Characterization of commercially available and synthesized polyethylenimines for gene delivery

Journal of Controlled Release 69 (2000) 309–322 www.elsevier.com / locate / jconrel

Characterization of commercially available and synthesized polyethylenimines for gene delivery 1

Anke von Harpe, Holger Petersen, Youxin Li , Thomas Kissel* Department of Pharmaceutics and Biopharmacy, Philipps-University, Ketzerbach 63, D-35032 Marburg, Germany Received 17 April 2000; accepted 17 August 2000

Abstract Five new polyethylenimines (PEI) were synthesized by polymerization of aziridine in aqueous solution and compared to several commercially available PEI used for gene transfer. Polymers were characterized by 13 C NMR spectroscopy, capillary viscosimetry, potentiometric titration and Cu(II) complex formation to gain insight into structural and functional properties. 13 C NMR analysis revealed differences in the extent of branching based on the ratio of primary, secondary and tertiary amino groups. An amino group ratio 18:28:3851:2:1 was obtained for the synthesized PEI, whereas commercially available PEI generally showed a higher degree of branching (1:1:1). Capillary viscosimetry of aqueous PEI solutions with a sufficient amount of salt gave Mark–Houwink parameters of a 50.26 and KV 51.00 cm 3 / g for the commercially available polymers. In case of the synthesized polymers, variation of reaction conditions yielded viscosity average molar masses (Mv ) in the range of 8000–24 000 g / mol. PEI solutions were investigated by potentiometric titration analysis showing that their buffer capacity was not significantly influenced by molar mass or polymer structure. The pKa values (8.18–9.94) and the buffer capacity b (0.08–0.014 mol / l) were of comparable magnitude. This study highlights the necessity of more detailed characterization methods for PEI used in gene transfer protocols since physico-chemical properties do not reflect the vast differences found in transfection efficiencies.  2000 Elsevier Science B.V. All rights reserved. Keywords: Polycations; Polyethylenimine; Synthesis; Buffer capacity; Intrinsic viscosity; Mark–Houwink parameters

1. Introduction Polyethylenimine (PEI) is a cationic polymer exhibiting the highest positive charge density when fully protonated in aqueous solution [1]. These properties are useful for a variety of industrial applications, e.g. in the paper industry for floccula*Corresponding author. Tel.: 149-6421-282-5881; fax: 1496421-282-7016. E-mail address: [email protected] (T. Kissel). 1 Present address: Schwarz Pharma AG; Alfred-Nobel-Str.10, 40789 Monheim, Germany.

tion of negatively charged fibers [2] or as an additive for production of ink-jet paper [3]. Its chelating properties are exploited in waste water treatment to remove metal ions [4]. Branched polyethylenimines are obtained by cationic polymerization of aziridine either at elevated temperatures in aqueous or alcoholic solution or in bulk at low temperatures following the reaction scheme shown in Fig. 1 [5]. The weight average molecular weights (Mw ) achieved with this synthesis are typically in the range 20 000–50 000 g / mol [5]. To generate higher molecular weights of branched polyethylenimine in technical synthesis, bifunctional

0168-3659 / 00 / $ – see front matter  2000 Elsevier Science B.V. All rights reserved. PII: S0168-3659( 00 )00317-5

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Fig. 1. Mechanism of acid catalysed polymerization of ethylene imine in aqueous solution (here: X5Cl), and the resulting polymer structure.

linkers such as dichloroethane or epichlorhydrine derivatives are used [6]. Meanwhile, new applications for PEI have emerged in biology and medicine. Branched and linear polyethylenimines are considered to be promising candidates as non-viral vectors for plasmid [7–9] and oligonucleotide delivery [10,11], both in vitro and in vivo. They provide an attractive alternative to cationic lipid formulations because they combine remarkable transfection efficiencies with high complex stability [12] and allow transfection in the presence of serum [13]. Recently, linear PEI has become commercially available as transfection reagent under the trademark ExGen 500  , with an apparently high transfection efficiency [14]. Different commercially available polymers have been described as transfection reagents which are offered with various molar masses by different suppliers. These PEI have not been characterized in detail with respect to their physico-chemical properties and in the literature conflicting information is provided regarding structural requirements and molecular weights necessary for efficient gene delivery. While some authors argue that lower molecular weight PEI are more effective transfection reagents [9,15], others report failing transfection for very low

