Conformations by Taylor Dispersion Analysis - ACS Publications

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Investigating the Influence of Phosphate Ions on Poly(L‑lysine) Conformations by Taylor Dispersion Analysis Xiaoyun Jin, Laurent Leclercq, Nicolas Sisavath, and Hervé Cottet* Institut des Biomolécules Max Mousseron, IBMM, UMR 5247 CNRS-Université de Montpellier 1, Université de Montpellier 2, Place Eugène Bataillon, CC 1706, 34095 Montpellier Cedex 5, France S Supporting Information *

ABSTRACT: In this work, the influence of the ionic strength and phosphate ions on poly(L-lysine) hydrodynamic radius, conformation and persistence lengths has been studied for molar masses comprised between 3000 and 70 000 g/mol. Mark−Houwink coefficients have been obtained via the determination of poly(L-lysine) hydrodynamic radius using Taylor dispersion analysis. The influence of phosphate ions and ionic strength on the solvent quality (poor, Θ, or good solvent) for poly(L-lysine) have been studied in details. Quantitative data on hydrodynamic radius, persistence length, Mark−Houwink coefficients are provided at pH 7.4, in the range of 10 mM to 1 M ionic strength, and for different phosphate ion concentrations from 0.1 mM to 50 mM under physiological conditions (154 mM ionic strength, pH 7.4). The strong influence of phosphate ions on poly(L-lysine) properties was finally illustrated by studying the interactions (stoichiometry, binding constant, and cooperativity) between poly(L-lysine) of DP 50 and human serum albumin, in the absence and in the presence of phosphate ions at pH 7.4. phobic domains.15 Analysis of these assemblies revealed the presence of large, sheet-like membranes for K20L20, thin fibrils for K40L20 and large vesicular assemblies for K60L20, revealing the importance of the block lengths on the structuration of the copolymer in solution. Lecommandoux’s group also reported on the self-assembly behavior of a short, zwitterionic diblock copolypeptide based on poly(L-glutamatic acid)-b-poly(Llysine).14 This polymer has the interesting characteristic that in aqueous solutions near neutral conditions (5 < pH < 9), both segments are charged and the polypeptide is dispersed as soluble chains. However, if pH < 4 or pH > 10, one of the segments is neutralized and the chains self-assemble into small vesicles. In addition to its influence on the self-assembling properties, the polypeptide size can also dramatically influence the biodistribution of the polymeric materials in the various organs, their circulation in blood, and furthermore, determines polymer degradation kinetics which affects the drug release rate and targeting efficiency.16−19 The polypeptide size is a key parameter that not only depends on its chain length (or its molar mass) but also depends on the physicochemical characteristics of the medium, especially ionic strength and the presence of multivalent ions20 that exist in blood at significant concentrations. Divalent anions (SO42−, HPO42−) and cations (Ca2+, Mg2+) are present in blood at approximatively 0.5 mM for SO42−, 8 mM for HPO42−, 2.5 mM for Ca2+, and 1.5 mM for Mg2+ ions.21 Generally,

1. INTRODUCTION The demand of polypeptides in pharmaceutical or biomedical field is increasing due to their biocompatibility and biodegradability. A significant number of studies on the use of synthetic polypeptides for biomedical applications focused on water-soluble polypeptides, in particular poly(L-lysine)1,2 or poly(L-arginine)2 as polycations and poly(L-aspartic acid)3 or poly(L-glutamic acid)4 as polyanions, as well as on various polypeptide copolymers using adapted synthetic routes.5−11 One way to get drug delivery complexes is to covalently bind the drug of interest to polypeptide side-chain functional groups. In order to improve their suitability for drug delivery, these conjugates can be typically modified by covalent coupling of hydrophobic reagents,3,4 by cell-targeting ligands,10 or by nonionic components8,9 (e.g., poly(ethylene glycol), PEG) often used to improve the plasma lifetime and/or the biocompatibility. The resulting materials are generally highly heterogeneous, both in terms of size and in terms of sequence and composition of the functional units on the chains. The success of polypeptide synthesis requires the ability to control the sequence and composition of amino acid residues along the chain as well as the chain length itself.12,13 In the case of block copolymers, it is important that the polypeptidic bloc size be well-defined so that the materials can self-assemble into precisely defined nanostructures, similar to the assembly found in proteins7−9,11,14,15 For instance, Deming’s group reported on the assembly of small charged diblock amphiphilic copolypeptides (poly(Llysine)-b-poly(L-leucine), KxLy) utilizing the structure directing properties of rodlike α-helical segments only in the hydro© 2014 American Chemical Society

