Sabrina Fabris

Federico Momo
email: momo@unive.it

Giampietro Ravagnan

Roberto Stevanato

ANTIOXIDANT PROPERTIES OF RESVERATROL AND PICEID ON LIPID PEROXIDATION IN MICELLES AND MONOLAMELLAR LIPOSOMES

The antioxidant activities of trans-resveratrol (trans-3,5,4'-trihydroxystilbene) and transpiceid (trans-5,4'-dihydroxystilbene-3-O-β-D-glucopyranoside), its more widespread glycosilate derivative, have been compared measuring their inhibitory action on peroxidation of linoleic acid (LA) and the radical scavenging ability towards different free radicals (such as DPPH) and radical initiators. It has been found that the two stilbenes have similar antioxidant capacity, while the comparison with BHT (2,6-di-tert-butyl-4-methylphenol) and αtocopherol (vitamin E, vit. E), taken as reference, points out a slower but prolonged protective action against lipid peroxidation. Furthermore, piceid appears more efficacious than resveratrol as a consequence of the reaction of the latter with its radical form.

The DSC profiles of phosphatidylcholine liposomes of various chain lengths, and EPR measurements of spin labelled liposomes demonstrated that the susceptible hydroxyl group of these compounds are located in the lipid region of the bilayer close to the double bonds of polyunsatured fatty acids, making these stilbenes particularly suitable for the prevention and control of the lipid peroxidation of the membranes.

INTRODUCTION

It is known that a diet rich in fruit and vegetables helps to prevent cardiovascular diseases, cancer, and ageing-related disorders [START_REF] Willet | Eat, Drink, and Be Healthy: The Harvard Medical School Guide to Healthy Eating[END_REF].

The effect can be traced back to the antioxidant activity of polyphenols of fruits and vegetables, able to inhibit lipid peroxidation, forced by free radicals, and related to chronic health problems like cancer, arthrosclerosis and ageing [START_REF] Marnett | Oxyradicals and DNA damage[END_REF][START_REF] Halliwell | Free Radicals in Biology and Medicine[END_REF][START_REF] Esterbauer | Chemistry and pathophysiology of oxidation of LDL[END_REF]. In particular resveratrol, a polyphenol mainly present in grapes and red wine, demonstrated interesting biomedical properties for its inhibitory effects on cancer promotion and propagation [START_REF] Fremont | Biological effects of resveratrol[END_REF], cardioprotective action due to inhibition of the oxidation of low-density lipoprotein (LDL) [START_REF] Frankel | Inhibition of human LDL oxidation by resveratrol[END_REF] and of platelet

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3 aggregation [START_REF] Bertelli | Antiplatelet activity of synthetic and natural resveratrol in red wine[END_REF][START_REF] Pace-Asciak | The red wine phenolics trans-resveratrol and quercetin block human platelet aggregation and eicosanoid synthesis: implications for protection against coronary heart disease[END_REF], anti-inflammatory activities and preventive effect on Alzheimer's disease and dementia [START_REF] Dorozynski | Wine may prevent dementia[END_REF].

Recently it was found that, in the grape juices, the average concentration of piceid, the glycoside form of resveratrol, is seven times that of resveratrol [START_REF] Romero-Perez | Piceid, the major resveratrol derivative in grape juices[END_REF] and this is probably the most abundant form of resveratrol in nature [START_REF] Regev-Shoshani | Glycosylation of resveratrol protects it from enzymic oxidation[END_REF].

A number of studies hypothesise that piceid may have biomedical properties similar to those above mentioned for resveratrol: anticarcinogenic effects [START_REF] Soleas | Do wine polyphenols modulate p53 gene expression in human cancer cell lines?[END_REF][START_REF] Jang | Cancer chemopreventive activity of resveratrol, a natural product derived from grapes[END_REF] and inhibition of platelet aggregation [START_REF] Chung | An antiplatelet principle of Veratrum formosanum[END_REF][START_REF] Orsini | Isolation, synthesis, and antiplatelet aggregation activity of resveratrol 3-O-beta-D-glucopyranoside and related compounds[END_REF] and of oxidation of LDL [START_REF] Pour Nikfardjam | Resveratrol-derivatives and antioxidative capacity in wines made from botrytized grapes[END_REF].

The aim of this work is to understand if, by analogy, piceid has also antioxidant properties comparable to resveratrol.

Unfortunately the antioxidant capacity of a compound and its effectiveness in preventing diseases cannot be unequivocally determined. Roughly the experimental methods can be grouped into two classes, based on hydrogen atom transfer (HAT) and on single electron transfer (ET) [START_REF] Huang | The chemistry behind antioxidant capacity assays[END_REF]. Therefore, we studied the antioxidant activity of resveratrol and piceid in terms of their inhibitory action on peroxidation of linoleic acid (LA), an HAT assay, and as radical scavenging ability towards 2,2'-diphenyl-1-picrylhydrazyl (DPPH method), an ET assay. The scavenging reaction of resveratrol is accompanied by the formation of a product which is not formed in the analogue reaction of piceid, and the data support the hypothesis of a reaction between one molecule of resveratrol and one molecule of its radical. This point, the possibility that an antioxidant may react with itself, is of general interest and must be accounted for in evaluating the antioxidant activity of a molecule.

At membrane level there is an assumed relationship between the rate of lipid peroxidation and membrane composition and fluidity [START_REF] Mowri | Effect of lipid composition of liposomes on their sensitivity to peroxidation[END_REF][START_REF] Viani | Studies on peroxidation processes of model membranes and synaptosomes: role of phosphatidic acid[END_REF][START_REF] Mclean | Effect of lipid physical state on the rate of peroxidation of liposomes[END_REF], implying that the efficacy of an antioxidant can be meaningfully modulated by its collocation inside the bilayer. From this point of view, liposomes are much more representative models of biological membranes than micelles, so Data point out how both these compounds are located in the lipid region of bilayer close to double bounds of LA and have, on average, a slower but longer antioxidant capacity than BHT and α-tocopherol taken as reference (fig. 1).

The comparison between micelles and monolamellar liposomes demonstrated as well that the inhibitory effect of vit. E, measured in liposomes, is about one half the same effect when measured in micelles. This will be explained in terms of a different accessibility of the phenolic groups of vit. E to the double bonds of unsaturated lipid chains, and demonstrated that the true antioxidant power of vit. E could be overestimated by usual measurements in micelles.

Materials and methods

Chemicals

All chemicals, of the highest available quality, were obtained from Sigma Chemical Co. (St.

Louis, USA). ABIP was a kind gift of Wako chemicals USA. Trans-piceid and transresveratrol, with a purity grade higher than 99%, have been supplied by the Istituto Agrario di S. Michele all'Adige (IT) [START_REF] Ravagnan | Use of extracts from spermatophyte plants with immunomodulating activity[END_REF]. The aqueous solutions were prepared with quality milliQ water.

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Inhibition of lipid peroxidation

The antioxidant activity of resveratrol and piceid to prevent LA peroxidation was studied in sodium dodecyl sulfate (SDS) micelles and in monolamellar liposomes of DPPC.

The peroxidation was initiated by the thermolabile water-soluble azo initiator 2,2'-azobis[2-

(2-imidazolin-2-yl)propane] (ABIP) and measured as rate of oxygen consumption. The reaction was carried on in a closed thermostated vessel (37 °C) and the oxygen consumption was followed using a Clark electrode.

In SDS micelles (50 mM) the concentration of LA was 10 mM, while in DPPC monolamellar liposomes (20 mM) LA was 2.5 mM; the choice of the concentrations was the result of a series of tests at different concentrations and represents the best compromise between a high rate of peroxidation and a minor change in lipid organization due to LA [START_REF] Castelli | Dipalmitoylphosphatidylcholine/linoleic acid mixed unilamellar vescicles as model membranes for studies on novel free-radical scavengers, 37[END_REF]; in both cases we used phosphate buffer (50 mM, pH 7.4).

To the solution, previously equilibrated with air and kept at constant temperature (37 °C), the azo initiator ABIP (4 mM final concentration) was injected; and the oxygen consumption was monitored. After a few minutes an ethanol solution of antioxidant was added (2•10 -6 M final concentration). Every experiment was repeated three times.