molecular weights in the range 600–1800 g / mol and increasing efficiency with increasing molecular weights of PEI [16]. The optimal molecular weight specifications for gene transfer is still not known with certainty, as it is difficult to compare different studies historically using various sources of PEI, transfection protocols, cell lines etc. Additionally, the purity, toxicity and biocompatibility of PEI is a matter of concern, e.g. high molecular weight polyethylenimine (800 000 g / mol) as non-biodegradable polymer can not be renally excreted and presents, therefore, problems for in vivo applications. Moreover, the issue of the optimal PEI architecture for gene delivery is not known. The concept explaining the transfection efficiency of PEI is based on the so-called proton sponge hypothesis [17]. After uptake of PEI / DNA complexes into the endo/ lysosomal compartment PEI should buffer the acidic pH of the lysosome, protecting the DNA from degradation and causing an osmotic swelling / rupture of the vesicles by which DNA is released into the cytoplasm. Protonation of the polycation leads to an expansion of the polymeric network due to intramolecular charge repulsion. A branched polymer structure is thought to be a prerequisite for this behavior. The proton sponge hypothesis does not

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explain why unbranched, linear PEI was demonstrating high transfection efficiencies in several studies [9,14,18]. Moreover, little is known about the relationship between molar masses or branching structure of PEI and their effect on the buffer capacity. Different molar masses of PEI as well as the choice of linear or branched PEI affect transfection efficiency as well as cytotoxicity of PEI / DNA complexes [19,20]. The buffer capacity of PEI solutions can be determined by the potentiometric titration with hydrochloric acid and the influence of branching and molecular weight on the buffer capacity of PEI can be investigated. The complexation and condensation of oligonucleotides and DNA is thought to occur mainly through electrostatic interactions of the positively charged PEI and negatively charged DNA [21]. These processes are influenced by the level of protonation on one hand and the flexibility of the polymer chains on the other. As a simple model for studying polymer chain flexibility, we investigated the ability of PEI to form metal complexes with Cu(II) ions in solution. The formation of these complexes requires a steric coordination of the nitrogen atoms of PEI and was used to probe the accessibility of the nitrogen atoms of these polymers as a function of the degree of branching and molecular weight. In this study, a more detailed characterization of commercially available branched PEI was carried out with respect to the use of these polymers for gene transfer. Additionally, we synthesized PEI using different reaction conditions in aqueous solution to modify molar masses and the degree of branching.

2. Materials and methods

2.1. Materials Eight commercially available polyethylenimines were studied. These are referred to as PEI 1 (Fluka, Deisenhofen, Germany Cat. No. 03880, Lot No. 345312 / 1 995, Mr 5600 000–1 000 000 g / mol (no method disclosed)), PEI 2 (Sigma, Deisenhofen, Germany Cat. No. P-3143, Lot No. 126H0142, Mw 5 750 000, Mn 560 000 (no method disclosed)), PEI 3 (Aldrich, Deisenhofen, Germany Cat. No. 40, 872-7,

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Lot No. AR 05601DQ, Mw 525 000 (light scattering, LS), Mn 510 000 (SEC)), PEI 4 (Aldrich Cat. No. 40,870-0, Lot No. DR 05525LQ, Mw 52000 (LS), Mn 51800 (SEC)), PEI 5 (Aldrich Cat. No. 40,871-9, Lot No. DR 08110MQ, Mw 5800 (LS), Mn 5600 (SEC)), PEI 6 (Polysciences Cat. No. 00618, Lot No. 411893, Mr 570 000 g / mol (no method disclosed)), PEI 7 (Polysciences Cat. No. 19850, Lot No. 403666, Mr 510 000 g / mol (no method disclosed)), PEI 8 (Polysciences Cat. No. 06088, Lot No. 434556, Mr 51200 g / mol (no method disclosed)). All commercially available polymers were dried in vacuo before analysis.

