Marie Frénéa-Robin

François Noël Burais

François Buret
email: francois.buret@ec-lyon.fr

Naoufel Haddour

Laurent Nicolas

Ronan Perrussel

Riccardo Scorretti

Nicolas Siauve

Damien Voyer

Electromagnetic characterization of biological cells

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

I. INTRODUCTION

The effects of electromagnetic fields on the human being has become a big concern for the public opinion who suspect most often some bad consequences on the health. This dark side is brought to the fore while some positive aspects of these interactions are kept hidden. Besides medical imagery which is commonly used and accepted by people, electromagnetic fields can be an instrument of sophisticated technologies for clinical or biotechnological applications.

This point can be illustrated by the phenomenon called electropermeabilization (often called electroporation). Indeed the permeability of the cell membrane towards molecules can be transiently increased when a micro or millisecond external electric field pulse is applied on a cell. Under suitable conditions depending mainly on the pulse parameters, the viability of the cell can be preserved. It is an elegant way to gain access to the cytoplasm and to introduce chosen foreign molecules, without irreversibly damaging the cell. For example, the microbiologists commonly use the electropermeabilization phenomenon in order to perform gene transfers into bacteria by introducing plasmid into the cytoplasm. Now this method is also proposed as an efficient way for drug, oligonucleotides, antibodies and plasmids delivery in vivo. Thus if the microbiologists use electropermeabilization in a rough way where only the efficiency of the gene transfer is taken into account without any consideration to the rate of lethal effect, it is crucial to monitor and characterize the effect of an applied transient electric field when considering medicinal or veterinary in vivo applications.

Owing to the fact that the permeabilization of cells takes place only where the local field reaches a critical value through the membrane, we are facing a key question: how can we locally control the field, and what happens on both membrane and cellular scales, when an electromagnetic field is applied at the tissue level?

To answer this question, we have to face a large range of sub-questions, some of which being:

-the dielectric characteristic of tissues at the macroscopic level, -a relevant model of a cell with regard to the problem, -the dielectric characteristics of the different part of a cell.

The problems mentioned in the non-exhaustive list above are strongly connected and each of them is a scientific issue for researchers involved in the study of the interaction between electromagnetic fields and living matter. Among these issues, the understanding and the control of this interaction at the cell scale can be seen as the basic requirement to understand also what happens at a higher scale.

This paper is mainly focused on one aspect of the electric field interaction with living cell. It concerns a method which can be implemented to extract the dielectric parameters of a single cell.

II. THE CELL

A. Basis

Cells are the elementary units of living creatures. They can be classified into two mains categories:

-prokaryotic cells which have no nucleus containing the genetic material. Their size is in the range of a few micrometers. Bacteria belong to this category.

-eukaryotic cells which have a nucleus. They are typically 10 times larger than prokaryotic cells. Tissues, organs of animals, fungi and plants are built with this kind of cell.

B. Structure

Of course the different cell species can present a large variety of shape and structure but these structures have always two common points: the cytoplasm and the membrane.

-The definition of the cytoplasm is slightly different between eukaryotic and prokaryotic cell but it does not matter in the present context. The cytoplasm is a jelly-like substance where water represents up to 70% of the cell mass. It contains the organelles and the nucleus in the case of an eukaryotic cell (Fig. 1).

-The membrane is the external envelop of the cell surrounding the cytoplasm. It acts as a selectively permeable barrier, keeping foreign entities out of the cell and its contents inside the cell (the cytoplasm), allowing in the same time selected materials to pass in and out of a cell. It is a structure consisting mainly of phospholipid molecules organized in a double layer, and proteins which control ion exchanges through the membrane. This membrane is thin compared with the size of the cell. Its thickness is in the 2-9 nanometers range (Fig. 2). This contrast in term of size is a well known problem in numerical modeling [START_REF] Meny | Finite Element Modeling of Cell Exposed To Harmonic and Transient Electric Fields[END_REF].

C. Magnitude of electromagnetic characteristics

Most of biological cells are diamagnetic with a volume magnetic susceptibility χ which corresponds more or less to the value of water near -10 -5 (χ = μ r -1 where μ r is the relative permeability). If the red blood cells have a higher susceptibility value (-6.5 10 -6 ) due to the small amount of iron that they contain, there are also cells which have intrinsic magnetization. For instance Magnetospirillum Magnotactitum is a bacterial specie which synthesizes chains of magnetic nanoparticles in the cytoplasm. The level of magnetization is sufficient to make the bacteria sensitive to the Earth's magnetic field.

Concerning cell dielectric properties, the description by a constant permeability and a constant conductivity is relevant in the range from 1000 Hz to 10 7 Hz [START_REF] Koynik | Theoretical evaluation of the distributed power dissipation in Biological cells exposed to electric Fields[END_REF]. The two main domains (cytoplasm and membrane) of a cell present a high contrast (Table 1) and play the most significant roles in the global dielectric behavior of the cell. It is the reason why attention is paid to these two regions in terms of modeling in a first approach. Indeed even if the volume of the membrane is negligible compared to the total volume of the cell, this latter has a great influence on the dielectric behavior. The almost high values of relative permittivity εr cyt and conductivity σ cyt in the cytoplasm are related to the content in water and the presence of ionic species.

III. INFLUENCE OF ELECTROMAGNETIC FIELDS ON A CELL.

As we want to characterize individual cell, we have to measure effects due to electromagnetic fields at the scale of the cell. This fact implies the use of micro technology. The characterization methods which will be presented below are based on the production of forces on a cell when it is submitted to a magnetic or electric field.

A. Magnetophoresis

A particle of volume V p and of susceptibility χ p immersed in a medium of susceptibility χ m is submitted to a force given by the expression [START_REF] Schenck | Safety of strong, static magnetic fields[END_REF]:

2 0 2 ) ( B V F p m p ∇ - = μ χ χ (1)
where B is the modulus of the induction field vector and µ 0 the permeability of vacuum (4π 10 -7 H.m -1 ).

The difference between the susceptibilities (Δχ = χ pχ m ) can be positive or negative:

-if Δχ is positive (positive magnetophoresis), the particle is attracted towards the maximum field region.

-if Δχ is negative (negative magnetophoresis), the particle is attracted towards the minimal field region, Equation ( 1) points out also that (i) the force is independent of the direction of the induction B, (ii) the gradient of B is more important than the magnitude of B. This last point is fundamental in the context of the cell. Indeed it is usually difficult to expect significant value of a force with diamagnetic material. At the micrometric scale, high values of field gradients can be obtained with a permanent micromagnet array. We can get an order of magnitude of the force on the basis of the following elements (Δχ = 10 -6 ; B max = 0.25 T; B min = 0 T; typical length l = 10 µm): F ≈ 10 4 V p (SI units).

By assuming that the main constituent of the particle is water, the value above can be compared to the weight which is in the same range: P ≈ 10 4 V p (SI units). The susceptibility contrast can be also increased by adding paramagnetic ions (Gd-DTPA: Gadoliniumdiethylenetriaminepenta-acetic acid is a paramagnetic complex used as a MRI contrast agent). The susceptibility of the medium can be measured thanks to a magnetic balance and thus we have a method to evaluate indirectly the susceptibility of a particle (cell) by measuring the velocity of the particle.

magnets cells

Nevertheless it must be noticed that the micromagnet array presented Fig. 3 is not well suited for the measurement of the susceptibility and is more likely to be used in cell positioning applications. The technique of cell and particle tracking velocimetry for cell magnetization measurement was carefully described by Moore [START_REF] Moore | Control of magnetophoretic mobility by susceptibility-modified solutions as evaluated by cell tracking velocimetry and continuous magnetic sorting[END_REF] and Häfeli [START_REF] Häfeli | Characterization of magnetic particles and microspheres and their magnetophoretic mobility using a digital microscopy method[END_REF].

The use of permanent magnets instead of coils and currents takes advantage of there is no heating of the medium and the cell. Nevertheless, in this case the only free parameter is the susceptibility (χ m ) of the medium.

B. Dielectrophoresis (DEP)

We consider a spherical particle (radius R, permittivity ε p and conductivity σ p ) immerged in a medium (permittivity ε m and conductivity σ m ) and exposed to a non-uniform electric field E. It is submitted to a force given by the expression [START_REF] Hughes | Strategies for dielectrophoretic separation in laboratory-on-a-chip systems[END_REF]:

2 3 )] ( [ Re 2 rms m E K R F ∇ = ω ε π (2)
where K is the Clausius-Mosotti factor which depends on the complex permittivities and is expressed as

: * * * * + - = m p m p K ε ε ε ε ω 2 ) ( (3) with ω σ ε ω ε j - = * ) ( ( 4
)
where ω is the pulsation of the electric field.

Equation ( 1) is similar to (2) and the main remarks which have been pointed out for magnetophoresis are still pertinent:

-insensitivity of the force to the direction of the electric field.

-the field gradient is the main parameter.

