Pasquale Crea

Concetta De Stefano

Demetrio Milea

Nunziatina Porcino

Silvio Sammartano
email: ssammartano@unime.it

Speciation of phytate ion in aqueous solution. † Protonation constants and copper(II) interactions in NaNO 3aq at different ionic strengths

Keywords: phytate, copper(II), protonation and complex formation constants, dependence on ionic strength, ion selective electrodes, sequestration. 1

The acid base behavior of phytate has been studied (at t = 25°C by potentiometry, ISE-H + glass electrode) in NaNO 3aq at different ionic strengths (0.1 ≤ I / mol L -1 ≤ 1.0). The interactions with copper(II) were investigated in the same experimental conditions in different metal to ligand (Phy) ratios (1:1 ≤ Cu 2+ :Phy ≤ 4:1), by using both ISE-H + and ISE-Cu 2+ electrodes. Phytate acid base behavior in sodium nitrate is very similar to that in sodium chloride, previously investigated. In the experimental conditions adopted, the formation of three Cu i H j Phy (12-2i-j)-species is observed: the mononuclear CuH 4 Phy 6-and CuH 5 Phy 5-, and the dinuclear Cu 2 H 5 Phy 3-. Analysis of complex formation constants at different ionic strengths reveals that both ISE-H + and ISE-Cu 2+ electrodes gave, within the experimental error, analogous values. Dependence of complex formation constants on ionic strength was modeled by EDH (Extended Debye-Hückel) and SIT (Specific ion Interaction Theory) equations. The sequestering ability of phytate toward copper(II) has been evaluated by the calculation of pL 50 (the total ligand concentration, as -log C L , able to bind 50% of metal cation), an empirical parameter already proposed for an objective "quantification" of this

Introduction

Many scientists and research groups have been studying phytic acid and its derivatives, paying particular attention to biological and environmental aspects (see, for example, references reported in previous contributions [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. Alkali metal complex formation in different ionic media[END_REF][START_REF] Stefano | Speciation of phytate ion in aqueous solution. Non covalent interactions with biogenic polyamines[END_REF][START_REF] Crea | Speciation of phytate ion in aqueous solution. Characterisation of Ca-phytate sparingly soluble species[END_REF][START_REF] Stefano | Speciation of phytate ion in aqueous solution. Thermodynamic parameters for protonation in NaCl[END_REF][START_REF] Stefano | Speciation of phytate ion in aqueous solution. Dimethyltin(IV) interactions in NaCl aq at different ionic strengths[END_REF][START_REF] Stefano | Speciation of phytate ion in aqueous solution. Sequestering ability towards mercury(II) cation in NaCl aq at different ionic strengths[END_REF][START_REF] Crea | Speciation of phytate ion in aqueous solution. Sequestration of magnesium and calcium by phytate at different teperatures and ionic strengths, in NaCl aq[END_REF][START_REF] Stefano | Speciation of phytate ion in aqueous solution. Cadmium(II) interactions in NaCl aq at different ionic strengths[END_REF][START_REF] Crea | Speciation of phytate ion in aqueous solution. Trimethyltin(IV) interactions in self medium[END_REF] and in reviews [START_REF] Maga | Phytate: Its Chemistry, Occurrence, Food Interactions, Nutritional Significance, and Methods of Analysis[END_REF][START_REF] Harland | Phytate: a Good or a Bad Food Component?[END_REF][START_REF] Harland | Food Phytate and Its Hydrolysis Products[END_REF][START_REF] Oatway | Phytic Acid[END_REF][START_REF] Raboy | myo-Inositol-1,2,3,4,5,6-hexakisphosphate[END_REF]). Due to the fact that the most of its properties are strictly correlated to its behavior in aqueous solution, during last years our group modeled its acid base properties and its binding ability toward many metal and organometal cations in various aqueous media, with the aim of studying the chemical speciation of phytic acid under different experimental conditions (this is of fundamental importance for a thorough comprehension of all processes involving this molecule) [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. Alkali metal complex formation in different ionic media[END_REF][START_REF] Stefano | Speciation of phytate ion in aqueous solution. Non covalent interactions with biogenic polyamines[END_REF][START_REF] Crea | Speciation of phytate ion in aqueous solution. Characterisation of Ca-phytate sparingly soluble species[END_REF][START_REF] Stefano | Speciation of phytate ion in aqueous solution. Thermodynamic parameters for protonation in NaCl[END_REF][START_REF] Stefano | Speciation of phytate ion in aqueous solution. Dimethyltin(IV) interactions in NaCl aq at different ionic strengths[END_REF][START_REF] Stefano | Speciation of phytate ion in aqueous solution. Sequestering ability towards mercury(II) cation in NaCl aq at different ionic strengths[END_REF][START_REF] Crea | Speciation of phytate ion in aqueous solution. Sequestration of magnesium and calcium by phytate at different teperatures and ionic strengths, in NaCl aq[END_REF][START_REF] Stefano | Speciation of phytate ion in aqueous solution. Cadmium(II) interactions in NaCl aq at different ionic strengths[END_REF][START_REF] Crea | Speciation of phytate ion in aqueous solution. Trimethyltin(IV) interactions in self medium[END_REF]. These studies are particularly interesting also from a mere chemico-physical point of view, because the determination of accurate protonation and stability constants for so complex molecules is always a challenging task (just remember, e.g., the theoretical dodecanionic form of the free anion or the various conformations that phytate can assume in solution). At the same time, these difficulties gave us the possibility to emphasize once again that potentiometry is one of the best instrumental techniques for speciation studies (as recommended, e.g., by IUPAC), even for complex systems [START_REF] Templeton | Guidelines for terms related to chemical speciation and fractionation of elements. Definitions, structural aspects, and methodological approaches[END_REF].

In the present paper, the acid base behavior of phytate has been studied (at t = 25°C by potentiometry, ISE-H + glass electrode) in NaNO 3aq at different ionic strengths (0.1 ≤ I / mol L -1 ≤ 1.0). Successively, its interactions with copper(II) were investigated in the same experimental conditions, by using both ISE-H + and ISE-Cu 2+ electrodes. We chose copper(II) because of the importance that this cation has in many areas [copper(II) is involved in many processes of environmental and biological relevance, see, e.g., refs. in [START_REF] Scheinberg | Metals and Their Compounds in the Environment: Occurrence, Analysis, and Biological Relevance[END_REF]] and as a further step toward a better definition of the network of interactions of phytate ion with the main metal and organometal cations. Moreover, among commercial ion selective electrodes, ISE-Cu 2+ gives quite good performances in terms of reproducibility, repeatability, and accuracy:

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

3 comparisons among data obtained by ISE-Cu 2+ and ISE-H + electrodes on the same Cu 2+phytate system allowed us to demonstrate again how different techniques, if properly used, yield to the same results.

Experimental section

Chemicals

Nitric acid and sodium hydroxide solutions were prepared by diluting concentrated ampoules (Riedel-deHaën) and were standardized against sodium carbonate and potassium hydrogen phthalate, respectively. NaNO 3 solutions were prepared by weighing pure salt (Fluka) dried in an oven at 110°C. Phytic acid solutions were prepared by weighing Aldrich dipotassium salt (K 2 H 10 Phy), and passing it over a strong cationic exchange resin (Dowex 50W X 8 from Fluka). Concentration was checked potentiometrically by alkalimetric titrations, and the absence of potassium was established by flame emission spectrometry.

Copper(II) was used in the form of nitrate salt (Fluka) without further purification, its solutions were standardized spectrophotometrically and its purity was always ≥ 99.5%. All solutions were prepared with analytical grade water (R = 18 MΩ cm -1 ) using grade A glassware.

Apparatus

As concerns ISE-H + measurements, in order to minimize systematic errors potentiometric titrations were carried out (at t = 25.0 ± 0.1°C) using two different apparatuses:

the first one consisted of a Model 713 Metrohm potentiometer, equipped with a half cell glass electrode (Ross type 8101, from Orion) and a double junction reference electrode (type 900200, from Orion), and a Model 765 Metrohm motorized burette; the second one was a Crison micro-pH 2002 potentiometer, with the same kind of equipment of the first apparatus.

Estimated accuracy was ± 0.15 mV and ± 0.003 mL for e.m.f. and titrant volume readings, respectively, and was the same for both systems. They were connected to a PC, and automatic titrations were performed using a suitable computer program to control titrant delivery, data acquisition and to check for e.m.f. stability. Some measurements were also carried out using a For ISE-Cu 2+ measurements, potentiometric titrations were carried out by using the same kind of apparatuses and equipment, except for the use of an ISE-Cu 2+ electrode (type 9429SC, from Orion) instead of the half cell glass electrode. During these titrations, free idrogen ion concentration was simultaneously measured by the above-mentioned potentiometric system.

Procedure for ISE-H + measurements

Potentiometric titrations were carried out in termostatted cells under magnetic stirring and bubbling purified presaturated N 2 through the solution in order to exclude O 2 and CO 2 inside. The titrand solution consisted of different amounts of phytic acid (2-5 mmol L -1 ), nitric acid (3-7.5 mmol L -1 ), copper(II) nitrate (2-4 mmol L -1 , not added during measurements for the determination of phytate protonation constants), and the background salt in order to obtain pre-established ionic strength values (0.1 ≤ I mol L -1 ≤ 1.0). Potentiometric measurements were carried out by titrating 25 mL of the titrand solution with standard NaOH solutions up to pH ~10.5 (for titration of solutions with no copper) or until the formation of precipitate occurs. For each experiment, independent titrations of strong acid solution with standard base were carried out under the same medium and ionic strength conditions as the systems to be investigated, with the aim of determining electrode potential (E 0 ) and acidic junction potential

(E j = j a [H + ]
). In this way, the pH scale used was the total scale, pH ≡ -log [H + ], where [H + ] is the free proton concentration (not activity). Experimental conditions are reported in Table 1 for phytate-copper(II) measurements. In this Table, pH values at which the formation of scarcely soluble species occurs are also reported for Phy-Cu(II) systems.

For each titration, 80-100 points were collected, and the equilibrium state during titrations was checked adopting some usual precautions. These included checking the time necessary to reach equilibrium and performing back titrations. For measurements performed at low ionic strengths, the contribution of the ligand has to be considered: in the most critical conditions (i.e. I = 0.1 mol L -1 ), this contribution to ionic strength is ~7-8%, which introduces a not dramatic error in calculation. However, this error was taken into account by giving appropriate weights to the results obtained at low ionic strengths in fitting different functions. 1.

Procedure for ISE-Cu

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 for the refinement of all the parameters of the acid-base titration (E 0 , K w , liquid junction potential coefficient, j a , analytical concentration of reagents). The BSTAC [START_REF] Stefano | Ionic Strength Dependence of Formation Constants. XVII. The Calculation of Equilibrium Concentrations and Formation Constants[END_REF] and STACO [START_REF] Stefano | Binding of Tripolyphosphate by Aliphatic Amines: Formation, Stability and Calculation Problems[END_REF] computer programs were used in the calculation of complex formation constants. Both programs can deal with measurements at different ionic strengths. The ES4ECI [START_REF] Stefano | Ionic Strength Dependence of Formation Constants. XVII. The Calculation of Equilibrium Concentrations and Formation Constants[END_REF] program was used to draw speciation diagrams and to calculate species formation percentages. The LIANA [START_REF] Stefano | Marine Chemistry -An Environmental Analytical Chemistry Approach[END_REF] program was used to fit different equations.

