Simona Sawan

Khalil Hamze

Ali Youssef

Rayyan Boukarroum

Kamal Bouhadir

Abdelhamid Errachid

Rita Maalouf

Nicole Jaffrezic-Renault

• Kamal Bouhadir

Voltammetric study of the affinity of divalent heavy metals for guanine-functionalized iron oxide nanoparticles

Keywords: Nucleosides, Heavy Metals, Nanostructures, Electrochemistry, Metal complexes ____

come

Introduction

Despite the many uses of heavy metals, excessive exposure, either externally or by ingestion, can be harmful to humans, animals and plants on several levels. They are nonbiodegradable and thus have the tendency to accumulate in living organisms. Besides being considered as environmental pollutants [1], some heavy metals can cause skin, liver, kidney, bone and neurological diseases [2]. Along with natural sources, heavy metals can be released from industrial sources such as fertilizers, household waste, cosmetics, paint, batteries and plastics [3]. The range of toxicity of heavy metals depends on several factors including their charges, concentrations, way of exposure… Although the main function of nucleic acids is encoding genetic information in human beings, they have been widely explored in the fields of catalysis and ligand binding [4]. Nucleic acids are known to have different metal binding sites, binding capacity and affinity for heavy metals [5]. For years, the interaction of metal cations with nucleic acids has been investigated. It was noted that metal ions impact differently the stability and structure of nucleic acids depending on the type and concentration of metal ion and its relative affinity to the phosphate and nucleobases. It has been hypothesized that bioavailable metal ion-induced toxicity inactivates vital processes, inhibits metabolic pathways and directly or indirectly displaces essential metals from the active sites of macromolecules and/or disrupts depolymerization or repair of nucleotide bases with subsequent errors in protein synthesis [6]. The study of the interaction between nucleic acids and heavy metal ions can help explain their biotoxicity mechanisms, and these interactions can be used for the detection of toxic heavy metals in waters.

Recently, nucleic acids, nucleotides, nucleosides, nucleobases and their derivatives have been gaining wide popularity in heavy metal sensing [7].

They are biodegradable, highly selective and can be produced by natural or synthetic methods. Many studies have relied on the stabilization or destabilization of G-quadruplex structure of guanine-rich DNA, formation of stable base pairs or catalytic cleavage of DNA substrates for the detection of heavy metals [8].

Among the five natural nucleobases, guanine and its derivatives have received considerable interest [9]. Guanine is a purine derivative that consists of a fused pyrimidine-imidazole ring system with conjugated double bonds. It has been well established that metal ions bind to the carbonyl oxygen O (6) and/or the imidazolyl nitrogen N(7) of guanine. Preference of the binding site depends on the metal ion itself [START_REF] Burda | Handbook of Computational Chemistry[END_REF]. In the present work, the voltametric behavior of guanine in the presence of divalent heavy metal ions was studied. It is known that the redox moiety of guanine is the imidazolyl nitrogen N (7) [START_REF] Subramanian | [END_REF]. The interaction of N (7) with heavy metal ions can then be monitored through the change of the electron transfer rate. For the sensitive detection of the oxidation of guanine, synthesized guanine hydrazide (GH) was immobilized on iron oxide nanoparticles that present a large specific surface area and a high electrical conductivity. Recently, magnetic nanoparticles, particularly magnetite Fe 3 O 4 nanoparticles, have attracted a lot of interest owing to their unique properties of superparamagnetism, low Curie temperature, high magnetic susceptibility, low toxicity and cost effectiveness [12,13]. The exclusive magnetic and electrical properties are the result of the transfer between Fe 2+ and Fe 3+ [14].

They have a wide variety of applications ranging from environmental to biological and medical. Synthesis conditions are crucial in determining their size and physicochemical properties, and thus several processes have been investigated for their production depending on the desired application. Moreover, Fe 3 O 4 nanoparticles have the tendency to aggregate due to magnetic dipole-dipole interactions between particles [15], which is why in most electrochemical studies they are either coated or functionalized [16];

i.e. iron oxide core encapsulated in an organic or inorganic shell [17]. Owing to their versatile properties, Fe 3 O 4 nanoparticles were extensively used in combination with biological recognition elements such as enzymes, antibodies and nucleic acids for various applications [18]. The guanine functionalized iron oxide nanoparticles were immobilized on the surface of a boron doped diamond (BDD) electrode. BDD electrodes are extensively investigated for electroanalytical applications, because of their electrochemical properties, as a low background current and a wide potential window in aqueous solutions (∼-1.35 to +2.3 V versus the normal hydrogen electrode), corrosion stability in aggressive media and resistance to biofouling [19]. The redox properties of guanine were detected in the presence of copper, lead and cadmium ions. From these results, adsorption of the three heavy metals on N(7) site of guanine was characterized and the sensitive electrochemical detection of these heavy metal could then be achieved. This study aims to show that the use of the proposed guanine functionalized nanoparticles associated with a voltammetric technique could present a great potential in the physico-chemical characterization of the guanine/metal interaction. was first protected by acetylation according to literature procedure [21].

Results and Discussion

Guanine hydrazide preparation and characterization

Then reaction of N 2 -acetylguanine 3 via a Michael addition with Ethyl acrylate and sodium ethoxide afforded, as expected, a mixture of two isomeric ethyl propionates resulting from guanine alkylation at either the N-9 (5) or N-7 (4) atom. These compounds were separated by Flash chromatography and, after their structural assignment, the reaction of the N-9 ester with hydrazine hydrate in ethanol led to the formation of the desired acyl hydrazide 6 according to an established literature procedure [22].

The synthesized guanine hydrazide was characterized using FTIR and

Preparation of GH-APTES functionalized Fe3O4 nanoparticles

The co-precipitation of ferrous and ferric ions in a basic medium is a classical method for the preparation of Fe 3 O 4 . The size of the iron oxide nanoparticles directly affects their magnetic properties and should therefore be optimized based on the desired application [13]. Nanoparticles that are too small (less than 20 nm) can't be manipulated by an external magnetic field. Hence, the coprecipitation procedure was carried out at 0 °C to ensure the synthesis of nanoparticles of adequate size. Upon the addition of NaOH, the color of the solution changed gradually from orange to brown to black.

Precipitation of Fe 3 O 4 is expected at pH > 7.5 [15]. The reactions involved in the production of Fe 3 O 4 are:

Fe 3+ + 3HO -⇌ Fe(OH) 3 (1) Fe(OH) 3 ⇌ FeO(OH) + H 2 O (2) Fe 2+ + 2HO -⇌ Fe(OH) 2 (3)
Fe(OH) 2 + 2FeO(OH) ⇌ Fe 3 O 4 + H 2 O ( 4
)
The process of amino modification of Fe 3 O 4 nanoparticles by direct immobilization of (3-aminopropyl)triethoxysilane on the surface of the nanoparticles can be expected to occur through a silanization reaction, leaving the NH 2 group of APTES exposed. This step is usually very complex and is influenced by several parameters including the reaction time, temperature and silane concentration.

Finally, the functionalization of the APTES-coated nanoparticles with guanine hydrazide was done using glutaraldehyde. The overall reaction for the synthesis of the functionalized electrode is shown in figure 3. confirmed with bands at 2902 cm -1 and 2973 cm -1 [13]. The absorption band corresponding to the Fe-O-Si bond can't be seen since it overlaps with that of Fe-O vibration. However, the shift in the Fe-O band from 550 cm -1 to 562 cm -1 indicates that there is an Fe-O-Si bond [16]. FTIR measurement after the functionalization of APTES coated nanoparticles with GH confirmed the crosslinking of GH to the APTES by the appearance of new peaks not characteristic of APTES. The shift in the peak corresponding to N-H stretching from 3672 cm -1 to 3440 cm -1 is consistent with N-H stretching of an amide group along with an increased peak intensity. The -CH 2 stretching peaks also increased in intensity due to the increased number of CH 2 groups from the hydrazide function.

Powder XRD patterns of the coated nanoparticles show diffraction peaks at 30.1°, 35.4°, 43.1°, 53.4°, 57.0°, and 62.6° corresponding to the characteristic pattern of pure magnetite Fe 3 O 4 (figure 4B). The diffraction peaks can be assigned to the (220), (311) (400), ( 422), ( 511) and ( 440) diffraction planes, respectively [17]. This proves that the coating doesn't affect the core magnetite and doesn't lead to a phase change.

The morphology of the prepared nanoparticles capped with (3aminopropyl)triethoxysilane was investigated using SEM as shown in figure 4C. The magnetic nanoparticles appear to be quasi-spherical, with uniform distribution and an average size of 45 nm. Energy-dispersive X-ray spectroscopy (EDX) was performed to study the elemental composition of the APTES coated Fe 3 O 4 nanoparticles (figure 4D). Peaks corresponding to iron (Fe) at about 0.6, 6.3 and 7 keV and oxygen (O) confirm the formation of iron oxide nanoparticles [18]. The presence of peaks corresponding to Si and N confirm that the APTES coating was successful.

Voltammetric study of the GH-APTES functionalized nanoparticles in the presence of divalent heavy metals

Prior to studying the voltammetric behavioral interaction of heavy metals with the modified electrode, each of the different elements were studied electrochemically to check for their respective signals. As shown in figure 5a, no observable peaks were detected with square wave voltammetry in the range between -1 and 1.5 V for the BDD electrode coated with APTES-Fe 3 O 4 NPs. However, upon functionalization of the nanoparticles with GH, a peak appears at 1.1 V as indicated in figure 5b. This peak is characteristic of the oxidation of guanine at a BDD electrode [START_REF] Subramanian | [END_REF]24] and not the hydrazide function which is oxidized at a higher potential (1.8 V) [25]. The oxidation reaction of guanine in aqueous media is presented in Fig.

6 [START_REF] Subramanian | [END_REF].

Adsorption isotherms of the divalent heavy metal ions on the GH-APTES functionalized nanoparticles

In order to characterize the interaction between heavy metals and the functionalized nanoparticles, adsorption isotherms were modeled.

