PhD Andrea Tura
email: tura@isib.cnr.it

S Sbrignadello

S Barison

S Conti

G Pacini

Impedance spectroscopy of solutions at physiological glucose concentrations

Keywords: Dielectric spectroscopy, blood, non-invasive, glycaemia, diabetes, monitoring

Impedance spectroscopy has been proposed as possible approach for non-invasive glycaemia monitoring. However, few quantitative data are reported about impedance variations related to glucose concentration variations, especially below the MHz band. Furthermore, it is not clear whether glucose directly affects the impedance parameters or only indirectly by inducing biochemical phenomena. We investigated the impedance variations in glucosewater, glucose-sodium chloride, and glucose-blood samples, for increasing glucose values (up to 300 mg/dl). In all the frequency range (0.1-10 7 Hz) glucose-water samples showed impedance modulus increases for increasing glucose values (up to 135%). In blood and sodium chloride samples the impedance modulus showed only slight variations (2% and 1.4%), but again in wide frequency ranges. Therefore: i) glucose directly affects the impedance parameters of solutions; ii) effects are more relevant at frequencies below the MHz band; iii) the influence on the impedance is decreased in high conductivity solutions, but still clearly present.

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

In recent years the measurement of tissue and blood impedance through an alternating current has been suggested as a non-invasive approach to determine glycaemia [START_REF] Khalil | Non-invasive glucose measurement technologies: an update from 1999 to the dawn of the new millennium[END_REF]. In [START_REF] Caduff | First human experiments with a novel non-invasive, non-optical continuous glucose monitoring system[END_REF], it was shown that variations in blood glucose concentration determine significant changes in the impedance of a subject's skin and underlying tissues in a range between 1 and 200 MHz.

However, the authors claimed that the observed impedance changes were not due directly to glucose, because the impedance of glucose solutions in pure water is independent by the glucose concentration. The impedance changes were due to biochemical reactions triggered by variations of glucose concentration, which cause variations in the electrolyte balance across the membrane of erythrocytes. In other studies, however, impedance variations were found in glucose-water solutions with different glucose concentrations, even at concentration values that mimic glycaemic levels in human blood [START_REF] Park | The correlation of the complex dielectric constant and blood glucose at low frequency[END_REF]. On the other hand, in [START_REF] Park | The correlation of the complex dielectric constant and blood glucose at low frequency[END_REF] the impedance differences were observed only in a relatively narrow frequency range.

These partially contradictory results and considerations show that it is not completely clear whether glucose directly affects the impedance behavior of a solution, especially when physiological concentration levels are considered. The aim of this study was to examine possible impedance variations in solutions at different glucose concentrations within the physiological range. We studied glucose solutions both in pure water and in blood in an in vitro context. We also studied the sodium chloride 0.9% solution, which has some similarities with blood (for instance, it presents the same osmotic pressure of plasma), but it lacks any cellular component. Special attention was devoted to the analysis of low frequencies, which were poorly investigated in previous studies, especially in blood.

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

Materials and methods

Preparation of samples

A sample of deionized water (18.5 MΩ • cm resistivity, Millipore MilliQ Element system, Billerica MA, USA) was prepared. The same water was used to prepare three glucose-water samples, at glucose concentrations spanning from normal glycaemia to that observed in severe diabetes, i.e. 100, 200, 300 mg/dl. Each sample consisted of 50 ml of water. Dglucose (99.5%, Fluka) was added to the water samples to reach the indicated concentrations. The solutions of sodium chloride 0.9% (Baxter) were prepared similarly.

For the preparation of blood samples we collected 500 ml of bovine blood immediately after the animal slaughter. Since it was necessary to prevent both coagulation and glycolysis [START_REF] Lakomek | Erythrocyte pyruvate kinase-and glucose phosphate isomerase deficiency: perturbation of glycolysis by structural defects and functional alterations of defective enzymes and its relation to the clinical severity of chronic hemolytic anemia[END_REF][START_REF] Van Wijk | The energy-less red blood cell is lost: erythrocyte enzyme abnormalities of glycolysis[END_REF] in the blood container we had previously poured 1 g of potassium oxalate (99.98%, Sigma-Aldrich) and 1.25 g of sodium fluoride (99.99%, Sigma-Aldrich), acting as anticoagulant and glycolytic inhibitor, respectively [START_REF] Chan | Effectiveness of sodium fluoride as a preservative of glucose in blood[END_REF]. We then measured the glucose concentration of the blood sample by two portable glucose meters (Freestyle, TheraSense, and Glucomen, Menarini Diagnostics). We performed two measures for each meter: the average value was 65 mg/dl. Blood was then stored into a refrigerator at 4 °C. In the following hours we checked again the glucose concentration several times: the differences compared to the first measures were always within the precision of the meters, thus confirming that glycolysis was properly inhibited. Then, we properly added D-glucose to obtain blood samples with concentrations similar to those indicated above.

We also tested the condition of erythrocyte cells after the impedance experiments. We used trypan blue dye (C 34 H 24 N 6 O 14 S 4 Na 4 ) to discriminate living from dead cells. The reactivity of trypan blue is based on the fact that it does not interact with the cell unless the membrane is

A C C E P T E D M A N U S C R I P T
damaged. Therefore, the dye penetrates the cell membrane of dead cells only, which consequently appear as blue under microscope observation; 10 ml of each sample were centrifuged at 250 g (1200 rpm) for 7 minutes, the pellet was then resuspended in 5 ml PBS buffer and after 5 minutes of incubation with trypan blue solution at room temperature, a 1/180 dilution was filled in a Burker's haemocytometer and observed under a microscope at 10x and 20x. All the samples showed that the majority of cells were still alive (at least 90%).

Therefore, we were confident that at the time of the impedance experiments the erythrocytes were in the condition of triggering mechanisms possibly affecting the measured impedance values.

It must be noted that for some of the samples to be studied we prepared three copies, and we evaluated the accuracy in sample preparation by measuring the glucose concentration of each copy: the differences were always within the precision of each meter (<5%). For the impedance analysis we considered the sample copy with glucose concentration in the middle.

Impedance measurement

Within 72 hours from sample preparation we performed the impedance measures through a Solartron 1260 impedance analyzer. For the measurement cell a probe from Delta OHM was chosen (SP06T model). A block diagram of the probe is reported in Figure 1 (top). The cell is characterized by plain platinum electrodes: four electrodes are present for separation between stimulation and sensing terminals (Figure 1 (bottom)), thus allowing minimization of possible secondary effects, such as inductance of cables or parasitic capacitances that can influence the accuracy of the impedance measurement [START_REF] Awan | Towards accurate measurement of the frequency dependence of capacitance and resistance standards up to 10 MHz[END_REF]. The electrodes are then surrounded by a covering bell: when the cell is immersed into the glass tube containing the solution sample to be studied, the measurement region is delimited and kept constant. The cell also includes a temperature sensor. The cell k-factor is 0.7 cm -1 .

Through the Solartron 1260 we applied a 100 mV r.m.s. voltage to the outer couple of electrodes. The electric current was read through the inner electrodes. We analyzed the impedance of the samples in the 10 -1 -10 7 Hz range. The impedance was measured in five frequency points for each decade.

For each sample studied, we performed two independent measures: after the first measure the cell was cleaned before immersing it again into the sample. The impedance values presented for each sample are the average between the two measures. In the frequency range of major interest (see Results) the differences between the two measures in a sample were always lower than the differences between the average values of two different samples. For instance, in the blood samples the worst difference between the two measures in a sample was in the order of 0.1 Ω, which was markedly lower than the average difference between samples at different glucose concentrations.

All the impedance measures were performed with the samples at ambient temperature (23 °C with maximum variations of ±0.3 °C). All the measures were corrected through open-short compensation technique.

