Interactions between Oppositely Charged Polyelectrolytes by

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Interactions between Oppositely Charged Polyelectrolytes by Isothermal Titration Calorimetry: Effect of Ionic Strength and Charge Density Feriel Meriem Lounis, Joseph Chamieh, Laurent Leclercq, Philippe Gonzalez, Amine Geneste, Benedicte Prelot, and Hervé Cottet J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.6b11907 • Publication Date (Web): 06 Mar 2017 Downloaded from http://pubs.acs.org on March 7, 2017

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The Journal of Physical Chemistry

Interactions between Oppositely Charged Polyelectrolytes by Isothermal Titration Calorimetry: Effect of Ionic Strength and Charge Density Feriel Meriem Lounis,1 Joseph Chamieh,1 Laurent Leclercq,1 Philippe Gonzalez,1 Amine Geneste,2 Benedicte Prelot,2 Hervé Cottet1* 1

Institut des Biomolécules Max Mousseron (IBMM, UMR 5247 CNRS, Université de Montpellier,

Ecole Nationale Supérieure de Chimie de Montpellier), Place Eugène Bataillon, CC 1706, 34095 Montpellier Cedex 5, France 2

Institut Charles Gerhardt de Montpellier, UMR 5253 CNRS-UM-ENSCM, Université de Montpellier,

CC1502, Place Eugène Bataillon, 34095 Montpellier, France *

Corresponding

author:

Tel:

+33

4

67143427,

Fax:

mail :[email protected]

1 ACS Paragon Plus Environment

+33

4

67631046.

E-


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Abstract In this study, binding of linear poly(L-lysine) to a series of acrylamide and 2-acrylamido-2methyl-1-propanesulfonate copolymers was examined by isothermal titration calorimetry (ITC). Binding constant and stoichiometry were systematically determined at different ionic strengths and for different polyanion charge densities varying between 15% and 100%. The range of investigated ionic strengths was carefully adjusted according to the polyanion charge densities to get measurable binding constants (i.e. formation binding constant typically comprised between 104 and 106 M-1) by isothermal titration calorimetry (ITC). The number of released counter-ions during the polyelectrolyte complex formation was determined from the log-log dependence of the binding constant according to the ionic strength, and was compared to the total number of condensed counter-ions estimated from the Manning theory. Experimental results obtained by ITC are in very good agreement with those previously obtained by frontal analysis continuous capillary electrophoresis (FACCE) and can be used to model and predict the binding parameters at any ionic strength or any polyanion charge density. Thermodynamic parameters of the complexation between the oppositely charged polyelectrolytes confirm that the complex formation was entropically driven together with a favorable (but minor) enthalpic contribution. For the first time, specificities, advantages / disadvantages of ITC and FACCE techniques for studying polyelectrolyte complexations are compared and discussed, using the same experimental conditions.


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1.

Introduction

Polyelectrolyte complexes (PEC) can form when oppositely charged polyelectrolytes (PE) are mixed in aqueous solutions1,2. Many industrial processes involve PEC formation such as wastewater treatment3,4, papermaking5,6, food industry7,8, microencapsulation9 and protein separation10,11. PEC are also involved in many biological and biotechnological applications such as drug delivery12–14, gene therapy15,16, enzyme immobilisation17 or DNA-ligand interactions18. Over the past several years, various experimental methods have been used to characterize the interactions between oppositely charged polyelectrolytes. Most of them (such as dynamic and static light scattering, optical microscopy, electron microscopy, turbidimetry and rheology) offer information on morphological, structural, and optical properties of the formed PEC19. However, there are only few experimental techniques that allow determining the thermodynamic binding parameters (binding constant, stoichiometry of interactions) between oppositely charged polyelectrolytes. Fluorescence spectroscopy has been widely used by Lohman et al.20–24to determine the binding constant Kobs between DNA (D) and oligopeptides (L) at different ionic strengths. A double logarithmic dependence was generally observed between the binding constant and the ionic strength following equation (1): log K obs = log K 0 − zϕ log  M + 

(1)

where Kobs and K0 are the equilibrium constants associated to the L+D ↔ L-D and L+D ↔ LD + zφ (M+) equilibriums, respectively, M+ is the DNA cationic counter-ion, z is the ligand (oligopeptide) nominal charge number and φ the fraction of M+ counter-ions associated to the DNA chain (PE). This double logarithmic dependence was attributed to a favorable entropic change due to the release of counter-ions upon complex formation. In equation (1), -zφ represents the number of cations initially condensed onto one DNA chain that are released in the medium after PEC formation. 3 ACS Paragon Plus Environment


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Frontal analysis continuous capillary electrophoresis (FACCE) is a separation technique that was successfully applied to study interactions between (macro)molecules. In FACCE, free ligands at equilibrium in substrate-ligand mixture are continuously introduced in the capillary by electrophoresis. Free ligands are detected in the capillary as a frontal band which can be quantified, yielding their concentration without perturbing the binding equilibrium25. It is thus possible to plot the isotherm of adsorption which can be fitted with an adequate model, giving the binding constant and the stoichiometry. FACCE was used to study interactions between polymers and proteins26–37 or between oppositely charged compounds38–40 including interactions between oppositely charged ligands and bacteria41. Isothermal titration calorimetry (ITC) probes the interaction between two species by titrating one binding partner with another one while directly measuring the heat involved by the reaction in the calorimetric cell42. ITC is a powerful technique for analyzing interactions between macromolecules in solution because it gives a complete thermodynamic profile of the binding process. Interactions between biomaterials43, synthetic polymers and biopolymers44–47, biomacromolecules and vesicles48, and also polymers and surfactant49–51 have been extensively characterized by ITC. The interactions between a series of oppositely charged polypeptides were investigated by Tirrell et al.

