Fanghua Wang

Wuchong Chen

Abdelkarim Abousalham

Bo Yang

Yonghua Wang

Exploring the influence of phospholipid monolayer conformation and environmental conditions on the interfacial binding of Gibberella Zeae lipase

Keywords: GZEL, Gibberella zeae lipase; DLPC, 1, 2-dilauroyl-sn-glycero-3-phosphocholine

Exploring the influence of phospholipid monolayer conformation and environmental conditions on the interfacial binding of Gibberella Zeae lipase

1,2-diarachidoyl-sn-glycero-3-phosphocholine; MIP, maximum insertion pressure; Π i , the initial surface pressure; ΔΠ, Surface pressure increase.

Highlight

1. Phospholipid head group, chain length and unsaturation influence the adsorption of GZEL into phospholipid monolayers.

2. The pH and NaCl concentration of subphase affect the binding of GZEL to phospholipid monolayers.

3. Different pH can influence the secondary structure of GZEL as investigated by circular dichroism spectroscopy.

A B S T R A C T

The involvement of different parameters on Gibberella zeae lipase (GZEL) membrane binding were characterized by using monomolecular film technology and circular dichroism spectroscopy. Among four kinds of phospholipid monolayers, 1,2-dimyristoyl-sn-glycero-3-phosphoethanolamine have the highest maximum insertion pressure (MIP) value. Comparing the GZEL adsorption to phosphatidylcholine monolayers with different acyl chains in sn-1 and sn-2 positions, the higher MIP values were found for 1,2-dilauroyl-sn-glycero-3-phosphocholine.

Significantly improvement between 1,2-dioleoyl-sn-glycero-3-phosphocholine and 1,2-distearoyl-sn-glycero-3-phosphocholine suggested that the presence of fatty acid unsaturation may affect protein adsorption by changing the chemical structure in each phospholipid. The MIP value was shown higher (48.6 mN m -1 ) at pH 5 and pH 6 (47.5±1.9 mN m -1 ) but decreased significantly (34.2 mN m -1 ) at pH 9. This may indicate that the proportion of helices in the protein decreases with the alteration of the catalytic center, thus affecting the binding of the protein to its substrate. The MIP values obviously decreased with increasing salt ion concentration, suggesting that excessive salt ion concentration may destabilize the secondary and tertiary structures of the protein, thereby affecting the characteristics of its adsorption at the interfaces.

Present studies improve our understanding on the protein-membrane interaction of this enzyme.

Keywords: Lipase, Gibberella zeae, Monolayer technology, Interfacial binding kinetics, Maximum insertion pressure

Introduction

Biologically, the binding of proteins to membranes are involved in many biological functions, such as ion conductivity, cell adhesion, membrane trafficking and cell signaling [START_REF] Cho | Membrane-protein interactions in cell signaling and membrane trafficking[END_REF][START_REF] Goñi | Non-permanent proteins in membranes: when proteins come as visitors[END_REF]. The binding process can be influenced by various factors.

Firstly, there is a large diversity of membrane glycerophospholipids at the polar headgroups and fatty acyl chains that are thought to modulate the binding properties of proteins to the membrane [START_REF] Dumas | Is the protein/lipid hydrophobic matching principle relevant to membrane organization and functions?[END_REF][START_REF] Kinnunen | Lipid dynamics and peripheral interactions of proteins with membrane surfaces[END_REF][START_REF] Boisselier | Influence of the physical state of phospholipid monolayers on protein binding[END_REF][START_REF] Calvez | Parameters modulating the maximum insertion pressure of proteins and peptides in lipid monolayers[END_REF]. Secondly, some environmental factors, such as pH condition, presence of metal ions, or detergents on the subphase were also found to modulate the binding of proteins to the membrane [START_REF] Calvez | Parameters modulating the maximum insertion pressure of proteins and peptides in lipid monolayers[END_REF][START_REF] Bénarouche | New insights into the pH-dependent interfacial adsorption of dog gastric lipase using the monolayer technique[END_REF]. Although a large amount of data is available on the structure of membranes, information on the selectivity of the interactions between proteins and membranes is still largely lacking [START_REF] Calvez | Analysis of the contribution of saturated and polyunsaturated phospholipid monolayers to the binding of proteins[END_REF]. The use of lipid monolayers at the air/water interface is an interesting and suitable model membrane system for studying protein-membrane interactions because it allows controlling many parameters, including both the conformation of membrane phospholipids and the environment in the subphase [START_REF] Dynarowicz-Latka | Modern physicochemical research on Langmuir monolayers[END_REF][START_REF] Brezesinski | Langmuir monolayers to study interactions at model membrane surfaces[END_REF]. Moreover, there is a direct thermodynamic relationship between lipid monolayers and bilayers [START_REF] Si-Shen | Interpretation of mechanochemical properties of lipid bilayer vesicles from the equation of state or pressure-area measurement of the monolayer at the air-water or oil-water Interface[END_REF][START_REF] Macdonald | Lipid monolayer states and their relationships to bilayers[END_REF], and it has thus been extensively used to study lipid-protein interactions. The maximum insertion pressure (MIP) and synergy factor 'a' of proteins in lipid monolayers has been shown to be useful in characterizing protein adsorption and lipid specificity without the need for radiolabels or other tags [START_REF] Calvez | Parameters modulating the maximum insertion pressure of proteins and peptides in lipid monolayers[END_REF][START_REF] Calvez | Analysis of the contribution of saturated and polyunsaturated phospholipid monolayers to the binding of proteins[END_REF].

