Thermodynamics of DNA Condensation Induced by Poly(ethylene

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Biomacromolecules 2010, 11, 1180–1186

Thermodynamics of DNA Condensation Induced by Poly(ethylene glycol)-block-polylysine through Polyion Complex Micelle Formation Wankee Kim,† Yuichi Yamasaki,*,†,‡ Woo-Dong Jang,† and Kazunori Kataoka*,†,‡,§,| Department of Materials Science and Engineering, Graduate School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan, Center for Disease Biology and Integrative Medicine, Graduate School of Medicine, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan, Center for NanoBio Integration, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan, and Core Research Program for Evolutional Science and Technology (CREST), Japan Science and Technology Agency (JST), Kawaguchi 332-0012, Japan Received November 17, 2009; Revised Manuscript Received February 25, 2010

Isothermal titration calorimetry (ITC) was carried out to explore the condensation process of plasmid DNA (pDNA) molecules induced by poly(ethylene glycol)-poly(L-lysine) block copolymer (PEG-PLL) as a condensing agent. The ITC curves measured can be divided into two distinctive endothermic binding processes: the first was the binding of PEG-PLL to the elongated pDNA, and the second was the binding that accompanied the pDNA conformational transition. The thermodynamic parameters were obtained by fitting each ITC curve using our recently developed fitting method. The binding of PEG-PLL to the pDNA was accompanied by a small increase in enthalpy, a large increase in entropy, and a large decrease in free energy. The binding stabilized as the polymerization degree of PLL on PEG-PLL increased and the salt concentration decreased. Changes in the thermodynamic parameters are discussed in relation to both the polymerization degree of PLL on PEG-PLL and the salt concentration.

Introduction DNA condensation is essential for the storage of a long chain of eukaryotic DNA in a small nucleus. For example, about 2 m of human diploid DNA is stuffed into a nucleus only several micrometers in diameter. Because the DNA chain is a negatively charged array of phosphate groups, it can be condensed when neutralized by the binding of cationic substances. In addition, this phenomenon has recently attracted much attention for its potential application to the construction of nonviral vectors (polyplexes) for gene therapy.1 The condensation of DNA can be treated as an important first step in the formation of a gene vector. While many polyplex systems have been suggested based on the polyion complex (PIC) formation between polycations and DNA, safe and efficient nonviral vectors as alternatives to the viral system are still under development, with very few nonviral systems having proceeded to clinical trials.2 Indispensable elements of vector systems applicable to in vivo study include low toxicity, prolonged circulation in the blood, and the ability to avoid foreign body recognition by reticuloendothelial systems. From these perspectives, bifunctional block copolymers composed of a hydrophilic poly(ethylene glycol) (PEG) and polycations seem to be promising, because PEG chains surrounding the PIC core formed between DNA and polycations prevent both secondary aggregation and nonspecific interaction with plasma components.3-5 Similar efforts to * To whom correspondence should be addressed. Tel.: +81-3-5841-7138 (K.K.); +81-3-5841-7145 (Y.Y.). Fax: +81-3-5841-7139 (K.K.); +81-35841-7139 (Y.Y.). E-mail: [email protected] (K.K.); [email protected] (Y.Y.). † Graduate School of Engineering, The University of Tokyo. ‡ Japan Science and Technology Agency. § Graduate School of Medicine, The University of Tokyo. | Center for NanoBio Integration, The University of Tokyo.

improve gene delivery have been made by employing cationic comb-type copolymers composed of PEG and poly(L-lysine) (PLL).6,7 Indeed, these advantages have been used to show that polyplex micelles from PEG-PLL block copolymers have prolonged circulation and effective gene expression in experimental animals.8 In spite of the recent achievement of PEG-PLL systems as gene vectors, a detailed mechanism of the complex formation of DNA with PEG-PLL has not yet been fully understood. Several complicated interactions that are typical in PIC formation obstruct physicochemical characterization. Even in a simplified system of DNA with low molar mass cations, the mechanism underlying DNA condensation remains controversial. Many studies on this mechanism have been intensively performed to elucidate the origin of the attractive interaction between DNA segments using thermodynamics and to elucidate possible mechanisms; for example, a fluctuation of condensed counterions,9,10 a charge-ordered structure,11 a release of structured water12,13 or of low molar mass counterions,14-18 and a delocalization of condensed counterions.19,20 These mechanisms can be classified into two groups. In one group, electrostatic interaction plays the predominant role in DNA condensation, while in the other group the increase in entropy is the dominant factor. When DNA condensation is induced by electrostatic interaction, it is accompanied by exothermic heat, whereas the increase in entropy is accompanied by endothermic heat. Thus, among the limited methodologies for determining the thermodynamic parameters of cation-induced DNA condensation, isothermal titration calorimetry (ITC), which measures the heat change that the binding reaction of two species generates, is a powerful tool. PEG-PLL that can prevent a secondary aggregation is the most suitable reagent for the investigation of the DNA condensation mechanism, whereas

