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Xanthan exopolysaccharide: Cu complexes affected from the pH-dependent conformational state; implications for environmentally relevant biopolymers Benjamin Causse, Lorenzo Spadini, Géraldine Sarret, Adeline Faure, Christophe Travelet, Dominique Madern , and Cécile Delolme Environ. Sci. Technol., Just Accepted Manuscript • DOI: 10.1021/acs.est.5b03141 • Publication Date (Web): 29 Jan 2016 Downloaded from http://pubs.acs.org on February 3, 2016
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Xanthan exopolysaccharide: Cu2+ complexes
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affected from the pH-dependent conformational
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state; implications for environmentally relevant
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biopolymers
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Benjamin Causse†§, Lorenzo Spadini‡§*, Géraldine Sarret§, Adeline Faure§, Christophe
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Travelet┴, Dominique MadernҰ, Cecile Delolme†
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† § ‡
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LEHNA / ENTPE / UCB / CNRS UMR 5023, F-69518 Lyon, France. ISTERRE, UMR 5275 CNRS / Université Grenoble Alpes / IRD, F-38041 Grenoble, France. LTHE, UMR 5564 CNRS / Université Grenoble Alpes / IRD, F-38041 Grenoble, France.
┴
CERMAV, CNRS UPR 5301 / F-38000 Grenoble, France.
Ұ
IBS, UMR 5075 / CNRS / Université Grenoble Alpes / CEA, 38000 Grenoble, France.
12 13
Correspondence:
Tel.: +33 (0) 4 56 52 09 95; fax: +33 (0) 4 56 52 09 87
14
Email: Lorenzo Spadini,
[email protected] 15 16 17
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KEYWORDS: xanthan, copper, biopolymer, soil, organic matter, humic acids, conformation,
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exopolysaccharide, copper, complexation.
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ABSTRACT
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The conformational impact of environmental biopolymers on metal sorption was studied
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through Cu sorption on xanthan. The apparent Cu2+ complexation constant (LogK; Cu2+ + L-
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CuL+) decreased from 2.9±0.1 at pH 3.5 to 2.5±0.1 at pH 5.5 (ionic strength I=0.1). This
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behavior is in apparent contradiction with basic thermodynamics, as usually the higher the pH
27
the more cations bind. Our combined titration, circular dichroism and dynamic light scattering
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study indicated that the change observed in Cu bond strength relates to a conformational change
29
of the structure of xanthan, which generates more chelating sites at pH 3.5 than at pH 5.5. This
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hypothesis was validated by the fact that the Cu sorption constants on xanthan were always
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higher than those measured on a mixture of Pyruvic and Glucuronic acids (LogK=2.2), which are
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the two constitutive ligands present in the xanthan monomer. This study shows the role of the
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structural conformation of natural biopolymers in metal bond strength. This finding may help to
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better predict the fate of Cu and other metals in acidic environmental settings such as aquatic
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media affected by acid mine drainage, as well as peats and acidic soils, and to better define
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optimal conditions for bioremediation processes.
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INTRODUCTION
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In a large number of both, natural and contaminated soils, the biogeochemistry of heavy metals
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and especially copper is controlled dominantly1,2 or at least significantly3–5 by their interaction
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with natural organic matter (NOM). Studies on interactions between NOM and metals were
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explored very early both for humic material6 and for bacterial extracellular substances.7 These
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interactions were studied and quantified mainly via a macroscopic approach that represented the
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retention of trace metal elements (TME) by mechanisms of complexation with proton exchanger
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sites present in the organic matter. The two basic parameters used to determine the reactivity
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between the NOM for metal cations are the densities of the complexing sites of NOM and the
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strength of the bond measured by the complexation constant. A recent study has shown that the
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densities of the sites on the different constituents of NOM are relatively homogenous: 1 to 5
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mmol/g dry weight.8
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However, the complexation constants between the transition metals Me and organic matter
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(logKMe-NOM) calculated for the different constituents of the NOM, namely free bacteria,
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biofilms, exopolymeric substances, humic substances, soils, sediments and sludges) present
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much higher variations. This affinity varies as a function of the nature of the metals that tend to
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complex the substrates more or less strongly. But for a given metal these variations of constants
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can reach four units for the log K values, which means four orders of magnitude for the constant.