We can also define (Fig. 4):

-positive dielectrophoresis when Re[K(ω)] is positive. The particle is attracted toward regions with high field values. In this case the global polarization of the particle has more or less the same direction as the electric field.

-negative dielectrophoresis when Re[K(ω)] is negative. The force is directed towards low field region and the direction of the particle polarization is opposite to the field. Practically, high gradient value of E can be produced by rectangular interdigitated electrodes (Fig. 5). It must be noticed that electric field values up to 10 5 V.m -1 can be obtained easily with an applied voltage of 10 volts and a gap in the range of 100 µm. AC operation, which is possible due to the dependence of the force on the square of the field modulus, avoid electrolysis of the medium and electrophoretic effects.

A B

C. Electrorotation (ROT)

Besides dielectrophoresis described above which is more precisely named conventional dielectrophoresis (c-DEP), another polarization effect, called electro-rotation can be obtained in a uniform rotating electric field.

When a rotating field with a constant modulus is applied to a particle, this latter is submitted to a torque which is given by the following expression [START_REF] Jones | Basic theory of dielectrophoresis and electrorotation[END_REF]:

2 3 )] ( Im[ 4 E K R Γ m ω ε π - = (5)
where ω is the rotation speed of the field.

The expression of the torque shows that electro-rotation only exists if at least one of the two materials (medium or cell) presents energy losses. The sign of the torque can be positive (co-ROT) or negative (anti-ROT) with reference to the rotation of the electric field. The rotation field can be produced by a system of four electrodes fed with an equilibrated quadri-phase voltage.

The field map on Fig. 6 shows that the modulus is almost constant around the center of the electrode system (white circle).

This system also permits to perform c-DEP in the region between two electrodes by simply changing the feeding mode of the electrodes: for example, top and down electrodes to + V and left and right electrodes to -V (Fig. 7). In Fig. 7 we see latex particles (R = 12 µm) submitted to a negative dielectrophoresis and which are grouped in the low field domain in the center of the electrodes while yeast cells (R = 3 µm) are attracted in the high field regions.

µm

IV. CHARACTERIZATION METHOD USING C-DEP/ROT

A. Principle

As we stated before, a biological cell can be reasonably described by the dielectric properties of the two main domains (cytoplasm and membrane). From (4) it can be deduced that each of these domains has a transition frequency f t defined by:

ε π σ 2 = t f (6)
Above f t these material can be considered as an insulating medium while below this frequency the medium is mainly conductive. Considering the values given above in table I, the transition frequency of the membrane is much lower than the one of the cytoplasm. This fact has two consequences. On a fundamental point of view, the Maxwell-Wagner interfacial polarization is important which allows getting high value of the dipolar moment and then facilitates the creation of efficient forces. On a practical point of view, the behavior of the global cell varies with the frequency of the applied field.

To link the dielectric property of a biological cell to the expression of the force and the torque established for a homogeneous particle, we need to use a model. ). It must be noticed that with the usual range of the ratio R/e (R/e about 1000), the apparent relative permittivity can be very high (several thousands) which renders a high polarization level of the cell as mentioned above.

The theoretical dielectrophoretic spectrum which corresponds to the variation of the Clausius-Mosotti factor K(ω) versus the frequency can be evaluated. The spectrum drawn on Fig. 9 shows that different types of behaviors can be obtained by varying the frequency. The ROT spectrum exhibits both anti-field and co-field resonances. At low frequency we have negative c-DEP and anti-ROT then above 200 kHz positive c-DEP and finally above 4 MHz co-ROT. The shape of this spectrum depends obviously of the dielectric parameter σ cyt , ε cyt , σ men , ε men and the geometrical parameters e, R. Inversely these parameters can be deduced from the experimental acquisition of the dielectophoresis spectrum. It must not be forgotten that the spectrum is also dependent of the dielectric characteristics of the medium. These characteristics are an adjustment parameter in the range where the media stay compatible with cell viability.

This spectrum can be obtained though measurement of the speed of a cell in c-DEP and/or ROT experiment. Assuming that the viscosity of the medium is η

2 ) ( v 3 )) ( Re( rms m E R K ∇ = ε ω η ω (8) 2 ) ( 2 )) ( Im( E K m ε ω η ω Ω - = (9)
where v(ω) and Ω(ω) are respectively the measured velocity and the measured rotation speed.

B. Experimental setup

We have developed a platform to acquire the dielectrophoretic spectrum.

The microelectrode structure used in the c-DEP or ROT experiments is composed of four polynomial electrodes disposed in a circular arrangement (Fig. 10). Those electrodes are powered by 4 generators which can deliver sine-wave voltages from a few Hz to 80 MHz with appropriate phases. Visualization of the applied voltage is achieved thanks to a wide band oscilloscope whose input impedance can be set to 50 Ohms for impedance matching.

zone of operation

Cell motion is observed under an inverted microscope and image acquisition is performed by a high speed camera.

These different functions are PC-controlled via GPIB interfaces (Fig. 11). This permits in particular to maintain constant the applied voltage over the whole frequency range, despite the variations of the micro device impedance. The acquisition of a dielectrophoretic spectrum by measuring the speeds with a stopwatch is a tedious work. We have developed a software that analyzes the video performed with the high speed camera to extract automatically the speeds. Fig. 12 presents the variation of the rotation velocity for viable and non viable cells.

C. Extraction of the parameters

Attention is more focused on the ROT spectrum the shape of which is complex. Thus this spectrum can give more information on the dielectric parameters than the c-DEP spectrum.

On a practical point of view, the rotation velocity is measured in a frequency range wide enough to take into account the interesting zones of the ROT spectrum: the two resonances and the transition frequency.

We are facing a problem with 8 parameters: σ cyt , ε cyt , σ men , ε men , e, R, E and η. The typical dimension R of the cell can be acquired by direct visualization (microscopy). Even if the electric field E can be measured, the evaluation of the viscosity η requires dedicated apparatus. Generally people work directly on the Ω(ω) curve which is assimilated to the dielectrophoretic spectrum by misuse of language.

)) ( Im( ) (

ω ε β ω K m ROT - = Ω (10)
where β ROT integrates the dependence for E and η. This term has no direct interest for the dielectric model but has a direct influence on the measured values Ω exp (ω).

Equation [START_REF] Hughes | Strategies for dielectrophoretic separation in laboratory-on-a-chip systems[END_REF] shows also that σ men , ε men and e cannot be determined separately but only the ratio σ men ,/e and ε men /e.

Finally the mathematic problem consists in extracting 5 parameters: σ cyt , ε cyt , σ men /e, ε men /e, and β ROT . The basic method to achieve this goal has been proposed in [START_REF] Gascoyne | Numerical analysis of the influence of experimental conditions on the accuracy of dielectric parameters derived from electrorotation measurements[END_REF]. The experimental ROT spectrum Ω exp is fitted with a simulated one Ω sim calculated thanks to (9). This is done by minimizing the distance between experimental and simulated data at the different frequency points f i (pulsation ω i = 2π f i ). This discrete least-square minimization problem can be summarized as follows:

⎪ ⎭ ⎪ ⎬ ⎫ ⎪ ⎩ ⎪ ⎨ ⎧ Ω - Ω ∑ i i sim i 2 exp ) ( ) ( min ω ω (11)
with each parameter included in their respective prospective range of values.

In the work of Gascogne and al. [START_REF] Gascoyne | Numerical analysis of the influence of experimental conditions on the accuracy of dielectric parameters derived from electrorotation measurements[END_REF] the minimization procedure was achieved by using the Nelder-Mead simplex optimization method. Nevertheless tests have given evidence that the reliability of this method is somewhat weak.

We have proposed an improvement of this method by [START_REF] Voyer | Improvements in the extraction of cell electric properties from their electrorotation Spectrum[END_REF]:

-weighting the summation terms in ( 11) by an appropriate frequency-dependent coefficient α i .

⎪ ⎭ ⎪ ⎬ ⎫ ⎪ ⎩ ⎪ ⎨ ⎧ Ω - Ω ∑ i i sim i i 2 exp ) ( ) ( min ω ω α (12)
-applying gradually the minimization process to the different parameters, using for each of them the suitable weighted spectrum instead of extracting all the parameter in one single step.

The underlying idea of this improved approach is that each parameter has an influence on the spectrum which varies with frequency as we have mentioned several time before. To evaluate this influence we have performed a sensitivity analysis (variance based) in order to ascertain how much the ROT spectrum depends on the different parameters.

Fig. 13 and Fig. 14 illustrate this point. Fig. 13 represents the dispersion of the spectrum (Ω i = Ω(ω i )) when parameters vary in their physical intervals. We observe that the dispersion is more important around the peak and that the position of the peaks is not sensitive. (Partial variance divided by the variance t the considered frequency)

Fig. 14 shows that as expected the dielectric properties of the cytoplasm have an impact mainly in the high frequency range and how much σ cyt and ε cyt impact the ROT spectrum. When the extraction of one of the parameters is under consideration, the relative partial variance of this parameter is a good candidate to be the weight term α i in (12).