2.2. Synthesis of monomer and polymers Aziridine monomer was prepared from monoethanolamine (Fluka, Germany) as described by Wenker [22]. In a typical polymer synthesis, 5.0 ml of aziridine were dissolved in 50 ml distilled water in a 100-ml glass reaction flask. Then, 0.5 ml of 32% (w / v) hydrochloric acid (HCl) were added to the mixture, the flask was closed and immersed in an oil bath of the desired temperature (see Table 1) under magnetic stirring. The rate of polymerization was followed monitoring change in refractive index. Solutions were kept at elevated temperatures until the refractive index remained constant for at least 24 h, which was in the range of 27 h (PEI 15) to 10 days (PEI 9). Sodium hydroxide was added for neutralization. Water was removed under reduced pressure (water bath 508C, 10 mbar) and the raw polymer was dried in vacuo for 24 h. The polymer was redissolved in 15 ml 96% (v / v) ethanol. After filtration to remove residual sodium chloride, and rinsing flask and filter with 335 ml ethanol, the polymer was recovered by precipitation in 200 ml diethyl ether and dried at 508C in vacuo for 3 weeks. These PEI are referred to as PEI 9–15.

2.3. Two dimensional NMR analysis Two dimensional 13 C INADEQUATE (incredible natural abundance double quantum transfer experiment) was carried out with 300 mg PEI in deuterium oxide (D 2 O, Merck, Darmstadt, Germany) in a LA 500 Eclipse1 Delta FT spectrometer (Jeol, USA) at 125 MHz with 512 scans at 308C probe temperature.

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Table 1 Reaction conditions, inherent viscosities and molecular weights (estimated from viscosity measurements) for self synthesized poly(ethylene imines)a Polymer

Initiator (HCl) to monomer ratio [mol%]

Temperature [8C]

hinh [dl / g]

Mv [g / mol]

Yield [%]

PEI PEI PEI PEI PEI PEI PEI

5.26 5.26 5.26 5.26 5.26 10.52 10.52

35 50 65 80 Reflux 50 80

0.130 0.113 0.104 0.102 0.100 0.101 0.100

24 300 13 900 9800 9100 8600 12 000 8600

63 54 85 65 45 53 32

9 10 11 12 13 14 15

a

For the calculation of molecular weights from viscosity measurements the determined values of a 50.26 and KV 50.10 cm 3 / g were used.

2.4. NMR Analysis 1

H NMR and 13 C NMR spectra were recorded from 100 mg PEI in D 2 O (Merck) in a LA 500 Eclipse1 Delta FT spectrometer (Jeol) at 500 MHz for 1 H and 125 MHz (8000 scans, probe temperature 308C) for 13 C spectra, respectively. To avoid any influence of the Nuclear Overhauser effect (NOE) all 13 C spectra used for quantitative analysis were recorded using inverse gated decoupling pulse sequences. Spectra were calculated with the NMR data processing program WinNuts 2D (Acorn NMR). Signal intensities were determined relative to signal 8 (Fig. 4, value was set as 1.00).

2.5. Capillary viscosity measurements Viscosity measurements were carried out with polymer concentrations of 0.5 g / dl in 0.5 M sodium nitrate (NaNO 3 , Merck) solution using an Ubbelohde capillary viscometer (Schott, Type Nr. 50101 / 0a) at 25.08C. For determination of intrinsic viscosities [h ], five polymer concentrations from 0.1 to 0.5 g / dl were investigated. Reduced (hred ), specific (hsp ) and inherent (hinh ) viscosities were calculated using Eqs. (1)–(3) (h : viscosity of PEI solution; h0 : viscosity of solvent) [23]:

hsp 5 (h 2 h0 ) /h0

(1)

hred 5 hsp /c

(2)

hinh 5 ln(h /h0 ) /c [dl / g]

(3)

The limiting viscosity number [h ] is given by extrapolation of the reduced viscosity to infinite dilution (Eq. (4)): [h ] 5 hred for c → 0

(4)

Following the Staudinger–Mark–Houwink relationship (Eq. (5)), a linear relation exists between log([h ]) and log(MV ) [23]: [h ] 5 KV M a

(5)

2.6. Buffer capacity of PEI First, 50.0 mg PEI was dissolved in 10.0 ml double-distilled water. Potentiometric titration was performed with a Schott CG 820 pH meter using 0.1 N HCl (Titrisol, Merck) as titrant. Each determination was carried out in triplicate at 2560.18C according to Ref. [24]. The buffer capacity was calculated as described in Ref. [25].