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The largest amount of data concerns the affinity constants of copper for NOMs. For example,
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regarding the carboxylic surface site of bacterial free living cells, LogKCu-Bacteria varies from 3.8
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to 69–13 , for humic substances LogKCu-Humic/Fulvic_acids varies from 2.5 to 3.8
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. Regarding
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activated sludges (that can be considered as mixtures of biofilms and humic substances since
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they are dosed with EPS, proteins, and nucleic and humic acids), LogKCu-activatedSludge varies from
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3 to 4.5.16,17
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This variability of constants has been little studied and has not or only rarely been explained,
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thus limiting the use of these data in modeling and predicting the fate of TMEs in the
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environment. Determining these constants is partly dependent on experimental and modeling
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conditions, as different effects affect the numerical values of metal-ligand constants of complex
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substrates, e.g. the operational definition of the total concentration of complexing surface sites,
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the analytical uncertainties affecting the proton mass balance calculations, correlative effects
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during fitting, the variable handling of apparent equilibrium states and electrostatic model
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assumptions. The Supporting Information section (SI) provides more explanatory details. Some
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authors have explained the increase of affinity of bacteria for metals with ageing.18,19 More
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recently the variation of the affinity of bacterial surfaces with metals has been studied as a
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function of time and external stresses to which bacterial strains are subjected.20 As indicated by
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the authors, the increase of metal sorption observed could be linked to an increase in the
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concentration in exopolysaccharides (EPS) or an increase in the intrinsic affinity of the substrate
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for metals. On the basis of another approach,21 affinity varying as a function of different
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substrates has been highlighted. The affinity of cadmium for the EPS produced by Rhizobium
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meliloti is preponderant in comparison to soil components and aqueous suspended matters. A
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study that compared the sorption of cadmium on four bacteria and their EPS concluded that the
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affinity of cadmium was finally very similar on these substrates.22 Overall, a considerable
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affinity of substrates for metals has been observed but not explained. These considerable
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variations suggest intrinsic differences of affinity of substrates for metals, i.e. variable bond
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strengths developed between the substrate and a given metal.
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The regular composition and pattern of exopolysaccharides (EPS) makes them good models
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for the detailed study of interactions between metals and organic substrates.23 The retention of
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metals by chitin and chitosan has been studied as well.24 With xanthan, a reduction of its
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viscosity with an increased concentration of absorbed bivalent cations has been observed. The
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13
C nuclear magnetic resonance (NMR) data have shown that the main association of cations on
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xanthan occurs on the pyruvates located at the end of the lateral chain of different monomers,25
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thus sorption involving the ends of different monomer chains. The study therefore supports the
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existence of intermolecular and intra-molecular “chelating” sites. The formation of this type of
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link certainly affects the stability of the metals sorbed. It could explain the variability of the
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constants observed between different metals. In addition, pH conditions may affect the
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conformation of biopolymers. Chemical equilibrium studies performed on organic polymers are
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rarely combined with studies investigating the unitary components of these polymers and do not
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take into account the conformation of these molecules with complex structures. In addition, the
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parameters affecting the conformation of these polymers (pH, ionic strength, T°) are not all
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controlled and monitored. However, we think that this information is vital to better understand
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the sorption capacity of metals on biopolymers and their variability.
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The objective of our study is therefore to determine the role of the conformational structure of
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biopolymers in the binding strength of metal complexes. Our aim is to show the extent to which
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the structure can explain the variations of sorption properties. We propose to study the reactivity
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of a model bacterial EPS, xanthan, to copper. Xanthan was chosen as a model EPS since we have
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detailed knowledge of its chemical structure and its acid-base properties.8 Copper Cu(II) was
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chosen as a model metal cation since, firstly, it is representative of urban and agricultural
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pollution26–29, secondly, it is known to have a specific affinity for organic matter;9,13,30,31and
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thirdly, free Cu2+ is easy to measure in aqueous solution using potentiometric methods.
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The study couples the determination of the constants of complexation of copper by xanthan
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performed by modeling experimental sorption data, with the characterization of molecule
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conformation for the different pHs tested. This affinity is compared to the simple ligands present
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in xanthan. Significant changes in sorption properties linked to the conformation of the molecule
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are highlighted and discussed in relation to the global reactivity of the simple and chelating
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ligands of the NOM.
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Material and Methods Titrations performed at fixed total Copper concentrations.
