Hajar Molaee

Mehdi Sahihi
email: m.sahihi@chem.ui.ac.ir

Majid Moghadam
email: moghadamm@sci.ui.ac.ir

Valiollah Mirkhani

Shahram Tangestaninejad

Iraj Mohammadpoor-Baltork

Hadi Amiri

Mehdi Sahihi⁎

Majid Moghadam⁎

Hadi Amiri Rudbari

A combined

Keywords: HSA binding, Schiff base ligand, Stabilizing agent, Fluorescence quenching, Molecular docking, Molecular dynamics simulation

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

Introduction

Due to the interesting chemical and physical properties, Schiff bases have received significant attention in recent years [START_REF] Amiri | Spectroscopic,electrochemical, docking and molecular dynamics studies on the interaction of three oxovanadium (IV) Schiff base complexes with bovine serum albumin and their cytotoxicity against cancer[END_REF][START_REF] Shahraki | Synthesis, characterization, In silico ADMET prediction and protein binding analysis of a novel zinc (II) Schiff-base complex: Application of multi-spectroscopic and computational techniques[END_REF]. In these compounds, imine bond is formed easily by condensation of primary or secondary amines with carbonyl groups. The Schiff base ligands have high coordination ability and very strong biological properties (Shahraki, et al., 2017). Although in the past decade these compounds have been extensively studied, still they are highly considered. These compounds exhibited many biological activity such as antitumor, antibiotics, antifungal, antimicrobial, anticancer and antibacterial properties and finally, they have appropriate for binding to DNA and HSA macromolecules [START_REF] Berendsen | Spectroscopic and molecular docking studies on the interaction of Pd (II) & Co (II) Schiff base complexes with β-lactoglobulin as a carrier protein[END_REF]. In the field of bioinorganic chemistry, the Schiff base ligands that derived from heterocyclic compounds such as pyridine are of high importance because of the presence of one or more ring containing nitrogen atom with a localized pair of electrons [START_REF] Shokohi-Pour | Cobalt (II) complex with novel unsymmetrical tetradentate Schiff base (ON) ligand: in vitro cytotoxicity studies of complex, interaction with DNA/protein, molecular docking studies, and antibacterial activity[END_REF]. Human serum albumin (HSA) is the most abundant plasma protein. Also, it is known as the dominant transporter plasma protein for endogenous and exogenous ligands (e.g. fatty acids and hormones) and is one of the most important targets in binding of various drugs (e.g. warfarin, diazepam and Ibuprofen) and metal ions. The HSA-binding of a drug increases its solubility in plasma, decreases its toxicity, protects it from oxidation, prolongs it's in vivo half-life and increases its pharmaceutical effect. Understanding of these interaction mechanisms help us to know the pharmacodynamics and pharmacokinetics effects of drugs. Hence, investigation of the interaction of small drug molecules with HSA is very important for the discovery of the mystery of life and the interaction mechanisms of drugs [START_REF] Shahraki | Binding forces between a novel Schiff base palladium (II) complex and two carrier proteins: human serum albumi and β-lactoglobulin[END_REF]. In this paper, two water soluble Schiff bases were synthesized by the reaction of 4pyridinecarbaldehyde or 4-pyridylmethyl ketone with ethylenediamine (Scheme S1). Then the bidentate Schiff base compounds were characterized by 1H NMR spectroscopies and elemental analysis. In addition, the molecular structure of one of these compounds was determined by single crystal X-ray diffraction technique. Then, the binding ability of these two Schiff bases with HSA was investigated using UV-Vis and fluorescence spectroscopy, molecular docking and molecular dynamics simulation methods.

Experimental

Materials and instruments

4-Pyridinecarboxaldehyde, 4-pyridylmethyl ketone and ethylenediamine were obtained from Merck chemical company and used without further purification. Human serum albumin (HSA), was purchased from Sigma-Aldrich. All salts used for buffer preparation were analytical grade and dissolved in double distilled water. All of the solutions were used freshly after preparation. 1H NMR spectra were recorded on a Bruker Avance 400 spectrometer using CDCl3 as solvent (Figure S1). The UV-Vis spectra were obtained on a JASCO V-570 spectrophotometer and the UV-Vis spectra for PE and MePE are shown in the Figures S2 andS3, respectivly. Also their details were stated in the Synthesis part. The fluorescence spectra were carried out on a Shimadzu RF-5000 (Kyoto, Japan) spectrofluorimeter equipped with thermostated cell compartment, was used at ± 0.1 oC.