The antioxidant capacity was calculated as change of slope of oxygen consumption before and after the addition of the antioxidant; in particular it is expressed by the percentage inhibition of the peroxidation [START_REF] Zhou | Antioxidative effects of flavonols and their glycosides against the free-radical-induced peroxidation of linoleic acid in solution and in micelles[END_REF]:

100 % ⋅ - = p inh p inh R R R P
Where R p is the rate of propagation of lipid peroxidation due to ABIP and R inh is the rate of inhibition of peroxidation after the addition of antioxidant.

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2,2-Diphenyl -1-picrylhydrazyl (DPPH) Radical Scavenging Capacity Assay

This method is based on the capacity of an antioxidant to scavenge the stable free radical DPPH [START_REF] Blois | antioxidant determinations by the use of a stable free radical[END_REF]. In the reaction DPPH goes through a change of color so its disappearance can be monitored spectrophotometrically at 515 nm (ε = 10800 M -1 cm -1 ) [START_REF] Fauconneau | Comparative study of radical scavenger and antioxidant properties of phenolic compounds from Vitis vinifera cell cultures using in vitro tests[END_REF]. The reaction was carried on at 25 °C in ethanol at various antioxidant concentrations (12.5, 25, 50 μM), while that of DPPH was fixed at 100 μM.

The radical scavenging ability towards DPPH was calculated as decrease of DPPH concentration in the first 40 seconds of reaction and expressed as initial reaction rate (V 0 ).

Reaction between radical initiators and antioxidants

Our compounds absorb in the UV region, so it is possible to follow spectrophotometrically their reaction with ABIP measuring their disappearance in the time.

Resveratrol and piceid show the same molar absorptivity, that is ε 317 = 30000 M -1 cm -1 , while for BHT is ε 272 = 1100 M -1 cm -1 .

The buffer solution and the reaction temperature conditions were the same of lipid peroxidation and the initial rate is calculated in the first 5 minutes of reaction.

The very high hydrophobicity of vit. E made the determination of its reactivity with ABIP impossible in water solution.

Liposome preparation

Multilamellar vesicles were prepared following the method of Kusumi et al. [START_REF] Kusumi | Oxygen transport parameter in membranes as deduced by saturation recovery measurements of spin-lattice relaxation times of spin labels[END_REF].

Phospholipids were dissolved in a 2:1 chloroform methanol mixture then dried with a stream of nitrogen gas and kept under vacuum for at least 14 hours. The dried lipids were suspended, when not otherwise specified, in a HEPES 0.1M, pH 7.2, buffer. The lipid dispersion, with a

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vigorously with a vortex for 30 seconds five times and used just as obtained for DSC measurements. When required, spin labels (1.8 mM final concentration) were added to the chloroform methanol phospholipid mixture.

Unilamellar liposomes were prepared combining the freeze-thawing and extrusion protocol [START_REF] Mayer | Vescicles of variable sizes produced by a rapid extrusion procedure[END_REF], starting from a 500 μl, 40 mM, phospholipid suspension. Extrusion was performed using the Avestin Liposofast apparatus, with 100 nm pore size filters.

Determination of the partition coefficients

The liposome-water partition coefficients of resveratrol and piceid were experimentally determined as described in [START_REF] Momo | Interaction of fluoxetine with phosphatidylcholine liposomes[END_REF].

UV-VIS, DSC and EPR measurements

Spectrophotometric measurements were recorded on a UV-VIS Beckman DU 640 instrument equipped with a thermostated quartz cell.

Calorimetric experiments were performed on a Setaram DSC 92. About 50 mg of phospholipid dispersion was placed in an aluminium crucible, while an identical crucible was filled with an equivalent weight of HEPES solution and placed in the reference cell. The temperature scanning rate was 0.5 °C min -1 . The transition temperature T c from the gel-tofluid phase of liposomes was taken at the peak of the DSC profiles.

EPR measurements were performed on a Bruker ER 200 D, 9 GHz spectrometer. Samples were placed in a gas permeable TPX tube 1 mm i.d. (Wilmad, N.J. USA) and centered in the resonant cavity, then deoxygenated under nitrogen flow above T c for 10 min.

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Results and Discussion

Antioxidant activity 1.Inhibition of lipid peroxidation

Fig. 2 shows the oxygen consumption vs time of the ABIP-initiated lipid peroxidation in LA/SDS micelles. The oxygen concentration stays unchanged till the addition of ABIP: when ABIP is added, the oxygen concentration decreases with a rate of 4•10 -7 M s -1 ; this rate is differently slowed down by the antioxidants: vit. E and BHT are able to stop almost completely the peroxidation reaction for an inhibition period (t inh ) of a few minutes, during which the consumption of oxygen is negligible; then the peroxidation restarts with roughly the same original rate of propagation of ABIP, as a consequence of the loss of the antioxidant capacity of the compounds. On the contrary, piceid and resveratrol do not display the inhibition time and their rates of oxygen consumption are almost constant and slower than those of BHT and vit. E after t inh . From this point of view, piceid and resveratrol could be considered less reactive antioxidants than BHT and vit. E, but having a prolonged protective effect against radicals.

The lipid peroxidation was studied in liposomial system too (fig. 3), as monolamellar liposomes are structurally more similar to cell membranes than micelles. In this case a lower rate of propagation was observed (4•10 -8 M s -1 ), which can be due both to the different concentration of LA in the two systems and to a different permeability of ABIP in the two matrices; the general trend of peroxidation inhibition is similar to that in micelles, with the exception of vit. E which, when inserted in a phospholipid bilayer, does not display any inhibition period and loses one half of its antioxidant power (fig. 4). The observation may be of some relevance because it demonstrates that the choice of a lipid moiety, micelles, rather than liposomes, can distort the scale of effectiveness of the antioxidants. Moreover, as it

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comes up from EPR studies, these molecules have different positions inside the bilayer, and this is a further modulating factor of their inhibitory action.

Radical scavenging capacity toward DPPH

It is commonly accepted that the first reaction step between an antioxidant and DPPH is the abstraction of a hydrogen atom from the antioxidant to give diphenylpicrylhydrazine (DPPH-H) and a phenoxyl radical [START_REF] Ancerewicz | Structure-property relationships of trimetazidine derivatives and model compounds as potential antioxidants[END_REF] which will undergo further reactions such as dimerization, complexation and donation of a second hydrogen atom [START_REF] Brand-Williams | Use of a free radical method to evaluate antioxidant activity[END_REF].

The initial rates V 0 of the reaction between DPPH and the antioxidants, as a function of the antioxidant concentration, are reported in fig. 5. At 50 μM concentration, vit. E shows a scavenging effect about 5 times faster than the other compounds; resveratrol and piceid, from this point of view, are not so efficient, but still remain comparable to BHT.

Reaction between radical initiators and antioxidants

Literature reports that antioxidant capacity of polyphenols is due to their ability to stop or to slow down lipid peroxidation, reacting with peroxyl radicals forming during the propagation phase [START_REF] Wright | Predicting the activity of phenolic antioxidants: theoretical method, analysis of substituent effects, and application to major families of antioxidants[END_REF][START_REF] Pryor | A rapid screening test to determine the antioxidant potencies of natural and synthetic antioxidants[END_REF]. Anyway, because by definition an antioxidant is a molecule able to react with all radicals present in the solution, we studied the reactivity of resveratrol and piceid toward ABIP, as the possibility exists that the lipid peroxidation is inhibited at the beginning by a direct interaction between antioxidants and radical initiators.

The consumption of antioxidant during the reaction with ABIP is plotted in fig. 6: resveratrol and piceid concentrations decrease with the time, while that of BHT stays constant, meaning that resveratrol and piceid, unlike BHT, react with ABIP.

At our experimental conditions, the kinetic rate constant of ABIP decomposition is 1.9•10 -4 min -1 [START_REF] Hanlon | The pH dependence of lipid peroxidation using watersoluble azo initiators[END_REF] and its rate of decomposition is 3.3•10 -7 M min -1 , which is almost identical to the

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value of 3.2•10 -7 M -1 min -1 we found for the initial rate of consumption of piceid, while that of resveratrol is 1.6•10 -6 M -1 min -1 , that is five times bigger.

This means that the rate of reaction between piceid and ABIP is limited by the thermolysis of ABIP and the production of carbon-centered amidinium radical. The higher rate of consumption of resveratrol implies secondary reactions between one resveratrol molecule and its radical form, generated from the reaction with ABIP, which can lead to the formation of new compounds, like dimmers, quinones and polymer. The formation of a secondary product is confirmed by the UV-VIS spectra which display two new bands with a maximum absorbance at 265 and 360 nm (fig. 7a), not present in the case of piceid (fig. 7b).