2.7. Complexation of Cu 21 by PEI In this case, 100.0 mg of PEI was dissolved in 20.0 ml double-distilled water. Titration was performed with 0.10167 mol / l Copper(II) nitrate (Cu(NO 3 ) 2 , Merck) as titrant [26] and following pH change using a Schott CG 820 pH meter. For determination of the extinction maximum, 2.5 mg PEI were dissolved in 0.5 ml double-distilled water. The amount of 0.10167 mol / l Cu(NO 3 ) 2 solution needed for 4:1 res. 6:1 complex formation was calculated from titration curves for each PEI sample. It was diluted to a final volume 0.5 ml with double

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distilled water and added to the PEI solutions. Spectra were obtained using a Shimadzu UV-160 spectrophotometer.

3. Results

3.1. Synthesis Acid-catalyzed polymerization of aziridine has been described previously [5]. Protonation of the aziridine monomer leads to an immonium cation which reacts with additional monomer for propagation or with an already formed polymer chain to form branches (Fig. 1). Bulk polymerization of anhydrous aziridine upon addition of initiator proceeds with violence and leads to higher molecular weight products. Polymerization in aqueous solution occurs more slowly and can be influenced by variation of reaction temperature or amount of initiator added [27]. Monitoring refractive index of the reaction mixture we found an increase from 1.341 up to 1.349, which is identical with the refractive index of a 4.07 g PEI / 50 ml water solution (Fig. 2). All reaction mixtures reached the final value of 1.349, which indicates complete conversion of the monomer. The reaction rate increased both with increasing temperatures and increasing concentrations of catalyst. The yields varied typically between 32 and 85%. Variation of reaction temperature and concentration of catalyst the polymerization of aziridine in aqueous solution led to PEI of molecular weights in the range from 8000 to 24 000 g / mol as determined by viscosimetry (Table 1). Higher amounts of initiator as well as higher process temperatures resulted in a decrease of molecular weight of the products. The synthesis was found to be reproducible with respect to molar masses (all polymers within mean 65%, n57) and branching (mean 61%). All polymers were obtained as free base, characteristically colorless, clear, highly viscous semi-solid masses.

3.2. Two dimensional NMR analysis We carried out an experiment based on a 2D- 13 C INADEQUATE NMR spectrum [28] (Fig. 3) to confirm the signal assignment. Coupling carbon

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atoms give satellite signals appearing at the same double quantum frequency plotted in F1 direction. These coupling pairs belong to directly neighbored methylene groups. In PEI these methylene groups form pairs, defined by the repeating unit N–CH 2 – CH 2 –N. These pairs differ in their chemical environment caused by the substitution of the flanking nitrogen atoms. Methylene groups represented by signals 1–8, 2–6 and 4–7 (Fig. 4) are forming these pairs. Methylene groups 3 and 5 are identical with respect to their direct neighbors and therefore only a single signal is observed. Signal 3 is too weak to be detected in the 2D-INADEQUATE spectrum. From the satellite signals coupling constants can be calculated. Since the hybridization of all PEI carbons is equal, coupling constants are only weakly influenced by their substituents. The C–H coupling constants are found at 34.6 Hz (H 2 N–CH 2 –CH 2 – NR 2 ), 32.0 Hz (H 2 N–CH 2 –CH 2 –NRH) and 26.7 Hz (RHN–CH 2 –CH 2 –NR 2 ), respectively.

3.3. NMR analysis In the 1 H NMR spectra at 500 MHz all PEI CH 2 signals resonate between d 52.5 and 2.7 ppm. Therefore, methylene groups with different amine substituents cannot be sufficiently separated for quantitative analysis. For this reason our study concentrated on 13 C NMR, where all structural elements show well separated signals in the typical area between 37 and 54 ppm. Additional signals from residual monomer traces (d 517.6 ppm in 13 C, d 51.5 in 1 H) could not be detected in any of the spectra recorded. Control experiments with varying PEI concentration and temperature showed optimal resolution at 100 mg PEI / 308C (data not shown). A typical 13 C NMR of PEI is shown in Fig. 4. The eight signals of the corresponding methylene groups were assigned as indicated. The results of our 2D-INADEQUATE 13 C NMR experiment verify the signal assignment which was already proposed previously [29]. The ratio of different amino groups in the polymer can be calculated from signal intensities using Eq. (6): 18:28:38 5 (A 7 1 A 8 ):(A 4 1 A 5 1 A 6 ) / 2:(A 1 1 A 2 1 A3)/3

(6)

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Fig. 2. Refractive index monitoring of aziridine polymerization under different conditions.