Lipases (triacylglycerol hydrolases, E.C. 3.1.1.3) are carboxylester hydrolases that catalyze the hydrolysis of insoluble long-chain triglycerides, yielding free fatty acids, diglycerides and monoglycerides. Most lipases display regio-and enantio-selectivity during hydrolysis, alcoholysis, acidolysis and transesterification reactions and several biotechnological applications of lipases have been described in the detergent, cosmetic, food and pharmaceutical industries [START_REF] Hasan | Industrial applications of microbial lipases[END_REF][START_REF] Jaeger | Lipases for biotechnology[END_REF][START_REF] Rios | Biotechnological potential of lipases from Pseudomonas: sources, properties and applications[END_REF].

Lipase, like other lipolytic enzymes, is a classical interfacial acting enzyme whose catalysis is preceded by the penetration of the enzyme into the lipid /water interface [START_REF] Bénarouche | New insights into the pH-dependent interfacial adsorption of dog gastric lipase using the monolayer technique[END_REF]. Research on the interfacial binding process is a hot topic and cause much concern. Gibberella zeae Lipase (GZEL), an extracellular enzyme secreted by Fusarium oxysporum, is involved in host infection and has pathogenic effects on wheat and maize [START_REF] Voigt | A secreted lipase of Fusarium graminearum is a virulence factor required for infection of cereals[END_REF]. The lipolytic activity of GZEL can be inhibited in vitro and in planta by ebelactone B, a known general serine esterase inhibitor (Voigt et al. Plant Journal 2005, 42, 364-375). For this enzyme, the crystal structure has been resolved by Lou et al. [START_REF] Lou | Crystal structure of a secreted lipase from Gibberella zeae reveals a novel "double-lock" mechanism[END_REF]. GZEL was shown to be a globular protein with a catalytic triad consisting of the nucleophilic serine (S144) belonging to the usual consensus sequence GXSXG, Aspartic acid (D198) and Histidine (H257) [START_REF] Lou | Crystal structure of a secreted lipase from Gibberella zeae reveals a novel "double-lock" mechanism[END_REF], which is characteristic feature of all enzymes within the /β hydrolase fold family [START_REF] Ollis | The alpha/beta hydrolase fold[END_REF][START_REF] Brady | A serine protease triad forms the catalytic centre of a triacylglycerol lipase[END_REF]. As reported for many lipase structures, the GZEL catalytic site is covered by a surface loop called the lid domain located at 3 helix including I83 to F94 residues [START_REF] Lou | Crystal structure of a secreted lipase from Gibberella zeae reveals a novel "double-lock" mechanism[END_REF].

Although the crystallization assays of the GZEL in the open conformation were unsuccessful, a model of the enzyme complexed with a lipase inhibitor ebelactone B was proposed and allowed to predict a GZEL structure in open conformation [START_REF] Lou | Crystal structure of a secreted lipase from Gibberella zeae reveals a novel "double-lock" mechanism[END_REF].

According to this model, the transition from the closed form (inactive) to the open (active) form is accompanied by a movement of the lid domain exposing both the active site and a larger hydrophobic surface [START_REF] Lou | Crystal structure of a secreted lipase from Gibberella zeae reveals a novel "double-lock" mechanism[END_REF]. Furthermore, this lid motion could be probably the structural basis for "interfacial activation" of lipases [START_REF] Ferrato | A critical reevaluation of the phenomenon of interfacial activation[END_REF][START_REF] Verger | Interfacial activation of lipase: facts and artifacts[END_REF][START_REF] Schmid | Lipases: Interfacial Enzymes with Attractive Applications[END_REF][START_REF] Brzozowski | A model for interfacial activation in lipases from the structure of a fungal lipase-inhibitor complex[END_REF][START_REF] Kim | The crystal structure of a triacylglycerol lipase from Pseudomonas cepacia reveals a highly open conformation in the absence of a bound inhibitor[END_REF].