The parameters are extracted in 4 successive steps with regards to the partial variances where they are involved.

In order to evaluate the efficiency of this approach a numerical experiment has been developed. From (10) 200 samples of spectra have been built choosing randomly the parameters in the bounded interval (Fig. 13). The parameters are then extracted using the weighted and the unweighted minimization. It appears that the weighted minimization gives more accurate results. For example the value of ε cyt has been recovered with a confidence limit around 8% (weighted) and 15% (unweighted).

V. CONCLUSION

The characterization of biological cells is still a domain in development which needs the implementation of sophisticated experimental techniques associated to judicious numerical methods than can be still widely improved.

As we stated in the introduction a better knowledge of the behavior of a cell is one way (but not the only one) to understand what happens at the tissue level. But now we have the possibility to go deeper in the dimension scale. Indeed simulations in molecular dynamics permit to study what happens at the membrane level when this one is submitted to an electric constraint. Among all the information we can get from these simulations, the permittivity and the conductivity of the membrane can be extracted.

Fig. 3 .

 3 Fig. 3. Yeast cell submitted to negative magnetophoresis. Matrix of square magnets (CoPt plots, thickness : 8 µm, side length: 25 µm) separated by 10 µm gaps). Suspension medium: Aqueous solution containing 20 mM Gd-DTPA [4].

Fig 4 .

 4 Fig 4. Positive (A) and negative (B) dielectrophoresis. The arrows indicate the direction of the force.

Fig. 5 .

 5 Fig. 5. Modulus of the electric field for one motif of the electrodes (up) and positive dielectrophoresis for Jurkat cells (down). High field region is circled.

(V/m) 2 Fig. 6 .

 26 Fig. 6. Map of the square of the field modulus for polynomial electrodes.

Fig. 7 .

 7 Fig. 7. Experiment of C-DEP in polynomial electrodes.

Fig. 8 .

 8 Fig. 8. Dielectric model of a single cell.The simplified model of a biological cell presented on Fig.8(left) is equivalent to a homogeneous sphere with a

Fig. 9 .

 9 Fig. 9. Theoretical dielectrophoresis spectrum of a Jurkat cell, real and imaginary part. See Table I for the dielectric properties of the cell; σ m = 50 mS.m -1 and ε m = 80 ε 0 for the medium. R = 5 µm, e = 5 nm.

2

 2

Fig. 10 .

 10 Fig. 10. Photo of the microsystem.

Fig. 11 .

 11 Fig. 11. Plateform for dielectrophoretic spectrum acquisition.

Fig. 12 :

 12 Fig.12: Experimental ROT spectrum for yeast cell (Saccharomyces cerevisiae). Medium: ε rm = 80, σ m = 1.1 mS.m -1 .

Fig. 13 .

 13 Fig. 13. Mean value of the spectrum and its dispersion (standard deviation) σ cyt ∈ [0.6,0.9] S.m -1 , ε rcyt ∈ [60, 140], σ mem /e ∈ [800, 1000] S.m -2 , ε mem ∈ [20,30] F.m -2 , β ROT ∈ [30,50] rad.s -1 R = 15 µm, ε rm = 80, σ m = 50 mS.m -1 .


This paper presents experimental and numerical results concerning Transmission Line Excited Chamber (TLEC).

This chamber is an alternative for electromagnetic compatibility tests, notably radiated immunity. The E-field profile, frequency response, SWR, and S parameters are addressed and compared. Besides application regarding performance assessment of electromedical equipment, this chamber could also be applied as a way to reload intra-body devices or to get biotelemetry information.

I. INTRODUCTION

In this work, the main focus is to evaluate the TLEC parameters that affect the chamber performance, in order to satisfy specified merit indexes.. A suitable TLEC performance is associated to a high working volume, and E-field average values. In order to compare these results, a numerical approach has been implemented by applying Finite Integration Technique (FIT).

The TLEC is proposed as a test environment for electric, electronic and electro-medical devices, as an alternative for the canonical chambers. The canonical chambers -Reverberation Chambers (RC) and TEM Chambers -are generally used for electromagnetic immunity testing. RCs using mechanical paddles or frequency stirring provide a statistical E-field uniformity in all the directions inside the work volume. Nevertheless, the frequency operation of RCs is inversely proportional to the chamber dimensions, and it represents a constraint for low frequencies tests. The International Standards recommend the RC configuration for immunity tests over 80 MHz frequencies [START_REF]Electromagnetic Compatibility (EMC), Part 4 -Testing and Measurement Techniques, Section 21 -Reverberation Chamber Test Methods[END_REF].

The TEM Chambers present, at low frequencies, a deterministic E-field uniformity over a work area parallel to the septum, but not in all directions in the chamber [START_REF]Electromagnetic compatibility (EMC), Part 4 -Testing and Measurement Techniques, Section 20 -Emission and immunity testing in Transverse Electromagnetic Waveguides (TEM)[END_REF].

Recently, the TLEC concept has been proposed based on a phase-shifting excitation of several transmission lines [START_REF] Perini | Extending the frequency of mode stir chambers to low frequencies[END_REF]. After this, other works has been carried out for TLEC performance evaluation through different approaches as well as numerical modelling and optimization [START_REF] Weinzierl | Numerical evaluation of non-canonical reverberation chamber configurations[END_REF]- [START_REF] Avila | Maximum working volume evaluation in a noncanonical reverberation chamber[END_REF].

At this paper we present both experimental and numerical approaches. The TLEC configuration, here presented, is based on two-wire excitation configuration, Fig. 1, with parallel wires, z-axis oriented.

Another possibility is to use this chamber in a way to reload a device installed inside a body or recover information for biotelemetry [START_REF] Ko | RF-Powered Cage System for Implant Biotelemetry[END_REF].

Section II presents the experimental procedures, with setup details. Section III describes some numerical aspects concerning the simulation parameters. Section IV shows some experimental and numerical results. A comparison is addressed, and some comments are presented. Finally, some remarks are made. Each transmission line was excited by a 5.0W sinusoidal signal, and the resulting E-field was measured at various points, for two different load conditions: 50 Ω and open circuit. Thus, the frequency response behavior and the spatial E-field profile of the chamber can be obtained.

After, S parameters were measured by using a vetorial network analyser, at the same conditions.

III. SIMULATION PROCEDURES

The simulated E-field calculation was performed by applying the FIT method [START_REF] Weinzierl | Numerical evaluation of non-canonical reverberation chamber configurations[END_REF], [START_REF] Cst | Advanced Topics[END_REF], [START_REF] Weiland | Time domain electromagnetic field computation with finite difference methods[END_REF]. Proposed analysis methodology is based on the E-field values as a function of the position and frequency, and network S parameters. Both data are exported in ASCII format and read by Matlab © . The analysis is based on graphical results allowing comparation between experimental and simulated data.

RESULTS

Some results were obtained based on measuring. The E-field results, at frequency domain, at chamber center point (0.3m, 0.3m, 0.6m) were compared with the numerical simulation ones, as show at Fig. 2 and Fig. 3. The values were parameterized by the maximum value of E-field for each curve. We can note that the curves shapes are almost the same. On the other hand, a frequency shift at maximum, less than Transmission Line Excited Chamber: Experimental and Numerical Analysis 10%, can be realized (Fig. 3). It can be probably caused by the PVC material placed inside the TLEC used to hold the probe fixed at the pré-defined point that was not considered at simulations. Other results were also obtained such as the measured and simulated S11 parameter regarding LT1 ended with 50 Ω load (Magnitude Fig. 4 and Phase Fig. 5).

IV. CONCLUSIONS

Some results concerning experimental and numerical simulation of TLEC, suitable for evaluate the chamber performance, and the validation methods is here presented. The comparison results lead us to a better comprehension of TLEC behavior, in order to recommend this kind of chamber to equipment and system test, as well as applications related to intra-body devices reloading, and biotelemetry information.

Fig. 1 -

 1 Fig. 1 -Sketch of two-wire TLEC configuration II. EXPERIMENTAL PROCEDURES A TLEC prototype was build which steel walls, dimensions (0.6m, 0.6m, 1.2m), and two conductor set, given by 2mm diameter conductors, parallel to z axis placed at positions (x1=0.1m, y1=0.45m) and (x2=0.5m, y2=0.5m), respectively.Each transmission line was excited by a 5.0W sinusoidal signal, and the resulting E-field was measured at various points, for two different load conditions: 50 Ω and open circuit. Thus, the frequency response behavior and the spatial E-field profile of the chamber can be obtained.After, S parameters were measured by using a vetorial network analyser, at the same conditions.

Fig. 2 -

 2 Fig. 2 -E-field (dBV/m) for LT1 excitation. Measured and Simulated values for 50 Ω load

Fig. 4 -

 4 Fig. 4 -Measured and Simulated S11 (dB) for LT1 with 50 Ω load.

Fig. 5 -

 5 Fig. 5 -Measured and simulated S11 Phase Diagram for LT1 with 50 Ω load.

Fig. 6 -

 6 Fig. 6 -Measured Smith Chart for LT1 with 50 Ω load. V. ACKNOWLEDGMENT This work was partially supported by Capes-Cofecub (07/0568), CNPq, and FAPESP (2007/51192-6).