A. von Harpe et al. / Journal of Controlled Release 69 (2000) 309 – 322 Fig. 3. 2D- 13 C INADEQUATE NMR of poly(ethylene imine). The conventional 13 C spectrum is running along the top of the diagram (for structural components represented by the signals, see Fig. 4). The satellite spectra are the line patterns joined by broken lines, their centres of gravity lie on a straight line. The double-quantum frequencies appear in the F1 direction.

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Fig. 4. Structure of PEI determined by

13

C NMR. Structural elements belonging to the different signals are given.

Table 2 Relative ratio of different amino functions in PEI calculated from 13 C NMR analysis a Polymer

PEI PEI PEI PEI PEI PEI PEI PEI PEI PEI PEI PEI PEI PEI PEI

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Amines [%] Primary

Secondary

Tertiary

28 / 38

34 34 31 36 42 35 36 40 26 28 27 28 29 27 28

35 35 39 34 33 34 34 34 51 50 50 49 48 51 50

31 31 30 30 25 31 30 26 23 22 23 23 23 22 22

1.13 1.13 1.30 1.13 1.32 1.10 1.13 1.31 2.22 2.27 2.17 2.13 2.09 2.32 2.27

a 28 / 38 amines represents the ratio of linear to branched structures in one molecule, for PEIs 1–8 nearly every second nitrogen, in PEIs 9–15 only every third forms a branch.

In contrast to earlier studies [29] we used inversely gated decoupling pulse sequences in our 13 C NMR experiments to avoid the influence of the Nuclear Overhauser effect on the signal intensities. This technique allows a quantitative analysis of 13 C NMR spectra. Our results are summarized in Table 2. For all samples obtained by ring-opening polymerization in solution, the ratio of different amino groups follows the theoretical ratio of 25% primary, 50% secondary and 25% tertiary amines, which can be explained from the usual polymerization reaction mechanism of aziridine catalyzed by acids [1]. The values found for commercial PEI samples are not consistent with the reported distribution and show almost equal proportions of the different amine groups. The high content of primary amines in PEI 5 may partly be explained by its very low molecular weight, consisting of only 16 repeating units per molecule. Pierre and Geckle [29] also report amine function ratios similar to our results for the commercially available PEI samples.

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These data can also be expressed as the relative ratio of linear to branched structures, calculated from integrals of secondary (28) amines to tertiary (38) amines. For PEI samples synthesized in solution, on average every third nitrogen is a tertiary amino function. In commercially available PEI nearly every second nitrogen is a tertiary one, forming a branching point. This fairly high content of branches in close proximity is represented by signal 3 (Fig. 4). Therefore, ¯25–30% of all tertiary nitrogen atoms are direct neighbors of another branching point for PEI 9–15, whereas, for PEI 1–8 this relative ratio is nearly 50%, reflecting the higher degree of branching of these polymers.

possible and yielded reliable values for the intrinsic viscosity [h ]. It should also be noted that this rather high salt concentration was necessary to achieve linearity of the above mentioned relationship due to the high charge density of PEI. Despite of that high salt concentration, no salting out of PEI was observed. For the double logarithmic [h ]–M plot, we used the molecular weight data provided by suppliers (Mw ). For polymers of molecular weight up to 70 kDa, we found a sufficiently linear relationship between log([h ]) and log(Mw ) (R50.998, Fig. 5). Mark–Houwink parameters were determined as a 5 0.26 and KV 51.00 cm 3 / g.