Protonation and complex formation constants are given according to the equilibrium i Cu 2+ + j H + + Phy 12-= Cu i H j Phy (12-2i-j)- β ij [START_REF] Stefano | Speciation of phytate ion in aqueous solution. Protonation constants in tetraethylammonium iodide and sodium chloride[END_REF] or i Cu 2+ + H j Phy (12-j)-= Cu i H j Phy (12-

2i-j)- K ij (2)
Dependence on ionic strength of phytate protonation constants in NaNO 3aq was taken into account by an equation already proposed for the same modeling in alkali metal chlorides [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. Alkali metal complex formation in different ionic media[END_REF]:

A C C E P T E D M A N U S C R I P T ACCEPTED MANUSCRIPT 6 log K j H = log T K j H + C j I -log (1 + 10 D j I) (3)
where K j H is the protonation constant, T K j H is the protonation constant at infinite dilution, C j and D j are empirical parameters. The parameter D j can be considered as a measure of the interaction between Na + and H j Phy (12-j)-, as already described [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. Alkali metal complex formation in different ionic media[END_REF].

Dependence on ionic strength of complex formation constants for Cu i H j Phy (12-2i-j)- species expressed in the molar (mol L -1 ) concentration scale was taken into account by a Debye-Hückel type equation:

log K ij = log T K ij + DH + C I ( 4
)
where C is an empirical parameter, and DH is the Debye-Hückel term DH = -z* 0.51 I 1/2 / (1 + 1.5

I 1/2 ) (5) with z* = Σ (charges) 2 reactants -Σ (charges) 2 products ( 6
)
By using appropriate density values, molar to molal [ m, mol kg -1 (H 2 O)] scale conversions of I and K ij were performed. When these are expressed in the molal concentration scale, eq. ( 4) becomes the classical and widely used SIT (Specific ion Interaction Theory) equation [START_REF] Biederman | Dahlem Workshop on the Nature of Seawater[END_REF][START_REF] Biederman | Metal complexes in solution[END_REF][START_REF] Grenthe | Modelling in Aquatic Chemistry[END_REF], where

C represents ∆ε ∆ε = Σ p ε(p, q) (7)
and where ε(p, q) is the SIT interaction coefficient of the p-th species (involved in the equilibrium represented by the formation constant K ij ) with the q-th component (of opposite charge). ∆ε parameters were determined too. Both STACO and BSTAC computer programs can refine the empirical parameters for eq. ( 4).

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

Results and discussion

Phytate protonation constants and their dependence on ionic strength

Acid base behavior of phytic acid in Na + media has been extensively investigated, mainly in perchlorate or chloride salts (see, e.g. [START_REF] Stefano | Speciation of phytate ion in aqueous solution. Protonation constants in tetraethylammonium iodide and sodium chloride[END_REF] for data in NaCl aq [START_REF] Stefano | Speciation of phytate ion in aqueous solution. Protonation constants in tetraethylammonium iodide and sodium chloride[END_REF]. The fitting of log K j H values to this equation gave a standard deviation on the whole fit of σ = 0.10, and yielded to refined empirical parameters reported in Table 3 for each protonation step. In the same Table, empirical parameters for the dependence of phytate protonation constants on ionic strength in NaCl aq [START_REF] Stefano | Speciation of phytate ion in aqueous solution. Protonation constants in tetraethylammonium iodide and sodium chloride[END_REF] are reported in parenthesis. From a rapid evaluation of the same parameters in NaCl aq and NaNO 3aq , it can be noted that phytate acid base behavior in sodium nitrate is very similar to that in sodium chloride: within the experimental error, C j and D j parameters in the two media are comparable, and this is better evidenced from the analysis of Table 4, where phytate protonation constants, calculated by eq.

3 using the empirical parameters of Table 3, are shown at different ionic strengths for the two sodium salts. This is a further evidence that, below I = 1 mol L -1 , phytate acid-base properties are scarcely affected by the nature of background salt anions. (12-2i-j)-species Phytate protonation constants in NaNO 3aq were used in calculations of stability constants for Cu i H j Phy (12-2i-j)-species. As concerns copper(II) hydrolysis, we took into account in our calculations the species and values taken from ref. [START_REF] De Robertis | Thermodynamic Parameters for the formation of Dimeric Hydrolytic Species of Copper(II) in Aqueous NaClO 4 Solution at Different Ionic Strengths[END_REF] that, although they were obtained in sodium perchlorate media, can be easily applied to nitrate solutions (both perchlorate and nitrate anions can be considered as weakly interacting with Cu 2+ properly used, yield to the same results. (12-2i-j)-species on ionic strength Complex formation constants reported in Table 5 proved to be fairly dependent on ionic strength. By applying eq. ( 4) to stability constants in both molar and molal concentration scales we were able to calculate corresponding infinite dilution values, reported in Table 6 together with refined C and ∆ε parameters for each set of constants. According to eq. ( 7), ∆ε in Table 6 correspond to the algebraic sum of all SIT interaction coefficients involved in the formation reaction of the Cu i H j Phy (12-2i-j)-species and, specifically, to

Stability of Cu i H j Phy

Dependence of stability constants of Cu i H j Phy

∆ε[Cu i H j Phy (12-2i-j)-] = i ε(Cu 2+ , NO 3 - ) + ε[H j Phy (12-j)-, Na + ] -ε[Cu i H j Phy (12-2i-j)-, Na + ] (8)
The goodness of fits can be easily appreciated by looking at Figures 234, where log K ij values of Cu i H j Phy (12-2i-j)-species are plotted vs. ionic strength in the molar scale. These

Figures also show the very good agreement between values obtained by ISE-H + and ISE-

Cu 2+ . The application of eq. ( 4) with parameters reported in Table 6 allows us to calculate,

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

9 with fairly good accuracy, complex formation constants at other ionic strength values than those experimentally investigated: some of these values are reported in Table 7.

Sequestering ability of phytate toward copper(II)

One of the most important features of phytate ion is its fairly strong binding ability toward several metal and organometal cations, with the formation of very stable complexes and/or scarcely soluble species. Of course, this characteristic modifies the speciation and the bioavailability of these cations in presence of phytate and, for direct applications, these changes must be accurately quantified. For this reason, we already proposed the use of a

Boltzman type equation for the determination of the sequestering ability of phytate (and other ligands) toward a given cation, once the experimental conditions are fixed [START_REF] Stefano | Speciation of phytate ion in aqueous solution. Cadmium(II) interactions in NaCl aq at different ionic strengths[END_REF]. By using any computer program able to calculate free concentrations of various species in solution (i.e., speciation diagrams obtained by, e.g., ES4ECI), the percentage of cation not complexed by a ligand (phytate in our case) can be plotted as a function of total ligand concentration (as -log C L ) at a fixed pH value, ionic strength, temperature and total metal concentration. Curve so obtained can be fitted to the equation

2 2 1 0 1 A e A A y S / ) x ( x + + - = - ( 9
)
where y represents the total percentage of not-complexed metal (Cu 2+ in our case). By considering A 1 = 0 and A 2 = 100 (the free cation percentage at minimum and maximum -log C L values, respectively) refined x 0 represents the value of -log C L at 50% of not-complexed cation, while S is the curve slope in that point. X 0 value refined in this way, which we defined for opportunity as pL 50 , is a very useful parameter because it can give an objective representation of the binding ability of a ligand (L) toward a given cation, once the experimental conditions are fixed. For example, for a given ligand, different authors may report different speciation schemes: especially for very complex systems, this is very frequent and it does not always mean that one of them is not correct, but it may be due to several reasons. In this case, calculation of pL 50 values may overcome this difficulty, making comparisons easier and faster than other methods commonly used to express the binding ability. The same considerations can also be made to compare the binding ability of different ligands: obstacles related to the different nature and number of species formed may be In the case of copper sequestration by phytate, as a results one may obtain curves like that reported in Figure 5, where n is plotted vs. pCu at I = 0.10 mol L -1 , at t = 25°C, pH = 5.5 and C Phy = 10 -3 mol L -1 . n is given by the ratio between the sum of concentrations of copper species (each multiplied by the number of copper ions forming the complexes) and the total phytate concentration, namely the average number of copper ions bound to phytate

Phy i - j) - 2i - (12 j i C ] Phy H [Cu i n ∑ = ( 10
)
At constant pH, eq. ( 10) become

∑ ∑ + + + = i i 2 ' i i i 2 ' i ] [Cu 1 ] [Cu i n ß ß ( 11
)
whete β i ' are conditional complex formation constants that, in the experimental conditions of diagram in Figure 5, are β 1 ' = 5.87 and β 2 ' = 7.50. However, with respect to these methods, sequestration curves built for the calculation of pL 50 allow to rapidly evaluate the minimal total ligand concentration able to bind a significant amount of cation. For example, in Figure 6 the copper(II) sequestration curve in presence of phytate is reported in Phy/Cu(II) system at the same temperature, pH, medium and ionic strength conditions as in Figure 5, and at a total concentration of Cu 2+ , C Cu = 10 -6 mol L -1 . In these conditions, pL 50 = 5.73, indicating a quite good sequestering ability of phytate toward copper(II): in fact, this value means that a total ligand concentration of C Phy = 1.8 10 -6 mol L -1 is already sufficient to bind 50% of Cu 2+ in solution. Practically, this figure describes better than Figure 5 how phytate behave toward copper(II): its rapid analysis also suggests the possibility of using phytate as sequestering agent for copper(II) and supports future studies both on the use of plants that naturally synthesize it for phytoremediation purposes or on its direct application in remediation techniques, especially if one takes into account that this ligand is non-toxic and naturally biosynthesized often in large amounts by many vegetal species (e.g., cereals, legumes potatoes, etc.) [START_REF] Maga | Phytate: Its Chemistry, Occurrence, Food Interactions, Nutritional Significance, and Methods of Analysis[END_REF][START_REF] Harland | Phytate: a Good or a Bad Food Component?[END_REF][START_REF] Harland | Food Phytate and Its Hydrolysis Products[END_REF][START_REF] Oatway | Phytic Acid[END_REF]. However, at the end of this discussion on the use of different models for the

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11 interpretation of the sequestering ability of a ligand toward a cation, it is important to stress that, whatever the method is, reliable data are essential, and this paper provides all elements necessary for the calculation of all those parameters required for the application of several different models to the determination of phytate sequestering ability toward copper(II) (from protonation and complex formation constants one can calculate free concentration of ions, formation percentages of species, n , pL 50 and others).