The reactivity of resveratrol and piceid towards initiators or stable free radicals, with trends similar to those reported in Fig. 6, is confirmed also with AAPH (2,2'-azobis(2amidinopropane)) and ABCPA (4,4'azobis(4-cyanopentanoic acid)), with the stable spin label TEMPO (2,2,6,6-tetramethyl-1-piperidinyloxy), with hydrogen peroxide and with the couple hydrogen peroxide-horseradish peroxidase (HRP), (data not shown). In all cases, BHT does not react, while we observe a faster decrease of resveratrol concentration with respect to piceid.

In literature it is generally accepted that the reaction between resveratrol and HRP-hydrogen peroxide leads to the formation of a resveratrol dehydrodimer known like δ-vinifrin [START_REF] Langcake | Oxidative dimerisation of 4-Hydroxystilbenes in vitro: production of a grapevine phytoalexin mimic[END_REF] which can be hardly identified with the secondary product we found. In fact, δ-vinifrin has an UV spectrum similar to resveratrol, centered at 307 nm [START_REF] Petez | Viniferin, a Resveratrol Dehydrodimer: One of the Major Stilbenes Synthesized by Stressed Grapevine Leaves[END_REF] and does not show the two bands at about 275 and 360 nm.

Thompson [START_REF] Thompson | Peroxidase-catalyzed oxidation of eugenol: formation of a cytotoxic metabolite[END_REF] demonstrated that the oxidation of eugenol by hydrogen peroxide in the presence of horseradish peroxidase (HRP) leads to the formation of a quinone methide which absorbs at 270 and 350 nm. We hypothesize, by analogy, that, also in our case, a quinone form of resveratrol is formed by the oxidative reaction (fig. 8). The discriminating factor

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11 between the different reaction pathways, leading to the quinone or to the dimer forms, is most likely the initial concentration of radical resveratrol: in fact the dimerization involves two radical molecules and is, by consequence, favored by a high concentration of radical resveratrol.

The question is now to understand the different behaviour between resveratrol and piceid, that differ only for a glycoside group in place of a hydroxyl group. Resveratrol has a phenol moiety, due to a hydroxyl group in 4'-position and a m-hydroquinone moiety due to hydroxyl groups in 3,5-positions (fig. 1). It has been demonstrated that the 4'-hydroxyl is the most reactive in scavenging free radicals because the corresponding phenoxly radical can delocalize the unpaired electron on the whole molecule [START_REF] Xu | A Dmol3 study on the reaction between trans-resveratrol and hydroperoxyl radical: dissimilarity of antioxidant activity among O-H groups of trans-resveratrol[END_REF][START_REF] Cao | Density functional theory calculations for resveratrol[END_REF], and it is possible that the most stable resonance form of the resveratrol radical is that where the unpaired electron is located in the 4-position close to 3 and 5 hydroxyl groups (fig. 8, form A). The lack of formation of a dimer of piceid could be explained on the same basis, as the substitution of an hydroxyl for a glycoside group makes the radical more stable for steric hindrance and prevents the reaction with an other molecule of piceid.

Interactions of antioxidants with membranes 2.1. Partition coefficients

The logarithm of octanol-water partition coefficient (log P) is used as a measure of the hydrophobicity of compounds and it is assumed to represent the general tendency of a chemical to partition between an aqueous and an organic phase. P is defined as P = (n oct /V oct )/(n w /V w ), where n denotes the number of moles of antioxidant, V the volume, and oct and w refer to octanol and water phase respectively.

It must be said that the notion of partition coefficient, when extended to liposomes/water dispersions, can be vague for a number of reasons, not least the difficulty of defining the

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volume of liposomes and considering it like a homogeneous phase; anyway it is commonly accepted and log P is used to quote the fraction of dopant adsorbed into the membrane.

The values of log P and the percent fraction (%) of antioxidant bound to liposomes in the gel state, are given in tab.1.

Data demonstrate that, as expected, the hydrophobicity is dependent on the substitution of the m-hydroxy group by a glucose residue, that makes piceid less hydrophobic than resveratrol; in any case both of them are quite lipophylic molecules, which, in a water dispersion of multilamellar liposomes are almost exclusively present in the lipid phase.

DSC studies

In Fig. 9 the DSC profiles of the gel-to-fluid state transition of DMPC (C14:0), DPPC (C16:0), DSPC (C18:0) multilamellar liposomes at increasing concentration of resveratrol and piceid are plotted.

Data show that the effects of resveratrol and piceid are similar: at increasing antioxidants concentration the DSC profiles are broadened and shifted towards lower temperatures; these effects are particularly evident in the case of piceid in DMPC liposomes where at 10 mM of the stilbene the transition is hardly detectable.

Because there is no reason to think that the interaction of resveratrol and piceid with DMPC is not the same as that of DPPC and DSPC, it is likely that the different behaviour in DMPC liposomes is related to the length of acyl chains: the longer are the acyl chains, the more stable and the less perturbable is the bilayer.

The spreading of the peaks suggests that the presence of the antioxidants induces the formation of defects in the ordered structure of membrane which is reflected in the fall of cooperativity; the decrease of transition temperature is a sign of a much looser bilayer. The

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13 contemporary featuring of these trends is usually determined by dopants localized in the interface region of bilayer.

EPR measurements

EPR spectra have been collected for stearic acids, spin labeled at the 5 th , 7 th , 10 th , 12 th and 16 th carbon positions (n-SASL) and incorporated in liposomes of DPPC, with and without dopants, as described in liposomes preparation.

The spectra were recorded below and above the gel-to-fluid transition temperature of DPPC with analogous results. Here we reported the values obtained in the gel phase and expressed as A max (the separation between the outer hyperfine lines) which is the most appropriate parameter for monitoring the effects of dopants in the gel phase [START_REF] Marsch | Electron Spin Resonance: Spin Labels[END_REF]. The differences between the A max values with and without antioxidant are reported in fig. 10.

As it emerges from the graph, the more marked variations of A max are related with the 7 th , 10 th and 12 th carbon positions for both the molecules, making plausible that the stilbenes compounds are located in this zone of bilayer, in some way anchored to the interfacial or polar region, with piceid closer to the membrane surface according to its higher hydrophilicity. As a consequence, this positioning facilitates the antioxidant action of the two molecules as the reactive hydroxy groups of resveratrol and piceid fall very near to the double bonds of polyunsatured fatty acid chains (PUFA) (fig. 11). Similar arguments are valid for BHT as well, which is a high lipophilic molecule, most likely located in the deepest region of the bilayer as can be gathered by analogy with 2,6-ditertbutylphenol [START_REF] Momo | Correlation between fluidising effects on phospholipid membranes and mitochondrial respiration of propofol and p-nitrosophenols homologues[END_REF].

Instead the hydroxy group of vit. E is close to the polar head groups of the phospholipids [START_REF] Buettner | The pecking order of free radicals and antioxidants: lipid peroxidation, αtocopherol, and ascorbate Arch[END_REF];

thus in the presence of lipid peroxidation, resveratrol, piceid and BHT can react more quickly with the peroxyl radical than vit. E for distance motives. It has been hypothesized [START_REF] Barclay | Autoxidation of biological molecules. 2. Autoxidation of a model membrane. Comparison of the autoxidation of egg lecithin phosphatidylcholine in water and in chlorobenzene[END_REF] that, once lipid peroxyl is formed, it diffuses to the surface of the membrane and in this way can be

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trapped by the hydroxy group of vit. E. If we suppose that this floating is faster in micelles than in the bilayer, we can explain the different activity of vit. E in liposomes and in micelles.

Conclusions

A univocal classification of the antioxidant substances is not easy, given the manifold types of reactions which are involved, and, actually, the antioxidant power coincides with the methods we use for determining it. Multiple tests, representative of various radical mechanisms, are perhaps the best strategy for stating an empirical and approximate scale of effectiveness.

In this paper resveratrol and piceid were compared with two common antioxidant like vit. E and BHT, in terms of inhibitory effect on lipid peroxidation and radical scavenging ability.