Adsorption isotherms are mathematical models describing the distribution of the adsorbate between the solution and the adsorbent. These models are based on to the possibility of interaction between the adsorbate species, type of coverage and the homogeneity/heterogeneity of the adsorbent surface [26]. The variation of the peak maximum (ΔI) (mean value of triplicate) is proportional to the adsorbed concentration of the heavy metals at the modified electrode surface. The adsorption isotherm of the heavy metals was then built from this value, the initial concentration of the heavy metals was not highly modified, due to the small surface area of the modified electrode in contact. Two models were tested: Langmuir and Freundlich.

i. Langmuir isotherm

The Langmuir model assumes that adsorption occurs on a structurally homogeneous adsorbent in a monolayer, or that the adsorption occurs at fixed sites that are identical and energetically equivalent. The linearized form of the Langmuir isotherm can be written as follows [27]:

c e /ΔI = 1/Q 0 b + c e /Q 0
where Q 0 is the adsorption capacity (µg g -1 ) and b is the energy of adsorption (L µg -1 ). Figure 8 mg.g -1 for Cu 2+ , Cd 2+ and Pb 2+ , respectively. Moreover, the essential characteristics of the Langmuir model can be expressed as the dimensionless constant separation factor R L as follows [27]:

R L = 1/(1 + Q 0 b)
In the case of the three different metals, R L falls in the range of 0 -1 indicating that the nature of the adsorption isotherm is favorable. The adsorption capacity of the functionalized nanoparticles towards the studied heavy metal ions decreases in the following order: Cu 2+ > Pb 2+ > Cd 2+ .

ii. Freundlich isotherm

Freundlich isotherm is another form of the Langmuir model describing a heterogeneous system with multiple adsorption sites. The linearized logarithmic form of the Freundlich model can be expressed as follows [START_REF] Vasudevan | Clean: Soil, Air[END_REF]:

log ΔI = log K F + (1/n) log c e
where K F is the Freundlich constant (µg g Langmuir model suggesting that the Langmuir model is more convenient in describing the adsorption process. This signifies that the adsorption is of a typical monomolecular layer form [29]. It assumes that the adsorption is localized, all active sites have similar energies and no interaction between the adsorbed molecules exists [30]. The different affinities and adsorption capacities rely on both the adsorbent (mainly its guanine moiety) and the adsorbate (ionic radius, electronegativity, charge…) [29,31]. Consequently, comparing the divalent metal ions, the orders of affinity and adsorption capacity decrease with increasing ionic radii and electronegativity. According to Sigel et al., guanine contains imidazole and pyridinetype nitrogens well suited for divalent metal ions binding [5], and in general the binding of metal cations is governed by the formation of energetically favorable coordination complexes [6], the interaction of guanine or a guanine derivative G with a divalent metal ion M 2+ yields M(G) 2+ complexes [32].

Most investigations about the complexation of the nucleobases with metal ions do not focus on the free nucleobases, but rather on DNA itself or DNAresembling structures and related bio-molecules [4]. Nonetheless, it is reported that amongst divalent metal ions that can bind both the phosphate and the DNA base, copper (II) has the strongest affinity to the base [6], which confirms our findings. It was shown that copper can be coordinated to guanine through the N(7) and O(6) atoms, as well as a possible monocoordination to the N(7) position only, depending on the guanine tautomer [33]. Lead on the other hand is known to weakly interact with the N(7) and O(6) atoms of guanine [6] knowing that Pb 2+ is an excellent oxidizer and strong Lewis acid [34]. Cadmium is classified as a soft metal that binds preferentially to DNA bases more than DNA phosphates. Notwithstanding the different studies dedicated to the interaction between Cd 2+ and nucleobases, the exact nature of binding remains uncertain. It was suggested that cadmium most likely binds to guanine at its N(7) center in a 1:1 ratio [35].

Comparing the behavior of the three divalent heavy metals with guanine, it is evident that the highest adsorption capacity is observed for Cu (II) followed by Pb (II) and Cd (II). This trend comes in accordance with a study done by Hammud et al. on the interaction of some nucleobase derivatives with divalent metals. They found that it follows the ionic radii of the cations such that as the radius increases, the stability of the formed complexes increases [36]. This order is also in agreement with a report by Sharma et al. who potentiometrically studied the stability constant of a pyrimidine derivative with divalent metal ions. According to their observations, the trend depends on both the ionic radius and the second ionization energy [37]. Based on a recent study, different factors affect the stability of metal complexes including the nature of the central metal ion, nature of the ligand, chelating effect, macrocyclic effect, resonance effect and steric effect/hindrance [START_REF] Muthaiah | Intech Open[END_REF]. Thus, this original and sensitive design can further help clarify the guanine-heavy metal interaction, with a possible application of these functionalized beads as advanced material for heavy metal ions complexation, removal and detection from aqueous solutions.

The effect of other divalent ions such as Ca 2+ was tested. The SWV signal decreased less than 10% for high concentrations (>100mg/L),

showing a very weak interaction.

Voltammetric detection of divalent heavy metals with the GH-APTES-Fe3O4 modified BDD electrode

Following the adsorption isotherms, the plots of each heavy metal were assessed to study the analytical behavior of the guanine hydrazide functionalized nanoparticles. Starting with cadmium in figure 9a, its plot can be divided into 2 linear parts: the first linear range was found between 0.232 and 0.809 μmol dm -3 with a correlation coefficient r 2 of 0.9274 and sensitivity of 101.4 μA μmol -1 dm 3 while the second linear range was observed between 0.925 and 1.815 μmol dm -3 with r 2 = 0.9775 and sensitivity of 13.4 μA μmol -1 dm 3 . Considering the first linear range, the obtained concentration range and limit of detection are comparable to reported values using Fe 3 O 4 nanoparticles for the detection of Cd (II) by square wave voltammetry (Table 2). The same behavior was noticed upon the subsequent addition of Pb 2 (II) and Cu (II) respectively. The measurements were carried out in a citrate 3 buffer solution pH 4. As shown in Fig. 9b, the calibration graph obtained for 4 Pb (II) detection exhibited two linear response ranges of 0.0483 -0.4521 5 μmol dm -3 (r 2 = 0.9113) and 0.550 -1 μmol dm -3 (r 2 = 0.98601) with the 6 sensitivities of 156.38 μA μmol -1 dm 3 and 28.25 μA μmol -1 dm 3 , 7 respectively. By comparing the results obtained with previously reported In the case of Cu (II), the calibration plots were divided between two linear ranges: the first range from 0.209 to 1.03 μmol dm -3 with r 2 = 0.92098 and a sensitivity of 171.6 μA μmol -1 dm 3 , and the second range from 1.44 to 3 μmol dm -3 with r 2 = 0.94262 and a sensitivity of 13.5 μA μmol -1 dm 3 . It is worth mentioning that the sensitivity for copper is much higher (more than ten folds) than in all other reported works using iron oxide nanoparticles [3, 11, 1, 41] with a comparable limit of detection of 0.069 μmol dm -3 .

Furthermore, the reproducibility among five independent GH functionalized Fe 3 O 4 electrodes was evaluated by comparing the linear ranges with each of the studied heavy metals. The data in figure 9 show that the electrochemical sensor demonstrates a good reproducibility over five independent measurements such that the maximum relative standard deviation RSD is 4% in the case of Cu (II), 5% for Pb (II) and 10% for Cd (II).

Conclusion

In the present work, we report the development of a novel material, GH-APTES functionalized iron oxide nanoparticles. These nanoparticles were used to modify a BDD electrode in order to assess the interaction between guanine hydrazide and divalent heavy metal ions. The adsorption isotherms were investigated and it was proven that the data are better modelled with Langmuir isotherm, with adsorption capacities decreasing in the order: Cu 2+ >Pb 2+ >Cd 2+ . This design allowed us to evaluate these ions such that the sensitivities and LODs were 171.61 μA μmol -1 dm 3 and 0.069 μmol dm -3 for Cu (II), 156 μA μmol -1 dm 3 and 0.0161 μmol dm -3 for Pb (II) and 101.4 μA μmol -1 dm 3 for 0.077 μmol dm -3 Cd (II), respectively.

Moreover, the sensitivity obtained in the detection of copper was at least ten times greater than all reported sensitivities using iron oxide. We anticipate that the synthesized GH-APTES-Fe 3 O 4 nanoparticles are promising materials that can be used rapidly and economically for heavy metal complexation and removal for water decontamination. Further tests utilizing the different hydrazide nucleobases derivatives for the detection of heavy metals could be of interest and could help better elucidate the sensitivity and the mechanism of interaction between nucleobases and heavy metal ions.

Experimental

Chemical Reagents

All the reagents used in this study were of analytical grade and used as received without any further purification. Ammonium hydroxide (NH

Synthesis and characterization of guanine hydrazide

A round bottom flask was charged with guanine (10 g, 66.22 mmol) N,N-dimethylacetamide (DMA, 30 cm 3 ) and acetic anhydride (16.5 cm 3 , 168 mmol). The reaction mixture was stirring overnight at 165°C after which it was cooled to room temperature. The precipitate was collected and triturated with water/ethanol 1:1 (30 cm 3 ) at 80°C for 2-3 h. The precipitate was collected and dried under reduced pressure at 70°C to yield a white solid.

The solid was transferred to a 500 cm 3 round bottom flask with dimethylformamide (50 cm 3 ). An ethanolic solution of sodium ethoxide (NaOEt, 2 cm 3 , 25.9 mmol) was added and the mixture was stirred for 15

Fabrication of APTES-coated iron oxide nanoparticles

Magnetic nanoparticles were synthesized according to a modified Massart's method [20] based on coprecipitation of an aqueous mixture of ferric and ferrous salt hydrates followed by the addition of a base. Briefly, was allowed to age for 24 hours, after which the nanoparticles were again washed with water followed by ethanol and dried for later use.

Characterization of iron oxide nanoparticles coated with APTES

FTIR spectra were collected at each step of the synthesis using PerkinElmer Spectrum Two spectrometer in order to verify the successful synthesis of the APTES coated magnetic nanoparticles. In order to identify the crystalline phase of the prepared nanoparticles, X-ray diffraction (XRD) was performed using a Bruker D4 ENDEAVOR with Cu/K-α radiation. The operating target voltage was 50 kV and the tube current was 50 mA. The morphology and size of the nanoparticles were investigated using Scanning Electron Microscopy (SEM) done using Tescan, Vega 3 LMU with Oxford EDX detector (Inca XmaW20).