10.1021/bm901305p  2010 American Chemical Society Published on Web 04/19/2010

Thermodynamics of DNA Condensation

both low molar mass cations and homopolymer cations induce precipitation, which may become an obstacle to precise heat measurement. Furthermore, for safe and effective gene therapy, the complexation mechanism underlying the promising nonviral gene vector pDNA/PEG-PLL system should be elucidated. In the present study, we measured the heat accompanied by the complex formation of pDNA with PEG-PLL by varying the average degree of lysine polymerization under various salt concentrations. The ITC curves measured can be divided into two distinctive endothermic binding processes: the first was PEG-PLL binding to the elongated pDNA, and the second was the binding that accompanied by the conformational transition of pDNA. The thermodynamic parameters were obtained by fitting each ITC curve using our recently developed fitting method.21 The binding of PEG-PLL to pDNA was accompanied by a small increase in enthalpy, a large increase in entropy, and a large decrease in free energy. The complex of PEG-PLL and pDNA stabilized against changes in the salt concentration when the polymerization degree of the lysine unit on PEG-PLL was increased. The results of ITC measurements were compared with those of AFM observation, and the validity of the thermodynamic parameters obtained was discussed in detail.

Materials and Methods Preparation of pDNA. A pGL3 control vector (5256 base pairs) purchased from Promega (Madison, WI) was used as the plasmid DNA (pDNA) in all the experiments. This pDNA was amplified in competent DH5R Escherichia coli and purified using the Qiafilter Giga kit (Qiagen, Hilden, Germany). The pDNA stock solution was prepared by dissolving purified pDNA in water with 10 mM NaCl. The concentration of the pDNA stock solution was spectrophotometrically determined using the relationship 1A260 ) 50 µg/mL ) 0.15 mM DNA phosphate (or nucleotide). Chemicals. PEG-PLL with a PEG average molecular weight of 12000 and average lysine polymerization degrees of 109, 73, 47, and 20 was synthesized using R-methoxy-ω-amino PEG to initiate polymerization of the N-carboxy anhydride of the Z-protected lysine.22 The length of the lysine segment was regulated by the ratio of the monomer to the PEG initiator. The lysine was deprotected under acidic conditions. 1 H NMR spectroscopy and size-exclusion chromatography were employed to characterize these block copolymers. The polymerization degree was deduced by the ratio of the PEG methylene proton to that on the lysine residue. We call the PEG-PLLs 12-109, 12-73, 12-47, and 12-20. PEG-PLLs 12-70 and 12-20, used for atomic force microscopy, were synthesized by the polymerization of N-carboxy anhydride of the trifluoroacetyl-protected lysine instead of the Zprotected lysine by a method similar to that described above. The lysine was deprotected under alkaline conditions. Isothermal Titration Calorimetry (ITC). ITC was measured by a VP-ITC instrument (Microcal, Century City, CA) equipped with an active cell volume of 1.4643 mL. A total cell volume is greater than 2 mL. After the cells were rinsed three times with a NaCl solution of the appropriate concentration (10, 100, 300, or 600 mM), 2 mL of a 0.3 mM pDNA solution (in nucleotide) prepared using the same concentration of NaCl without the buffer, was added to the cells. A PEG-PLL aqueous solution of 3 mM (in the lysine unit) was titrated into the pDNA solution in a sample cell using an injection syringe. Each titration consisted of a preliminary 1 µL injection followed by 29 subsequent 10 µL injections at 3 min intervals at 30 °C. As a control experiment, each PEG-PLL solution was titrated into a NaCl solution without pDNA to determine the dilution heat of the added PEG-PLL solution. The dilution heat was then subtracted to obtain the binding heat. The calorimeter’s heat measurement was verified by carrying out a Tris base protonation reaction using hydrochloric acid (∆H ) -11.58 kcal/ mol) as calibration. The power of the instrument is controlled in the 10-6 µcal/sec of resolution. The long-term baseline drift was less than

