Thermodynamic Characterization of Polypeptide Complex

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Thermodynamic Characterization of Polypeptide Complex Coacervation Dimitrios Priftis,*,†,‡ Nicolas Laugel,†,§ and Matthew Tirrell†,‡ †

Department of Bioengineering, University of California, Berkeley, California 94720, United States The Institute for Molecular Engineering, University of Chicago, 5735 South Ellis Avenue, Chicago, Illinois 60637, United States § Materials Sciences Division, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, California 94720, United States ‡

ABSTRACT: The interactions between a series of oppositely charged polypeptide pairs are probed using isothermal titration calorimetry (ITC) in combination with turbidity measurements and optical microscopy. Polypeptide complex coacervation is described as a sequence of two distinct binding steps using an empirical extension of a simple ITC binding model. The first step consists of the formation of soluble complexes from oppositely charged polypeptides (ion pairing), which in turn aggregate into insoluble interpolymer complexes in the second step (complex coacervation). Polypeptides have identical backbones and differ only in their charged side groups, making them attractive model systems for this work. The poly(L-ornithine hydrobromide) (PO)/poly(L-glutamic acid sodium salt) (PGlu) system is used to examine the effects of parameters such as the salt concentration, pH, temperature, degree of polymerization, and total polymer concentration on the thermodynamic characteristics of complexation. Complex coacervation in all probed systems is found to be endothermic, essentially an entropy-driven processes. Increasing the screening effect of the salt on the polyelectrolyte charges diminishes their propensity to interact, leading to a decrease in the observed energy change and coacervate quantity. The pH plays an important role in complex formation through its effect on the degree of ionization of the functional groups. Plotting the change in enthalpy with temperature allows the calculation of the heat capacity change (ΔCp) for the PO/PGlu interactions. Finally, ITC revealed that complex coacervation is promoted when higher total polymer concentrations or polypeptide chain lengths are used.

1.0. INTRODUCTION

chloride) (PAH) complexation, including the effects of the above parameters, have also been presented recently.8 The determination of the parameters that can lead to complex coacervation has allowed this procedure to find application in various fields. Complex coacervation is currently being used in processed food, cosmetics, paper, and textiles and in the pharmaceutical and food industries as microencapsulates for drugs, aromas, and flavors.9−12 In the case of paper and textiles or in water treatment, cationic polyelectrolytes are added to form complexes with oppositely charged species. These complexes are then removed by filtration, sedimentation, or adsorption to surfaces. Although the parameters that affect coacervation have been identified and described in detail, more insight is required as to what causes this phenomenon and how it is affected by polymer and solution characteristics. Isothermal titration calorimetry (ITC) is an experimental technique that can provide useful information about the formation of complexes between oppositely charged species. In a typical experiment, a titrant is added to a solution

When oppositely charged polyelectrolytes are mixed in aqueous solutions, complexes can be formed from the cooperative electrostatic interactions. In many cases, this mixing results in a liquid−liquid phase-separation phenomenon named complex coacervation. This associative phase separation results in the formation of a dense, fluid, polymer-rich phase (coacervate phase) and a very dilute polymer-deficient phase (aqueous phase), which exist in equilibrium. The term complex coacervation was introduced by Bungenberg de Jong in a study of mixtures of gum arabic and gelatin.1 Theoretical studies by Overbeek and Voorn based on this system suggested that coacervation results from a combination of electrostatic attractions and mixing entropy terms.2 Later, Veis et al. introduced the idea of the formation of soluble complexes prior to coacervation.3 In more recent studies on synthetic polymers and biomaterials, the influence of a variety of parameters on complex coacervation was identified experimentally.4−7 The most important factors are the ionic strength, stoichiometry, pH, polymer chain length, total polymer concentration, and temperature. Extensive phase diagrams for poly(acrylic acid) (PAA)/poly(allylamine hydro© 2012 American Chemical Society

Received: July 6, 2012 Revised: October 16, 2012 Published: October 19, 2012 15947

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containing a second interacting material, and the heat flow required to maintain a constant temperature is monitored. The thermodynamic parameters of the interactions between species, such as the Gibbs free energy, enthalpy and entropy changes, and the binding constants and ratio can be deduced by the use of appropriate models. ITC has been extensively used for the characterization of interactions between biomaterials,13,14 polymers and ligands,15,16 crystals,17 and surfactants18 and also for the study of the association of amphiphilic polyelectrolytes in aqueous solutions.19 Notably, there are only a few studies on the use of ITC for complex formation between oppositely charged polyelectrolytes.20−22 In all of these cases, complex formation was driven by a combination of entropic and enthalpic effects. Our intention here is to use ITC to increase our understanding of the complex formation between oppositely charged polypeptides and other polyelectrolyte pairs. Recently, we presented data showing that such polyelectrolytes can undergo phase separation and form complex coacervates when mixed in aqueous salt solutions.23 Parameters such as the ionic strength, pH, temperature, and polymer chain length were found to affect the complex formation process. The interfacial energy between polypeptide complex coacervates and the aqueous phase was measured with the use of a surface forces apparatus (SFA) and was found to be extremely low (below 1 mJ/m2 ).24 This low interfacial energy is desirable for applications ranging from surface coatings to wet adhesives to the encapsulation of a wide range of materials. In this report, we present ITC results for the interactions between polypeptides that provide useful insights into the thermodynamics of complex coacervation and are necessary for a comprehensive understanding of the process. ITC consists here of injecting small amounts of a polyanion solution into a larger volume of a polycation solution while maintaining the temperature of the latter constant. An empirical extension of a simple ITC binding model is successfully used for the thermodynamic study. We show that polyelectrolyte mixing, which results in complex formation, is driven by a combination of entropic and enthalpic effects, with entropy generally being dominant. The effect of a series of parameters (salt concentration, pH, temperature, degree of polymerization, and total polymer concentration) on the thermodynamic characteristics of the complexation will be presented with the use of the poly(L-ornithine hydrobromide) (PO)/(PGlu) system. Plotting the changes in enthalpy with temperature allows the calculation of the heat capacity change (ΔCp) for the PO/PGlu interactions.