Finally, as concerns diagrams in Figures 56, worth of mention is also the fact that speciation of Phy/Cu(II) system at pH > 4.5 was not experimentally investigated in the present work. However, the low total metal concentration let us suppose that, in the conditions of the sequestration diagram, pH = 5.5 or higher can be experimentally achieved without precipitation phenomena. Nevertheless, increasing pH values may yield to the formation of other less-protonated Cu i H j Phy (12-2i-j)-species than those experimentally determined: this aspect was taken into account in the calculation of free copper(II) concentrations, including in the speciation model the formation of the triprotonated CuH 3 Phy 7-species. As concerns its stability, we hypothesized log T K 13 ~ 12.8 and log K 13 ~ 9.0 at I = 0.1 mol L -1 . These values come from a linear extrapolation of log K 14 and log K 15 values at infinite dilution and at different ionic strengths, justified by the fact that other cation/phytate s ystems already evidenced several regularities in the stability of their complexes, allowing the formulation of many predictive equations that correlate this stability to the ligand protonation step and/or to the number of metal cations bound to phytate (see, e.g., refs. [START_REF] Stefano | Speciation of phytate ion in aqueous solution. Alkali metal complex formation in different ionic media[END_REF][START_REF] Stefano | Speciation of phytate ion in aqueous solution. Dimethyltin(IV) interactions in NaCl aq at different ionic strengths[END_REF][START_REF] Stefano | Speciation of phytate ion in aqueous solution. Sequestering ability towards mercury(II) cation in NaCl aq at different ionic strengths[END_REF][START_REF] Stefano | Speciation of phytate ion in aqueous solution. Cadmium(II) interactions in NaCl aq at different ionic strengths[END_REF]). However, this rough extrapolation did not significantly alter results

shown in Figures 56because in the most critical conditions of the diagrams, changes of ~1 log units in the stability of CuH 3 Phy 7-species do not sensibly affect phytate sequestering ability. At the same time, the presence in the model of this species better describe phytate and copper(II) speciation in that experimental conditions and cannot be neglected.

Literature comparisons

In our previous contributions [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. Alkali metal complex formation in different ionic media[END_REF][START_REF] Stefano | Speciation of phytate ion in aqueous solution. Non covalent interactions with biogenic polyamines[END_REF][START_REF] Crea | Speciation of phytate ion in aqueous solution. Characterisation of Ca-phytate sparingly soluble species[END_REF][START_REF] Stefano | Speciation of phytate ion in aqueous solution. Thermodynamic parameters for protonation in NaCl[END_REF][START_REF] Stefano | Speciation of phytate ion in aqueous solution. Dimethyltin(IV) interactions in NaCl aq at different ionic strengths[END_REF][START_REF] Stefano | Speciation of phytate ion in aqueous solution. Sequestering ability towards mercury(II) cation in NaCl aq at different ionic strengths[END_REF][START_REF] Crea | Speciation of phytate ion in aqueous solution. Sequestration of magnesium and calcium by phytate at different teperatures and ionic strengths, in NaCl aq[END_REF][START_REF] Stefano | Speciation of phytate ion in aqueous solution. Cadmium(II) interactions in NaCl aq at different ionic strengths[END_REF][START_REF] Crea | Speciation of phytate ion in aqueous solution. Trimethyltin(IV) interactions in self medium[END_REF] we stressed several times that, in spite of the wide number of papers dealing with metal-phytate interactions (with particular emphasis given to the bioavailability of the metal in presence of the ligand) that can be found in literature, few papers report thermodynamic parameters (such as stability constants) of metal/phytate complexes. In this specific case, to our knowledge and at present time, just six papers deal directly with copper(II)-phytate system [START_REF] Martin | Phytic Acid: Divalent Cation Interactions. III. A Calorimetric and Titrimetric Study of the pH Dependence of Copper(II) Binding[END_REF][START_REF] Martin | Phytic Acid: Divalent Cation Interactions. IV. A Spectroscopic Determination of Co(II) and Cu(II) Binding[END_REF][START_REF] Persson | Binding of Cu 2+ , Zn 2+ , and Cd 2+ to Inositol Tri-, Tetra-, Penta-, and Hexaphosphates[END_REF][START_REF] Bebot-Brigaud | 31 P NMR, potentiometric and spectrophotometric studies of phytic acid ionization and complexation properties toward Co 2+ , Ni 2+ , Cu 2+ , Zn 2+ and Cd 2+[END_REF][START_REF] Vasca | Complex Formation between Phytic Acid and Divalent Metal Ions: a Solution Equilibria and Solid State Investigation[END_REF][START_REF] Torres | Solution behaviour of myo-inositol hexakisphosphate in the presence of multivalent cations. Prediction of a neutral pentamagnesium species under cytosolic/nuclear conditions[END_REF] (two further papers are concerned with

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12 "interactions" [START_REF] Champagne | Binding differences of Zn(II) and Copper (II) ions with phytate[END_REF] between phytate and copper and "binding differences" of phytate toward copper(II) [START_REF]Phytic acid-trace element (Zn, Cu, Mn) interactions[END_REF], but only from a qualitative and medical point of view). In two of them, by

Martin and Evans [START_REF] Martin | Phytic Acid: Divalent Cation Interactions. III. A Calorimetric and Titrimetric Study of the pH Dependence of Copper(II) Binding[END_REF][START_REF] Martin | Phytic Acid: Divalent Cation Interactions. IV. A Spectroscopic Determination of Co(II) and Cu(II) Binding[END_REF], authors evaluated the binding ability of phytate toward copper(II) by potentiometric, calorimetric and spectrophotometric studies at t = 25°C in KNO 3 0.2 mol L -1 aqueous solution. In these papers the authors infer about the amount of metal bound to the ligand as a function of pH and of metal to ligand ratio and make hypothesis about the structure of complexes, but, unfortunately, they do not report any thermodynamic parameter for the formation of copper(II)-phytate complexes, except for an "apparent heat of binding and precipitation" of Cu 2+ to phytate of ~22 kcal mol -1 , indicating that complexation reaction is endothermic in nature.

With the aim of studying the solubility of some metal ions under pH conditions that may be encountered in the duodenum, Persson et al. [START_REF] Persson | Binding of Cu 2+ , Zn 2+ , and Cd 2+ to Inositol Tri-, Tetra-, Penta-, and Hexaphosphates[END_REF] studied the interaction between Cu 2+ (and Zn 2+ and Cd 2+ ) and phytate (and other isolated fractions of inositol phosphates with 6, 5, 4 and 3 phosphate groups) by potentiometry, at t = 25°C and in NaClO 4 + NaCl at I = 0.1 mol L -1 (NaCl = 10 mmol L -1 + NaClO 4 = 90 mmol L -1 ), by considering total metal and ligand concentrations to be constant (C Cu = 3.22 mmol L -1 and C Phy = 10.0 mmol L -1 ) and varying pH (3 ≤ pH ≤ 7). These authors do not report any thermodynamic data, but some important consideration can be made. In the above conditions, they show graphically that phytate binds ~50% of total copper(II) at pH ~5.5. This is in agreement with what we can calculate from our pL 50 value at I = 0.1 mol L -1 and pH = 5.5 (Figure 5): pL 50 ~5.7, indicating that 50% of copper(II) is bound to phytate when its total concentration is C Phy ~ 2 10 -6 mol L -1 , corresponding to a ligand to metal ratio of L:M ~ 2:1, i.e. in very similar ratios to those utilized in ref. [START_REF] Persson | Binding of Cu 2+ , Zn 2+ , and Cd 2+ to Inositol Tri-, Tetra-, Penta-, and Hexaphosphates[END_REF] (L / M ~ 3:1). Howerer, we have some problems in comparing our results to those by Persson et al., because the real conditions of ionic strength and ligand to metal ratio are not uniformly defined (differences between data reported in figures and those along the text).

Quantitative data on phytate-copper(II) complexes were reported for the first time by Bebot-Brigaud et al. [START_REF] Bebot-Brigaud | 31 P NMR, potentiometric and spectrophotometric studies of phytic acid ionization and complexation properties toward Co 2+ , Ni 2+ , Cu 2+ , Zn 2+ and Cd 2+[END_REF], using 31 P-NMR spectroscopy, potentiometry and spectrophotometry, in tetraethylammonium perchlorate (I = 0.17 mol L -1 ) at t = 20ºC. Before this paper, as also stated by the same authors, there was "no published work concerning the nature and stability of the species appearing in aqueous solution, and the sites of phytic acid which are involved in complex formation". Unfortunately, the particular experimental conditions of temperature and ionic medium adopted by these authors make comparisons fairly difficult to do. Further problems are also represented by the fact that authors considered

A C C E P T E D M A N U S C R I P T ACCEPTED MANUSCRIPT 13
just the formation of 1:1 species, owing to the fact that they worked with metal to ligand ratios that favor the second one, avoiding the formation of polynuclear species and favoring the investigation of wider pH ranges with the absence of precipitation phenomena, whilst the opposite choice was made in the present study, where we worked with a metal excess.

However, as stated in previous paragraph, a comparison among pL 50 value calculated by the protonation and stability constants by Bebot-Brigaud et al. and that calculated by our dataset in the most similar conditions may be performed and could be very helpful. From their data, at pH = 5.5 and C Cu = 10 -6 mol L -1 , pL 50 = 6.35, whilst we obtained pL 50 = 5.55 at I = 0.15 mol L -1 from our stability constants in NaNO 3aq . This difference, i.e. ∆pL 50 = 0.8, should be ascribed to sodium complexation. In fact, at fixed experimental conditions (pH, ionic strength, temperature), difference between pL 50 values calculated by complex formation constants in one ionic medium considered as scarcely interacting with a ligand (e.g., Cu i H j Phy (12-2i-j)- complexes in tetraalkylammonium salts) and in an interacting medium (e.g., Cu i H j Phy (12-2i-j)- complexes in alkali metal cation salts), respectively, should be equal to pL 50 value determined for the sequestration of cations of interacting medium by the ligand (e.g., Na i H j Phy (12-i-j)- complexes in tetraethylammonium media [START_REF] Stefano | Speciation of phytate ion in aqueous solution. Alkali metal complex formation in different ionic media[END_REF]). By this procedure, calculations performed at pH = 5.5 and I = 0.15 mol L -1 by sodium complex formation constants already determined [START_REF] Stefano | Speciation of phytate ion in aqueous solution. Alkali metal complex formation in different ionic media[END_REF] gave a calculated pL 50 of ~1.1 units, which is in fairly good agreement with ∆pL 50 : residual differences may be ascribed to the slightly different temperature.

As concerns the last two, and most recent works on copper(II)/phytate complexes [START_REF] Vasca | Complex Formation between Phytic Acid and Divalent Metal Ions: a Solution Equilibria and Solid State Investigation[END_REF][START_REF] Torres | Solution behaviour of myo-inositol hexakisphosphate in the presence of multivalent cations. Prediction of a neutral pentamagnesium species under cytosolic/nuclear conditions[END_REF], the experimental conditions (of temperature, medium and ionic strength) make comparisons not significant (in the paper by Vasca et al. [START_REF] Vasca | Complex Formation between Phytic Acid and Divalent Metal Ions: a Solution Equilibria and Solid State Investigation[END_REF], authors worked in NaClO 4 at I = 3 mol L -1 and t = 25ºC, while we reached a maximum of I = 1 mol L -1 ; Torres et al. [START_REF] Torres | Solution behaviour of myo-inositol hexakisphosphate in the presence of multivalent cations. Prediction of a neutral pentamagnesium species under cytosolic/nuclear conditions[END_REF] worked at t = 37°C). K j H refers to the equilibrium: H + + H j-1 Phy (12-j+1)-= H j Phy (12-j)-; ± standard deviation; b) mean ionic strength value during titration. c) ± standard deviation, values in parenthesis are referred to NaCl aq (ref. [START_REF] Stefano | Speciation of phytate ion in aqueous solution. Protonation constants in tetraethylammonium iodide and sodium chloride[END_REF]).