Received: May 21, 2014 Revised: July 2, 2014 Published: July 16, 2014 5320

dx.doi.org/10.1021/ma501058v | Macromolecules 2014, 47, 5320−5327

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exploring the solvent quality according to the phosphate concentration and ionic strength. The influence of phosphate ions on poly(L-lysine) behavior was finally illustrated by studying the interactions between poly(L-lysine) of DP 50 and human serum albumin (HSA) at 154 mM ionic strength and pH 7.4.

divalent ions interact electrostatically with polyelectrolyte of opposite charges, either leading to gelification (intermolecular interactions) or to a decrease of the polymer dimensions (intramolecular interactions).22−26 For example, the addition of Ca2+ not only changed the conformation of partially hydrolyzed polyacrylamides but also completely destroyed the ordered structure of interfacial water molecules.22 The addition of phosphate into poly(L-lysine) solutions induced a decrease in the electrophoretic mobility of the polymer,20,27,28 especially in neutral and basic conditions, due to strong HPO42−/poly(Llysine) electrostatic interactions. Stoichiometry of poly(Llysine)/polyanions complexes depended on the presence of phosphate in the complexation medium.26 The variation of the size (or hydrodynamic radius) with molar mass can be generally obtained from viscosity measurements via the Mark−Houwink coefficients (K and a). A huge number of experimental data have been reported in literature for uncharged synthetic polymers.29−31 In contrast, very few data are available in literature for charged polymers, and especially for polypeptides. This is also due to complicated dynamic processes occurring in dilute polyelectrolyte solutions as a function of ionic strength.32 Poly(L-lysine hydrobromide) formed random coils in 1.0 M sodium bromide at pH 4.5.33 Poly(L-glutamic acid) under its sodium salt showed random coils in 0.3 M sodium phosphate at pH 7.8.34 To our knowledge, no data were reported about the effect of ionic strength and of divalent counterions such as phosphate on the size of polypeptides, probably because well-defined polypeptide standards were not easily available until recently. Controlled αamino acid N-carboxyanhydride (NCA) polymerization at low temperature in the presence of urea enables to synthesize welldefined polypeptides,35,36 some of them being nowadays commercially available. Although many techniques are available for size measurement, viscosimetric measurements which give access to the intrinsic viscosity (reduced viscosity extrapolated at infinite dilution)29 require time-consuming determinations at various polymer concentrations. Dynamic light scattering (DLS) is well suited to the sizing of objects larger than typically 5 nm and is very sensitive to the presence of dusts.37 More recently, Taylor dispersion analysis in narrow capillaries (50 μm i.d.) has becoming an attractive and straightforward sizing technique due to low injection volume (∼nL), absolute determination (without calibration), large size range (from angstrom to submicrometer), and online coupling to capillary electrophoresis.38−40 TDA has been successfully applied to small molecules,41 drugs,42 polymers,38,43−45 nanoparticles,46,47 polymeric drug delivery systems,47 dendrimers,40,48 therapeutic peptides,37 proteins,49,50 and liposomes.51 TDA is particularly suitable for objects smaller than 100 nm, including those below 5 nm, down to angstroms. TDA leads basically to weightaverage hydrodynamic radius for mass sensitive detector, which means that each solute is weighted by its mass proportion in the mixture. For this reason, TDA is not biased by the presence of a tiny amount of aggregates or dusts in the sample. As a consequence, sample filtration that may denaturate the sample is not required in TDA. In the present study, the hydrodynamic radii Rh of lowpolydispersity poly(L-lysines) with molar masses comprised between 3000 and 70 000 g/mol were determined using TDA, at pH 7.4, for different ionic strengths, in presence or in absence of phosphate ions. The contraction of poly(L-lysine) due to interactions with phosphate ions has been studied by

