Article pubs.acs.org/Macromolecules
Experimental and Theoretical Studies of Polyanion−Polycation Complexation in Salted Media in the Context of Nonviral Gene Transfection Mahfoud Boustta,† Laurent Leclercq,† Michel Vert,† and Valentina V. Vasilevskaya‡,* †
Max Mousseron Institute of Biomolecules, UMR CNRS 5247, Faculty of Pharmacy, University Montpellier 1, 15 avenue Charles Flahault, BP 14491, 34093 Montpellier Cedex 5, France ‡ Nesmeyanov Institute of Organoelement Compounds RAS, ul. Vavilova 28, Moscow 199991, Russia ABSTRACT: Positively and negatively charged molecules, endothelia, and cells play important roles in biological salted aqueous media. This work aimed at studying artificial polyelectrolyte complexes in terms of formation and stability in the context of the increasing interest for the use of polyelectrolyte systems in drug delivery or as polyelectrolyte complexes or polyplexes for gene transfection. The effect of salt concentration on model polyelectrolyte complexes was studied both experimentally and from a theoretical viewpoint. The critical salt concentration at which phase separation appeared when multifunctional polyanions, namely poly(Llysine citramide) and poly(L-lysine citramide imide) were mixed with poly(L-lysine) showed that salt concentration, degree of polymerization and charge density conditioned the formation and the stability of corresponding polyelectrolyte complexes. Data agreed well with the trends indicated by the theoretical approach and they are discussed in comparison with the case of nonviral transfection using polyplexes. well exposed in reviews.27,28 Emphasized problems are the formation and/or stability of such complexes in the presence of an imposed ionic strength and of positively and negatively charged species present in blood like proteins, cell membranes, etc. To avoid the complexity of blood in terms of chemistry and physical-chemistry, we thought of interest to minimize the difficulties by considering model polyions and media according to a stepwise strategy based on previous observations of the dramatic toxicity of polycations in contact with blood in vitro29 and in vivo as well as after iv injection.30 Recently, some of us found that at the scale of 13 μg/mL poly(L-lysine), PLL, led to limpid media with nanodispersed (apparently soluble) stoichiometric PECs when mixed under physiological ionic strength (0.15 NaCl) with anionic macromolecules of poly(L-lysine citramide), PLCA, and poly(L-lysine citramide imide), PLCAI, two poly(carboxylic acid)s whose backbone is multifunctional and bears one hydrophilic hydroxyl group on each lysyl-citryl repeating unit20 (Figure 1). In contrast, the mixture of poly(L-lysine) with poly(acrylic acid), PAA, whose backbone is hydrophobic, always led to macroscopic powder, i.e., never generated nanodispersed particles under similar conditions as is often observed with monofunctional polyanions.20 The dispersion of PLCA and PLCAI complexes as nanoparticles was assigned to the
1. INTRODUCTION Intermolecular polyelectrolyte complexes (PECs) have attracted considerable attention for a long time with first studies performed in the middle of the 20th century.1−5 PECs formed spontaneously in solution when positively and negatively charged polyions are mixed thanks to strong cooperative electrostatic interactions.1−4 PECs play essential roles in nature where many charged systems, namely proteins, polysaccharides, and various cells, are dispersed in fluids and tissues in the absence of macroscopic precipitation.5 They are involved in many biological phenomena that condition life, some of them being very complex like DNA−protein interactions occurring in cell machineries.5,6 On the other hand and somewhat related, PECs have potentials for various biomedical applications, including surface modification, encapsulation of bioactive substances for delivery, gene transfection, and gene therapy.5−10 A great number of comprehensive experimental studies of PECs have been reported in recent decades.2−7,11−26 It has been shown that the formation and stability of PECs are affected by various factors including the following: strength of involved polyelectrolytes in terms of acidity or basicity, charge density and concentration, proportion of opposite charges, molecular weight of the polyions, pH and ionic strength of the medium, and also order of addition.2−4,11−26 Therefore, when polyelectrolytes or polyelectrolytic systems including the socalled “polyplexes” are introduced in a biological milieu, they may be perturbed and/or they can perturb the charged elements present in this milieu. Related problems have been © 2014 American Chemical Society
Received: February 28, 2014 Revised: May 13, 2014 Published: May 28, 2014 3574
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Figure 1. Structures of the oppositely charged polymers involved in the present work.