Synthesis of the Schiff base ligands

Two Schiff base ligands PE and MePE have been synthesized in various articles for different applications, before [START_REF] Yang | Temperature-Dependent in Situ Ligand Cyclization via C C Coupling and Formation of a Spin-Crossover Iron (II) Coordination Polymer[END_REF]. Here, these compounds were resynthesized in a simple method in order to investigate their interaction with HSA. To a stirring solution of 4-pyridinecarboxaldehyde (2 mmol) or 4-pyridylmethyl ketone (2 mmol) in methanol (10 mL), a solution of ethylendiamine (1 mmol) in methanol (10 mL) was added dropwise. The reaction mixture was stirred for 3 h at the 50 Ċ and then filtered. Suitable single crystals of PE for X-ray crystallography were obtained by leaving the filtrate undisturbed at room temperature in stable state for 2 days. The crystals were filtered off, were washed with cold methanol, and were dried in vacuum. Crystal data, together with other relevant information on structure determination for PE, are listed in Table S1. The molecular structure and atom-numbering scheme of PE is presented in Figure S4. Selected bond distances, and bond angles are also given in Table S2. Also inter and intra molecular hydrogen bond geometries (Å) and their informations were shown in Figure S5 and Table S3. PE: Yield 93%. Anal. calculated for C14H14N4 (M.W. = 214.02 g/mol): C,70.57;H,5.92;N,23.51. Found: C,71.43;H,5.92;N,23.48. 1H NMR (CDCl3,400 MHz,298 K) δ/ppm: 8.4 (d,4H,HAr),8.2 (s,2H,Himine),7.5 (d,4H,HAr),4 (s,4H,Hen)

Preparation of stock solutions

A Stock solution of HSA (5 mg/ml for fluorescence and UV-Vis studies) was made by dissolving HSA in phosphate buffer (50 mM, pH=7). The exact concentration of HSA was determined spectrophotochemically using molecular absorption coefficient of 35700 M-1cm-1 at 278 nm. Schiff bases were completely dissolved in water and kept in the dark. All solutions were used freshly after preparation. UV-Vis spectra of compounds were recorded at different times and no changes were observed in these spectra.

Fluorescence spectroscopy

Fluorescence quenching is the best method to compute the binding constant and to quantify the binding affinities of macromolecules with drugs such as Schiff bases. Fluorescence of the proteins is created by three inherent fluorophores in the protein structure; tyrosine (Tyr), tryptophan (Trp) and phenylalanine(Phe) residues. Among them, phenylalanine has very low quantum yield, so normally fluorescence of protein was produced by tryptophan and tyrosine residues. When the excitation wavelength of HSA is set at 295 nm, fluorescence is created by the tryptophan residues.

The band widths of the emission and excitation slits were set at 5.0 and 10 m. In generic experiments, emission spectra were recorded after addition of Schiff bases solutions (50 μM) at 298, 303 and 308 K to 2 ml of protein solution (5 μM). In these experiments, the observed fluorescence intensities were corrected for the dilution and inner filter effect. The excitation was performed at 295 nm and the emitted light was recorded from 300 to 450 nm. The solutions were incubated for 5 min before recording the emission spectra.

Absorption spectroscopy

The HSA solution was freshly prepared just before the measurements. The absorption study of HAS was performed in phosphate buffer (pH = 7) at 298 K. In typical experiments, 2 ml of HSA solution (10 μM) was placed in the cuvette and the absorbance spectra were recorded at 220-350 nm, after addition of the stock solutions (70 μM). In these experiments, the observed absorbencies corrected for the dilutions. The solutions were incubated for 5 min, before recording the absorption spectra. The absorption spectrum of HSA illustrate maximum absorption band at 279 nm assigned to 𝝅→𝝅 * transitions of aromatic amino acids and a higher maximum at 205 nm devoted to 𝝅→𝝅 * transitions of amide groups of peptide bonds [START_REF] Shahabadi | Investigation of the effects of Zn 2+, Ca 2+ and Na+ ions on the interaction between zonisamide and human serum albumin (HSA) by spectroscopic methods[END_REF]. Also, it should be noted that the UV-Vis spectra of these compounds have not overlap with the fluorescence spectrum of HSA in the same concentration. So, there is no energy transfer between the Schiff base ligands and HSA.

Docking procedure

For the docking calculations, the 3D structure of PE was provided by converting its crystallographic .cif file to .pdb file. However, the 3D structure of MePE was made using Gauss view 5.0. Calculation of structure optimization was carried out at the 6-31G** level by employing the Becke three-parameter Lee-Yang-Parr (B3LYP) hybrid density functional theory using the quantum chemistry software Gaussian 03 [START_REF] Frisch | Gaussian 09, revision D. 01[END_REF]. The crystal structure of HSA (PDB ID: 1AO6) was taken from the Brookhaven Protein Data Bank (http://www.rcsb.org/pdb). The molecular docking software, AutoDock Version 4.2, using the implemented empirical free energy function and the Lamarckian Genetic Algorithm (LGA) was used for docking. The protein input file for docking was prepared by adding Gasteiger charges. Grids were calculated using AutoGrid.

In the first step, for two compounds the dimensions of the grid box were set on the 126×126×126 points along with x, y and z axis. Then, the most numerous cluster with the lowest docking energy was selected for the second docking run using a grid map with 60×60×60 points and a grid-point spacing of 0.375 Å. 150 docking runs with 25,000,000 energy evaluations for each run were performed.