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0.05 µ cal/sec averaged over one hour time intervals with short-term noise level less than 0.005 µ cal/sec per minute. The temperature is controlled in the 10-5 °C order of resolution. The temperature drift over the experiment was less than 0.05 °C. The above operating conditions were verified for all the measurements. Reproducibility was tested for both calibration and all the measurements of PEG-PLL samples in 10 mM NaCl under the above conditions. Analysis of ITC Data. The raw data curves were integrated using the specific add-on module in Microcal Origin software as described in the VP-ITC manual. To accurately represent the original data, the baseline was not adjusted. The novel fitting method we developed, which we precisely described in a previous paper,21 was applied to each integrated ITC curve to obtain the thermodynamic parameters by using the nonlinear fitting tool in Origin, which adopts the LevenbergMarquardt algorithm. This fitting method assumes two distinctive binding processes of the ligand to pDNA: the first ligand binds to the elongated pDNA followed by the second binding during DNA condensation. Let us introduce the summary of the novel fitting model that is based on the combination of the single set of identical sites (SSIS) model. On the basis of the SSIS model, a general ITC curve should be produced as a decreased sigmoidal curve depending on the three parameters, the ratio of the occupied binding sites to the total binding sites (stoichiometry) N, the molar heat of ligand binding ∆H and the binding constant K. The ITC curves obtained in this work were fitted by the sum of two functions corresponding to the initial and second binding stages. The resultant composed function represents the relation of the total heats accompanied by ligand binding on DNA to the mixing ratio. Although the function for the initial binding stage is defined by the set of three parameters, N1, K1, and ∆H1, another function for the second binding stage is defined by the set of six parameters, N1, K1, ∆H1, N2, K2, and ∆H2. Here, Ni, Ki, and ∆Hi correspond to the stoichiometry, the binding constant, and the change in enthalpy for the ith binding stage, respectively. Because, during the transition region from elongated to collapsed DNA, the increase in the population of collapsed DNA leads to the decrease in the fraction of ligands bound to the elongated DNA and the residual ligands not involved in the initial binding stage ideally contribute to the second binding stage. In this method, both functions were simultaneously fitted. To obtain the optimum six parameters, the sum of squares of the difference between experimental and calculated data at each data point should be minimized. A standard error was given as a second root of the product of the above sum and covariance divided by the difference between the number of times injected and six independent variables. This approach allows us to take into account the effect of pDNA conformational change on ligand binding. This fitting method, unlike the conventional ones such as the “two sets of independent sites” (TSIS) model, is not restricted to the condition that the binding constant for the first binding process (K1) is greater than that for the second (K2) and, therefore, has greater applicability than the conventional methods.23 Atomic Force Microscopy (AFM). The complex of pDNA with PEG-PLL was prepared by titrating 0.462 mM of PEG-PLL solution (in the lysine monomer unit) to 0.2 mL of 0.154 mM pDNA solution (in nucleotide) using a syringe pump to deliver 30 portions of 3.33 µL at 10 min intervals. The concentrations of pDNA and PEG-PLL at the end of titration were 0.102 and 0.154 mM, respectively, for a molar ratio of 1.5. For AFM imaging, this solution was diluted by 10% and 5 µL of each sample solution was deposited on a substrate of a freshly cleaved highly oriented pyrolytic graphite for 30 s. The solution was dried under a gentle flow of nitrogen gas. AFM imaging was performed in tapping mode with standard silicon probes (Type: MPP-11100, Veeco Instruments, Woodbury, NY) using a Nanoscope MultiMode scanning probe microscope (Veeco Instruments) under usual laboratory conditions. The cantilever oscillation frequency was tuned to the resonance frequency of the cantilever, 200-400 kHz.