eters. Theory and experimental data collected in the particular cases of PLL−PLCA and PLL−PLCAI complexes were in good agreement qualitatively.33 In another experimental approach, PLL was added stepwise to a solution of PLCA and PLCAI.22 It was found that the longer polyanionic macromolecules precipitated first when the positive to negative charge ratio, NPC/NPA (where NPC and NPA reflect the number of positive and negative charges present in the medium, respectively) increased. The shorter macromolecules remained in the solution phase. Therefore, PLL was able to fractionate PLCA and PLCAI in terms of molecular mass at each stage, a feature that suggested difference in binding energy. The different fractions were decomplexed at high salt concentration and formed again by decreasing this salt concentration progressively. Microphase separation and thus recomplexation, occurred at a certain salt concentration referred to as Crecomp, reflected by a sudden appearance of turbidity. The value of Crecomp was smaller than that of n*S and increased with the charge density and the molecular mass of the polyelectrolytes in presence. The present work aimed at better understanding the origin of Crecomp changes. For this, additional experimental investigations were made and confronted to a theoretical approach of complex formation and microphase separation in the case of polyanions bearing hydrophilic functions other than the charged groups. Particular attention was paid to cases where Crecomp in NaCl solution is lower than 0.15 N, the salt concentration corresponding to the ionic strength of blood where polyplexes of DNA, a good example of multifunctional polyanion, are injected for the purpose of gene transfection.
presence of hydrophilic hydroxyl groups along the main chains. The corresponding hydrophilic zones contributed to form a water-friendly corona thanks to interaction with the aqueous surrounding medium. A theory was proposed to explain the difference of behavior between PAA and the hydroxyl bearing PLCA and PLCAI.31 This theory was based on the assumption that nanodispersed PECs had a core−shell structure composed of an inner part where segments of both polyelectrolytes interacted and an external part that consisted exclusively of the most hydrophilic part of macromolecules. Consequently the charged hydrophilic shell prevented the complex from aggregating and precipitating. The formation of a shell was assigned to the energetic gain that occurred when hydrophilic segments were exposed to the surrounding solvent rather than inserted within the hydrophobic core. The factor that acted against the formation of such a layer was Coulomb attraction between the excess of negative and positive groups in the internal and external parts of the PEC, respectively. The balance of these two opposite effects determined the formation and the thickness of the external layer compatible with the surrounding aqueous medium. The theory also suggested that increasing salt concentration causes changes in the structure of nanosized complex particles.32,33 At low salt concentration the particles have defined structure and size. At a critical salt concentration ncrS the particle size increases sharply to a larger dimension. At higher salt concentrations, the interpolymer complex is no longer stable and is fully destroyed at a salt concentration n*S with opposite macroions being independent in solution. ncrS and nS* characteristics depend on the physical characteristics of polyions such as degree of polymerization, degree of ionization and macroion-solvent interaction param3575