Molecular dynamics (MD) simulation

MD simulation on the compound-protein complex was used for further investigation on the structural changes of protein. A 20 ns MD study was carried out using GROMACS 4.5.6 software package [START_REF] Berendsen | Spectroscopic and molecular docking studies on the interaction of Pd (II) & Co (II) Schiff base complexes with β-lactoglobulin as a carrier protein[END_REF]. The GROMOS96 43a1 force field was used, and the SPC water model was employed for the water molecules. The system is required to be neutral, so charges were balanced with 15 sodium counter ions. A cubic box was chosen, with periodic boundary conditions. The number of the total atoms in the system were 43641 and 43638 for PE and MePE, respectively. The force field parameters were obtained from PRODRG web server. Gaussian 03 at the level of B3LYP/6-31G** was used for calculating of atomic charges.

Energy minimization was performed in the first step with the steepest descent method for the 3000 time steps [START_REF] Hess | LINCS: a linear constraint solver for molecular simulations[END_REF]. After energy minimization process, position restraint procedure was performed in association with NVT and NPT ensembles. An NVT group was adjusted at constant temperature of 300 K with 200 ps time duration. After stabilization of temperature an isothermal-isobaric ensemble (NPT) was performed at constant pressure of 1.0 bar with 200 ps time duration. Finally, a 20 ns MD simulation was carried out at 300 K and 1 bar.

A brendsen thermostat (300 K) and the Particle-Mesh Ewald (PME) method were used to correct the long-range electrostatic interaction and the cut-off method (1.2 nm) was used to treat the van der Waals interactions. The leap-frog algorithm with the 2 fs time steps was used for integration of the equation of motion. For further analysis, the atomic coordinates were recorded to the trajectory file every 0.5 ps.

Result and Discussion

Absorption spectroscopy UV-Vis absorption study is the most usual technique to investigate the HSA structural changes through its interaction with other compounds. In this experiment, these studies were carried out using different concentrations of the synthesized Schiff bases. The binding constant (Ka) of these interactions have been determined using the Benesi-Hildebrand equation; (Eq. 1), 1/(A -A0) = 1/(Amax -A) + 1/Kb(Amax -A) [M] (1) In this equation, A0 and A are the absorbance of HSA in the absence and presence of other compounds, respectively. Amax is the obtained absorbance at saturated concentration and [M] is the compound concentration. Ka was obtained from the ratio of the intercept to the slope in the plot of 1/(A-A0) versus 1/[M]. A significant reduction in the maximum absorbance of two spectra was observed as a function of compound concentration (figures are not shown). This observation demonstrates that HSA interacts with the synthesized Schiff base compounds. The values of the binding constant (Ka) were determined from Eq. 1 and were reported in Table 1.

Fluorescence spectroscopy

As mentioned above, the fluorescence of HSA is dominated by the residue Trp-214 in subdomain IIA. The binding of Schiff bases as small quencher molecule to HSA changes the environment of tryptophan residue. The intrinsic fluorescence intensity of HSA is induced by these changes. In these experiments, the observed fluorescence intensities were corrected for the dilutions. The absorbance of protein solution was less than 0.1 at both excitation and emission wavelengths. Hence, reabsorption effect can be ignored in our experiments.

The Stern-Volmer equation (Eq. 2) was used for analysis of HSA fluorescence quenching:

F0/F = 1+ Ksv[Q] = 1 + τkq[Q] (2)
Where F0 and F are fluorescence intensities of HSA in the absence and the presence of the quenching agent (Schiff base compounds), respectively. Ksv is the Stern-Volmer quenching constant, [Q] is the quencher concentration, kq is the bimolecular quenching constant and τ is the average lifetime of protein in the absence of quencher (10-8 s) [START_REF] Kazemi | Synthesis, characterization and biological application of four novel metal-Schiff base complexes derived from allylamine and their interactions with human serum albumin: Experimental, molecular docking and ONIOM computational study[END_REF]. KSV and kq were determined from the plot of F0/F vs.

[Q] at 298, 303 and 308 K (Figure S8 and Table 1).

If the Stern-Volmer plot is linear, the quenching fluorescence has only one mechanism, dynamic or static (In the static mechanism, the macromolecule and the quencher collide together in the ground state but they collide together at the excited state in the dynamic mechanism). For the synthesized compounds, the values of KSV increase with increasing the temperature. This observation supports that quenching fluorescence of HSA by Schiff bases occurs via a dynamic mechanism .

If there are n substantive sites on the surface of protein to bind the compound molecules, the binding constant (Ka) can be calculated as follows (Eq. 3) :

ln(F0 -F)/F = lnKb + n ln[Q] (3)
The values of Ka and n are reported in Table 1. The obtained results indicate that the Ka for MePE is larger than the obtained value for PE at all temperatures. Really, MePE is bound to HSA more tightly than PE and the affinity of HSA for binding of this compound is greater than the other one. Also, for two compounds at all temperatures the n value is about 1 which indicates that HSA and the Schiff base interact in a 1:1 ratio.