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a) K j H refers to the equilibrium: H + + H j-1 Phy (12-j+1)-= H j Phy (12-j)-; ± standard deviation;

b) log K j H = log T K j H + C j I -log (1 + 10 D j I); c) values in parenthesis, from ref. [START_REF] Stefano | Speciation of phytate ion in aqueous solution. Protonation constants in tetraethylammonium iodide and sodium chloride[END_REF]. b) K ij refers to the equilibrium: : i Cu 2+ + H j Phy (12-j)-= Cu i H j Phy (12-2i-j)-; c) ± standard deviation; d) to be used for stability constants expressed in the molar concentration scale;

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

e) mean deviation of fit;

f) to be used for stability constants expressed in the molal concentration scale. b) in both molar mol L -1 , or molal mol kg -1 (H 2 O) concentration scales;

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

c) K ij refers to the equilibrium: i Cu 2+ + H j Phy (12-j)-= Cu i H j Phy (12-2i-j)-, ± standard deviation;

  Titrando apparatus controlled by Metrohm TiAMO 1.0 software for the automatic data acquisition.

  determination of pL 50 . Between these other methods, widely used are those where the average number ( n ) of metal ions bound by a ligand are expressed as a function of pH or pM (= -log [M], M = metal cation).

1 Figure 1 . 1 Figure 2 . 1 Figure 3 . 1 Figure 4 .Figure 5 .Figure 6 .

 1112131456 Figure 1. Distribution diagram of Cu i H j Phy (12-2i-j)-species vs. pH at I = 0.75 mol L -1 and t = 25°C. Experimental conditions: C Phy = 0.002 mol L -1 ; C Cu = 0.004 mol L -1 . Species: 1. Cu 2 H 5 Phy 3-; 2. CuH 4 Phy 6-; 3. CuH 5 Phy 5-; Σ = percentage of complexed phytate.

  and refs. therein). Although, in this kind of studies, different anions of background salts do not dramatically influence phytate protonation constants, we opted for the determination of these values in sodium nitrate aqueous solutions at different ionic strengths, in order to obtain more accurate data to use in the estimation of stability constants for phytate-copper species in NaNO 3aq . From

potentiometric measurements performed in the experimental conditions reported in Table 1, we obtained log K j H values shown in Table 2. Dependence on ionic strength of protonation constants reported in this Table was modeled by eq. 3, in analogy with the procedure followed

  Potentiometric data by ISE-H + measurements evidenced, in the experimental conditions of Table1, the formation of three Cu i H j Phy(12-2i-j)-species: the mononuclear CuH 4 Phy 6-and CuH 5 Phy 5-, and the dinuclear Cu 2 H 5 Phy 3-. Values of complex formation constants at different ionic strengths are reported in Table5, both in molar and molal concentration scales (molar to molal conversions were performed by using appropriate density values). In the same Table,stability constants of pentaprotonated CuH 5 Phy 5-and Cu 2 H 5 Phy 3-species, obtained by ISE-Cu 2+ electrode, are also shown. The narrow pH range explored during these last measurements (respect to that by ISE-H + , see Table1) did not allow the determination of the CuH 4 Phy 6-species, which is formed at higher pH values than those investigated during ISE-Cu 2+ measurements (as shown in Figure1, where a speciation diagram of phytate in presence of Cu 2+ is reported for example). However, the analysis of complex formation constants reported in Table5for CuH 5 Phy 5-and Cu 2 H 5 Phy 3-species at different ionic strengths reveals

	ACCEPTED MANUSCRIPT
	the model did not affect the stability of copper-phytate complexes in these experimental
	conditions.
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	8

). The formation of a further Cu 3 (OH) 4 2+ species was initially considered, as previously proposed (see, e.g., refs. in [26]), but preliminary calculations demonstrated that its presence/absence in that both ISE-H + and ISE-Cu 2+ electrodes gave, within the experimental error, analogous values: as already stated in the introduction, this demonstrate how different techniques, if

Table 1 .

 1 Experimental conditions for potentiometric measurements at t = 25°C a)

	C Cu	a)	C Phy	a)	C NaNO 3	a)	pH range	C NaOH	a)
					ISE-H +
	0.002	0.002	0.096		2.27 -4.19	0.2033 b)
	0.003	0.002	0.096		2.29 -3.82	0.2033 b)
	0.004	0.002	0.096		2.26 -3.54	0.2033 b)
	0.002	0.002	0.253		2.27 -4.18	0.2033 b)
	0.003	0.002	0.253		2.19 -3.77	0.2033 b)
	0.004	0.002	0.253		2.23 -3.99	0.2033 b)
	0.002	0.002	0.507		2.22 -3.98	0.2033 b)
	0.003	0.002	0.507		2.21 -3.83	0.2033 b)
	0.004	0.002	0.507		2.22 -3.80	0.2033 b)
	0.002	0.002	0.748		2.20 -4.18	0.2033 b)
	0.003	0.002	0.748		2.19 -4.00	0.2033 b)
	0.004	0.002	0.748		2.17 -3.82	0.2033 b)
	0.002	0.002	0.997		2.17 -4.18	0.2033 b)
	0.003	0.002	0.997		2.16 -3.99	0.2033 b)
	0.004	0.002	0.997		2.18 -3.82	0.2033 b)
					ISE-Cu 2+
	0.01324 b)	0.001	0.103		4.29 -3.70	0.006
	0.01324 b)	0.002	0.103		4.13 -3.89	0.012
	0.01324 b)	0.001	0.247		4.09 -3.73	0.006
	0.01324 b)	0.002	0.247		3.96 -3.67	0.012
	0.01324 b)	0.001	0.497		4.05 -3.80	0.006
	0.01324 b)	0.002	0.497		3.97 -3.74	0.012
	0.01324 b)	0.001	0.748		3.93 -3.79	0.006
	0.01324 b)	0.002	0.748		3.76 -3.65	0.012
	0.01324 b)	0.001	0.938		3.80 -3.70	0.006
	0.01324 b)	0.002	0.938		3.79 -3.70	0.012
	a) Total concentrations expressed in mol L -1 , 2 -3 titrations for each experimental condition;
	b) as titrant.

Table 2 .

 2 Experimental phytate protonation constants a) in NaNO 3aq at different ionic strengths and at t = 25 °C

	I / mol L -1 b)	log K 1	H	log K 2	H	log K 3	H	log K 4 H	log K 5	H	log K 6	H	log K 7	H
	0.117 0.165 0.338 0.339	9.54 ± 0.10 9.46 ± 0.10 8.40 ± 0.10 8.41 ± 0.07	9.86 ± 0.09 9.70 ± 0.09 9.25 ± 0.07 10.17 ± 0.07	9.44 ± 0.05 9.36 ± 0.04 9.18 ± 0.04 8.83 ± 0.04	8.15 ± 0.05 8.07 ± 0.04 7.62 ± 0.03 7.62 ± 0.03	6.48 ± 0.03 6.29 ± 0.03 6.02 ± 0.02 5.98 ± 0.02	5.30 ± 0.06 5.08 ± 0.06 4.64 ± 0.04 4.51 ± 0.04	2.95 ± 0.03 2.81 ± 0.03 2.80 ± 0.02 2.69 ± 0.02
	0.562 1.039	8.60 ± 0.06 8.46 ± 0.12	9.50 ± 0.06 9.13 ± 0.12	8.74 ± 0.03 8.50 ± 0.05	7.56 ± 0.03 7.33 ± 0.04	5.87 ± 0.02 5.65 ± 0.02	4.55 ± 0.02 4.44 ± 0.08	2.61 ± 0.02 2.50 ± 0.06
	a)

Table 3 .

 3 Empirical parameters of eq. (3) a) for the dependence of phytate protonation constants on ionic strength in NaNO 3aq , at t = 25°C

	j	log T K j	H b)	C j	c)	D j	c)
	1	18.17	-0.13 ± 0.20	9.67 ± 0.12
				(0.13)	(9.59)
	2	15.32	0.26 ± 0.18	6.37 ± 0.10
				(0.12)	(6.50)
	3	12.76	-0.02 ± 0.07	4.23 ± 0.05
				(0.06)	(4.27)
	4	10.05	0.14 ± 0.07	2.86 ± 0.05
				(0.08)	(2.91)
	5	7.59	0.15 ± 0.04	2.08 ± 0.03
				(0.13)	(2.06)
	6	6.13	0.19 ± 0.15	1.92 ± 0.09
				(0.14)	(1.83)
	7	3.52	0.41 ± 0.10	1.39 ± 0.05
				(0.27)	(1.56)
	a) log K j H = log T K j H + C j I -log (1 + 10 D j I);
	b) from ref. [1];

Table 4 .

 4 Phytate protonation constants a) calculated by eq. (3) b) in NaNO 3aq and NaCl aq c) at different ionic strengths and at t = 25 °C

	I / mol L -1	log K 1	H	log K 2	H	log K 3	H	log K 4 H	log K 5	H	log K 6	H	log K 7	H
	0.10	9.48 ± 0.11	9.98 ± 0.09	9.53 ± 0.05	8.20 ± 0.05	6.49 ± 0.03	5.17 ± 0.06	3.02 ± 0.03
		(9.58)	(9.84)	(9.50)	(8.14)	(6.50)	(5.25)	(2.88)
	0.25	9.07 ± 0.08	9.62 ± 0.08	9.13 ± 0.04	7.83 ± 0.04	6.13 ± 0.02	4.84 ± 0.05	2.77 ± 0.02
		(9.20)	(9.46)	(9.11)	(7.76)	(6.15)	(4.90)	(2.59)
	0.50	8.73 ± 0.06	9.39 ± 0.06	8.82 ± 0.03	7.57 ± 0.03	5.88 ± 0.02	4.59 ± 0.02	2.60 ± 0.02
		(8.93)	(9.19)	(8.83)	(7.48)	(5.88)	(4.65)	(2.37)
	0.75	8.52 ± 0.07	9.28 ± 0.08	8.64 ± 0.03	7.43 ± 0.03	5.75 ± 0.01	4.46 ± 0.04	2.54 ± 0.04
		(8.78)	(9.04)	(8.67)	(7.32)	(5.74)	(4.51)	(2.27)
	1.00	8.36 ± 0.11	9.22 ± 0.11	8.51 ± 0.04	7.34 ± 0.04	5.66 ± 0.01	4.39 ± 0.07	2.52 ± 0.06
		(8.69)	(8.95)	(8.56)	(7.21)	(5.65)	(4.42)

Table 5 .

 5 Experimental complex formation constants a) for copper-proton-phytate species in NaNO 3aq at different ionic strengths, at t = 25°C

	I b)	I c)	log K 14		log K 15		log K 25
					ISE-H +
	0.134 0.135 0.291 0.294	--5.83 ± 0.09 b,d) 5.81 c) --	5.04 ± 0.07 b,d) 5.04 c) 3.95 ± 0.06 3.93	7.40 ± 0.08 b,d) 7.38 c) 6.52 ± 0.06 6.50
	0.538 0.549 0.770 0.791 1.019 1.055	5.47 ± 0.07 5.35 ± 0.07 5.30 ± 0.11	5.46 5.33 5.28	3.61 ± 0.06 3.38 ± 0.07 3.52 ± 0.11	3.60 3.37 3.51	6.00 ± 0.06 6.58 ± 0.09 6.94 ± 0.12	5.97 6.55 6.92
					ISE-Cu 2+
	0.103 0.104	--	--	4.75 ± 0.08	4.75	7.55 ± 0.08	7.53
	0.247 0.250 0.497 0.506 0.748 0.768	------	------	3.95 ± 0.06 3.47 ± 0.05 3.30 ± 0.07	3.95 3.46 3.29	6.65 ± 0.07 6.17 ± 0.06 6.36 ± 0.08	6.63 6.14 6.33
	0.938 0.968	--	--	3.47 ± 0.10	3.46	7.07 ± 0.11	7.05

a) K ij refers to the equilibrium: i Cu 2+ + H j Phy (12-j)-= Cu i H j Phy (12-2i-j)-; b) in the molar concentration scale, mol L -1 ; c) in the molal concentration scale, mol kg -1 (H 2 O); d) ± standard deviation.