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50 ml of a solution containing 1 g/L xanthan and 0.028, 0.046 and 0.13 mmol/L Cu2+ total
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concentrations from Cu(NO3)2 stock solutions (Cu(NO3)2x2.5 H2O, SIGMA ALDRICH) were
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titrated from pH 3.0 to pH 10.0 (and from pH 10.0 to pH 2.75) with 0.1 M NaOH (or 0.1 M
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HNO3, both from Titrisol Merck). As verified through PHREEQC modeling32 Nitrate complex
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less than 12% of Cu(II) ions in the given conditions. A previous combined 13C and 1H NMR,
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chromatographic and titrimetric analysis revealed that proton and cation sorption properties are
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due to its monocarboxylic functional groups. The determined proportions of pyruvic and
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glucuronic groups were 33 and 66%, respectively.8 To compare the sorption properties of the
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entire polymer to its specific reactive site in glucuronic and pyruvic sugars, solutions containing
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1 mmol/L Glucuronic acid (GlcA) (D-(+)-Glucuronic acid γ-lactone, ≥99%, SIGMA-Aldrich)
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and 1 mmol/L Pyruvic acid (PyrA) (SIGMA-ALDRICH, 98%), i.e. a total site concentration of 2
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mmol/L carboxylic functional groups, were titrated under equivalent conditions. This mixture of
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monomeric acid-base reactive ligands (present in xanthan in polymerized form) is hereafter
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referred to as ‘equivalent mixture’. The proportion of each PyrA and GlcA at 50% compared to
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their occurrence at 1/3 – 2/3 in xanthan EPS analyzed by us stemmed from the initially unknown
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ratio, which was not unique and varied according to the bacterial strain and the chemical
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environment.33
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Free copper [Cu2+] concentrations were obtained in the solution from a concentration-
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calibrated Metrohm 6.0502.140 copper-specific electrode and a Metrohm 6.0733.100 Ag/AgCl
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reference electrode calibrated to Cu2+ concentration standards. The concentrations of complexed
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copper and protons were both calculated from the difference in the mass balance of total
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introduced concentrations minus the free concentration. All the solutions were prepared in a
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0.100 M NO3- background medium, with Na+ as the dominant counter-ion. As more detailed in
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the supporting information, this allowed fixing ion activities and xanthan surface electrostatics
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reducing thereby the number of adjustable parameters in the fitting process. Other experimental
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conditions (potential stabilization criteria, CO2 exclusion) were the same as those of the
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experimental procedures given in.8 All the experiments were triplicated
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Copper-sorption isotherms.
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Xanthan solutions (70 mL at 1 g/L) and the equivalent mixture solution at equivalent
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concentrations were titrated stepwise at fixed pH=3.5±0.1 and 5.5±0.1 with a total copper
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concentration [Cu2+]tot = 10-3 mol/L containing titrant solutions delivered by a Metrohm Titrino
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burette controlled by the TIAMO Metrohm software. The pH was fixed by a base (0.1 mol/L)
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supplied by a 718 pH-Stat Titrino (Metrohm) programmed independently. Other experimental
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conditions were the same as those given above. All the experiments were triplicated.
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Equilibrium modeling.
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Xanthan is assumed to complex copper(II) ions via its monocarboxylic functional groups
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present in the polymer chains at a site density of 1.65 mmol/gdw (dw: dry weight). A combined
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NMR, chromatographic and titrimetric analysis revealed that 1/3 of them were due to the pyruvic
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group and 2/3 were due to the glucuronic group.8
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The GRFIT code,34 an FITEQL substitute,35 was as used to model the acid-base and Cu
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equilibrium data.
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The model developed is described in detail in the results section and is based on the 1 pK
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xanthan acid-base constant determined previously.8
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Circular dichroism.
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In order to characterize the modification of the xanthan conformation with pH, circular
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dichroism experiments were performed in 0.1 cm to 0.5 cm optical path cells on xanthan
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solutions in the pH range 2.7 to 11.0 (1 g/L, in 0.1 mol/L KF ionic medium - including small
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amounts of HCl to fix the pH), from 190 to 260 nm (CD6 JOBIN YVON at the Institut de
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Biologie Structurale –IBS- CEA Grenoble).
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Dynamic light scattering.
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Spectra of 1g/L xanthan solutions between pH 3.0 and pH 7.3 (in 0.1 mol/L KF ionic medium,
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including small amounts of HCl to fix the pH) were obtained on a high performance light
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scattering device (ALV/CGS-8F S/N 069, at CERMAV – CNRS – Grenoble) operating at a laser
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wavelength of 632.8 nm and at a maximum power of 35mW. The results were obtained at an
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angle of 90°.
