**2.2.5 Binding affinity and complexation thermodynamics**

As done for the DNA-chitosan polyplexes, ITC was performed to evaluate the DNApDADMAC binding affinity and complexation thermodynamics. Striking results were obtained as compared to the chitosan systems. Firstly, the DNA binding affinity of pDADMACs was found to be favored with valence; secondly, the complexation process was completed in three successive stages. Main results are discussed below.

Polycation-Mediated Gene Delivery: The Physicochemical Aspects Governing the Process 403

Table 6 summarizes the enthalpy, entropy, binding constant, and the stoichiometry of the

**p(1, < 619)** 1.02 ± 0.26 0.44 ± 0.12 0.26 ± 0.07 0.023 **p(1, 929)** 3.10 ± 0.48 0.39 ± 0.11 0.20 ± 0.07 0.026 **p(1, 1703)** 51.6 ± 0.31 0.28 ± 0.07 0.07 ± 0.01 0.030 **p(1, 2786)** 55.1 ± 0.26 0.28 ± 0.07 0.06 ± 0.01 0.031 **p(0.26, 668)** 1.72 ± 0.14 0.86 ± 0.13 0.17 ± 0.03 0.024

**p(1, < 619)** 0.06 ± 0.04 0.33 ± 0.10 2.34 ± 1.86 0.020 **p(1, 929)** 0.12 ± 0.07 0.26 ± 0.10 0.92 ± 0.74 0.022 **p(1, 1703)** 0.42 ± 0.08 0.15 ± 0.06 -0.40 ± 0.11 0.019 **p(1, 2786)** 0.43 ± 0.07 0.16 ± 0.06 -0.39 ± 0.11 0.020 **p(0.26, 668)** 0.17 ± 0.04 0.24 ± 0.04 -0.81 ± 0.07 0.020 Reproduced from (Alatorre-Meda et al., 2010b) with permission of AMERICAN CHEMICAL SOCIETY

Table 6. Thermodynamic parameters of the DNA-pDADMAC binding process. Sub-indices

It can be observed from this table that the DNA binding constants obtained for all pDADMACs are on the order of 105-106 and 103-104 M-1 for the first and second class of binding sites, respectively. These global ranges are in good agreement with the DNAchitosan binding data; however, it is clear that the present case exhibits an opposite behavior regarding the DNA binding affinity, namely, it increases with the polycationic valence. This opposite trend might be ascribed to the high water solubility of pDADMAC. That is, although higher valence pDADMACs produced bulkier polyplexes (see section 2.2.2), it appears that the ion-pair electrostatic interactions are not hindered at all by steric restrictions (see sections 2.1.1 and 2.1.5). On the other hand, concerning the energetic implications, the DNA binding with all polymers showed slight enthalpic contributions in both sites. This outcome depicts an entropically driven reaction typically observed in polyelectrolyte associations (Matulis et al., 2000; Prevette et al., 2007; Srinivasachari et al., 2007) where less favourable (more endothermic) ∆H values might be associated with breaking hydrogen bonds between polymer and water molecules (breaking a hydrogen bond in water corresponds to an enthalpy increase of 1.9 kcal/mol) (Silverstein et al., 2000).

To determine the transfection efficiency of the DNA-pDADMAC polyplexes, we performed exactly the same protocols as those described for the chitosan systems (see section 2.1.6). Similarly to the chitosan complexes, the transfer rate of the pDADMAC polyplexes was very low compared to that of the DNA-MEP lipoplex. Even worse, polyplexes within the whole range of ratios rendered levels of β-galactosidase and luciferase expressions comparable to that of naked DNA (data not shown). Given that no cytotoxic effects can be argued

Δ**H1 (kcal mol-1)** 

Δ**H2 (kcal mol-1)** 

Δ**S1 (kcal mol-1 K-1)** 

Δ**S2 (kcal mol-1 K-1)** 

DNA–pDADMAC interaction derived from the data fitting of figure 9.

