Article pubs.acs.org/Macromolecules
Effective Charge Determination of Dendrigraft Poly‑L‑lysine by Capillary Isotachophoresis Amal Ibrahim,† Dušan Koval,‡ Václav Kašička,‡ Clément Faye,§ and Hervé Cottet*,† †
Institut des Biomolécules Max Mousseron, UMR 5247 CNRS, Université de Montpellier 1 and Université de Montpellier 2, place Eugène Bataillon CC 1706, 34095 Montpellier Cedex 5, France ‡ Institute of Organic Chemistry and Biochemistry, Academy of Sciences of the Czech Republic v.v.i., Flemingovo n. 2, 166 10 Prague 6, Czech Republic § COLCOM, Cap Alpha Avenue de l’Europe, Clapiers 34940 Montpellier, France S Supporting Information *
ABSTRACT: In this work, capillary isotachophoresis (ITP) was used to determine the effective charge of the first five generations of dendrigraft poly-L-lysines. This approach, which is based on the linear dependence of ITP zone length of the solute on its concentration and effective charge, offers a simple and straightforward method for effective charge determination. The cationic ITP system employed in this work yields good linearity, repeatability and sharp zones. The value of effective charge number per one lysine residue obtained for long linear poly-L-lysine is in a good agreement with the Manning theoretical value (0.5). Results obtained for dendrigraft poly-L-lysines show a dramatic decrease in the effective charge number per lysine residue with increasing generation number, from 0.84 for short oligolysines (generation 1) down to 0.08 for the fifth generation. This decrease in effective charge is due to the proximity of charged groups in the dendrigraft structure of higher generation number.
1. INTRODUCTION Dendrigraft poly-L-lysines (DGL) are dendritic cationic polypeptides synthesized by polymerization of N-carboxyanhydride of Nε-trifluoroacetyl-L-lysine in aqueous conditions.1 DGL can be easily functionalized2 and used for drug or gene delivery,3,4 for transport through cellular membranes5 or can be used as nanosized magnetic resonance imaging contrast agents.6 Compared to dendrimers, DGL are much more flexible, as demonstrated by the decrease by a factor 2 of the DGL hydrodynamic radii in DMF compared to water.7 DGL are also non immunogenic8 with excellent biocompatibility.3,6 In gene or drug delivery, the effective charge of the vector is one of the major parameters which control the dendrimer−drug or dendrimer−DNA interactions,9 the stability, and the bioactivity of the complexes.10 Effective charge is also strongly involved in the control of cytotoxicity11−13 and can be controlled by surface charge modification or coating.14,15 Apart from the dissociation of the charged groups which depends on the pH of the medium, the effective charge of a macromolecule depends on the counterion condensation.16 Counterion condensation represents the fraction of bound counterions to the macromolecule backbone, which in turn affects the binding thermodynamics17−19 between oppositely charged compounds via entropic effects due to the release of counterions after binding. This counterion condensation is mainly controlled by the distance between charged monomers, as stated in the Manning theory.16 This distance is well-defined © 2012 American Chemical Society
in the case of linear polyelectrolytes. Nevertheless, in the case of dendritic structures, the distance between charged groups is much more complex to define. This distance is not only related to the distance between two successive monomers, but may also depend on closely related monomers coming from different branches of the dendritic structure. Therefore, counterion condensation of charged dendrimers has been the topic of experimental or theoretical investigations.20−22 Effective charge of dendrimers was estimated theoretically using fully atomistic molecular dynamics simulations.20 It was also determined experimentally using small-angle neutron scattering (SANS)21,23 or using a combination of SANS with computer simulation.24 Poisson−Boltzmann equation for spherical particles was applied to dendrimers to obtain the effective surface charge density from the surface potential, determined experimentally by titration.25 Attempts were reported in the literature to estimate effective charge of dendrimers from the zeta potential determined from the electrophoretic mobility,26,27 considering the dendrimer as a spherical hard-core nanoparticle in the framework of the Henry or O’Brien−White modelings. Böhme et al.28 applied Nernst− Einstein relationship to polyamidoamine dendrimers (PAMAM) for effective charge determination using diffusion Received: October 10, 2012 Revised: December 14, 2012 Published: December 28, 2012 533
dx.doi.org/10.1021/ma302125f | Macromolecules 2013, 46, 533−540
Macromolecules
Article
Total electric current I passing through electrolyte solution containing N components i can be viewed as summation of partial currents Ii:
and electrophoretic NMR. Nevertheless, Nernst−Einstein relationship is only valid at infinite dilution where relaxation and electrophoretic effects can be neglected.29,30 The determination of linear (or dendritic) polyelectrolyte effective charge is somewhat more complex than for hardcore nanoparticles or small ions, since there is no available theoretical modeling yet allowing to determine the effective charge of polyelectrolytes from the experimental determination of the electrophoretic mobility and the hydrodynamic radius at a finite ionic strength.30 Recently, indirect UV detection (IUV) in capillary zone electrophoresis was used to determine the effective charge from the transfer ratio (i.e., the quantity of chromophores displaced by mole of analyte).30,31 IUV method is based on the sensitivity of detection (i.e., on peak area) and not on the electrophoretic mobility (i.e., migration time). This approach, which is based on the Kohlrausch regulation function,32 can be used for any type of the solutes, including polyelectrolytes. However, it requires the use of a chromophore with the following characteristics: (i) it should have a known charge of the same sign of the solutes, (ii) it should not chemically interact with the solutes, and (iii) it should absorb at a wavelength of detection for which the solute is transparent. These conditions are sometimes difficult to fulfill. Alternatively, capillary isotachophoresis (ITP) was recently introduced by Bücking et al.33 and used by Pyell et al.34 for the determination of effective charge or solute concentration. This method relies on the linear dependence of the ITP zone length on the solute charge and concentration. No chromophore is required and direct UV or conductivity detections can be used. In this work, the effective charge number per one lysine residue (z1) for the first five successive generations of DGL was determined using the ITP approach. The results were compared to those obtained for linear poly-L-lysine (PLL) of three different degrees of polymerization (DPn = 20, 50 and 100), allowing to investigate the influence of the branching on the effective charge.
N
I=
∑ Ii
(1)
i=1
Conversely, partial electric current Ii is a product of the total current I and transport number τi: Ii = Iτi
(2)
Transport number τi expresses here the contribution of i-th component in all its ionic states to total electric conductivity of the electrolyte solution: π
τi =
∑zi= ν |z|ci , zμi , z i
N
π
∑i = 1 ∑zi= ν |z|ci , zμi , z + cHμH + cOHμOH i
(3)
Here ci,z, cH, and cOH denote the molar concentration of ionic forms of i-th component bearing charge number z, hydrogen ions H+, and hydroxide ions OH−, respectively. Then, μi,z, μH, and μOH are the actual ionic mobilities of the respective species. However, in further description of the ITP method for determination of effective charge, we will assume that each component i of electrolyte system is present exclusively in one of its ionic forms (e.g., fully ionized solute). Thus, electric charge Qi required for a displacement of ionic species i is given by Faraday law as
Q i = |zi|niF
(4)
where zi means the effective charge of i-th component under above specified conditions, ni is the total substance amount of ith component (in moles) and F is Faraday constant. Since ITP is run at constant electric current, the electric charge Qi necessary for displacement of i-th component can be expressed using eq 2 as Qi = IiΔti = τiIΔti, where Δti is time of passage of zone of i-th component through the detection point. Further, substance amount of displaced ions ni is equal ni = ciVi, where ci stands for the total molar concentration and Vi is the volume of a solution of i-th component used in ITP experiment. Substitution into eq 4 provides after rearrangement:
2. THEORETICAL BACKGROUND Capillary isotachophoresis has been used mostly as analytical technique for separation of ionic species. 35−37 Sample components to be separated are introduced at the interface of two electrolytes denoted as leading and terminating, electrophoretic mobilities of which are greater and smaller, respectively, relative to mobilities of the sample components. Upon application of the electric field, typically at constant current mode, ions start moving as a train of zones at constant velocity down the separation capillary. As such, either cations or anions can be separated in a single separation run at given system of leading (LE) and terminating (TE) electrolytes. Historically, ITP can be considered as a successor of moving boundary technique, a classical method of electrochemistry for determination of transport numbers and electrophoretic mobilities of ions. For introduction of isotachophoretic approach for determination of effective charge34 we adopt notation of electrophoretic systems used by Gaš and coworkers.38−40 We consider electrolyte system of total N components i, which can be strong and weak acids, bases, and ampholytes. Each component i can in turn exist in several ionic states of valence z (neutral form of i has z = 0). The most negative charge number is denoted as νi, the most positive as πi (see, e.g., ref 41 for details).