52,53

by ITC. Polypeptide complex

coacervation was described as a sequence of two distinct binding steps. The first step describes the formation of soluble complexes (ion pairing) between oppositely charged polypeptides, which in turn aggregate in the second step into insoluble interpolymer complexes (coacervation). Similar interpretation was proposed by Vitorazi et al. for the complexation of poly(diallyldimethylammonium chloride) (PDADMAC) and poly(sodium acrylate)54. In addition to this “two-steps” model, various models have been developed and used to analyze ITC data of polyelectrolyte complexation depending on the studied polyelectrolyte system53,55–58. In some cases, it was reported that the thermodynamic analysis


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of ITC data was not possible due to kinetically frozen structures resulting in out of equilibrium state, as described for the interactions between PDADMAC and potassium poly(vinyl sulfate) (strong polyelectrolytes), between polyvinylamine (PVAm) and carboxymethyl cellulose (weak polyelectrolytes)59, between sodium hexametaphosphate and linear poly(allylamine hydrochloride)60, or between PDADMAC and poly(sodium acrylate)54. Such experimental difficulties are however often encountered in the absence or at very low ionic strength, where the binding constant is expected to be very high61. From a fundamental perspective, but also for developing applications, there is an interest in understanding the interactions between PE via the modelling and the prediction of the thermodynamic binding parameters. However, so far, there are a limited number of works with systematic determination of binding parameters describing the PEC formation according to the ionic strength and the charge density of the PE partners. However, theoretical approaches, including Voorn-Overbeek theory or self-consistent field theory coupled to liquid state, have been recently developed for the study of oppositely charged polyelectrolytes62,63. The present study aims at determining the ionic strength dependence of binding parameters (association constant and stoichiometry) between oppositely charged PE by ITC for variously charged polyanions (PA). In this work, statistical copolymers of acrylamide and 2acrylamido-2-methyl-1-propanesulfonate PAMAMPS, considered as the substrate, are titrated by linear polylysine (PLL), considered as the ligand. ITC results presented in this work are compared to previously published results obtained by FACCE for the same PE system64. Both advantages / disadvantages and specificities of ITC and FACCE techniques are discussed in details. 2.

Theoretical section

In a typical ITC experiment, a solution of a substrate (S) is titrated by a ligand (L). The change in heat accompanying the interaction between the substrate and the ligand is directly 5 ACS Paragon Plus Environment


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measured providing a complete thermodynamic characterization of this interaction, allowing the measurement of the binding constant, the stoichiometry, as well as the changes in enthalpy and entropy accompanying the process. In order to extract correctly the thermodynamic information from experimental measurements, a careful data processing from the raw ITC thermograms should be performed and an appropriate theoretical models should be used to fit the data. 2.1.

Analysis of the ITC data for substrate-ligand interaction: the case of n identical independent sites

Here is presented the model of n independent sites in the case of ITC studies. This model assumes that the substrate (S) carries n independent interaction sites (-s) of similar energy. The interaction between one site (-s) on the substrate and the ligand (L) is described by the equilibrium (2):

 →L−s − s + L ← 

(2)

The binding site constant k related to this equilibrium is defined by equation (3):

k=

θ (1 − θ ) [ L ]

(3)

where θ is the fraction of sites occupied by the ligand and [L] the concentration of free ligand. The mass conservation equation leads to equation (4):

[ L]tot = [ L] + nθ [ S ]tot

(4)

n is the stoichiometry of interaction (total number of independent sites on the substrate), [L]tot and [S]tot are the total concentrations in ligand and substrate, respectively. The molar ratio of total ligand to total substrate r is defined as follows: r=

[ L]tot [ L] 1 θ = + nθ = × + nθ [ S ]tot [ S ]tot k[ S ]tot (1 − θ )

(5)


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From equation (5), θ can be determined by solving the second order equation (6): 

r n

θ 2 − θ 1 + + 

1  r + =0 kn[ S ]tot  n

(6)

2    1 r 1 r 1  4r  θ = 1+ + ± 1 + +  − 2  n kn[ S ]tot n kn[ S ]tot  n    

(7)

The total heat content Q of the solution in the sample cell of volume V0 at fractional saturation θ is: Q = V0 ∆H [ S ]tot nθ

(8)

where ∆H is the enthalpy of binding per mole of bound ligand. Combining equations (7) and (8) yields the following expression of the total heat content: 2    r V0 ∆H [ S ]tot n  r 1 1  4r  Q= 1+ + − 1 + +  −  n kn[ S ]tot 2 n   n kn[ S ]tot   

(9)

In the ITC experiments, ∆Q measures the differential change in heat from the complexation between i-1 and i injection. The parameter ∆Q is defined by equation (10) taking into account the displaced volume effects:

∆Qi = Qi − Qi −1 +

∆Vi  Qi + Qi −1   V0  2 

(10)

wheredVi is the injection volume at injection i. The change in heat per mole of injected ligand ∆Q’ from the complexation between i-1 and i injection is calculated by equation (11):



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∆Qi ' =

∆Qi dVi [ L ]0

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(11)

where [L]0 is the initial concentration in ligand before titration. Fitting experimental values of ∆Qi’ with equation (11) gives experimental values for n, k, ∆H.