Determination of the thermodynamic parameters

In order to find the nature of the interaction between Schiff bases and biomacromolecules, the thermodynamics parameters were determined at different temperatures (298, 303 and 308 K). The changes in both enthalpy (ΔHº) and entropy (ΔSº) were determined using Van't Hoff equation (Eq. ( 4)): ln Kb=-ΔH°/RT + ΔS°/R (4) Where Ka is the binding constant at the corresponding temperature, T is the absolute temperature in Kelvin and R is the gas constant. The values of ΔHº and ΔSº can be determined from the linear relationship between ln Ka and the reciprocal of absolute temperature. Moreover, according to Eq. ( 5), the binding free energy change (ΔGº) was calculated as a function of temperature and the obtained data are listed in Table 2. ΔG°=ΔH°-TΔS° (5) Thermodynamic parameters (ΔHº) and (ΔSº) provide significant information on the type of interactions. There are four main forces between biomacromolecule and small compounds: hydrogen bonding, van der Waals forces, electrostatic and hydrophobic interactions [START_REF] Zolfagharzadeh | A comparison investigation of DNP-binding effects to HSA and HTF by spectroscopic and molecular modeling techniques[END_REF]. The positive values for ΔH° and ΔS° imply a hydrophobic force but the negative values for both of them reflect the van der Waals force or hydrogen bond formation. Finally, the positive value for ΔS° and small amount of ΔH° (ΔH°≈0) suggest the electrostatic forces. As shown in Table 2, the negative values for Gibbs free energy change (ΔG°< 0) means that the binding process for HSA is spontaneous. Additionally, the positive values for enthalpy (ΔH° > 0) andentropy (ΔS° > 0) changes indicate that the binding is mainly entropy-driven, and the hydrophobic forces play a major role in this interaction. Also, for both Schiff bases, the negative value of ΔG° increased with raising the temperature, so that the interaction was done more spontaneous at higher temperatures. Besides, in each temperature the value of ΔG° for MePE is more negative than PE. Therefore, the affinity of HSA for binding to MePE is more than that of PE. Hence, replacing the hydrogen atom in PE with methyl group in MePE could have basic role in the stability of HSA-MePE complex. Really, the methyl group enhances the electron density on pyridine ring and increases the probability of π stacking interaction of MePE and HSA. This hypothesis should be examined by molecular docking calculation which can show the atomic details of macromolecule-ligand interactions.

Docking procedure

HSA is a monomeric protein with three α-helical domains that consists of 585 amino acids. These domains are divided into six-helix subdomains (A and B) [START_REF] Gelamo | Interaction of bovine (BSA) and human (HSA) serum albumins with ionic surfactants: spectroscopy and modelling[END_REF]. The previous analyses showed that aromatic compounds can be located within two famous hydrophobic sites known as Sudlow's Site 1 and 2 in sub-domains IIA and IIIA, respectively. Also, there is a D-shaped cavity in subdomain IB (termed as site 3) for binding of some compounds such as hemin [START_REF] Assaran Darban | Multi-spectroscopic and molecular modeling studies of interaction between two different angiotensin I converting enzyme inhibitory peptides from gluten hydrolysate and human serum albumin[END_REF].

The results of the interaction between Schiff bases and protein in docking procedure are shown in Figure 2. As it can be seen in this figure, PE and MePE are situated within subdomain IB in site 3 with the binding energy of -6.69 and -7.08 kcal.mol-1 for PE and MePE, respectively. Furthermore, these compounds were adjacent to some hydrophobic residues in subdomain IB of HSA (Tyr 161, Tyr 138, Tyr 133, Phe 149, Leu 185, Arg 186, Gly 189 and Met 123). Also, there is a high binding affinity between HSA and MePE compared to PE. This result is in agreement with UV-Vis spectroscopy and fluorescence quenching results. MePE has two hydrogen bonds between imine and pyridine nitrogen with the oxygen atoms of Tyr 161 and Tyr 138 residues and there are two π-π interaction between the pyridine ring of this compound and the aromatic rings of Tyr 161 and Tyr 138 residues. This observation is in consistent with thermodynamic results (see previous section).

As it mentioned before, the methyl group increases the electron density of pyridine ring and causes stabilizing the HSA-MePE complex with π-stacking interactions. As a result, these bonds play an important role in stabilizing MePE compared to PE in IB binding site of HSA.