From this point of view, the following considerations can be underlined: i) resveratrol and piceid show similar behaviour as inhibitors of the lipid peroxidation; maybe piceid and resveratrol are, on average, slightly less efficacious than vit. E and BHT, but their slower reactivity against lipid peroxidation combined to a prolonged protective action, could be of interest in clinical or dietary applications;

ii) a greater reactivity with different types of radicals or initiators has been found for the stilbenes with respect to BHT, suggesting a wide action spectrum against radical injury, i.e. a potential preventive effect;

iii) the lipophilicity of resveratrol and piceid and their collocation into the membrane with the susceptible hydroxyl group close to the double bonds of PUFA, make these stilbenes particularly suitable for the prevention and control of the lipid peroxidation in membranes; iv) as demonstrated in the case of resveratrol, the possibility that an antioxidant may react with itself must be accounted for in evaluating the antioxidant activity of a

A

  C C E P T E D M A N U S C R I P Tthe peroxidation measurements were repeated in monolamellar liposomes. Contemporarily the interactions of resveratrol and piceid with multilamellar liposomes of satured L-αphosphatidylcholine (PC) of various chain lengths (dimyristoyl, DMPC, dipalmitoyl, DPPC, distearoyl, DSPC) were investigated, determining the partition coefficients of the drugs, the decay of the ordered lipid organisation they produce, and their position in membranes using differential scanning calorimetry (DSC) and spin labelling EPR techniques.

Fig. 2 .Fig. 3 .

 23 Fig. 2. Oxygen consumption during ABIP-initiated peroxidation of LA (10 mM) in SDS

Fig. 4 .

 4 Fig. 4. Percentage inhibition (P inh %) of the ABIP-initiated peroxidation of LA in SDS micelles and DPPC monolamellar liposomes after addition of antioxidants (2 μM); pH 7.4, T

Fig. 5 .

 5 Fig. 5. Initial reaction rate (Vo) of DPPH (100 μM) disappearance vs. antioxidant concentration at 515 nm and 25 °C in ethanol. vit. E; ▲ BHT; ■ resv; • pic.

Fig. 6 .Fig. 7

 67 Fig. 6. Decay of antioxidant concentration for the reaction with ABIP vs. time at 37 °C and pH 7.4. [antioxidant] = 2.5•10 -5 M, [ABIP] = 2•10 -3 M.

Fig. 8 .

 8 Fig. 8. Possible mechanism of reaction between resveratrol and a radical initiator.

Fig. 9 .

 9 Fig. 9. DSC profiles of the gel-to-fluid state transition of PC multilamellar liposomes (100

Fig. 10 .Fig. 11 .Fig. 11

 101111 Fig. 10. The differences (ΔA max ) between the A max values (in 10 -4 Tesla) with and without

Acknowledgments

The authors thank Fulvio Mattivi of the Istituto Agrario di S. Michele all'Adige (IT) for the supply of piceid and resveratrol.

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Francesco Crea

Concetta De Stefano

Nunziatina Porcino

Silvio Sammartano
email: ssammartano@unime.it

SEQUESTERING ABILITY OF PHYTATE TOWARDS PROTONATED BPEI AND OTHER POLYAMMONIUM CATIONS IN AQUEOUS SOLUTION ‡

Keywords: Poly(ethylenimine), Phytate, Complexes, Speciation, Sequestering ability

 hexakis (di-hydrogen phosphate) myo-inositol) [Phy] was studied potentiometrically. The measurements were carried out at t = 25 °C and at low ionic strength values, without addition of supporting electrolyte, to avoid interferences with other anions and cations. In order to simplify the data treatment, BPEI was considered as a simple tetramine. Different species Phy(BPEI)H j , with j = 6,7,8, and Phy(BPEI) 2 H 7 were found, having quite high stability. The ability of phytate to sequester BPEI was quantified by considering the parameter pL 50 , namely the concentration (-log [Phy] tot ) necessary to bind 50% of polyammonium cation (as trace). In our experimental conditions, for the system phytate-BPEI-proton we have pL 50 = 7.01, at pH = 7.4 and I = 0.04 mol L -1 . As for other phytate-polyammonium cation systems, the stability of the phytate-BPEI species is strictly proportional to the charges involved in the formation reactions. Therefore, it was possible to calculate the free energy contribution per bond, 0 b G Δ = 4.4±0.4 kJ mol -1 . The dependence on temperature and ionic strength of the stability of phytate-low/high molecular weight polyammonium cations species, was studied using some semiempirical equations and enthalpy data for the protonation of both components. The dependence on temperature of the stability is quite low and the variation of pL 50 in the range 15 ≤ t/°C ≤ 37 is less than 0.5 log units. On the contrary, the effect of ionic strength is highly significant, with a lowering of pL 50 of ≈ 2 log units (I = 0 to 0.15 mol L -1 ).

Introduction

Natural organic matter (constituted to a great extent by macromolecules) is quite rich in functional groups which act as binding sites for inorganic and organic cations or anions over a wide pH range. The study of the physical and chemical properties of natural organic matter is very difficult owing to the fact that in these macromolecules, the protonation and complexation reactions depend on several factors, such as molecular weight, distance between functional groups, distribution of binding sites and structure

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(in terms of cross linking, etc.). To simplify the thermodynamic study of some natural organic molecules, such as humic and fulvic acids [START_REF] Stevenson | Humus chemistry, composition, reactions[END_REF], often high molecular weight polyelectrolytes were chosen as model molecules in order to obtain information about the behaviour (acid-base properties and complexing ability) of natural macromolecules.

The literature reports several thermodynamic data for the interaction properties of some high molecular weight polyelectrolytes [START_REF] Stefano | Polyacrylates in aqueous solution. The Dependence of Protonation on Molecular Weight, Ionic Medium and Ionic Strength[END_REF][START_REF] Stefano | Thermodynamics of proton association of polyacrylates and polymethacrylates in NaCl(aq)[END_REF][START_REF] Stefano | Speciation of Organic Matter in Natural Waters-interaction of polyacrylates and polymethacrylates with major cation components of seawater[END_REF][START_REF] Crea | Modelling of natural synthetic polyelectrolyte interactions in natural waters by using SIT, Pitzer and Ion Pairing approaches[END_REF][START_REF] Crea | Binding of acrylic and sulphonic polyanions by open-chain polyammonium cations[END_REF]; in particular these data regard the acidbase properties of polycarboxylates and their interactions with alkali, alkaline earth metals [START_REF] Stefano | Polyacrylates in aqueous solution. The Dependence of Protonation on Molecular Weight, Ionic Medium and Ionic Strength[END_REF][START_REF] Stefano | Thermodynamics of proton association of polyacrylates and polymethacrylates in NaCl(aq)[END_REF][START_REF] Stefano | Speciation of Organic Matter in Natural Waters-interaction of polyacrylates and polymethacrylates with major cation components of seawater[END_REF][START_REF] Crea | Modelling of natural synthetic polyelectrolyte interactions in natural waters by using SIT, Pitzer and Ion Pairing approaches[END_REF] and some low molecular weight polyamines [START_REF] Crea | Binding of acrylic and sulphonic polyanions by open-chain polyammonium cations[END_REF]. Natural and biological fluids contain also amino compounds (amines, polyammonium cations, polyaminocarboxylates, etc.) that are among the fundamental molecules of biological interest, widely present in aminoacids, proteins and enzymes, and are responsible for the most of complex functions that make life possible. The biological function of natural polyelectrolytes is often mediated by interactions with other macromolecules such as, for example, proteins and natural surfactants (lipids). A very important example is the interaction of DNA with proteins. Among these macromolecules, polyammoniun cations have a quite relevant role [START_REF] Bencini | Proton coordination by polyamine compounds in aqueous solution[END_REF]. In the literature the interaction of polyammonium cations with carboxylic anions was widely reported, whilst a lesser number of data is reported for other ligands containing, for example, phosphate groups, despite their widespread involvement in biological systems. Few examples of phosphate complexation by synthetic polyammonium receptors in water were reported by Garcia-España et al. [START_REF] Garcìa-España | Anion coordination chemistry in aqueous solution of polyammonium receptors[END_REF]; other papers also report [START_REF] Bazzicalupi | Thermodynamics of Phosphate and Pyrophosphate Anions Binding by Polyammonium Receptors[END_REF][START_REF] Arranz | Thermodynamics of sulfate anion binding by macrocyclic polyammonium receptors[END_REF][START_REF] Anda | A thermodynamic and spectrophotometric study of anion binding with a multifunctional dipyridine-based macrobicyclic receptor[END_REF] the enthalpy and entropy changes, which are important to interpret the main contribution for the stability of anion complexes in water.