Results

Modulus and phase of the impedance of water, and of glucose-water mixtures, are reported in Figure 2. The modulus increased for increasing glucose concentration values in a wide frequency range, though the variations were nonlinear: an increase step of 100 mg/dl in glucose concentration did not produce impedance variations of the same magnitude (this nonlinearity was observed also in blood and sodium chloride samples, as shown below). The

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

phase decreased for increasing glucose values, though variation was less marked than that observed in the modulus. More precisely, the frequency range where the differences were more evident for the modulus was 0.1-800 Hz (we define it as reference range). Outside this range, the differences were less clear, as the modulus curves showed relatively frequent intersections at some frequency values. As regards the phase, the reference range was 80

Hz-10 7 Hz, though from 10 5 Hz onwards the differences were small. Thus, in all the studied frequency range a clear variation in at least one of the two impedance parameters was observed for increasing glucose concentration values. Percentage difference values between the blank sample (i.e. that with no glucose) and that at the highest glucose concentration were reported in Table 1 for both modulus and phase in their own reference ranges.

As regards blood, the impedance of the sample with endogenous glucose only and that of samples with added exogenous glucose is reported in Figure 3. When looking to the whole modulus and phase curves, almost no variation can be appreciated for the different samples.

However, when the analysis was focused on a specific frequency range, some differences emerged. In fact, in a wide frequency range, i.e. 8-2•10 6 Hz, there was a slight but evident difference in the impedance modulus: similarly to glucose-water samples, the modulus increased for increasing glucose concentrations in the whole range (Figure 3, top right).

Outside the reported reference range, the modulus curves showed frequent intersections.

Similar analysis for the phase showed that there was again a relatively wide frequency range, i.e. 2•10 5 -8•10 6 Hz, where a slight phase decrease for increasing glucose concentration was observed in the whole range (not shown). Thus, in a frequency range which almost covers all the studied range at least one between impedance modulus and phase showed clear variations for increasing glucose concentrations. Percentage difference values between the sample with endogenous glucose only and that at the highest glucose concentration were reported again in Table 1.

A C C E P T E D M A N U S C R I P T ACCEPTED MANUSCRIPT 8
Glucose-sodium chloride samples showed impedance patterns similar to those observed in blood samples (Figure 4). Again, some differences in the impedance parameters emerged when a specific frequency range was considered. In the frequency range 80-8•10 6 Hz the modulus slightly increased for increasing glucose concentrations in the whole range (Figure 4, top right), whereas the phase decreased in the 8•10 3 -2•10 4 Hz range (not shown).

Differently to glucose-blood samples, almost all the modulus increase was observed between the first two samples, i.e. the blank sample and that at 100 mg/dl glucose. In fact, the further increase in the modulus value for increasing glucose concentrations was extremely small.

Percentage difference values between the blank sample and that at the highest glucose concentration were reported again in Table 1. It must be noted that the percentage differences for the phase were very high compared to the results found on glucose-blood samples. However, this finding may be biased by the fact that in the phase reference range the phase value was very low (mean value equal to -0.0021 rad), and small measurement error may have great influence on the computation of the percentage difference, which may result erroneously high.

Discussion

In the recent years there has been a continuous effort in the development of new glucose sensors for improved performance in terms of stability or efficiency [START_REF] Wang | A novel multi-walled carbon nanotube-based biosensor for glucose detection[END_REF][START_REF] Rk | A novel method for glucose determination based on electrochemical impedance spectroscopy using glucose oxidase self-assembled biosensor[END_REF]. In parallel, a different effort has been carried on aimed at the development of techniques for non-invasive glucose measurement [START_REF] Khalil | Non-invasive glucose measurement technologies: an update from 1999 to the dawn of the new millennium[END_REF]. Some of these approaches have lead to the production of noninvasive glucose meters [START_REF] Tura | Non-invasive glucose monitoring: Assessment of technologies and devices according to quantitative criteria[END_REF], but for several reasons many of them remained at prototype level. The only one available today is the GlucoWatch [START_REF] Tierney | Clinical evaluation of the GlucoWatch (R) biographer: a continual, non-invasive glucose monitor for patients with diabetes[END_REF], and it has several drawbacks [START_REF] Tura | Non-invasive glucose monitoring: Assessment of technologies and devices according to quantitative criteria[END_REF][START_REF] Sieg | Reverse iontophoresis for noninvasive glucose monitoring: the internal standard concept[END_REF].

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

A promising approach for non-invasive measurement of glycaemia is impedance spectroscopy. Some device prototypes have been developed based on this approach, and one of them also reached the market [START_REF] Caduff | First human experiments with a novel non-invasive, non-optical continuous glucose monitoring system[END_REF][START_REF] Pfutzner | Impact of posture and fixation technique on impedance spectroscopy used for continuous and noninvasive glucose monitoring[END_REF][START_REF] Weinzimer | PENDRA: the once and future noninvasive continuous glucose monitoring device?[END_REF], but it was withdrawn and the company filed for bankruptcy [START_REF] Wentholt | Pendra goes Dutch: lessons for the CE mark in Europe[END_REF]. A new company seems to be currently working on a similar device [START_REF] Forst | Impact of environmental temperature on skin thickness and microvascular blood flow in subjects with and without diabetes[END_REF][START_REF] Caduff | Noninvasive glucose monitoring in patients with diabetes: a novel system based on impedance spectroscopy[END_REF],

but at the moment no device is on the market.

In [START_REF] Caduff | First human experiments with a novel non-invasive, non-optical continuous glucose monitoring system[END_REF] the authors claimed that the measurement of glycaemia through impedance spectroscopy is possible as variations in blood glucose concentration induce some transportation phenomena of electrolytes through the cell membrane, and that results in variations in the dielectric properties of the medium. The most relevant phenomenon is the plasma sodium concentration lowering in the presence of hyperglycaemia [START_REF] Hillier | Hyponatremia: evaluating the correction. factor for hyperglycemia[END_REF][START_REF] Kashyap | Hyperglycemia-induced hyponatremia: is it time to correct the correction factor?[END_REF]. In [START_REF] Caduff | First human experiments with a novel non-invasive, non-optical continuous glucose monitoring system[END_REF] it was claimed that these effects are entirely responsible for the impedance variation of blood and underlying tissues, since glucose variations do not directly affect the dielectric properties of the investigated medium in the MHz band, as also stressed in other studies from the same research group [START_REF] Hayashi | Dielectric spectroscopy study of specific glucose influence on human erythrocyte membranes[END_REF][START_REF] Caduff | Specific D-glucose Influence on Electric Properties of Cell Membrane at Human Erythrocyte Studied by Dielectric Spectroscopy[END_REF]. In fact, some references were provided to other studies where the effect of variations in glucose concentration was studied in water [START_REF] Fuchs | Molecular dynamics of carbohydrate aqueous solutions. Dielectric relaxation as a function of glucose and fructose concentration[END_REF][START_REF] Mashimo | The structure of water determined by microwave dielectric study on water mixtures with glucose, polysaccharides, and Lascorbic acid[END_REF]. In [START_REF] Mashimo | The structure of water determined by microwave dielectric study on water mixtures with glucose, polysaccharides, and Lascorbic acid[END_REF] it was shown that at glucose concentrations lower than 1 g/cc the dielectric properties of the glucose-water solution are not different from those of pure water. However, a more recent study contradicts these findings. In [START_REF] Park | The correlation of the complex dielectric constant and blood glucose at low frequency[END_REF] the dielectric properties of glucose-water solutions were found different for glucose concentration values varying within the physiological range. In particular, the impedance modulus increased for increasing glucose concentrations within the 1 kHz -1 MHz band.