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Table 1. Molecular Masses (in g/mol) and Polydispersity of PLCA and PLCAI Macromolecules Engaged in Fraction of Complex for PLL of Different Molecular Massesa PLLBr5
PLLBr2
PLLBr1
fraction
ionic strengthb
Mw
Ip
Mw
Ip
Mw
1
0.159
81200 (103600)c
2.01 (2.43)
96700 (111100)
1.93 (2.35)
2 3 4 5 6 7 8 9 supernatant (S) S1 S2
0.168 0.176 0.184 0.191 0.198 0.205 0.211 0.217 0.217 − −
− − 101800 (128000) 86700 (110800) 73600 (97500) 60800 (84300) 50400 (74400) 47000 (64300) 34200 (58500) 32600 (56700) 21400 (31600) 24500 (36500) 17000 (25500)
62500 50500 40100 35900 28300 23900 18900 16800 15200
(84100) (71300) (59300) (47500) (41100) (37000) (32200) (27700) (17000) − −
1.73 1.70 1.53 1.53 1.45 1.46 1.40 1.41 1.84 − −
(2.09) (1.89) (1.73) (1.65) (1.58) (1.54) (1.45) (1.53) (1.47)
65400 55700 42800 37800 33000 28100 23300 20700 14200 17000 12500
(96600) (79300) (64600) (56700) (46300) (40400) (36600) (34000) (21500) (25000) (18000)
1.75 1.67 1.55 1.46 1.51 1.53 1.42 1.46 1.37 − −
(2.15) (1.94) (1.81) (1.66) (1.63) (1.52) (1.48) (1.48) (1.56)
Ip − − 2.11 1.71 1.66 1.58 1.56 1.50 1.55 1.46 1.50 − −
(2.42) (2.43) (2.59) (2.12) (2.01) (1.97) (1.98) (1.90) (1.80)
a
The changes in ionic strength is due to the generation of NaBr in the medium during successive phase separations. bThe ionic strength includes 0.15 M NaCl + NaBr generated during complexation. cParenthesized are data obtained for PLCAI. whereas the polyanion was eluted. The retained PLL was released from the gel later on using a 2 M NaCl eluant. 2.5. Size Exclusion Chromatography (SEC). SEC experiments were performed using a Pharmacia Biotech LCC-501 chromatograph equipped with a UV−visible detector and an anionic CM-CL6B Sepharose gel column. The mobile phase was 1.6 M NaCl. The detector operated at 214 nm. The elution rate was 0.30 mL/min. Poly(styrenesulfonate) (PSS) standards (from Wheaton) were used for calibration. The PSS-based calibration was correlated to PLCA molecular masses using three PLCA of known molar masses, namely 56000, 34000, and 26000 g/mol, respectively, determined by static light scattering. The log[ M w (PLCA)]/log[ M w (PSS)] correction factor was 1.030. The molecular mass of PLL molecules engaged in the various PEC fractions was determined by SEC using a DEAE Sepharose cationic gel column. The mobile phase was 1.6 M NaCl adjusted to pH = 4.0. The detector operated at 214 nm. The elution rate was 0.30 mL/min. Poly(2-vinylpyridinium) (P2VP) standards (from Fluka) were used for calibration. The P2VP-based calibration was correlated to PLL molecular masses using four PLL whose molecular masses were respectively 73500, 51000, 26300, and 12700 g/mol according to static light scattering. The log[ M w (PLL)]/ log[ M w (P2VP)] correction factor was 1.065. 2.6. Dynamic Light Scattering (DLS). Vertically polarized DLS measurements (λ = 514.5 nm) were performed at 25 °C with a commercial BI-200SM instrument (from Brookhaven Instrument Corporation) equipped with a BI-9000AT correlator. The values of the hydrodynamic radius Rh of species present in the last supernatant was determined using the Stokes−Einstein equation for the three PLLs. The viscosity of polymer solutions was determined using a Rheometer Rheostress RS 100 (from Haake) at 25 °C.