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Figure 1. Raw data of PEG-PLL (12-109) binding to plasmid pGL3 DNA in water containing 10 mM NaCl. The upper curve shows the dependence of power on time for each injection of PEG-PLL into the DNA solution. The lower curve was obtained by the titration without pDNA and shows the dilution heat of the PEG-PLL solution.

Results and Discussion Raw Data Acquisition and Integrated ITC Curve. The ITC measurement records the electric power supplied to the heater that is attached to the sample cell to compensate for the heat change in the reaction system and to maintain the cell at a constant temperature. Figure 1 shows the typical raw data ITC curves obtained for a PEG-PLL (12-109) binding to pDNA in a 10 mM NaCl aqueous solution. The upper curve shows the dependence of the power on time for each injection of PEGPLL into the pDNA solution. The supplied power increases and returns to the baseline position, thus, forming a peak for each injection of PEG-PLL. The binding reaction of PEG-PLL to pDNA is endothermic, indicating that this reaction is accompanied by an increase in entropy. After the pDNA molecules in the sample cell were fully neutralized by the added PEGPLL, small exothermic peaks appeared. These were attributed to the dilution heat of the PEG-PLL solution. The lower curve, obtained by a control experiment, shows the exothermic change as a result of the PEG-PLL dilution heat during titration. As described above, the normalized heat is obtained by integrating each peak in each curve of Figure 1, dividing the normalized heat by the moles in each injected volume, and then subtracting the lower curve from the upper to remove the dilution heat (see Figure 2). All the data showing both the dependence of the degree of polymerization (DP) of lysine unit on PEG-PLL and the dependence of NaCl concentration on the ITC curves were obtained in the same way (see Figure 3). In these figures, the solid lines indicate the connections among the data points. All the experiments produced endothermic ITC curves, indicating that these bindings are accompanied by an increase in entropy. However, the absorbed heat values were low: less than 1 kcal/mol even in 10 mM NaCl. The endothermic heat decreased as the salt concentration increased. ITC Curve Fitting for Data Analysis. The pDNA was neutralized by polycations through two distinctive binding processes: the polycations bind first to the elongated pDNA, after which they bind to the pDNA during the pDNA conformational change into a collapsed state. If the pDNA did not change into the collapsed state in this reaction, the integrated ITC curve would be a simple sigmoidal one based on the single set of identical sites (SSIS) model.24 However, none of the ITC curves obtained under various salt concentrations were consistent

Kim et al.

Figure 2. Integrated ITC curve of PEG-PLL (12-109) binding to plasmid pGL3 DNA in water containing 10 mM NaCl. This curve is obtained by subtracting the lower curve from the upper curve in Figure 1.

with the SSIS model. Thus, we resolved each integrated ITC curve into two parts, corresponding to the first and second binding processes, by using an appropriate binding model described in our previous paper.21 As a typical example, the resolution of the ITC curve for the binding of PEG-PLL (12-109) to the pDNA is shown in Figure 4. The NDH curve corresponds to the original ITC curve. Both curves NDH1 and NDH2, corresponding to the first and second binding processes, were simultaneously determined by fitting NDH1+NDH2 to the NDH by totally changing six distinctive parameters; more exactly, three (N1, K1, ∆H1) for NDH1 and six (N1, K1, ∆H1, N2, K2, ∆H2) for NDH2. Here, Ni, Ki, and ∆Hi correspond to the stoichiometry, the binding constant, and the change in enthalpy for the ith binding process, respectively. Because the second binding process is affected by the first, the curve NDH2 should be optimized by both sets of thermodynamic parameters for the first and second binding processes. These thermodynamic parameters corresponding to each binding process are shown in Tables 1 and 2. Thermodynamic Parameters Obtained for PEG-PLL Binding to pDNA. Table 1 shows the thermodynamic parameters corresponding to the first binding process obtained by the curve fitting of each experimental ITC curve. The ratio of the bound PEG-PLL in the first binding process to the total bound PEG-PLL decreases as the salt concentration increases and reaches a minimum at around 300 mM NaCl. This tendency is numerically reflected in the stoichiometry N1 in Table 1. Generally, the stoichiometry N1 tends to decrease with an increase in the salt concentration in accord with a screening of electrostatic interaction, because the first binding process is the polyion complexation. The binding constant K1 also decreases as the salt concentration increases, and its dependence on NaCl becomes much more remarkable with the decrease in the DP of the PLL segment, indicating that the complex formation of PEG-PLL with pDNA becomes more dependent on the salt concentration as the DP of PLL decreases. These tendencies of K1 on the salt concentration and on the DP of PLL should also be reflected in the free energy change ∆G1. The change in enthalpy, ∆H1, corresponding to the heat supplied from the heater, decreases as the salt concentration increases and as the DP of PLL decreases. The free energy ∆Gn is obtained from Kn, using the relationship between ∆Gn and Kn, ∆Gn ) -RT ln(Kn), where R