Table 1. Molecular Characteristics of the Oppositely Charged Polypeptides Used in the Present Study sample

molecular weight (Mn) g/mol

PLys400 PLys200 PLys30 PO400 PO100 PEI200 PHis200 PAH700a

64 300 32 700 4600 80 000 18 500 10 000 5000−25 000 70 000

PAsp200 PAsp30 PGlu400 PGlu200 PGlu100 PGlu30 PAA700

26 700 3800 59 000 29 900 15 900 4000 17 241

polydispersity (Mw/Mn) Polycations 1.38 1.24 1.02 1.03 1.02

degree of polymerization (N) 391 199 28 410 95

750 Polyanions 1.24 1.03 1.06 1.22 1.01 1.07 2.9

195 28 391 198 105 25 696

a

Molecular weight and degree of polymerization by weight (Mw and Pw). The subscript in every polyelectrolyte corresponds to an approximate number of binding sites per chain (degree of polymerization). 7.0 by adding small amounts of either NaOH or HCl to these stock solutions. Final mixtures with different polyanion/polycation mixing ratios (ranging from 1/9 to 9/1 w/w) are then prepared by the sequential addition of equal amounts of the polycation (first) and polyanion (second) stock solutions to aqueous solutions. Polycations and polyanions used together always have similar degrees of polymerization. The polyelectrolyte mixtures are prepared in microcentrifuge vials and are vigorously shaken with a vortex mixer after each separate component is added. The order of mixing is kept the same for all experiments, with the polyanion being added by small aliquots to the polycation solution. All complex coacervates are prepared immediately before measurements and studied at room temperature (25 °C). All water is dispensed from a Milli-Q water purification system at a resistivity of 18.2 MΩ.cm. 2.3. Analysis of Polyelectrolyte Complex Systems. 2.3.1. Turbidity Measurements. A plate reader equipped with a UV spectrophotometer (Tecan, Infinite M200) is employed at a wavelength of 500 nm for the turbidity measurements. None of the polypeptides absorb light at this wavelength. The turbidity (T) is defined by T = −ln(I/I0), with I0 being the incident light intensity and I being the intensity of light passing through the sample volume. Turbidity is measured in absorbance units (au). 2.3.2. Optical Microscopy. An optical microscope (Nikon, Eclipse TE 200) is used to obtain physical images of complexes formed for turbidity experiments, before and after centrifugation. The polypeptide mixture (as previously described) is placed on a glass slide to image the resultant coacervate droplets. To image the coacervate phase, centrifugation is used to coalesce the droplets, as referred to in the preparation of PEC nanoparticles.25 Samples used for imaging are centrifuged for 15 min at 10 000 rpm using a microcentrifuge to achieve rapid phase separation. After centrifugation, the supernatant equilibrium phase is carefully removed by using a micropipet whereas the coacervate (transparent gel) is left at the bottom of the vial. The coacervate phase is placed on a glass slide for imaging. The same optical microscope is used to obtain physical images of coacervates formed during ITC experiments. In a similar way, the coacervate mixture that remains in the ITC cell at the end of each experiment is placed on a glass slide, and the coacervate droplets are imaged. 2.3.3. Isothermal Titration Calorimetry (ITC). ITC experiments are performed on a VP-ITC apparatus from MicroCal, LLC. Unless

2.0. EXPERIMENTAL SECTION 2.1. Materials. Poly(L-aspartic acid sodium salt) (PAsp), PGlu, and PAA are used as the polyanions and poly(L-histidine) (PHis), PLys, PO, and PAH are used as the polycations in this present study. PHis (catalog no. P9386), branched PEI and PAH were purchased from Sigma-Aldrich. PAA was purchased from Polyscience as a 25 wt % solution in water. All of the other polypeptides were purchased from Alamanda Polymers, Inc. The polymers were used as received without any further purification. The molecular characteristics of all of the polymers used (as determined by the suppliers) are presented in detail in Table 1. The molecular weights (Mn) and the degrees of polymerization of the polypeptides were determined by NMR, and GPC was used for the determination of the polydispersities (Mw/Mn) of the polymers. 2.2. Preparation of the Mixtures. First, separate stock solutions of 1 wt % of each polymer are prepared. The pH is then adjusted to 15948

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otherwise noted, the polyanion is injected in 12 μL aliquots of a 1 mg/ mL solution in the 1.44 mL cell containing the polycation solution. Polycations and polyanions used together always have similar degrees of polymerization. A waiting time of at least 3 min is allowed between injections. Constant stirring is applied with the paddle-shaped tip of the syringe at a rate of 307 rpm. The syringe contains a 1 mg/mL solution of the polyanion, referred to as the injectant. When polycation is present in the microcalorimeter cell, its concentration is 0.1 mg/mL. In all cases, the pH and supporting salt concentration are identical in the syringe and cell solutions so as to minimize interfering mixing and dilution heat signals. The cell contents are extracted after each coacervation experiment and observed under an optical microscope.

polycation PO, and small quantities of polyanion PGlu are injected. It should be noted here that turbidity experiments performed between the same polymers,23 where the polycation was added to the polyanion (in contrast to what we describe above), showed no significant difference in the amount of complex formation. Furthermore, in a reverse titration ITC experiment (with the polycation added to the polyanion in the cell) comparable ITC data were collected, indicating that the direction of titration is not essential to the characterization of the coacervation process. Therefore, for every experiment described in this study the polyanion was always added to the polycation in the cell. Two types of phenomena produce changes in the heat of the cell: reactions between the cell material (polycation) and the injectant (polyanion) and their dilutions. For all subsequent isotherms presented in this article, the heat of dilution of the injectant is subtracted. It is measured in a separate reference experiment performed under identical conditions but in the absence of polycation in the cell. Heats of dilution of the cell material are much smaller, considering the volumes involved, and are treated as nonsignificant. Enthalpies are expressed in units of kJ/mol of injectant. They are typically plotted against molar ratios (in terms of repeat unit concentrations) of polyanion over polycation, as in Figure 1B. The common use of ITC is the characterization of the reaction between two oppositely charged materials featuring multiple binding sites. Corresponding models, provided by the microcalorimeter manufacturer, have been used to discuss the thermodynamics of polyelectrolyte complexation, including cases where coacervation was observed.13,22 The electrostatic charges of the injected material play the role of the titrant, binding to the charges of opposite sign borne by the material in the cell. However, the simple model of a single set of sites is insufficient to describe the features observed when macromolecules interact and coacervation occurs. In particular, it allows only for monotonic isotherms, with decreasing absolute values. Alternative models exist that allow for a satisfactory mathematical fit to the observed curves, such as the two sets of sites model (as described in ITC Data Analysis in Origin Tutorial Guide by MicroCal, LLC, 2004). However, in the study of β-lactoglobulin with acacia gum13 the authors acknowledge that the existence of two different and independent binding sites in the two set of sites model has no clear physical meaning when dealing with interactions between macromolecules. In another example of complexation between oppositely charged macromolecules,22 the difficulties in fitting a curve to the ΔH data with the known models that will provide reliable ΔG and K values are also pointed out. We propose a model that describes the complexation between oppositely charged macromolecules (Figure 2) and relies on parameters for complex coacervation that are easy to interpret macroscopically. Because all polyelectrolytes in this study have only one type of binding site (amine or carboxylic groups) and complexation proceeds in two different steps, as we will discuss later, we decided to use the expression two-step model. The first step of the complexation process describes the binding of polyelectrolytic charges of opposite sign. The second step describes coacervation, a complex set of associative interactions, and is an enthalpy signal directly related to the amount of coacervate existing at a particular composition. The global enthalpy (ΔQ), calculated with the use of the model, is