Fabrication of the electrochemical sensor

Guanine hydrazide was immobilized on the APTES coated iron oxide nanoparticles using glutaraldehyde (GA) as a crosslinking agent. Briefly, a 1 mg/mL solution of GH dissolved in DMSO was mixed with 100 mg dm -3 of the APTES coated nanoparticles. 20 mm 3 of this mixture were dropped on a clean BDD electrode and left for 20 minutes in saturated glutaraldehyde vapor. The electrode was left to dry at room temperature. Afterwards, it was placed on the electrochemical cell where a 300 mT cylindrical magnet will permit the paramagnetic nanoparticles to remain attracted to the electrode's surface.

Electrochemical measurements

All electrochemical measurements were performed using a PalmSens4. A conventional three-electrode system was employed: a bare or modified boron doped diamond electrode as the working electrode, Platinum plate as a counter electrode and Ag/AgCl as a reference electrode. Citrate buffered solutions (0.1 mol dm -3 , containing 0.

912-922

Fig. 1 6 ,C 8 H

 168 Fig. 1 Schematic diagram showing the steps of guanine hydrazide synthesis

Fig. 2

 2 Fig. 2 (a) FTIR spectrum, (b) 1 H NMR, (c) 13 C NMR and (d) HRMS of

Fig. 3

 3 Fig. 3 Schematic diagram showing the process of synthesizing the GH-

1 2Fig. 4 (

 14 Fig. 4 (A) FTIR spectrum of (a) bare Fe 3 O 4 NPs, (b) APTES-Fe 3 O 4 NPs and

Fig. 5 Fig. 6

 56 Fig. 5 SWV of (a) APTES-Fe 3 O 4 nanoparticles and (b) APTES-Fe 3 O 4

Fig. 7

 7 Fig. 7 SWV of (a) Cd (II) at the GH-APTES-Fe 3 O 4 NP electrode over a

  shows the Langmuir plot c e /ΔI versus c e for the different heavy metals, each in their respective concentration range. The plots indicate that the experimental data are well fitted with the model with r 2 > 0.999. The values of the adsorption capacities were 400, 280.1 and 343.6

Fig. 8

 8 Fig. 8 Langmuir adsorption isotherms for (a) Cd 2+ , (c) Cu 2+ and (e) Pb 2+ in

Fig. 9 3

 93 Fig. 9 Linear ranges of (a) cadmium, (b) lead and (c) copper at the GH-

2. 7 g

 7 of FeCl 3 .6H 2 O and 1.2 g of FeCl 2 .4H 2 O were mixed with a molar ratio of 2:1 and dissolved in 90 cm 3 of deionized water. Afterwards, 100 cm 3 of 1 mol dm-3 NaOH solution was added dropwise under vigorous stirring and nitrogen gas at 0°C. A change in color indicated the formation of iron oxide nanoparticles. The solution was subjected to magnetic stirring for 4 hours to ensure nucleation and growth of magnetite nanoparticles. The latter were collected with an external magnet, washed several times with water followed by ethanol, and finally dried under vacuum. The solution was subjected to magnetic stirring for 60 minutes to ensure nucleation and growth of magnetite particles. APTES coating was carried out afterwards. Iron oxide nanoparticles were sonicated for 25 minutes before the addition of NH 4 OH and (3-aminopropyl)triethoxysilane under nitrogen atmosphere. The mixture

Fig. 1 Fig. 2 (Fig. 3 Fig. 4 (Fig. 5 Fig. 6 Fig. 7 3 Fig. 8 3 Fig. 9

 12345673839 Fig. 1 Schematic diagram showing the steps of guanine hydrazide synthesis

Figure 1 Figure 2 Figure 3

 123 Figure 1

Figure 4

 4 Figure 4

Figure 5 Figure 6 Figure 7

 567 Figure 5

Figure 8 Figure 9

 89 Figure 8

  -1 ) and n is the Freundlich exponent. The different isotherms for each heavy metal are shown in figure8where log ΔI is plotted versus log c e . It should be noted that the concentration range over which this model was linear was much smaller than that with the Langmuir model for all the studied metal ions. The values of n lie between 1 and 10, which implies that the adsorption is favorable and heavy metals are easily extracted from the solution. This result agrees with the values of R L from Langmuir's isotherm. Langmuir and Freundlich model parameters and linear regression correlations calculated from curve fittings are shown in Table1. Better regression correlations were calculated for

Table 1

 1 Constant parameters and correlation coefficients calculated for different adsorption models for Cu 2+ , Cd 2+ and Pb 2+ adsorption

	Isotherm	Langmuir				Freundlich
	Constants Q0	b	RL	r 2	n	kF	r 2
		(µg g -1 )	(L µg -1 )				(µg g -1 )
	Cd 2+	280.1	0.087	0.0394 0.9999 6.06	118.2	0.9614
	Cu 2+	400	0.0707	0.0341 0.9998 5.447 150.7	0.9796
	Pb 2+	343.6	0.1046	0.0271 0.9999 7.776 174.3	0.9961

Table 2

 2 Comparison of the linear detection range and sensitivity with previously reported values for the electrochemical detection of Cd (II)

	Electrode	Method Concentration	LOD	Sensitivity	Reference
	modification		Range (μmol	(μmol	(μA μmol -1
			dm -3 )	dm -3 )	dm 3 )
	Polydopamine-Fe3O4 SWASV 0.02 -0.59	9.2×10 -5 196	[39]
	Reduced graphene	SWASV 0 -0.8	0.056	14.82	[40]
	oxide-Fe3O4
	Chitosan-Fe3O4	SWASV 1.2 -1.7	0.0392 8.11	[1]
	Fe3O4	SWASV 0.3 -1.3	0.154	3.18	[41]
	Terephthalic acid-	SWASV 0.4 -1.1	0.2	12.15	[42]
	Fe3O4
	GH-APTES-Fe3O4	SWV	0.232 -0.809	0.077	101.4	Current
						work
	1

Table 1

 1 Constant parameters and correlation coefficients calculated for 1 different adsorption models for Cu 2+ , Cd 2+ and Pb 2+ adsorption 2

	Isotherm	Langmuir				Freundlich
	Constants Q0	b	RL	r 2	n	kF	r 2
		(µg g -1 )	(L µg -1 )				(µg.g -1 )
	Cd 2+	280.1	0.087	0.0394 0.9999 6.06	118.2	0.9614
	Cu 2+	400	0.0707	0.0341 0.9998 5.447 150.7	0.9796
	Pb 2+	343.6	0.1046	0.0271 0.9999 7.776 174.3	0.9961
	3

Table 2

 2 Comparison of the linear detection range and sensitivity with 4previously reported values for the electrochemical detection of Cd (II) 5

	Electrode	Method Concentration
	modification	Range (μmol

dm -3 ) LOD (μmol dm -3 ) Sensitivity (μA μmol -1 dm 3 ) Reference Polydopamine-Fe3O4 SWASV

	Terephthalic acid-	SWASV 0.4 -1.1	0.2	12.15	[42]
	Fe3O4
	GH-APTES-Fe3O4	SWV	0.232 -0.809	0.077	101.4	Current
						work
	1
	2
			0.02 -0.59	9.2×10 -5 196	[39]
	Reduced graphene	SWASV 0 -0.8	0.056	14.82	[40]
	oxide-Fe3O4
	Chitosan-Fe3O4	SWASV 1.2 -1.7	0.0392 8.11	[1]
	Fe3O4	SWASV 0.3 -1.3	0.154	3.18	[41]

Table 3

 3 Comparison of the current concentration range and sensitivity with 3previously reported values for the electrochemical detection of Pb (II) 4

May 2014

Acknowledgements

The authors acknowledge the financial support of the EU H2020 research and innovation program entitled Kardia Tool grant #768686.


Garcia Aubin
email: aubin.garcia@aphp.fr

Marie Legendre
email: marie.legendre@aphp.fr

Sandra Chantot-Bastaraud
email: sandra.chantot-bastaraud@aphp.fr

Jean-Pierre Siffroi
email: jean-pierre.siffroi@aphp.fr

Sophie Christin-Maitre

Unraveling a case of 46,XY DSD due to 17ß-Hydroxysteroid Dehydrogenase type 3 mutations at the age of 49 Un cas complexe de DSD 46,XY dû à des mutations de la 17ß-Hydroxystéroid Déshydrogénase de type 3 à l'âge de 49 ans

Keywords: 46, XY DSD Difference of sexual development Variation 46, XY DSD Différence

of sexual development 17-ß Hydroxysteroid Dehydrogenase type 3 Primary amenorrhea a b s t r a c t 17-ß Hydroxysteroid dehydrogenase type 3 (17␤-HSD3) is an enzyme transforming Delta 4 androstenedione into testosterone. It is involved in the early development of the male genital tract. In this case report, we describe a 46,XY Difference of Sexual Development (DSD) individual with a female phenotype, primary amenorrhea, facial dysmorphia and mental retardation. Gene sequencing using a panel of genes involved in DSD revealed two heterozygous loss-of-function mutations in the HSD17B3 enzyme. Furthermore, a microarray analysis revealed a 37Mb segmental 3p duplication and a recurrent 16p13.11 microduplication. The large 3p duplication is responsible for her mental retardation and her facial dysmorphia. Interestingly, HSD17B3 mutations were identified only in adulthood, at the age of 49. Furthermore, the patient's severe mental retardation and facial dysmorphia are due to genetic abnormalities different from the ones involved in her DSD.