The interaction of polyammonium cations with inorganic and organic polyanions [START_REF] Bencini | Proton coordination by polyamine compounds in aqueous solution[END_REF][START_REF] Garcìa-España | Anion coordination chemistry in aqueous solution of polyammonium receptors[END_REF][START_REF] Bazzicalupi | Thermodynamics of Phosphate and Pyrophosphate Anions Binding by Polyammonium Receptors[END_REF][START_REF] Arranz | Thermodynamics of sulfate anion binding by macrocyclic polyammonium receptors[END_REF][START_REF] Anda | A thermodynamic and spectrophotometric study of anion binding with a multifunctional dipyridine-based macrobicyclic receptor[END_REF][START_REF] Lomozik | Coordination chemistry of polyamines and their interactions in ternary systems including metal ions, nucleosides and nucleotides[END_REF][START_REF] Daniele | Binding of Inorganic and Organic Polyanions by Protonated Open Chain Polyamines in Aqueous Solution[END_REF] was mainly studied for low molecular weight molecules. In our previous papers, we already studied the interaction of different polyphosphates [START_REF] Daniele | Binding of Inorganic and Organic Polyanions by Protonated Open Chain Polyamines in Aqueous Solution[END_REF][START_REF] Stefano | Thermodynamic parameters for the formation of pyrophosphate-protonated polyamine complexes[END_REF][START_REF] Stefano | Formation and Stability of Pyrophosphate Complexes with Aliphatic Amines in Aqueous Solution[END_REF][START_REF] Stefano | Binding of Tripolyphosphate by Aliphatic Amines: Formation, Stability and Calculation Problems[END_REF] and nucleotides [START_REF] Stefano | Chemical speciation of nucleotide 5'-monophosphates in the presence of biogenic amines[END_REF] with biogenic amines. More recently the interaction of some polyammonium cations [ethylenediamine, 1-4-diaminobutane (putrescine), 1,5-diaminopentane (cadaverine), diethylenetriamine, N,N'-bis[3-aminopropyl]-1,4-diaminobutane (sperimine), N-[3-aminopropyl]-1,4-diaminobutane (spermidine), tetraethylenpentamine and pentaethylenehexamine] with phytate [START_REF] Stefano | Speciation of phytate ion in aqueous solution. Non covalent interactions with biogenic polyamines[END_REF], some polymers, such as polyacrylate (MW = 2 kDa), polystirenesulphonates (MW = 70 and 1000 kDa) and polyvinylsulphonate (MW = 9 kDa) [START_REF] Stefano | Polyacrylates in aqueous solution. The Dependence of Protonation on Molecular Weight, Ionic Medium and Ionic Strength[END_REF], and alginic and fulvic acids [START_REF] Stefano | Sequestration of biogenic amines by alginic and fulvic acids[END_REF] were studied.

As a further contribution to the study of the acid-base properties and complexing ability of polyelectrolytes already undertaken [START_REF] Stefano | Polyacrylates in aqueous solution. The Dependence of Protonation on Molecular Weight, Ionic Medium and Ionic Strength[END_REF][START_REF] Stefano | Thermodynamics of proton association of polyacrylates and polymethacrylates in NaCl(aq)[END_REF][START_REF] Stefano | Speciation of Organic Matter in Natural Waters-interaction of polyacrylates and polymethacrylates with major cation components of seawater[END_REF][START_REF] Crea | Modelling of natural synthetic polyelectrolyte interactions in natural waters by using SIT, Pitzer and Ion Pairing approaches[END_REF][START_REF] Crea | Binding of acrylic and sulphonic polyanions by open-chain polyammonium cations[END_REF], in the present paper we studied the interaction of an high molecular weight ammonium polyelectrolyte (branched polyethylenimine MW = 750 kDa) with an high charged polyphosphate, such as phytate. This high molecular weight polyamine has a monomeric unit which contains primary, secondary and tertiary amino groups in the ratio 1:2:1, as shown in Figure 1. It is a polymer obtained from the aziridine through ring-opening cationic polymerisation.

Poly(ethylenimine) [BPEI], has several applications in the biological, industrial and pharmaceutical fields [START_REF] Godbey | Poly(ethylenimine) and its role in gene delivery[END_REF][START_REF] Bahulekar | Polyethylenimine in immobilization of biocatalysts[END_REF][START_REF] Salt | Selective flocculation of cellular contaminants from soluble proteins using polyethylenimine: a study of several organisms and polymer molecular weights[END_REF][START_REF] Crea | Thermodynamic Study for the Protonation of Branched Poly(EthylenImine) in NaCl aq and its Dependence on Ionic Strength[END_REF]. For example, it is used in bioprocesses to facilitate the transfer of nucleic acids through biological membranes, for purification of DNA binding proteins, to transfer genes and oligonucleotides into living cells, as a flocculating agent and to immobilise enzymes and bacteria, as backbone of artificial enzymes. BPEI binds also heavy metal cations [START_REF] Osipova | Voltammetric determination of copper(II), lead(II), and cadmium(II) in aqueous solutions of polyethylenimine using electrodes made of carbon materials[END_REF][START_REF] Tauler | Spectroscopic resolution of macromolecular complexes using factor analysis: copper(II)-polyethylenimine system[END_REF][START_REF] Ermakov | The effect of solution pH on the rate of electroreduction of copper(II) complexes with polyethylenimine at a dropping mercury electrode[END_REF], and therefore can be used in several environmental applications [START_REF]Mine Waste Technology Program[END_REF].

Phytate [Phy], is widely present in nature and has an important biological activity; it modifies the bioavailability of several metal ions (such as calcium, iron, zinc, copper: see, e.g., [28 and references therein]); it is regarded as the primary storage form of both phosphate and inositol in plant seeds and grains, and to be an antioxidant [28 and references therein]; it shows marked anticarcinogenic/antineoplastic properties; it may reduce and prevent kidney stone formation and it plays key roles in a number of crucial

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3 physiological activities, in addition to the treatment of different pathologies. Among its industrial and/or technological applications, very important is the use of phytate in remediation problems, such as the immobilization and in-situ treatment of soils contaminated by many metals (including heavy metals and radionuclides).

Owing to their high charges, BPEI and phytate can be considered as model molecules for the study of the interactions between natural polycations and polyanions. The problems that can be encountered in such a study are connected to the interpretation/elaboration of the experimental data; different methods were used to explain the acid-base properties of BPEI: by applying the Ising model to short-range interactions [START_REF] Borkovec | Proton binding characteristics of branched polyelectrolytes[END_REF], by relating the BPEI protonation with ion condensation [START_REF] Nagaya | Relationship between protonation and ion condensation for branched poly(ethylenimine)[END_REF] and by calculating the deprotonation quotient at different pHs [START_REF] Junghun | Ionization of poly(ethylenimine) and poly(allylamine) at various pH's[END_REF]. In our previous work [START_REF] Crea | Thermodynamic Study for the Protonation of Branched Poly(EthylenImine) in NaCl aq and its Dependence on Ionic Strength[END_REF], we used a new approach to study the acid-base properties of BPEI; using this approach the branched poly(ethylenimine) was treated as a simple aliphatic tetramine. Since this approach is suitable to describe the acid-base properties of BPEI, it was used for studying its complexation with phytate.

Experimental section

Chemicals

All the reagents were Fluka analytical grade. A 50% aqueous solution of BPEI was used without further purification; its concentration was determined by potentiometric titrations, assuming the ligand as a monomer. Phytic acid solutions were prepared by weighing pure dipotassium salt K 2 H 10 Phy (Fluka). Hydrochloric acid working solutions were prepared by diluting concentrates, and standardized against sodium carbonate. Tetraethylammonium hydroxide solutions were prepared from concentrated Et 4 NOH (Fluka puriss. Electrochemical grade) and standardized against potassium biphthalate. All the solutions were prepared by using analytical grade water (R ≥ 18 MΩ cm -1 ) and preserved from atmospheric CO 2 by means of soda lime traps. Grade A glassware was employed.