**(M-1) n1**

**(M-1) n2**

**polymer K1** <sup>×</sup> **10-5**

**polymer K2** <sup>×</sup> **10-5**

**2.2.6 Transfection efficiency**

in the format Journal via Copyright Clearance Center.

next to each parameter stand for the corresponding sites 1 and 2.

Figure 9 shows the heat of interaction resulting from the titration of pDADMACs to DNA as a function of N/P. Three consecutive processes along the DNA-pDADMAC binding are observed. The first phase of binding occurred at N/P molar ratios lower than ~1, drawing a biphasic nature of the binding profiles for all polymers (except for p(1,<619)). As the polymer chains began to saturate the DNA, the slightly endothermic binding enthalpy decreased and reached an exothermic minimum at an N/P ratio of ~0.5. Similar slight endothermic heats have been ascribed to entropy-driven binding processes (Matulis et al., 2000; Srinivasachari et al., 2007) and ligand interactions with the DNA minor groove (Privalov et al., 2007) Concerning the reduction in the heat of interaction Q, it might result from the combination of both a decreased accessibility of binding sites to polymer molecules due to partial saturation of DNA molecules and from the dipole-dipole interactions between water molecules oriented favorably on adjacent DNA and polymer molecules (Strey et al., 1998). At this stage, bending of single DNA strand, bridging of neighboring DNA molecules by polymer chains and hydration can contribute to DNA collapse (Rau & Parsegian, 1992).

The second phase of binding was characterized by an additional post-transition endothermic heat which finished in a maximum for pDADMACs at an N/P molar ratio of ~0.75, with a subsequent decrease in enthalpy due to phosphate saturation. This endothermic heat increment with a subsequent peak or discontinuity has been suggested to represent the DNA collapse (Matulis et al., 2000). The increase in Q, from the zone in which DNA chains are partially saturated (the exothermic minimum) up to the observed maximum before phosphate saturation, is attributed to a binding of further polymer molecules to the partially saturated DNA. Finally, the third phase of binding was characterized by exothermic post-transition heats after complete phosphate saturation.

Reproduced from (Alatorre-Meda et al., 2010b) with permission of AMERICAN CHEMICAL SOCIETY in the format Journal via Copyright Clearance Center.

Fig. 9. Integrated heats of interaction of the titration of pDADMAC to DNA vs. N/P. Polymers p(1, <619) squares, p(1, 919) circles, p(1,1703) triangles, and p(1, 2786) diamonds were employed. The solid line in the inset represents the data fitting of the DNA-p(1, 1703) interaction.


Table 6 summarizes the enthalpy, entropy, binding constant, and the stoichiometry of the DNA–pDADMAC interaction derived from the data fitting of figure 9.

Reproduced from (Alatorre-Meda et al., 2010b) with permission of AMERICAN CHEMICAL SOCIETY in the format Journal via Copyright Clearance Center.

Table 6. Thermodynamic parameters of the DNA-pDADMAC binding process. Sub-indices next to each parameter stand for the corresponding sites 1 and 2.

It can be observed from this table that the DNA binding constants obtained for all pDADMACs are on the order of 105-106 and 103-104 M-1 for the first and second class of binding sites, respectively. These global ranges are in good agreement with the DNAchitosan binding data; however, it is clear that the present case exhibits an opposite behavior regarding the DNA binding affinity, namely, it increases with the polycationic valence. This opposite trend might be ascribed to the high water solubility of pDADMAC. That is, although higher valence pDADMACs produced bulkier polyplexes (see section 2.2.2), it appears that the ion-pair electrostatic interactions are not hindered at all by steric restrictions (see sections 2.1.1 and 2.1.5). On the other hand, concerning the energetic implications, the DNA binding with all polymers showed slight enthalpic contributions in both sites. This outcome depicts an entropically driven reaction typically observed in polyelectrolyte associations (Matulis et al., 2000; Prevette et al., 2007; Srinivasachari et al., 2007) where less favourable (more endothermic) ∆H values might be associated with breaking hydrogen bonds between polymer and water molecules (breaking a hydrogen bond in water corresponds to an enthalpy increase of 1.9 kcal/mol) (Silverstein et al., 2000).