In our previous research, the recombinant His-tagged GZEL has been expressed in E. coli (cultured by erlenmeyer flask) and the soluble enzyme has been purified to homogeneity using Ni 2+ -affinity resins followed by anion-exchange chromatography on DEAE-Sepharose column [START_REF] Wang | Recombinant Lipase from Gibberella zeae Exhibits Broad Substrate Specificity: A Comparative Study on Emulsified and Monomolecular Substrate[END_REF]. We have further characterized the substrate specificity, regio-and stereoselectivity of the recombinant GZEL using the emulsified and monomolecular film technique [START_REF] Wang | Recombinant Lipase from Gibberella zeae Exhibits Broad Substrate Specificity: A Comparative Study on Emulsified and Monomolecular Substrate[END_REF]. Moreover, functions of the C-terminal segment for the specific activity and interfacial binding properties of GZEL were also characterized in detail [START_REF] Wang | Function of C-terminal peptides on enzymatic and interfacial adsorption properties of lipase from Gibberella zeae[END_REF]. However, previous research mainly focuses on the enzymatic properties of the protein itself, the parameters responsible for the modulation of the membrane binding of GZEL are still largely unknown.

This study was thus performed to determine the involvement of different parameters on GZEL membrane binding. Various monolayers of phospholipids bearing different fatty acyl chain lengths (12:0, 14:0, 16:0, 18:0, 18:1, 20:0) or head groups (choline, serine, ethanolamine, glycerol) were prepared respectively by using monolayer technology to determine the influence of phospholipid conformation on protein binding. Moreover, microenvironment conditions in the subphase of water were also considered to determine the effect of different pH value (4, 5, 6, 7, 8, 9) and ion concentration (0, 0.2, 0.4, 0.6, 0.8, 1.0 M of NaCl) on interfacial binding of GZEL to phospholipid monolayers.

Results and Discussion

In order to study the adsorption parameters of GZEL into phospholipid monolayers, we expressed a recombinant GZEL in which the catalytic Ser144 was mutated to Ala [START_REF] Van Kampen | The phospholipase activity of Staphylococcus hyicus lipase strongly depends on a single Ser to Val mutation[END_REF]. The purified mutant was analyzed by SDS-PAGE and a single protein band with an apparent molecular mass of 60 KDa was observed (Fig. S1).

Effect of different head group phospholipid on the binding of the GZEL to phospholipid monolayer

From our previous studies, we found that the final equilibrium surface pressure of GZEL was 24.2 mN m -1 and a saturation concentration for GZEL was obtained at ~150 nM [START_REF] Wang | Function of C-terminal peptides on enzymatic and interfacial adsorption properties of lipase from Gibberella zeae[END_REF]. To ensure maximum interaction between the protein and the phospholipid monolayer, a concentration of 150 nM of purified inactive GZEL (Ser144Ala mutant) was chosen in the following experiments.

MIP correspond to the maximum insertion pressure at which proteins or peptides cannot be inserted into a single phospholipid monolayer and is widely used to characterize protein adsorption and lipid selectivity [START_REF] Calvez | Parameters modulating the maximum insertion pressure of proteins and peptides in lipid monolayers[END_REF]. The higher the MIP value, the stronger the binding ability between protein and phospholipid monolayer. When the surface pressure exceeds this value, the intercalation of the protein into lipid monolayer cannot occur. As shown in Fig. 1A and Supplemental Fig. S2, MIPs of GZEL were found to be 36.9 ± 1.6 mN m -1 , 47.5 ± 1.9 mN m -1 , 45.2 ± 1.9 mN m -1 and 43.1 ± 0.9 mN m -1 in the presence of DMPC, DMPE, DMPG and DMPS, respectively.