Molecular dynamics simulation

The trajectories of free HSA and HSA-ligands systems were investigated based on Root Mean Square Deviations (RMSDs) of back bone atoms of protein, Radius of gyration (Rg), and Root Mean Square Fluctuation (RMSF) of protein residues. The stability of the system (protein, Schiff base, ions, water, etc.) was examined by RMSD. RMSD values as a function of simulation time for free HSA and HSA-ligand complexes during 20 ns MD simulations (Figure 3a). It is observed that for all molecular systems, the RMSD remains stable with some fluctuations after 6 ns of simulation, so all of the following analysis was carried out based on the stability of the simulation after the 14 ns of equilibration and the stability of the whole protein structure makes it possible to obtain reliable analysis on compound binding and its effect on HSA structure through MD simulation.

Also, the compactness of protein was specified by radius of gyration (Rg) values of the HSA and HSAligand complexes. The results were plotted versus simulation time (Figure 3b). Stabilization of Rg values about 8 ns indicated that the MD simulation could achieve equilibrium after this time. There is no conformational changes during the simulation, because the radius of gyration of all systems are approximately similar to each other . The mobility of protein was also investigated by calculating the time averaged root mean square fluctuation (RMSF) [START_REF] Jana | Exploring structural change of protein bovine serum albumin by external perturbation using extrinsic fluorescence probe: spectroscopic measurement, molecular docking and molecular dynamics simulation[END_REF] of free HSA and HSA-ligand complexes based on the last 14 ns of trajectory data (Figure 3c). The general profiles of atomic fluctuations were found to be very similar to each other and were showed that the fluctuations of residues in the IB cavity are lower than the others which indicates that during the MD simulation, the binding site remains approximately rigid. In addition, the RMSF of the atomic positions of the Schiff bases (Figure 3d)

indicated that the atoms of the Schiff bases showed limited fluctuations (<0.25 nm). Hence, it can be concluded that the interactions of HSA and the Schiff bases were stable during the simulation time.

Conclusions

In the present study, two Schiff base ligands, PE and MePE, were synthesized and characterized using elemental analysis, UV-Vis and 1H NMR spectroscopies. The crystal structure of PE was also determined using single crystal X-ray analysis. Furthermore, Binding of the Schiff base ligands to HSA was investigated using fluorescence spectroscopy at three temperatures and full thermodynamics study was done on the fluorescence results. Also, UV-Vis spectroscopy method was used to approve the fluorescence results. Furthermore, computational molecular docking study was done to investigate the atomic details of these bindings and to obtain the theoretical binding constants. All of the obtained results by the used experimental methods were in good agreement with molecular docking results. The obtained results from both experimental and theoretical methods indicated that the MePE binds to HSA more tightly than PE. Also, the thermodynamics parameters for binding of two synthesized Schiff bases to HSA were determined at 298, 303 and 308 K. The negative values of ΔG° increased with raising the temperature for both Schiff bases and the values of ΔG° for MePE is more negative than PE at all temperatures. Moreover, based on the enthalpy and entropy changes of interaction, the binding is mainly entropy-driven, and the hydrophobic forces play a major role in the stability of ligand-HSA complexes. Molecular docking results revealed that both of the ligands bind in the IB domain of HSA. Also, it can be concluded that methyl group in MePE increases the electron density of pyridine ring and causes stabilizing the HSA-MePE complex with πstacking interactions. As a result, π-stacking interactions play important role in stabilizing MePE in its binding site. Finally, analysis of MD trajectories suggested that these Schiff base ligands can interact with HSA without any modification of protein structure.

Appendix A. Supplementary data CCDC 1536516 contains the supplementary crystallographic data for PE. These data can be obtained free of charge via http://www.ccdc.cam.ac.uk/conts/retrieving.html, or from the Cambridge Crystallographic Data Centre, 12 Union Road, Cambridge CB2 1EZ, UK; fax: (+44) 1223-336-033; or e-mail: deposit@ccdc.cam.ac.uk.

  The fluorescence emission spectra of HSA at various concentrations of Schiff bases at 298 K are shown in Figure1. The experiment was repeated at 303 and 308 K and the related quenching plots are shown in FiguresS6 and S7. The HSA showed a strong fluorescence emission with a peak around 340 nm at λex=295 nm.During the titration of a fixed concentration of HSA with various amounts of the Schiff bases, a remarkable decrease was observed in the fluorescence intensity with increasing the concentration of Schiff bases. The strong quenching of HSA fluorescence clearly indicated that both Schiff bases bound to HSA and changed its tertiary structure[START_REF] Trynda-Lemiesz | Studies on the interactions between human serum albumin and imidazolium [trans-tetrachlorobis (imidazol) ruthenate (III)][END_REF].

Acknowledgment

The authors are grateful to research council of the University of Isfahan for financial support of this work.


Y Le Guennec
email: leguenne@enserg.fr

G Maury
email: maury@enserg.fr

B Cabon
email: cabon@enserg.fr

Performance of interferometric systems for optical processing of microwave signals: influence of laser and microwave phase noises

Keywords: Inte nsity modulation (IM), laser-phase noise, microwave (MW) phase noise, optical telecommunications, unbalanced Mach-Zehnder (UMZ) interferometer

An unbalanced Mach-Zehnder interferometer (UMZ) is used to convert microwave (MW) frequency modulation (FM) of a laser diode into intensity modulation (IM). In coherent interference regime, it is shown that parasite FM, induced by laser-phase noise and the MW-phase noise of the modulation source , causes negligible intensity noise but significant phase noise in the photodetected intensity at the output of the UMZ. Theoretical study is realized in linear-and nonlinearinterference regimes. Results are validated experimentally.