2. THEORETICAL SECTION 2.1. Hydrodynamic Radius and Solvent Quality. For a given polymer, there is a relationship between the hydrodynamic size Rh and the intrinsic viscosity [η] according to Einstein’s law, as described by eq 1: ⎛ 3[η]M ⎞1/3 Rh = ⎜ ⎟ ⎝ 10πNA ⎠

(1)

Here NA is the Avogadro number and M is the molar mass of the polymer. Using the well-known Mark−Houwink−Sakurada (MHS) equation establishes the correlation between the instrinsic viscosity [η] and the molar mass M of the polymer [η] = KM a

(2)

where K and a are constants that depend on the polymer, the solvent quality, and the temperature. Combining eqs 1 and 2 leads to ⎛ 3KM1 + a ⎞1/3 Rh = ⎜ ⎟ ⎝ 10πNA ⎠

(3)

The scaling law in eq 3 can be written as R h = CM α

(4)

where C = ((3K)/(10πNA))1/3 and α = (1 + a)/3. C and α are two constants that are related to the nature of the polymer solute, the solvent quality and temperature. α is known as the Flory exponent. Figure 1 illustrates the solvent quality according to a (or α) values and the corresponding typical

Figure 1. Schematic representation of different solvent qualities and the corresponding polymer conformations and scaling law exponents. a is the MHS exponent. α is the scaling exponent in the Rh ∼ Mα relationship. 5321


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Table 1. Buffer Compositions Studied in This Work and the C, a, K, and a Constants Obtained by TDA for PLKC Samples (DP from 20 to 400) I (mM)

Tris [mM]

[HCl] (mM)

NaCl [mM]

[NaOH] (mM)

[phosphoric acid] (mM)

C (nm)

α

K (mL/g)

a

d (nm)

q (nm)

8.5 50 150 1000 21 62 162 1012 154 154 154 154 154 154 154

8 8 8 8 0 0 0 0 8 8 8 8 8 8 8

6.5 6.7 6.8 6.8 0 0 0 0 6.6 6.0 0 0 0 0 0

2 42 142 992 2 42 142 992 147 147 135 117 93 68 28

0 0 0 0 13.6 14.0 14.2 14.1 0 0 7.0 19.0 36.5 54.0 81.0

0 0 0 0 8 8 8 8 0.1 0.5 8 15 25 35 50

0.018 0.016 0.014 0.014 0.049 0.040 0.027 0.016 0.024 0.025 0.024 0.028 0.043 0.057 0.057

0.568 0.574 0.575 0.567 0.428 0.456 0.510 0.574 0.512 0.514 0.520 0.503 0.443 0.426 0.418

0.036 0.025 0.018 0.018 0.733 0.407 0.125 0.025 0.088 0.093 0.082 0.137 0.498 1.187 1.193

0.705 0.723 0.724 0.701 0.283 0.369 0.529 0.721 0.535 0.542 0.559 0.509 0.330 0.278 0.253