2. MATERIALS AND METHODS 2.1. Materials. Poly(L-lysine) hydrobromide of various molecular masses, namely PLLBr1, DPw = 60, Mw = 12 700 g/mol and I = 1.4; PLLBr2, DPw = 120, Mw = 26 300 g/mol and I = 1.9 and PLLBr5, DPw = 240, Mw = 51 000 g/mol and I = 1.7, were purchased from Sigma. Poly(L-lysine citramide) and poly(L-lysine citramide imide) sodium salts, respectively PLCANa (DPw = 110, Mw = 39 000 g/mol and I = 2.0) and PLCAINa (DPw = 170, Mw = 51 000 g/mol and I = 2.5), were synthesized as previously described.34,35 The polyionic species are rather weak polyelectrolytes that are almost totally ionized at pH = 7.4. Deionized water was obtained using a Milli-RO system from Millipore. Analytical grade NaCl and NaH2PO4 were purchased from Aldrich. Phosphate buffer saline (PBS) was prepared at 0.15 M and pH 7.4. 2.2. Preparation of the PECs. Typically, 33 μL of 0.3 M (in H+) PLLBr1 solution were added stepwise to 1 mL of 0.1 M (in Na+) polyanion solution in PBS placed in a plastic vial at room temperature. The coacervate formed after this first addition (NPC/NPA = 0.11) was collected by centrifugation using a Sigma 112 centrifuge at 6000 rpm for 5 min. The coacervate was washed once with 20 μL PBS. The washing solution was combined to the supernatant phase. The same protocol was repeated for the next additions of 33 μL of the PLLBr1 solution. At the end, nine fractions of PLL-polyanion complexes were obtained. The same protocol was applied to the PLLBr2 and PLLBr5. The last supernatant phase (S) was dialyzed against deionized water using SpectraPor 1000 Da cutoff membranes. The molecular mass of the polycationic molecules engaged within all the precipitated PECs remained unchanged in agreement with the stepwise addition process. In contrast, the molecular mass of the polyanionic molecules involved in the various coacervates decreased progressively (Table 1). The complexation between PLLBr and sodium polyanion produced sodium bromine, thus explaining the increase of ionic strength from one fraction to the other as shown in Table 1. 2.3. Measurement of Crecomp. Typically, an aliquot of a PEC fraction was decomplexed using 1.2 mL of a NaCl solution at a concentration slightly higher than Crecomp evaluated previously. The optical density (OD) at 520 nm was then zero. A 10 μL aliquot of deionized water was added. The total addition of water never exceeded 120 μL, i.e., less than 10% of the initial volume so that dilution could be neglected. Crecomp was taken as the salt concentration that generated 0.03 optical density. 2.4. Gel Filtration. Gel filtration experiments were performed using an anionic CM-CL6B Sepharose gel column in order to separate the polyanion and polycation components of the PEC fractions as previously described. 19 Typically, a solid PEC fraction was decomplexed in 2 M NaCl and prior to injection at the top of the column. On elution with 1 M NaCl, PLL was retained by the gel
3. RESULTS AND DISCUSSION The PECs with various characteristics were prepared according to a fractionation protocol that consisted in stepwise addition of PLLBr to a solution of either PLCANa or PLCAINa in PBS buffer at pH = 7.4 with collection of fractions at each step,22 as recalled in the Materials and Methods. The protocol led to 9 fractions of freeze-dried complex plus one fraction issued from the last supernatant phase because it still contained macromolecules of PLCA and PLL despite of the overall stoichiometry (NPC/NPA = 1). These macromolecules had low molecular masses, as previously observed and discussed.19 The ratio between soluble macromolecules present in the supernatant to those involved in freeze-dried solid 3576
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dialysis and freeze-drying was fractionated again to yield two new fractions of complex (S1 and S2 in Table 1). It is noteworthy that corresponding molecular mass and Crecomp circled data points took place on the curve issued from the stepwise protocol (Figure 2 and 3). Therefore, it was concluded that molecular mass conditioned the binding strength with PLCA and PLCAI complexes. The lower the molecular mass of the involved polyelectrolytes, the lower the Crecomp and thus the lower the stability of the resulting complexes in PBS. To determine the effect of salt on the composition of the separated phase, PEC fractions were prepared in initially pure water and in nonbuffered NaCl 0.15 M solution, respectively. At the first stage, the amount of precipitate was found to be at least twice greater in the salted medium than in salt-free water, depending on the PLL molecular mass. It is worth noting that during the first stage, the initially pure water was progressively salted by minor amounts of sodium bromine produced when mixing PLLBr with the sodium polyanions. The concentration of sodium bromine generated by the complexation was less than 9 mM at each stage and cumulated at 67 mM at the last stage. This small amount of salt was high