3.0. RESULTS AND DISCUSSION 3.1. Thermodynamic Characterization of the Complexation Between Oppositely Charged Polypeptides. Isothermal titration calorimetry measures the electrical power needed to maintain the sample at a constant temperature while controlled volumes of a second solution are injected. The raw output is a thermograph such as the one presented in Figure 1A. Each peak corresponds to one injection. Positive values are

Figure 1. ITC titration data describing the formation of the complex coacervate from PO and PGlu (total polymer concentration at a ratio of 1.0, Ctotal = 0.02 wt %; salt concentration CNaCl = 200 mM; pH 7.0; degree of polymerization N = 100; temperature T = 25 °C). (A) Differential power signal recorded in the experiment as a function of time and (B) integrated data of molar enthalpy versus the molar ratio of PO to PGlu.

the cases when the cell needs to be heated (i.e., when endothermic processes are at work). The integration of the thermograph peaks with respect to time yields the global enthalpy of the phenomena induced by each injection. Normalization with respect to the amount of material injected then produces an isotherm curve, such as that presented in Figure 1B. In the example presented, the cell contains 15949

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change upon coacervate formation in kJ/mol of injected polyanion. ΔQc is then defined with respect to Qc the same way that ΔQIP is defined above. The idea in introducing a Gaussian function is to account roughly for the fact that the formation of a coacervate phase involves a set of similar but different interactions among the charged macromolecules. The sum ΔQ = ΔQIP + ΔQc is calculated for each injection and fitted in the least-squares sense against experimental isotherms with respect to six parameters n, ΔHIP, Ka, nc, ΔHc, and a using Matlab software (MathWorks, Inc., Notick, MA). It should be noted that this description of the coacervation process implies a number of assumptions, including a composition ratio in polymers within the coacervate phase nc that is not dependent on the bulk composition, and a symmetrical shape of the quantity of coacervate versus bulk composition. These assumptions are simplified relative to more detailed theoretical descriptions54 and experimental results from other techniques. (See, for example, the comparison between the model’s assumed curve and turbidity results in Figure 3B.) However, they allow a consistent determination of the coacervation parameters discussed in this report, nc, ΔHc, and a, which can be pictured, respectively, as the x-axis position, height, and the width of the peak representing coacervate quantity versus bulk composition. Moreover, these assumptions allow us to keep the adjustable parameters to a practically manageable number, where a more refined model is likely to fail to do so. The fitting of an experimental binding isotherm with respect to this model is presented in Figure 3A. For this pair of polyelectrolytes (PO/PGlu), the two contributions to the enthalpy change indicating the two structuring stages during complexation, ΔQIP and ΔQc, are also distinguished. ΔQIP describes the formation of soluble interpolymer complexes termed ion pairing (red line), and ΔQc describes their aggregation into interpolymer complexes (i.e., complex coacervation (green line)). Note that the signal associated with the coacervate changes sign (ΔQc) when the composition of maximum coacervate content is reached. This corresponds to coacervate dissolution when the mixture is diluted beyond the composition of maximum coacervate content. The binding stoichiometry (n), the binding constant (Ka), the enthalpy (ΔHIP) and entropy changes (calculated following TΔSIP = ΔHIP − ΔGIP), and the variation of the Gibbs free energy (ΔGIP = −RT ln(Ka)) as determined from the curve fittings of all polyelectrolyte pairs studied are presented in Table 2. The values of −TΔSIP and ΔGIP are derived from the model but are not direct parameters. They are notably based on the assumption that the ion pairing is a reversible reaction. Thermodynamic parameters nc, ΔHc, and a are given in Table 3 for the second complex coacervation step. During the first structural stage, soluble interpolymer complexes are formed that later aggregate to form insoluble interpolymer complexes (Figure 2). The existence of two stages during the complexation of oppositely charged species was reported earlier13,14,26 and is also in agreement with the Tainaka thermodynamic theory on complex coacervation.27,28 The spontaneous character of the interactions between the oppositely charged polyelectrolytes is underlined by the negative Gibbs free energies presented in Table 2. In the first step, the oppositely charged polyelectrolytes interact with high affinity, as seen from the high Ka values. Furthermore, the binding between the polymers is entropically driven with strongly favorable −TΔSIP (19−32 kJ/mol) and weaker

Figure 2. Schematic representation of the two-step binding process of polyelectrolyte complexation. The optical micrograph illustrates complex coacervates formed from a PO/PGlu mixture (Ctotal = 0.02 wt %, CNaCl = 200 mM, pH 7.0, N = 100, T = 25 °C).

the sum of enthalpies from these two processes named ion pairing (ΔQIP) and complex coacervation (ΔQc). For the first step of the complexation (ion pairing) we use an analogy with the widely used one set of sites model that describes the binding of the titrant to a specific site born by the macromolecule in the cell. Here, injected polyanion chains (titrant) react reversibly with n binding sites of the polycation macromolecules in the cell. Along with the ratio n, which gives the stoichiometry of the ion pairing, a binding constant Ka and a characteristic change in enthalpy ΔHIP (in kJ/mol of injectant) are used as the adjustable parameters in the fitting procedure. The expression for the heat of the system due to ion pairs at the ith injection is Q IP(i) = nM t(i)V0ΔHIPΘ(i)