0.83 0.73 0.58 0.55 − − 0.57 0.83 0.50 0.58 0.60 0.58 0.48 0.50 0.43

4.25 3.65 2.85 2.10 − − 2.25 3.30 1.75 1.85 1.90 1.85 1.20 1.30 1.20

polymer conformations. As a general trend, when 0.5 < a < 0.8 (i.e., 0.5 < α < 0.6), the polymer chains exist as flexible random coils. The limit a = 0.8 (i.e., α = 0.6) corresponds to good solvent conditions with excluded volume. When 0.8 < a < 1.0 (i.e., 0.6 < α < 0.66), the polymer chains are inherently stiff29 (e.g., cellulose derivatives, DNA). When 1.0 < a < 2.0 (i.e., 0.66 < α < 1.0), the polymer chains are highly extended (e.g., polyelectrolytes at very low ionic strength).29 When a (or α) is close to 0.5, the polymer chain is under Θ conditions (statistical coil without excluded volume). Under Θ conditions, eq 2 is true for all molar masses but is temperature-dependent.52 In contrast, when a > 0.7 (i.e., α > 0.56), eq 2 depends on the investigated molar mass range but is not temperaturedependent (at least for a variation of temperature of ±10 °C).52 It is worth noting that when dealing with Mark− Houwink coefficients, it is generally better to use Mw than Mn in eqs 2.52 2.2. Persistence Length. Persistence length, q, allows to estimate the stiffness of a polymer chain. For polymer chain having a contour length shorter than the persistence length, the polymer conformation is like a rod, while for longer polymer chains, the polymer conformation can be described statistically by a three-dimensional random walk. The persistence length is related to the intrinsic viscosity via the Fuji−Yamakawa relationship,53,54 which is expressed for wormlike chains as ⎡ Φ∞M1/2 ⎢ [η] = 1− (ML /2q)3/2 ⎢⎣

from the combination of the dispersive velocity profile with the molecular diffusion that redistributes the molecules over the tube cross section.55 The band broadening resulting from Taylor dispersion can be quantified via the temporal variance (ο2) of the elution profile. The determination of temporal variance is usually done by fitting the elution peak by a Gaussian fitting in the case of monodisperse samples or by integration of the peak in the case of polydisperse sample:40,57

∫ ht (t − t0)2 dt σ = ∫ ht dt 2

where ht is the detector response (generally the UV absorbance vs time at a given detection point) and t0 is the average elution time. The molecular diffusion coefficient (D) and Rh values are then calculated by the following equations: D=

Rh =

−1

for L /2q > 2.28

(5) −1

where [η] is expressed in cm ·g , Φ∞ is the theoretical Flory constant for infinitely large molecular weights (Φ∞ = 2.87 × 1023 mol−1), ML is the mass per unit length (ML = M0/h = M/ L, where M0 is the molar mass of the monomer unit, h is the length of the monomer unit), L is the contour length and M is the weight-average molar mass of the polymer. Ci coefficients are those used in ref 53 (see the Supporting Information for numerical values). 2.3. Taylor Dispersion Analysis. Taylor dispersion analysis is issued from pioneering work of Taylor,55 later extended by Aris.56 It is based on the dispersion of a solute plug in a laminar Poiseuille flow.55,56 The peak dispersion results 3

Rc 2t0 24σ 2

(7)

kBT 4σ 2kBT = 6πηD πηRc 2t0

(8)

where Rc is the capillary radius (in m), kB is the Boltzmann constant (1.38 × 10−23 J K−1), T is the absolute temperature (in K) and η is the viscosity of the eluent (in Pa·s). Equation 8 is valid when (i) t0 is much longer than the characteristic diffusion time of the solute in the cross section of the capillary (i.e., t0 ≥ 1.25Rc2/D for a relative error ε on the determination of D lower than 3%58) and (ii) when the axial diffusion is negligible compared to convection (i.e., when the Peclet number Pe = Rc u/D is superior to 40 for ε lower than 3%,46,58,59 with u being the linear mobile phase velocity). When the volume of the injected plug is smaller than 1% of the capillary volume to the detector, corrections on the temporal variance and elution time are negligible. In this case, TDA with single detection points leads to similar results compared to TDA with two detection points.57

⎛ L ⎞−i /2 ⎤ ∑ Ci⎜ ⎟ ⎥⎥ , ⎝ 2q ⎠ ⎦ i=1 4

(6)

3. METHODS AND MATERIALS 3.1. Raw Materials. Poly(L-lysine) under its chloride form of DP = 20, 50, 100, 250, and 400 and of polydispersity index PI = 1.05, 1.04, 1.13, 1.15, and 1.07 (PLKC20, PLKC50, PLKC100, PLKC250 and PLKC400, respectively) were kindly provided from Alamanda Polymers 5322