2.2.

Analysis of the ITC data for interaction between oppositely charged polyelectrolytes: the case of n identical independent sites

In this study, we assume that the substrate is a PAMAMPS polyanionic chain with a degree of polymerization DP-and with a chemical charge density f, defined as the molar ratio in charged monomers (AMPS) to total monomers. For a given chemical charge density f, the PAMAMPS chain carries n identical sites (-s). Each site is able to bind with one ligand (L) and is defined as a fragment of the PAMAMPS chain. The ligand (L) is a complete PLL chain having a degree of polymerization DP+ corresponding to the total number of lysine residues in the chain. At the pH of the study, all lysine residues are fully protonated. The intrinsic equilibrium associated to one binding site and the related equilibrium constant k are given by equations (12) and (13): k  → PLL − s − s + PLL ← 

k=

(12)

[ PLL − s ] θ = [− s][ PLL] (1 − θ ) [ PLL ]

(13)

where [PLL] and [PLL-s] are the free and complexed PLL concentrations at equilibrium respectively, [-s] is the concentration of free sites and θ is the fraction of sites occupied by PLL. The total number of AMPS monomers within a PAMAMPS chain DPAMPS is given by: DPAMPS = DP − × f

(14)


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According to the Manning condensation theory65,66, the number of Na+ (respectively, Cl-) counter-ions initially condensed onto one PAMAMPS (respectively, one PLL) chain, are given by equations (15) (respectively, equation (16)):

N Na+ = θ − × DPAMPS

(15)

N Cl − = θ + × DP +

(16)

where θ-and θ+ are the fractions of condensed charged monomers on PAMAMPS and PLL chains respectively. For PLL, θ+is0.5 as predicted by the Manning theory and verified experimentally by Ibrahim et al.67 for chains with DP+ ≥ 50.For PAMAMPS chains θ- = 0 for f ≤ 35%,and θ − = 1 −

0.35 68 for f > 35%. According to equation (9), the total heat content in f

this case can be expressed as follows: 2   r  4r  V0 ∆H [ PAMAMPS ]tot n  r 1 1 Q= 1+ + − 1 + +  −  n kn[ PAMAMPS ]tot 2 n kn[ PAMAMPS ]tot  n     (17)

where r is the molar ratio of total ligand to total substrate defined as =

[]

[ ]

and

[PAMAMPS]tot and [PLL]tot are the total concentrations of PAMAMPS substrate and PLL ligand, respectively. Thus, according to equations (10) and (11), the change in heat per mole of injected PLL ligand from the complexation between i-1 and i injection is calculated by equation (18): ∆Qi ' =

∆Qi dVi [ PLL ]0

(18)

[PLL]0 is the initial concentration of the ligand PLL. Fitting equation (18) with experimental values of ∆Qi’ gives best-fit values for n, k, ∆H. The change in free energy ∆G is calculated by equation (19) while the change in entropy -T∆S of the interaction is calculated according to equation (20).



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∆G = − nRT ln k

(19)

−T ∆ S = ∆G − ∆ H

(20)

where R is the constant of ideal gases and T is the cell temperature. Attention should be drawn to the fact that the change in free energy expressed in eq. (19), corresponds to the binding of n PLL chains (ligands) to the n sites of one PAMAMPS chain expressed as: βn  → PAMAMPS − PLLn PAMAMPS + nPLL ← 

(21)

where is the global constant of the equilibrium (21). It is important to notice that in the case of identical sites the relation between the binding site constant k and the global constant is:

βn = k n

(22)

Taking into account the release of counter-ions, equilibrium (21) becomes:

PAMAMPS N

Na+

(

)

(

)

βn  → PAMAMPS − PLLn + χ + N + Cl − + χ − N − Na + + nPLLN − ←  Na Cl Cl

(23)

where is the global constant of the equilibrium (23) and χ+ and χ-are the fractions of the counter-ions Na+ and Cl- effectively released after the association of PAMAMPS and PLL chains. Using the mass action law, is related to according to:

β n0 = β n × Cl − 

χ −N

Cl −

×  Na + 

χ+N

Na +

(24)

which can be rewritten as:

(

) (

log β n = log β n0 − χ + N Na+ + χ − NCl − log  Na + , Cl − 

)

(25)

where [Na+, Cl-]=[Na+]=[Cl-]. In this work, [Na+, Cl-] can be assimilated to the ionic strength due to the high concentration in NaCl used in the experiments. According to equation (25), a linear relationship exists between the logarithm of the global equilibrium constant and the logarithm of the ionic strength. A direct determination of the number of effectively released


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counter-ions during the formation of the PAMAMPS − PLLn complex can be obtained from the slope of this linear dependence. This experimental determination of the number of released counter-ions can be compared to the total number of initially condensed counter-ions Ncounter-ions of the individual chains constituting the PAMAMPS − PLLn complex before the association. Ncounter-ions can be estimated from the Manning theory using equation (26): N counter −ions = N Na + + N Cl − = θ − DPAMPS + n × θ + × DP +

(26)

It is worth noting that the estimation of Ncounter-ions within the framework of the Manning condensation theory presents some limitations. It has been demonstrated using hybrid MonteCarlo/molecular dynamics simulations that an increase of the ionic strength leads to a decrease of the fraction of condensed counter-ions69. On the contrary, Muthukumar70 predicted an increase of the condensed counter-ion fraction with increasing ionic strength. Because of the complexity of the counter-ions condensation phenomenon, in this work, the number of condensed counter-ions has been assessed using the Manning theory.