(1)

where V0 is the volume of the cell, Mt(i) is the concentration in the macromolecule, in our case the polycation, and Θ(i) is the fraction of sites on the macromolecule that are bound when equilibrium is reached after the ith injection. Θ is determined by the definition of the binding constant and the concentrations at the ith injection. The heat at the previous injection QIP(i − 1) is subtracted from QIP(i), with a small correction for the volume of solution expelled from the cell upon injection. The result (i.e., the change in global heat upon the ith injection) is then normalized by the number in moles of repeat units of polyanion injected to yield ΔQIP(i). ΔQIP(i) is the quantity to be compared to the enthalpy change in the isotherms obtained experimentally. The second step in complexation, corresponding to the formation of the complex coacervate, is described by an additional contribution to the heat of the system Qc. Qc is proportional to the amount of polymer that is present in coacervate domains at a given composition. Qc, for the ith injection, has a definition similar to that of QIP Q c(i) = ncM t(i)V0ΔHc Θc(i)

(2)

where Θc is arbitrarily defined by a Gaussian with respect to the molar fraction f of polyanion over the total polymer content f(i) = cPA/(cPA + cPC): 2

Θc(i) = e−(f (i) − fc) /a

2

(3)

a gives the order of magnitude of the width at half height of the Gaussian curve (fwhh = 2a(ln(2))1/2 ≈ 1.7a). fc and nc describe the composition in polymers of the mixture at maximum coacervate quantity in terms of the molar fraction or ratio of injectant, respectively, fc = nc/(1 + nc). ΔHc is the enthalpy 15950

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unfavorable ΔHIP (1.7−3.0 kJ/mol). This is caused by the release of counterions and the restructuring of water molecules around the charged sites during complexation.22,29 Changes in the polyelectrolyte conformation also contribute to the overall entropy change. In most of the systems presented in Table 2, an endothermic ion pairing (positive values of ΔHIP) is observed, as illustrated for the PO/PGlu system (Figure 1). The only exception of exothermic complexation is the PHis/PGlu system, where a different pH is used. This different behavior will be discussed later (section 3.3). At this point, it is important to note that all of the experiments presented in Table 2 were performed at pH 7.0 (with the exception of the PHis/PGlu system). Under these conditions, all polyelectrolytes used are highly charged and the complexation is endothermic, driven by the large counterion release entropy gain and opposed by a smaller unfavorable enthalpy change. This observation is in agreement with the data collected through Langevin dynamics simulations on the energetics of complexation between oppositely charged polyelectrolytes.30 In Table 3, the thermodynamic characteristics of the second step in the binding are presented. Here, the bound polyelectrolyte chains of the first step (ion pairing) aggregate to form a dense, intermolecular, fluctuating polymer network (complex coacervates), as seen in Figure 2. Earlier studies relate this second step to both enthalpic and entropic changes. The interactions of free charged polyelectrolyte chains in the mixture with the residual net charge of the bound polyelectrolyte chains from ion pairing result in an enthalpic contribution.27,31 The counterion release caused by these interactions can result in a positive entropy gain. The entropic contributions in this step have also been described as a result of the rearrangement of the coacervates in the solution and the dilution of the coacervate phase.32 Because the counterion release in the second step is smaller than that in the first step (less-available binding sites), the observed energy changes are also smaller as seen in Table 3. The two steps in the complexation were also observed and discussed in terms of energy changes in systems containing polyelectrolytes and proteins such as bovine serum albumin/poly(dimethyl-diallylammonium chloride).33,34 As can be seen both in Table 3 and in the illustration of Figure 3, the enthalpies involved in complex coacervation are typically 1 to 2 orders of magnitude lower than those involved in ion pairing. Moreover, they appear to vary from system to system to a greater extent. The absolute values of ΔHIP vary by less than a factor of 3 between the extremes. Although the values of Ka, also related to ion pairing, do vary by more than an order of magnitude, the corresponding change in free energy,

Figure 3. (A) Experimental data (squares) of molar enthalpy from the complexation of PO with PGlu versus the molar ratio of PGlu and resulting fitting curves (blue line) using the proposed model. (B) Turbidity measurements (black line) and Qc, the heat associated with the coacervate phase forming and dissolving (red line), derived from the ITC isotherm fitting in A (see the text). All data are plotted against PGlu content (for both experiments, Ctotal = 0.02 wt %, CNaCl = 200 mM, pH 7.0, N = 100, and T = 25 °C). (C) Comparison of the polymer composition (in mol % of PGlu) at a maximum in Qc and in turbidity, respectively, for all of the polyelectrolyte pairs presented in Table 2. The line represents perfect agreement between the results from ITC and turbidity experiments.

Table 2. Thermodynamic Parameters of the First Binding Step (Ion Pairing) between Aqueous Solutions of Different Oppositely Charged Polyelectrolytes thermodynamic parametersa

PEI200/PGlu200

PEI200/PAsp200

PO100/PGlu100

PLys200/PAsp200

PLys200/PGlu200

PAH700/PAA700

PHis200/PGlu200b

ΔHIP −TΔSIP ΔGIP Ka (×10−3) n

2.4 −30 −28 70 0.20

1.7 −30 −28 88 0.22

3.0 −25 −22 6.5 0.85

1.9 −29 −27 44 0.68

1.9 −27 −25 24 0.62

2.6 −32 −29 139 1.17

−4.3 −19 −24 13 0.92

a Ctotal = 0.02 wt %; CNaCl = 200 mM; pH 7.0; N = 100; T = 25 °C; ΔHIP, ΔGIP, and −TΔSIP in kJ/mol; and Ka in 103 L/mol. bThe experiment was performed at pH 5.0. The subscript in every polyelectrolyte corresponds to an approximate number of binding sites per chain (degree of polymerization).