The first aim of our study was to reproduce the reported experiments on glucose-water solutions. Our results essentially confirm those of the study [START_REF] Park | The correlation of the complex dielectric constant and blood glucose at low frequency[END_REF], but in even wider frequency band: in fact, in all the investigated range, i.e. 0.1 Hz -10 MHz, we observed a significant variation in the impedance modulus, phase, or both, though the greater differences were

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

10 found for frequencies lower than 100 kHz. Thus, we can claim that variations in glucose concentration even at low values such as physiological ones should directly affect the dielectric properties of a solution, independently from other mechanisms that may be induced by glucose variations. On the other hand, it is confirmed that the impedance variations due to variations in glucose are certainly more evident at low frequencies, and this may partially explain why they were not observed in the studies [START_REF] Fuchs | Molecular dynamics of carbohydrate aqueous solutions. Dielectric relaxation as a function of glucose and fructose concentration[END_REF][START_REF] Mashimo | The structure of water determined by microwave dielectric study on water mixtures with glucose, polysaccharides, and Lascorbic acid[END_REF] where frequencies over 1 MHz were considered.

It must also be noted that the partial differences between our results and those of study [START_REF] Park | The correlation of the complex dielectric constant and blood glucose at low frequency[END_REF] may be due to the use of a different measurement cell. In fact, we used a four electrodes cell instead of simple two electrodes cell, thus allowing four terminal measurements less prone to noise effects at medium-high frequencies [START_REF] Awan | Towards accurate measurement of the frequency dependence of capacitance and resistance standards up to 10 MHz[END_REF]. Furthermore, we used platinum instead of stainless steel electrodes, the latter being more sensitive to the effects of possible reactions with the solution at low frequencies. A limitation of our measurement cell may be the cell kfactor value, which was 0.7 cm -1 . For impedance measurements in solutions at relatively high conductivity, like blood or sodium chloride 0.9%, higher k-factor values may be more adequate, and that may be investigated in future studies.

Few data can be found in the literature on impedance in blood at different frequencies related to glucose concentration values. In [START_REF] Caduff | First human experiments with a novel non-invasive, non-optical continuous glucose monitoring system[END_REF] some impedance data were reported from an in vivo experiment on humans where glycaemia was 100 and 200 mg/dl, though only frequencies above 1 MHz were investigated. It was shown that both impedance modulus and phase were different between the two glucose concentration values in some frequency ranges, and similarly to our results higher values were found for the 200 mg/dl concentration. As regards the modulus, which was the impedance parameter of major interest, it was claimed that the sensitivity to glucose changes was between 20 and 60 mg/dl glucose/Ω, and this was in acceptable agreement to our results, though the sensitivity that we found was slightly lower.

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

In fact, the best sensitivity that we observed for the modulus between the 100 and 200 mg/dl samples was about 110 mg/dl glucose/Ω (100 mg/dl: 72.2 Ω; 200 mg/dl: 73.1 Ω), at frequencies around 1 kHz. In [START_REF] Park | The correlation of the complex dielectric constant and blood glucose at low frequency[END_REF] the dielectric properties of blood for different glucose concentrations were studied in vivo on hamsters, and variations in the dielectric parameters were observed for glucose concentrations varying between 150 and 300 mg/dl. However, only one frequency value was investigated (10 kHz), and only semi-quantitative results were reported.

In [START_REF] Gourzi | Study of a new electromagnetic sensor for glycaemia measurement: in vitro results on blood pig[END_REF] the dielectric properties of blood with glucose varying in a wide range were studied by a sensor made of two induction coils coupled through two glass tubes containing porcine blood. The ratio between the voltages at the two inductors varied for different glucose values. However, despite the wide glucose concentration interval that was studied including also non-physiological values (from 130 mg/dl up to 10 g/dl), the observed differences were weak, being only 17.72% between the extreme values of the glucose interval. In the hypothesis that the voltage ratio variations were linear to glucose variations, for a possible variation in glucose of 100 mg/dl only a 0.18% variation in the output signal would be observed. Furthermore, results were presented only in a narrow frequency interval (2.4-2.9

MHz). Similar results were found in another study from the same authors [START_REF] Gourzi | Non-invasive glycaemia blood measurements by electromagnetic sensor: study in static and dynamic blood circulation[END_REF].

Some studies investigated the dielectric properties for different glucose concentrations of PBS buffers with suspended erythrocytes [START_REF] Hayashi | Dielectric spectroscopy study of specific glucose influence on human erythrocyte membranes[END_REF][START_REF] Caduff | Specific D-glucose Influence on Electric Properties of Cell Membrane at Human Erythrocyte Studied by Dielectric Spectroscopy[END_REF]. In [START_REF] Hayashi | Dielectric spectroscopy study of specific glucose influence on human erythrocyte membranes[END_REF] different glucose concentrations were considered ranging from zero to about 400 mg/dl, and the analysis was performed between 10 kHz to 100 MHz. Variations in the dielectric properties of the buffers were found for the different glucose concentrations. However, the dielectric parameters showed a non-monotonic pattern for increasing glucose values, differently to our results. In [START_REF] Caduff | Specific D-glucose Influence on Electric Properties of Cell Membrane at Human Erythrocyte Studied by Dielectric Spectroscopy[END_REF] the analysis was extended to 2 GHz, with similar findings. The authors claimed that this non-

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

monotonic behavior may be due to erythrocytes activities at the membrane level, but no further details were provided.

In our study huge variations in the impedance parameters for different glucose values were observed only in water. This suggests that the ability of glucose to induce variations in the dielectric properties of the solution may depend on the conductivity levels involved. In fact, both in blood and sodium chloride solutions, which have conductivity much higher than water, the impedance variations were modest compared to those in water. That may also explain the slightly higher variations of the impedance modulus (which is probably more relevant than the phase) observed in blood compared to sodium chloride, as the former is slightly less conductive than the latter. However, we cannot exclude that the slightly higher variations in blood may be due to the indirect phenomena involving cells discussed above.

It must be acknowledged that in blood the impedance measures may be affected by the selected approach for sample preparation, and they may be partially biased by the addition of exogenous compounds, i.e. potassium oxalate and sodium fluoride. However, as all the blood samples derived from the same 500 ml blood container (where the blood was treated with potassium oxalate and sodium fluoride), we are confident that possible exogenous compounds effects on the impedance vales were similar in all the blood samples. Thus, these compounds may have affected the absolute impedance values of the samples, but not the relative impedance difference between the samples, and that was of interest in this study.

Despite the findings that variations in glucose concentration induce some impedance changes in blood, the practical utility of such results for non-invasive glycaemia monitoring still remains to be demonstrated. In fact, in this study we did not assess whether the impedance spectroscopy approach may be able to distinguish between glucose concentration values relatively similar, but with very different clinical meaning: for instance, fasting glycaemia of 100 mg/dl is still considered a normal value, whereas 126 mg/dl already Furthermore, in an in vivo context, non-invasiveness implies that blood cannot be directly accessed, and hence the electrodes should be placed in contact with the skin. As a consequence, many confounding factors related to physiological changes in tissues surrounding the blood vessels may be present. For instance, it is known that hyperglycaemia may cause accelerated collagen aging and elastic fiber fraying [START_REF] Khalil | Non-invasive glucose measurement technologies: an update from 1999 to the dawn of the new millennium[END_REF]. Even when focusing on blood vessels alone, other confounding factors for impedance measurements may be possible variations in microcirculation and in blood cell morphology related to hyperglycaemia [START_REF] Khalil | Non-invasive glucose measurement technologies: an update from 1999 to the dawn of the new millennium[END_REF], as well as variations in blood composition and especially hematocrit [26]. Furthermore, the nonlinear variations in the impedance values related to the differences in glucose concentration may be another confounding factor to be addressed with proper calibration curves. Variations in body temperature may also have a relevant effect on the impedance measurements.