enough to minimize the difference between the two experiments and explained that for both media and for the three PLLs, 10−15% macromolecules remained in the last supernatant solution that was also found to be free of bromine ions after dialysis against water as observed by capillary electrophoresis analysis (data not shown, see ref 24 for more information). The presence of the centrifugation-resisting macromolecules raised the question of whether they were complexed or separated as independent polyanions and polycations. According to DLS, particles with 300−340 and 240−300 nm average hydrodynamic radius Rh were detected for PLCANa and PLCAINa systems, respectively, when combined with PLLBr1 and PLLBr2. When large amounts of salt was added, there was no more particle detected by DLS, a feature that suggested the destruction of the scattering particles present in the last supernatant. In the case of PBS medium, the presence of hydrodispersed complexes in the last supernatant depended on the size of polycation molecules since the amount of materials present in the last supernatant decreased from PLLBr1 to PLLBr5. To check whether some independent macromolecules could be present beside the dispersed complex, the last supernatant of a PLLBr2/PLCANa system was dialyzed against a PBS solution of similar ionic strength using a 300 kDa cutoff membrane. It was found that ca. 25% of the materials present in the supernatant were able to cross through the membrane, the complex particles being retained. Uncomplexed macromolecules had rather low molar masses, i.e., ca. 6900 g/mol for PLL and 10 400 for PLCA to be compared with 10 000 g/mol for PLL and 14 200 g/mol for PLCA in the supernatant prior to dialysis. 3.2. Theoretical Calculations. The macroscopic phase separation observed when PLL with different molecular masses were mixed with the two polydispersed PLCA and PLCAI polyanions to supply polyelectrolyte complexes of different molecular mass showed different stability characteristics as reflected by Crecomp. In the following, these features were tentatively compared with a theoretical approach of complex formation and stability. Salt-Free System. Let us consider a homogeneous solution of oppositely charged macroions. Let us propose that both macroions are flexible macromolecules and that, in both cases,
fractions was 3%, 15% and 35% for 51 000, 26 000, and 12 700 g/mol PLLs, respectively. Therefore, it was concluded that phase separation depended on the polycation molecular mass. The higher the PLL molecular mass the smaller the amount of macromolecules remaining in the last supernatant was. The plots of Crecomp as a function of PLCA and PLCAI molecular mass are shown for the three PLL polycations in Figures 2 and 3, respectively. It is important to note that the
Figure 2. Changes of Crecomp deduced from the fractions of PLL− PLCA complex obtained for the different PLLs.
Figure 3. Changes of Crecomp deduced from the fractions of PLL− PLCAI complex obtained for the different PLLs.
charge density of PLCANa was modulated along the main chain because of head-to-head and head-to-tail enchainments of citryl and lysyl moieties and because of internal isomery as shown in Figure 1 and discussed in ref 34. Anyhow, it was much smaller in average than that of PLCAINa. In both cases, fraction 1 involved polyanion macromolecules with high molecular masses whereas the ninth one included low molecular mass ones. The fraction issued from the last supernatant contained small polyanionic molecules (Table 1). Polydispersity decreased from one fraction to the other, except for the supernatant one (Table 1). Crecomp values increased with increasing the molecular mass of PLL. To further support this trend, the material collected from the last supernatant after 3577
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fraction φC of another component is directly connected with it using eq 1: φC = fAφ/f C and the spinodal curve of solution can be calculated as37
monomeric units can be characterized by the same spatial size a. Some fractions of the repeating units are charged and carry unity charge which is equal to elementary charge e in case of the polyanion and to -e in case of the polycation. Let us denote NA the degree of polymerization of polyanion A and fA its degree of ionization. Accordingly, let NC and f C be the degree of polymerization and degree of ionization of polycation C. Let us propose that the macroions have different degrees of polymerization and different degrees of ionization, NA ≠ NC and fA ≠ f C respectively. The stoichiometric solution is electroneutral in toto. Therefore, the average volume fraction of anionic φA and cationic φC macroions in solution can be connected by the following relationship: fA ϕA = fCϕ
C
∂ 2F0(φ) ∂φ 2
Fmix =
(3)