3.4. Viscosity measurements

3.5. Analysis of buffer capacity by potentiometric titration

We measured hsp at five different concentrations and plotted hred against c. Using a salt concentration of 0.5 M NaNO 3 we obtained a linear relationship of the data so that extrapolation to infinite dilution was

Since Suh et al. [24] demonstrated that pKa values of polyamines strongly depend on pH and polymer concentration, we examined buffer capacities of PEI

Fig. 5. Intrinsic viscosities of commercially available PEIs determined by extrapolation of the reduced viscosity to infinite dilution (insert, example for PEI 1).

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solutions of equivalent nitrogen concentration to determine the influence of structure and molecular weight. Potentiometric titration yielded titration curves as shown in Fig. 6 (insert). Buffer capacity ( b ) was calculated from these data using Eq. (7) [25]:

b 5 dc (HCl) / dpH

(7)

These graphs represent changes in the buffer capacity as a function of the pH (Fig. 6). Maxima appeared at the pH with highest buffer capacity, their height representing its extent. The values found for the different PEI samples are given in Table 3. These graphs demonstrate that PEI, like most other polyamines, yield their highest buffer capacity at pH values above 8. The pKa values (and with them the basicity of the polymers) decreased with increasing molecular weight from 9.94 to 8.18. It is worth noting, that differences in the range of pH 4–6, which has been attributed to the endo / lysosomal compartment, are not significant and independent of molecular mass or branching.

Table 3 pKa values and buffer capacities (at pKa ) determined by potentiometric titration with HCl Polymer

pKa value

Buffer capacity [mol / l]

1 2 3 4 5 6 7 10 12 14 15

8.25 8.18 8.4 9.38 9.94 8.3 8.3 9.1 9.65 9.45 9.31

0.012 0.011 0.008 0.011 0.014 0.011 0.011 0.010 0.011 0.009 0.010

3.6. Complexation of copper( II) ions Upon addition of copper(II) ions, PEI forms a dark blue cuprammonium complex, in a concentration dependent manner at a N:Cu ratio of 6:1 or 4:1, respectively. According to Perrine et al. [26],

Fig. 6. Buffer capacities ( b ) of different PEIs in solution (0.1165 mol N / l) as function of pH. Symbols show PEI 1 (h), PEI 3 (앳), PEI 5 (\),PEI 6 (^),PEI 10 (j) and PEI 12 (m). Buffer capacities were calculated from potentiometric titration curves (insert) according to Ref. [26].

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complex formation can be followed by titration of PEI solution using copper nitrate and potentiometric detection. The inflection points of these graphs represent the formation of the 6:1 and 4:1 complex, respectively. Using this method, compositions of these complexes were calculated for the polymers examined. The complexes show a slightly different extinction maximum of lmax 5640 nm for the 6:1 and lmax 5619 nm for the 4:1 complex. Complex stability can be described using complex formation constant (K) given by Eq. (8): K 5 [Cu–PEI] /([Cu][PEI])

(8)

Here [Cu–PEI] represents the concentration of copper and PEI bound in the complex, [Cu] represents free copper ions and [PEI] free PEI nitrogens. As reported in Ref. [26], a constant amount of 5% of copper added does not take part in complex formation. High formation constants are characteristic for complexes of high stability. In our case these constants are dependent on the relative ratio of nitrogen atoms in the polymer chain which are excluded from

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participation in complex formation, probably due to steric hindrance. Results for 6:1 complexes of Cu 21 with PEI are shown in Fig. 7 (4:1 complexes show similar tendencies). By comparison, we observe an effect of the molar mass on Cu 21 –PEI complex formation. With increasing molar masses the complex formation constant decreases (PEI 4, 5 and PEI 10 samples) leveling off at 10 000 g / mol, where no further significant changes in the complex formation constant could be observed. The degree of branching seems to have no direct influence complex formation constant. In contrast to the buffer capacity determined by potentiometric titration, where pKa values were dependent on molar mass of PEI, the influence of the molecular weight on the complex formation is only important with low molecular weight polymers.

4. Discussion The aim of this study was to validate methods for the characterization of polycations such as PEI. Such

Fig. 7. Complex forming constants for 6:1 Cu(II) complexes according to Eq. (6). Dotted line indicates a decrease of complex forming ability with increasing molecular weight for PEI of low and moderate molecular weight.