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RESULTS
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The metal sorption study below is based on a previous acid-base study.8
Copper titrations.
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The percentages of copper complexed to xanthan and to the equivalent mixture (i.e. mixture of
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monomeric glucuronic acid (GlcA) and pyruvic acid (PyrA) obtained at 0.1 ionic strength and
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0.023, 0.046, 0.13 mmol/L total copper concentrations [Cutot]) are given in Figure 1.
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Above pH ~6 the concentration of adsorbed Cu ([Cuads]) for both xanthan and the ligand
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mixture increased to 100%. This agrees with the formation of aqueous Cu(OH)2 and the
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precipitation of solid Cu(OH)2(s). Model calculations attest that below pH 5.9 the Cu+2 activity
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will not be oversaturated with respect to tenorite or other more soluble Cu oxides/hydroxides. In
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this pH < 5.9 range, the xanthan and ligand mixture curves differed considerably. Cu sorption on
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xanthan was higher than the sorption on the equivalent mixture whatever the pH. For the ligand
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mixture, sorption started at pH 3 and increased up to 25% of adsorbed [Cutot] at pH 5.5.
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Regarding xanthan, sorption started at an initial titration pH of 2.7 and increased up to 40 to 50%
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of adsorbed [Cutot] at pH 3.5. Then, the sorbed copper decreased to about 25 to 37% of [Cutot] at
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pH 5.5. Thus, surprisingly, between pH 3.5 and 5.5, the sorbed Cu concentration decreased as pH
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increased. This unusual sorption pattern has never been described before. Cu-xanthan sorption
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isotherms at pH 3.5 and 5.5, obtained separately, confirmed the original sorption trend (Figure
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2): concordantly, [Cu]ads for xanthan exceeded [Cu]ads in the ligand mixture at both pH values,
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and [Cu]ads for xanthan at pH 3.5 exceeded [Cu]ads for xanthan at pH 5.5, contrary to the
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equivalent mixture data. Thus the Cu-pH and Cu-isotherm experiments performed independently
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concurred. This confirms and questions the unusual sorption pattern, while simultaneously
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raising questions on why this unusual sorption behavior occurred. Indeed, the decrease of sorbed
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copper at increasing pH is a priori energetically unfavorable, since the dominant aqueous Cu2+
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species compete with protons for sorption sites the more the pH decreases. Consequently [Cuads]
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should increase with increasing pH. The results suggest that a concurrent process more than
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balances the proton-Cu competition effect. Such a process could be linked to a conformational
200
change of the xanthan substrate.
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202
Xanthan conformation.
203
The molecular dichroism and light scattering measurements showed that the conformation of
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xanthan changed drastically with pH (Figure 3). As for the dichroism data, high pH spectra (pH
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8.3, 6.2, 5.1) reached their maxima at 204nm and their minima at 222nm. Conversely, acidic
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spectra (pH 2.7 and 3) shifted to a higher wavelength, with the maxima shifting to 210nm and
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the minima to 232nm. The amplitude also appeared to be lower (Figure 3a). The spectra obtained
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at pH 4 are intermediate between the acidic and basic groups. Similarly, light scattering spectra
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(Figure 3b) may also be distinguished in two families. Neutral pH radius distributions (pH 7.3,
210
7.2, 5.4) have a single peak pointing to a hydrodynamic particle radius of 32nm to 36nm with a
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polydispersity (PDI) of 0.247 to 0.297. At low pH another hydrodynamic radius prevails (127nm
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for pH 3.03, PDI=0.354), pointing to a change in molecular aggregation. The pH 4.0 distribution,
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whose amplitudes are almost equal at both hydrodynamic radii (22nm and 160nm, PDI=0.441),
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appears to be the intermediate state in terms of molecular aggregation. These measurements
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show a change in xanthan conformation and/or aggregation dependent on pH. By considering the
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references36,37, the ordered state should prevail at neutral pH and the disordered state at acidic pH
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(Figure S2). Both dichroism and light scattering data indicate a change of state at
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pHtransition=4.0±1 for an ionic strength fixed at I=0.1.
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Titration modeling.
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For memory, the previous characterizations showed that the xanthan monomer weighs 900
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Daltons, that it contains respectively 0.5 PyrA and one GlcA per monomer and that the site
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density determined from structural and spectroscopic constraints equals 1.65 mmol sites/gdw.8
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These studies yielded the single pKaI=0.1 = 2.59 ± 0.05 acid-base equilibrium constant. This is
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the basis for modeling the copper sorption data at an ionic strength of I=0.1. It is based on the
225
non-electrostatic modeling approach.