Among the four kinds of phospholipid monolayers, DMPE have the highest MIP value and the lowest was found for DMPC. Statistical analysis indicates that there was no significant change between DMPC, DMPS and DMPG (p>0.05). However, the low MIP value of GZEL toward DMPC may indicate that this enzyme has a low affinity for DMPC than other substrates. Synergy factor 'a' is another parameter used to evaluate the binding characteristics of protein to monolayer [START_REF] Calvez | Analysis of the contribution of saturated and polyunsaturated phospholipid monolayers to the binding of proteins[END_REF][START_REF] Bussières | Binding of a truncated form of lecithin: retinol acyltransferase and its N-and C-terminal peptides to lipid monolayers[END_REF]. As it can be seen from Fig. 1B, the synergy factor 'a' was found to be > 0 for GZEL toward different monolayer substrates, which indicated that there was a positive interaction between GZEL and the phospholipid monolayer. Proteins were easy to migrate from underwater phase to interface and bind to phospholipids. When the synergy factor a approaches zero, there is no attraction or repulsion between the protein and the monolayer of the substrate [START_REF] Calvez | Parameters modulating the maximum insertion pressure of proteins and peptides in lipid monolayers[END_REF][START_REF] Calvez | Analysis of the contribution of saturated and polyunsaturated phospholipid monolayers to the binding of proteins[END_REF].

Effect of different acyl chain phospholipid on the binding of the GZEL to phospholipid monolayer

Comparing the penetration of GZEL into different kind of PCs with same acyl chain in sn-1 and sn-2 positions can help to evaluate the effect of acyl chain length in sn-1 and sn-2 positions on protein adsorption. As can be seen from Fig. 2A and Supplemental Fig. S3, the higher MIP values were found for DLPC (43.7±1.8 mN m -1 )

and DOPC (43.3±1.2 mN m -1 ) that have acyl chains with 12 and 18 carbons, respectively, in sn-1 and sn-2 positions. While statistical analysis indicates that there are significant change in the MIP value between DLPC with other groups, there is no significant difference in the MIP value between DMPC, DPPC, DSPC and DAPC.

Furthermore, the MIP value toward DOPC bearing two monounsaturated C18:1 was shown to be significantly improved (43.3±1.2 mN m -1 ) than the one (36.1±2 mN m -1 ) obtained using DSPC carrying two saturated C18:0 (Fig. 2A). These results indicate that the presence of unsaturation in the acyl chain may affect protein adsorption by changing the chemical structure in each phospholipid. It can be seen from the Fig. 2B that the synergy factor 'a' are all greater than 0, which indicates that all of the PC tested have positive interaction toward GZEL.

Effect of pH on the ability of GZEL binding to phospholipid monolayer

The reaction buffer is also an environmental factor that can affect the protein adsorption properties. Various buffers that have different pH may have influence on the protein structure, thus affecting the protein activity. From our previous studies [START_REF] Wang | Recombinant Lipase from Gibberella zeae Exhibits Broad Substrate Specificity: A Comparative Study on Emulsified and Monomolecular Substrate[END_REF], we found that when reaction buffer pH was 6, the GZEL catalytic activity was the highest and decreased in both too acid and too alkaline environments. In the present study, we used monolayer technology to further evaluate the effect of pH on protein adsorption characteristics into phospholipid monolayers. It can be found from the Figure 3A and Supplemental Fig. S4 that the maximum MIP value of GZEL (48.6±1.7 mN m -1 ) occurred at pH 5. There is no significant difference between the MIP value obtained at pH 5 and pH 6 (47.5±1.9 mN m -1 ). When pH was 4, the MIP value of the protein decreases to 41.4±1.2 mN m -1 and when pH was 9, the MIP value decreases to 34.2±0.9 mN m -1 . As it can be seen from Fig. 3B, we found that the synergy factor 'a' was all found to be > 0 in different pH, which indicated that different pH may affect the binding properties of protein to the phospholipid monolayer but there was still a positive interaction between GZEL proteins and the phospholipid monolayer.

Circular dichroism (CD) is a useful analytical tool for probing possible conformational transitions and modifications of secondary and tertiary structures of proteins [START_REF] Shen | Biochemical Properties and Potential Applications of Recombinant Leucine Aminopeptidase from Bacillus kaustophilus CCRC 11223[END_REF][START_REF] Wallace | Analyses of circular dichroism spectra of membrane proteins[END_REF]. As can be seen from the results in Table 1, the main backbone conformation of GZEL at pH of 6.0 was -helix (28.7%), β-sheet (20%), turn (17.7%) and random (35.7%). However, the content of these structures changed when GZEL dissolved in other buffer of pH value (Figure 4). These results indicated that the solution of different pH could influence the secondary structure of protein molecules so that further influence the binding ability of GZEL to phospholipid monolayer. The main backbone conformation of GZEL at pH 9.0 was -helix (24.6%), β-sheet (23%), turn (18.5%) and random (39.5%) and that could partly explain why GZEL had low enzymatic activity in higher pH values such as 9.0 [START_REF] Wang | Recombinant Lipase from Gibberella zeae Exhibits Broad Substrate Specificity: A Comparative Study on Emulsified and Monomolecular Substrate[END_REF]. This may be due to the fact that the catalytic center of lipase is usually covered by a loop, an -helix or multiple helix structures, forming the lid domain of the majority of lipases. When the pH is 9, the proportion of -helix decreases, and the catalytic center is modified, thus affecting the binding properties of protein to the phospholipid monolayer.