Thermodynamics of DNA Condensation

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Figure 3. Dependence of integrated ITC curves of PEG-PLL binding to pGL3 DNA on DP of PLL in various NaCl concentrations: (a) 10 mM, (b) 100 mM, (c) 300 mM, and (d) 600 mM; PEG-PLL (12-109; 9), PEG-PLL (12-73; b), PEG-PLL (12-47; 2), PEG-PLL (12-20; 1).

Figure 4. Representative resolution of ITC curves of PEG-PLL (12-109) binding into two parts using the recently introduced fitting method:21 (a) 10 mM, (b) 100 mM, (c) 300 mM, and (d) 600 mM NaCl. (9) NDH: experimental ITC curves shown in Figure 3; (b) NDH1: curves corresponding to the binding of PEG-PLL to pDNA without DNA condensation (first binding stage); (2) NDH2: curves corresponding to the binding of PEG-PLL during DNA condensation (second binding stage); and (1) NDH1 + NDH2.

is the gas constant 1.9872 cal/mol · K and T is the temperature in Kelvin (K). As shown in Table 1 and Figure 5, the absolute value of ∆G1 decreases as the salt concentration increases, and the correlation between ∆G1 and the salt concentration weakens as the DP of PLL increases, as indicated by the value of the correlation coefficient, R, for each fitting. This result reflects

that the binding of PEG-PLL with longer PLL segments is insusceptible to the electrostatic shielding of high salt concentrations. The entropic contribution T∆S1 obtained from the equation T∆S1 ) ∆H1 - ∆G1 is significantly higher than ∆H1. From the endothermic process clarified in the ITC experiments, the PEGPLL binding to pDNA appeared to accompany a large increase

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Table 1. Thermodynamic Parameters Corresponding to the First Binding Stage Obtained by Fitting Each Experimental ITC Curve According to the Method Described in Ref 21a PEG-PLL

[NaCl] (mM)

N1

K1/105 (M-1)

∆H1 (cal/mol)

∆G1 (cal/mol)

T∆S1 (cal/mol)

12-109 12-109 12-109 12-109b 12-73 12-73 12-73 12-73b 12-47 12-47 12-47 12-47b 12-20 12-20b 12-20b 12-20c

10 100 300 600 10 100 300 600 10 100 300 600 10 100 300 600

0.810 ( 0.026 0.435 ( 0.037 0.351 ( 0.036 0.351 ( 0.072 0.819 ( 0.029 0.498 ( 0.022 0.372 ( 0.049 0.449 ( 0.122 0.799 ( 0.036 0.459 ( 0.019 0.440 ( 0.053 0.381 ( 0.151 0.765 ( 0.014 0.302 ( 0.029 0.594 ( 0.251 0.700

2.66 ( 0.62 3.40 ( 3.65 1.69 ( 1.51 2.75 ( 5.76 4.16 ( 1.14 6.12 ( 4.47 0.89 ( 0.77 0.87 ( 0.97 8.41 ( 3.72 5.59 ( 3.62 0.46 ( 0.24 0.50 ( 0.68 10.00 ( 1.85 1.26 ( 0.99 0.52 ( 0.24 0.21

585 ( 5 470 ( 18 365 ( 22 280 ( 27 537 ( 6 456 ( 12 342 ( 35 260 ( 39 528 ( 10 443 ( 13 271 ( 43 200 ( 81 516 ( 5 400 ( 36 320 ( 57 200

-7520 ( 140 -7670 ( 647 -7250 ( 539 -7540 ( 1261 -7790 ( 165 -8020 ( 439 -6860 ( 517 -6850 ( 668 -8210 ( 266 -7970 ( 390 -6470 ( 305 -6510 ( 830 -8320 ( 111 -7070 ( 470 -6540 ( 273 -5992