Introduction

Male sex determination notably relies on the presence of the SRY gene located on the short arm of the Y chromosome [START_REF] Nef | Characterizing the bipotential mammalian gonad[END_REF]. It is involved in the transformation of the undifferentiated gonads into testis, which produces two major hormones: anti-Mullerian hormone (AMH) and testosterone. AMH induces the regression of the Müllerian ducts and testosterone allows the development of the male genital tract [START_REF] Josso | Women in reproductive science: anti-Müllerian hormone: a look back and ahead[END_REF]. An international classification is currently used in order to characterize Differences of Sexual development (DSD) [START_REF] Lee | International Consensus Conference on Intersex organized by the Lawson Wilkins Pediatric Endocrine Society and the European Society for Paediatric Endocrinology. Consensus statement on management of intersex disorders. International Consensus Conference on Intersex[END_REF]. It includes sex chromosome DSD, 46,XY DSD and 46,XX DSD. 46,XY DSD include disorders of gonadal (testicular) development and anomalies in androgen synthesis and/or action. Some 46,XY individuals having a full Y sex chromosome including the SRY gene, may present with a female phenotype [START_REF] Bertelloni | Disorders/differences of sex development presenting in the newborn with 46,XY Karyotype[END_REF]. The most well-known causes of this type of DSD are loss-of-function mutations in the androgen receptor, leading to complete androgen insensitivity syndrome (CAIS) [START_REF] Hughes | Androgen insensitivity syndrome[END_REF]. Its prevalence is approximately 1:20,000 births. Less frequently, loss-of-function mutations in the 5 alpha-reductase have been reported [START_REF] Mendonca | Steroid 5␣-reductase 2 deficiency[END_REF]. This enzyme transforms testosterone into dihydrotestosterone. Other causes are exceptional. In the litterature, few cases of 17-ß Hydroxysteroid Dehydrogenase type 3 (17ß-HSD3) loss-of-function mutations have been reported [START_REF] Boehmer | 17Beta-hydroxysteroid dehydrogenase-3 deficiency: diagnosis, phenotypic variability, population genetics, and worldwide distribution of ancient and de novo mutations[END_REF]. We report the exceptional case of a patient with a 46,XY DSD due to a complete loss of function of 17ß-HSD3 enzyme. Furthermore, this patient had associated genetic abnormalities with a partial trisomy of chromosome 3 and a recurrent 16p13.11 microduplication.

Case report

Our patient was born from non-consanguineous Caucasian parents. In her family history, two brothers died respectively at the age of 4 months and 2 days of life, both from heart malformations. At birth, the patient presented with a female phenotype but abnormal genitalia were observed with a clitoris enlargement, a blind vaginal cavity and gonads palpated at the inguinal level. In addition, she had a facial dysmorphia including a large mouth, a small chin and protruding frontal bumps. Her karyotype, performed on day 2 of life was XY and it revealed an abnormal chromosome 3 with a large short arm. Gonadal biopsies performed at one year of life revealed normal testicular tissue. A bilateral gonadectomy was performed at the age of two years. The patient was lost to follow-up during childhood.

At the age of 31, she was referred for the first time to our Endocrinology Department by her attending physician. The patient had an intellectual deficit with aphasia and abnormal movements. She lived in an institution and was under guardianship. Clinically, her height was 175 cm with a body mass index (BMI) of 17 kg/m 2 . Breast development was graded S1 according to Prader stages. She had very poor axillary and pubic hair. A breast ultrasound revealed a fibroglandular frame of dystrophic tissue located predominantly in the retro-mammary region without any identifiable breast tissue. An absence of gonads was checked by ultrasound. Those findings were confirmed by a pelvic scanner and a pelvic magnetic resonance imaging (MRI). Given her familial history, electrocardiogram and a cardiac ultrasound were performed. They were normal.

The patient's hormonal evaluation is presented in Table 1. At the age of 31, estradiol level was low and her gonadotropins were elevated. Due to her low E2 level, hormone replacement therapy (HRT) including estrogens and progestins was initially given with a second generation contraceptive pill containing 30 micrograms of ethinylestradiol and levonorgestrel (Adepal ® ). After 2 years, this treatment was switched to transdermal 17 beta-estradiol (2 pulses per day) associated with natural oral progesterone, 10 days per month. The patient was then lost to follow-up until 49-year-old when she was referred to the Center of Rare Endocrine Diseases of Growth and Development (CMERC: Centre des maladies endocriniennes rares et de la croissance et du développement), located in the Endocrinology department of Saint Antoine Hospital (Paris). Her BMI was 17 kg/m 2 . Her spinal bone densitometry found a T-score of -5 SD. Unfortunately, the patient died few months later, at the age of 51 years of an unknown etiology.

Genetic analyses

At the age of 49 years, after authorization from the patient's guardian and the guardianship judge, DNA was extracted from peripheral blood leucocytes on a QiaSymphony (Qiagen) automate.

In order to investigate the abnormal sexual phenotype of our patient, a panel of genes involved in DSD were sequenced by Next Generation Sequencing (NGS) in Trousseau Hospital, AP-HP, Paris. It uses a custom targeted-capture panel (SeqCap EZ Choice, Roche Diagnostics, Hg19) that encompasses 32 genes implicated in DSD (AMH, AMHR2, AR, ARX, ATRX, CBX2, CYP17A1, DHH, DMRT1, DMRT2, EMX2, FGF9, FGFR2, FOXL2, GATA4, HSD17B3, INSL3, LHCGR, MAMLD1, MAP3K1, NR0B1, NR5A1, RSPO1, RXFP2, SOX10, SOX8, SOX9, SRD5A2, SRY, WNT4, WT1, ZFPM2). The library was prepared following the manufacturer's instructions and sequenced on a MiSeq sequencing platform (Illumina). Data were analyzed through an in-house double pipeline based on Bowtie2 and BWA tools [START_REF] Jeanson | Mutations in GAS8, a gene encoding a nexin-dynein regulatory complex subunit, cause primary ciliary dyskinesia with axonemal disorganization[END_REF]. Reads were visualized with the IGV viewer (Broad Institute). Copy number variation analysis was performed with a depth-ratio comparison between subjects sequenced in the same run. The patient was also genotyped using HumanOmniExpress-24 microarrays (Illumina, San Diego, CA, USA). Automated Illumina microarray experiments were performed according to the manufacturer's instructions. Images were acquired using an iScan System (Illumina). Image analysis and automated CNV calling were performed using GenomeStudio v.2.0 and CNV Partition v.3.1.6. SNP profiles were analysed by examination of signal intensity (Log R ratio, i.e. ln (sample copy number/reference copy number)) and allelic composition (BAF, i.e. B Allele Frequency).

Using NGS, two heterozygous mutations have been identified in the HSD17B3 gene (NM 000197.2): c.277+4A>T or p.? and c.645A>T or p.(Glu215Asp) (Fig. 1). Microarrays analysis identified an interlayer heterozygous duplication of the 3p26.2 band to the 3p22.1 band of the short arm of chromosome 3 of around 37Mb (Fig. 2). This band involves 153 genes referenced in the OMIM database (genomic coordinates: chr3:3158485-39924901, GRCh37/hg19 (Feb. 2009)). It does not encompass any gene implicated in differences of sexual development. Furthermore, SNP array identified a 1.2Mb recurrent duplication at 16p13.11 (genomic coordinates: chr16:15129940-16363239, GRCh37/hg19 (Feb. 2009)) involving 8 OMIM referenced gene including MYH11 gene. Unfortunately, metaphase chromosomes were no more available for Fluorescent in situ analysis of the 3p duplicated segment. A genetic analysis of the parents is not available as the patient's father was deceased and the mother declined any genetic analysis.

Discussion

We report a complex case of a 46,XY DSD with a large segmental duplication of chromosome 3, a recurrent 16p13.11 duplication, and two heterozygous loss-of-function mutations in HSD17B3, identified at the age of 49. 17 ß-Hydroxysteroid dehydrogenase type 3 is a 310 amino acid enzyme allowing the transformation of delta-4 androstenedione into testosterone, preferentially using NADPH co-factor. It is mainly expressed in the testis [START_REF] Boehmer | 17Beta-hydroxysteroid dehydrogenase-3 deficiency: diagnosis, phenotypic variability, population genetics, and worldwide distribution of ancient and de novo mutations[END_REF]. The gene encoding this protein is located in chromosome 9q22 and contains 11 exons. The 17 ß-hydroxysteroid dehydrogenase type 3 protein was first described by Saez et al. [START_REF] Boehmer | 17Beta-hydroxysteroid dehydrogenase-3 deficiency: diagnosis, phenotypic variability, population genetics, and worldwide distribution of ancient and de novo mutations[END_REF]. Loss of function of the enzyme leads to decreased serum testosterone level and elevated delta 4androstenedione level. In some cases, after stimulation with hCG, a testosterone/delta 4-androstenedione ratio below 0.8 has been reported [START_REF] Ahmed | The testosterone:androstenedione ratio in male undermasculinization[END_REF]. The incidence of 17 ß-hydroxysteroid dehydrogenase type 3 deficit is extremely low, reaching from 1/147,000 births [START_REF] Sullivan | 17-ß-hydroxysteroid dehydrogenase type 3 deficiency: identifying a rare cause of 46, XY female phenotype in adulthood[END_REF]. It is more frequent in patients from North of Africa. Its main differential diagnosis are complete androgen insensitivity syndrome and 5 alpha reductase deficiency [START_REF] Hughes | Androgen insensitivity syndrome[END_REF].

In most cases, a deficit in 17␤-HSD3 is revealed in neonates in front of a female phenotype, fusion of labia majora, blind vagina and clitoridomegaly [START_REF] Lee | Phenotypic variability in 17beta-hydroxysteroid dehydrogenase-3 deficiency and diagnostic pitfalls[END_REF]. Rare cases of microphallus associated to hypospadias have been described. In such patients, Müller's structures are absent due to the secretion of AMH by the foetal testis. Internal genital organs are phenotypically male with epididymis, vas deferens and seminal vesicles. The gonads are often located in the inguinal region. Few histological studies have reported the presence of Leydig and Sertoli cells in the testicular tissue, in the absence of germ cells [START_REF] Yang | 17␤-Hydroxysteroid dehydrogenase 3 deficiency: three case reports and a systematic review[END_REF]. Some cases have been diagnosed at puberty with primary amenorrhea. Furthermore, cases of progressive virilization during adolescence have been reported [START_REF] Sullivan | 17-ß-hydroxysteroid dehydrogenase type 3 deficiency: identifying a rare cause of 46, XY female phenotype in adulthood[END_REF]. During this period, androstenedione levels increase and CYP 19 in peripheral tissues aromatizes androstenedione into testosterone, inducing patients' virilization. 17ß-HSD3 is not only expressed in the gonads but also in peripheral tissues, such as adipose tissue, brain, bone marrow and sebaceous glands [START_REF] Lee | Phenotypic variability in 17beta-hydroxysteroid dehydrogenase-3 deficiency and diagnostic pitfalls[END_REF]. Finally, testosterone can also be partially synthesized by the testis, as another isoform of 17ß-HSD called 17ß-HSD type 5 is expressed in Leydig cells [START_REF] Lee | Phenotypic variability in 17beta-hydroxysteroid dehydrogenase-3 deficiency and diagnostic pitfalls[END_REF]. There is a wide range of phenotypic features of 17ß-HSD3 deficiency with variable hormonal profiles. There are no genotype phenotype correlation but in null mutation, testes are with normal architecture, there is an atrophy of the deferens, no uterus and a female phenotype. At puberty, there is a virilization due to the other HSD17 [START_REF] George | The clinical and molecular heterogeneity of 17␤HSD-3 enzyme deficiency[END_REF]. To our knowledge, no case of DSD involving 17ß-HSD3 mutations has been reported in adults at such an advanced age (49-years-old).