Apparatus

The potentiometric measurements were carried out by using a potentiometer (Metrohm mod. E605) coupled with a combinated ISE-H Orion Ross type glass electrode (mod. 8172), and with an automatic titrant dispenser (Metrohm Dosimat mod. 665). The potentiometer and the dispenser were connected to a PC and a suitable home made software allows monitoring of the titrations. The program allows the equilibrium potentials to be read and determination of the titrant volume to be added, based on the actual buffering properties of the solution under titration, so that the differences in successive readings were of ~ 0.1 as -log [H + ]. The estimated precision of the system was ± 0.15 mV in the e.m.f. and ± 0.003 ml in the titrant volume. The measurement cell was thermostatted at t = 25±0.2 °C, and pure nitrogen presaturated with an ionic media solution at the same ionic strength of the working solution, was bubbled into the solution in order to avoid O 2 and CO 2 interference. The solutions were magnetically stirred.

Procedure

25.0 ml of solution containing 0.50 ≤ C BPEI ≤ 1.1 mmol L -1 (calculated as a monomer) and 1 ≤ C Phy ≤ 2 mmol L -1 (Phy = phytate), were titrated with standard Et 4 NOH; titration were carried out in the pH range from ≈ 7.0 to ≈ 10.4 and without any addition of supporting electrolyte. The mean ionic strength value of titrated solutions was I = 0.04 ± 0.01 mol L -1 . For each titration, a separate calculation of the formal potential (E 0 ) was carried out by titrating HCl 10 mmol L -1 with standard NaOH; this determination was carried out both before and after each experiment. Proton concentration is given as pH = -log [H + ], i.e. the free hydrogen ion concentration scale was used. All the titrations were carried out in duplicate.

Calculations

The non-linear least squares computer program ESAB2M [START_REF] Stefano | Computer analysis of equilibrium data in solution. ESAB2M: an improved version of the ESAB program[END_REF] was used to refine the parameters of the acid-base titrations (species concentrations, formal potential of electrode couple (E 0 ), water ionic product (K w )). The formation constant values were refined by the computer program BSTAC [START_REF] Stefano | Ionic Strength Dependence of Formation Constants. XVII. The Calculation of Equilibrium Concentrations and Formation Constants[END_REF] which minimize the error squares sum on electromotive force values. In all the paper, phytate-polyammonium complex formation equilibria refer to the general equations:

p A 0 + Phy 12-+ i H + ⇄ A p PhyH i (12-i)- β pi (1) p AH i i+ + PhyH z (12-z)-⇄ A p PhyH j (12-j)-(j = pi +z) K pj (2)
where AH i i+ is a generic polyammoiun cation species and PhyH z (12-z)-a phytate protonated species; A 0 is the neutral polyamine and Phy 12-the fully deprotonated form of phytate. Throughout the paper errors are given as ± standard deviation. The dependence of stability constants on temperature can be taken into account by the equation:

1 T F H log log θ θ Δ + = K K ( 3
)
where K is a generic formation constant; and

10 ln R / T 1 1 F 1 ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ - θ =
with R = 8.309 J⋅mol -1 ⋅K -1 ; θ is the reference temperature in K, and ΔH in J⋅mol -1 . ΔH values were obtained from empirical relationships already reported [START_REF] Stefano | ΔG 0 and TΔS 0 charge relationships for the binding of carboxylic anions by open-chain polyammonium cations[END_REF][START_REF] De Robertis | ΔG 0 and TΔS 0 -Charge Relationships for the Binding of Inorganic and Organic Anions by Open Chain Polyammonium Cations: a Short Review[END_REF], whilst the dependence of formation constants on ionic strength was taken into account by an extended Debye -Hückel type equation [START_REF] De Robertis | Binding of Carboxylic Ligands by Protonated Amines[END_REF][START_REF] De Robertis | Medium effects on the protonation of carboxylic acids at different temperature[END_REF].

Results

Protonation constants

For the determination of high molecular weight polyelectrolytes protonation constants [6 and references therein], the dependence of log K H on the degree of protonation (or on the degree of ionisation) must be taken into account; this implies the use of different calculation methods [START_REF] Katchalsky | Potentiometric Titrations of Polymethacrylic Acid[END_REF][START_REF] Högfeldt | Application of a Simple Three-Parameter Model to Titration Data for Some Linear Polyelectrolytes[END_REF]. Nevertheless, in a previous work [START_REF] Crea | Thermodynamic Study for the Protonation of Branched Poly(EthylenImine) in NaCl aq and its Dependence on Ionic Strength[END_REF], a simple new approach to calculate the protonation constants, and enthalpy changes, of BPEI was proposed. By this approach BPEI polyelectrolyte can be considered as a simple low molecular weight tetramine, and the protonation steps were studied taking into account the following protonation equilibrium:

A C C E P T E D M A N U S C R I P T ACCEPTED MANUSCRIPT 5 AH i-1 (i-1)+ + H + ⇄ AH i i+ (i =1 to 4) K i H (4)
This approach gives a simple picture of the acid-base proprieties of BPEI. As regards phytate, in some recent papers, we reported its protonation constants [START_REF] Stefano | Speciation of phytate ion in aqueous solution. Protonation constants in tetraethylammonium iodide and sodium chloride[END_REF][START_REF] Crea | Speciation of phytate ion in aqueous solution. Protonation in CsCl aq at different ionic strengths and mixing effects in LiCl aq + CsCl aq[END_REF] and enthalpy changes in different ionic media [START_REF] Crea | Formation and stability of phytate complexes in solution[END_REF][START_REF] Stefano | Speciation of phytate ion in aqueous solution. Protonation constants in tetraethylammonium iodide and sodium chloride[END_REF][START_REF] Stefano | Speciation of phytate ion in aqueous solution. Thermodynamic parameters for protonation in NaCl[END_REF]. In Tables 1 and2 we report K i H values for BPEI and phytate, respectively.

Phy-BPEI species

The interaction of phytate with some biogenic amines, namely, ethylendiamine (En), 1-4-diaminobutane (putrescine, Ptr), N-[3-aminopropyl]-1,4-diaminobutane (spermidine, Spd), and N,N'-bis[3-aminopropyl]-1,4-diaminobutane (sperimine, Sper) was already studied [START_REF] Stefano | Speciation of phytate ion in aqueous solution. Non covalent interactions with biogenic polyamines[END_REF]. In this study, we observed that phytate forms fairly strong mixed (proton-amine) complexes, in particular when the charges of reactants involved in the formation equilibrium are quite high. In this order, here we investigated the interactions of phytate with an high molecular weight polyammonium cation (MW = 750 kDa), such as BPEI; the interactions were studied at low ionic strength values and without addition of supporting electrolyte, owing to the strong interference that phytate anion may undergo with alkali and alkaline earth metal cations [START_REF] Stefano | Speciation of phytate ion in aqueous solution. Alkali metal complex formation in different ionic media[END_REF][START_REF] Crea | Speciation of phytate ion in aqueous solution. Sequestration of magnesium and calcium by phytate at different temperatures and ionic strengths, in NaCl aq[END_REF]. Table 3 reports the overall complex formation constants obtained [equation ( 1)], whilst the equilibrium constants, according to the reaction (2), are reported in Table 4. The first three equilibria refer to the generic reaction (2) (1:1 metal-ligand ratio), and the last one refers to the interaction of one mole of phytate with two different protonated species of BPEI, namely mono-and diprotonated species. From the formation constants reported in Tables 3 and4, it appears that phytate forms with BPEI complexes whose stability is comparable with that of low molecular weight polyammonium cations [START_REF] Stefano | Speciation of phytate ion in aqueous solution. Non covalent interactions with biogenic polyamines[END_REF]. It is interesting to observe, as already reported [START_REF] Stefano | Speciation of phytate ion in aqueous solution. Non covalent interactions with biogenic polyamines[END_REF], the dependence of log K pj on charges product