8110 ( 136 8140 ( 634 7610 ( 520 7820 ( 1240 8330 ( 162 8480 ( 432 7210 ( 485 7110 ( 632 8740 ( 260 8410 ( 381 6740 ( 265 6710 ( 752 8830 ( 108 7470 ( 438 6860 ( 224 6192

a N1, stoichiometry; K1, binding constant; ∆H1, change in enthalpy; ∆G1, change in free energy; T∆S1, change in entropy. b Data obtained by setting a lower boundary of ∆H1 for a good convergence and a reasonable value for ∆H1. c Data obtained by changing each parameter manually, because meaningless and unreasonable values were returned by an automatic regression method. The calculated values of ∆Gi and T∆Si were rounded to the nearest 10.

Table 2. Thermodynamic Parameters Corresponding to the Second Binding Stage Obtained by Fitting Each Experimental ITC Curve According to the Method Described in Ref 21a PEG-PLL

[NaCl] (mM)

N2

K2 /105 (M-1)

∆H2 (cal/mol)

∆G2 (cal/mol)

T∆S2 (cal/mol)

12-109 12-109 12-109 12-109b 12-73 12-73 12-73 12-73b 12-47 12-47 12-47 12-47b 12-20 12-20b 12-20b 12-20c

10 100 300 600 10 100 300 600 10 100 300 600 10 100 300 600

0.184 ( 0.031 0.565 ( 0.044 0.597 ( 0.044 0.489 ( 0.091 0.197 ( 0.035 0.501 ( 0.028 0.565 ( 0.063 0.345 ( 0.180 0.179 ( 0.048 0.498 ( 0.025 0.438 ( 0.070 0.408 ( 0.244 0.175 ( 0.021 0.616 ( 0.033 0.100 ( 0.358 0.300

51.10 ( 14.00 7.46 ( 1.92 4.00 ( 0.80 4.13 ( 1.86 56.30 ( 19.50 6.18 ( 1.29 2.93 ( 0.60 1.14 ( 0.32 27.40 ( 12.70 6.05 ( 1.21 1.85 ( 0.23 0.55 ( 0.13 18.30 ( 3.49 10.20 ( 2.35 0.56 ( 0.21 0.21

899 ( 37 659 ( 24 557 ( 22 408 ( 37 865 ( 48 697 ( 23 595 ( 35 552 ( 113 1020 ( 120 722 ( 23 707 ( 54 528 ( 147 1188 ( 73 679 ( 22 1161 ( 545 380

-9300 ( 165 -8140 ( 155 -7770 ( 121 -7790 ( 271 -9360 ( 208 -8030 ( 125 -7580 ( 123 -7010 ( 171 -8930 ( 278 -8020 ( 120 -7300 ( 76 -6570 ( 146 -8680 ( 114 -8330 ( 139 -6590 ( 226 -5992

10200 ( 193 8800 ( 171 8320 ( 136 8190 ( 298 10200 ( 246 8730 ( 143 8170 ( 147 7560 ( 235 9950 ( 378 8740 ( 138 8010 ( 104 7090 ( 233 9870 ( 178 9010 ( 153 7750 ( 376 6372

a N2, stoichiometry; K2, binding constant; ∆H2, change in enthalpy; ∆G2, change in free energy; T∆S2, change in entropy. same meaning as described in the footnote of Table 1.

in entropy. For the first binding process, this suggestion was numerically supported here by the change in entropy. A large increase in entropy is a typical feature of an entropy-driven process; that is, the release of the low molar mass counterions localized around the vicinity of the DNA and polycations is significant in the polyion complex formation.9,10 Table 2 shows the thermodynamic parameters corresponding to the second binding process. The dependences of all the thermodynamic parameters K2, ∆H2, ∆G2, and T∆S2 on both the salt concentration and the DP of PLL are similar to those in the first binding process. It is noted that the absolute values of these parameters are higher than those in the first binding process. Although conventional fitting models that can treat multiple binding sites require that K1 > K2, our model is not restricted by this requirement. The magnitude relationship of the binding constants observed in this study is consistent with the theoretical prediction that the DNA conformational change to the collapsed state takes place when K2 > K1.25 Recently, Ehtezazi also suggested that a cooperative binding occurs during the second binding process, while a noncooperativity was observed in the first binding.26 This suggestion also corresponds to the situation of K2 > K1. The dependences of ∆G2 on both the salt concentration and the DP of PLL are shown in Figure 6.

b,c

The superscript has the

Figure 5. Dependence of the free energy change for the first binding stage on the salt concentration in each PEG-PLL. The red line is generated by a linear regression of the four data points in each PEGPLL. The intercept A and the slope B show the sensitivity of the free energy change to the salt concentration. R is the correlation coefficient.