Table 6 .

 6 Empirical parameters of eq. (4) a) for the dependence of complex formation constants of Cu i H j Phy (12-2i-j)-species b) on ionic strength in the molar and molal concentration scales in

	NaNO 3aq , at t = 25°C
	Species			z*	log T K ij	b)	C d)	m.d. e)	∆ε f)	m.d. e)
	CuPhyH 4	6-	32	10.28 ± 0.14 c)	1.58 ± 0.20	0.08	1.56 ± 0.20 c)	0.09
	CuPhyH 5	5-	28	7.79 ± 0.09	1.36 ± 0.16	0.22	1.35 ± 0.16	0.22
	Cu 2 PhyH 5	3-	48	12.53 ± 0.09	4.20 ± 0.17	0.22	4.13 ± 0.17	0.23
	a) log K ij = log T K ij + D.H. + C I;

Table 7 .

 7 Complex formation constants for copper-proton-phytate species in NaNO 3aq at different ionic strengths, at t = 25°C, calculated by eq. (4) a) .94 ± 0.12 d) 6.93 ± 0.12 e) 4.87 ± 0.08 d) 4.87 ± 0.07 e) 7.70 ± 0.08 d) 7.69 ± 0.08 e) 0.15 6.51 ± 0.11 6.51 ± 0.11 4.50 ± 0.07 4.50 ± 0.07 7.16 ± 0.07 7.15 ± 0.07 0.25 6.01 ± 0.10 6.01 ± 0.09 4.05 ± 0.06 4.05 ± 0.06 6.59 ± 0.07 6.57 ± 0.07 0.50 5.47 ± 0.07 5.46 ± 0.07 3.57 ± 0.05 3.57 ± 0.05 6.23 ± 0.06 6.19 ± 0.06 0.75 5.31 ± 0.07 5.30 ± 0.07 3.43 ± 0.07 3.42 ± 0.07 6.46 ± 0.08 6.40 ± 0.08 1.00 5.33 ± 0.10 5.31 ± 0.10 3.44 ± 0.10 3.43 ± 0.10 6.94 ± 0.12 6.86 ± 0.12 a) log K ij = log T K ij + D.H. + C I;

	I b)	log K 14	c)	log K 15	c)	log K 25	c)
	0.10 6

Acknowledgements

We thank University of Messina (PRA) for financial support.

A C C E P T E D

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M A N U S C R I P T


M R Mangione

D Giacomazza

G Cavallaro

D Bulone

V Martorana

P L San Biagio

M R Mangione # ¥

D Giacomazza # ¥

D Bulone #

Relation between structural and release properties in a polysaccharide gel system

Keywords: K-carrageenan, Ketoprofen, gel structural properties, drug release, Franz's cells

come   L'archive ouverte pluridisciplinaire

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M A N U S C R I P T

Introduction

In the last years, a number of natural polysaccharides forming gels were studied to prepare drug-release devices. The drug release rate is strongly dependent on the characteristics of the gel structure, which, in some cases, can be easily modified [START_REF] Castelli | Influence of different parameters on drug release from hydrogel systems to a biomembrane model. Evaluation by differential scanning calorimetry technique[END_REF][START_REF] Colombo | Swelling controlled release in hydrogel matrices for oral route[END_REF][START_REF] Giammona | Crosslinked α,β-polyasparthydrazide hydrogels: effect of crosslinking degree and loading method on cytarabine release rate[END_REF]. Under this respect matrices based on κ-carrageenan deserve great interest. κ-carrageenan a linear water soluble polysaccharide extracted from different species of red algae with a primary structure based on alternating disaccharide units of α-(1-3)-D-galactose-4-sulphate and β-(1-4)-D-galactose. In aqueous solutions and in presence of various cations, κ-carrageenan forms thermoreversible gels on cooling. It is extensively used as thickening, gelling agent, texture enhancer or stabilizer in the food, pharmaceutical and cosmetic industries [START_REF] Makino | Design of a rate and time-programming drug release device using a hydrogel: pulsatile drug release from κ-Carrageenan hydrogel device by surface erosion of the hydrogel[END_REF][START_REF] Garcia | Preliminary spherical agglomerates of water soluble drug using natural polymer and crosslinking technique[END_REF][START_REF] Campanella | Hydrogen peroxide determination in pharmaceutical formulation and cosmetics using a new catalase biosensor[END_REF]. More recently drug delivery systems based on κ-carrageenan gels were tested in vitro [START_REF] Sipahigil | Preparation and in vitro evaluation of verapamil HCl and ibuprofen containing carrageenan beads[END_REF][START_REF] Valenta | Influence of carrageenan on the rheology and skin permeation of microemulsion formulations[END_REF]. In this study the structural properties of κcarrageenan gels have been correlated to its capability of release an active agent.

Previous studies on κ-carrageenan gels have shown that the internal structure of the gel can be easily and opportunely modulated using different proportions of K + and Na + ions [START_REF] Mangione | Thermoreversible gelation of κ-Carrageenan: relation between conformational transition and aggregation[END_REF][START_REF] Mangione | K + and Na + effects on the gelation properties of κ-Carrageenan[END_REF]. In fact, these cations play a different and specific role in the κ-carrageenan gelation pathway: the K + induces a coil?double helix transition preceding and promoting the formation of an ordered gel, whereas the Na + ion does not promote the coil?double helix transition, but takes part in the aggregation process probably through a phase separation mechanism. In this case the resulting structure is more disordered with respect to that one obtained in the presence of K + [START_REF] Mangione | K + and Na + effects on the gelation properties of κ-Carrageenan[END_REF]. Both different gelation mechanisms (i.e. the formation and lengthening of the helices induced by K + ions, or coil aggregation induced through phase separation by Na + ions) can compete when the two cations are both present in solution depending on the K + /Na + ratio and temperature [START_REF] Mangione | K + and Na + effects on the gelation properties of κ-Carrageenan[END_REF]. The gelation pathway can be modulated to produce gels with different texture.

The aim of the present study is to evaluate i) the possibility of modulating the release rate of a model drug loaded in the κ-carrageenan gels by controlling the gel texture through the use of different cationic concentration, ii) the relationship between salt composition and release profiles iii) the potential advantages offered by κ-carrageenan matrices as drug delivery system in comparison with other commercial pharmaceutical products.

In order to perform this study three κ-carrageenan gels prepared with different salt composition have been loaded with Ketoprofen sodium salt, a known non steroidal anti-inflammatory drug (NSAIDs); the obtained Ketoprofen release profiles have been compared with those obtained by Artrosilene Gel ® and Fastum Gel ® , two commercial products containing the same active agent.

Materials and methods

Materials

A C C E P T E D M A N U S C R I P T ACCEPTED MANUSCRIPT 3
The κ-Carrageenan (type X-6913, Lot 63-80270) was from Copenhagen Pectin A/S, Denmark. The κ-Carrageenan powder was dissolved in Millipore deionised water at 70 °C (in the presence of 200 ppm sodium azide as bacteriostatic agent) and stirred at the same temperature for 2 h. [START_REF] Mangione | Thermoreversible gelation of κ-Carrageenan: relation between conformational transition and aggregation[END_REF][START_REF] Meunier | Structure and kinetics of aggregating κ-Carrageenan studied by light scattering[END_REF]. The pH of the solution was 8.7 to prevent hydrolysis during preparation [START_REF] Meunier | Structure and kinetics of aggregating κ-Carrageenan studied by light scattering[END_REF][START_REF] Rochas | Acid and enzymic hydrolysis of kappa Carrageenan[END_REF]. Then, the solution was dialysed against Millipore water to eliminate excess salt. Hot Millipore water, containing the appropriate amount of KCl and/or NaCl, was added to set the final ionic composition. The solution was finally filtered at high temperature through a 0.22 µm Corning filter.

Ketoprofen sodium salt was obtained from salification of the acidic form (as supplied by Sigma) using NaOH 0.1 M in equimolar amount and freeze -drying the final solution.

The sodium salt form was chosen because of the very low solubility of the acidic form. The use of the sodium salt form at 2.5% w/w determines a contribution of approximately 100 mM of Na + ions which is sufficient to appreciably affect the aggregation process [START_REF] Mangione | K + and Na + effects on the gelation properties of κ-Carrageenan[END_REF].

The drug was incorporated under stirring into the filtered colloidal dispersion at 60 °C, to avoid destabilization of the Ketoprofen. The dispersion was then put in the cuvette for static light scattering measurements or in the rheometer plate for viscoelastic measurements at 20°C and kept at this temperature for 24 hours to obtain stable gels.

Commercial products, used in release experiments with Franz's cells, were Fastum Gel ®, containing 2.5% (w/w) Ketoprofen acid form and Artrosilene Gel ®, containing Ketoprofen lysine salt 5% (w/w).

Static light scattering measurements

Static light scattering measurements were done using a Brookhaven Instrument BI-9000 digital correlator and an ILT 550 Argon laser tuned at 514.5 nm. Samples, prepared as described above, were put into a thermostatic cell compartment of Brookhaven Instrument BI200-SM goniometer system at 20 °C. The sample was kept at this temperature for 24 h and heated at 37 °C before starting the measurement. The intensity of light scattered by gelled samples was measured at different scattering vector q= 4 π n sin(θ /2) / λ 0 , where n is the refraction index of solution, λ 0 is the wavelength of the incident light and θ is the scattering angle. Due to the non-ergodic character of the gel, the intensity was measured over different regions of the specimen, using a motor-driven cell holder.

Rheological measurements

Viscoelastic spectra under low amplitude oscillatory shear were measured on a controlled stress AR-1000 rheometer (TA Instruments, UK) using a titanium cone-plate geometry (angle 0.0174 rad, radius 20 mm, gap 26 µm). All experiments were done in the 0.02 -30 Hz frequency range at 4 x 10 -3 strain. The hot solution was loaded on the rheometer plate, set at 65 °C. Then, the temperature was quickly lowered to 20 °C. The sample was kept at this

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Drug release studies

Release studies, performed at pH = 5.5, were done using Franz's cells to simulate the topical release [START_REF] Franz | Percutaneous absorption. On the relevance of in vitro data[END_REF]. Franz's cells with a receiving compartment volume of 4.2 ml and an effective diffusion area of 0.95 cm 2 were used in this study. The receiving phase was a buffer solution at pH 5.5 (K 2 HPO 4 , KH 2 PO 4 ). The buffer, degassed before using, was continuously stirred (600 rpm) and maintained at 37°C during all the experiment. A cellulose acetate membrane with a pore size of 0.45 µm and a thickness of 115 µm was used. 500 mg of each gel was placed on the membrane surface previously moistened with the receiving phase. Aliquots (100 µl) of the receiving phase were withdrawn at proper time intervals and replaced with an equal volume of fresh buffer solution. Sink conditions were maintained during the experiments. The amount of drug released was determined by measuring the absorbance at 260 nm of the removed aliquots. UV measurements were done using a Jasco V-530 UV-VIS spectrophotometer.