A first clue of possible variations in the impedance values due to differences in blood composition came from the study of a second animal, with basal blood glucose concentration of 115 mg/dl (not shown). When the blood sample of this second animal at 300 mg/dl of glucose (obtained again by proper addition of exogenous glucose) was compared to the corresponding sample of the first animal, we found impedance differences comparable to those observed between the samples at different glucose concentrations in each animal. For instance, at 10 kHz the impedance modulus of the 300 mg/dl sample in the first animal was 74.0 Ω, while in the second animal it was 71.3 Ω. This suggests that possible clinical applications of the impedance spectroscopy approach would require calibration over each subject.

It must also be noted that the use of platinum skin electrodes may be extremely expensive for a device aimed at personal domestic monitoring, but the use of other electrode materials, such as stainless steel, may cause electrode polarization phenomena possibly affecting the measurement accuracy. In fact, previous experiences based on impedance spectroscopy for non-invasive glycaemia monitoring showed how much difficult is reaching the ultimate goal [START_REF] Wentholt | Pendra goes Dutch: lessons for the CE mark in Europe[END_REF].

In conclusion, this study investigated the effect of glucose concentration on the impedance of different solutions, i.e. glucose in water, blood, and sodium chloride. Few studies showed the impedance variations of blood for different glucose concentrations within the physiological range, and to our knowledge no study examined in detail the frequency values below the MHz band: this is one of the main novelties of this study. The advantage of focusing on frequency values below the MHz for possible clinical applications may consist in a lower sensitivity to the electromagnetic noise in the environment. Furthermore, there was no study at all on the impedance in glucose and sodium chloride. Although practical applicability of the approach for non-invasive glycaemia monitoring still needs to be proved, this study showed that glucose is able to directly affect the impedance of the investigated samples. In

  . Possible ability of the approach to reveal hypoglycaemic values should also be investigated.

  blood, slight but clear impedance variations for different glucose values were observed in a wide frequency range, and especially below 1 MHz. Possible indirect mechanisms involving cells may only contribute to the observed total variations. A C C E P T E D M A N U S C R I P T ACCEPTED MANUSCRIPT

Figure 1 -

 1 Figure 1 -Block diagram of the measurement cell (top), and photograph of its inner part

Figure 2 -

 2 Figure 2 -Impedance modulus (top) and phase (down) for glucose-water samples (empty

Figure 3 -

 3 Figure 3 -Impedance modulus (top) and phase (down) for glucose-blood samples (empty

Figure 4 -

 4 Figure 4 -Impedance modulus (top) and phase (down) for glucose-sodium chloride samples

Table 1 -

 1 Mean±standard deviation of percentage difference between the samples at lowest and highest glucose concentration for both modulus and phase in their own frequency reference ranges. Maximum and minimum percentage differences are reported in square brackets. The maximum total difference (sum of the differences in modulus and phase) is also reported together with the corresponding frequency value.

	Tables
		Glucose-water	Glucose-blood	Glucose-sodium chloride
	Modulus
	Difference (%)	125±17 [135; 63] 2.00±0.09 [2.24; 1.68]	1.41±0.24 [1.69; 0.56]
	Phase
	Difference (%)	43±56 [157; 0.1]	1.51±0.11 [1.60; 1.27]	51±33 [73; 13]
	Max. total difference (%)	291	3.69	75
	Frequency for max.	80	5.1 • 10 5	1.3 • 10 4
	total difference (Hz)

grant from Regione Veneto (DGR 2702/10-09-04) and from CNR in the framework "Ricerca Spontanea a Tema Libero" (Research number: 946).

T.X. Zhao, Electrical impedance and haematocrit of human blood with various anticoagulants, Physiol. Meas. 14 (1993) 299-307.

Acknowledgements

The authors thank Dr. Franceschini for supply of bovine blood, and Dr. G. Sbrignadello and Dr. M.C. Scaini for their useful comments and help. The study was partially supported by a


Georgi D Georgiev

Georgi As Georgiev

Z Lalchev
email: lalchev@biofac.uni-sofia.bg

Influence of Steroid Hormone Progesterone on the Properties of Phosphatidyl Serine Monolayers and Thin Liquid Films

Keywords: Monolayers, Thin Liquid Films, Foam films, Progesterone, Acrosome reaction

In this work the capability of Progesterone (Prog) to penetrate to phosphatidyl serine (PS) monolayers (detected by equilibrium and dynamic surface tensions) and to induce rupture of PS thin liquid films (TLFs, known as foam films) in presence of Ca 2+ ions is studied. TLF studies reveal that the presence of Ca 2+ ions changes the type of PS films from thicker common black films to bilayer Newton black films and that the addition of Prog results in film destabilization and rupture. The effects of Prog in presence of Ca 2+ ions were observed with the films consisting of negatively charged PS but not of neutral phospholipids. The results correlate with the proposed physiological role of Prog and Ca 2+ in the acrosome reaction. The model of TLFs is used for the first time to study membrane fusion during acrosome reaction and proposes several new qualitative and quantitative parameters for studying of this reaction.

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

Introduction

The mammalian sperm acrosome reaction is one of the central events preceding fertilisation. The key molecular event during the acrosome reaction is the fusion of the outer acrosomal membrane with the overlying plasma membrane, resulting in formation of membrane vesicles and simultaneous release of the acrosomal content [START_REF] Yanagimachi | Calcium dependence of the acrosome reaction and activation of guinea pig spermatozoa[END_REF][START_REF] Shivaji | Steroid-induced perturbations of membranes and its relevance to sperm acrosome reaction[END_REF][START_REF] Kopf | Biology and Chemistry of Mammalian Fertilization[END_REF]. Numerous molecules, presenting in vivo, are proposed to be physiological initiators of the membrane fusion during the acrosome reaction, alone or in cooperation with each other [START_REF] Shivaji | Steroid-induced perturbations of membranes and its relevance to sperm acrosome reaction[END_REF][START_REF] Meizel | Development in Mammals[END_REF]. Such molecules are serum albumin, glucosaminoglycans, prostaglandins, steroid sex hormones and other pellucida components. Among all molecules, most controversial data are reported for steroid sex hormones (progesterone, estradiole and testosterone). Despite the results showing that progesterone (Prog) induced membrane fusion [START_REF] Shivaji | Steroid-induced perturbations of membranes and its relevance to sperm acrosome reaction[END_REF][START_REF] Yang | Progesterone and RU486: opposing effects on human sperm[END_REF][START_REF] Sirivaidyapong | Acrosome reaction in dog sperm is induced by a membrane-localized progesterone receptor[END_REF] during the acrosome reaction, in cell cultures and liposomes at concentrations corresponding to the physiological ones, the mechanisms of action and the physiological relevance remain still unclear. There are also data demonstrating that Prog effects are strongly increased in presence of divalent cations and especially of Ca 2+ [START_REF] Osman | Steroid induced exocytosis: the human sperm acrosome reaction[END_REF][START_REF] Thomas | Phosphatidylinositol 4,5-bisphosphate hydrolysis in human sperm stimulated with follicular fluid or progesterone is dependent upon Ca2+ influx[END_REF][START_REF] Blackmore | Progesterone and 17 alpha-hydroxyprogesterone. Novel stimulators of calcium influx in human sperm[END_REF][START_REF] Blackmore | Cell surface-binding sites for progesterone mediate calcium uptake in human sperm[END_REF].

Resent studies showed that progesterone [START_REF] Sirivaidyapong | Acrosome reaction in dog sperm is induced by a membrane-localized progesterone receptor[END_REF], Ca2+ ions or cooperation of the two agents [START_REF] Thomas | Phosphatidylinositol 4,5-bisphosphate hydrolysis in human sperm stimulated with follicular fluid or progesterone is dependent upon Ca2+ influx[END_REF][START_REF] Blackmore | Progesterone and 17 alpha-hydroxyprogesterone. Novel stimulators of calcium influx in human sperm[END_REF][START_REF] Blackmore | Cell surface-binding sites for progesterone mediate calcium uptake in human sperm[END_REF][START_REF] Thomas | An influx of extracellular calcium is required for initiation of the human sperm acrosome reaction induced by human follicular fluid[END_REF] could drive induction of acrosome reaction in vivo. It is also proven in vitro that Prog could induce aggregation and fusion of membrane vesicles (the central event of acrosomal reaction) and this effect is strongly enhanced in presence of Ca 2+ [START_REF] Shivaji | Steroid-induced perturbations of membranes and its relevance to sperm acrosome reaction[END_REF][START_REF] Thomas | An influx of extracellular calcium is required for initiation of the human sperm acrosome reaction induced by human follicular fluid[END_REF].