Clinically, our patient did not present signs of virilization during adolescence as she had bilateral gonadectomy at the age of 2 years. Unfortunately, hormonal evaluations at birth and during infancy are not available. Furthermore, an hCG test was not available. Her serum estradiol level measured at the age of 49 was normal reaching 195 pmol/L, as she was taking HRT. However, the patient had severe osteoporosis. It is probably related to her past gonadectomy as well as her HRT poor compliance, as she had severe mental retardation. Nowadays, a gonadectomy would be discussed in a multidisciplinary meeting and potentially delayed. In the discussion, one should take into account the fact that there are virilization at puberty and that female to male gender changes generally occur in late adolescence to early adulthood.

Concerning her genetic evaluation, the splice mutation c.277+4A>T or p.? has been described in few cases of gonadal dysgenesis [START_REF] Sullivan | 17-ß-hydroxysteroid dehydrogenase type 3 deficiency: identifying a rare cause of 46, XY female phenotype in adulthood[END_REF]. When present in a homozygous state, this mutation leads to a complete loss of enzyme function [START_REF] Hiort | Pubertal development in 17Beta-hydroxysteroid dehydrogenase type 3 deficiency[END_REF]. It is rare in control populations (94 out of 282,304 control alleles in gnomAD). It alters the donor splice site of intron 3 (MaxEntScan score: 5.93 vs. 11.11 for the usual site; SpliceAI score: 66% probability to alter intron 3 splicing) which probably causes a decrease in protein production through nonsense-mediated mRNA decay or the production of a non-functional truncated protein. Functional studies have not been performed but this mutation is highly suspected to be deleterious on prediction software and previous reported cases [START_REF] Boehmer | 17Beta-hydroxysteroid dehydrogenase-3 deficiency: diagnosis, phenotypic variability, population genetics, and worldwide distribution of ancient and de novo mutations[END_REF][START_REF] Castro | Clinical and molecular spectrum of patients with 17␤-hydroxysteroid dehydrogenase type 3 (17-␤-HSD3) deficiency[END_REF]. The second mutation of our patient, c.645A>T or p.(Glu215Asp) is a pathogenic missense mutation. It has previously been described [START_REF] Ahmed | The testosterone:androstenedione ratio in male undermasculinization[END_REF][START_REF] Costa | The dilemma of the gender assignment in a Portuguese adolescent with disorder of sex development due to 17␤-hydroxysteroid-dehydrogenase type 3 enzyme deficiency[END_REF][START_REF] Mendonca | Male pseudohermaphroditism due to 17 beta-hydroxysteroid dehydrogenase 3 deficiency. Diagnosis, psychological evaluation, and management[END_REF][START_REF] Andersson | Molecular genetics and pathophysiology of 17 beta-hydroxysteroid dehydrogenase 3 deficiency[END_REF] and is rare in the gnomAD control populations (14 out of 282,866 alleles). It has no predicted effect on splicing (MaxEntScan, SpliceAI). It targets an amino acid that is highly conserved in vertebrates (UCSC 100 vertebrate's alignment) and is located within the catalytic domain of the enzyme. In vitro functional assessment showed a loss of enzymatic activity [START_REF] Boehmer | 17Beta-hydroxysteroid dehydrogenase-3 deficiency: diagnosis, phenotypic variability, population genetics, and worldwide distribution of ancient and de novo mutations[END_REF]. Therefore, the two HSD17B3 mutations identified in our patient induce a total loss of function and therefore explain her DSD.

In addition, our patient presented a partial duplication of chromosome 3p. To our knowledge, large exclusive duplications localized exclusively in the segments 3p26.2p22.1 have never been reported. Few cases of partial trisomy 3p syndrome have been described, with variable phenotypes including craniofacial dysmorphism (hypertelorism, telecanthus, large nose) associated with psychomotor delay, moderate to severe intellectual disability, cardiac, genitourinary, gastrointestinal, skeletal and brain anomalies [START_REF] Benito | A patient with a duplication of chromosome 3p (p24.1p26.2): a comparison with other partial 3p trisomies[END_REF][START_REF] Reiss | Partial trisomy 3p syndrome[END_REF]. However, most cases are not fully characterized with Highresolution molecular cytogenetic techniques such as microarray hybridization. Our patient's duplication arose probably de novo but the hypothesis of an unbalanced transmission of a parental insertion cannot be ruled out. In our patient, facial dysmorphia is probably due to the duplication of chromosome 3 and is not related to her DSD.

Finally, recurrent 16p13.1 duplications have also been associated with mental retardation. In some cases, an autistic spectrum has been reported. The expression of this genetic defect is variable according to its degree of penetrance [START_REF] El Khattabi | 16p13.11 microduplication in 45 new patients: refined clinical significance and genotype-phenotype correlations[END_REF]. Some cases of cardiac malformations have been reported in patients carrying such a duplication. As both her brothers died early in their life, one can make the hypothesis that they had cardiac malformation. However, this duplication is still considered a susceptibility factor for neurodevelopmental disorders. Its involvement in our patient's phenotype of mental retardation is certainly minor compared to the large 3p duplication. A genetic study of the parents would have been interesting to better understand the respective pathogenicity of those abnormalities.

Conclusion

To our knowledge, we report the first case of HSD17B3 mutations in a 46,XY DSD adult patient, carrying a complex karyotype, associating a partial trisomy of chromosome 3 and an interstitial duplication of chromosome 16. The etiology of this 46,XY DSD was identified only at the age of 49. The patient'sose different genetic abnormalities explain her complex phenotype including 46 XY DSD, facial dysmorphy as well as severe mental retardation. Interestingly, thorough genetic evaluations have shown that her facial dysmorphy and her severe mental retardation are not related to 17␤-HSD3 mutations. This case report illustrates the added value of performing CGH array as well as NGS. Nowadays, thanks to hormonal evaluation by LC/MS-MS and Next generation sequencing of genes involved in DSD, the diagnosis would be made during infancy. A genetic diagnosis identifying HSD17B3 loss-offunction performed during infancy or at puberty would improve the patient's care.

Fig. 1 .

 1 Fig. 1. Location of the mutations in the 17ß-HSD3 protein. Dashed line shows intron 3 c.277+4A>T splice mutation that probably lead to nonsense-mediated mRNA decay and lower/absence of protein production. Domain prediction based on SMART, Uniprot and InterPro tools. TM: transmembrane domain; NBD: NADP binding domain; SDR: short-chain dehydrogenase/reductase domain.

Fig. 2 .

 2 Fig. 2. SNP array profile of patient's chromosome 3. The 3p segmental duplication is highlighted in blue.

Table 1

 1 Hormonal investigations in the patient.

	Hormonal values	Normal female adult values	31-years-old	33-years-old	49-years-old
	FSH (IU/L)		46	37	35.8
	LH (IU/L)		5	5.6	20.5
	Estradiol (pmol/L)	73-440	47.7	25.7	195
	Androstenedione (nmol/L)	0.50-1.50		1.01	1.82
	Testosterone (nmol/L)	0.30-1.70		0.87	0.52
	17 hydroxyprogesterone (nmol/L)	0.10-0.90			0.55
	SDHEA (mol/L)	2-13			4.43

Funding

This work did not receive any grant from funding agencies in the public, commercial, or not-for-profit sectors.

Human and animal rights

Not applicable.

Informed consent and patient details

The authors declare that this report does not contain any personal information that could lead to the identification of the patient(s).

Not applicable.

Disclosure of interest

The authors declare that they have no competing interest.

Author contributions

All authors attest that they meet the current International Committee of Medical Journal Editors (ICMJE) criteria for Authorship.

Appendix A. Supplementary data

Supplementary data associated with this article can be found, in the online version, at https://doi.org/10.1016/j.ando.2022.01.003.


Fares Zouaoui

Nadia Zine

Abdelhamid Errachid

Nicole Jaffrezic-Renault

Mathematical model and numerical simulation of conductometric biosensor of urea

Keywords: Conductometry, urea, urease, modelling, analytical performance

In this article, a mathematical model was developed to describe and optimize the configuration of the urea biosensor. The biosensor is based on interdigitated gold microelectrodes modified with a urease enzyme membrane. The model presented here focuses on the enzymatic reaction and/or diffusion phenomena that occur in the enzyme membrane and in the diffusion layer. Numerical resolution of differential equations was performed using the finite difference technique. The mathematical model was validated using experimental biosensor data. The responses of the biosensor to various conditions were simulated to guide experiments, improve analytical performance, and reduce development costs.