Results and Discussions

The sol-gel transition of many polysaccharide systems strongly depends on the concentration and type of ions in solution [START_REF] Totosaus | Effect of added salt on textural properties of heat-induced gels made from gum-protein mixtures[END_REF][START_REF] Macartain | Physical characteristics of calcium induced kappa-carrageenan networks[END_REF]. In the case of κ-carrageenan, K + and Na + ions play a fundamental role in establishing the gelation pathway [START_REF] Mangione | Thermoreversible gelation of κ-Carrageenan: relation between conformational transition and aggregation[END_REF][START_REF] Mangione | K + and Na + effects on the gelation properties of κ-Carrageenan[END_REF]. Previous studies, performed on gels without drug [START_REF] Mangione | K + and Na + effects on the gelation properties of κ-Carrageenan[END_REF], have shown that it is possible, by using an appropriate [K + ]/[Na + ] ratio, to obtain gels with very different structural properties, spamming from an ordered matrix formed by double helix aggregation, up to a much more disordered structure, formed by coil condensation.

Since the aim of this study is to correlate the structural properties of different gels with the release profiles of a loaded drug, it is necessary to evaluate how the drug addiction may change the structural properties of the κ-carrageenan matrices. In order to investigate this aspect, static light scattering (SLS) measurements were performed on three different gels of 0.4% (w/w) κ-carrageenan at different K + and Na + concentrations and containing 2.5% (w/w) Ketoprofen sodium salt. Results were compared with those obtained on the same samples without drug.

Table 1 reports the cationic concentrations used for preparing the three 0.4% (w/w) κ-carrageenan gels with or without the drug.

The internal structure of these gels was characterized by determining their fractal dimension, d f , defined by the relationship M ∝ R -df , where M is the mass of the fractal object within a sphere of radius R [START_REF] Brinker | Sol-Gel Science: The Physics and Chemistry of Sol-Gel Processing[END_REF][START_REF] Bulone | Ordering of agarose near the macroscopic gelation point[END_REF]. The value of this parameter in a gelled system allows determining the unravelling of the polymer chain in the space, i.e. how the polymeric network fills the space. The fractal dimension value can be determined by measuring, over a large q range, the light scattered intensity, I (q), and applying the relationship:

f d q q P q S q I - ∝ ⋅ = ) ( ) ( ) ( A C C E P T E D M A N U S C R I P T
where S(q) is the structure function, q is the scattering vector and P(q) is the form factor which, for this system, can be considered equal to 1 due to the small size of single polymer chains with respect to the light wavelength.

Figure 1 show log-log plots of S(q), for all samples containing Ketoprofen (straight lines are the data best fit). The d f values of samples with and without drug are reported in table 1. In all cases, the drug presence does not modify the fractal dimension. For sample A, a value d f ≈ 1.3 was found, which is consistent with an overall loose packing of ramified double-helices [START_REF] Mangione | K + and Na + effects on the gelation properties of κ-Carrageenan[END_REF]. The gel prepared with 3.5 mM KCl and 300 mM NaCl (sample B) has the highest d f value (2.4). This result has been explained by considering that the small amount of K + is not sufficient to promote a significant conformational ordering (double helix), so that the aggregation process follows from a liquid -liquid phase transition (demixing process) leading to a disordered more compact structure [START_REF] Mangione | K + and Na + effects on the gelation properties of κ-Carrageenan[END_REF]. Finally, sample C presents an intermediate d f value. In this case the K + concentration is sufficient to promote the double helix formation, followed by a disordered aggregation as a consequence of the presence of Na + [START_REF] Mangione | K + and Na + effects on the gelation properties of κ-Carrageenan[END_REF].

To obtain more information on the internal structure of gels containing Ketoprofen sodium salt, the visco-elastic properties were investigated by mechanical spectra measurements. The results, reported in figure 2, show that: (i) for each sample the elastic modulus, (G'), and the viscous modulus, (G''), are almost flat with G' larger than G'', as expected for solid-like materials, (ii) the values of visco-elastic modules are very different for the three samples and

(iii) they are dependent on the ionic composition but independent on the ionic strength. Mechanical spectra of the commercial products Artrosilene gel ® and Fastum gel ® were performed in the same conditions for comparison.

Rheological results for κ-carrageenan gels lead to conclude that it is possible to modulate the visco-elastic properties of gels by opportunely varying the K + and Na + concentrations. In particular, for the gel prepared with 3.5 mM KCl and 300 mM NaCl, the Na + ions have a dominant effect in the aggregation process: in this case the gel network will contain a great number of very weak bonds, since the flexible coils can be arranged in a huge number of non-specific mutual contacts. This justifies the formation of a very disordered gel with a low G' value and high d f value. On the opposite, in presence of 150 mM of KCl the gelation mechanism is governed by the formation of rigid double helices, which aggregate into super-strands. This regular structure presents a low d f value and high G' value. Finally, the gel prepared with 20 mM KCl and 300 mM NaCl is still able to form strands and helices, but the presence of Na + introduces in these structures a number of defects enhancing the flexibility and bond number. In this case, in fact, interconnected regions of partially formed double helices or more flexible and shorter super-strands are obtained, as suggested in the literature [START_REF] Hermansson | Effects of potassium, sodium, and calcium on the microstructure and rheological behaviour of kappa-Carrageenan gels[END_REF].

All these findings agree with previous results obtained in absence of Ketoprofen, supporting the hypothesis that the drug does not interfere significantly in the aggregation process.

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To evaluate the release profile of Ketoprofen from each gel and correlate the release with the different structural properties of each system, drug release experiments were done using the Franz's cells. Results, reported in figure 3, were compared with those obtained using two commercial pharmaceutical products: Fastum Gel™ and Artrosilene Gel ® , containing Ketoprofen acid at 2.5% (w/w) and its lysine salt at 5% (w/w), respectively.

Figure 3 shows that: i) the profile of drug release is affected by the salt composition of the gels; ii) κ-carrageenan gels release a very high amount of drug; iii) the release from commercial pharmaceutical products is incomplete and it is very slow in comparison with the release from κ-carrageenan gels.

Release profiles are quite interesting as they suggest that the release can be controlled by simply choosing the appropriate [K + ]/ [Na + ] ratio. Moreover, the release from sample B is almost complete in eight hours. In the same time interval samples (A and C) release a high amount of drug. At difference, commercial products release, in the same interval, a much smaller amount (< 30%). It is important to emphasize that the time window chosen in this study corresponds to the characteristic time elapsing between two subsequent topical applications; consequently it is very important that a consistent amount of drug is released in this interval time.

To obtain more information about the kinetics of release, data are fitted to the simple power law:

n t Kt M M ) ( = ∞ (1)
where M t is the amount of drug released at time t, M 8 is the amount of loaded drug in the gel, K is the rate constant and n is an exponent characterizing the release mechanism.

The power law can be used for fitting the release data at short time intervals with M t /M ∞ = 0.6, as shown in Fig 3 . The calculated exponent, n, gives an indication of the release mechanism. Indeed, n = 0.5 when the release is controlled by diffusion and n = 1 for a time-dependent release (Case -II transport). For 0.5 < n < 1 the release is called "anomalous" and both swelling and diffusion play an important role [START_REF] Macheras | On the Heterogeneity of Drug Dissolution and Release[END_REF][START_REF] Martin | Physical Pharmacy[END_REF].

Table 2 shows that the drug release depends on the gel structures. Release from samples A and C is governed by pure diffusion, whereas for sample B, like as for commercial products, the release appears to be anomalous.

The amount of Ketoprofen released has been also plotted as a function of the square root of time as shown in Fig. 4. A linear region can be observed for each κ-carrageenan sample until t 1/2 = 1.44. Data have been compared with those obtained from Artrosilene gel and Fastum gel in the same interval time. The linear behaviour indicates that the release is well described by the mathematical model postulated by Higuchi for the release of a drug from semisolids [START_REF] Giammona | New biodegradabile hydrogels based on a photo-cross-linkable polyaspartamide and poly(ethylene glicol) derivatives. Release studies of a anticancer drug[END_REF][START_REF] Higuchi | Physical chemical analysis of percutaneous absorption: process from creams and ointments[END_REF]: q = 2C 0 (Dt/π) 1/2 (2)

of the drug and t is the time. D values, calculated from the slope in figure, for κ-carrageenan gels and for commercial products are reported in table 2.

The resulting n and D values are in good agreement with the structural characteristics of κ-carrageenan samples.

Indeed, D decreases on increasing the visco-elasticity. Moreover, in samples A and C, which are more elastic (having G' larger) and ordered (having d f smaller) than sample B, the release is controlled by diffusion (n = 0.5), and D value are lower than that of sample B, which is less elastic and ordered.

CONCLUSIONS

The study of κ-carrageenan gels containing a drug and prepared with different salt compositions shows the versatility of this polymer for the realization of gel matrices apt to drug release for external uses. Under the chosen experimental conditions, the incorporation of a drug in sodium salt form does not seem to change the gelation mechanism discussed in details in previous works [START_REF] Mangione | Thermoreversible gelation of κ-Carrageenan: relation between conformational transition and aggregation[END_REF][START_REF] Mangione | K + and Na + effects on the gelation properties of κ-Carrageenan[END_REF]. The structural and visco-elastic characteristics of gels can be controlled by the K + / Na + ions composition.

Drug release studies, using Franz's cells, allowed evaluating the release properties of κ-carrageenan gels. Data have been compared with those obtained from two commercial products. These results suggest that the drug release kinetics in κ-carrageenan gels is affected by the salt composition, and is related to visco-elastic and structural properties. The release by all κ-carrageenan samples is almost completed in eight hours, at difference with commercial products. This result seems very promising for external drug formulations, considering that a time interval of several hours between two subsequent applications is generally required.

Overall, this work suggests that structural characteristics of κ-carrageenan gels can be easily modulated by choosing the appropriate salt solution ([K + ] or [Na + ] or mixture). This, in turn, determines the release kinetic without significantly interfere with the mechanism of drug release. This aspect can provide useful advantages for the pharmaceutical development of external gels.

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Figure captions

Fig. 1. Log-log plot of the light scattered, I( q), vs. q of κ-carrageenan samples containing drug: sample A triangles; sample B squares; sample C circles. Samples composition is reported in table 1. Solid lines are data fit to a power law (eq. 1 in the text).

Fig. 2 .

 2 Fig. 2. Mechanical spectra of κ-Carrageenan gels: sample A full triangles, sample B full squares, sample C full circles, Artrosilene gel open squares, and Fastum gel open triangles. Panel a) elastic modulus, panel b) viscous modulus.

Fig. 3 .

 3 Fig. 3. Release profiles at pH 5.5 of Ketoprofen from κ-carrageenan gels and two commercial products. Sample A full triangles; sample B full squares; sample C full circles; Artrosilene gel open squares and Fastum gel open triangles.

Fig. 4 .

 4 Fig. 4. Ketoprofen amount released from κ-carrageenan gels and commercial products as function of square root of time. Sample A full triangles, sample B full squares, sample C full circles, Artrosilene gel open squares, Fastum gel open triangles. Solid lines are data fit to the eq. 2 in the text.