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Table 3. Thermodynamic Parameters of the Second Binding Step (Complex Coacervation) between Aqueous Solutions of Oppositely Charged Polyelectrolytes thermodynamic parametersa

PEI200/PGlu200

PEI200/PAsp200

PO100/PGlu100

PLys200/PAsp200

PLys200/PGlu200

PAH700/PAA700

PHis200/PGlu200b

ΔHc a nc

0.64 0.11 0.54

0.62 0.12 0.61

0.09 0.09 1.21

0.03 0.08 0.71

0.01 0.04 0.71

0.93 0.08 0.76

0.07 0.06 0.72

Ctotal = 0.02 wt %, CNaCl = 200 mM, pH 7.0, N = 100, T = 25 °C, and ΔHc in kJ/mol. bThe experiment was performed at pH 5.0. The subscript in every polyelectrolyte corresponds to an approximate number of binding sites per chain (degree of polymerization). a

−TΔSIP, varies only by 50%. In contrast, the highest enthalpy of complex coacervate formation, ΔHc, observed is about 70 times the smallest value. It seems that, as a general trend, lower values of ΔH c are found when both polymers involved are polypeptides, as seen in earlier studies.35 This could be related to the nature of the polymers used in the other systems (PEI is a branched polymer) or the difference in the size of the polymer chains (longer polymer chains are used in these mixtures). One can also conclude that the thermodynamics underlying complex coacervation are more sensitive to differences between different species of polymers than the ones leading to simple ion pairing. The polyacid/polybase composition at the point where the coacervate formation reaches a maximum value was determined by turbidity and ITC measurements in terms of the molar percentage of the polyacid. The results are presented together in Figure 3B,C. For the case of the PO/PGlu system, the turbidity measurements presented in Figure 3B show that the maximum coacervate formation is achieved when a polyacid/ polybase ratio of close to 1:1 is used. Under these conditions, the number of charges available to interact is the highest. Therefore, the aggregation of the bound polyelectrolyte chains, which leads to the formation of the coacervate, reaches its highest value. Figure 3C shows the comparison of the maximum values calculated by the two techniques for various systems (each point in the graph corresponds to two maximum values as calculated by the two techniques). The reasonable agreement between two different methods over a range of systems leads us to conclude that the second step in the binding process correlates with the creation of a dense intermolecular polymer network (complex coacervation) from the bound polyelectrolyte chains in the first step (ion pairing) and suggests the relevance of the approach taken here in the ITC modeling of complex coacervate formation and dissolution. 3.2. Effect of Salt Concentration on the Thermodynamic Characteristics of Polypeptide Complex Coacervates. The thermodynamic characteristics of polypeptide complex coacervates are determined with the use of ITC with respect to changes in parameters such as polyelectrolyte pairs, salt concentration, pH, temperature, and others. The effect of the salt concentration on the thermodynamic characteristics of a PO/PGlu system is summarized in Table 4. As noted above, complexation involves two steps: the initial ion pairing and the complex coacervation. We observe that the thermodynamic characteristics of both steps are affected by the addition of salt to the mixtures. More specifically, the overall change in energy (enthalpic and entropic) becomes smaller as the salt concentration is increased, which means that the driving force for complexation weakens. The addition of salt above a critical point suppresses complexation, as shown experimentally for a variety of polyelectrolyte systems.8,23 This change can be explained by the screening effect of the salt on the polypeptide charges, limiting their ability to interact.

Table 4. Thermodynamic Parameters of PO/PGlu Mixtures with Different Salt Concentrations thermodynamic parametersa ΔHIP −TΔSIP ΔGIP Ka (× 10−3) n ΔHc a nc

0 mM

100 mM

200 mM

Ion Pairing 8.9 3.7 3.0 −32 −27 −25 −23 −23 −22 13 11 6.5 0.50 0.68 0.85 Complex Coacervation 0.26 0.12 0.09 0.05 0.08 0.09 0.63 1.13 1.21

375 mM

500 mM

800 mM

2.4 −26 −23 9.5 0.93

2.2 −22 −20 3.4 1.81

0.9 −21 −20 3.0 1.30

0.05 0.11 1.34

0.02 0.06 1.62

0.01 0.05 1.53

a Ctotal = 0.02 wt %; pH 7.0; N = 100; T = 25 °C; ΔHIP, ΔHc, ΔGIP, and −TΔSIP in kJ/mol; and Ka in 103 L/mol.

Weakened electrostatic interactions between oppositely charged polyelectrolytes result in decreased counterion release. Given that the enthalpic and entropic contributions are attributed to the electrostatic interactions and the counterion release, respectively, it is clear that both are affected by the increasing screening effect. The reduction of the entropy gain from released counterions with the increase in salt concentration has also been verified with computer simulations.30 These simulations, however, showed that the decrease in the counterion release entropy by the addition of salt could not be attributed to changes in the number of adsorbed counterions. Alternatively, this effect was explained by the changes in the counterion osmotic pressure induced by the salt. The higher concentration of free counterions in the solution reduces the release of adsorbed counterions from the polyelectrolyte chains and causes a smaller macroscopic entropy change. Studies of DNA binding with polycations, lipids, and other cationic species have also shown the suppression of counterion release entropy by the increase in the salt concentration.36−38 Our results indicate that the effect of salt on polyelectrolyte complexation is mostly explainable by the vanishing of the entropic change ΔS, identified as the driving force for both ion pairing and complex coacervation. The second binding step of the polyelectrolyte complexation involves interactions of free charged polyelectrolyte chains in the mixture with the residual net charge of the polyelectrolyte chains already bound from the first step. These interactions lead to an enthalpic change that is reduced as the salt concentration in increased. This effect of salt is verified from the data in Table 4. Furthermore, the observation of the binding curves presented in Figure 4A shows a reduction in the coacervation signal (contribution illustrated in Figure 3A by a green line). We reason that the increased screening effect of salt on the polyelectrolyte charges diminishes their ability to 15952

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at two different pH values, and the results are summarized in Table 5 and Figure 5A. At pH 7.0, the chains of both Table 5. Thermodynamic Parameters of PO/PGlu Mixtures with Different pH Values and Degrees of Polymerization thermodynamic parametersa ΔHIP −TΔSIP ΔGIP Ka (× 10−3) n ΔHc a nc

pH 8.8, N = 100

pH 7.0, N = 100

Ion Pairing 1.7 3.0 −30 −25 −28 −22 90 6.5 0.41 0.85 Complex Coacervation 0.08 0.09 0.07 0.09 0.55 1.21

pH 7.0, N = 400 3.2 −25 −22 7.3 0.94 0.12 0.09 1.05

Ctotal = 0.02 wt %; CNaCl = 200 mM; T = 25 °C; ΔHIP, ΔHc, ΔGIP, and −TΔSIP in kJ/mol; and Ka in 103 L/mol. a

Figure 4. (A) Experimental data (squares) of molar enthalpy from the complexation of PO with PGlu versus the molar ratio of PGlu and resulting fitting curves using the proposed model corresponding to various titration experiments at different salt concentrations (Ctotal = 0.02 wt %; pH 7.0; CNaCl = 200 mM; N = 100; T = 25 °C). (B) Changes in turbidity and enthalpy for the second binding step (complex coacervation) as a function of the salt concentration in the mixtures.