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(Huntsville, AL). Human Serum Albumin, orthophosphoric acid 85% (H3PO4), Tris 99.9% (CH2OH)3CNH2, poly(diallyldimethylammonium chloride) (PDADMAC, Mw = 4 × 105 g mol−1) and HSA fraction V were purchased from Sigma-Aldrich (Steinheim, Germany). N,N-dimethylformamide (DMF) and sodium chloride (NaCl) were purchased from Carlo Erba (Paris, France). Deionized water was further purified with a Milli-Q system from Millipore (Molsheim, France). 3.2. Taylor Dispersion Analysis Measurements (TDA). Taylor dispersion analysis (TDA) was carried out on a P/ACE MDQ CE system (Beckman, Fullerton, CA). Uncoated fused silica capillaries were purchased from Composite Metal Services (Worcester, UK) with dimensions 40.6 cm total length (30.3 cm to the UV detector) × 50 μm i.d. PDADMAC coated capillaries were used. Coating was realized by the following rinses: 1 M sodium hydroxide (NaOH) for 30 min, water for 15 min, 0.2% PDADMAC solution in water for 30 min and then water for 15 min. Between runs, the capillaries were flushed with water for 3 min, and with the eluent for 5 min. Concentration of PLL samples was 1.67 g/L. All samples were diluted in the eluent (viscosity η = 0.89 × 10−3 Pa·s at 25 °C) and injected hydrodynamically (35 mbar, 4 s). Under these conditions, the ratio of the injected volume to the capillary volume up to detector did not exceed 1%. Rh of all samples was determined in various eluents at pH 7.4: (i) 8 mM Tris and various NaCl concentrations, (ii) 8 mM phosphate ions and various concentrations of NaCl, and (iii) 8 mM Tris and various concentrations of phosphate ions at constant 154 mM ionic strength. Table 1 gathers all the buffer compositions that were studied in this work. Mobilization pressure of 50 mbar was applied with eluent vials at both ends of the capillary. The temperature of the capillary cartridge was set at 25 °C. UV detection was performed at 214 nm. Data were collected using the Beckman System Gold software. t0 was taken at the peak apex of the taylorgrams. σ2 was obtained by integration of the left part of the peak using eq 6 as explained in details elsewhere in the case of polydisperse samples.60 The starting point for the integration of the elution profile corresponds to the elution times for which the response signal equals 4 times the baseline noise standard deviation.60 The peak broadening is directly related to the size of the sample (diffusion coefficient); the broader the peak, the larger the size. The polydispersity of the sample is related to the non-Gaussian shape of the taylorgram: a Gaussian (broad or thin) peak corresponds to a monodisperse sample (single size); a non-Gaussian peak corresponds to a polydisperse sample (multiple sizes). Rh was calculated using eq 8. In the case of polydisperse samples, the integration of the taylorgram leads to a weight-average hydrodynamic radius (whatever the polydispersity of the sample). For each sample studied, the hydrodynamic radius (Rh) was measured three times. The standard deviations never exceeded 3%. 3.3. Preparation of PLKC50/HSA Mixtures. Stock solutions of HSA (1 g/L, i.e., 15 μM) in Tris buffer (10 mM Tris, 8.4 mM HCl, 145.6 mM NaCl, pH 7.4) and in phosphate buffer (8 mM H3PO4, 13.5 mM NaOH, 135 mM NaCl at pH 7.4) were prepared at room temperature. Solutions of PLKC50 at various concentrations were prepared for the calibration curve by dilution in the appropriate buffer. HSA/PLKC50 mixtures for isotherms of adsorption were prepared by mixing the same volume (0.5 mL) of HSA and PLKC50 solutions. HSA concentration before (50/50) mixture was 1 g/L and 1, 0.75, 0.5, 0.375, 0.25, 0.125, 0.0625, and 0.03125 g/L for the PLKC50. 3.4. Frontal Analysis Continuous Capillary Electrophoresis (FACCE). The principle of FACCE for the study of substrate (HSA)/ ligand (PLKC50) interactions is based on the quantification of the free ligand concentration in different equilibrated substrate/ligand mixtures. For that, the capillary is first filled with the background electrolyte (Tris or phosphate buffer). Then, the inlet background electrolyte vial is replaced by the equilibrated substrate/ligand sample mixture. The free ligand is then selectively introduced in the capillary by a continuous application of an electric field (with a copressure in the present study, as described below). FACCE experiments were carried out using a 3D-CE Agilent system (Waldbronn, Germany) equipped with a diode array detector. Bare fused silica capillaries (50 μm i.d. × 8.5 cm (to the detector) × 33.5