Table 1

 1 Ionic composition and fractal dimension for κ-carrageenan 0.4% (w/w) gels with and without 2.5% (w/w) Ketoprofen

	sodium salt
	Sample	[K + ] mM	[Na + ] mM	d f -drug	d f -no drug
	A	150	0	1.3 ± 0.1	1.1 ± 0.1
	B	3.5	300	2.4 ± 0.1	2.3 ± 0.1
	C	20	300	1.7 ± 0.1	1.8 ± 0.1

Table 2 n

 2 and D values, calculated by data fit to equation 1 and 2 in the text, for κ-carrageenan gels and commercial products.

	Sample	n	D (cm 2 /h)
	A	0.498	0,1523
	B	0.569	0,2508
	C	0.490	0,1035
	Artrosilene gel	0.540	0,0159
	Fastum gel	0.616	5,7255e-3

temperature for 24 h and heated at 37 °C before starting the measurement. The temperature was controlled by the builtin Peltier system. The thin sample-air interface was coated with silicone oil to avoid solvent evaporation.

Acknowledgements

We are in debt with Mauro Manno and Rosetta Noto for helpful discussions. We also thank Mario Lapis, Gaetano Lapis, Fabrizio Giambertone and Fulvio Ferrante for technical support.

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


Magda Przybylo
email: magdalena.przybylo@pwr.wroc.pl

Agnieszka Ol¿yñska

Stefan Han

Andrzej O¿yhar

Marek Langner

Magda Przybyło

Agnieszka Olżyńska

Andrzej Ożyhar

A fluorescence method for determining transport of charged compounds across lipid bilayer

Keywords: fluorescence method, membrane permeability, charged compounds

There is a constant need for simple, economical and time-efficient methods which allow evaluating a compound's ability to penetrate the biological membrane, one of the key parameters needed to characterize biologically active compounds. In the paper we propose a new method of a permeability determination. Instead of detecting the compound's concentration directly, we employ an approach in which the membrane interface is labeled with a fluorescein lipid probe; the probe is sensitive to the presence of charged compounds. The fluorescence intensity changes of the dye permanently attached to both sides of a model lipid bilayer are measured. Specifically, the time course of the fluorescence intensity changes following a rapid induction of a nonequilibrium state of the sample allows the evaluation of the membrane permeability for the compound. The method was validated by the determination of the phenyltin compound's transport through the model phosphatidylcholine unilamellar liposome bilayer.

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M A N U S C R I P T

Introduction

The ability to cross biological membranes (permeability) is one of the most important functional parameters for a compound which is considered biologically active. The membrane permeability allows predicting a compound's toxicity [START_REF] Olzynska | Di-and tri-phenyltin chlorides transfer across a model lipid bilayer[END_REF] or determining its capability to become a pharmacological agent [START_REF] Van De Waterbeemd | Property-based design: optimization of drug absorption and pharmacokinetics[END_REF]. There are continuous efforts to develop an efficient, cheap and reliable method which allows estimating the ability of a compound to penetrate biological membranes. Biological membranes are complex structures and there are no simple experimental models available at present [START_REF] Watt | Approaches to higher-throughput pharmacokinetics (HTPK) in drug discovery[END_REF]. Consequently, to determine the ability of a compound to penetrate biological membranes, tests on live cells are frequently used. Different variations of this approach are available but they are relatively expensive and time-consuming [START_REF] Avdeef | Caco-2 permeability of weakly basic drugs predicted with the Double-Sink PAMPA pK(a)(flux) method[END_REF]. These difficulties spur the search for in vitro tests applicable to a raid screening of a large number of compounds. Therefore, a well-defined and stable model membrane, mimicking relevant biological membrane parameters, needs to be employed. Since majority of pharmaceuticals are small molecular mass molecules, which cross the biological membranes via passive diffusion, a biological membrane can be safely reduced to a model lipid bilayer. The major challenge in the development of such models is the determination of a compound's flux across the membrane. To achieve that, changes of its concentrations on both sides of the lipid bilayer should be sampled.

There are two in vitro methods currently applied for permeability measurements, namely Parallel Artificial Membrane Permeation Assay (PAMPA) and the liposome-based, spectroscopic method which determines non-symmetrical oriented dipoles distribution using the second harmonic signal generation spectroscopy (SHG). The PAMPA is the application of the filter -supported lipid membrane system developed for industrial purposes. The assay allows for an evaluation of

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5 the compound's permeability, but, in addition to problems with the lipid bilayer stability, it requires the additional measurement for the determination of the compound's concentration in the trans-compartment with the help of the appropriate analytical technique [START_REF] Ruell | PAMPA -a drug absorption in vitro model 5. Unstirred water layer in iso-pH mapping assays and pK(a)(flux) -optimized design (pOD-PAMPA)[END_REF][START_REF] Balimane | Cell culture-based models for intestinal permeability: a critique[END_REF]. The SHG method, on the other hand, is capable of measuring molecular transport across model lipid bilayers (liposomes) in real time and without the need for direct compound detection [START_REF] Srivastava | Kinetics of molecular transport across a liposome bilayer[END_REF][START_REF] Yan | Application of second harmonic generation to molecular transport across liposome bilayers[END_REF]. According to the conditions of the SHG signal detection, it allows differentiating molecules present in the bulk solution from those molecules in the region of interest, namely the interface of bilayer and water.

Since the SHG signal directly responds to the water molecules polarized by the charged liposome surfaces it may also serve as a complementary technique to other methods in investigating the electrostatic properties of lipid bilayer surfaces. Although the technique provides straightforward results, its main disadvantages are: high cost and complexity of the instrumentation. In the paper we present a fluorescence method to determine the permeability of a model lipid bilayer to charged amphiphilic compounds. The method is fast, can be performed on commercially available fluorescence equipment and automated for high throughput screening (HTS) applications.

Materials and Methods

Materials

Egg phosphatidylcholine (eggPC) and cholesterol were purchased from Avanti Polar Lipids Inc. (Birmingham, AL, USA) and N-(5-Fluoresceinthiocarbamoyl)-

Labeled liposome preparation

Liposomes were prepared by the extrusion method as described elsewhere [START_REF] Olson | Preparation of liposomes of defined size distribution by extrusion through polycarbonate membranes[END_REF]. In short, appropriate amounts of phosphatidylcholine (eggPC) (and cholesterol) were mixed with Fluorescein-labeled phosphatidylethanolamine (Fluoresceine-PE) in chloroform, giving probe: lipid molar ratio 1:250. The organic solvent was evaporated under the stream of argon followed by a two-hour incubation in the vacuum to remove remnants of the solvent. Finally, the dry lipid film was hydrated with PBS buffer (pH = 6.5, 147 mM NaCl) and the sample was vortexed for 4 minutes. The milky multilamellar vesicle suspension obtained was subsequently passed through the polycarbonate filter with the pore size of 100 nm.

Fluorescence measurements

Unless otherwise specified, 150 μl of both the labeled liposome suspension and the phenyltin solution were rapidly mixed in the stopped-flow chamber and fluorescence intensity was

I I I I F i i - - = , (1)
where F i is the normalized fluorescence intensity corresponding to I i (the measured fluorescence intensity at the specific time point), I min and I max are the minimal and maximal fluorescence intensities, respectively. All the measurements were performed on the SF-61 stopped-flow spectrofluorimeter from Hi-Tech Scientific (Salisbury, UK) with dead time of 1.6 msec.

Experimental design

All approaches, except SHG method, developed for the membrane permeability evaluation are based on the direct measurements of the amount of a compound passing through the membrane. Such an experimental design requires the model system to consist of two macroscopically well-defined compartments separated by the membrane and passing compound quantities at various time points need to be determined. For example, the two most frequently used permeability assays, namely PAMPA and cell monolayer systems, are constructed according to this scheme [START_REF] Avdeef | Caco-2 permeability of weakly basic drugs predicted with the Double-Sink PAMPA pK(a)(flux) method[END_REF][START_REF] Zhang | Study on selectivity of permeating chiral complexes in bilayer lipid membranes (BLMs)[END_REF].

In this paper, we propose the method based on the assumption that the membrane compound permeability can be measured with the properly selected fluorescent probe whose location within the membrane is well-defined. The application of fluorescent probes opens the possibility to use liposome as a model membrane system, therefore, simplifying the experimental design.

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Consequently, the two distinct compartments can be precisely identified and monitored with an appropriately selected fluorescent probe sensitive to the presence of the compound.

To evaluate the transfer of a compound through a lipid bilayer, the fluorescence stopped-flow technique has been implemented and the membrane-associated fluorophore, sensitive to changes of its local environment, applied. The liposome suspension is driven out of equilibrium in the stopped-flow apparatus chamber while mixed with the isotonic solution of the compound. The resulting concentration difference across the lipid bilayer induces the flux of the compound which is detected with the changing fluorescence intensity of the fluorophore covalently attached to a lipid at both sides of the lipid bilayer.

When liposome suspension is mixed with the isotonic solution of the compound, first, the molecules adsorb onto the liposome outer surface. This process is diffusion-controlled and should be completed within a few milliseconds (Fig. 2a). Next, the compound crosses the lipid bilayer and appears at the inner liposome surface. It will last as long as the electrochemical potentials on both membrane surfaces equilibrate. Each of the above mentioned processes will result in corresponding changes in the fluorescence intensity. Therefore, its continuous recording should contain information on both adsorption and permeation processes.

Initially, the overall signal acquired from the sample is a sum of the fluorescence intensities originating from the two distinct populations of fluorescent dye; one located on the inner and the other on the outer side of the liposome membrane (Fig. 1).

0 0 0 out in tot F F F + = , (2)
where F 0 tot indicates the overall fluorescence intensity, and F 0 in and F 0 out the fluorescence intensities of dyes located on the inner and the outer leaflets of the untreated liposomal lipid bilayer, respectively.

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In the subsequent analysis, we assume that any changes of the fluorescence intensity are the sum of the independent changes taking place at the inner and outer membrane surfaces, therefore:

) ( ) ( ) ( 0 0 0 t F F t F F t F F out out in in tot tot Δ + + Δ + = Δ + (3)
This equation is valid only if F 0 in and F 0 out are independent of time, meaning that the photobleaching effect can be ignored. Independent experiments show that there is no significant decrease of the total fluorescence intensity when fluorescently labeled vesicles are present in the measurement chamber for relevant extent of time.

The process of compound permeation through the lipid bilayer can be divided into stages which occur on different time scales. The compound diffusion to and adsorption onto the membrane surface requires a few milliseconds (Fig. 2a). This process is reflected by the change of the fluorescence intensity of fluorophores located at the outer vesicle surface, whereas the membrane crossing by the compound occurs within tens of seconds followed by its rapid dissociation from the other membrane surface. Therefore, when the membrane permeability is analyzed, the adsorption onto and desorption from the membrane can be considered as instantaneous. The initial fluorescence of the sample, shortly after compound adsorption, can be described by the equation:

) ( ) ( 0 0 0 t F F F t F out out in t Δ + + = ≈ (4)
If the water/membrane partition coefficient of the compound is large and its flux through the membrane slow, it can be safely assumed that the amount of adsorbed compound at the outer surface is constant in the course of the measurement. This will result in the initial fluorescence increase on the outer membrane surface to the maximum value F max and ensure that it will not change as long as the amount of the compound in the outer aqueous phase is large compared to

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10 that in the liposome interior. The initial amount of the compound on the outer membrane surface can be evaluated if the partition coefficient is predetermined. Consequently, cross-membrane flux of the compound will result in increase of its concentration on the inner side of the vesicle, whereas its quantity on the outer surface will not change. This will induce corresponding fluorescence intensity changes:

max 0 0 ) ( ) ( F t F F t F in in t + Δ + = > , (5)
where ΔF in and F max represent fluorescence changes at the outer liposome surface and fluorescence intensity originating from the outer surface, respectively. When the amount of the adsorbed compound on the outer surface is constant the fluorescence intensity does not change.