3. 3.1.

Experimental part Chemicals

Random

copolymers

of

acrylamide

and

2-acrylamido-2-methyl-1-propanesulfonate

(PAMAMPS), with different chemical charge densities f of 15%, 30%, 55%, 70%, and 100% were synthesized by free radical copolymerization and characterized as described in a previous work71. PAMAMPS were characterized by SEC-MALS (molar mass distribution) and

capillary

zone

electrophoresis

(charge

density

distribution)71.

Poly(L-Lysine

hydrochloride) (PLL) with a degree of polymerization DP+= 50 (Mw = 8200 g/mol and polydispersity index PDI = 1.04) was supplied by Alamanda Polymers (Huntsville, USA). Hydrochloric acid 37% and sodium chloride were purchased from VWR (Leuven, Belgium). Tris hydroxymethyl amino methane (CH2OH)3CNH2 99.9% was purchased from Merck 11 ACS Paragon Plus Environment


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(Darmstadt, Germany). Deionized water was further purified using a Milli-Q system (Millipore, Molsheim, France). All chemicals were used without any further purification.

3.2.

Isothermal Titration Calorimetry

Isothermal titration calorimetry (ITC) was performed using a differential TAM III micro calorimeter (TA instrument, Paris, France) at 25°C. Before titration, polyelectrolyte solutions were prepared by dissolving PLL and PAMAMPS in the same Tris-HCl-NaCl buffer pH 7.4 (12mM Tris, 10mM HCl, and the appropriate amount of NaCl) at room temperature. The ionic strength of the buffer was controlled by the amount of added NaCl. The 1ml glass cell was filled with 800 µL of PAMAMPS solutions. Pulse injections of an appropriate PLL stock solution were performed making use of a computer-controlled microsyringe injection device. The homogeneity of the mixture was maintained by means of an agitation system equipped with a Gold paddle stirrer (90 rpm). The initial concentrations of PLL and PAMAMPS solutions were varied according to the charge density (see Table S1 for the values of the initial concentrations of PLL and PAMAMPS solutions). The operational parameters were kept the same for all calorimetry experiments, namely: 25 injections of 10 µL during 10 s, and time of equilibration between two successive injections equal to 35 min, i.e. duration necessary to reach thermodynamic equilibrium, when no more energy was released or absorbed in the reaction cell. Thermograms were collected using TAM Assistant software.

4.

Results and Discussions

A representative ITC experiment corresponding to the interaction between PAMAMPS 100% and PLL in a Tris-HCl-NaCl buffer at pH 7.4 (12mM Tris, 10mM HCl, 1390 mM NaCl) is shown in Figure 1. The thermogram (raw ITC data) is shown in Figure 1A, where the peaks correspond to an exothermic heat effect. The peak intensity diminished when increasing injected PLL. The small peaks of similar constant intensity for the five to seven last injections 12 ACS Paragon Plus Environment

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correspond to the dilution of PLL in the Tris-HCl-NaCl buffer in the final experimental conditions. This dilution heat effect constant area was subtracted from the raw data to obtain the change in heat corresponding only to interactions between PLL and PAMAMPS. The differential heat effect between two successive injections ∆Qi was determined from the peak area. The change in heat per mole of titrant (PLL) ∆Qi’ was calculated according to equation (18) and plotted as a function of the molar ratio r to get the Wiseman diagram (Figure 1B). The experimental data of the Wiseman plot were fitted by non-linear least-square routine on Microsoft Excel using equations (17-18). Wiseman curve fitting yielded the thermodynamic parameters of the interactions within the framework of n identical sites of equal energy: the binding site constant k, the stoichiometry n, the enthalpy change ∆H, and the entropy change T∆S. All Wiseman diagrams and corresponding curve fittings are provided in supporting

information (Figures S1 to S5). It is worth noting that all the Wiseman diagrams had a sigmoidal shape and could be fitted with the simple model of n independent sites of equal energy. This is different from the results obtained by Tirrell et al.53 for the interactions between oppositely charged polypeptides where they observed a two-steps process in the complexation. It could be surprising that the model of n independent sites of equal energy leads to good fitting of experimental data. However, because this simple model was able to fit the experimental data, we did not try more complex interaction models incorporating cooperative effects. Actually, on a pure theoretical basis, the binding sites may present a certain heterogeneity due to copolymerization statistics. However, the number of AMPS monomers per interacting site typically varies between 33 at f = 15% and 50 at f= 100% (e.g. for PLL DP+= 5064). The relatively high number of AMPS monomers per site tends to average the

heterogeneity on each interacting site.