interact for the same reasons presented in the case of ion pairing, leading to a limited energy change. Fewer interactions between the polyelectrolytes during the first binding step also correspond to a smaller yield in coacervate formation. The change in the coacervate yield with increasing salt concentration in the mixtures has also been monitored through turbidity measurements.8,23 Although turbidity is not a quantitative measure of the amount of coacervate formed, changes in the light transmission depend on the size and also on the composition of the formed coacervate or precipitate. A higher polymer concentration in the droplets, or a higher droplet concentration, will result in a stronger contrast in terms of the refractive index and a greater amount of turbidity. Therefore, the measurement does reflect the extent of polyelectrolyte complex (PEC) formation, albeit qualitatively. In Figure 4B, the changes in turbidity and enthalpy in the second binding step are presented together as a function of salt concentration. This confirms that the increasing salt concentration decreases the number of electrostatic interactions between oppositely charged sites as a result of the screening effect, leading to smaller energy changes and finally to less complex coacervate formed. 3.3. Effect of pH on the Thermodynamic Characteristics of Polypeptide Complex Coacervates. The effect of pH on the thermodynamic characteristics of polypeptide coacervates is also investigated with the use of ITC. Two independent experiments with the PO/PGlu and PHis/PGlu systems revealed the strong influence that changes in pH have on the complexation. In the first example, the interactions between the two oppositely charged polypeptides are examined

Figure 5. (A) Experimental data (squares) of molar enthalpy from the complexation of PO with PGlu versus the molar ratio of PGlu and resulting fitting curves using the proposed model corresponding to various titration experiments at different pH values (Ctotal = 0.02 wt %, CNaCl = 200 mM, N = 100, and T = 25 °C). (B) Experimental data (squares) of molar enthalpy from the complexation of PHis with PGlu versus the molar ratio of PGlu and the fitting curve using the proposed model corresponding to a titration experiment at pH 5.0 (Ctotal = 0.02 wt %, CNaCl = 200 mM, T = 25 °C, and N = 200).

polypeptides are almost fully charged, with degrees of ionization of greater than 99%. However, at pH 8.8, which is closer to the pKa value of the polycation, the number of charged sites in PO is significantly reduced, but PGlu remains fully charged. This reduction in the degree of ionization results in a shift of the isotherm toward smaller values along the molar ratio axis because a significantly smaller number of repeat units of the 15953

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polycation should be expected to bear an active binding site. It also results in a smaller number of sites for intermolecular interactions, which explains the smaller enthalpy change per polyanion charge observed in the first binding step (Table 5). As noted earlier, the second binding step corresponds to the aggregation of the initially formed complexes into the coacervate phase. As seen in the curves presented in Figure 5A, the second step signal that describes this process is slightly reduced when a pH of other than 7.0 is used. This shows that the degree of ionization has an effect on the coacervate formed. In fact, turbidity measurements performed on a variety of polyelectrolyte systems have shown that complex formation is reduced when the degree of ionization of the polymers used for complexation is smaller.8,23 Similar experimental studies and computer simulations have also proposed that upon complex formation decreased ionization leads to fewer ionic bonds between oppositely charged polyelectrolytes.30,39−41 At this point it should be noted that in cases where the two polymers are not in the same charge state (i.e., have different numbers of charged sites), the effect of one polyelectrolyte on the pKa of the other could not be eliminated. However, earlier studies with the use of turbidity in the same systems23 (where one of the two polyelectrolytes or both were fully charged) have not shown any evidence that indicate a significant shift in the pKa of one polyelectrolyte due to the charge state of the other. In the second example of the PHis/PGlu system, presented in Figure 5B, the titration experiment is performed at a different pH (5.0). Even though that decision was made for solubility reasons (PHis is insoluble in water at pH 7.0), this experiment highlights even further the effect of pH on polyelectrolyte complexation. Under these conditions, the two-step process can still describe the interactions between oppositely charged polypeptides. However, in contrast to all other systems, the complexation is exothermic. This behavior can be related to the different nature and pKa value of PHis compared to that of other polyelectrolytes used in this study. PHis has aromatic heterocycles (imidazole rings) with a pKa value of approximately 6.0.42 Therefore, at pH 5.0, where complexation takes place, relatively small changes in the local pH (caused by the complexation) can change the average charge significantly. Earlier reports on complex formation between chitosan/PAA and other systems have proposed that upon complex formation ionization can shift to give more ionic bonds.30,39−41 This shift in the degree of ionization of the polypeptides was used to explain a similar swing in the heat effects between weak polyelectrolytes and carboxy methyl cellulose.26 3.4. Effect of Temperature on the Thermodynamic Characteristics of Polypeptide Complex Coacervates. A number of studies have been conducted on the influence of temperature on PEC formation. In the cases of biopolymerbased complexes, the temperature-induced denaturation and related conformational changes play dominant roles.11,43 Similarly, the effect of temperature on synthetic polyelectrolyte complexes was related to increased dissociation and enhanced hydrophobic interactions.8,23 Herein, the effect of temperature on the thermodynamic characteristics of polypeptide coacervates was investigated in the temperature range from 25 to 45 °C. The data obtained through ITC for the PO/PGlu system are presented in Table 6 and Figure 6A. During complexation, at any temperature, the two typical steps (ion pairing and complex coacervation) are observed. The prevalence of entropic over enthalpic contributions during the

Table 6. Thermodynamic Parameters of PO/PGlu Mixtures at Different Temperature or Total Polymer Concentrations Ctotal (wt %) thermodynamic parametersa ΔHIP −TΔSIP ΔGIP Ka (× 10−3) n ΔHc a nc

0.2

0.02 (25 °C)

Ion Pairing 1.9 3.0 −20 −25 −18 −22 1.6 6.5 0.83 0.85 Complex Coacervation 0.19 0.09 0.11 0.09 1.22 1.21

temperature (°C) 35

45

2.4 −26 −24 12 1.06

2.3 −28 −26 20 1.04

0.08 0.09 1.27

0.06 0.08 1.09

Ctotal = 0.02 wt %; CNaCl = 200 mM; pH 7.0; N = 100; T = 25 °C; and ΔHIP, ΔHc, ΔGIP and −TΔSIP in kJ/mol and Ka in 103 L/mol.

