to Manning’s theory,10,11 entropy of binding should decrease by increasing the salt concentration. However, the entropy calculated is actually a net effect of contributions from different processes (e.g., association of molecules, release of counterions, buffer protonation, release of water molecules). Therefore, ∆S°com in Table 1 is not solely the entropy of p(BAP-2MP)-DNA binding, and it includes the entropy change of demonstrated buffer protonation. Therefore, the increase of ∆S°com with increasing salt concentration could be attributed to the effect of the protonation of buffer. Interestingly, in the present study the entropy change does not play an important role, while it has been previously reported that the interaction of condensing agents with DNA is primarily an entropic process. However, the systems used in these studies are very different (i.e., cationic lipids were investigated where hydrophobic contributions due to interaction of hydro(39) Lee, B.; Graziano, G. J. Am. Chem. Soc. 1996, 118, 5163. (40) Murphy, K. P.; Xie, D.; Garcia, C.; Amzel, M.; Freire, E. Proteins: Struct., Funct., Genet. 1993, 15, 113.
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Table 4. Calculated Parameters of Interaction of DNA with p(BAP-2MP) in Three Buffers by Applying the Complexation-Condensation Model buffer
νc
ncom
Kobs (M-1 × 105)
∆H°com (kJ/mol)
∆G°com (kJ/mol)
∆S°com (kJ/(mol K))
ncon
∆H°con (kJ/mol)
phosphate citrate Tris-HCl
0.010 0.011 0.009
50 ( 6 49 ( 2 60 ( 2
0.46 ( 0.14 0.63 ( 0.12 0.60 ( 0.05
-273.9 ( 15.67 -448.9 ( 7.62 867.6 ( 16.20
-26.6 ( 0.78 -27.4 ( 0.47 -27.3 ( 0.28
-0.8 ( 0.03 -1.41 ( 0.02 3.0 ( 0.05
54 ( 6 69 ( 3 57 ( 1
-191.82 ( 1.33 -382.12 ( 0.69 719.41 ( 3.24
Figure 8. Variation of observed enthalpy for the interaction of p(BAP-2MP) with DNA as a function of buffer ionization enthalpy.
phobic tails would be important and which are also permanently charged species).42 A comparison with previously published data also shows that ∆Hint in this study is significantly higher than values reported for the interaction of small cationic ligands with DNA.14,43 The polycation was used in this study; therefore the enthalpy is a summary of the individual enthalpies of interaction between each monomeric unit and DNA nucleotide. 3.1.6. Salt Dependence of ncom. The values of complexation site exclusion size, ncom, at different salt concentrations are given in Table 1. These values are found to be independent of salt concentration and vary around 50-60. The changes in ionic strength of the medium could have affected the conformation of the polycation molecule; however, data here and the literature report for a polycation-DNA binding32 both indicate that a mild increase in the ionic strength does not produce an appreciable effect. 3.2. Salt Dependence of Condensation of DNA by p(BAP-2MP). 3.2.1. Salt Dependence of ∆H°con. The enthalpy of condensation of the DNA-p(BAP-2MP) complex, ∆H°con, at different salt concentrations is also given in Table 1. The data showed that ∆H°con represents an exothermic reaction and is strongly salt dependent. ∆H°con contains ∆H°com (because the way it is calculated assumes that before the condensation occurs p(BAP-2MP) complexes with DNA). However, the absolute values of ∆H°com are larger than those of ∆H°con (Table 1) and there is therefore some small positive ∆∆H°, suggesting that during the condensation process the number of consumed protons from buffer is low in comparison to the number of protons consumed during complex formation. Also, other processes, such as conformational changes of the polymer and precipitation of the DNA-polymer condensates, could have compensated the enthalpy of complex formation. 3.2.2. Salt Dependence of ncon. Table 1 shows that condensation site exclusion size, ncon, varies around 50 and is nearly equal to complexation site exclusion size, ncom. This suggests that in the condensed state the ratio (41) Rungsardthong, U.; Armes, S. P.; Garnett, M. C.; Stolnik, S. Biomacromolecules, in press. (42) Matulis, D.; Rouzina, I.; Bloomfield, V. A. J. Am. Chem. Soc. 2002, 124, 7331. (43) Bronich, T.; Kabanov, A. V.; Marky, L. A. J. Phys. Chem. B 2001, 105, 6042.