| zi | =
τiI Δti FciVi
(5)
In order that experimental ITP data could be well interpreted in terms of effective charge, component of interest i needs to be well separated from other co-ions of the system. Further, actual pH of ITP zone of component i should be in the “safe region” 4−10, which makes it possible to neglect H+ and OH− in eq 3 (i.e., cHμH = cOHμOH = 0). Thus, the ITP zone of component i at steady state can be considered as binary system (N = 2) of ion of interest and buffering counterion originating from LE. Using electroneutrality condition in simple form ΣNi=1zci,z = 0 (see, e.g., refs 38 and 41 for general formula), eq 3 simplifies to
τi =
μi , z μi , z + μc , z
(6)
where μc,z is the actual ionic mobility of the counterion in the ITP zone. By combination of eq 5 and 6, a formula for calculation of effective charge zi is obtained: 534
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Macromolecules | zi | =
μi , z I Δti FciVi μi , z + μc , z
Article
capillary cartridge was maintained constant at 25 °C. Samples were diluted in deionized water and injected hydrodynamically (50 mbar, 3 s). Each sample injection was followed by hydrodynamic injection (5 mbar, 3 s) of 0.02 g·L−1 DMF solution used as a neutral electroosmotic flow marker. A voltage of −30 kV was applied and data were collected at 200 nm using Agilent Chemstation software. Electroosmotic mobility was calculated from the migration time of DMF. Electropherograms were plotted in electrophoretic mobility scale (μep) using the following equation:
(7)
Thus, eq 7 makes it possible to achieve effective charge determination directly from experimental data. Nevertheless, we found it useful to reduce experimental bias by using a reference substance with well-defined charge number (zref) and actual ionic mobility (μref,z) at conditions of the ITP run. Then, for ratio zi/zref, we can write Δticref Vref μi , z (μref , z + μc , z ) zi = zref Δtref ciVi μref , z (μi , z + μc , z )
⎛ 1 1 ⎞ lL μep = ⎜⎜ − ⎟⎟ teo ⎠ V ⎝ tapp
(8)
where μep is the electrophoretic mobility, l is the effective capillary length to the detection point, L is the total capillary length, V is the applied voltage, teo is the migration time of the neutral (EOF) marker (DMF), and tapp is the migration time of solute. Further, tapp was taken at the peak apex for symmetrical peaks. For polydisperse samples, tapp was obtained by integration of the whole peak using tapp = ∫ h(t)t dt/ ∫ h(t) dt where h(t) is the detector response. 3.3. Determination of Intergeneration Purity and Cationic Impurities by Capillary Zone Electrophoresis. CZE was carried out on an Agilent 3D-CE instrument (Waldbronn, Germany) equipped with a diode array detector. A capacitively coupled contactless conductivity detector (C4D), purchased from TraceDec (Innsbruck, Austria) was coupled to the CE instrument. The detection cell was placed along the separation capillary without the need to remove the polyimide layer (external capillary coating). HPC (neutral polymer) coated capillaries of 50 cm total length (41.5 cm to the UV detector, 36 cm to the C4D detector) × 50 μm i.d. were used. Coating procedure is detailed elsewhere.42 Before use, the coated capillaries were rinsed with water for 10 min. Background electrolyte composed of 2 M AcOH/1 mM H2SO4/ 25% MeOH (v/v) was used and prepared using two stock solutions composed of 8 M AcOH or 10 mM H2SO4 in water. The stock solutions were diluted to the desired concentrations in a 100 mL flask containing 25 mL of MeOH and completed with ultrapure water to the final volume. Between runs, the capillary was flushed for 3 min with water then for 5 min with the BGE. Temperature of the capillary cartridge was maintained constant at 25 °C. Samples were diluted in deionized water and injected hydrodynamically (50 mbar, 3 s) and a voltage of +30 kV was applied. The prepunchers and electrodes were cleaned on daily basis to remove any cationic residues. C4D signals were collected using Tracedec monitor software, version 0.08c with the following parameters: frequency, 2 × high; voltage, −6 dB; gain, 150%; and offset, 170. In the same conditions, a calibration was performed for the quantification of Na+ and NH4+ impurities. Limits of detection (LOD) and limits of quantification (LOQ) were calculated on the basis of a peak height equals 3 and 10 folds of the baseline noise, respectively. 3.4. Determination of Effective Charge by Capillary Isotachophoresis. Isotachophoretic analyzer EA101 (Villa Labeco, Spišská Nová Ves, Slovakia) was used for all here reported ITP experiments. The apparatus consists of two fluorinated ethylene propylene copolymer (FEP) capillary columns coupled in series in vertical arrangement. It enables preseparation and removal of macrocomponents from the sample in large bore tube (0.8 mm i.d., 160 mm length) which is followed by fine separation of components of interest in a narrow bore column (0.3 mm i.d., 160 mm length). For purpose of determination of effective charge, total substance amount of injected sample components was transferred entirely to the narrow bore column. Migrating zones were detected by contactless conductivity detector. For cationic ITP analysis, the leading electrolyte was composed of 20 mM AcOH and 10 mM NH4OH buffer, pH 4.7, and 20 mM AcOH, pH 3.2 was used as the terminating electrolyte. Polymer samples were dissolved in deionized water at 1 g·L−1 as well as 2.5 mM ammediol, which was used as reference internal standard. Solutions of samples and standard were injected separately in volume of 5 μL by Hamilton syringe. Driving current in ITP runs was initially
If the reference compound is used as internal standard or injected separately at same volume (i.e., Vi = Vref), eq 8 further simplifies to zi = zref
Δticref μi , z (μref , z + μc , z ) Δtref ci μref , z (μi , z + μc , z )
(10)
(9)
This approach reduces some experimental uncertainties, namely due to precision and stability of electric current, injected volume and residual electroosmotic flow, which can be generated in the separation capillary, notably in hydrodynamically open ITP arrangements. In the case of a polymeric solute, it is convenient to introduce the effective charge per charged monomer (z1). In that case, z1 is obtained by eq 9, considering ci as the injected molar concentration of charged monomer in the polymer sample.