Progesterone also induces coexistence of phases with different ratios of progesterone and phospholipidc with distinctive molecular packing characteristics [START_REF] Korkmaz | Effect of progesterone on DPPC membrane: evidence for lateral phase separation and inverse action in lipid dynamics[END_REF]; also it is well known, that fusion could be driven by the domain boundary tension in heterogeneous

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

4 membranes [START_REF] Lipowsky | The morphology of lipid membranes[END_REF][START_REF] Dobereiner | Budding and fission of vesicles[END_REF]. These data suggest the possibility for direct induction of acrosomal reaction by interaction of progesterone and Ca 2+ with spermatozoon membrane phospholipid components, working in parallel with the already reported receptormediated mechanisms [START_REF] Sirivaidyapong | Acrosome reaction in dog sperm is induced by a membrane-localized progesterone receptor[END_REF].

The current work tests the effects of Prog and Ca 2+ induced membrane aggregation and fusion with two well known model membrane systems at the air-water interface, namely phospholipid monolayers and Thin Liquid Films (TLFs). Phospholipid monolayer films (MFs) and TLFs, are preferred models for investigating in vitro the interactions between the membrane phospholipids and membrane active compounds present in the surrounding solution [START_REF] Christova | Effects of pulmonary surfactant proteins SP-B and SP-C and calcium ions on the surface properties of hudrophobic fractions of lung surfactant[END_REF][START_REF] Georgiev | Thin lipid films and monolayers of DMPC mixed with PEG and phospholipid linked PEG[END_REF][START_REF] Dimitrov | Interaction of sex hormones and cholesterol with monolayers of dipalmitoylphosphatidylcholine in different phase state[END_REF]. TLFs, being of several types, are composed of two mutually adsorbed, oriented "head-to-head", phospholipid monolayers (Fig. 1 A-C), thus representing the contact area occurring between the cis-monolayers of two fusing membranes [START_REF] Naydenova | Pure and mixed lipid black foam films as models of membrane fusion[END_REF][START_REF] Georgiev | Model study of interactions of high-molecular dextran sulfate with lipid monolayers and foam films[END_REF].

Fig. 1 The phospholipid TLFs have been successfully used as a model system to study membrane-membrane interactions, membrane fusion and adhesion, bio-surfactant behaviour at interfaces, lung surfactant, etc. [START_REF] Naydenova | Pure and mixed lipid black foam films as models of membrane fusion[END_REF][START_REF] Exerowa | Foam and Foam Films-Theory, Experiment, Application[END_REF][START_REF] Eksperova | Prenatal diagnosis of the idiopathic respiratory distress syndrome by using thin liquid films (foam films) at the solution/air phase interface[END_REF][START_REF] Lalchev | Properties and behavior of lipids and proteins in model membrane systems[END_REF][START_REF] Lalchev | Surface Properties of Lipids and Proteins at Bio-Interfaces[END_REF][START_REF] Lalchev | Phospholipid Foam Films -Types, Properties and Applications[END_REF][START_REF] Lalchev | Effect of Lipid Phase State and Foam Film Type on the Properties of DMPG Stabilized Foams[END_REF]. Phospholipid MF (Fig. 1,D) could be regarded as a "half" of the TLF and was used for a long time as a model system for studying the interactions between membrane components with different agents and ions presenting in the liquid subphase [START_REF] Christova | Effects of pulmonary surfactant proteins SP-B and SP-C and calcium ions on the surface properties of hudrophobic fractions of lung surfactant[END_REF][START_REF] Lalchev | Molecular mobility in the monolayers of foam films stabilized by porcine lung surfactant[END_REF][START_REF] Christova | Effects of pulmonary surfactant proteins SP-B and SP-C and calcium ions on the surface properties of hydrophobic fractions of lung surfactant[END_REF][START_REF] Alahverdjieva | A kinetic study of the formation of beta-cyclodextrin complexes with monomolecular films of fatty acids and glycerides spread at the air/water interface[END_REF][START_REF] Minkov | Reorganization of lipid nanocapsules at air-water interface 3. Action of hydrolytic enzymes HLL and pancreatic PLA2[END_REF][START_REF] Ransac | Monolayer techniques for studying lipase kinetics[END_REF].

A C C E P T E D M A N U S C R I P T ACCEPTED MANUSCRIPT 5
The aim of the current work is to study the interactions and effects of the steroid sex hormone progesterone on the properties (stability, surface tension decrease, hydrodynamic behaviour etc.) of phosphatidyl serine (PS) monolayers and thin liquid films (TLFs) at air-water interface, in presence and absence of Ca 2+ ions. Other aim is to estimate quantitatively the degree of penetration of progesterone to PS monolayers at equilibrium and at dynamic conditions (during monolayer compression and decompression). PS is chosen because it is known to be the representative phospholipid of the sperm plasma membrane and sperm acrosome membrane [START_REF] Shivaji | Steroid-induced perturbations of membranes and its relevance to sperm acrosome reaction[END_REF]. Progesterone is preferred among other hormones (testosterone, estradiol etc.) because, according to other studies [START_REF] Shivaji | Steroid-induced perturbations of membranes and its relevance to sperm acrosome reaction[END_REF], Prog showed strongest effects of aggregation and fusion on PS containing membranes. Progesterone is dissolved in chloroform, which is subsequently removed by at least 30 minutes evaporation under nitrogen stream and the sample is kept overnight under vacuum, as previously described [START_REF] Belsito | Molecular and Mesoscopic Properties of Hydrophilic Polymer-Grafted Phospholipids Mixed with Phosphatidylcholine in Aqueous Dispersion: Interaction of Dipalmitoyl N-Poly(Ethylene Glycol)Phosphatidylethanolamine with Dipalmitoylphosphatidylcholine Studied by Spectrophotometry and Spin-Label Electron Spin Resonance[END_REF]. The dry film obtained is hydrated at 70°C with electrolyte water solutions and the mixture is sonicated for breath periods (up to 2 min) until homogenous dispersion is formed which is not used for more than 2 h after its formation. Prog is involved in the monolayer studies by injection of 20 µl into the monolayer subphase and of 5 µl into the menisci of TLF-forming biconcave drop, as previously described [START_REF] Naydenova | Pure and mixed lipid black foam films as models of membrane fusion[END_REF][START_REF] Georgiev | Model study of interactions of high-molecular dextran sulfate with lipid monolayers and foam films[END_REF].

Materials and Methods

Materials

Thin Liquid Films (TLFs)

TLFs are formed by the method of Scheludko and Exerowa [START_REF] Exerowa | Foam and Foam Films-Theory, Experiment, Application[END_REF] using the modified measuring cell of Lalchev et al. [START_REF] Lalchev | Surface Properties of Lipids and Proteins at Bio-Interfaces[END_REF]. A biconcave drop (50 µl volume) of the phospholipid dispersion (pH=6.8-7.0; I=0.25 M in presence or absence of 1 mM CaCl 2 )

is incubated in the measuring cell cylinder at T= 37 o C (corresponding to liquid-crystalline phase state of PS) for 30 minutes. After sucking some volume of the drop solution, thick TLF (above 1000 Å) is formed (Fig. 1). Further the film spontaneously gets thinner and after a characteristic film thinning time, t 0-1 , critical film thickness (ca. 300 Å) is reached.