Laboratório de Eletromagnetismo Aplicado LMAG/PEA/EPUSP. 05508-900 -São Paulo/SP -Brazil

Centro Universitário Jaraguá do Sul -Rua dos Imigrantes 500, 89254-430 -Jaraguá do Sul/SC -Brazil

Ampère (CNRS UMR5005), Université de Lyon, Ecole Centrale de Lyon, 69134, Ecully Cedex -France

Centro Tecnológico da Marinha em São Paulo -05508-000 -São Paulo/SP -Brazil


Thierry Rabilloud

Laurent Vuillard

Claudine Gilly

Jean Jacques Lawrence

Silver staining of proteins in polyacrylamide gels: a general overview

Keywords: AcOH: acetic acid, AcOK: potassium acetate, AMPSO:3-[

On the basis of the physico-chemical principles underlying silver staining of proteins, which are recalled in this paper, several methods of silver staining of proteins after SDS electrophoresis in polyacrylamide gels or isoelectric focusing were tested. The most valuable protocols are presented in this report, including standard methods for unsupported gels and new methods devised for thin (0.5mm) supported gels for SDS electrophoresis or isoelectric focusing and for staining of small peptides. Generally speaking, the most rapid methods were found to be less sensitive and less reproducible than more time-consuming ones. Among the long methods, those using silver-diammine complex gave the most uniform sensitivity. They require however special home-made gels, and cannot be applied to several electrophoretic systems (e.g. systems using

Tricine or Bicine as the trailing ion, or isoelectric focusing in immobilized pH gradients). For these reasons, protocols based on silver nitrate are of a more general use and might be favored.

Future trends for silver staining will also be discussed.

INTRODUCTION

The introduction of silver staining of proteins in polyacrylamide gels in 1979 [START_REF] Switzer | A highly sensitive silver stain for detecting proteins and peptides in polyacrylamide gels[END_REF]) has been a breakthrough in the field of protein detection, raising the sensitivity from the microgram range obtained with dyes such as Coomassie blue to the nanogram range. This breakthrough as well as the numerous problems encountered with this first protocol (cost, background, non specific surface staining) led to extensive research and to the description of various silver staining methods (reviewed in [START_REF] Rabilloud | Mechanisms of protein silver staining in polyacrylamide gels: a ten years synthesis[END_REF]. To summarize these data, we can consider that every staining protocol is divided into five main phases.

In the first phase, the gel is fixed to eliminate the interfering substances otherwise giving a high background and therefore poor contrast (e.g. SDS, ampholytes, amino acids, Tris).

In the second phase, the gels is sensitized, i.e. treated with an agent which will eventually increase the sensitivity and/or the contrast.

In the third phase, the gel is impregnated with the silvering agent. Two main families of silver staining methods can be distinguished at this step, those using silver nitrate solutions as the silvering agent (acidic methods) and those using a basic silver-ammonia or less frequently a silver-amine complex (basic methods).

In the fourth phase, the image is developed, generally by a dilute formaldehyde solution. In the last phase, the reaction is stopped to prevent overdevelopment and the gel is prepared for storage.

The basic physico-chemical principles underlying these methods will be recalled in the next section. Based on these principles, selected silver staining protocols will be described and some results shown. The future trends for silver staining will be finally discussed

SILVER STAINING PRINCIPLES

The silver staining principles have been detailed in a previous paper [START_REF] Rabilloud | Mechanisms of protein silver staining in polyacrylamide gels: a ten years synthesis[END_REF]). They will be just briefly summarized here 2.1 Silver image formation Two main phenomena underline the formation of a silver image. The first one is the key of the photographic processes and is the autocatalytic reduction of silver. This means that the reduction of silver ion into metallic silver is greatly accelerated when some metallic silver is already present (latent image). This phenomenon can be extended to some other chemicals such as other rare metals (gold, palladium platinum) and some heavy metals sulfides (silver, lead, mercury sulfides for example). When applied to image formation in silver staining, this means that the image will appear at the places where the reduction begins, since image growth will be much faster there than anywhere else. In the case of silver staining of macromolecules, this is unfortunately in contradiction wioth the second principle, which is that the tighter the complex between silver ion and a molecule, the less reactive the silver ion. The simple application of these two principles in a silver staining protocol is outlined in figure 1 an results in negative staining, as shown by Merril's group [START_REF] Merril | Detection of polypeptides in two-dimensional gels using silver staining. in Two-dimensional gel electrophoresis of proteins[END_REF].

In order to obtain a positive stain, one must use the complexing power of proteins for silver ion. This is easily done by using a very weak developer based on formaldehyde at alkaline pH, and by rinsing the gel after the silver impregnation and before development. The result is schematized on figure 2. During the rinse, the silver ion or complex will diffuse out of the gel much faster from the places where the complexation is weak (background) than from the places where the complexation is strong (protein). The key of silver staining lies in the fact that there is a point (developing point) where the resulting excess of silver ion at the protein level will increase the speed of reduction to a point where it will overcome the slowing effect due to complexation. The reduction will therefore begin at the location of proteins and therefore ensure a positive image through the autocatalytic phenomenon desribned above. The post silver rinse is a critical step which must be carefully timed. Too much rinse will eventually decrease the silver ion concentration and lead to a reduced sensitivity, whereas insufficient rinsing will give a high background. On an other hand, the speed of reduction is also very critical. It has been shown that only certain aldehydes at a defined alkaline pH (11 to 12) can produce a positive image [START_REF] Heukeshoven | Silberfärbung von Proteinen: Untersuchungen zum Mechanismus und Einfluss einiger Parameter auf die Effektivität der Silberfärbung in Elektrophorese forum[END_REF]. To achieve such conditions, dilute solutions of formaldehyde in sodium or potassium carbonate are used with silver nitrate-treated gels [START_REF] Merril | Detection of polypeptides in two-dimensional gels using silver staining. in Two-dimensional gel electrophoresis of proteins[END_REF]. With silver-ammonia-treated gels, solutions of formaldehyde containing very small amount of citric acid are used [START_REF] Oakley | A simplified ultrasensitive silver stain for detecting proteins in polyacrylamide gels[END_REF]. This acidification is necessary because of the very high pH prevailing in the silver -ammonia bath (ca. 13) leadind to a too high reducing activity of formaldehyde. This results in poor contrast and high background. Because of this acidic development bath, the absolute reduction speed within the gel is degressive since the progresive diffusion of the acid into the gel will decrease the activity of the developer. However, the autocatalytic activity ensures sufficient image formation under these conditions. This diffusion-driven staining mechanism also explains why silver staining is so difficult in agarose gels or in immobilized pH gradients gels. In these cases, the gel itself significantly binds silver ion, yielding a poor contrast between the protein zones and the background, as well as a poor sensitivity.

Another important consequence of this diffusion-driven mechanism is the variety of colors of the developed silver. It has been shown [START_REF] Merril | Coloration of silver stained protein bands in polyacrylamide gels is caused by light scattering from silver grains of characteristric sizes[END_REF] that this color depends on the size of the silver grain. The bigger the silver grain, the darker the color. This size of the silver grain is dictated by the speed of reduction, a faster reduction leading to a bigger grain. This fact, as well as the mechanism outlined in figure 2, explain the color effects (chromatism) frequently encountered in silver staining.

When proteins are present at a very high concentration (e.g. albumin in plasma) the center of the gaussian electrophoretic band or spot will contain a very high amount of protein, able to achieve a tight binding of silver ions. Oppositely, the edges of the zone will contain much less protein and then will bindi a lesser amount of silver ion. In this diffusion-driven mechanism, the edges of the zone will reach the developing point earlier than the center of the zone, where the complexation of the silver is so high that it prevents silver reduction. Due to the autocatalytic process, this difference between the center and the edges will be amplified and lead to a fast reduction and therefore to a dark color on the edges, whereas limited reduction will take place at the center, giving a light color. In extreme cases, the complexing power of the protein for silver ion is so high that the developing point cannot be reached [START_REF] Yüksel | The quantitation of proteins in silver stained polyacrylamide gels[END_REF], leading once again to negative staining. The chromatism effects can therefore be explained by various abilities of different proteins to release the silver ion during the development step, leading to different reduction speeds and therefore to different colors.

It must be stressed that such simple silver staining protocols are not optimal. For silver nitrate staining, the sensitivity is very low, while acceptable results are obtained with silver-ammonia staining [START_REF] Wray | Silver staining of proteins in polyacrylamide gels[END_REF], although many proteins are weakly stained and some are not stained at all. To alleviate these problems, the gel is very often treated with various reagents prior to silver impregnation in order to increase both sensitivity and contrast and to obtain a more uniform staining of different proteins. This sensitization process will be described below.