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methods should allow determination of the degree of branching and molar mass of PEI used for gene or oligonucleotide transfer both in vitro and in vivo. Transfection efficiencies, polymer cytotoxicity and DNA binding characteristics seem to be influenced by molar mass and structural components of the polycations, such as PEI [16,19]. Therefore, a more detailed characterization of the polycations and their complexes with DNA would be desirable to define a structure–function relationship for PEI and similar compounds as transfection reagent and to optimize transfection properties of those polymers. The characterization of molar masses and distributions are of critical importance, yet size exclusion chromatography (SEC) often used for non-ionic polymers is considered to be problematic for the analysis of polyelectrolytes, due to their interactions with column materials and lack of suitable calibration standards. Methods, like vapor pressure osmometry, are not suitable for polyelectrolytes due to counterion–polyion dissociation processes and membrane osmometry gives only reliable results for molar masses .10 4 g / mol. The most suitable technique is static light scattering since it provides an absolute method for determining Mw . Our intention was to establish a method, which should be easy in handling and instrumentally simple. Therefore, we applied capillary viscosimetry. Nevertheless, the determination of the molecular weight of PEI by this method is problematic for two reasons. The determination of the molecular weight of PEI by this method is problematic for two reasons. Firstly, PEI is a polycation and shows in aqueous solution the so-called ‘polyelectrolyte effect’ [30]. An abnormal behaviour of polyelectrolyte solutions is observed due to intramolecular interactions of the charges bound to the polymer backbone. With increasing dilution the reduced viscosity is increased. Thus, extrapolation of the reduced viscosity to infinite dilution is not possible. This problem is easily overcome by adding salt in sufficient concentration to the polymer solution approaching the behavior of a ‘normal’ uncharged polymer. Secondly, PEI is a highly branched polymer. For some branched polymers like glycogen, no relationship between the density of the molecule and its molecular weight (a 50) can be defined. Therefore, prior to using viscosimetry for characterization of PEI, we de-

termined if a relation between intrinsic viscosity and the molecular weight exists in the case of PEI. The rather low value of a 50.26 is consistent with the highly branched structure of the polymers. Nevertheless, a is still high enough to show a clear intrinsic viscosity–molar mass dependency. Thus, determination of molecular weight of PEI by capillary viscosimetry is possible if the degree of branching is known. This is true only for the molecular weight region up to 70 kDa, since Fig. 5 shows that for higher molecular weights the slope of the relationship between log([h ]) and log(Mw ) seems to decrease and a becomes close to a value of zero. This can be explained by the way these PEI are synthesized [6]. The bifunctional linkers used in that synthesis do probably not only form links intermolecularily to increase molecular weight but may also form intramolecular links to a certain extent. Hereby, compact polymer structures of higher densities can be formed resulting in a lower intrinsic viscosity. The determination of molecular weight by viscosimetry is only applicable for PEI with a similar degree of branching. To evaluate the Mark–Houwink parameters we exclusively used PEI with an amino group ratio 18:28:3851:1:1. Since our synthesized PEI obtain an amino group ratio of 18:28:3851:2:1, indicative for a less branched structure, the above mentioned Mark–Houwink parameters are not entirely valid, but allow some estimates. Since they are more linear in their structure, the a parameter should be higher than 0.26. For our calculations we used the parameters obtained by the measurement of commercially available PEI. Thus, the calculated values for Mv of the synthesized PEIs will be higher than the real molecular weight of our polymers. Values calculated for the synthesized PEI are given in Table 1. Further, it should be noted that due to the low a parameter, Mv is not close to Mw , but clearly smaller than Mw . The Mv of PEI 10 calculated from viscosity measurement is slightly higher compared to Mw given by light scattering in an earlier study, which was 11 900 g / mol [19]. This can, as above mentioned, be explained by the lower degree of branching of this polymer in comparison to commercially available samples, which results in a higher hydrodynamic volume in relation to molecular weight.