ζ = ⏐(ΣZ cation ) ⋅ Z anion ⏐ (5)
In particular, we can see that the ratio log K pj /ζ is fairly constant for all the species, with a mean value of 0.41±0.07. By using empirical equations [START_REF] Stefano | ΔG 0 and TΔS 0 charge relationships for the binding of carboxylic anions by open-chain polyammonium cations[END_REF][START_REF] De Robertis | ΔG 0 and TΔS 0 -Charge Relationships for the Binding of Inorganic and Organic Anions by Open Chain Polyammonium Cations: a Short Review[END_REF][START_REF] De Robertis | Binding of Carboxylic Ligands by Protonated Amines[END_REF][START_REF] De Robertis | Medium effects on the protonation of carboxylic acids at different temperature[END_REF] and enthalpy data for the protonation of BPEI and phytate, we calculated the formation constants of Phy(BPEI) p H j species at different temperatures (15, 37 °C) and ionic strengths (0, 0.04, 0.15 mol L -1 ). From the complex formation constants reported in Table 4 and equation ( 5), we calculated the log K pj /ζ values. Therefore it is possible to derive the free energy contribution per bond [START_REF] Stefano | ΔG 0 and TΔS 0 charge relationships for the binding of carboxylic anions by open-chain polyammonium cations[END_REF][START_REF] De Robertis | ΔG 0 and TΔS 0 -Charge Relationships for the Binding of Inorganic and Organic Anions by Open Chain Polyammonium Cations: a Short Review[END_REF] given by 0 0 kJ mol -1 . In Figure 2, we report a speciation diagram for the system studied in this work. Yields of phytate-BPEI-proton species are very high in the whole pH range. In particular, at pH values of seawater (pH ≈ 8.1) or blood (pH ≈ 7.4), the species PhyBPEIH 7 and PhyBPEIH 8 become the predominant ones. Also the binuclear species, Phy(BPEI) 2 H 7 , reaches a formation percentage of about 60% at pH ≈ 9.2, in the reported experimental conditions. In considering these formation constants and formation percentages, one must take into account that they were obtained in absence of an interacting supporting electrolyte such as NaCl, which is present in all natural and biological fluids. This is particularly important if we take into account that phytate forms stable complexes with alkali metals [START_REF] Crea | Formation and stability of phytate complexes in solution[END_REF][START_REF] Stefano | Speciation of phytate ion in aqueous solution. Alkali metal complex formation in different ionic media[END_REF], and this interaction may change significantly the speciation of the system. The interaction of a polyammonium cation with phytate is dependent on the concentration of the supporting electrolyte; in fact, in a previous work [START_REF] Stefano | Speciation of phytate ion in aqueous solution. Non covalent interactions with biogenic polyamines[END_REF], we calculated the competition between Na + and two polyammonium cations, in particular ethylenediamine (diamine) and sperimine (tetramine), vs. phytate. It was pointed out that in the phytate-ethylenediamine system, phytate there is a strong competition of Na + whith the ammonium cation, at low sodium concentrations (C Na ≥ 0.05 mol L -1 ), whilst in the case of spermine the competition with Na + can be considered negligible up to C Na > 0.1 mol L -1 , owing to the high charge (4+) of this amine with respect to ethylenediamine (2+). In the case of the Phy-BPEI system, by taking into account the log K pj and log K pj /ζ values with respect to other phytate-polyammonium cation systems (Table 5), it can be observed that BPEI behaves, in the interaction with phytate, approximately like a diamine or a triamine, rather than a tetramine.

G G b Δ = Δ /

Sequestering ability of phytate towards BPEI

In a previous paper [START_REF] Crea | Speciation of phytate ion in aqueous solution. Sequestration of magnesium and calcium by phytate at different temperatures and ionic strengths, in NaCl aq[END_REF], we proposed a Boltzman type equation able to define the sequestering ability of phytate towards cations, such as Mg 2+ and Ca 2+ , by means of a function that takes into account the sum of formation percentages of all cation-ligand complexes, Σ(%), vs. pL, where pL ≡ -log [L] tot ([L] tot is the total ligand concentration). This function is assimilable to a sigmoid curve (or a dose response curve) with asymptotes of 100 for pL → -∞ and 0 for pL → +∞:

⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ + × = Σ ] 1 - ] S / ) pL pL exp[( 1 1 100 (%) 50 - (6)
where pL 50 and S are empirical parameters. In particular, pL 50 represents the ligand concentration necessary to sequester 50% of metal ion; therefore this parameter can be used as a measure of the sequestering abilities of different ligands. The parameter S is a measure of the slope in the flex of the function Σ(%) vs. pL. The Boltzman type equation was also applied to the phytate-BPEI and other phytate-polyammonium cation systems (namely: En, Ptr, Spd, Sper); the sequestering diagram reported in Figure 3 was drawn at pH = 7.4 and I ≈ 0 mol L -1 , at a very low polyammonium cation concentration (as trace) and phytate concentration from ≈ 10 -11 to 10 -3 mol L -1 . From the fit of equation ( 6) we obtained, for example, that the concentration of phytate necessary to sequester 50% of the initial BPEI, in this experimental condition, was 9.77 10 -8 mol L -1 (pL 50 = 7.01). The sequestering ability of phytate towards polyammonium cation follows the trend:

Sper >> Spd > BPEI > > Ptr > En
The pL 50 and S values for each phytate-polyammonium cation system, calculated at pH = 7.4 and I ≈ 0 mol L -1 , are reported in Table 6. From Figure 3 and from the pL 50 values reported, it can be observed that the sequestering ability of phytate towards BPEI is intermediate between those observed for Spd and Ptr, that are a tri-and a diamine, respectively. This behaviour is due to the partial deprotonation of BPEI at pH > 6; in fact two protonation constants of BPEI are in the acidic region (log K 3 H = 5.62 and log K 4 H = 2.23, at I = 0.04 mol L -1 and t = 25 °C). The log K pj /ζ values reported in Table 5, for the phytate-BPEI and phytate-Ptr systems are, within the standard deviation, equal. Since the potentiometric measurements were carried out in the pH range from ≈ 7.0 to ≈ 10.4, two aminic groups are deprotonated and BPEI behaves as a dicharged cation. In particular we must notice the sequestering behaviour of phytate towards spermine. The

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7 stability of the species formed in this systems is evidenced by the high formation constant and pL 50 values and also by the sharp slope of the curve Σ% vs. pL (S = 0.20 in comparison with S = 0.43 for the other systems). Two factors contribute to this behaviour: the first one is related to the complete protonation of spermine in a wide pH range, as above discussed, and, very likely to the favourable distance between ammonium groups that render easier the binding to phytate. Two factors that can influence the sequestering ability of BPEI towards phytate are the variation of ionic strength and temperature; these effects are shown in Figures 4 and5, respectively. In Figure 4 we report a sequestering diagram of phytate-BPEI system at three different ionic strengths and t = 25 °C; we obtained the following pL 50 values: pL 50 = 7.70 (I = 0 mol L -1 ); pL 50 = 6.89 (I = 0.04 mol L -1 ); pL 50 = 5.91 (I = 0.15 mol L -1 ) and S = 0.43. Figure 5 shows a sequestering diagram at I = 0.15 mol L -1 and t = 15, 25 and 37 °C, respectively. In this case we obtained: pL 50 = 5.67 (t = 15 °C); pL 50 = 5.91 (t = 25 °C); pL 50 = 5.99 (t = 37 °C) and S = 0.43. From the pL 50 values obtained by fitting data of Figures 4 and5, it is evident that the sequestering ability of phytate towards BPEI is mostly depend on the variation of ionic strength rather than the variation of temperature. In fact, from the pL 50 values above reported is evident that a variation of temperature from t = 15 to 37 °C, gives a relatively low variation of 0.5 units in pL 50 . Instead ionic strength gives a higher contribution in the variation of pL 50 that differs of ≈ 2.0 log units in the ionic strength range from I = 0 to 0.15 mol L -1 .