cm) were purchased from Composite Metal Services (Worcester, U.K.). Cationic capillary coating was realized by first flushing with NaOH (1 M) for 30 min, then with a 0.2% (w/w) PDADMAC solution in water for 10 min, and finally washed with Tris buffer for 10 min. The conditioning between two successive runs was done according to the following protocol: water for 2 min, 0.2% (w/w) PDADMAC in water for 2 min and then Tris buffer for 2 min. The temperature of the capillary cartridge was set at 25 °C. Detection was performed at 193 nm. Continuous FACCE was performed by applying a normal polarity voltage of 1 kV and a +4 mbar copressure to allow the entrance and quantification of the noncomplexed PLKC50 molecules while avoiding the entrance of HSA and HSA/PLKC50 complexes.61

4. RESULTS AND DISCUSSION It is well-known that the nature of the solvent, the ionic strength, and the temperature may have a strong influence on the polymer (or polyelectrolyte) conformation. Correlation between solvent quality and the polymer conformation are displayed in Figure 1. In this work, the hydrodynamic behavior of poly(L-lysine) has been investigated at pH 7.4 for different ionic strength, in presence or in absence of phosphate ions using Taylor dispersion analysis. Examples of taylorgrams of low-polydispersity PLKC of various degree of polymerization (20, 50, 100, 250, 400) in 8 mM sodium phosphate and 992 mM NaCl at pH 7.4 are shown in Figure 2. Because of the low-polydispersity of

Figure 2. Normalized typical taylorgrams obtained for PLKC. Experimental conditions: PDADMAC coated capillary, 40.6 cm total length (30.3 cm to the UV detector) × 50 μm i.d. Eluent: 8 mM phosphate and 992 mM NaCl at pH = 7.4. Mobilization pressure: 50 mbar. UV detection: 214 nm. Temperature: 25 °C.

the PLKC samples, taylograms are close to Gaussian shape. As expected, the taylorgrams becomes broader for PLKC of larger molar mass. The higher the molar mass, the higher the hydrodynamic radius, the lower the diffusion coefficient, and the higher the peak dispersion is. Rh was determined by peak integration using eq 6−8. Since UV detection is sensitive to the mass concentration of the polymer, the average Rh values determined by TDA are weight-average hydrodynamic radii,39 which is less sensitive to dusts or large size aggregates compared to the harmonic z-average value obtained by DLS.39 Weight-average hydrodynamic radii obtained by TDA are supposed to be representative of the entire polymer sample, where each constituent of the mixture contributes to the 5323


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value. However, this ionic strength effect only affects the C (or K) values and not the scaling exponent α (or a) as displayed in Figure 4 (triangles). Thus, the quality of the solvent (Tris-NaCl

average value proportionally to his mass (or weight) in the mixture. 4.1. Influence of the Ionic Strength in Absence of Phosphate. Hydrodynamic radii of PLKC were determined at pH 7.4 in a 8 mM Tris buffer for different ionic strengths (set by addition of NaCl) from 10 mM to 1 M. Results are plotted in Figure 3A in a double logarithmic scale (log Rh = log Mw) to

Figure 4. Influence of the ionic strength on solvent quality in Tris (▲) and in phosphate (■) buffers, pH 7.4. Ionic strength was adjusted by NaCl (see Table 1 for buffer compositions).