3. MATERIALS AND METHODS 3.1. Chemicals and Samples. Ammediol (2-amino-2-methylpropane-1,3-diol) was purchased from Avocado (Heysham, England). N,N-Dimethylformamide (DMF), methanol (MeOH) and glacial acetic acid (AcOH) were purchased from Carlo Erba (Paris, France). Ammonium hydroxide, sulfuric acid and sodium hydroxide were from VWR (Leuven, Belgium). Poly(diallyldimethylammonium chloride) (PDADMAC) of Mw = 4 × 105 g mol−1 and hydroxypropylcellulose (HPC) of Mw = 105 g mol−1 were purchased from Sigma-Aldrich (Steinheim, Germany). Deionized water was further purified with a Milli-Q system from Millipore (Molsheim, France). Linear poly-Llysine (PLL), hydrochloride salt, of DP 20, 50, and 100 were supplied by Alamanda Polymers (Huntsville, AL, USA). Dendrigrafts poly-Llysine (DGL), trifluoroacetate salts of five generations (G1 − G5) were from Colcom (Montpellier, France). To increase the intergeneration purity, DGL (G2 − G5) were purified by size exclusion chromatography (SEC) using an AKTApurifier 100 (GE Healthcare). The running buffer was ammonium bicarbonate 0.1 M (Sigma-Aldrich, Steinheim, Germany) and the purification was performed using a superose 12-GL 10/300 column (GE Healthcare) at 0.7 mL.min−1. Then the running buffer was removed under vacuum 3 times and DGLs were freeze-dried. This purification procedure converts DGLs (G2 − G5) from trifluoroacetate into bicarbonate salts. 3.2. Determination of Poly-L-lysine Electrophoretic Mobility by Capillary Zone Electrophoresis. Capillary zone electrophoresis (CZE) was carried out on an Agilent 3D-CE instrument (Waldbronn, Germany) equipped with a diode array detector. PDADMAC (cationic polymer) coated capillaries of 35 cm total length (26.5 cm to the UV detector) × 50 μm i.d. were used for electrophoretic mobility determination of all samples in the leading electrolyte used in ITP (i.e., 20 mM AcOH/10 mM NH4OH). Coating was realized using the following rinsing protocol: 1 M NaOH for 30 min, water for 5 min, 0.2% (w/v; i.e., 0.2 g/100 mL) PDADMAC solution in water for 30 min. Between runs, the capillary was flushed with water for 3 min then with the BGE for 5 min, all flushes at 1 bar. Temperature of the 535
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Figure 1. 3D representation (upper part) and simplified topological structures (lower part) of the first three generations of DGL. For the 3D representation (drawn by Chemdraw 3D Ultra using MM2 routine with steric energy minimization): carbon atoms are in gray, nitrogen in blue and oxygen in red. For the simplified structures, each dot represents a Lys residue and the colors allow representing the internal topology of DGL generation by generation. G1 (in red) is a linear poly-L-lysine with a number-average DP of 8 Lys residues. G2 (red + blue) is a comb poly-L-lysine with an average of 48 Lys residues. G3 (red + blue + black) is a branched poly-L-lysine containing an average of 123 residues. b represents the average distance between charges which is well-defined for a G1 in a fully extended conformation (b = 0.35 nm).16
Table 1. Physico-Chemical Characteristics and Effective Charge Number per Lysine Residue z1 or per Entity zeff of the Solutes Studied in This Work cationic impurities (mM)a sample G1 G2 G3 G4 G5 α-PLL20 α-PLL50 α-PLL100
DPn
i
e
8 48e 123e 365e 963e 20g 50g 100g
NH4+ f