0

B

-10

∆ Q ' (kJ/mol)

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-20 -30 -40 -50 -60 0

50

100

150

200

r (PLL/PAMAMPS)

Figure 1. Raw ITC thermogram (A) and the corresponding Wiseman diagram (B) for the interaction between PLL and PAMPS at 1400 mM ionic strength. Experimental conditions: titration of PLL solution (17 g/L) into PAMPS solution (3 g/L) in 12 mM Tris, 10 mM HCl and 1390 mM NaCl at pH 7.4 and 25 °C. 25 injections of 10 µL each. The thermodynamic binding parameters obtained from curve fitting (red line) of Wiseman plot using equations (17-18) were: k = (1.95± 0.51) × 105 M-1; n = 65± 1 (PLL/PAMAMPS) and ∆H = -52± 2 kJ/mol. It is well known that high ionic strength inhibits the formation of PEC due to the screening of electrostatic interactions between oppositely charged polyelectrolytes and as predicted by the mass action law in equation (23). Previous investigations allowed us to determine the ionic strength of recomplexation Irecomp71 that corresponds to the salt concentration at which PAMAMPS / PLL PEC previously destabilized at high ionic strength, re-formed when water was added. Irecomp was determined by turbidity measurements and numerical values are: 1730, 1430, 1237, 692, 343 mM for PAMAMPS 100%, 70%, 55%, 30% and 15%, respectively71. In this work, binding parameters (stoichiometry and binding constant) between oppositely charged PAMAMPS / PLL were systematically determined by ITC at different ionic strengths and for PAMAMPS of different charge densities f varying between 15% and 100%. For each f value, four different ionic strengths were investigated to get the ionic strength dependence of the binding parameters (k and n). To avoid unmeasurable (too high) binding constants, the 14 ACS Paragon Plus Environment

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investigated range of ionic strength was adapted for each PA charge density f to ionic strengths between 45% and 80% of Irecomp value (see Table S1 in the Supporting Information for the values of the investigated ionic strengths which are of course very different depending on the PA charge density). 4.1.

Influence of the ionic strength on the stoichiometry

The interaction stoichiometry n obtained by ITC (this work) and by FACCE64 methods for different ionic strengths and different charge densities fare represented in Figure 2A, and in terms of lysine residues per AMPS monomer ratios (/ , Figure 2B). It is worth noting that this stoichiometry corresponds to the number of PLL chain that can interact at saturation with one PAMAMPS substrate (i.e. in the presence of a large excess of PLL). Figure 2A shows that chain stoichiometry increases with PAMAMPS charge density (at least up to f=70% for the FACCE method), due to a higher number of negative charges per PAMAMPS chain to be compensated by PLL chains in the PEC. On the other hand, the stoichiometry appears almost independent of the ionic strength. Expressed in terms of charge ratio

/ (Figure 2B), stoichiometry is close to unity for PAMAMPS 100% and increases up to ~1.5 for the PAMAMPS 15%. These stoichiometries obtained by ITC and FACCE are in perfect agreement with the predicting rule recently enounced for PEC stoichiometry obtained by 1H-NMR for the same PE system and verified in the literature for many other PE systems71. This predicting rule can be enounced as: if the polyelectrolyte of the highest charge density is initially introduced in excess, the PECs formed are non-stoichiometric and have an apparent charge of the same sign as the polyelectrolyte of the highest charge density. Conversely, if the polyelectrolyte of the highest charge density is initially introduced in default, the PECs are stoichiometric in charges. As for the PLL/PAMAMPS system, PAMAMPS 100% has a higher charge density than PLL. Therefore, the corresponding PLL/PAMAMPS 100% PEC, in the presence of a default of PAMAMPS 100%, is expected to 15 ACS Paragon Plus Environment


be stoichiometric in charges (/ = 1). In the case of PAMAMPS 15%, which has a weaker charge density than PLL, the PEC obtained in excess of PLL is expected to be positively charged (/ > 1) in good agreement with the experimental data. Comparing ITC and FACCE stoichiometries, it was observed that the charge stoichiometry/ obtained by FACCE was always higher than the one obtained by ITC(Figure 2B). Actually, the two methods do not measure exactly the same parameter. ITC method measures the change in heat involved following the formation of ion pairs between lysine residues and AMPS monomers. Therefore, ITC stoichiometry should basically counts the number of lysine residues that do effectively interact with AMPS monomers. In the case of FACCE method, it quantifies the free PLL chains at equilibrium in the mixture. It means that any lysine monomer on a bound PLL chain is counted as an interacting monomer, even if it is not effectively involved in an ion pair with an oppositely charged monomers (AMPS). This can explain why FACCE lead to higher stoichiometry than ITC. Within the model where the ligand is an entire PLL chain, FACCE should give access to the ‘real’ or effective stoichiometry n, while ITC should slightly underestimate n values.

100 80 60

3.0

A

B

f ITC FACCE 100% 70% 55% 30% 15%

2.5

f ITC FACCE 100% 70% 55% 30% 15%

2.0

n Lys/AMPS

120

n

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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40

1.5 1.0 0.5

20 0 0.0

0.5

1.0

1.5

0.0 0.0

0.5

1.0

1.5

I (M)

I (M)

Figure 2. Variation of the interaction stoichiometry n expressed in PLL/PAMAMPS chains (A) or in charge ratio (/ ) (B) according to the ionic strength and for different


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PAMAMPS charge densities. All experimental data were obtained by ITC in the same conditions as those described in Figure 1, and by FACCE64. 4.2.