The spinodal curve could be considered as a boundary for the field of phase separation within which the homogeneous state is unstable and the solution separates macroscopically into two different phases with two different volume fractions of polymer: diluted supernatant (φS) and concentrated precipitant (φP). Generally speaking, the spinodal curves show the boundary of absolute instability of mixture (inflections of free energy) and allow just estimate roughly the values of polymer volume fraction in coexisting phases. The real coexistence region is limited by binodal curve with equal chemical potentials (minima of free energy) of all species within coexisting phases.37 Since the spinodals just slightly differ from binodals and require less complex numerical calculations, here and below we calculate the spinodals. We did not address here the microstructure of solution as well as the microstructuring of coexisting phases but one can propose that actually macroions can both move independently or form electroneutral interpolymer complexes. Relative fraction of free macroions depends on the characteristic of macroions (degree of polymerization and ionization) and volume fraction of polymer. The composition of coexisting phases of φS and φP for fixed parameters (e.g., degree of polymerization and degree of ionization of macroions) does not depend on the total volume fraction φ of polymer in solution and the increase of the volume fraction of polymer φ here leads to increase of the relative volume of the system occupied by the precipitant and to decrease of the relative volume of the system occupied by diluted precipitant. The results of calculations are shown in Figures 4 and 5. Figure 4 presents the spinodal curves for symmetrical solution
(1)
Each polyion releases a corresponding number of counterions into the solution so that the polyanion and polycation subsystems (polyion and corresponding counterions) are electrostatically neutral. It was shown36 that interpolymer complex formation with further precipitation can be considered as a process of spinodal segregation in solution of two different macromolecules and described successfully on the basis of Flory−Huggins theory.37 We apply here this approach together with the theoretical consideration developed by some of us for the description of phase separation in solutions of polyelectrolyte macromolecules.38−40 To follow this approach let us write the free energy of macroions solution on the assumption of its homogeneity and study its stability upon macrophase separation by calculation of spinodal curve. The total free energy Fo (per unit volume) of an homogeneous solution of such macromolecules in salt-f ree case can be presented as the sum of the free energy of mixing of macroions and the free energy of the electrostatic interaction FD−H relationships below
Fo = Fmix + FD − H
=0
(2)
⎛ϕ ⎞ ⎛ϕ ⎞ ϕ ln⎜ A ⎟ + C ln⎜ C ⎟ NA ⎝ NA ⎠ NC ⎝ NC ⎠ ϕA
+ (1 − ϕA − ϕC) ln(1 − ϕA − ϕC) FD − H = −
2 π u3/2(fA ϕA + fC ϕC)3/2 3
where u = (e2/εkT) is a characteristic dimensionless parameter (T, temperature; ε, dielectric constant of medium; e, elementary charge). In the case of aqueous solution (ε ∼ 80) at room temperature (T ∼ 300 K) and for a size of monomer units a ∼ 1 nm, the parameter u is approximately equal to unity: u ∼ 1. Analysis shows that electrostatic interactions do govern the interpolymer complex formation and that nonCoulombic interactions are negligible in comparison with electrostatic interactions. That is why we neglect here the interaction term in the free energy of mixing to avoid useless complication. It is clear that the condition of electroneutrality given by eq 1 is valid not only for the whole solution but also for both coexisting phases as well as in the case of macroscopic separation. Therefore, the free energy F0 can be rewritten as a function of only one variable defined here as the volume fraction of anionic macromolecules φ ≡ φA (the volume
Figure 4. Spinodal curve in variables N and φ for the salt-free solution of oppositely charged macroions having equal degree of polymerization and degree of ionization.
of oppositely charged macroions having same degree of polymerization NA = NC, the same degree of ionization fA = f C = 1, and the same volume fraction of both macroions φA = φC = φ. Meanwhile, one can see that the lower degree of ionization f the narrower the field of phase separation and the higher the critical degree of polymerization N above which the solution becomes unstable. Small highly charged (f = 1) macroions form complexes and phase separate, whereas for weakly charged (f = 0.25) macroions only much longer 3578
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FS =
f ϕ ⎛ ϕC ⎞ ϕ ⎛ϕ⎞ ln⎜ ⎟ + A ln⎜ ⎟ NA ⎝ NA ⎠ fC NC ⎝ NC ⎠ ⎛ ⎛ ⎛ f ⎞ ⎞ ⎛ f ⎞ ⎞ + ⎜⎜1 − ⎜⎜1 + A ⎟⎟ϕ⎟⎟ ln⎜⎜1 − ⎜⎜1 + A ⎟⎟ϕ⎟⎟ fC ⎠ ⎠ ⎝ fC ⎠ ⎠ ⎝ ⎝ ⎝ 4 2π u 3/2(fA ϕ + ns)3/2 + 2ns ln ns − 3
Accordingly the spinodal of such solution is given by ∂ 2Fs ∂ϕ2
Figure 5. Spinodal curves in variables NC and φA for the solution of macroions with different degree of polymerization NA ≠ NC and the same degree of ionization: fA = f C = 1.