Introduction

Urea is the breakdown product of nucleic acids and proteins into nitrogenous waste in the liver. It is eliminated from the body primarily through urine, but it is also secreted in bodily fluids such as blood and saliva [1]. Humans have a normal urea level of 0,25 to 0,6 mM in the blood and 155 to 390 mM in the urine thus providing key information on kidney function and in the diagnosis of various kidney disorders and hepatic [2]. Regarding the environment, urea is used in agriculture as a fertilizer, deicing agent, etc. However, these molecules lead to the acidification and eutrophication of fertile soil. Thus the contamination of surface water by runoff disrupts the ecosystem and causes the death of aquatic life [3]. Therefore, it becomes necessary to monitor urea levels in urine and blood and in different fields such as agriculture, food, pharmacy, etc. The use of enzymatic hydrolysis of urea by urease in the development of a urea biosensor has attracted considerable attention from biochemical and clinical analyzes [4]. Hydrolysis of urease in urea generates ionic products, such as NH4 + , HCO3 -and OH -. The ions produced are monitored by several techniques, such as an optical transducer [5,6], potentiometry [7,8], colorimetry [9,10], amperometry [11,12], and conductometry [13,14]. Conductometric biosensors have significant advantages, as they do not require the use of a reference electrode; they operate at an alternating voltage of low amplitude, they are insensitive to light; and they can be miniaturized and integrated easily [START_REF] Dzyadevych | Conductometric biosensors[END_REF]. The conductometric measurement method can be used in enzymatic catalysis involves either the consumption or the production of charged species, therefore, lead to an overall change in the ionic composition of the sample tested. The conductivity measured by the biosensor is easily modified by the presence of other ions or those produced by the enzymatic reaction, which affects the selectivity of the method. However, in the case of an integrated microbiosensor, this limitation can be overcome by using a differential measurement scheme which compensates for changes in the conductivity of the medium [START_REF] Jaffrezic-Renault | [END_REF]. This article aims to investigate the problem of optimizing biosensor design using an interdisciplinary approach that combines mathematical and computational modeling with electrochemical and biochemical techniques. A mathematical model was developed to analyze the response of a conductometric enzyme biosensor for the detection of urea. The transducer is composed of interdigitated inert gold microelectrodes coated with a layer of urease enzyme. The main components of the biosensor are based on well-known physical processes such as diffusion as well as biological and electrochemical reactions. The finite difference method was used to solve partial differential equations coupling diffusive mass transfer to enzymatic kinetics. Experimental urea detection data were used to validate the mathematical model. The numerical results are compared with the experimental results and appear to be in good agreement. The responses of the biosensor to various conditions (such as the thickness of the diffusion layer, thickness of the enzyme membrane, urea concentration, etc.) were simulated. This exploitation can guide experiments to improve analytical performance and reduce development costs.

Materials and Methods

Reagents and Apparatus

Bovine serum albumin (BSA), Urease (Type III from Jack Beans), glutaraldehyde (25% aqueous solution), glycerol (>99%) and phosphate buffered saline (PBS) were obtained from Sigma-Aldrich. All aqueous solutions were prepared using ultrapure water. The conductometric transducers contain two identical pairs of gold interdigitated electrodes. The dimension of each interdigital space and digit was 20µm and the length of the digits was 1 mm. The area of each pair of electrodes was 1 mm². Measurements were performed at 23±2°C by applying to the differential pairs of electrodes an alternative voltage (10 mV amplitude, 100 kHz frequency) generated by a low-frequency wave form generator (SR830 lock-in amplifier from Stanford Research Systems).

Preparation of the urea biosensor

The suspension system contains 6% of BSA, 4% of urease and 10% of glycerol dispersing in 5 ml of phosphate buffer with a concentration of 20 mM (pH 7,3). The mixture was mixed for 1 hour. 0,2 µL of this solution was deposited onto interdigitated microelectrodes. For the preparation of the reference microelectrode, the same steps previously were followed, but in the absence of the urease in the initial mixture. The interdigitated microbiosensors were then placed in saturated glutaraldehyde vapours for 30 min. Finally, the biosensors were dried at room temperature for 30 min and stored at 4 °C before the experiments [17].

Conductometric measurements

Interdigitated microelectrodes modified by urease film were placed in a glass cell filled with 5 mL of PBS with a concentration of 5 mM (pH 7.3±0.1). The solution was stirred vigorously. Measurements were performed by applying to the differential pairs of electrodes an alternative voltage with the amplitude of 10mV and a frequency of 100 kHz generated by the generator. The measurements were repeated after adding urea to the PBS solution in a range of 1x10 -8 to 3x10 -6 mol/cm 3 . Experiments were carried out at ambient temperature.

Conductometric biosensor model

Description of the system

Urea in the bulk analyte solution diffuses through a diffusion boundary layer to the enzyme membrane, where its hydrolysis is catalyzed by urease. The ions formed by the reaction increase the electrical conductivity of the solution at the surface of the sensor. This change in conductivity is detected by a change in the electrical conductance of the array of interdigitated electrodes, which depends on the conductivity of the solution near the sensor surface. The concentrations of ionic products were used to calculate the spatial and temporal distribution of electrical conductivity. The operation of the conductometric urea sensor was modeled by solving the coupled problem of mass transport and enzymatic reaction to determine the concentration of ionic products at the surface of the electrode. The structure of the conductometric urea biosensor is illustrated schematically in Figure 1.For the development of a mathematical model it is assumed that, the geometry of the electrode is symmetrical. The enzyme membrane is uniform with a homogeneous distribution. It is also assumed that the transport process of all species is defined in a one-dimensional spatial domain. The structure of the biosensor is divided into two zones; the diffusion layer from δm to δd where the bulk solution substrate diffuses without reaction, and the porous enzymatic membrane from 0 to δm where the substrate is hydrolyzed by urease immobilized to the electrode surface during diffusion.

Enzymatic reaction

The detection principle due to ions generated by the hydrolysis of the urea catalysis by urease according to the reaction [4]:

𝐶𝐶𝐶𝐶(𝑁𝑁𝑁𝑁 2 ) 2 + 3𝑁𝑁 2 𝐶𝐶 𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈 �⎯⎯⎯� 2𝑁𝑁𝑁𝑁 4 + + 𝑁𝑁𝐶𝐶𝐶𝐶 3 -+ 𝐶𝐶𝑁𝑁 -Eq.1
The enzymatic rate depends only on urea concentration; therefore the speed of the urease reaction can calculate according to the Michaelis-Menten mechanism [18]:

𝑉𝑉 = 𝑉𝑉 𝑚𝑚𝑚𝑚𝑚𝑚 .𝑆𝑆 𝐾𝐾 𝑚𝑚 +𝑆𝑆 Eq.2
Where Vmax is the maximum of catalysis speed, Km is Michaelis-Menten constant and S is the urea concentration at the sensor surface.

In the experiments conducted for this study, enzyme was immobilized only at the sensor surface, so the term V will be zero except at the sensor surface.

The kinetic paramaters of the enzymatic reaction

Figure 2 shows the graphic presentation of the linearization from the Michaelis-Menten equation:

1 𝑉𝑉 = 𝐾𝐾 𝑚𝑚 𝑉𝑉 𝑚𝑚𝑚𝑚𝑚𝑚 1 𝑆𝑆 + 1 𝑉𝑉 𝑚𝑚𝑚𝑚𝑚𝑚 Eq. 3
The enzymatic speed corresponds to the slope of tangent at the origin [19]. The conductivity values at 120 s are considered to estimate the kinetic parameters of the urease enzyme immobilized to the sensor. The linear equation found is y = 7.72*10 -7 x + 0.406 with a correlation coefficient R² = 0.998. This linearization method gives the maximum of catalysis speed Vmax = 2.46 µS cm -1 .s -1 and the constant Km = 19.01*10 -7 mol/cm 3 .

Figure 2.

Lineweaver-Burk plot of urease kinetic for different urea concentrations.

Governing equations For x ϵ] δm, δd [:

In the diffusion layer, concentrations of urea and products of enzymatic reaction depend on the time and position. The equations governing the system are based on the principle of conservation of mass. They can be described according to the second Fick's law by the following equations:

𝜕𝜕𝑆𝑆 𝜕𝜕𝜕𝜕 = 𝐷𝐷 𝑈𝑈𝑠𝑠 𝜕𝜕²𝑆𝑆 𝜕𝜕𝜕𝜕² Eq.4 𝜕𝜕𝜕𝜕 𝜕𝜕𝜕𝜕 = 𝐷𝐷 𝑝𝑝𝑠𝑠 𝜕𝜕²𝜕𝜕 𝜕𝜕𝜕𝜕² Eq.5
Where S: is the concentration of urea, P: is the concentration of the products of enzymatic reaction (NH4 + ; HCO3 -; OH -), t: is the time, x: is the position and Dsd/Dpd: is Diffusivity of the substrate/products in the diffusion layer.

For x ϵ] 0, δm [: In the enzymatic membrane, concentrations of urea and products of enzymatic reaction depend on the time, position and the rate of the enzymatic reaction. This system is described by the following mass balance equations:

𝜕𝜕𝑆𝑆 𝜕𝜕𝜕𝜕 = 𝐷𝐷 𝑈𝑈𝑠𝑠 𝜕𝜕²𝑆𝑆 𝜕𝜕𝜕𝜕² - 𝑉𝑉𝑠𝑠𝑈𝑈𝜕𝜕 . 𝑆𝑆 K 𝑚𝑚 +𝑆𝑆
Eq.6

𝜕𝜕𝜕𝜕 𝜕𝜕𝜕𝜕 = 𝐷𝐷 𝑝𝑝𝑠𝑠 𝜕𝜕²𝜕𝜕 𝜕𝜕𝜕𝜕² + 𝜐𝜐 𝑝𝑝 𝑉𝑉𝑠𝑠𝑈𝑈𝜕𝜕 . 𝑆𝑆 K 𝑚𝑚 +𝑆𝑆
Eq. 7

Where υp: stoichiometric coefficients of the ion.

Initial conditions:

Initial conditions assume spatially uniform concentrations of all species; the initial conditions are as follows:

S(δm+δd, 0)=S0 Eq.8 S(x,0)=0 Eq. 9 P(x,0)=0 Eq.10

Where S0 is the concentration of urea in bulk solution.

Boundary conditions:

At the diffusion layer-bulk solution interface (x= δm+ δd), the concentrations of the substrate and the products are equal to the bulk solution values during the biosensor operation:

S(δm+δd,t)=S0 Eq.11 P(δm+δd,t)=0

Eq.12 At the enzymatic membrane-diffusion layer interface (x= δm), the flux of substrate and products passing from one layer to another are assumed to be equal. This is defined by the following conditions (t> 0):

𝐷𝐷 𝑈𝑈𝑠𝑠 𝜕𝜕𝑆𝑆 𝜕𝜕𝜕𝜕 � 𝜕𝜕=δm = 𝐷𝐷 𝑈𝑈𝑠𝑠 𝜕𝜕𝑆𝑆 𝜕𝜕𝜕𝜕 � 𝜕𝜕=δm
Eq.13

𝐷𝐷 𝑝𝑝𝑠𝑠 𝜕𝜕𝜕𝜕 𝜕𝜕 � 𝜕𝜕=δm = 𝐷𝐷 𝑝𝑝𝑠𝑠 𝜕𝜕𝜕𝜕 𝜕𝜕𝜕𝜕 � 𝜕𝜕=δm
Eq.14

At the electrode surface (x=0), the substrate is electroinactive substance, and the concentration of the products at the sensor surface is being permanently reduced to zero due to the polarization of the electrode (t> 0) [18,20]:

𝜕𝜕𝑆𝑆 𝜕𝜕𝜕𝜕 � 𝜕𝜕=0 = 0
Eq.15 P(0,t)=0 Eq.16 The conductivity response of the biosensor was calculated using equation 17 below [21]:

𝜎𝜎 𝑖𝑖 𝑗𝑗 = ∑ |𝑍𝑍 𝑛𝑛 | 𝑛𝑛 ℷ 𝑛𝑛 𝑃𝑃 𝑛𝑛𝑖𝑖 𝑗𝑗
Eq.17

Where σi j : is the conductivity of the i th layer at the j th time (µS.cm -1 ), Zn: is the charge of ion n, ℷn: is the equivalent ionic molar conductivity of the ion n (µS.cm².mol -1 ), Pni j : is the concentration of the ion n in the i th layer at the j th time (mol.cm -3 ).