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The copper data model is based on the simplifying assumption that a change of the
227
conformational state of xanthan affects metal chelation and thus metal sorption constants but not,
228
or only insignificantly, the acid-base constants of the carboxylic functional groups involved.
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As shown above, the experimental results indicate that the conformational change of xanthan
230
affects Cu-xanthan bond strength. This means that the corresponding complexation constant
231
becomes a function of pH. In classical thermodynamics such changes do not occur, changes of
232
complexation constants therefore cannot be easily integrated in existing speciation codes.
233
Integrating a change dependent on the ordered state of xanthan required defining an original
234
stoichiometric setup. The change from a disordered (low pH, Xd-) to an ordered (high pH, Xo-)
235
state is represented through a 1 pK protonation reaction in which, conceptually, no proton is
236
exchanged between the reactant and the product. As the ordered/disordered transition is effective
237
between pH 3 and 7, we initially and arbitrarily fixed the pK value of the transition at 5.0 and
238
optimized the constant value during the modeling of the experimental sorption curves. The final
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pKtransition was equal to 4.5.
240 241
Xd- Xo- + H+ ; Ktransition = 10-4,5
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In this deliberately non equilibrated reaction, Xd- and Xo- represent both deprotonated carboxyl
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sites in the disordered and ordered states. The (Xd-) and (Xo-) activities are equal at pH 4.5, the
245
conformation transition pH defined accordingly agrees with that determined from light scattering
246
experiments (pH 4±1). The conformational change modeled extends over two pH units, i.e. at pH
247
5.5 and pH 3.5 most of the carboxyls (91%) are in the ordered and disordered states,
248
respectively. This also agrees with our experimental dichroism and light scattering data, as they
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show a conformational evolution over about two pH units. This approach thus allows smartly
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combining chemical speciation and molecular conformational changes, which are usually not
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expressible together on such a compact and robust base.
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The whole reactions taken into account and their stoichiometries are given in Table 1. The
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protons relating to the conformational states of xanthan between the ordered and disordered state
254
are written in brackets. It is important to understand that these protons are virtual, they do not
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enter in the mass balance calculation for each chemical species and are defined as follows:
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[XdH] + [Xd-] + [Xo-] + [XdCu+] + [XoCu+]
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For xanthan:
[Xan]tot
=
258
For copper:
[Cu]tot =
[Cu2+] + [XdCu+] + [XoCu+] + [CuOH+] + [Cu(OH)2]
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For protons:
[H]tot =
[H+] - [OH-] + [XdH] - [CuOH+] - 2[Cu(OH)2]
260 261 262
We underline that the concentration of XoH was very low compared to the other species and was therefore not considered in the data modeling.
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These mass balances thus differ from those calculated mathematically by the equilibrium
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analysis GRFIT,34 a code which necessarily also includes the protons representing the
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conformational state (brackets in Table 1). The LogK value of the XdH/Xd- is then equal to the
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sum of the pKtransition (4.5) and the xanthan protonation constant (pKa =2.6, Table 1).
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This model definition allows associating two different copper complexation constants for the
268
ordered and disordered state, respectively. The fitted Cu-xanthan constants are finally equal to
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LogK=2.5 for a high pH and LogK=2.9 for a low pH and are presented in Table 1. In Figure 1
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the optimized model fits the data points related to xanthan well by first increasing from pH 2 to
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3.5 and then decreasing from pH 3.5 to 5.5. In the copper isotherms (Figure 2) the model also
272
follows the trend of the data points for xanthan. The model thus adequately reproduces the
273
xanthan sorption pattern, demonstrating its ability to reproduce the conformation-dependent
274
change of the Cu-xanthan bond strength. Figure S1 represents the corresponding speciation
275
diagrams. It is noteworthy that the proton charge curve changes only slightly in the presence or
276
absence of copper. Cu interacts only weakly with protonated sites, therefore the proton charge
277
curve did not yield useful information for the evaluation of the reaction stoichiometries and is
278
not shown.