Effect of salt concentration on the ability of GZEL binding to phospholipid monolayer

Different concentrations of salt ions in the reaction solution also affect the adsorption characteristics of the protein. We chose NaCl that is one of the most common salt ions for research. As it can be seen from the Figure 5A and Supplemental Fig. S5, the MIP values of GZEL towards DMPE monolayers were found to be 47.5±1.9 mN m -1 and 49.2±1.4 mN m -1 , using a subphase without and with 200 mM NaCl, respectively. The MIP values of GZEL protein decreased obviously with the increase of salt ions concentration. It can be seen from the Fig. 5B that the synergy factor 'a' are all greater than 0, which indicates that there was still a positive interaction between GZEL proteins and the phospholipid monolayer even in high salt ions concentration. This effect may be attributed to the fact that excessive concentration of salt ions can contribute to desorganization of the secondary and tertiary structures of the protein, thereby affecting its adsorption characteristics. The specific mechanism should be further studied.

In conclusion, present studies provide detail information on the effect of various parameters on GZEL membrane binding and improve our understanding on the protein-membrane interaction of this lipolytic enzyme. In the further work, the effects of structural changes on protein adsorption and hydrolysis properties can be further studied.

Material and methods

Material

Phospholipids used in the present studies were all purchased from Larodan (Solna,

Sweden): 1,2-dilauroyl-sn-glycero-3-phosphocholine (DLPC) (>99%), 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC) (>99%), 1,2-dimyristoyl-sn-glycero-3-phosphoethanolamine (DMPE) (>99%), 1,2-dimyristoyl-sn-glycero-3-phosphoserine (DMPS) (>99%), 1,2-dimyristoyl-sn-glycero-3-phospho-(1-rac-glycerol) (DMPG) (>99%), 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) (>99%), 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC) (>99%), 1,2-distearoyl-sn-glycero-3-phosphocholine (DSPC) (>99%),
1,2-diarachidoyl-sn-glycero-3-phosphocholine (DAPC) (>99%) and used without further purification unless otherwise stated. Expression vectors of pFL-B62cl were from GeneCopoeia Inc. (USA). Escherichia coli SHuffle T7 Express Competent cells were purchased from New England BioLabs (Beijing, China). IPTG (isopropyl β-D-1-thiogalactopyranoside) and Ampicillin were from Sangon Biotech, Shanghai Co., Ltd. (Shanghai, China). All other reagents were of analytical grade.

Recombinant expression and purification of inactive GZEL

In the present study, the single Ser144Ala mutation of wild-type GZEL was used to determine the kinetic binding parameters of GZEL. The mutant was constructed and expressed as previously reported. [START_REF] Wang | Recombinant Lipase from Gibberella zeae Exhibits Broad Substrate Specificity: A Comparative Study on Emulsified and Monomolecular Substrate[END_REF][START_REF] Wang | Function of C-terminal peptides on enzymatic and interfacial adsorption properties of lipase from Gibberella zeae[END_REF]. Briefly, recombinant E. coli SHuffle T7 cells that harbored pFL-B62cl-GZEL-S144A plasmid were grown at 37 °C in Luria-Bertani liquid medium supplemented with 50 μg mL-1 ampicillin. The seed culture was induced at an optical density of 0.8 by IPTG to a final concentration of 0.05 mM. After 24 h of induction at 20 °C, cells were harvested, re-suspended in 100 Protein Assay Kit (Sangon Biotech, Shanghai Co.Ltd., Shanghai, China).