Influence of the ionic strength on binding constants

The variations of the binding site constants k with the ionic strength are represented in Figure 3A.Within the chosen ionic strength range (45%-80% of Irecomp), binding site constants k between 2.47±0.42×104 and 1.42±0.80×106 M-1 were determined. This adjusted range of ionic strength provided measurable binding constant and led to sigmoidal shape of Wiseman diagrams. When the ionic strength was increased above 80% of Irecomp, the interactions between oppositely charged polyelectrolytes was too weak leading to unexploitable thermograms / Wiseman diagrams. On the other hand, at ionic strength below 45% of Irecomp, the interaction between the polyelectrolytes was too strong yielding to Wiseman diagrams with abrupt step-like jump corresponding to binding site constant that was too high to be correctly measured in our ITC experimental conditions. Figure 3A shows that the logarithm of the binding site constant (log k) decreased linearly with the logarithm of the ionic strength (log I). The slope of these lines (-p) varied between -4.74 and -7.78 depending on PAMAMPS chemical charge density f (average value of -6.50 ± 1.18 (± one SD)). It should be noted that the slope –p corresponds to the exponent in the scaling law in the k ~I

–p

dependence. It also represents the number of released counter-ions

accompanying the binding of one PLL chain on one interaction site –s of the PAMAMPS chain. Similarly to what was observed by FACCE64, at a given ionic strength, stronger binding site constants k were obtained for higher f values. This is due to the increasing number of AMPS monomers per interaction site –s with increasing f values64.



10

600

A

f ITC FACCE 100% 70% 55% 30% 15%

6

10

5

500

f ITC FACCE 100% 70% 55% 30% 15%

B

400

nlogk

7

k (M -1)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 18 of 36

10

300 200 100

4

10

0 3

10

-100

0.1

1

10

0.1

I (M)

Figure 3.

1

10

I (M)

Variation of the binding site constant k with the ionic strength in double

logarithmic scale for the PLL / PAMAMPS interactions (A) and variation of the logarithm of

βn with the logarithm of the ionic strength (B) for different PAMAMPS charge densities. All experimental data were obtained by ITC in conditions similar to those described in Figure 1 (more details in the experimental section) or by FACCE64. See Table1 for the numerical

−

values.

The double logarithmic linear dependence between the global binding constant βn (log βn = n ×log k as suggested by equation 22) and the ionic strength is displayed in Figure 3B. Such graphical representation is very useful to predict the global binding constant for any chemical charge densities and at any required ionic strength. A bundle of lines converging to a common point at about log I = 0.8 is observed. The slope of the lines increases with increasing the chemical charge density up to f =70%. On the whole, the uncertainty on the slope, and therefore on the determination of the number of released counter-ions, increases with f due to steeper decrease. However, the experimental uncertainties on the slopes have been determined from the least squared linear correlation as reported in Table 1. For instance, it should be noticed that the slopes for PAMAMPS 70% (ITC: 610 ± 149; FACCE: 714 ± 205) and for PAMAMPS 100% (ITC: 565 ± 172; FACCE: 876 ± 388) are similar within experimental


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errors. At the intersection point, the ionic strength is higher than Irecomp and all the PEC are dissociated. Therefore, this intersection point does not seem to have a physical meaning. Nevertheless, data points from ITC and FACCE are consistent giving more credits to the results and a better accuracy on the curve fitting by increasing the number of experimental points. On a physico-chemical point of view, the slopes −

! !

of the lines displayed in Figure 3B

are a direct determination of the number of counter-ions effectively released (

χ + N + χ − N ) after the binding of the n PLL chains onto a single PAMAMPS substrate Na

+

Cl

−

(see equation (23)). The slopes of each line were determined by nonlinear regression taking into account ITC and FACCE results independently. The numerical values are presented in Table 1. These values were confronted to the total number of condensed counter-ions (Ncounterions)

contained in n PLL chains and one PAMAMPS substrate before the association. Ncounter-

ions

is therefore an estimation of the total entropic reservoir and was calculated based on

Manning theory according to equation (26). The numerical values of Ncounter-ions as well as the intermediate parameters yielding to its calculations (the fraction of condensed counter-ion θ+ and θ- before association according to Manning theory; the total number of condensed counter-ions NCl- and NNa+ according to equations 15 and 16 for each partner and the stoichiometry of interaction n expressed in chain ratio) are given in Table 1. Ncounter-ions is obviously related to the chain stoichiometry (see equation (26) and Table 1 for numerical values) which explains why the values obtained by FACCE experiments were slightly higher compared to ITC experiments. Finally, the fractions of counter-ions that are effectively released "

$ %&'() $ &'(*

#

+,-%./01%2

3are given in the last column of Table 1 and in Figure 4. These

fractions were similar for both ITC and FACCE within the experimental error (see Figure 4 and Table 1) and was ~19%on average for chemical charge densities f ≥ 55%, and ~ 34% on 19 ACS Paragon Plus Environment


average for chemical charge densities f ≤ 30% (see Figure 4). This difference in behavior could be related either to the occurrence of counter-ion condensation at f ≥ 35% or to the f value (f = 50%) for which PLL and PAMAMPS partners have the same charge density parameter64. Fractions lower than 100% were attributed to the formation of PE loops within the PEC and/or a mismatching of the charge spacing between the two partners, which means that there are portions of PLL and PAMAMPS chains that are not involved into electrostatic interactions between both partners64 in accordance with the picture of the “scrambled egg” model for the PEC72. 100

Average % released counter-ions

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

80

ITC FACCE

60

40

20

0 0

20

40

60

80

100

f (%)

Figure 4. Variation of the average percentage of released counter-ions as a function of PAMAMPS chemical charge density: comparison between ITC and FACCE methods.