Therefore, its flux across the membrane will result in the change of the total fluorescence originating exclusively from the inner liposome surface. When the quantity of the passing compound is small the change of the fluorescence intensity will be proportional to the concentration of the compound appearing on the inner liposome surface. Consequently, the change of the total fluorescence intensity will reflect the flux of the compound through the membrane:

) ( . ) ( t F const t F in tot Δ + ≈ (6)
Assuming that the time needed to cross the membrane is much longer than the diffusion time to the liposome surface, the increase of the fluorescence intensity can be directly correlated with the compound concentration change:

) ( ) ( ) ( t C a t F t F in m in tot Δ = Δ ≈ Δ , ( 7
)
where a is a constant which can be independently determined. Consequently, the fluorescence change can be approximated with a single exponential function:

A C C E P T E D M A N U S C R I P T ACCEPTED MANUSCRIPT 11 ) exp( ) ( ) ( 0 0 t A F t F F t F tot in tot tot τ - = Δ ≈ Δ , ( 8
)
where τ is a measure of the membrane permeability for the compound.

Results

To test the proposed method both the fluorescence probe and an example of a compound, whose permeability will be determined, have been chosen. Phenyltins are chemicals with welldocumented biological activity and with the capability to cross the lipid bilayer by passive diffusion [START_REF] Olzynska | Di-and tri-phenyltin chlorides transfer across a model lipid bilayer[END_REF][START_REF] Chicano | Organotin compounds alter the physical organization of phosphatidylcholine membranes[END_REF][START_REF] Ortiz | Effect of triorganotin compounds on membrane permeability[END_REF]. It has been shown previously that adsorption of such compounds results in the electrostatic surface potential generation which can be detected with the fluorescent probe located at both membrane surfaces. Fluorescein-PE is a probe which satisfies the two conditions.

First, the fluorophore is hydrophilic and its covalent attachment to the lipid molecule forces it to stay close to the membrane surface, and second, its sensitivity to local proton concentration suits it for the detection of an amount of the surface charges [START_REF] Langner | The effect of the lipid bilayer state on fluorescence intensity of fluorescein-PE in a saturated lipid bilayer[END_REF][START_REF] Sjoback | Absorption and fluorescence properties of fluorescein[END_REF][START_REF] Soucaille | Use of a fluorescein derivative of phosphatidylethanolamine as a pH probe at water/lipid interfaces[END_REF]. The model lipid bilayer in the form of liposomes has a number of advantages; they are relatively easy to form and when formed from egg-PC there is no phase transition in the relevant temperature range. This guarantees that the fluorescence intensity changes are due exclusively to the phenyltin presence on the membrane surface [START_REF] Langner | The effect of the lipid bilayer state on fluorescence intensity of fluorescein-PE in a saturated lipid bilayer[END_REF]. In addition, liposomal system has two well-defined compartments, i.e. the bulk aqueous phase and the liposomes interior separated by the tight lipid bilayer [START_REF] Langner | The effect of the lipid bilayer state on fluorescence intensity of fluorescein-PE in a saturated lipid bilayer[END_REF].

The cationic compound added to the liposome suspension initially will adsorb onto the outer lipid layer generating the surface potential and subsequent increase of the fluorescence intensity of Fluoresceine-PE, which will respond to increasing local pH induced by the surface potential

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12 [START_REF] Langner | Estimation of the organotin compounds partition into phosphatidylcholine bilayers with a pH sensitive fluorescence probe[END_REF][START_REF] Langner | Adsorption of phenyltin compounds onto phosphatidylcholine/cholesterol bilayers[END_REF]. The process of adsorption will be completed within a few miliseconds as shown in Fig. 2a. At the same time the fluorescence of probes located at the inner lipid layer will not be altered.

Subsequent changes of the fluorescence intensity will result exclusively from the phenyltin flux.

Experiments performed using lidocaine hydrochloride, where no signal change was observed (Fig. 2b), justified the above interpretation of fluorescence changes. An example of the fluorescence intensity dependence on time and the lipid composition is presented in Fig. 3. The analysis of these plots shows that the curves can be fitted sufficiently with an exponential function with the time constant being proportional to the phenyltin permeability through the membrane. Since the addition of cholesterol stiffens the lipid bilayer the kinetics for Ph 2 SnCl 2 observed are slower with respect to egg-PC vesicles, as expected. The prediction of the presented theory was also confirmed by similar results obtained for another compound, namely triphenyltin chloride (data not shown).

Discussion

Estimation of a compound's capability to penetrate the biological membrane is a major parameter used by the pharmacological industry to select drug candidates from a pool of chemicals. Due to the large number of compounds tested, the financial and time efficiency are important requirements. Therefore, simple and fast tests in vitro are preferred for that purpose.

A method for the permeability determination of biological membranes is based on Caco-2 cell monolayer which requires a time-consuming cells growth stage and relatively complex and labor intensive measurements [START_REF] Balimane | Current industrial practices of assessing permeability and P-glycoprotein interaction[END_REF][START_REF] Artursson | Cell-Cultures as Models for Drug Absorption across the Intestinal-Mucosa[END_REF]. Due to those problems, the permeability tests on model membrane systems are preferred. Such an experimental setup has been constructed and is based

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13 on a lipid bilayer formed on porous material (PAMPA) [START_REF] Balimane | Current industrial practices of assessing permeability and P-glycoprotein interaction[END_REF]. All available permeability tests relay on determination of the tested compound concentration. This imposes certain limitation on the experimental systems -namely probing of solutions from well-defined compartments should be possible. The application of fluorescence spectroscopy is well-established for the measurements of the membrane permeability and/or integrity. The most frequent methods include the leakage of the fluorescent tracers [START_REF] Frezard | Permeability of lipid bilayer to anthracycline derivatives. Role of the bilayer composition and of the temperature[END_REF][START_REF] Bryl | Mechanism of the leakage induced on lipid model membranes by Rz1 lipoprotein, the bacterophage λ Rz1 gene product: a fluorescent study[END_REF][START_REF] Katsu | Application of calcein-loaded liposomes for the determination of membrane channel size[END_REF][START_REF] Rausch | A high-throughput screen for identifying transmembrane pore-forming peptides[END_REF], the permeability of the fluorescent probe quencher [START_REF] Langner | Dithionite penetration through phospholipid bilayers as a measure of defects in lipid molecular packing[END_REF][START_REF] Langner | Interaction of free fatty acids with phospholipid bilayers[END_REF], and the utilization of the energy transfer between entrapped probes [START_REF] Duzgunes | Lipid mixing during membrane aggregation and fusion: Why fusion assays disagree?[END_REF]. However, each of these methods has weak points. The major problem is that each of them requires the permeating molecule to be fluorescent. As a result these approaches are used to study the membrane itself rather than the permeability to compounds of interest. Therefore, they were not employed as a method of choice in the pharmaceutical industry for permeability determination.

The method presented in the paper proposes a different approach, namely using fluorescently labeled lipids having fluorophores located on both surfaces of the model membrane. Therefore, there are two populations of probes and each of them is sensing the compound concentration in different water compartment. Such an experimental design allows for the application of economically attractive and convenient to use liposomal membrane models. The method should be applicable to a wide range of compounds since most biologically active and pharmacologically relevant molecules are weak acids or bases. In addition, different fluorescent probes can be used, which allows detecting changes in different membrane parameters [START_REF] Davenport | Fluorescence probes for studying membrane heterogeneity[END_REF][START_REF] Epand | Flourescent probes of membrane surface properties[END_REF][START_REF] Haugland | Handbook of fluorescent probes and research chemicals[END_REF][START_REF] Hudson | Flourescence probe studies of proteins and membranes[END_REF]. Such an approach is exemplified by a similar detection system designed by Melchior, where hydrophobic fluorescent probe was used to monitor insertion of various molecules into a model lipid membrane [START_REF] Melchior | A rapid empirical method for measuring membrane bilayer entry equilibration of molecules[END_REF]. In contrast to our method, the fluorescent assay proposed by Melchior permits measuring the membrane entry of compounds only. Since DPH (1,6 diphenyl-1,3,5-haxatrien), probe used in

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this design [START_REF] Melchior | A rapid empirical method for measuring membrane bilayer entry equilibration of molecules[END_REF] carries a very hydrophobic group and exhibits a rigid rod-like shape, which allows to pack well in the fatty acyl chains, it is located deeply within membranes [START_REF] Kaiser | Location of diphenylhexatriene (DPH) and its derivatives within membranes: Comparison of different fluorescence quenching analyses of membrane depth[END_REF].

Therefore, DPH is able to probe the interior of the lipid bilayer and to monitor the entrance of a molecule. Nevertheless, it provides no direct evidence of the molecular transport across the lipid bilayer. Summarizing, the charge-sensitive fluorescent probe, fluorescein-PE, positioned within the lipid bilayer interface and distributed uniformly on its both sides, serves as an excellent tool for the real time monitoring of an amphiphilic compound flux across model membranes. Such an experimental setup allows for rapid evaluation of the ability of a compound to cross the lipid bilayer barrier, an important parameter used to evaluate the candidates for pharmacological application. The presented method allows for a frequent probing of a large number of samples and its simplicity makes the method a good candidate for automated screening systems.

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  measured as a function of time. Changes in fluorescence intensity were detected at the right angle to the incident light beam at the temperature of 22°C ±1°. The excitation wavelength was 485 nm and the emission light was collected using a cut-off filter. To ensure the reproducibility of the A C C E P T E D M A N U S C R I P T ACCEPTED MANUSCRIPT 7 experimental kinetic traces, each measurement was repeated at least three times. The fluorescence intensity was normalized according to the following expression: min max min

Fig. 2

 2 Fig.2. (a),(b) Fig.3.

Fig. 1 .

 1 Fig. 1. A schematic diagram of a labeled lipid bilayer. Both fluorescence (F out, F in fluorescence intensity originating from the outer and inner lipid layer) and relevant concentrations of a charged compound (C om,, C im concentration of the compound adsorbed at the outer and inner lipid layer, respectively, C aq concentration in the aqueous compartment), are indicated.

Fig. 2 .

 2 Fig. 2. (a) Fluorescence kinetic trace acquired in the millisecond range after the Fluorescein labeled liposome solution was mixed with the 20μM isotonic solution of triphenyltin. (b) Fluorescence kinetic trace obtained after mixing lidocaine hydrochloride with Fluorescein labeled eggPC liposomes of the same concentration as for the example (a).

Fig. 3 .

 3 Fig. 3. The kinetic traces of fluorescence changes in the time range of hundreds of seconds approximated with an exponential function in the absence (straight line) and presence (dashed line) of cholesterol (30mol%) in the egg-PC lipid membrane after addition of 80 μM Ph 2 SnCl 2 are shown.

Acknowledgments

This work was possible thanks to financial support from the Centre of Biomedical Engineering at Wroclaw University of Technology, Institute of Physics, and the Grant Agency of the Czech Republic (A.O. via 203/05/H001).