Sensitization

Owing to the basic principles described above, two main methods can be envisioned to sensitize the gel. In the first method, outlined in figure 3, the gel is treated with a reagent which is adsorbed by proteins and which then binds silver ion or silver complexes. The gel is then rinsed in order to remove the reagent from the background. The gel is then impregnated with the silvering agent.

This treatment provides extra binding sites for the silvering agent, and there is more silver ion adsorbed to the protein. Upon development, this extra silver ion will be reduced, which will increase the sensitivity. The effect is generally magnified by the fact that these reagents bind silver less avidly than proteins. This implies in turn that silver ion bound to the sensitization reagent will be easily reduced. The reduction will therefore start earlier and more efficiently at the protein level, leading to increased sensitivity and contrast.

Such reagents are listed in Table 1. It must be stressed that silver-ammonia methods can use several different reagents whereas silver nitrate methods can use only SDS and the agents containing nucleophilic groups such as Coomassie blue.

The second method to sensitize the gels (which can be used in combination with the former) is schematized on figure 5. Here, the gel is treated with a reagent exhibiting some affinity for the proteins and able to form either metallic silver or silver sulfide. With this sensitization process, the latent image will be formed during the silvering step, so that silver reduction will be very fast at the protein level, ensuring good sensitivity and contrast.. It must be stressed that the sulfiding agents (listed in table1) are generally only used in silver nitrate methods. In the silver-ammonia methods, the concentration of free silver ion is very low, thus reducing the formation of silver sulfide. As opposed to the sulfiding agents, the reducing agents (both listed in table 1) can be used with both types of methods. It must however be stressed that the aldehydes can reduce silver only at an alkaline pH which makes them efficient as sensitizers for in silver-ammonia methods only.

An other way to increase sensitivity: the use of thiosulfate

Despite the use of various sensitizers in silver staining, the contrast and the sensitivity of silver staining remain mostly inadequate because of a strong tendency to background increase, imposing premature termination of the development (i.e. before optimal sensitivity can be reached). This is due to the fact that minute silver deposition at the background level will give strong background because of the autocatalysis. The remedy to that problem is to use very low amounts of thiosulfate during development. Thiosulfate at neutral and basic pH is able to give very strong complexes with silver, since it is able to dissolve silver halides. Such strong complexes are therefore not prone to reduction in the weak conditions used for silver staining. By adding micromolar amounts of thiosulfate in the developing bath of a silver nitrate-based method, it has been shown [START_REF] Blum | Improved silver staining of plant proteins, RNA and DNA in polyacrylamide gels[END_REF] that a dramatic reduction of the background is obtained, probably because the thiosulfate prevents any spurious silver or insoluble silver salts to deposit, thereby cleaning the background. The same effect can be obtained in silver-ammoniastained gels by adding thiosulfate to the gel at the polymerization stage (Hochstrasser and Merril 1988). In silver ammonia-stained gels, it is not possible to add thiosulfate into the developing bath because the penetration of the thiosulfate will sequester the silver present and prevent image formation. This is due to the fact that the acidic developing bath gives a lower reduction speed than the alkaline bath used with silver nitrate. As opposed to citric acid developers, carbonatebased developers favor image formation over its prevention by thiosulfate.

In conclusions, the features required for a modern and efficient silver stain are: -the presence of a sensitizing step, using preferably both types of sensitization -the use of thiosulfate in the development process On these bases, numerous protocols have been tested in various electrophoretic techniques [START_REF] Rabilloud | A comparison between low background silver diammine and silver nitrate protein stains[END_REF][START_REF] Rabilloud | Modified silver staining for immobilized pH gradients[END_REF]. The most performant protocols in each class will be detailed in the following sections.

3.MATERIALS AND METHODS

Sample preparation. 3.1.1 SDS-PAGE

Bio-Rad molecular weight markers (high and low ranges) were diluted into sample buffer (Bis-Tris 0.24M pH 6.5; SDS 2%; glycerol 20%, DTT 50mM) and boiled for 5 minutes. When alkylation of the sample was performed, 1/20th volume of iodoacetamide (IAM) stock solution (4M in methyl formamide (MF), made freshly by adding 1g IAM to 1 ml MF )was added and the mixture left at room temperature for 30-120 minutes before loading onto the gel. Serial dilutions were performed after alkylation in sample buffer minus DTT.

Isoelectric focusing

Two-dimensional electrophoresis

Plasmocyte cells (P3-X63-Ag8), grown in RPMI 1640 medium supplemented with 10% FCS and 50µM mercaptoethanol, were collected and washed twice in PBS. The cell pellet (10 8 cells) was resuspended in 40µl of solution A [CHAPS 20% (w/v), thioglycerol 50% (v/v)]. 360µl of solution B [urea 10M, Tris-phosphate pH 7 50mM, PMSF 1mM] made fresh and kept until use at 37°C were added while vortexing. After extraction for 1 hour at room temperature with occasional vortexing, the viscous mixture was centrifuged at 200000 g for 1 hour to pellet the DNA. 10 µl Pharmalytes 3.5-10 were added to the supernatant, and the protein concentration was determined by a modified Coomassie blue assay [START_REF] Ramagli | Quantitation of microgram amounts of protein in twodimensional polyacrylamide gel electrophoresis sample buffer[END_REF].

Gel electrophoresis

SDS PAGE

SDS PAGE was generally performed in a discontinuous gel system (gel dimension 190 x 160 x 1.5 mm) with the following buffer compositions: Resolving gel: Tris-HCl 0.33M pH 8.4

Stacking gel: BisTris-HCl 0.24M pH 6.5

Electrode buffer: 100mM Tris, 100mM taurine, 0.1% SDS Some tests were also carried out with different electrophoresis systems using different trailing ions such as glycine [START_REF] Johnson | Enhanced resolution in two-dimensional electrophoresis of low-molecular weight proteins using enlarged gels[END_REF], Tricine or borate [START_REF] Patton | Tris-Tricine and Tris-borate buffer syttems provide better estimates of human mesothelial cell intermediate filament protein molecular weights than the standard Tris-glycine system Anal[END_REF], Bicine [START_REF] Wiltfang | A new multiphasic buffer system for sodium dodecyl sulfate polyacrylamide gel electrophoresis of proteins and paptides with molecular masses 100000-1000, and their detection with picomolar sensitivity[END_REF], and homemade systems using Tris-HCl buffers at a pH selected to give a relative mobility of -0.2 to -0.23 relative to sodium ion with the following trailing ions: Asparagine, Mops, Hepes, Ampso, Tes, Bes.

The stacking gels were acrylamide-Bis gels (4.5%T, 2.6% C), but two types of resolving gels were used depending on the silver staining method to be used.

For gels to be stained with silver nitrate methods, standard acrylamide-Bis gels (10%T, 2.6% C) were used. The gel mixture was filtrated (0.2µm) before use but not degassed. Polymerization was initiated by adding 500µl APS10% and 25µl Temed per 60ml gel mixture. For gels to be stained with silver diammine methods, acrylamide-PDA(Bio-Rad) gels were used (10%T, 2.6%C), with thiosulfate added to the initiator system (Hochstrasser et al 1988b;.Hochstrasser and Merril 1988) After filtration of the gel mixture, polymerization was initiated by the sequential addition of 500µl of sodium thiosulfate pentahydrate (STS)10%, 50µl Temed and 500µl APS 10% per 60ml of gel. These acrylamide-PDA gels were also tested with silver nitrate methods but were not further used, because no improvement was observed in this case over standard Bis crosslinked gels.

In some cases, the gels were photopolymerized [START_REF] Lyubimova | Photopolymerization of polyacrylamide gels with methylene blue[END_REF]) was used. In this case, the initiator sytem was (final concentrations in gel) 25µM diphenyliodonium chloride, 500µM sodium toluene sulfinate and 20µM methylene blue. Polymerization was initiated by irradiating the gel with visible light (500W halogen lamp at a 40 cm distance). In some cases, sodium thiosulfate (1mM final concentration) was added to the gel mixture prior to polymerization.

Separations were carried out in a Protean II cell (Bio-Rad) thermostated at 4°C and operated at a constant current of 40mA/gel, which resulted in 5 to 6 hours migrations.

Peptide separations

For the separations of small peptides, an electrophoretic system based on the Tris-HCl-Tricine system [START_REF] Schägger | tricine-sodium dodecyl sulfate-polyacrylamide gel electrophoresis for the separation of proteins in the range from 1 to 100 kDa[END_REF]. The resolving gel had the following composition: Acrylamide-Bis 16.5%T, 6%C in 1M Tris-HCL pH 8.45 and 11% glycerol. It was overlaid with a spacer gel (10%T, 3%C in the same buffer without glycerol). A stacking gel (4%T, 3%C in 0.75M Tris-HCL pH 8.45) was cast on the top.