Numerical method

Finite difference method was used to solve simultaneously equations ( 4)-( 16), to predict the response of the conductometric biosensor as a function of time.

In order to simplify the modeling: The diffusion coefficients of the ionic species in each diffusion layer are equal. The time step (Δt) and the space step (Δx) are the same in the two diffusion layers. The approximation of the equations of substrate (S) and products (P) in diffusion layer and enzymatic layer were given as follows, respectively: Where: i ranging from 0 to (δm+δd)/Δx, and j ranging from 0 to final time/Δt.

For xϵ] δm, δd [ -𝐷𝐷 𝑈𝑈𝑠𝑠 ∆𝜕𝜕 ∆𝜕𝜕 2 𝑆𝑆 𝑖𝑖-1 𝑗𝑗+1 + (1 + 2𝐷𝐷 𝑈𝑈𝑠𝑠 ∆𝜕𝜕 ∆𝜕𝜕 2 )𝑆𝑆 𝑖𝑖 𝑗𝑗+1 -

Numerical simulation

At each time step, discretized version of different equations was solved applying Thomas algorithm [START_REF] Lee | Tridiagonal Matrices: Thomas Algorithm[END_REF].

The numerical simulation of the biosensor responses has been carried out using Matlab software. The unknown parameters (δm, δd, Dsd, Dsm, Dpd, Dpm) are determined by minimizing the error between the experimental and the theoretical values of the conductivity. This error is calculated according to the following relationship.

𝑒𝑒 = ∑ � σ 𝑡𝑡ℎ𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑡𝑡𝑒𝑒𝑒𝑒𝑚𝑚𝑒𝑒 -σ 𝑒𝑒𝑚𝑚𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑚𝑚𝑒𝑒𝑒𝑒𝑡𝑡𝑚𝑚𝑒𝑒 σ 𝑡𝑡ℎ𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑡𝑡𝑒𝑒𝑒𝑒𝑚𝑚𝑒𝑒 � Eq. 31
The general algorithm of the simulation is represented in Figure 3, and the parameters used during this simulation are gathered in Table 1.

Results and Discussion

Model Validation

The various parameters of the conductometric biosensor determined by the model for the different concentrations of urea are gathered in Table 2. The diffusion layer and the thickness of the enzymatic membrane are estimated at 0.0022 cm and 0.0211 cm, respectively. The values of diffusion coefficient of the substrate in the diffusion layer (Dsd) was between 1.40 10 -8 and 2.23 10 -8 cm²/s (Dsd medium = 2.23 10 -8 cm²/s). The diffusivity of urea in the enzymatic layer was estimated between 9.50 10 -7 and 4.12 10 -7 cm²/s (Dsm medium = 6.81 10 -7 cm²/s). For the products, the diffusion coefficient in the enzymatic membrane is approximated to a value between 4.20 10 -8 and 7.10 10 -8 cm²/s (Dpm medium = 5.65 10 -8 cm²/s). While, the diffusivity value of the products in the diffusion layer is negligible (Dpd <10 -22 cm²/s).

The numerical simulation of the mathematical model previously described was successfully applied to calibrate the response of the urea biosensor. Figure 4.a shows that a better fit is achieved between the experimental and theoretical data with an adjustment error less than 10 -3 .

Considering the steady state conductivity, a good linear relationship between the experimental and theoretical conductivity as a function of the urea concentration is achieved (Fig.

Concentration and conductivity profiles

By using the mathematical model developed, it is possible to determine the concentrations of the substrate and the products as a function of time in the vicinity of the electrodes.

Figure 5 shows the variation of the concentration of urea in the diffusion layer and the enzymatic membrane for a concentration of urea in solution equal to S0= In another side, the figure 6.a represents the concentration profiles of HCO3 -and OH -, and the figure 6.b represents the concentration profiles of the NH4 + in the enzyme membrane. This difference is due to the stoichiometric coefficients. The concentrations of the products of the enzymatic reaction in steady state are maximum for x = δm, such that [HCO3 -] = [OH -] = 0.5824 mol/cm 3 and [NH4 + ] = 1.1647 mol/cm 3 . These concentrations decrease as they approach the surface of the electrode. They are 3.3 more weaker at x = 2/3 δm, 18.4 more weaker at x = 1/3 δm and 69.3 more weaker at the electrode surface. The concentration profiles made it possible to see how conductivity varies as a function of time and distance x. Figure 7 represents the conductivity at different points in the enzyme membrane. The conductivity in steady state is maximum at x = δm (σ = 27241 µS/cm). Conductivity values decrease as they approach the surface of the electrode. In steady state, it takes a value of 6967.4 µS/cm at x = 2/3 δm, 1226.3 µS/cm at x = 2/3 δm and 327,975 µS/cm at the surface of the electrode.

Influence of diffusion layer and enzyme membrane thicknesses

The study of the conductivity in function of time was performed using different values of diffusion layer thickness (δd) (from 2 to 40 µm) for S0= 3*10 -6 mol/cm 3 , δm=0.02cm, Dsd=2*10 -8 cm²/s, Dsm=4*10 -7 cm²/s, Dpd=10 - 22 cm²/s and Dpm=7*10 -8 cm²/s (Fig. 8.a). For small values of diffusion layer thickness, the conductivity of the biosensor is bigger and increases rapidly until to reach the steady state condition. For greater value of diffusion layer thickness, the conductivity of the biosensor decrease, and the time required to establish the steady state increases. This behavior because the concentration gradient that is established in the diffusion layer is greater for greater thicknesses. Based on these observations, it is recommended to keep the detection enclosure stirred. It is preferable to use maximum agitation possible in order to further reduce the thickness of the diffusion layer. This agitation should not be greater in order to avoid affecting the enzyme membrane. In addition to the diffusion layer effect, the thickness of the enzyme membrane can also affect the response of the biosensor. conductivity in function of time using different values of enzyme membrane thickness (δm) (from 100 to 300 µm) for δd=0,002cm, Dsd=2*10 -8 cm²/s, Dsm=4*10 -7 cm²/s, Dpd=10 -22 cm²/s and Dpm=7*10 -8 cm²/s. The conductivity is inversely proportional to the thickness of the enzyme membrane. It is larger with a thinner enzymatic membrane and it is weak with a thicker enzyme membrane. For the thick films, the effect of the resistance to mass transfer in the membrane enzyme becomes important, and then the resistance to mass transfer in the enzyme membrane decreases with the decrease in the thickness of the membrane.

Figure 8. a)

The effect of diffusion layer on the conductometric response of the biosensor for S0= 3*10 -6 mol/cm 3 , Vmax=2.46 µS/cm.s, Km=19.01*10 -7 mol/cm 3 , δm=0.02cm, Dsd=2*10 -8 cm²/s, Dsm=4*10 -7 cm²/s, Dpd=10 - 22 cm²/s and Dpm=7*10 -8 cm²/s. b) The effect of enzyme membrane on the conductometric response of the biosensor for S0= 3*10 -6 mol/cm 3 , Vmax=2.46 µS/cm.s, Km=19.01*10 -7 mol/cm 3 , δd=0.002cm, Dsd=2*10 -8 cm²/s, Dsm=4*10 -7 cm²/s, Dpd=10 -22 cm²/s and Dpm=7*10 -8 cm²/s.

Influence of urea concentration (S0)

In figure 9 is shown the conductometric response of the biosensor for different values of the concentration of urea in solution from 10 -9 to 3 mol/cm 3 for δd=0.002cm, δm=0.02cm, Dsd=2*10 -8 cm²/s, Dsm=4*10 -7 cm²/s, Dpd=10 - 22 cm²/s and Dpm=7*10 -8 cm²/s. It is observable that for the lowest concentrations (<10 -8 mol/cm 3 ) the conductivity is almost zero. With increasing concentration from 10 -8 to 1 mol/cm 3 , conductivity significantly increases and the time required to establish the steady state decreases. Then, for higher concentrations (>1 mol/cm 3 ) the conductivity is maximum and almost without variation.

Figure 9. The effect urea concentration on the conductometric response of the biosensor for Vmax=2.46 µS/cm.s, Km=19.01*10 -7 mol/cm 3 , δd=0.002cm, δm=0.02cm, Dsd=2*10 -8 cm²/s, Dsm=4*10 -7 cm²/s, Dpd=10 - 22 cm²/s and Dpm=7*10 -8 cm²/s. For the highest concentrations of urea in solution, figure 10.a shows the concentration profiles of urea and figure 10.b shows the concentration profiles of OH -in the enzyme membrane determined by the mathematical model using two high concentrations of urea in solution 2 and 3 mol/cm 3 for δd=0.002cm, δm=0,02cm, Dsd=2*10 -8 cm²/s, Dsm=4*10 -7 cm²/s, Dpd=10 -22 cm²/s and Dpm=7*10 -8 cm²/s. At each position of x, the urea concentration is large if S0 is large (fig. 10.a). This indicates that the substrate is present in the enzyme membrane and its concentration is proportional to S0. But the concentrations of OH -are the same for each position in the enzymatic membrane whatever the S0 concentration in solution (fig 10.b). This indicates that the enzyme is saturated and its activity is maximum. It is for this reason that the conductivity of passes varies with the large concentrations S0. In this case to significantly detect large concentrations it is recommended to use a higher enzyme concentration. 3mol/cm 3 2mol/cm 3 1mol/cm 3 10 -1 mol/cm 3 10 -2 mol/cm 3 10 -3 mol/cm 3 10 -4 mol/cm 3 10 -5 mol/cm 3 10 -6 mol/cm 3 10 -7 mol/cm 3 10 -8 mol/cm 3 10 -9 mol/cm 3 0 100 200 300 400 500 600 700 800 900 1000 0,000 The substrate and product concentration profiles were studied in order to understand why the conductivity is almost zero with low concentrations and why it does not vary with high concentrations. mol/cm 3 , δd=0.002cm, δm=0.02cm, Dsd=2*10 -8 cm²/s, Dsm=4*10 -7 cm²/s, Dpd=10 - 22 cm²/s and Dpm=7*10 -8 cm²/s.