Then a black spot (local thinning in the film) appears (as schematically shown in Fig. 1 A), expands with characteristics rate (black spot expansion time t 1-2 ) and fills the whole film area (black film is formed). Two types of black films are formed: 150-200Å thick common black films (CBFs, Fig. 1B), with thin free liquid core between the monolayers, and ca.70 Å thick truly bilayer (without free liquid core) Newton black films (NBFs, Fig. 1C). All the films studied are with film diameter d f = 200 µm. The concentrations of film

A C C E P T E D M A N U S C R I P T ACCEPTED MANUSCRIPT 7
forming PS dispersions used in our experiments were in the range 150-400 µg/ml depending on the type of the films formed.

The probability (W) for formation of stable black films depends strongly on the phospholipid concentration C [START_REF] Lalchev | Properties and behavior of lipids and proteins in model membrane systems[END_REF][START_REF] Lalchev | Surface Properties of Lipids and Proteins at Bio-Interfaces[END_REF][START_REF] Lalchev | Phospholipid Foam Films -Types, Properties and Applications[END_REF][START_REF] Lalchev | Effect of Lipid Phase State and Foam Film Type on the Properties of DMPG Stabilized Foams[END_REF] and can be calculated by the equation W=ΔN / N, where N is the total number of trials (at least 20 for each concentration) and ΔN is the number of trials in which stable black films are formed. Thus, W varies between 0 and 1 indicating respectively that the films always rupture (W=0) and that the films always are formed stable (W=1). The dependence W(C) is extremely steep which allowed to define a threshold concentration (C t ) as the minimum phospholipid concentration at which stable black films are always (with W=1) formed [START_REF] Georgiev | Thin lipid films and monolayers of DMPC mixed with PEG and phospholipid linked PEG[END_REF][START_REF] Georgiev | Model study of interactions of high-molecular dextran sulfate with lipid monolayers and foam films[END_REF][START_REF] Exerowa | Foam and Foam Films-Theory, Experiment, Application[END_REF][START_REF] Lalchev | Properties and behavior of lipids and proteins in model membrane systems[END_REF][START_REF] Lalchev | Surface Properties of Lipids and Proteins at Bio-Interfaces[END_REF][START_REF] Lalchev | Effect of Lipid Phase State and Foam Film Type on the Properties of DMPG Stabilized Foams[END_REF]. W(C) dependence and C t value are extremely sensitive to the phase state of phospholipids used, composition of the film forming solution, temperature, presence of ions and different membrane-active agents in the bulk solutions [START_REF] Georgiev | Thin lipid films and monolayers of DMPC mixed with PEG and phospholipid linked PEG[END_REF][START_REF] Naydenova | Pure and mixed lipid black foam films as models of membrane fusion[END_REF][START_REF] Georgiev | Model study of interactions of high-molecular dextran sulfate with lipid monolayers and foam films[END_REF][START_REF] Exerowa | Foam and Foam Films-Theory, Experiment, Application[END_REF]. Thus in our study W(C) dependence of pure PS films is used as a control curve to estimate the effects on film stability of the interaction between the film building lipid (PS) and the added Progesterone (in absence or presence of Ca 2+ ions). The changes in the film type, hydrodynamic behaviour and formation kinetics are measured by monitoring the film by inverted light microscope connected with digital photo camera, type Olympus C-7070 Wide Zoom. Thus the t 0-1 and t 1-2 values are determined.

Monolayer Films (MFs)

Spread monolayers of PS (with surface concentration corresponding to 80 Å

Results

Monolayer Films

PS pure monolayers

As control experiments, surface tension measurements vs. time of PS spread monolayers (80 Å 2 area per molecule) in presence or absence of 1 mM Ca 2+ ions are conducted. After reaching the equilibrium surface tension (γ eq ), five consecutive compression/decompression cycles are performed. It can be seen (Fig. 2) that in absence of Ca 2+ γ eq is lower than 50 mN/m while in presence of Ca 2+ ions γ eq equals 53 mN/m. It can be seen also, that PS monolayers spread in absence of Ca 2+ much faster (reaching γ eq in 5 minutes) in comparison to the films formed in presence of Ca 2+ , where γ eq is reached after 15 minutes. For all compression/decompression cycles of PS monolayers (Fig. 3A), lower (with more than 7 mN/m) γ max values are observed in absence of Ca 2+ ions than in presence of Ca 2+ . The presence of Ca 2+ ions also increased γ min values, with more than 11

mN/m at the 3 rd cycle, compared to the value in absence of Ca 2+ . Fig. 3 A, B andC The results showing lower degree of spreading, delayed formation kinetics and higher surface tension values (at equilibrium and dynamic conditions) of PS monolayers in presence of Ca 2+ (Figs. 2 and3A) could be explained by the adsorption and adhesion of divalent Ca 2+ ions to PS polar heads. The adhesion screens the head group negative charges, decreases electrostatic repulsion and the cohesive forces between the PS acyl chains became dominant in the film plane [START_REF] Christova | Effects of pulmonary surfactant proteins SP-B and SP-C and calcium ions on the surface properties of hudrophobic fractions of lung surfactant[END_REF][START_REF] Papahadjopoulos | Studies on membrane fusion. III. The role of calcium-induced phase changes[END_REF][START_REF] Portis | Studies on the mechanism of membrane fusion: evidence for an intermembrane Ca2+-phospholipid complex, synergism with Mg2+, and inhibition by spectrin[END_REF][START_REF] Wilschut | Ca2+-induced fusion of phospholipid vesicles monitored by mixing of aqueous content[END_REF]. This hypothesis agrees with the increase of compression/decompression hysteresis area (proportional to the cohesive forces between the lipid tails, according to Hills [START_REF] Hills | The Biology of Surfactant[END_REF]) for PS films from 0.1 mN in absence of Ca 2+ to 0.7 mN in presence of Ca 2+ ions (data not shown).

Dynamic behaviour of PS monolayers at addition of Progesterone

The dependencies of γ max and γ min during compression/decompression cycling of PS monolayers (in absence and presence of Ca 2+ ) on the addition of Prog are shown in dependence can be explained with the loss of surface active material from the interface to the bulk phase at dynamic compression/decompression conditions. The increased slope of the dependence in presence of Prog and Ca 2+ could be related to the enhanced stability of the PS aggregates in the liquid subphase, since Ca 2+ ions neutralize the head group negative charge normally preventing the adhesion between PS molecules [START_REF] Exerowa | Foam and Foam Films-Theory, Experiment, Application[END_REF].

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

Penetration of Progesterone to PS monolayers

For studying the penetration of progesterone to the equilibrium monolayers in presence of Ca 2+ , the hormone is added in the film subphase in concentration range 1x10 -

Thin Liquid Films

In absence of Ca 2+ ions pure PS formed stable common black films (CBFs, Fig. 1 B) at threshold PS concentration C t =200 µg/ml (2.87x10 -4 M). The PS film thinning time, t 0-1, is 45 sec and the black spot expansion time, t 1-2 , is 15 sec. The effect of Prog addition on film hydrodynamic behaviour is estimated by measuring t 0-1 and t 1-2 values (Fig. 5).

An increase of t 0-1 values from 45 sec to 60 sec (at 4x10 -4 M Prog) due to the addition of Prog is observed. In contrast, steep t 1-2 decrease from 15 sec to 3 sec is measured with increase of Prog concentration in very narrow range (1.0x10 -4 -1.6x10 -4 M). When Prog concentration is higher than 2.5x10 -4 M strong destabilisation effect of Prog on the common black PS films is observed, resulting in film lifetime decrease from hours to 2-5 sec, after which CBFs always rupture (see also Fig. 6). It is worth to be noted that in our

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

12 previous study on DMPC films with added lipid-linked PEGs [START_REF] Georgiev | Thin lipid films and monolayers of DMPC mixed with PEG and phospholipid linked PEG[END_REF] we showed good correlation between both t 0-1 and t 1-2 increase and stabilisation effect of added lipid-linked PEGs on DMPC films. Obviously, this was not the case for the system PS-Prog, where t 1- 2 values sharply decreased by addition of Prog, leading to film destabilisation and rupture.