Morphology of pDNA Condensates. To examine the obtained thermodynamic parameters from the viewpoint of the

Thermodynamics of DNA Condensation

Figure 6. Dependence of the free energy change for the second binding stage on the salt concentration in each PEG-PLL. The red line is generated by the same linear regression method as described in the legend to Figure 5.

Figure 7. AFM images of the complexes of pDNA with PEG-PLL (a) 12-20 and (b) 12-70 (1.5 × 1.5 µm2). These complexes were prepared by titrating PEG-PLL at a molar ratio of lysine monomer to nucleotide of 1.5.

morphology of the condensed pDNA, the complexes of pDNA/ PEG-PLL were visualized by the AFM (Figure 7). While dynamic and static light-scattering measurements were employed prior to the AFM imaging, no systematic differences were observed in diameter or in scattered light intensity toward the change in the salt concentration (data not shown). Thus, we tested AFM imaging of the salt-free system. All the samples were prepared by the titration of PEG-PLL with a molar ratio up to 1.5. This condition corresponds to the region where no endothermic peak was observed and thus indicates that the PEGPLL binding was completed. Obviously, the degree of condensation on pDNA/PEG-PLL (12-70) is much higher than that on pDNA/PEG-PLL (12-20). A similar tendency was observed in the morphology of the pDNA condensate induced by PEG-PLL with 40 or longer PLL segments. In the case of pDNA condensation induced by low molar mass counterions, pDNA condensates often aggregate among themselves to generate a large precipitate, in a process called secondary aggregation.27,28 However, no aggregation was observed in pDNA condensate induced by PEG-PLL. This result was also supported by the results of the turbidity measurement, which showed that the aqueous solution including pDNA condensed by PEG-PLL slightly decreased the transmittance, whereas a large decrease was observed in the case of the PLL homopolymer (data not shown). The AFM images shown in Figure 7 suggest that almost all of the pDNA condensates induced by PEG-PLL are each composed of a single pDNA molecule.7 This is a typical difference

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from pDNA condensates induced by conventional condensing agents, such as spermine, spermidine, and hexaminecobalt. Validity of the Fitting Model. There are a few reports on the thermodynamic analysis of two-stage binding of low molar mass cations to pDNA,29 although a lot of studies concerning only the binding constant K1 of such cations to DNA have been performed.16,30 As for the high molar mass cations, the twostage binding of the block copolymer poly(ethylene oxide)block-poly(2-(diethylamino)ethyl methacrylate) (PEO113-bPDEAEMA70) to pDNA, which is similar to those observed in this work, was reported by Tan et al.31 Their titration isotherm was not explained by a simple sigmoidal curve, the presence of a peak or a significant discontinuity in the isotherm indicates the second binding stage. From these results, the two-stage binding of cations to DNA is a common feature in DNA condensation regardless of the cations’ molar masses, although exceptions, in which there was no second binding peak, have been reported.26 The second binding stage is generally assigned to the DNA conformational change into the collapsed state.29,32 Although the binding isotherm is not usually divided into two stages, this may be due to the lack of an appropriate fitting model to analyze two-stage binding. In our previous study, we demonstrated the suitability of our novel fitting model for both low molar mass cations and polycations.21 Because of the dearth of previous studies, it is impossible to compare the binding constant for the second binding process in the present study with those in other works. The discussion should thus still be limited to the first binding process. Lohman et al. reported reliable data on binding constants for the pentalysine-T7DNA system obtained by measuring differences in boundary sedimentation velocity.16 The reported value of the binding constant increases in the range of 7.6 × 102 to 3.2 × 104 M-1 when the concentration of NaCl decreases from 0.19 to 0.091 M. It is reasonable that the data on the first binding process in our system show a similar dependence; the data are at least an order of magnitude higher than those for the pentalysine system because of the longer lysine segment of PEGPLL employed in our study. The binding constant’s dependence on the NaCl concentration shows the same trend Lohman et al. reported. It is rather plausible that the dependences of the other thermodynamic parameters, ∆H1, ∆G1, and T∆S1, follow similar trends. To estimate the stability of the complex versus changes in the salt concentration, a value of d ln(K)/d ln([NaCl]) is well adopted.16,33 According to Record et al.16,33 and Manning,34 the logarithm of the binding constant, that is, the free energy change, is linearly related to the logarithm of the salt concentration in aqueous solution, in the case of the electrostatic binding of low molar mass condensing agents (multivalent ions) to an oppositely charged polyelectrolyte. The stability of the complex against changes in the salt concentration can be described by the coefficient of the logarithm of the salt concentration, which corresponds to the value of B obtained by linear regression against four data points of the free energy in each binding process for each PEG-PLL (Figures 5 and 6). This value is obtained by dividing B by the gas constant R and then dividing the result by the absolute temperature T. The calculated values are 0.65, 0.92, 0.92, and 1.10 in the order of decreasing DP of PLL. In comparison, the values for other polycations, such as pentalysine16 and poly(bis-acryloylpiperazine-2-methyl-piperazine) with the DP of 50 (p(BAP-2MP)50),26 were reported to be 4.5 and 2.6, respectively. The values for the PEG-PLL are significantly lower, indicating that the complex of pDNA with PEG-PLL is more stable than the DNA condensates induced