Effects of the maximum enzymatic rate Vmax

Figure 12 shows the variation in conductivity as a function of the maximum enzymatic rate. This study shows that the conductivity is proportional to Vmax. Such that more than Vmax is large, the sensitivity of the sensor is stronger. Practically, it is possible to accelerate the rate of the reaction by increasing the concentration of the enzyme in the membrane or else by increasing the temperature on condition that it does not go beyond the denaturation temperature [START_REF] Shu | [END_REF].

Effects of the kinetic constant Km

The response of the sensor also depends on the value of the kinetic constant. Figure 13 summarizes the conductometric responses for different values of the kinetic constant, where conductivity is plotted against time. For higher values of Km, the conductivity increases only slightly. This generally reflects a low sensitivity to urea. For lower values of K the signal rises higher. This shows that the sensitivity of the sensor for urea is very high. The kinetic constant is a parameter which can, in practice, be difficult to modify substantially [20] Figure 13. The effect of the kinetic constant (Km) on the conductometric response of the biosensor for Vmax=2.46 µS/cm.s, δd=0.002cm, δm=0.02cm, Dsd=2*10 -8 cm²/s, Dsm=4*10 -7 cm²/s, Dpd=10 -22 cm²/s and Dpm=7*10 -8 cm²/s.

Conclusion

In this paper, a mathematical model was developed to simulate the response of the conductometric biosensor for the detection of urea. It is based on an interdisciplinary approach which combines the law of diffusion, the enzymatic kinetics of Michaelis-Menten, numerical methods, electrochemistry and computer science. The model has been successfully applied to describe the enzymatic reaction/diffusion system of the urea biosensor.

The presented study demonstrates that the model developed could also be used to predict the conductometric response as a function of the various parameters which allows to guide the experiments, and to optimize the biosensor by improving these analytical characteristics and reducing development costs.

Figure 1 .

 1 Figure 1. Scheme of principal structure of conductometric biosensor for urea detection. S: urea, positive and negative charges: product ions of the enzymatic reaction.

  (s.cm/µS) 1/[Urea] (cm 3 /mol)

Figure 3 .

 3 Figure 3. Simulation algorithm of the mathematical model.

Figure 4 .

 4 Figure 4. a) Theoretical results and the experimental data of the conductometric biosensor response for different concentrations of urea. b) Experimental and numerical calibration curves of the conductometric urea biosensor

[Figure 5 .

 5 Figure 5. a) Urea concentration profiles in the diffusion layer and in the enzyme membrane for S0=3x10 -6 mol/cm 3 . b) Enlargement of figure 5.a.

Figure 6 .

 6 Figure 6. a) HCO3 -and OH -concentration profiles b) NH4 + concentration profiles: in the enzyme membrane for S0=3*10 -6 mol/cm 3 .

Figure 7 .

 7 Figure 7. Conductivity profiles in the enzyme membrane for S0=3*10 -6 mol/cm 3 .

Figure 8 .

 8 b represents the study of the

3 ]

 3

3 Figure 10 .

 310 Figure10. a) Urea concentration profiles b) OH - concentration profiles: in the enzyme membrane with S0=2 mol/cm 3 and S0=3 mol/cm 3 for Vmax=2.46 µS/cm.s, Km=19.01*10 -7 mol/cm 3 , δd=0.002cm, δm=0.02cm, Dsd=2*10 -8 cm²/s, Dsm=4*10 -7 cm²/s, Dpd=10 -22 cm²/s and Dpm=7*10 -8 cm²/s.

Figure 11 .

 11 a shows the concentration profiles of urea and figure11.b shows the concentration profiles of OH -in the enzyme membrane determined by the mathematical model using two low concentrations of urea in solution 10 -8 and 10 -9 mol/cm 3 for δd=0,002cm, δm=0.02cm, Dsd=2*10 -8 cm²/s, Dsm=4*10 -7 cm²/s, Dpd=10 -22 cm²/s and Dpm=7*10 -8 cm²/s. With low concentrations S0 in solution, the concentration of urea (fig.11.a) and products (fig.11.b) at x=0 is almost negligible which explains the absence of the conductometric response. But at the same position of x close to δm, the urea and product concentrations for S0= 10 - 8 mol/cm 3 are greater than that for S0= 10 -9 mol/cm3 . Therefore to have a significant signal and to move towards the detection of very low concentrations, it is recommended to use a thin enzymatic membrane.

Figure 11 .

 11 Figure 11. a) Urea concentration profiles b) OH - concentration profiles: in the enzyme membrane with S0=10 -8 mol/cm 3 and S0=10 -9 mol/cm 3 for Vmax=2.46 µS/cm.s, Km=19.01*10 -7mol/cm 3 , δd=0.002cm, δm=0.02cm, Dsd=2*10 -8 cm²/s, Dsm=4*10 -7 cm²/s, Dpd=10 - 22 cm²/s and Dpm=7*10 -8 cm²/s.

Figure 12 .

 12 Figure12. The effect of the maximum enzymatic rate (Vmax) on the conductometric response of the biosensor for Km=19.01*10 -7 mol/cm 3 , δd=0.002 cm, δm=0.02 cm, Dsd=2*10 -8 cm²/s, Dsm=4*10 -7 cm²/s, Dpd=10 -22 cm²/s and Dpm=7*10 -8 cm²/s.

  ,62 µS/cm.s V max =1,23 µS/cm.s V max =2,46 µS/cm.s V max =4,92 µS/cm.-5 mol/cm 3 K m =10 -6 mol/cm 3 K m =10 -7 mol/cm3

Table 1 .

 1 Parameters and variables used in the numerical simulation.

	Parameters/Variables		Dimensional parameters	Value/Variation range
	Time			t, s	0-630
	Diffusion layer thickness		δd, cm	0.0001-0,01
	Enzymatic layer thickness		δm, cm	0.0001-0,01
	Initial concentration of urea		S0, mol/cm 3	1*10 -8 -3*10 -6
	Michaelis-Menten constant		Km, mol/cm 3	19.01*10 -7
	Maximum of catalysis speed	Vmax, µS/cm.s	2,46
	Diffusivity of the substrate in the	Dsd, cm²/s	10 -6 -10 -9
	diffusion layer.
	Diffusivity of the products in the	Dpd, cm²/s	10 -6 -10 -9
	diffusion layer.
	Diffusivity of the substrate in the	Dsm, cm²/s	10 -6 -10 -9
	enzymatic layer.
	Diffusivity of the products in the	Dpm, cm²/s	10 -6 -10 -9
	enzymatic layer.
	Equivalent	ionic	molar	ℷ, µS.cm²/mol	7350/4450/19800
	conductivity of NH4 + /HCO3 -/OH -
	Experimental conductivity		σ, µS/cm	/

4.b). The regression equations are σ = 0.107*10 8 [urea] + 19,4; R²=0.96 and σ = 0.106*10 8 [urea] + 21.4; R²=0.97; respectively with a 1.80% relative standard deviation.

Table 2 .

 2 Different parameters of the conductometric biosensor estimated by the model for different concentrations of urea.

	Concentration	Dsd (cm²/s)	Dsm (cm²/s)	Dpm (cm²/s)	δd (cm)	δm (cm)	error
	(mol/cm 3 )
	1x10 -8	2.23 10 -8	9.50 10 -7	4.20 10 -8	0.0022	0.0211	3.12 10 -4
	6x10 -8	1.65 10 -8	6.05 10 -7	4.50 10 -8	0.0022	0.0211	1.75 10 -4
	1x10 -7	1.50 10 -8	5.75 10 -7	4.80 10 -8	0.0022	0.0211	3.66 10 -4
	2,5x10 -7	1.90 10 -8	5.05 10 -7	5.30 10 -8	0.0022	0.0211	1.78 10 -4
	5x10 -7	1.40 10 -8	5.25 10 -7	6.10 10 -8	0.0022	0.0211	5.76 10 -4
	1x10 -6	1.60 10 -8	4.65 10 -7	6.50 10 -8	0.0022	0.0211	4.32 10 -4
	3x10 -6	1.80 10 -8	4.12 10 -7	7.10 10 -8	0.0022	0.0211	1.42 10 -4

  The urea concentration is lower and lower for an x close to zero, at x=0 it is equal to 1.897*10 -10 mol/cm 3 , that is to say it is 15814.4 more weaker than S0.

			24
	3*10 -6 . The concentration of urea at x= δm+ δd equal to S0. At x= δm+ 9/10 δd, the concentration of urea in steady state (2.279*10 -7 mol/cm 3 ) is 13.16 times weaker than S0. Urea	mol/cm 3 [Urea] 10 8	8 10 12 14 16 22 20 18	x=0 x=1/3δ m x=2/3δ m x=9/10δ m x=δ m x=δ m +1/3δ d x=δ m +2/3δ d x=δ m +9/10δ d
			6	For x=δ m +δ d
			4
			2
			0
			0	100 200 300 400 500 600 700 800 900 1000
				Time (s)

concentration continues to decrease, at x= δm the steadystate concentration equal to 4.294*10 -8 mol/cm 3 , this value is 69.86 times weaker than S0. In the enzyme membrane, at x= 9/10 δm the concentration of urea in steady state equal to 2.377*10 -8 mol/cm 3 , it is 128.21 times weaker than S0 and 1.8 times weaker than the value at x= δm.

Acknowledgements

The authors acknowledge the financial support of the EU H2020 WIDESPREAD Program entitled Bionanosens grant agreement # 951887.