a

Figure 6. (A) Experimental data (squares) of molar enthalpy from the complexation of PO with PGlu versus the molar ratio of PGlu and resulting fitting curves using the proposed model corresponding to various titration experiments at different temperatures (Ctotal = 0.02 wt %, CNaCl = 200 mM, pH 7.0, and N = 100). (B) Temperature dependence of ΔHIP (blue) and ΔHc (red) for the binding of PO/ PGlu. Squares correspond to experimental data, and lines, to linear fits.

first binding step is clear, although both appear to be temperature-dependent (decreasing with increasing temperature). Even though the curves in Figure 6A appear to be very similar, changes in the thermodynamic characteristics can be seen in the data produced by the fitting, which are presented in Table 6. These changes can be related to the decrease of coacervate formation with increased temperature that leads to smaller energy changes (Table 6). Indeed, earlier studies performed in PAH/PAA and polypeptide systems with salt have shown that the amount of complex formed is reduced when the temperature is increased.8,23 This lower complex formation at higher temperature was explained by the decrease 15954

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in the number of electrostatic interactions between acid/base units and the reduced bonding strength of the intermolecular ion pairs. Another objective of this study was to examine the effect of temperature, in the range of 25 to 45 °C, on the heat capacity of the systems (Figure 6B). These heat capacity changes are generally very sensitive to interactions between macromolecule residues and solvent molecules44 and have been used in predicting the surface-exposed polar and nonpolar surface area changes upon ligand−macromolecule binding.45 Using a plot of ΔH versus T (ΔCp = d(ΔH)/dT), we can calculate the molar heat capacity change ΔCp for the polyelectrolyte interaction from the slope. The ΔCp of the first binding step was found to be −0.0363 kJ/(mol·K), and that of the second, −0.0019 kJ/ (mol·K). The linear correlation coefficients were 0.885 and 0.968, respectively. If the complex is considered to be the reference state, then negative ΔCp means that the free polymers in total have a higher heat capacity than the complex itself, which indicates that ΔCp is not mainly a result of changes in molecular vibrations and may arise from changes in the degree of hydration.46−48 This type of hydrophobic effect arises from the release of hydration water when the nonpolar, surfaceaccessible surface areas come together to form a hydrophobic complex.49,50 The linear plots (Figure 6B), however, show that in the specific temperature range examined the ΔCp is not temperature-dependent. This suggests that the area of surface contact or the difference in the vibrational content between the complex and its components does not vary over the temperature range studied.44 3.5. Effect of Total Polymer Concentration and Polyelectrolyte Chain Length on the Thermodynamic Characteristics of Polypeptide Complex Coacervates. Two different total polymer concentrations (0.2 and 0.02 wt % at 1:1 polyacid/polybase) and molecular weights (degrees of polymerization of 100 and 400) of PO/PGlu mixtures were employed to examine their effects on the thermodynamic characteristics as reflected by ITC measurements. The results of this study are presented in Tables 5 and 6 and Figure 7. The effect of the polyelectrolyte chain length on the extent and stability of complex coacervate formation has been studied on both the theoretical2 and experimental level.51 Considering the complex coacervation phenomenon, an increase in the molecular weight of the polyelectrolytes used is expected to result in more dense phases and more extended coacervate domains in the phase diagram. In this study, a similar increase in coacervate formation can be seen in Figure 7A, where the intensity of the second-step signal in the system with a higher degree of polymerization (red line) is also increased. The enthalpic and entropic changes that describe the first binding step are also higher when polypeptides with higher molecular weights are used. These changes can be related to the difference in the charge density in the mixtures and the cooperativity of the electrostatic interactions, which is slightly higher with increased polypeptide chain length. More electrostatic interactions between the oppositely charged polypeptides lead to increased counterion release and therefore a larger entropic gain. In Figure 7B, the binding isotherms of two polyelectrolyte systems with different total polymer concentrations are depicted. As in the previous case an increase in coacervate formation with the increase in the total polymer concentration is indicated by the change in the signal associated with the

Figure 7. Experimental data (squares) of molar enthalpy from the complexation of PO with PGlu versus the molar ratio of PGlu and resulting fitting curves using the proposed model corresponding to various titration experiments with (A) different chain lengths (Ctotal = 0.02 wt %, CNaCl = 200 mM, T = 25 °C, and pH 7.0) and (B) different total polymer concentrations (pH 7.0, CNaCl = 200 mM, T = 25 °C, and N = 200).

second step of the binding isotherm. A higher concentration of polypeptides in the mixture means more interactions and thus more complex formed per mole of injectant. This trend has been discussed for various polyelectrolyte systems8,23 and was also related to the higher PEC volume fractions in the more concentrated whey protein/gum arabic mixtures.52 Theoretical calculations have indicated the influence of ion pair formation between counterions and ions on polymer chains on the phase behavior of polyelectrolytes.53 According to this study, the number of ion pairs increases with the total polymer concentration. Ion pairing leads to a decrease in the effective charge of the chain and the number of mobile counterions promoting phase separation. Furthermore, the attraction between ion pairs and multiplets (aggregated ion pairs) causes the gelation of polymer solutions (coacervation). These findings are in complete agreement with our experimental results and our two-step thermodynamic description of the coacervation phenomenon.

4.0. CONCLUSIONS The thermodynamic characterization of polypeptides and other polyelectrolyte interactions is studied using ITC in combination with other techniques such as turbidity measurements and optical microscopy. The microcalorimetry data analyzed with the use of an empirical extension of a simple ITC binding model, demonstrate the presence of two distinct steps in the complexation of the polyelectrolyte systems. The first step describes the formation of soluble interpolymer complexes (ion pairing) between oppositely charged polypeptides. The second step describes the aggregation of these complexes into insoluble 15955