Comparison with other similar systems

In the literature several data can be found on the interaction of open chain linear polyammonium cations with several polyanions [START_REF] Daniele | Binding of Inorganic and Organic Polyanions by Protonated Open Chain Polyamines in Aqueous Solution[END_REF][START_REF] Stefano | Thermodynamic parameters for the formation of pyrophosphate-protonated polyamine complexes[END_REF][START_REF] Stefano | Formation and Stability of Pyrophosphate Complexes with Aliphatic Amines in Aqueous Solution[END_REF][START_REF] Stefano | Binding of Tripolyphosphate by Aliphatic Amines: Formation, Stability and Calculation Problems[END_REF][START_REF] Stefano | Chemical speciation of nucleotide 5'-monophosphates in the presence of biogenic amines[END_REF][START_REF] Stefano | Speciation of phytate ion in aqueous solution. Non covalent interactions with biogenic polyamines[END_REF][START_REF] Stefano | Sequestration of biogenic amines by alginic and fulvic acids[END_REF]. As reported [START_REF] Stefano | Polyacrylates in aqueous solution. The Dependence of Protonation on Molecular Weight, Ionic Medium and Ionic Strength[END_REF][START_REF] Stefano | Formation and Stability of Pyrophosphate Complexes with Aliphatic Amines in Aqueous Solution[END_REF][START_REF] Stefano | Binding of Tripolyphosphate by Aliphatic Amines: Formation, Stability and Calculation Problems[END_REF][START_REF] Stefano | Speciation of phytate ion in aqueous solution. Non covalent interactions with biogenic polyamines[END_REF], the stability of these complexes is strictly dependent on the charges involved in the formation reaction, and when the charges are the same, similar values of formation constants were obtained. These behaviours can be observed in the formation constant values and the log K pj /ζ ratio obtained for the interaction of phytate with some biogenic amines (ethylenediamine (En), 1-4-diaminobutane (putrescine, Ptr), 1,5-diaminopentane (cadaverine, 1,5d), diethylenetriamine (Dien), N,N'-bis[3-aminopropyl]-1,4diaminobutane (sperimine, Sper), N-[3-aminopropyl]-1,4-diaminobutane (spermidine, Spd), tetraethylenpentamine (Tetren) and pentaethylenehexamine (Penten)) [START_REF] Stefano | Speciation of phytate ion in aqueous solution. Non covalent interactions with biogenic polyamines[END_REF] and of some polyammonium cations with polycarboxylate (i.e. tartrate (Tar); citrate (Cit); glutamate (Glu); 1,2,3-propanetricarboxylate (Tca) and 1,2,3,4-butanetetracarboxylate (Btc)) [START_REF] De Robertis | Thermodynamic parameters for the binding of inorganic and organic anions by biogenic polyammonium cations[END_REF] (see Table 5). Nevertheless in this last work [START_REF] De Robertis | Thermodynamic parameters for the binding of inorganic and organic anions by biogenic polyammonium cations[END_REF], we also observed that the structure of both polyammonium cations and polyanions plays a less important role. Taking into account the same phytate-polyammonium cation systems, we observe that the log K pj /ζ ratio can be considered constant, with a slight decrease of its value when the number of amino groups in the molecules increases. In the case of phytate-BPEI interaction, we obtained, as above seen, a mean value of log K pj /ζ = 0.41, that is comparable with the interaction of phytate with a diamine (such as putrescine). Moreover, comparison can be made with other polyammonium cation-ligand systems reported in Table 5.

Free energy contribution per bond

As already seen in the previous sections, there is a relationship between the logarithm of formation constants and the charges involved in the formation reaction; the different log K pj /ζ values observed for the various systems, and the lower log K pj /ζ values of the phytate-BPEI-proton system with respect to other polyammonium cation-polyphosphate systems is imputable to the conformational arrangement of its phosphate groups [START_REF] Crea | Formation and stability of phytate complexes in solution[END_REF] and to the charge density. For the phytate-BPEI-proton system, we calculated the free energy contribution per bond, that is 4.4 kJ mol -1 , whilst for the polyammonium cation-polyphosphate systems reported in Table 5 we calculated a mean value of 0 b G Δ = 9.4 kJ mol -1 . Similar comparison can be made with the polyammonium cation-polycarboxylate systems; in this case we obtained 0 b G Δ = 6.7 kJ mol -1 . Greater differences are observed if we take into account high molecular weight molecules; in fact in a previous work [START_REF] Crea | Binding of acrylic and sulphonic polyanions by open-chain polyammonium cations[END_REF] we obtained for the interaction of an high molecular weight polycarboxylate (polyacrylate 2kDa) with polyammonium cations a free energy contribution per bond of 0 b G Δ = 16.1 kJ mol -1 and for two polysulphonates (9 and 1000 kDa) with polyammonium cations a value of 0 b G Δ = 13.8 kJ mol -1 . This sharp difference in the stability of low and high molecular weight polyanion and polycation complexes is due to the high charge density of polyelectrolytes with respect to low molecular weight systems. In a recent work some correction for the effective charge (higher than the formal ones) were considered too [START_REF] Stefano | Sequestration of biogenic amines by alginic and fulvic acids[END_REF]. This parameter is a simple evidence of the different sequestering ability of several polycations towards polyanions. Similar investigations were carried out by Bazzicalupi et al. [START_REF] Bazzicalupi | Thermodynamics of Phosphate and Pyrophosphate Anions Binding by Polyammonium Receptors[END_REF] on the interaction of phosphate and pyrophosphate with several polyammonium receptors. They observed that although the electrostatic attraction is the driving force in anion interactions with polyammonium receptors, the stability trends of such complexes are not strictly determined by electrostatic contributions, in contrast with the general trend of increasing stability with increasing charge of receptors and anions. In fact considering the stability of the complexes formed by phosphate and pyrophosphate in a given protonation degree, with the same receptors, they did not observed a trend in contrast to electrostatic expectations, and that the less charged anion can form more stable complexes. They concluded that the stability of complexes is strictly dependent on the ability of ligands (phosphate and pyrophosphate) to involve one or more phosphate moieties in the interaction with a single polyammonium cations, and this assumption is in agreement with the results reported in our work, especially for the systems involving phytate.

A C C E P T E D

M A N U S C R I P T

A C C E P T E D M A N U S C R I P T

A C C E P T E D M A N U S C R I P T

Thermodynamic parameters for the formation of phytate-BPEI-proton complexes at different temperature and ionic strength Reaction a) t = 25 °C Empirical parameters of equation ( 6

ζ b) log K pj log K pj /ζ log K pj log K pj /ζ log K pj log K pj /ζ -ΔG c) TΔS c) ΔH c) I = 0 d) I = 0.

A C C E P T E D M A N U S C R I P T ACCEPTED MANUSCRIPT

  04 b) I = 0.15 b) I = 0 c) I = 0.15 c) I = 0 c) I = 0.15

  07 a) According to eq. (2); b) product of charges (ζ) involved in the reaction [see eq. (5)]; c) kJ mol -1 ; d) I/mol L -1 .

2 HNFigure 1 .Figure 2 .

 212 Figure 1. Representation of BPEI monomeric unit.

Figure 3 Figure 4

 34 Figure 3 Sum of percentages of phytate-polyammonium cations species vs. pL at I = 0 mol L -1 , t = 25 °C and pH = 7.4. Concentration: C polyammonium cation = (trace).

Figure 5

 5 Figure 5 Sum of percentages of phytate-BPEI species vs. pL at different temperatures at pH = 7.4 and I = 0.15 mol L -1 . Concentration: C BPEI = (trace).

Table 1

 1 Protonation constants of BPEI at different ionic strength and temperatures

	species	log Κ i

Table 3

 3 Overall formation constants of phytate-BPEI-proton

	complexes at t = 25 °C
	species	log β pi	a)
	PhyBPEIH 6 PhyBPEIH 7	77.16 ± 0.03 b) 86.20 ± 0.03
	PhyBPEIH 8 Phy(BPEI) 2 H 7	93.75 ± 0.05 90.65 ± 0.02
	a) According to eq. (1);
	b) ± std. dev.

Table 5

 5 Literature values of log Κ pj /ζ ratio for some polyphosphate-polyammonium cation systems at

	infinite dilution, at t = 25 °C
	systems				log Κ pj /ζ	Number of species systems	log Κ pj /ζ	Number of species
	BPEI-phytate a)	0.41±0.07 g)	4	Spd-Tar f)	0.52±0.10 g)	4
	En-phytate b)	0.40±0.04	9	Spd-Cit f)	0.43±0.03	5
	Ptr-phytate b)	0.41±0.06	8	Spd-Glu f)	0.58±0.08	4
	Spd-phytate b)	0.31±0.05	8	Spd-Tca f)	0.39±0.04	5
	Sper-phytate b)	0.35±0.05	6	Spd-Btc f)	0.49±0.05	6
	En-PO 4	3-c)		0.77±0.03	3	Sper-Tar f)	0.68±0.15	6
	Dien-PO 4 3-c)	0.95±0.20	4	SperCit f)	0.62±0.13	7
	Trien-PO 4	3-c)	1.18±0.43	5	Sper-Tca f)	0.53±0.08	6
	Penten-PO 4	3-c)	0.64±0.11	8	Sper-Btc f)	0.49±0.06	7
	En-P 2 O 7 4-c)		0.80±0.15	6	En-Tar f)	0.48±0.06	3
	Dien-P 2 O 7	4-c)	0.85±0.16	6	En-Cit f)	0.63±0.12	4
	Trien-P 2 O 7 4-c)	0.86±0.14	8	En-Tca f)	0.64±0.11	4
	Tetren-P 2 O 7 4-d)

Acknowledgements:

We thank University of Messina (PRA) for financial support