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Contrary to xanthan, the titrations of the equivalent mixture present the usual pH-dependency
280
for Cu sorption. Fits based on the adjustment of a single site acid-base exchange constant give a
281
pKaI
282
showing that the Cu-ligand mixture complexes are clearly weaker than the Cu-xanthan
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complexes for both ordered and disordered states (Figures 1 and 2). Moreover, this constant is
284
0.5 log units higher than the theoretical Cu-PyrA and Cu-GlcA constants (LogKI=0.1=1.6 for both,
285
Table 2). We consider this difference to be related to the keto-diol condensation reactions,
286
leading to the dimerization of the two acids.8,38. Such reactions depend on pH and may be slow.
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The non-ideal curvature of the data curves observed (non-smooth slope increase in Figure 1, and
=0.1
= 2.74±0.05,8 yielding a mean copper complexation constant LogKCu-LI=0 = 2.2 and
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unusual bending at high log[Cu2+]aq in Figure 2) is probably related to the kinetics of this
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condensation reaction. This dimerization thus increases the copper complexation strength of the
290
component acids. We therefore consider the unbound Cu-constants of PyrA and GlcA as
291
reference states.
292 293
294
Discussion
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This study questions whether the conformation of biopolymers impacts the bond strength of
296
complexing metals. This is addressed by comparing the Cu(II)-xanthan bond strength at
297
various pH to that of Cu(II) ions complexing a mixture of xanthan constituting monomeric
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ligands (i.e. glucuronate and pyruvate).
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The effect of pH on Cu complexation strength.
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Xanthan definitely presents unusual sorption behavior as Cu sorption decreases at increasing
301
pH between pH 3.5 to pH 5.5. According to equilibrium thermodynamics, and by considering all
302
the existing literature on cation sorption on natural biopolymers, copper(II) sorption should
303
increase with pH as the competition between protons and Cu(II) ions for sorption sites decreases
304
with increasing pH. Light scattering and dichroism measurements both indicate that the
305
conformation of xanthan changes between pH 3.5 and 5.5. The parallel between these two
306
phenomena and the change in Cu binding strength lead us to assume that they are linked, i.e. that
307
the conformational change of xanthan affects Cu(II)-xanthan bond strength.
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Persistence length (q) measurements expressing the polymer rigidity on the basis of solution
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viscosity measurements showed that xanthan changes strongly its q value dependent on ionic
310
strength, temperature and pH. Thus, high q values of 110 to 150 nm are obtained in high ionic
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strength conditions and ambient temperature (0.01 ≤ I ≤ 0.1, T=25 °C).37,39–47 This q value
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represents about 10 times the rigidity of cellulose and compares to double strained DNA (q = 150
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nm, high ionic strength), or to triple helix structures, e.g. schizophyllan (q = 150-200 nm) or
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collagen (q = 170 nm).48 Thus, at high ionic strength xanthan has an astonishingly high rigidity
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representative of a high molecular order state.37,40,41,44,45,49,50
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At high temperature (T>60°C, I kept constant) or at low ionic strength (I
337
4 induces an ordered state (helix) (Figure S2). The combination of this result to titration data
338
leads to the conclusion that the disordered state increases the Cu-xanthan bond strength.
339
The effect of ligand nature on Cu-complexation strength.
340
At both pH 3.5 and 5.5, the bond strength of the Cu-xanthan complex (mean LogKCu-Xanthan
341
equal to 2.9 and 2.5) is higher than that developed between Cu and the equivalent monomer
342
mixture (i.e. pyruvate and glucuronate; 1.6 ≤ LogKCu-Ligand ≤ 2.2; Table 2). This indicates that
343
the biopolymer structure increases Cu sorption strength whatever the conformational state. Thus
344
this result further validates the initial working hypothesis that the polymeric nature of xanthan
345
increases Cu bond strength
346
Comparison of referenced Cu-xanthan bond strength data.
347
Table S1 lists model ligands and associated Cu binding constants.60 The bond strength between
348
Cu and carboxyl-bearing model ligands increases in the following order: monocarboxylic ligands
349
(LogKI=0.1~1.7) < keto-carboxylic ligands (1.4 ≤ LogKI=0.1 ≤ 2.15)
350
monocarboxylic ligands (LogKI=0.1~ 2 ) < 2-Hydroxo-monocarboxylic ligands (LogKI=0.1~2.5)
4.5). Thus five- and six-ring coordination form the
352
strongest chelates for dicarboxylic moieties.61 Increasing the ring size of dicarboxylic acids
353
strongly decreases bond strength (Table S1). At nine ring atoms (e.g. pimelic acid, Table S1) the
354
bond strength decreases to that of monocarboxylic moieties. This accounts not only for Cu(II),
355
but also for Zn(II) and Cd(II) constants.18
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