buffer) remains unchanged for all ionic strengths. The dependence of the hydrodynamic radius with ionic strength scales as Rh ∼ I−0.06. The exponent observed is slightly lower (between −0.15 and −0.24) than what was observed for various polyvinylpyridinium of high molar mass (105−106 g/mol).64 However, the authors mentioned the tendency that the slope decreases with decreasing chain length. Persistence lengths of PLKC were determined by curve fitting of the MHK curves using eq 5 by adjusting the parameters d and q. As expected (see numerical values in the four first lines of Table 1), q decreases with the ionic strength from 4.25 nm at 8.5 mM down to 2.10 nm at 1 M in the presence of 8 mM Tris buffer, in good agreement with the values reported in literature for other polyelectrolytes such as polylysine derivatives,65−69 vinylic polyanions54 and charged polysaccharides.70 4.2. Influence of the Ionic Strength in the Presence of Phosphate. TDA experiments were conducted on the same PLKC samples in the presence of 8 mM phosphate ions (instead of Tris) and for different ionic strength (lines 5 to 8 in Table 1). log Rh vs log Mw linear correlations are presented in Figure 3B. Contrary to what was obtained in Tris buffer, the correlation lines are not parallel, revealing a substantial change in the quality of the solvent with the ionic strength. The a value varies from 0.28 at 10 mM ionic strength (relatively poor solvent) up to 0.72 at 1 M ionic strength (almost good solvent), as displayed in Figure 4. The lower solvent quality in the presence of phosphate can be explained by the contraction of the polymer coil due to electrostatic interaction between multivalent phosphate ions and the positively charged polyelectrolyte. This effect of contraction was screened by increasing the ionic strength. Theta condition is obtained at ∼120 mM ionic strength in the presence of 8 mM phosphate. To conclude, phosphate buffer at pH 7.4 is a relatively poor solvent for PLKC, but the quality of solvent can be gradually improved by the addition of salt. 4.3. Influence of Phosphate Concentration in Physiological Conditions. The influence of the phosphate

Figure 3. Dependence of the hydrodynamic radius Rh of PLKC vs the molar mass Mw in 8 mM Tris buffer (A) and 8 mM phosphate buffer (B) at pH 7.4 for different NaCl concentrations: 2 mM (⧫), 42 mM (■), 142 mM (▲), and 992 mM (●). See Table 1 for buffer compositions.

extract the C and α parameters (see eq 4) that are reported in Table 1 (first four lines). It is worth noting that with these parameters, anyone can estimate the size of a polylysine sample at physiological pH, in a range of degree of polymerization between 20 and 400 and for ionic strength in the range of 10 mM to 1 M. Whatever the ionic strength, the a values are close to 0.7 (α close to 0.57). This means that the PLKC are close to good solvent conditions at pH 7.4, in absence of phosphate. The conformation of poly(L-lysine) chains are close to expanded coils in these conditions (physiological pH), in good agreement with previously reported results by Applequist et al.62 and by Brant et al.33 in 1.0 M sodium bromide at pH 4.5. The transition from coil to helices is likely to occur at higher pH (pH > 10.7).62,63 As expected, the PLKC hydrodynamic radius decreases with increasing ionic strength due to screening of electrostatic repulsion. From 10 mM to 1 M ionic strength, Rh value decreases by ∼20−25% of it is initial 5324


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concentration (from 0.1 mM to 50 mM) on PLKC hydrodynamic radius was studied at constant 154 mM ionic strength and pH 7.4. K, a, and α values for the different phosphate concentrations are given in Table 1 (last seven lines). Exact compositions of the buffers are also provided in Table 1. As expected, the higher the phosphate concentration is, the lower the hydrodynamic radius. Figure 5 displays the variation of a

Figure 6. Isotherms of adsorption of PLKC (DP 50) onto HSA in physiological conditions. Experimental conditions: PDADMAC coated capillary 33.5 cm (8.5 cm to detector) × 50 μm i.d. buffer electrolytes: Tris 10 mM + HCl 8.4 mM + NaCl 145.6 mM at pH 7.4 and H3PO4 8 mM + NaOH 13.5 mM + NaCl 135 mM at pH 7.4. Applied voltage: +1 kV with a cohydrodynamic pressure of +4 mbars. Samples are prepared in the buffer electrolyte by mixing 50/50 (v/v) the following solutions. HSA at 1 g/L in corresponding buffer with PLKC at 1, 0.75, 0.5, 0.375, 0.25, 0.125, 0.0625, and 0.03125 g/L. Figure 5. Influence of the phosphate concentration on solvent quality (a exponent, plain squares) and on persistence length (q, open circles) in 8 mM Tris at pH 7.4 and 154 mM ionic strength.