Fig. 5 The effect of Prog addition on the stability (in terms of W(C) dependence) of both PS CBFs and NBFs, in absence and presence of Ca 2+ , is shown in Figure 6. We found that in presence of Ca 2+ ions it is possible to form stable Newton black films (NBFs, Fig. 1 C) from PS. Bilayer NBFs of PS are formed at C t = 355 μg/ml (5.30x10 -4 M) as shown in Fig. 6. The values of t 0-1 and t 1-2 of PS NBFs were 35 sec and less than 1 sec respectively, both much lower than these of PS CBFs formed in absence of Ca 2+ (Fig. 5).

The acceleration of the film formation kinetics and the change of film type from thicker (ca. 150 Å) CBFs to truly bilayer (ca. 70 Å) NBFs in presence of Ca 2+ ions could be explained with the neutralisation of PS head negative charge by Ca 2+ ions, resulting in strong decrease of the electrostatic repulsion between the film monolayers. It can be seen in Fig. 6 that in absence of Ca 2+ the addition of Prog (at concentration > 2.5x10 -4 M) leads to rupture (W = 0) of CBF at 200 μg PS/ml, while at the same concentration the film without Prog is stable, (W=1). Thus, an additional increase of PS concentration to 210 μg PS/ml was necessary in order to form stable CBFs in presence of Prog (curve 1' in Fig. 6). Using the Boltzman equation, ΔG=RT ln (C t * /C t ), as described in [START_REF] Georgiev | Model study of interactions of high-molecular dextran sulfate with lipid monolayers and foam films[END_REF], we

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

13 calculated an increase of PS film free energy (ΔG) in presence of Prog, being with appr.

0.125 kJ/mol higher compared to pure PS film.

Fig. 6 In presence of Ca 2+ the addition of Prog at concentration of PS = 355 μg/ml (where the NBF without Prog is stable) ruptures the films (Fig. 6), i.e. destabilisation effect of Prog on NBF is also observed as in case of CBF. It should be noted that in contrast to CBFs, where Prog concentration causing film rupture is higher than 2.5x10 -4

M, the rupture of NBFs is observed at Prog concentration as low as 10 -8 M, i.e. the shorter distance between film surfaces the stronger destabilisation effect of Prog is observed. Other difference of Prog action on CBFs and NBFs is that the Newton black films rupture in Prog presence immediately at the moment of black spot formation (t 1-2 is less than 1 sec), in contrast to much higher t 1-2 values (3 sec, Fig. 5) for CBFs. The free energy difference ΔG between NBFs in presence and absence of Prog is 0.037 kJ/mol, being significantly lower compared to Prog induced free energy increase observed for CBFs.

Discussion

The aim of this study is to elucidate the effects of progesterone (Prog) and Ca 2+ ions on some aspects of membrane fusion, which plays a key-role in the acrosome reaction. Phosphatidyl serine (PS) monolayers and thin liquid films (TLFs, known also as foam films) serve as models of sperm plasma and acrosome membranes. Negatively

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

14 charged PS is a representative phospholipid for these membranes.

The properties of phosphatidyl serine monolayer and bilayer films are strongly affected by Ca 2+ ions and presence of Prog. Our experimental data are in agreement with the hypothesis [START_REF] Papahadjopoulos | Studies on membrane fusion. III. The role of calcium-induced phase changes[END_REF][START_REF] Portis | Studies on the mechanism of membrane fusion: evidence for an intermembrane Ca2+-phospholipid complex, synergism with Mg2+, and inhibition by spectrin[END_REF][START_REF] Wilschut | Ca2+-induced fusion of phospholipid vesicles monitored by mixing of aqueous content[END_REF] that Ca 2+ adhesion to PS head group neutralizes the negative head group charge, decreases electrostatic repulsion and increases the magnitude of Van der Vaals attraction forces in the films. Generally some of the results also correlate to the literature data [START_REF] Shivaji | Steroid-induced perturbations of membranes and its relevance to sperm acrosome reaction[END_REF][START_REF] Thomas | Phosphatidylinositol 4,5-bisphosphate hydrolysis in human sperm stimulated with follicular fluid or progesterone is dependent upon Ca2+ influx[END_REF][START_REF] Blackmore | Progesterone and 17 alpha-hydroxyprogesterone. Novel stimulators of calcium influx in human sperm[END_REF][START_REF] Blackmore | Cell surface-binding sites for progesterone mediate calcium uptake in human sperm[END_REF][START_REF] Thomas | An influx of extracellular calcium is required for initiation of the human sperm acrosome reaction induced by human follicular fluid[END_REF] about the non-additive synergetic action of Prog and Ca 2+ on membrane fusion step of the acrosome reaction. However, in the frame of the models used we obtained some new quantitative and qualitative parameters and additional information for the fusion process.

The experiments with PS monolayers in presence of Ca 2+ show delayed formation kinetics, decreased surface activity and increase of the compression/decompression cycle hysteresis area, due to enhanced acyl chains cohesion between PS molecules in the membrane plane (Figs. 2,3A). Monolayer surface tension measurements demonstrate also easily penetration of Prog to the PS monolayers, stronger in presence of Ca 2+ ions (Fig. 4). Monolayer experiments in this study serve (as monolayer film could be regarded as a "half" of the TLF, Fig. 1) practically only to describe some details on the main findings in this work revealed by the model of TLFs. The reduced by Ca 2+ ions electrostatic component of the disjoining pressure resulted in decreased repulsion between the TLF monolayers and improved head to head adhesion, leading to additional thinning of the equilibrium black films (Fig. 6): from thicker CBFs (15 nm) to truly dehydrated bilayers, much thinner NBFs (7 nm). This film type transformation by Ca 2+

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

15 ions is shown experimentally for the first time for the system PS TLF -Ca 2+ and confirms that the fusion between the apposing surfaces requires closer contact [START_REF] Kozlov | Possible mechanism of membrane fusion[END_REF].

In addition, the TLF experiments show for the first time destabilization effects (i.e. film rupture and free energy increase) on the black films induced by Prog (Fig. 6).

These results correlate with data [START_REF] Korkmaz | Effect of progesterone on DPPC membrane: evidence for lateral phase separation and inverse action in lipid dynamics[END_REF] that Prog induces gel/liquid crystal phase separation in the membrane plane [START_REF] Tsuda | Synergistic role of progesterone and nitric oxide in the regulation of membrane fluidity of erythrocytes in humans: an electron paramagnetic resonance investigation[END_REF]. We found stronger destabilisation effect of Prog (occurring at very low Prog concentration) on PS Newton black films ("dry" films, composed of mutually adhered monolayers) compared to that on CBFs (containing free liquid core between monolayers). Our results for detected increase of the minimal concentration for stable black film formation, C t value for NBFs, agree also with the data [START_REF] Exerowa | Foam and Foam Films-Theory, Experiment, Application[END_REF] that the formation of Newton bilayers requires very dense molecular packing at the film surface (80 % of the maximal value), in contrast to CBFs (40 % molecular packing density). The data might account for the strong the strong cooperation between Prog and Ca 2+ in fertilisation as the steroid hormone alone is incapable to induce transformation in the PS black film type (data not shown). Since dense molecular packing is decisive for stable black film formation [START_REF] Georgiev | Thin lipid films and monolayers of DMPC mixed with PEG and phospholipid linked PEG[END_REF][START_REF] Georgiev | Model study of interactions of high-molecular dextran sulfate with lipid monolayers and foam films[END_REF][START_REF] Exerowa | Foam and Foam Films-Theory, Experiment, Application[END_REF] further investigations are necessary to clarify whether phase separation occurs in mixed Prog-PS films and its importance for TLF destabilisation. Obviously the negatively charged PS head groups play a major role in that process since no penetration to monolayers of neutral phosphatidyl cholines was observed, as shown in [START_REF] Dimitrov | Interaction of sex hormones and cholesterol with monolayers of dipalmitoylphosphatidylcholine in different phase state[END_REF].