Figure 9. Quantification of free DNA in p(BAP-2MP) and DNA solution in 1 mM phosphate buffer adjusted to pH 7.4.
of nucleotide to p(BAP-2MP) monomer units is nearly equal to 1 (see section 1.2). It is entropically favorable for DNA condensate to be electrically neutral.36,44 The small deviation of ncon/ncom in Table 1 can be attributed to the numerical variations and interconnection of parameters during their calculation. 3.2.3. Salt Dependence of νc. It can be seen from Table 1 that the critical binding density, νc, does not change considerably with salt concentration, and its value equals 0.01 at [M+] ) 0.014 and decreases to 0.009 at [M+] ) 0.064. It was found that the value of νc in order to obtain a good curve fitting with smaller standard deviations for the calculated parameters is a rather unique value, which varies in a very narrow range. To experimentally estimate νc, we determined the amount of soluble and complexed DNA at different polymer to DNA ratios. Figure 9 depicts the ratio of soluble to total DNA versus total p(BAP-2MP) concentration in the solution at [M+] ) 0.014 M. The graph demonstrates initially a gradual and then a substantial decrease in soluble DNA when the polymer concentration reaches 7.21 × 10-6 M. Figure 9 also shows a curve generated using binding parameters at [M+] ) 0.014 M from Table 1 and applying the complexation-condensation model to calculate the ratio of free to complexed DNA. Although the theoretical curve does not agree very well with the experimental data, it has a similar trend and predicts a substantial decrease in the soluble DNA at a polymer concentration of 7.21 × 10-6 M, which is in good agreement with experimental data. The discrepancy in the curves and the gradual decrease in the experimental curve may be ascribed to the disproportion phenomenon, as described by polyelectrolyte theory.45 We also performed light scattering experiments to study the interaction of p(BAP-2MP) with DNA. Figure 10 illustrates the intensity of scattered light versus total p(BAP-2MP) concentration at different salt concentrations. It can be seen that for all salt concentrations, the intensity of scattered light starts to increase at a polymer concentration of approximately 2.81 × 10-6 M, rising until the polymer concentration of approximately 5.49 × 10-6 (44) Kabanov, V. A.; Zezin, A. B. Sov. Sci. Rev., Sect. B 1982, 4, 207. (45) Kabanov, V. A.; Zezin, A. B. Makromol. Chem., Suppl. 1984, 6, 259.
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assumption for the complexation-condensation model that the process can be divided into two stages.
Figure 10. Scattering intensity study from the titrations of p(BAP-2MP) into DNA in 1 mM phosphate buffer adjusted to pH 7.4 at varying concentrations of monovalent salt.
M, when it starts to decrease. The results thus indicate that there is no significant phase separation of DNA complexes with p(BAP-2MP) at low polymer concentrations, when complexation is occurring. As the polymer concentration increases, the condensates are formed and at a certain point these phases separate from the solution resulting in a decrease in light scattering (visually flocs/ filaments were observed). These results, together with fluorimetry, analysis of soluble DNA, and microcalorimetry (Figures 5, 6, and 9), clearly show that complexation (binding of polymer to DNA) is the process that is occurring even at low polymer concentrations while higher concentrations are required for condensates to form and phase separate. The experiments thus clearly support our initial
4. Conclusions The work demonstrated that p(BAP-2MP) interaction with DNA is a two-stage process including complexation and condensation phases. The proposed complexationcondensation model was applied to experimental data and allowed binding parameters for the complexation (Kobs, ncom, ncon, ∆H°com, and ∆H°con) and condensation stages of p(BAP-2MP)-DNA interaction to be determined. Calculation of Kobs at different salt concentrations allows assessment of the fraction of electrostatic forces in complex formation between a polycation and DNA and also prediction of the sensitivity of the DNA-polycation complex to different biological environments with different ionic strengths. The work demonstrates that ∆H°com and ∆H°con are buffer dependent and they contain the intrinsic binding values as well as enthalpy of buffer ionization. Performing the calorimetric experiment in buffers with different ionization enthalpies allowed the intrinsic enthalpy to be determined, and the use of citric buffer allows intrinsic binding parameters to be determined. The studies here clearly show that the thermodynamics of interaction of a polycation with DNA can be studied by applying isothermal titration microcalorimetry. Acknowledgment. U. Rungsardthong acknowledges support via the University of Nottingham half studentship and the Thai government. LA0268799