tration at equilibrium. Interestingly, Figure 6 shows that the PLKC/HSA stoichiometry of interaction is 1:1 in Tris buffer (without phosphate) and 2:1 in the presence of phosphate, in physiological conditions (pH 7.4, 154 mM ionic strength). This observation is in good agreement with the contraction of PLKC in the presence of phosphate which may facilitate the access of a second ligand to the substrate. In absence of phosphate, curve fitting of the isotherm using the following equation

exponent (plain squares) and q (open circles) as a function of phosphate ion concentration. When the concentration in phosphate ions increased, keeping 154 mM ionic strength, the solvent quality dramatically changed. Even at very low amounts of phosphate (0.1 mM), a value dropped from 0.72 (without phosphate) to 0.53. The persistence length also drops from 2.9 nm without phosphate to 1.8 nm at 0.1 mM phosphate. The variations of a exponent and q with phosphate concentration follow a decreasing sigmoidal shape. This is reminiscent to the existence of an equilibrium constant describing the interaction between phosphate ions and polylysines. Θ conditions in physiological conditions are obtained for a phosphate concentration of ∼16 mM. The lower limits for a exponent and for q at high phosphate concentration are ∼0.25 and 1.2 nm, respectively. 4.4. Influence of Phosphate Ions on the Interactions between PLKC and Human Serum Albumin. To further study the influence of phosphate ions on PLKC properties, we investigated the interactions between PLKC (DP 50) and human serum albumin (HSA) by frontal analysis continuous capillary electrophoresis (FACCE). Using this methodology recently adapted to the study of interactions between dendrigraft polylysine and HSA,61 the isotherms of adsorption of PLKC onto HSA were obtained in presence (open square) or in absence (open circle) of phosphate, as displayed in Figure 6. The y-axis represents the average number of PLKC bound to the HSA and the x-axis is the free ligand (PLKC) concentration. These isotherms were built step by step by determining the free ligand concentration at equilibrium for different PLKC/HSA ratios (see section 3.3 for the preparation of the PLKC/HSA mixtures). FACCE is used to determine the free PLKC concentration at equilibrium for each PLKC/HSA mixture. Knowing the introduced PLKC concentration, it is then straightforward to determine the bound PLKC concen-

n̅ =

K1[L] 1 + K1[L]

(9) −1

leads to a K1 binding constant of 6.7 × 10 M . In presence of phosphate, strong cooperativity between interaction sites was found as demonstrated by the value of the z exponent (z = 1.6 > 1) using the Hill equation: 5

n̅ =

C1[L]Z 1 + C2[L]Z

(10)

This series of experiments clearly shows the strong impact of phosphate ions, not only on PLKC conformation, but also on physicochemical properties such as binding affinity, stoichiometry and cooperativity.

5. CONCLUSIONS At pH 7.4 and in the absence of phosphate ion, poly(L-lysines) are almost in good solvent conditions whatever the ionic strength. Quantitative data provided in this work allow to estimate the hydrodynamic radius of any poly(L-lysine) having a molar mass between 3000 and 70 000 g/mol, at pH 7.4, and for ionic strength ranging between 10 mM to 1 M. Persistence lengths and Mark−Houwink parameters are also provided and tabulated in various conditions. The addition of phosphate ions at a concentration as low as 0.1 mM considerably changes the solvent quality, approaching poor solvent conditions due to strong electrostatic interactions. Increasing the ionic strength at a constant phosphate concentration tends to screen the effect 5325


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of phosphate ions. In conditions close to physiological (154 mM ionic strength, pH 7.4), Θ conditions are obtained at 16 mM phosphate, while conditions close to poor solvent are obtained at phosphate concentrations higher than 25 mM. Finally, the presence of phosphate ions changes the stoichiometry of interaction between poly(L-lysine) and HSA, as well as the binding constant and the cooperativity of the interaction.

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ASSOCIATED CONTENT

S Supporting Information *

Coefficients Ci used in eq 5. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*(H.C.) E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS H.C. gratefully acknowledges the support from the Institut Universitaire de France (2011−2016). REFERENCES

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