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Table 1. Physico-chemical properties of oppositely charged polyelectrolytes (PLL and PAMAMPS) and the corresponding parameters of the interactions obtained by ITC (this work) and FACCE64. PLL DP+

θ +(a)

PAMAMPS NCl-(b)

f (%)

100

70

55 50

0.5

DP-(c)

4170

4637

4060

DPAMPS(d)

4170

3246

2233

θ-(e)

0.65

0.50

0.36

N Na+(f)

2711

1623

812

25

30

15

3691

3400

1107

510

0

0

0

0

n

I (M)

FACCE64 80

Interaction PLL / PAMAMPS 4 56789 − N counter-ions(h) 4 678: FACCE64 FACCE64 ITC ITC 4411 4289 4718

1 1.1

ITC(g) 68 63

1.2

68

81

4412

4737

1.3

-

88

-

4904

1.4

65

80

4347

4715

0.75

63

84

3190

3718

0.8

62

87

3164

3792

0.9

60

77

3114

3560

1

57

83

3039

3691

0.565 0.678 0.791

49 46 49

60 54 58

2038 1961 2048

2315 2158 2250

1 0.31 0.327 0.37

28 25 26

53 35 32

1597 615 646

2141 887 792

0.458

26

37

660

916

0.5 0.154

26 13

37 -

652 325

919 -

0.195 0.2 0.234 0.252 0.267

11 14 13

16 19 16

281 348 324

403 476 397

% released counter-ions FACCE64 ITC

565±172

876±388

13±4

18±2

610±149

714±205

19±5

19±1

403±54

472± 59

21±4

21±1

240±44

258±113

37±7

29±3

117±42

127± 82

37±13

31±9

0.301 15 382 see reference67; (b)calculated according to eq. (16); (c) determined by SEC-MALLS as described in reference71; (d)calculated according to eq. (14); (f) (g) calculated according to eq. (15); determined by curve fitting of Wiseman diagrams; (h)calculated according (a)

21

ACS Paragon Plus Environment

(e)

see reference 68; to eq. (26).


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4.3.

Influence of the ionic strength on the enthalpy and entropy changes

It is well known that when two oppositely charged polyelectrolytes form complexes, the electrical double layers surrounding the polyelectrolytes are destroyed to a certain extent and the counter-ions are released in a form of an ordinary salt in solution73. This implies changes in enthalpy and entropy of the system. Both contributions vary with the ionic strength73. ITC allows determining the entropic / enthalpic contribution of the binding constant without additional experiments, which is not the case for FACCE. Figure 5 shows the variations of enthalpy (determined by nonlinear fitting using equations (17-18)) and entropy changes (calculated using equation (20)) associated to the formation of the PEC as a function of the ionic strength for different PAMAMPS charge densities. It can be observed that the higher the charge density f is, the higher the entropic gain |-T∆S| is, which is in good agreement with the increase number of released counter-ions −

according to f reported in Table 1. As

expected, the enthalpy changes |∆H| were much smaller than the entropy changes |-T∆S|. The percentage of the enthalpic changes to the global free energy |∆G| was 3.3%, 3.7%, 3.5%, 4.9%, 6.3% for the interactions PLL-PAMAMPS 100%, 70%, 55%, 30%, and 15%, respectively. These observations confirm that PLL/ PAMAMPS interactions are mainly entropically driven. As can be observed in Figure 5, the entropic contributions -T∆S became lower as the ionic strength increased. The reduction of entropy gain from the released counterions with the increase in ionic strength was previously observed experimentally53,74,75 and verified with computer simulations 76. These simulations showed that the reduction of entropy gain could be explained by the changes in the counter-ions osmotic pressure.


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Page 23 of 36

0

Heat (kJ/mol)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


-1x10

3

-2x10

3

-3x10

3

0.0

f 100% 70% 55% 30% 15%

0.5

1.0

1.5

∆H -T∆S

2.0

2.5

I (M)

Figure 5. Variation of the enthalpic ∆H and the entropic -T∆S contribution to the binding constant to the ionic strength and for different PAMAMPS charge densities. All experimental data were obtained by ITC in the same conditions as those described in Figure 1. ∆H was determined by nonlinear fitting using equations (17-19), while -T∆S was calculated using equation (20). 4.4.

