A B INITIO MODELING OF PAMAM 6/DNA ENTITIES AT LOW P H

to estimate the amount of DNA wrapped around the dendrimers, the program DAMMIN^{75, 80} is used to establish low-resolution bead models. In order to improve the reliability of the model and to further refine the solution, averaging of results obtained from independent runs with random initial conditions is used. The shape of the structure is well recovered in all runs.

A graphical representation of the reconstructed shape is given in Figure 8-26. Figure 8-26a shows that the bead model matches the observed I(q) data in the whole experimental q range with good accuracy. Therefore, the model provides a fair reproduction of the shape of the scattering entities. Consistent with suggestions based on the course of p(r), the bead model shows a cylindrically shaped particle with almost circular cross-section. The particle diameter is estimated to aDAMMIN = 10.8nm, whereas its height is about bDAMMIN = 6.6nm. The resolution of PAMAM 6/DNA entities is sufficient to unambiguously determine a pH induced transition of the structure of PAMAM 6/DNA entities.

8. DNA Compaction: Do Dendrimers Mimic Histones?

Figure 8-26: DAMMIN model of PAMAM 6/DNA scattering entities at pH = 5.5.

Assigning again a dDNA = 2.0nm hard-core diameter to the DNA,⁵³ these results suggest a PAMAM 6 dendrimer radius of

b nm d

R_P a^{DAMMIN DNA DAMMIN} 3.3

2 2

2^.

6 ≈ − ≈ = . (8-7)

Consistent with observations of PAMAM 6/DNA entities at pH = 8.5 in chapter 8.2.3, this value is slightly smaller than the radius of PAMAM 6 dendrimers (RP6(pH = 5.5) = 3.55nm) determined in chapter 6.4. Therefore, one can conclude that independent of pH conditions dendrimers seem to shrink upon the interaction with the oppositely charged DNA.

In Figure 8-27, the obtained averaged bead model of PAMAM 6/DNA scattering entities at low pH conditions is compared to the structure of NCPs obtained from crystallographic X-ray diffraction data (protein data base file 1eqz.pdb).²³⁶ Analogue to Figure 8-11, Figure 8-27 shows the DAMMIN model of PAMAM 6/DNA scattering entities (a), the structure of NCPs obtained from the crystallographic data (b), and a superposition of both (c). Consistent with results obtained from the corresponding pair

8. DNA Compaction: Do Dendrimers Mimic Histones?

Figure 8-27: Comparison of PAMAM 6/DNA scattering entities and NCPs. (a) PAMAM 6/DNA, (b) NCP, (c) superposition of (a) and (b). (d) Schematic representation of the proposed structure of PAMAM 6/DNA entities.

8. DNA Compaction: Do Dendrimers Mimic Histones?

Table 8-1: Characteristics of PAMAM 6 dendrimers and DNA at pH = 5.5 and pH = 8.5.

distance distribution functions p(r), the similarity in size and shape of PAMAM 6/DNA and NCP is striking.

Based on the derived bead model, a schematic representation of the proposed structure of the PAMAM 6/DNA scattering entities is given in Figure 8-27d. In NCPs, a total of 146 base pairs are wrapped around the histone core in approximately 1.7 turns.

Figure 8-27c suggests that a similar amount of DNA base pairs is wrapped around PAMAM 6. Therefore, the DNA length associated to PAMAM 6 increases significantly with reduction of pH. Contrary to high pH conditions, the dendrimer seems to be completely encompassed by the DNA. Principle parameters derived from the bead model are listed in Table 8-1. For comparison, corresponding values obtained at pH = 8.5 are given.

At pH = 8.5, attractive electrostatic interactions of the two components are not strong enough to completely overcome the elastic counterbalances and to induce a complete DNA wrapping. As a consequence, the charge density of Σ = 1.46e⁺/nm results in an adsorption of an approximately 12nm long stretch of DNA. A charge density of about

8. DNA Compaction: Do Dendrimers Mimic Histones?

1.6-1.9e⁺/nm at pH = 5.5 is needed in order to enable a complete wrapping of the DNA in approximately 1.7 turns corresponding to 46nm. Therefore, the presented results show experimentally that a wrapping transition occurs from an adsorption of a finite length of DNA to a full wrapping with increasing the valence of the spherical macroion. This is in good agreement with theoretical studies on the interaction of a spherical macroion and a linear, oppositely charged polyelectrolyte using the linearized Poisson-Boltzmann theory.7, 243, 247

For a semi-flexible polyelectrolyte with a certain bending rigidity and therefore a finite persistence length LP, the chain bending upon adsorption onto a sphere surface disfavors wrapping. Two effects are included in LP, namely the mechanical bending rigidity of the uncharged chain and the electrostatic repulsions of like-charged chain segments.^{247, 248} With the parameters in Table 8-1 at hands, it is possible to estimate the bending penalty, which has to be overcome by adsorption energies in order to enable a wrapping of the determined stretches of DNA around the sphere. The DNA bending energy Eb around a PAMAM 6 sphere can be considered in terms of kT according to following equation:²⁴⁸

Variables in equation 8-8 are chosen to be consistent to those defined in Table 8-1.

RP6C+dDNA/2 estimates the curvature of the DNA. Obtained results show that an energy gain upon adsorption of approximately 62kT is needed in order to achieve a complete DNA wrapping in about two turns around the dendrimer. However, obtained values represent a lower estimate, since e.g. contributions due to twist and torsion of the polyelectrolyte chain are neglected.

At pH = 5.5, the large amount of DNA adsorbed on the dendrimers leads to a strong, overall overcharging of the spherical cation: The overall charge of the DNA adsorbed on the PAMAM 6 surface exceeds the initial charge of the dendrimer, so that the net charge of the entity changes sign. The phenomenon of overcharging of spherical macroions complexed with oppositely charged, linear polyelectrolytes is well known in literature.^{240, 251} In the X-ray patterns, it is reflected by the strong inter-particle repulsions, which are observed at all studied conditions as pronounced downturns in the low q region. Consequently, these inter-particle repulsions prevent the organization of long-range ordered complex structures. It is important to point out, that at pH = 8.5 overcharging effects are also present. However, they are only locally encountered, but are more pronounced (Table 8-1).

8. DNA Compaction: Do Dendrimers Mimic Histones?