∂ 2Fs ∂ϕ∂ns
macromolecules (N > 300) phase separate. In the case of fixed value of f, the longer the macroions (the higher degree of polymerization N), the lower the concentration φS of polymer in supernatant (left branch of spinodal) and the higher the concentration φP of polymer in precipitate (right branch of spinodal). In asymmetrical case of macroions with different lengths (NA ≠ NC), equal degrees of ionizations (Figure 5) and growth of the degree of polymerization NA and NC of macroions, the field of phase separation broadens and the concentration of macroions in solute decreases. As can be seen in Figure 6, in case of macroions with equal degree of polymerization (NA = NC) and different degrees of
∂ 2Fs ∂ϕ∂ns ∂ 2Fs
(4) 39,40
=0
∂ϕ2
(5)
The results of the calculations are shown in Figures 7−11.
Figure 7. Spinodal curves in variables N and φA for mixtures of oppositely charged macroions with equal degree of ionization and degree of polymerization in the presence of salt at different concentration ns = 10−7 (a), 10−5 (b), 10−3 (c).
As one can see in Figure 7, in the selected particular case (NA = NC and fA = f C) the addition of salt leads to rather significant shift of left branch of spinodal curves to the field of larger volume fraction of polymer φ. It means that, in a salted solution for fixed degree of polymerization N, the phase separation starts at higher concentration of polymer and the solute is more concentrated. The greater the salt concentration, the greater the material in solute phase. The critical degree of polymerization Ncr increases slightly with the salt concentration whereas the polymer concentration in precipitant is almost unchanged. Figures 8 and 9 show the diagrams of states in variables nS and φ. One can see that the addition of salt ns narrows the field of phase separation and above some critical value of the salt concentration ncrs the solution does not separate macroscopically in the whole range of polymer volume fraction φ (remember that in the case under consideration we propose that both macroions have no energetic interactions with solvent). The higher the degree of ionization f of the macroion and the degree of polymerization N, the higher the critical salt concentration ncrs . It is worth noting that ncrs is comparable to the Crecomp parameter defined in the experimental section and accessible experimentally. For the sake of comparison with experimental data, the theoretical dependences of the critical salt concentration on the degree of polymerization of the polyanion NA for fixed values of the degree of polymerization of the polycation NC are shown in
Figure 6. Spinodal curve in variables N and φA for the salt-free solution of macroions having equal degree of polymerization and different degrees of ionization.
ionization ( fA ≠ f C), with growth of the degree of ionization f C, the volume fraction φS of polymer in solute decreases, the volume fraction φP of polymer in precipitant increases, and the field of phase separation becomes wider and phase separation proceeds for shorter macroions. Salt-Containing Systems. The free energy Fs of the described-above macromolecular solution in the presence of a 1−1 salt at concentration ns can be written as the following function of two variables: the volume fraction of polyanion φ and the salt concentration ns 3579
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Figure 11. Dependence of critical salt concentration on degree of polymerization NA at NC = 120, f C = 0.5 and different degree of ionization fA. Figure 8. Spinodal curves in variables ns and φA for mixtures of oppositely charged macroions for NC = 120, NA = 40, f C = 0.5 and different degree of ionization of polyanion fA.