The anode buffer was Tris-HCl 0.2M pH 8.9 and the cathode buffer was Tris 0.1M, Tricine 0.1M SDS 0.1% For a 12cm separating gel overlaid with a 2cm spacer gel and a 1.5 cm staking gel, the running conditions were: 2 hours at 30V, then 18hours at 120V and 4 hours at 320V 3.2.3. Isoelectric focusing Starting from a commercial pH 4 to 7 immobilized pH gradient plate (Pharmacia), individual 3 mm wide strips were cut and reswollen overnight at room temperature in 0.4% carrier ampholytes (Pharmacia 3-10). The sample (5-20µl in the rehydrating medium) was applied on a paper applicator (Pharmacia) at the cathodic side of the gel. Running conditions were the following: 100V, 1hr; 300V 1 hr; 500V 1 hr; 800V overnight.

Two-dimensional electrophoresis

Two-dimensional electrophoresis was performed essentially as described by [START_REF] O'farrell | H High resolution two-dimensional electrophoresis of proteins[END_REF] with some modifications (Hochstrasser et al 1988a), using 1.5 mm capillary tubes in the first dimension for the IEF (carrier ampholytes generated gradients). IEF was carried out for 16000

Vh. The extruded rod gel was held on the top of the second dimension gel without any agarose (Hochstrasser et al 1988a). The second dimension gel was a continuous 10% T, 2.7%C gel without stacking (Hochstrasser et al 1988a), including PDA and thiosulfate when silver diammine staining was to be carried out. Running conditions as for standard SDS gels (see 3.2.1)

Silver staining

The silver staining methods tested were classified into four types:

-fast methods (completed in less than 5 hours) using silver nitrate -long methods using silver nitrate -methods using silver diammine -methods devised for thin supported gels (0.5mm) either for SDS PAGE or IEF

General features

All the chemicals used were analytical grade and were generally purchased from Fluka (unless otherwise indicated), except ethanol which was technical grade absolute ethanol and HEPES hemisodium salt coming from Sigma. Deionized water with a resistivity higher than 10MΩ/cm was used. Gels were stained in plastic containers with up to 4 gels per container unless otherwise indicated. The solution to gel ratio was 250ml/gel (except for silver diammine (100ml/gel)), with a minimum of 500 ml per container (silver diammine 300ml).

Fast methods for unsupported SDS gels

Previous tests including the protocols devised by Merrill et al (1981), [START_REF] Hempelmann | Free SH-groups are important for the polychromatic staining of proteins with silver nitrate in Electrophoresis[END_REF], Morissey (1981), [START_REF] Doucet | A discontinuous and highly porous sodium dodecyl sulfate polyacrylamide slab gel of high resolution[END_REF], [START_REF] Blum | Improved silver staining of plant proteins, RNA and DNA in polyacrylamide gels[END_REF] and [START_REF] Rabilloud | Improvement and simplification of low-background silver staining of proteins by using sodium dithionite[END_REF], have been described elsewhere [START_REF] Rabilloud | A comparison between low background silver diammine and silver nitrate protein stains[END_REF]. It appeared that the first threee protocols were plagued with either a low sensitivity and/or a high background (even with the addition of thiosulfate as a background preventing agent ). Among the latter protocols, the test showed that the best methods were those of [START_REF] Blum | Improved silver staining of plant proteins, RNA and DNA in polyacrylamide gels[END_REF] and [START_REF] Rabilloud | Improvement and simplification of low-background silver staining of proteins by using sodium dithionite[END_REF] the latter being slightly superior to the former. The protocols for these methods are given in Table 2. The variant in table 2 column C is designed for the staining of small peptides in a Tricine-based electrophoretic system avoiding any fixation in acid-alcohol mixtures which could lead to leakage of the peptides from the gel.

3.3.3. Long (>5 hours) silver nitrate methods. When compared to the fast methods, these protocols often use an overnight fixation step and extensive washes to remove the excess sensitizing agent. Although its sensitivity is claimed to be very high [START_REF] Ochs | Silver staing for proteins in polyacrylamide gels: A comparison of six methods[END_REF] the method of [START_REF] Sammons | Ultrasensitive silver-based color staining of polypeptides in polyacrylamide gels[END_REF] was not tested since it consistently gives a deep yellow background which is often not desirable. The basic method in this family is therefore the one described by [START_REF] Heukeshoven | Neue Ergebnisse zum Mechanismus der Silberfärbung in Elektrophorese forum[END_REF]. We described recently a variant which proved more sensitive and less prone to background development. This method is detailed in Table 3 col A.

Silver diammine methods.

These methods are generally based on the work of [START_REF] Oakley | A simplified ultrasensitive silver stain for detecting proteins in polyacrylamide gels[END_REF], but were recently dramatically improved (Hochstrasser et al 1988b;.Hochstrasser and Merril 1988). The improved method of Hochstrasser et al.(1988b) was used as a basis. We however found that the addition of NDS in the sensitization process gave improved sensitivity, especially for rather acidic proteins such as soybean trypsin inhibitor which are otherwise poorly detected. This improved staining protocol is described in Table 3 col B.

Protocols for thin supported gels

The basic protocol for staining thin supported gels is the one devised by [START_REF] Heukeshoven | Improved silver staining procedure for staining in PhastSystem Development unit. I. Staining of sodium dodecyl sulfate gels Hochstrasser[END_REF]. However, it was shown previously that this protocol could be greatly improved by adding thiosulfate to the developing agent [START_REF] Rabilloud | Modified silver staining for immobilized pH gradients[END_REF]). The latter protocol (listed in Table 4 col. 1) is quite adequate for thin SDS gels. For gels which do not contain SDS, further increase in sensitivity and resolution is afforded by replacing the acid-alcohol fixation by a TCA fixation (Table 4 col.2).

RESULTS

Sensitivity tests on MW markers in SDS PAGE

The selected protocols, generally issued from a previous comparative study [START_REF] Rabilloud | A comparison between low background silver diammine and silver nitrate protein stains[END_REF] were tested with molecular weight markers in different systems. Owing to the recent development of electrophoretic systems which do not use glycine as the trailing ion [START_REF] Patton | Tris-Tricine and Tris-borate buffer syttems provide better estimates of human mesothelial cell intermediate filament protein molecular weights than the standard Tris-glycine system Anal[END_REF][START_REF] Schägger | tricine-sodium dodecyl sulfate-polyacrylamide gel electrophoresis for the separation of proteins in the range from 1 to 100 kDa[END_REF][START_REF] Wiltfang | A new multiphasic buffer system for sodium dodecyl sulfate polyacrylamide gel electrophoresis of proteins and paptides with molecular masses 100000-1000, and their detection with picomolar sensitivity[END_REF] we tested these various protocols on such sytems. It appeared that the silver nitrate methods (Tables 2 and3A) were not sensitive to the nature of the trailing ion, provided that correct fixation (at least 3 x 30 minutes) was carried out. In all the systems tested, results were quite similar to the one shown in figure 5A, with detection limits in the lower (2-10) nanogram range. A result obtained with small peptides is shown in figure 6, showing that the protocol modified for does not give rise to any increased background.

Oppositely, the silver-ammonia methods proved to be very sensitive to the trailing ion. High background preventing the use of such methods was obtained with the following trailing ions: MOPS, BES, TES, HEPES, Tricine and Bicine Correct results were obtained with simple amino acids (glycine, taurine, asparagine) with borate and with AMPSO, the latter two ions showing however decreased electrophoretic resolution. A typical result is shown on figure 5B. Here again, the detection limits are in the low nanogram range.

Concerning gels polymerized with the photoinitiating system of [START_REF] Lyubimova | Photopolymerization of polyacrylamide gels with methylene blue[END_REF], results equivalent to those obtained with persulfate-polymerized gels were obtained with silver nitrate methods. This was not the case however with silver-ammonia methods. In the case on thiosulfate-free gels, a huge surface staining developed quite early, preventing the use of the methods. When 1mM (half the concentration used in Hochstrasser and Merril 1988) was included in the gels. The sensitivity dropped dramatically (data not shown). We interpret this phenomenon by a much greater grafting of the thiosulfate in the gel with the photoinitiating system, leading to excessive complexation of the silver ion by the gel and thus reduced sensitivity.

Tests in isoelectric focusing gels

Typical results obtained for staining of IEF-IPG gels are shown on figure 7. When compared to the results obtained with SDS gels, it can be seen that the stains are much less sensitive (detection limits ca. 50ng instead of <10 ng) and quite variable from one protein to another. This is related to the fact that staining of native proteins is known to be mauch more, variable and less sensitive than staining of SDS-denatured proteins [START_REF] Marshall | Silver staining of human salivary proteins following two-dimensional electrophoresis using either protein denaturing or non denaturing conditions[END_REF]

Tests on complex mixtures

In order to assess the homogeneity of the stains (i.e. the protein to protein variation) and their proneness to artefacts such as hollow or negative staining, further testing was performed using two dimensional electrophoresis of acidic, neutral (O'Farrell 1975) and basic proteins (Rabilloud in press). Typical results are shown on figures 8 and 9. For acidic and neutral proteins (figure 8), both methods give comparable sensitivity. It can be observed that the intensity of a same spot is not conserved from one method to another. However, we could not find a spot detected by a method and not by the other one. This is however not true with basic proteins, as shown in figure 9. Here, the silver-ammonia methods proved much more sensitive than the silver nitrate methods.