I. Introduction

Optical processing of MW signals, like MW mixing for up/down-conversions, is very interesting for a wide range of applications including fiber-radio and radar systems [START_REF] Helkey | A dow n Conversion Optical Link with RF Gain[END_REF]. In these systems, the MW phase noise and intensity noise detected by the photo-detector at the end of the optical link may be of drastic importance [START_REF] Kitayama | Ultimate performance of Optical DSB Signal Based Millimeter-Wave Fiber Radio System: Effect of Laser Phase Noise[END_REF].

It has already been demonstrated the use of a UMZ to generate conversion of MW subcarriers of digital signals when UMZ operates respectively in non-linear interference regime [START_REF] Maury | Microwave -frequency conversion methods by optical interferometer and photodiode[END_REF], [START_REF] Le Guennec | BER Performance Comparison Between Active Mach-Zehnder Modulator and Passive Mach-Zehnder Interferometer for Conversion of Microwave Subcarriers of BPSK Signals[END_REF]. The basic principle of this system is based on the conversion of the FM of the light emitted by a laser diode into IM (FM/IM conversion). The optical phase noise of the laser source as well as the phase noise of the MW modulation signal are also converted into IM. These phase noises may have a significant influence on the phase noise and on the amplitude noise of the photo-detected intensity at the output of the UMZ. In this article, we have developed a theoretical approach, confirmed by experiments, to show the influence of the laser and MW phase noises through the FM/IM conversion with the UMZ interfer ometer. To quantify this impact, we consider a LD directly modulated by a single RF signal, followed by an UMZ working in coherent regime, like in the case of optical MW mixing. In section II, the general expression of the photo-detected intensity at the output of the UMZ is established with optical and MW phase noises. In section III, the influence of the laser phase noise is considered. In section IV, the effect of the phase noise of the MW subcarrier on the FM/IM conversion is studied. Experimental results are then discussed in section V and successfully compared to the theory.

II. General expression of the intensity at the output of the UMZ

The optical field E(t) at the output of a laser diode is directly modulated by a RF signal at frequency f RF . If we ta ke into account phase noises, the expression of E(t) can be written as:

( ) ( ) ( ) ( ) [ ] { } ( ) ( ) ( ) t i t r t t f j t t f m t m E t j t r t m t E RF RF RF RF RF RF φ φ π β φ π πν exp and )) ( 2 sin( exp )) ( 2 cos( 1 with 2 exp ) ( 0 0 = + × + + = × ⋅ ⋅ = (1)
where E 0 is the amplitude of the optical field, ν 0 is the optical carrier frequency, m RF and β RF are the amplitude and frequency modulation index at f RF respectively. The phase term φ RF is the MW random phase fluctuation leading to the broadening of the MW spectral line. The multiplicative term r(t) includes random variations of the optical field phase φ(t) which leads to the broadening of the optical spectral line of the laser.

The optical field is coupled into an integrated glass substrate UMZ interferometer as shown on Fig. 1. The delay between the two arms of the UMZ is τ. The detected instantaneous intensity at the output of the UMZ is given by :

( )( ) * ) ( ) ( . ) ( ) ( 4
1 ) ( τ τ + + + + = t E t E t E t E t I inst (2)
We consider that the amplitude modulation index is low (mRF <<1) and that FM is dominant over AM. As the optical receiver is not fast enough to follow the variations of optical phase, the detected intensity I(t) is the average of the instantaneous intensity (2) over several optical periods . Since the variables, it can be derived that:

( ) ( ) ( ) ( )         + - + + + + Φ - + - + + + + Φ + = )) ( 2 sin( )) ( ) ( 2 sin( 2 sin , )) ( 2 sin( )) ( ) ( 2 sin( 2 cos , cos 1 2 ) ( 0 0 2 0 t t f t t f t in s t t f t t f t E t I RF RF RF RF RF RF RF RF RF RF RF RF φ π β τ φ τ π β τ ν π τ φ π β τ φ τ π β τ ν π τ (5)
where ( ) ( ) ( )

t t t φ τ φ τ - + = Φ ,
is the optical phase fluctuation that relates to the random optical phase change between t and t+τ.

III. Influence of laser phase noise

The optical phase fluctuation Φ(τ) is usually a zero-mean stationary random Gaussian process [START_REF] Gallion | Quantum Phase Noise and Field Correlation in Single Frequency Semiconductor Laser Systems[END_REF].