Comparison between FACCE and ITC, and specificities of the two techniques

In this work, we demonstrated that both FACCE and ITC techniques can be successfully used to extract the binding parameters (stoichiometry and binding constant) of the interactions between strong oppositely charged polyelectrolytes, as far as the ionic strength was adjusted so that the binding site constant was accessible (typically, 104-106 M-1). Experimental results obtained by the two techniques are consistent. This work also shed more light about the specificities, advantages / disadvantages belonging to each technique for the study of oppositely charged PE interactions. Table 2 gathers the differences and specificities of both techniques revealed by this work. As discussed earlier, since the two techniques are based on different principles, the experimentally determined stoichiometry are slightly higher in FACCE as compared to ITC. The total experimental time of plotting one isotherm of adsorption is evaluated to 30h for ITC (one binding isotherm, duplicated) and 16 h for FACCE (one binding isotherm, duplicated; or 24h for triplicates), using the experimental 23 ACS Paragon Plus Environment


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setup described in this work and in reference64. If the effect of mixing order can be easily studied in FACCE, this is not the case in ITC. In fact, it is straightforward to prepare the same PE mixture by changing the order of mixing, while it is not directly transposable with the common ITC setup. Reversing the role of ligand / substrate in ITC change the PE in excess at the end of the titration, which is a different experiment. When the kinetics of PEC formation is slow, FACCE has the advantage that the mixture can be prepared in advance to let the system reach the equilibrium. In the case of ITC experiment, it is time-consuming to wait after each injection during the titration. On the other hand, ITC gives direct access to the enthalpy / entropy change, which is basically not accessible by FACCE. Regarding the quantity of ligand required to plot one isotherm of adsorption: 7 to 20 mg of PLL was used in this work for ITC experiments (depending on PAMAMPS charge density), while 3 mg was required for each isotherm for FACCE64. Similar quantities of PAMAMPS are required for both methods.

Table 2. Comparison of the characteristics of FACCE and ITC methods for the study of oppositely charged PE based on the comparison of the present work with ref 64. 24 ACS Paragon Plus Environment

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Experimental parameter

measured

Stoichiometry Total experimental time for one isotherm of adsorption (c) Study of the effect of the mixing order on binding parameters (d)

ITC Heat changes related to ion pairing formation between oppositely charged monomers ITC counts the monomers of the ligand PE chain forming ion pairs with oppositely charged monomers (a)

FACCE

64

Free ligand PE chain concentration in the equilibrated mixtures FACCE counts the ligand PE chains bound to the substrate (b).

30 h for duplicates

~16 h for duplicates; 24 h for triplicates

Not possible

Possible

Study of slow kinetics of complexation

Complicated / time-consuming because of long waiting time between two successive incremental injections

Possible by preparing in advance the different ligand / substrate mixtures

Determination of enthalpy and entropy changes

Feasible in a single experiment

Not accessible

3 mg for one binding isotherm, regardless of PAMAMPS chemical charge density 2.3-6 mg for one binding isotherm Quantity of PE substrate 3-7.5 mg for one Wiseman diagram (e) depending on PAMAMPS chemical required for one isotherm charge density (a) Monomers on a bound ligand PE chain that are not involved in ion pairing with an oppositely charged Quantity of PE ligand required for one isotherm

7-20 mg for one Wiseman diagram depending on PAMAMPS chemical charge density (e)

monomer are not counted in the stoichiometry. ITC gives lower stoichiometry values than FACCE. (b) Monomers on a bound ligand PE chains that are not involved in ion paring with an oppositely charged monomer are counted in the stoichiometry. FACCE gives higher stoichiometry values than ITC. (c) In order to get one Wiseman diagram in ITC, 25 injections were realized each 35 min. Then, the total time required for one ITC experiment is. 15 h. In order to get one binding isotherm in FACCE, 12 mixtures were prepared per isotherm. Each mixture was analyzed three times by FACCE, and each analysis lasted 35 min (including capillary conditioning). Furthermore, five PLL solutions for the calibration curve were prepared and analyzed in the same conditions. Thus, the total time required was 1435 min (i.e. 24h) for triplicate experiments. (d) Adding PA into PC or PC into PA at a same molar ratio. Reversing the role of ligand / substrate in ITC change the PE in excess at the end of the titration, which is a different experiment. (e) See Table S1 in the supporting Information for the initial concentration of PLL ligand [PLL]0.

5.

Conclusion

The interaction of PLL with variously charged PAMAMPS was systematically studied by ITC performed at different ionic strengths. Binding constants and stoichiometries were determined and compared with those obtained from FACCE experiments. For the first time, the data measured from the two methods were compared on the same PE system. The experimental 25 ACS Paragon Plus Environment


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results were consistent which give some credits to the general trend observed in this study. For both methods, chain stoichiometries n decreased with increasing PAMAMPS charge density and was almost independent of the ionic strength. The difference in stoichiometry values observed by ITC and FACCE was attributed to the difference in the experimental parameters measured by each method. The logarithm of the binding site constants (and of the overall complex formation equilibrium, βn) varied linearly with the logarithm of the ionic strength which is interesting for predicting the binding constant according to the PAMAMPS charge density and the ionic strength. Thermodynamic analysis confirmed that the mechanism of interactions involved between oppositely charged PLL/ PAMAMPS is an entropically driven process. Interestingly, the fraction of released counter-ions compared to the total number of condensed counter-ions before the association was ~19% on average for chemical charge densities f ≥ 55%, and ~ 34% on average for chemical charge densities f ≤ 30%. Supporting Information Available The concentrations of PLL and PAMAMPS solutions used for the ITC experiments (Table S1). Wiseman diagrams and curve fittings (Figure S1-S5). Acknowledgments We thank the ANR for funding for the MESOPIC Project (2015−2019), No. ANR-15-CE070005. We thank Willy Vayaboury (Alamanda Polymers, Inc.) for the kind supply of PLL polymers. H. C. thanks the support from the Institut Universitaire de France (junior member, 2011-2016). F.M.L. thanks the Ministry of High Education and Scientific Research of Algeria for the research fellowship. References (1)

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