constant to be equal to the average degree of polymerization DPw of PLLBr1. Theoretical findings in Figures 10 and 11 show that under certain conditions including low molecular mass and low charge density, oppositely charged polyelectrolyte complexes may stay separated in solution, not forming polyelectrolytic complexes, the phenomenon being minimized by the presence of salt that generate ionic strength. These features were experimentally found as shown by comparison of data in Figures 3, 4, 10, and 11, despite the fact that data in Figures 3 and 4 reflect the stability of formed complexes whereas Figures 10 and 11 show the dependence of the critical salt concentration of complexes formation. Indeed it was previously shown that the action of NaCl on the formation and the destabilization of formed complexes is hysteresis-dependent.18 In other words, the salt concentration necessary to destabilize a complex is higher than that at which the complex was formed from given polyelectrolytes. In sense of this paper the hysteresis could be easily understood and explained by the fact that the field of phase separation is rather wide: the complex formation (left branch of spinodal curve) starts at lower salt concentrations than the salt concentration calling the precipitant dissolution (right branch of spinodal curve). The experimental data (Figure 3 and 4) and theoretical curve (Figure 10 and 11) have rather good qualitative correspondence in spite of high salt concentration close to the limit of Debye−Huckel theory application. In the case of introduction of polycations into blood where the ionic strength is well-defined, interaction with local charged species (proteins, cell membranes, extracellular matrix), complexation may occur or not depending on the structural and physicochemical characteristics of the charged species. In the case of polyplexes involving polynucleotides, the uncomplexed polycationic chains free in the solution of polyplexes at N:P > 6 was recently found to play a critical role in promoting in vitro gene transfection28,41−43 by penetrating cell membranes; in vivo they are under sink conditions and are very likely to interact with blood elements prior to get to their targets. Polyplexes themselves can also be stable or destabilized depending on the effect of local ionic strength and size, especially when dealing with small siRNA or oligonucleotides. The peculiarities of macroscopic separation of DNA−polycation mixtures with and without low-molecular salt will be studied in forthcoming papers. Another important factor, which we are going to take into consideration, is the
Figure 9. Spinodal curves in variables ns and φA for mixtures of oppositely charged macroions for NC =240, fA = f C = 0.5 and different degree of polymerization NA.
Figures 10 and 11. The parameters of calculations are chosen to be in qualitative correspondence with experimental part. Thus, the degree of polymerization NC of polycation was kept
Figure 10. Dependence of critical salt concentration on degree of polymerization NA at fA = f C = 0.5 and different degree of polymerization NC. 3580
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Macromolecules
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alteration of the effective degree of ionization of macroions due to the counterions condensation.
4. CONCLUSIONS The influence of salt concentration on the behavior of interpolymer complexes composed of oppositely charged macroions having different degree of ionization and degree of polymerization was studied both experimentally and from a theoretical viewpoint. Both experimental and theoretical approaches well agree to support the conclusion that when oppositely charged polyions are mixed, macroscopic phase separation depends on the medium and some complex particles and independent macromolecules can remain dispersed in solution, depending on molar mass and charge density. Experimental data collected in the particular cases of poly(Llysine)−poly(L-lysine citramide) and poly(L-lysine)−poly(Llysine citramide imide) suggest that not any polycation can be used to form polyplexes for gene transfection. Some polycations could form polyplexes stable in water or be decomplexed at physiological ionic strength. Indeed, in vivo, the ionic strength is imposed by the living medium and a DNA− polycation complex, especially long polynucleotides with rather short polycation or long polycation with short polynucleotide may be stable or not in a physiological medium, depending on structural and polyelectrolytic characteristics of the partners. Whether a complex can be destabilized in blood, in endosomes or in cell cytosol because of the physicochemical characteristics of the local medium or because of exchange with sulfate-bearing membranes is important to know if one wants to use polyelectrolyte complexes for the delivery of bioactive species. Destabilization prior to the targeted site may ruin the expectations.
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AUTHOR INFORMATION
Corresponding Author
*(V.V.V.) E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS V.V.V. acknowledges financial support from Program of Chemistry and Material Science Department of Russian Academy of Sciences “Creation and Study of Macromolecules and Macromolecular Structures of New Generations”.
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REFERENCES
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dx.doi.org/10.1021/ma500447k | Macromolecules 2014, 47, 3574−3581