If the frequency fluctuation ra ndom process is a white noise, it can be shown that [START_REF] Salvadé | Limitations of interferometry due to flicker noise of laser diodes[END_REF]:

( )       - = Φ opt t j τ τ τ exp , exp (7)
where τ opt is the coherent time of the source, this coherent time is linked to the spectral linewidth ∆ν opt of the optical source as:

1 opt opt ν π τ ∆ = (8)
In the case of DFB laser diodes, the optical spectral linewidth is usually smaller than 10 MHz. For our DFB laser, τ opt =32 ns. The delay τ of the longest arm of our integrated UMZ is about 0,33 ns that corresponds to a free spectral range (FSR) of the UMZ of 3 GHz. τ<<τ opt means that we work in a strong coherent regime. We can conclude from [START_REF] Aeroflex | Automated Phase Noise Measurement System Application Note #1[END_REF] that in a very good approximation:

0 ) , ( sin( 1 ) , ( cos( ≈ Φ ≈ Φ τ τ t and t (9)
hanges of optical phase between t and t+τ are negligible because of the very long coherence time of the source compared to τ.

The frequency-noise spectrum of a laser diode under free running conditions is composed of white noise and flicker noise. It has been already demonstrated that in a very coherent regime, contribution of the flicker noise in the photo-detected phase noise at the output of a UMZ is dominant over the contribution of white noise but these contributions are both very low [START_REF] Salvadé | Limitations of interferometry due to flicker noise of laser diodes[END_REF].

Equation ( 9) is then still perfectly valid.

The expression of I(t) (5) can be simplified as:

( ) [ ] )) ( 2 sin( )) ( ) ( 2 sin( 2 cos 1 2 ) ( 0 2 0 t t f t t f E t I RF RF RF RF RF RF φ π β τ φ τ π β τ ν π + - + + + + + = (10)
It can then be concluded that, in the coherent regime, the photo-detected intensity does not hold any terms induced by laser phase noise.

IV . Influence of microwave phase noise

A. Linear regime

In linear regime of interference 2 πν 0 τ=(2p+1) π /2, k ∈Z [START_REF] Maury | Microwave -frequency conversion methods by optical interferometer and photodiode[END_REF]. The detected intensity (10) can be rewritten as:

( ) [ ] )) ( 2 sin( )) ( ) ( 2 sin( sin ) 1 ( 1 2 ) ( 2 0 t t f t t f E t I RF RF RF RF RF RF p φ π β τ φ τ π β + - + + + - + = (11)
We introduce instantaneous frequency fluctuations ∆f RF (t) defined by:

t t f t RF RF ) ( 2 ) ( ∆ = π φ (12)
After a Bessel expansion of equation (11), it is shown that only odd harmonics of f RF are photodetected. We also see that the amplitude of the spectral line at frequency f RF depends on the value of fRF, meaning that the UMZ acts as a linear filter. Frequency fRF has to check a relation depending of the FSR of the UMZ to maximise the power detected at f RF [START_REF] Maury | Microwave -frequency conversion methods by optical interferometer and photodiode[END_REF]:

( ) ' , 2 1 2 Ν ∈ + = k FSR k f RF ( 14
)
The spectral line at frequency f RF can be approximated by the dominant terms of (13) expressed as:

( ) ( ) ( )       Φ       + - = 2 , cos 2 ) , ( 2 sin ) 1 ( 2 ) ( 1 0 2 0 τ τ ψ π β β t t t f J J E t I RF RF RF RF RF p f RF (15) where ( ) ( ) ( ) ( )      + + = - + = Φ t t t t t t RF RF RF RF RF RF φ τ φ τ ψ φ τ φ τ ) , ( ) , (
Ψ RF (t,τ) is the MW phase fluctuation that expresses the random MW phase change between t and t+τ.

In the case of MW synthesiser, spectral linewidth of the MW subcarrier is typically smaller than 10 kHz which corresponds to a coherence time of the MW source of τ MW >33 µs>>τ opt >>τ. This inequality means that the fluctuation of MW phase is even slower than optical phase fluctuation. In these conditions, MW phase fluctuation between t and t+τ is also negligible and Eq. ( 15) can be written as:

( ) ( ) ( ) ( ) t t f J J E t I RF RF RF RF p f RF φ π β β + - = 2 sin ) 1 ( 2 ) ( 1 0 2 0 (16)
Finally, in conditions of coherent and linear regime, after photo-detection, the detected intensity holds the term of MW phase noise from the source but no terms of parasite IM induced by MW phase noise.

B. Non-linear regime

In the non-linear regime of interference (maximum or m inimum), 2 πν 0 τ=qπ , k ∈Z. Detected intensity (10) can be expressed as:

( ) [ ] )) ( 2 sin( )) ( ) ( 2 sin( cos ) 1 ( 1 2 ) ( 2 0 t t f t t f E t I RF RF RF RF RF RF q φ π β τ φ τ π β + - + + + - + = ( 17
)
After a Bessel expansion, we note that only even harmonics are present in the MW spectrum.