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(3) Veis, A.; Aranyi, C. Phase separation in polyelectrolyte systems. I. Complex coacervates of gelatin. J. Phys. Chem. 1960, 64, 1203−1210. (4) Antonov, M.; Mazzawi, M.; Dubin, P. L. Entering and exiting the protein−polyelectrolyte coacervate phase via nonmonotonic salt dependence of critical conditions. Biomacromolecules 2010, 11, 51−59. (5) Wang, X.; Lee, J.; Wang, Y.-W.; Huang, Q. Composition and rheological properties of β-lactoglobulin/pectin coacervates: effects of salt concentration and initial protein/polysaccharide ratio. Biomacromolecules 2007, 8, 992−997. (6) Weinbreck, F.; Tromp, R. H.; de Kruif, C. G. Composition and structure of whey protein/gum arabic coacervates. Biomacromolecules 2004, 5, 1437−1445. (7) Bohidar, H.; Dubin, P. L.; Majhi, P. R.; Tribet, C.; Jaeger, W. Effects of protein−polyelectrolyte affinity and polyelectrolyte molecular weight on dynamic properties of bovine serum albumin− poly(diallyldimethylammonium chloride) coacervates. Biomacromolecules 2005, 6, 1573−1585. (8) Chollakup, R.; Smitthipong, W.; Eisenbach, C. D.; Tirrell, M. Phase behavior and coacervation of aqueous poly(acrylic acid)− poly(allylamine) solutions. Macromolecules 2010, 43, 2518−2528. (9) Bhatia, S. R.; Khattak, S. F.; Roberts, S. C. Polyelectrolytes for cell encapsulation. Curr. Opin. Colloid Interface Sci. 2005, 10, 45−51. (10) Philipp, B.; Dautzenberg, H.; Linow, K. J.; Kotz, J.; Dawydoff, W. Polyelectrolyte complexes: recent developments and open problems. Prog. Polym. Sci. 1989, 14, 91−172. (11) Schmitt, C.; Sanchez, C.; Desobry-Banon, S.; Hardy, J. Structure and technofunctional properties of protein-polysaccharide complexes: A review. Crit. Rev. Food Sci. Nutr. 1998, 38, 689−753. (12) Penchev, H.; Paneva, D.; Manolova, N.; Rashkov, I. Novel electrospun nanofibers composed of polyelectrolyte complexes. Macromol. Rapid Commun. 2008, 29, 677−681. (13) Aberkane, L.; Jasniewski, J.; Gaiani, C.; Scher, J.; Sanchez, C. Thermodynamic characterization of acacia gum−β-lactoglobulin complex coacervation. Langmuir 2010, 26, 12523−12533. (14) Girard, M.; Turgeon, S. L.; Gauthier, S. F. Thermodynamic parameters of β-lactoglobulin−pectin complexes assessed by isothermal titration calorimetry. J. Agric. Food Chem. 2003, 51, 4450− 4455. (15) Sinn, C.; Dimova, R.; Antonietti, M. Isothermal titration calorimetry of the polyelectrolyte/water interaction and binding of Ca2+: effects determining the quality of polymeric scale inhibitors. Macromolecules 2004, 37, 3444−3450. (16) Kimhi, O.; Bianco-Peled, H. Microcalorimetry study of the interactions between poly(N-isopropylacrylamide) microgels and amino acids. Langmuir 2002, 18, 8587−8592. (17) Dimova, R.; Lipowsky, R.; Mastai, Y.; Antonietti, M. Binding of polymers to calcite crystals in water: characterization by isothermal titration calorimetry. Langmuir 2003, 19, 6097−6103. (18) Seng, W. P.; Tam, K. C.; Jenkins, R. D.; Bassett, D. R. Calorimetric studies of model hydrophobically modified alkali-soluble emulsion polymers with varying spacer chain length in ionic surfactant solutions. Macromolecules 2000, 33, 1727−1733. (19) Raju, B. B.; Winnik, F. M.; Morishima, Y. A look at the thermodynamics of the association of amphiphilic polyelectrolytes in aqueous solutions: strengths and limitations of isothermal titration calorimetry. Langmuir 2001, 17, 4416−4421. (20) Feng, X.; Leduc, M.; Pelton, R. Polyelectrolyte complex characterization with isothermal titration calorimetry and colloid titration. Colloids Surf., A 2008, 317, 535−542. (21) Oppermann, W.; Schultz, T. Interaction between oppositely charged polyelectrolytes in aqueous-solution. Makromol. Chem. Symp. 1990, 39, 293−299. (22) Bucur, C. B.; Sui, Z.; Schlenoff, J. B. Ideal mixing in polyelectrolyte complexes and multilayers: entropy driven assembly. J. Am. Chem. Soc. 2006, 128, 13690−13691. (23) Priftis, D.; Tirrell, M. Phase behavior and complex coacervation of aqueous polypeptide solutions. Soft Mater 2012, 8, 9396−9405.

interpolymer complexes (complex coacervates) as well as their dissolution when the polyelectrolyte composition diverges from its value at maximum coacervate quantity. Using the PO/PGlu system, we showed that parameters such as the ionic strength, pH, temperature, degree of polymerization, and total polymer concentration have significant effects on the thermodynamic characteristics of the complexation. The addition of a monovalent salt was found to affect the energetics of complex formation strongly. As the salt concentration is increased, electrostatic screening increases and the entropy gains due to the release of counterions decrease. This limits both ion pairing and the formation of the coacervate. pH also plays an important role in complex formation because of its direct effect on the degree of ionization of the functional groups. In contrast to all other systems, the first-step complexation of the PHis/PGlu system is exothermic. Interestingly, the formation of the complex coacervate is endothermic in all experiments, including that with the PHis/ PGlu system, and their dissolution is always found to be exothermic. Plotting the change in enthalpy with temperature allows the calculation of the heat capacity change (ΔCp) for the PO/PGlu interactions. Finally, the study of the thermodynamic characteristics of the PO/PGlu complexation revealed that increased total polymer concentrations and polypeptide chain lengths promote complex coacervation. The present study was focused on the understanding of the nature of interactions between oppositely charged polypeptides and the thermodynamic mechanisms involved during the binding processes and stabilization of these assemblies. The important ITC results presented here provide useful insight into the complexation process of a variety of polyelectrolyte systems that can determine their potential applicability in a variety of fields.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We acknowledge Dr. Matthew Kade, Dr. Lorraine Leon, and Dr. Sarah Perry for their helpful discussions on thermodynamics during the preparation of this article. We also acknowledge the Kuriyan laboratory in the molecular and cell biology department at the University of California, Berkeley, for generously allowing us to use their isothermal titration calorimetry instrument and Jeff Iwig for his technical help and insight. This work was supported by the National Science Foundation under award no. DMR-0710521 and by the Laboratory Directed Research and Development Program of Lawrence Berkeley National Laboratory under U.S. Department of Energy contract no. DE-AC02-05CH11231 and Argonne National Laboratory under U.S. Department of Energy contract no. DE-AC02-06CH11357.

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