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So far literature reports about the application of PEI as a transfection reagent assume that the degree of branching should follow the theoretical values giving a ratio of primary to secondary to tertiary amino groups of 1:2:1 [17]. Our results demonstrate that a higher degree of branching for all commercially available samples is obtained. These findings are in agreement with the literature [29], where deviations from the ideal branching structure of PEI were observed. Polymerization in aqueous solution is compatible with the reaction mechanism described in Fig. 1 and PEI with the theoretically expected amino group ratio is obtained. Although polymer molar masses could be varied to some modest degree, the branching structure of these polymers was not affected, affording an amino group ratio of 1:2:1. Therefore, differences in amino group ratio will ultimately lead to modified structures of PEI in solution. PEI with different degrees of branching could be used as tools to determine the role of the three dimensional structure of PEI for the interaction with DNA and possibly for transfection or toxicity. In view of the fact that higher PEI concentrations often lead to increased transfection efficiencies, a less toxic PEI would be desirable so that polymer toxicity should not become the limiting factor for gene transfer [19]. Potentiometric titration of PEI does allow classification of the polymers according to their molecular weight, but not to their structure. For all PEI, the area of high buffer capacity lies above the physiological pH range, typically between 8 and 9.5. With an increase of molecular weight a decrease of pKa could be observed. In the range between 7.4 and 4.5, characteristic for the lysosomal compartment, there are only marginal differences in buffer capacity between all PEI studied so far. Relating these results to the proton sponge hypothesis, where the endosomal buffering capacity of PEI seems to play a critical role for transfection, we can observe two things. Firstly, transfection is dependent on molecular weight of PEI [16], although we could not determine a clear relationship between polymer molecular weight and buffer capacity in the physiological range between pH 7.4 and 4.5. Secondly we could demonstrate that protonation levels are not influenced by the structure of PEI, but transfection and toxicity were found to be different in high and low branched PEI [19]. The biological activity of PEI seems to rely

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on additional factors influencing DNA binding, cellular uptake and intracellular processing of PEI / DNA complexes, biological and biophysical phenomena currently not very well defined and incompletely understood for polycations. The formation of Cu(II) / PEI complexes was studied for two reasons. For one, a qualitative and quantitative assay allowing the determination of PEI was of general interest. The formation of intensively blue colored Cu 21 –chelate complexes with ethylene diamine in aqueous solution could serve as analogous example. Secondly, structure and composition Cu 21 –chelate complexes with PEI in aqueous solution have not been described in detail as a function of the molecular weight and degree of branching. One could consider Cu 21 as a probe to study properties of different PEI with respect to the formation of chelate complexes. The accessibility of nitrogen atoms in PEI is not only important for chelate complexes, but also for the complexation and condensation of DNA, properties which are based on electrostatic interactions. Therefore we speculated, that the complex formation constant K may also reflect structural parameters important in the context of PEI as transfection reagent. If we postulate, that this ability of complexation reflects the accessibility of the polymer nitrogen atoms, we observe the following tendencies. For low molecular weight PEI the complex formation constant is increasing with a decrease of molecular weight. These differences are not as prominent as in the case of pKa values. At a plateau in the range of ¯ .10 4 g / mol, no further significant change in the complexation constant K is observed. Interestingly, above this threshold no dependency of complex formation on molecular weight or branching was noted. Molar masses of PEI in the range of 10 4 g / mol were also found to be suitable for the transfection different cell lines [19]. Clearly, more data would be necessary to define a structure–function relationship for PEI and other polycations as transfection reagents.

5. Conclusions The physico-chemical characterization of commercially available PEI is insufficient to predict their performance as transfection reagents. A more de-

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tailed description would be helpful based on analytical methods, such as 13 C NMR spectroscopy to describe not only molecular weight and molecular weight distribution but also information about the structure of the PEI used as gene delivery system. A detailed study of the branched structure of PEI using 2D- and inverse gated-decoupled spectra produced reliable results. PEI synthesized by cationic polymerization of aziridine in aqueous solution led to an amine ratio of 1:2:1 which differed from the 1:1:1 ratio of commercially available materials. Potentiometric titration demonstrate that pKa values are dependent on the molecular weight, but buffer capacity at physiological pH does not vary in a systematic manner for PEI of different molecular weights, suggesting that other factors than protonation contribute to the transfection properties of different PEI. If buffer capacity, as proposed [17], is the fundamental principle of transfection, these findings are in contrast to biological activities of the polymers [9,19].

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