Considering that changes of MW phase between t and t+τ are again negligible, the dominant term detected at harmonic 2n at frequency 2nf RF is expressed by:

( ) ( ) ( ) t n t nf J E t I RF RF RF n q nf RF φ π β 2 2 2 cos ) 1 ( 2 ) ( 2 2 2 0 2 + - = (18)
Under coherent interference and at maximum or minimum of interference, the detected intensity holds a MW phase noise term 2nφ RF depending of the source and of the the rank of the harmonic, but no term of parasite IM induced by MW phase noise appears.

V. Experimental validation

In this paragraph, we first define the theoretical expressions of the power spectral density (PSD)

that have been measured after photo-detection in linear and non-linear regimes.

A. Expression of the PSD of the MW phase noise at f RF in the linear regime

In linear regime, assuming that the fluctuation of random phase is very low, detected intensity at f RF (17) can be simplified as:

( ) ( ) t t f A t I RF RF f RF φ π + = 2 sin ) ( 0 (19)
where A 0 is the amplitude of the detected intensity at f RF depending on E 0 , β RF and p according to

(16). The PSD ) (f S RF f of the photo-detected intensity ) (t I RF f
is then expressed by [START_REF] Aeroflex | Automated Phase Noise Measurement System Application Note #1[END_REF]: as the ratio between the phase noise PSD per unit bandwidth and at a frequency f from the carrier and the power of the signal at f RF : The values are about 6 dB higher than the same PSD measured in the linear regime at f RF . This result is in agreement with theory, (23) with n=1.

( ) ( ) ( ) [ ] RF RF RF RF f f f S f f S f f f f A f S RF RF RF + + - + + + - = φ φ δ δ ) ( ) ( 4 ) ( 2 0 (20)
( ) ( ) ( ) [ ] RF RF f f f S f f S f S RF RF RF + + - = φ φ φ 2 1 log . 10 ) ( (21)
) ( ) ( ) [ ] RF n RF n RF RF n nf nf f S nf f S nf f nf f B f S RF RF RF 2 2 ) 2 ( ) 2 ( 4 ) (

VI. Conclusion

The influence of both optical and MW phase noise on the photo-detected microwave signal at the output of an interferometer has been investigated theoretically and expe rimentally. It was shown that, in coherent interference regime, no terms of parasite amplitude noise exist, neither induced by laser phase noise nor by the MW phase noise, after FM/IM conversion.

Considering the phase noise of the photo-detected microwave signal, the theoretical approach has shown also that, in the linear regime, the PSD at frequency fRF is equal to the PSD of MW phase noise of the source used to modulate the laser diode. In non-linear regime, the PSD of the phase noise at harmonic number 2n detected at the output of the UMZ, is increased by 20.log(2n).

Both conclusions are confirmed by measurements of the phase noise PSD detected at UMZ output, in linear and non-linear regimes.

  Sidebands of the signal detected at frequency f RF are induced by the random fluctuation of the MW phase. We typically define )

  Expression (21) directly shows that the PSD of the detected phase noise ) is the same as the PSD of the phase noise of the MW subcarrier that modulates the laser source.B. Expression of MW phase noise PSD at 2nf RF n∈N in the non-linear regimeIn non-linear regime, if B 2n is the amplitude of the detected intensity at the harmonic 2nf RF , we can

(

  shows that the PSD of the detected phase noise is increased by 20.log(2n) in nonlinear regime, when compared to linear regime (21).C. Experimental resultsExperimental measurements of the phase noise PSD of the MW signal detected at the output of the UMZ have been carried out to check previous theoretical results (21) (23). These measurements have been realized as shown on Fig.1using a spectrum analyzer with a very low phase noise.Interference regime is controlled fixing temperatures of the laser diode and of the glass substrate of the UMZ and adjusting the bias current of the laser diode in order to change slightly the optical wavelength. Amplitude modulation index at f RF is m RF =0,05. Results are presented on Fig.2. Single sideband PSD have been measured at a frequency offset up to 10 kHz from the carrier frequency f RF . Error bars due to the analyzer noise have been added to all measured points. Fig.2shows measured points for phase noise PSD of the photo-detected intensity at f RF , at the output of UMZ in linear regime, and for phase noise PSD measured for the MW source independently. Both measureme nts are equal as expected by theory (21). Fig.2also shows measured points for the phase noise PSD of the photo-detected intensity at 2f RF at the output of the UMZ in non-linear regime.

FiguresFig. 1

 1 Figures

Fig. 2

 2 Fig.1Experimental set-up for measurement of intensity converted phase noise using a UMZ

  the MW source at 1.44 GHz Phase noise of IM at 1,44 GHz with UMZ Phase noise of 2 nd harmonic at 2*1,44 GHz with UMZ PSD(dBc/Hz) Offset frequency from the carrier frequency (Hz)


Sk Imran Hossain

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This research was funded by the European Regional Development Fund, project DAPPEM-AV0021029.