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by pentalysine or p(BAP-2MP)50. It should be noted that PEGPLL with a DP lower than 50 is more stable than p(BAP-2MP)50. It is interesting that ∆G1 is linear only for PEG-PLL 12-20, while the others (12-47, 12-73, 12-109) with higher DP of PLL do not follow the relationship pointed out by Record et al.16,33 and Manning34 at 100 mM NaCl. It can be considered that PEGPLL (12-20) behaves as a low molar mass cation, whereas this relationship could not be applied to condensing agents of polyelectrolytes, that is, the other PEG-PLL (12-47, 12-73, 12109). From a morphological perspective, the AFM results clearly indicated the differences in the shapes of pDNA condensates. The degree of condensation of a pDNA condensate induced by PEG-PLL (12-20) would be milder than those induced by the other PEG-PLL (12-47, 12-73, 12-109). Olins et al. performed melting temperature experiments and pointed out that the behavior of oligolysine or polylysine toward DNA could be classified into three types.35 Tetralysine behaves like low molar mass cations, such as spermine and spermidine, while polylysines with average DPs of 200 and 359 behave as polyelectrolytes. Interestingly, octalysine and oligolysine, with DPs from 14 to 18, show intermediate properties between those of tetralysine and polylysine.35 Considering the average DP of PEG-PLL employed in this study, it is hard to judge this classification system, because the role of the PEG segment on the PEG-PLL block copolymer when the complex with DNA is formed remains unclear. Obviously, the morphological difference observed in this study was not considered in the linear relationship on ∆G1. Whereas the binding model we employed in this study is phenomenologically derived for the ITC measurement, the apparent values of thermodynamic parameters can be deduced for this kind of complicated experimental system. Recently, correlational studies between ITC experiments and conformational characterizations of DNA/ε-Lys oligomers systems36 have been reported, although quantitative thermodynamic analyses based on two-stage binding have not been carried out because of the lack of an appropriate fitting model. Despite some limitations of the analysis, the magnitude relationship between the first and second binding constants observed in this study is consistent with the theoretical prediction suggested by Teif and Lando25 and with the experimental results obtained by Ehtezazi et al.26 It is premature to expect a complete understanding of the thermodynamics of pDNA condensation induced by polyelectrolytes, but similar systems should be tested to gain a better understanding of polyplex formation and to develop a practical gene carrier for the realization of nonviral gene therapy. Acknowledgment. Grant-in-Aid for Scientific Research on Priority Areas “Soft Matter Physics” from the Ministry of Education, Culture, Sports, Science, and Technology of Japan (19031003 to Y.Y.).

Kim et al.

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