Finally, we found also that Prog influenced the hydrodynamic behavior of TLFs: t 0-1 increase and t 1-2 decrease in Prog presence (Fig. 5). The increase of t 0-1 indicates decreased tangential mobility of film surfaces (formation of more rigid membrane

A C C E P T E D M A N U S C R I P T ACCEPTED MANUSCRIPT 16
phases) and agrees with hypothesis for gel/liquid crystalline phase coexistence induced by Prog.

In order to estimate the physiological relevance of the obtained results in this paper one could compare the Prog concentrations used in our work to the hormone concentrations per spermatozoid observed in vivo. The PS concentrations used in our study were ≥ 200 µg/ml, which corresponds to ≥ 2x10 7 spermatozoids/ml [START_REF] Yanagimachi | Physiology of Reproduction[END_REF]. Prog concentration necessary to rupture PS films was ≥ 2.5x10 -4 M and corresponds to ≤ 2.7

ng Prog/spermatozoid [START_REF] Mann | Male Reproductive Funciton and Semen[END_REF] which correlates to the values of 5 ng Prog/ml found in the Phalopian tube in vivo [41].

Conclusion

Using the models of PS monolayers and TLFs some of the findings in this paper confirm our knowledge that Ca 2+ ions screens the negative charge on PS and that the membrane fusion requires dehydration of the apposing surfaces and their close contact, which causes increase of membrane surface tension and membrane fusion [START_REF] Kozlov | Possible mechanism of membrane fusion[END_REF]. The latter proved that we were able to choose an appropriate experimental approach, especially the model of TLF (composed of two mutually adsorbed, oriented "head-to-head" phospholipid monolayers, Fig. 1 A-C

  Brain phosphatidyl serine (PS) and the steroid sex hormone Prog are purchased from Sigma. CaCl 2 and NaCl are purchased from Merck and used without further purification. Lipid dispersions are made with bidistilled water with conductivity less than 1 µS and used further to form TLFs. Film forming dispersions used (stock solution with PS concentration = 1000 µg/ml) are with constant (evaluated with conductivity measurements) ionic strength I = 0.25 M. For the experiments in absence of Ca 2+ the desired ionic strength is reached by using NaCl solution only, while for the experiments in presence of Ca 2+ (1mM), NaCl and CaCl 2 solutions are mixed. A C C E P T E D M A N U S C R I P T ACCEPTED MANUSCRIPT 6

8 PS

 8 2 area per molecule) are formed from PS solution in chloroform (stock solution of 1000 μg A C C E P T E D M A N U S C R I P T ACCEPTED MANUSCRIPT /ml). Few μl of the solution are carefully deposited using Hamilton micro syringe at the air/water interface of the Langmuir through. After that at least one hour is given for chloroform evaporation. Then the surface tension -time dependence is measured by the method of Wilhelmy with accuracy ±0.5 mN/m, as previously described [15, 19]cycles from 100 % (recording γ max value) to 50 % (γ min value) of the initial monolayer area are conducted (only the results from the first three cycles are shown). Duration of one cycle is 3 minutes, 1.5 minutes for compression and 1.5 minutes for decompression. For each cycle the values of γ min , γ max , and the cycle hysteresis area (A H , mN) are measured. Experiments are made at T=37 o C, pH=6.8-7.0, I=0.25 M in presence or absence of CaCl 2 (1 mM) into the subphase.

Fig. 2

 2 Fig.2

10 Figure 3 ,

 103 Figure3, panel B and C. The addition of Prog leads to decrease of γ max (Fig.3 B) and the effect is stronger in presence of Ca 2+ where γ max dropped from 58 mN/m to less than 50

8 M

 8 -1x10 -2 M and the change of the equilibrium surface tension ( can be seen in Figure4the progesterone penetration to PS films is stronger in Ca 2+ presence for all Prog concentrations up to 10 -3 M at which Δγ reaches plateau value of 6.5 mN/m. The first Δγ change is detected at concentrations as low as 10 -7 M Prog which proves very high surface activity and penetration capacity of Prog to the negatively charged PS monolayers.

Fig. 4

 4 Fig.4

23 [

 23 41] M. J. K. Harper, Germ Cells and Fertilization: Reproduction in Mammals, ed. T. Mann and C. Lutwak-Mann, Vol. 1, (Cambridge University Press, Cambridge, UK, 1982) 269-336.

Fig. 1 .Fig. 2 .

 12 Fig.1. Schematic representation of phospholipid thin liquid films (TLFs) and phospholipid monolayer film formed at the air/liquid interface. Two types of black TLFs are shown: common black film -CBF (panel B) and Newton black film -NBF (panel C).Thick TLF with local thinning called black spot (panel A) is also presented. On panel D is shown the phospholipid monolayer, which can be regarded as a half of a thin liquid film.

Fig. 3 .Fig. 4

 34 Fig. 3. Dependence of PS spread monolayers maximal (γ max ) and minimal (γ min ) surface tension on the compression/decompression (from 80 Å 2 to 40 Å 2 area per PS molecule) cycle number in presence or absence of Ca 2+ . Panel A shows dependence of γ max (open symbols) and γ min (filled symbols) on cycle number of pure PS monolayers in absence (■,□) or in presence of Ca 2+ (▲, ). Also shown are dependencies of γ max (Panel B) and of γ min (Panel C) on cycle number in absence (filled symbols) or in presence (open symbols) of Ca 2+ for pure PS films (▲, ) and for PS films with Prog added in the subphase (■, □). Ca 2+ ions were added as 1 mM CaCl 2 . Experiments were conducted at I=0.25 M, T=37 °C, pH 6.8-7.0.

Fig. 5 . 24 and 3 .

 5243 Fig. 5. Dependence of film thinning time (t 0-1 , •) and black spot expansion time (t 1-2 , ■ and □) of PS thin liquid films on the progesterone concentration (C Prog ). Dashed line (□) denotes the onset of formation of metastable common black films. Experiments are conducted at threshold concentration C PS =200 µg/ml, d f = 200 µm, T=37°C, I= 0.25 M, pH 6.8-7.0.

  , thus representing the contact area occurring between the cis-monolayers of two fusing membranes), which is used for the first time to study the membrane fusion step of acrosome reaction. Proposed as a new experimental model, the TLFs reveal some new quantitative parameters for studying of this reaction, e.g. film thinning time, black spot expansion time, minimal concentration for stable black film formation, film stability in terms of film lifetime or film rupture (obligatory step for the onset of membrane fusion), investigation of the effects of membrane active agents, e.g. Prog and Ca 2+ , on TLF stability etc. In addition, the model of TLFs could provide direct visualisation of intermembrane adhesion (i.e. film type transformation), film formation kinetics and morphology by monitoring the film behaviour by inverted light microscope connected with photo camera.In this paper we showed that Prog is able strongly to penetrate to PS monolayers and to destabilise PS TLFs. Ca 2+ ions alone increases the threshold (minimal) concentration necessary for formation of stable PS TLFs. We proved that the simultaneous action of Ca 2+ and Prog results in strong destabilisation of PS NBFs at very low Prog concentration, which correlates well to its values found in vivo.

Acknowledgements

This work was supported by NSFB -Bulgarian Ministry of Education and Science (grant N U-B-04/05 and partially N BU-B-2/05).