Silver ammonia methods also gave darker spots and were less prone to "hollow" staining. The tendency towards hollow staining seems to be strongly dependent on silver concentration, decrearing from high with methods using 0.1% silver nitrate,to moderate for methods using 0.2% silver nitrate and very low for silver diammine methods using silver concentration of 0.4 to 0.8%, provided that the development period is long enough. Indeed, hollow spots were observed at the early stages of image development, but were reversed into regular dark spots as the development proceeded. It was therefore essential to use long (at least 10 minutes) development times to obtain consistent results and the developing solutions were modified for this purpose.

DISCUSSION

The main problems associated with silver staining at the early stages of the method were -the high and erratic background (thereby decreasing the sensitivity), -the extreme protein to protein variability in staining and the wide range of colors obtained for various proteins, leading in some cases to "hollow staining"with a transparent or weakly colored center of the protein zone and a more deeply colored periphery.

These drawbacks impaired the use of silver staining limited as a routine procedure, as well as prevented any real quantitative use of the data obtained. These difficulties in the use of silver staining were exemplified by the great number of different protocols which appeared in the litterature in the early 80's (more than 60), suggesting that no protocol gave very adequate results.

. A landmark in silver staining was to introduce the use of thiosulfate to sequester silver ion weakly bound to the matrix, thus preventing its spurious reduction at the development stage and thereby dramatically reducing the background. As pointed out by [START_REF] Blum | Improved silver staining of plant proteins, RNA and DNA in polyacrylamide gels[END_REF] and further examplified by [START_REF] Rabilloud | Improvement and simplification of low-background silver staining of proteins by using sodium dithionite[END_REF], thiosulfate has allowed to use very powerful sensitizing compounds which would have been impossible otherwince, as this would have led to excessive background.

A first protocol with thiosulfate as background reducer using a silver diammine staining was described by [START_REF] Wiederkehr | Two-dimensional gel electrophoresis of cerebrospinal fluid proteins from patients with various neurological diseases[END_REF], but the post-silver thiosulfate step had to be very carefully timed to achieve reproducibility. A much more convenient protocol was described by [START_REF] Blum | Improved silver staining of plant proteins, RNA and DNA in polyacrylamide gels[END_REF] for silver nitrate methods. There, thiosulfate was directly added to the developing solution. Such an approach could not be used for silver diammine methods, since it would lead to a dramatic decrease in sensitivity.

A convenient method for using thiosulfate in silver diammine methods has been recently described by Hochstrasser and Merril (1988), who included thiosulfate in the gel formulation to graft it into the matrix upon polymerization. It must be emphasized, however, that the success of this copolymerization approach is very dependent on the polymerization conditions, since the use of a different initiating system (photopolymerization) gave completely different results, showing that an adaptation of the thiosulfate concentration in the gel is mandatory. Moreover, this approach cannot be used with gels polymerized under acidic conditions, since the thiosulfate decomposes under pH 4, generating sulfide, a polymerization inhibitor.

The most surprising fact observed in the course of this study is the wide divergence existing between silver nitrate and silver-ammonia methods in their behavior in different electrophoretic systems. The first important point is the requirement for a different crosslinker, namely Piperazine Diacrylamide (PDA) (Hochstrasser et al 1988b). This can be easily explained when taking into account the very basic conditions prevailing in the silver ammonia bath (pH 13).

Under such conditions, there is an alkaline hydrolysis of the matrix. While acrylamide hydrolyzes into acrylic acid and ammonia, having no effect on the staining process, the hydrolysis of Bis will produce formaldehyde (see figure 10) thus reducing silver and producing a latent image throughout the gel turning into a high background upon development. This noxious hydrolysis does not arise with PDA, which is more resistant than Bis to alkaline hydrolysis because it is a tertiary amide. Moreover, the hydrolysis products of PDA (piperazine and acrylic acid) do not induce background formation in silver staining.

Another problems derives from the fact that various trailing ions cannot be used in silver ammonia methods. Several hypotheses can be taken into account. i) this is due to a side reaction between the trailing ion remaining in the gel and the glutaraldehyde used for fixation. This hypothesis can be ruled out easily because some trailing ions such as Bicine and BES bear tertiary amine moieties (which are much less reactive toward glutaradehyde than primary amines (glycine, taurine) are) and still give rise to high background. This is easily shown when direct fixation in glutaraldehyde after electrophoresis is performed. In gels containing primary amino acids (e.g. glycine) a deep brown color develops immediately because of the reaction of glutaraldehyde with glycine. This color will persist in the gel during the washing process and will be converted into high background upon silver staining. This does not happen with Tricine (figure 6), so that the hypothesis of a glutaraldehyde effect can be ruled out.

ii) The second hypothesis is based on the assuption that complex trailing ions (e.g. Tricine) are less efficiently washed out from the gel than simpler ones (such as glycine). Owing to the high concentrations of the trailing ions present in the gels at the end of the electrophoresis run (over 0.1M) some is kept in the gel up to the silver impregnation. In the case of silver nitrate methods, it must be assumed that the complex between these compounds and silver does not interfere with subsequent staining or that any negative effect is masked by the use of thiosulfate in the developer. In the case of silver-ammonia methods, an orange-brown color develops already in the silver-ammonia bath. This indicates that, under these very alkaline conditions, the trailing ion is able at least to form an unstable complex with silver. This hypothesis is favored by the fact that many of these complex trailing ions are known to exhibit high affinities for heavy metal ions. For example the Ka of Tricine with copper ion is over 10 7 , implying a strong binding, which will be even increased at very high pH, were the ionization of the OH group begins to play an synergistic role with the amino group. In the case of hydroxylated trailing ions (Tricine, Bicine), another phenomenon can take place. at very alkaline pH, the alcohol can be oxidized by the dissolved oxygen to give the aldehyde and the acid. This process can also be driven by the presence of silver ion and induce silver ion reduction and thus background formation.

Another major difference between the two types of staining concerns the detection of prteins with very acidic or very basic pIs. in the case of acidic proteins (e.g. soybean trypsin inhibitor) the silver nitrate stain are superior to the ammoniacal stain. This is probably linked with the rather low lysine content of these proteins, since a positive correlation between the lysine content and the staining with ammoniacal methods has been described [START_REF] Dion | Ammoniacal silver staining of proteins: mechanism of glutaraldehyde enhancement Anal[END_REF]. The opposite is true for basic proteins, where the silver nitrate methods are quite not optimal. This can be explained by the fact that at the acidic pH of the silver nitrate solution (ca. 6) the basic proteins behave as cations, which induces an electrostatic repulsion between the protein and the silver ion, thereby decreasing the extent of silver bound and thus the staining intensity. This hypothesis is supported by the fact that the addition of HEPES buffer in the silver bath enhances the detection of basic protein with silver nitrate methods, although the sensitivity remains lower than the one of silver-ammonia methods (result not shown). It must be stressed at this point that pH must be carefully controlled, since spurious reduction of the silver nitrate by the formaldehyde of the bath begins at pH 7.8. HEPES hemisodium salt was therefore used to avoid any problem coming from inaccurate pH adjustment.

In the case of isoelectric focusing gels with immobilized pH gradients, a further problem comes from the grafting of the buffering groups within the gel. This is especially a problem with basic compounds which bear tertiary amine functions which bind silver quite comparably to proteins. This induces a gradient in background increasing from the acidic to the basic part, which is especially pronounced with ammoniacal silver methods where a silver mirror is frequently obtained [START_REF] Rabilloud | Modified silver staining for immobilized pH gradients[END_REF]. We therefore focused our effort on silver nitrate methods. Based on a previously tested protocol [START_REF] Rabilloud | Modified silver staining for immobilized pH gradients[END_REF], we tested several compounds to try to increase the sensitivity and the contrast. These compounds included thiourea, phenylthiourea, dithionite , thiosulfate and tetrathionate, already tested for SDS gels [START_REF] Rabilloud | Improvement and simplification of low-background silver staining of proteins by using sodium dithionite[END_REF]. Of these tetrathionate proved superior to thiosulfate, which was itself clearly superior to the other compounds. This superiority of tetrathionate over thiosulfate, also observed for SDS gels [START_REF] Rabilloud | A comparison between low background silver diammine and silver nitrate protein stains[END_REF], is probably linked to the difference in the stability of the two compounds. It is well known that thiosulfate is very unstable at moderately acid pH, with strong decomposition at pH 4 and below with generation of sulfide which is a very powerful background promoting agent, since the hydrogen sulfide produced at low pH has probably a very weak (if any) affinity for proteins. As the fixation process generally uses very acidic pH, the thiosulfate sensitization must be carried out at a controlled pH [START_REF] Heukeshoven | Improved silver staining procedure for staining in PhastSystem Development unit. I. Staining of sodium dodecyl sulfate gels Hochstrasser[END_REF]. It is however not sure that the buffering effect coming from the diffusion of the buffer into the gel will always be fast enough to increase the pH everywhere in the gel before any thiosulfate decomposition occurs. This could explain why some erratic results with a high background are sometimes obtained with thiosulfate. Tetrathionate, on the other hand, is much more stable to the acid, so that this spurious decomposition does not occur. Moreover, tetrathionate is a much bigger anion that thiosulfate. If we assume that proteins behave to some extent as weak ion exchange materials, this combination of large size with multivalency (-2 both for thiosulfate and tetrathionate) is very favorable for binding. This more efficient binding of tetrathionate would also explain the better results obtained with this ion. We would like to conclude this discussion in adressing the future developments of silver staining.

The principal aim would be to break the "nanogram barrier", since, at least in SDS gels, all the methods tested to date reproducibly give a detection limit of a few nanograms. In order to increase the sensitivity, we have tried to increase the latent image formation by coupling covalently the proteins (before or after electrophoresis) to compounds able to give silver sulfide (e.g. isothiocyanates) or to strongly reducing compounds (e.g. polyhydroxy aromatic compounds). The latter class was chosen on the basis of a work showing a much faster image formation for proteins bearing hyperhydroxylated tyrosine residues [START_REF] Wells | Detecting proteins containing 3-4 dihydroxyphenylalanine by silver staining of polyacrylamide gels Anal[END_REF].

The results were however rather disappointing. The image formation was indeed very fast, but the final results were not superior to those obtained with the methods described here. This suggested that the current limiting factor in silver staining is not the latent image formation, but the extent of the silver binding. In our model of silver staining, this would imply that the formation of the image uses mainly (and maybe only) the silver bound to the proteins, and not the silver present in the remaining of the gel. We therefore tried to increase the number of binding sites on the proteins either by coupling the proteins with reactive dyes bearing amino , sulfonic and /or heterocyclic groups prior to electrophoresis [START_REF] Bosshard | The use of a new reactive dye for quantitation of prestained proteins on polyacrylamide gels[END_REF] or by impregnating the gels after electrophoresis with various sulfonated dyes such as Coomassie blue [START_REF] De Moreno | Silver staining of proteins in polyacrylamide gels: Increased sensitivity through a combined Coomassie Blue-silver stain procedure[END_REF], copper phtalocyanine tetrasulfonate [START_REF] Bickar | A high affinity protein stain for western blots, tissue prints, and electrophoretic gels[END_REF] or other acidic dyes. No increase in sensitivity was observed for the covalent coupling, whereas some increase in sensitivity was observed for the post electrophoretic treatments, at the expense of a great increase in the background precluding the routine use of such techniques. The latter effect can be explained by the fact that such dyes effectively bind silver, but with such an affinity that ecven minute amounts of dye remaining in the gel will give background. The problem turns therefore to the search of conditions where the concentration of the dye within the gel will be very low (which implies more than numerous washes) while some dye will still be bound on the proteins to increase the binding. This requires dyes with a very high affinity for proteins and a very high solubility. Coomassie dyes are therefore good candidates, but their affinity proved too low to meet the requirements to break the nanogram barrier. On the other hand, preelectrophoretic coupling of reactive dyes gave no increase in sensitivity. This is probably due to the fact that the sites where these dyes react (Lys, Cys, Tyr) are already binding sites for silver in the proteins. This means that the increase in silver binding is only marginal with such a process, leading to no increase in sensitivity.

This means that silver staining may have reached a plateau in its sensitivity, which would be broken only if different mechanisms for staining can be found, since the affinity of proteins for silver is now fully used. The use of cold water in the silver ammonia protocol has been found to decrease the background (Hochstrasser et al 1988b). this could be due to the fact that cold water prevents the spurious grafting of glutaraldehyde onto the polyacrylamide gel itself (see [START_REF] Rabilloud | Mechanisms of protein silver staining in polyacrylamide gels: a ten years synthesis[END_REF])

Figure 1 :

 1 Figure 1: Schematic representation of a negative silver stain. the dotted zone represents the protein in the gel, the open circles the silver ion, the dark circles metallic silver.

Figure 2

 2 Figure 2 Schematic representation of a positive silver stain. Symbols as in Figure 1. The long arrows show the important silver ion diffusion out of the gel, while the short arrows show the weak diffusion from the proteins due to silver binding.

Figure 3

 3 Figure 3 Schematic representation of sensitization by amplification of silver binding. Symbols as in figure 1. the rectangles symbolize the sensitizing agent

Figure 5 :Figure 6 :

 56 Figure 5: Staining of molecular weight standards using silver nitrate and silver -ammonia stains. Serial dilutions of molecular weight markers (broad molecular weight range from Bio-Rad) were loaded on alternate lanes (1cm wide, giving a mean band area of 10 mm 2 ) on a standard acrylamide-Bis gel or an acrylamide/PDA/thiosulfate gel for silver ammonia staining.. From top to bottom: MYO: myosin(200 kDa); GAL: ß-galactosidase (112 kDa); PHO: phosphorylase A (94 kDa),; BSA: bovine serum albumin (69 kDa); OVA: ovalbumin (43 kDa); CAR: carbonic anhydrase (30 kDa); STI: Soybean trypsin inhibitor (21 kDa); LYS: hen egg white lysozyme (14kDa). APR aprotinin (6.5 kDa) Protein loads : lanes a: 100 ng per band; lanes b: 50 ng; lanes c: 20 ng; lanes d: 10 ng; lanes e: 5 ng; lanes f: 2 ng; lanes g: 1ng; lanes h: 0.5 ng.left panel: gel stained with a long silver nitrate method (table 3 col A) right panel: gel stained with a silver ammonia method (Table3 col B)

Table 1 :

 1 Main sensitizing agents

	Mode of action and nature of the reagent	used in silver	used in silver
		nitrate staining ammonia staining
	INCREASED SILVER BINDING
	Coomassie Blue R or G 250	+	+
	Naphtalene disulfonic acid	-	+
	SDS	+	+
	Sulfosalicylic acid	+	+
	Di sulfo POPOP	+	-
	SILVER SULFIDE FORMATION
	Sodium thiosufate	+	-
	Potassium tetrathionate	+	-
	Farmer's reducer (thiosulfate + ferricyanide)	+	-
	(phenyl)thiourea	+	-
	SILVER ION REDUCTION
	Sodium phosphite and hypophosphite	+	-
	borohydrides	+	-
	low valency copper or iron salts	+	-
	formaldehyde	-	+
	glutaraldehyde	-	+
	UNCLEAR MECHANISM
	DTT	+	-

Table 2 :

 2 Rapid silver nitrate protocols for staining unsupported SDS gels

	PROTOCOL	BLUM et al (1987) RABILLOUD	et	al	small peptides
			(1988)
	FIXATION	AcOH 10% EtOH 30% 3x30'	AcOH 10% EtOH 30% 3x30'			Glutaraldehyde 5% 1hr
	RINSE	EtOH 20% 10'	EtOH 20% 10'			water 6x20' at least*
		then water 10'	then water 10'
	SENSITIZATION STS 0.2 g/l 1'	dithionite 0.3 g/l 1'		dithionite 0.3 g/l 1'
	RINSE	water 3x20"	water 2x1'			water 2x1'
		SUBSEQUENT STEPS COMMON TO THE 3 METHODS
	SILVER	silver nitrate 0.2%; 37%HCHO 0.7ml/l : 30-60'
	RINSE		water 5-10"
	DEVELOPMENT	Potassium carbonate 3%, 37%HCHO 0.25 ml/l, STS 10mg/l: 5-15'
	STOP		Tris 50g/l, AcOH 25 ml/l 30'
	STORE		water, several rinses

Table 4 :

 4 protocols for staining of thin (0.5 mm) supported gels

	PROTOCOL	SDS GELS	IEF-IPG GELS
	FIXATION	AcOH 10%; EtOH 30% 3x30'	TCA 10% 3x30' *
		SUBSEQUENT STEPS COMMONT TO BOTH METHODS
	SENSITIZATION AcOK 0.5M; EtOH 25%; KTT 3 g/l; glutaraldehyde 0.5% 45-60'
	RINSE	Water 4x 15'
	SILVER	silver nitrate 0.2%, HCHO 0.5 ml/l 30'
	RINSE	water 5-10"
	DEVELOPMENT	Potassium carbonate 3%, 37% HCHO 0.25ml/l, STS 10mg/l 5-10'
	STOP	Tris 50g/l, AcOH 25ml/l 30'
	STORE	water, several rinses

ml of gel; TES: tris(hydroxymethyl)aminoethanesulfonic acid; Tricine: N-tris(hydroxymethyl) glycine; Tris: Tris(hydroxymethyl)aminomethane