Interfacial adsorption measurements by using monolayer technology

GZEL protein interfacial binding measurements was performed using Microtrough from Kibron (Helsinki, Finland). The subphase (1.2 mL) buffer contained 50 mM Tris-HCl (pH 6.0) and filtered through a 0.45 μm membrane was added into the Microtrough at the start of experiment. Magnetic stirrer (diameter 0.5 cm) was used at 100 r.p.m. Protein concentration must be saturated to ensure the measurement of the MIP under the maximum interaction between the protein and the phospholipid monolayer [START_REF] Lhor | Comparison between the behavior of different hydrophobic peptides allowing membrane anchoring of protein[END_REF][START_REF] Momsen | The adsorption to and hydrolysis of 1, 3-didecanoyl glycerol monolayers by pancreatic lipase, Effects of substrate packing density[END_REF]. A few microliters of the phospholipid chloroformic solution (1.0 mg mL -1 ) were spread at the surface until the initial surface pressure (Π i )

was reached and then 50 μL of the enzyme solution (0.3 mg mL -1 ) was injected underneath the phospholipid monolayer. The GZEL adsorption onto phospholipid monolayers was observed until equilibrium surface pressure (Π e ) was reached. The surface pressure increase (ΔΠ) is the difference between Π e and Π i [START_REF] Momsen | Interfacial structure and lipase action. Characterization of taurodeoxycholate-didecanoylglycerol monolayers by physical and kinetic methods[END_REF][START_REF] Barque | Enzyme-substrate interaction in lipid monolayers. II. Binding and activity of lipase in relation to enzyme and substrate concentration and to other factors[END_REF]. When ΔΠ is graphed as function of Π i the linear extrapolation of the plot to the x-axis allows the determination of the MIP, which corresponds to the value of the surface pressure above which no increase occurs upon enzyme injection. The synergy factor 'a' could be deduced by adding 1 to the slope of ΔΠ = f(Π i ) [START_REF] Momsen | Interfacial structure and lipase action. Characterization of taurodeoxycholate-didecanoylglycerol monolayers by physical and kinetic methods[END_REF][START_REF] Barque | Enzyme-substrate interaction in lipid monolayers. II. Binding and activity of lipase in relation to enzyme and substrate concentration and to other factors[END_REF]. The values of MIP, synergy factor 'a' and each value's uncertainty (calculated with a confidence interval of 95% from the covariance of the experimental data on the linear regression) were all determined by using the freely accessible web tool (http://www.crchudequebec.ulaval.ca/BindingParametersCalculator/).

Effect of different head group phospholipid on the binding of the GZEL to phospholipid monolayer

Four kinds of phospholipids with the myristoyl in both sn-1 and sn-2 positions (DMPS, DMPE, DMPC, DMPG) to determine the effect of the head group in phosphatidyl-moiety on the insertion of proteins into phospholipid monolayers.

Various phospholipid solubilized in chloroform (0.02 mg mL -1 ) were slowly spread at the surface of a buffer (50 mM Tris-HCl, pH 6.0) poured in one of the multi-well of the multi-well plate until the desired surface pressure was reached.

Effect of different acyl chain length on the binding of the GZEL to phospholipid monolayer

Six kinds of PC with different acyl chain in both sn-1 and sn-2 positions were chosen for present studies (DLPC, DMPC, DPPC, DSPC, DOPC, DAPC) to determine the effect of the acyl chain in phosphatidyl-moiety on the insertion of proteins into monolayers.

Effect of pH of subphase buffer on the ability of GZEL binding to phospholipid monolayer

The effect of subphase pH value for GZEL binding to phospholipid monolayer was determined by changing the subphase buffer with pH ranging from 4.0 to 9.0 which was added to multi-well plate. The buffers used in this study including 50 mM citric acid-sodium citrate buffer (pH 4.0 and 5.0), 50 mM Bis-Tris-HCl (pH 6.0 and 7.0), 50 mM Tris-HCl (pH 8.0), 50 mM Gly-NaOH (pH 9.0).

Effect of salt concentration of the subphase buffer on the ability of GZEL binding to phospholipid monolayer

Effect of salt concentration of the subphase buffer was determined by adding different amounts of NaCl, one of the most common salt, ranging from 0 to 1.0 M L -1 .

Circular Dichroism Spectroscopy

Circular dichroism measurements were carried out with a JASCO J-815 spectropolarimeter (Jasco,Tokyo, Japan) according to the method of Wang et al. ( 2012) [START_REF] Wang | Biochemical Properties of Recombinant Leucine Aminopeptidase II from Bacillus[END_REF]. The specific parameters are set as follows: scanning wavelength 180-260 nm, 0.1 mm colorimetric, the scanning time is 0.2 nm and the scanning speed is 50 nm/min. Protein samples (0.27 mg/ml) dissolved in buffers at different pH values (4.0, 5.0, 6.0, 9.0) were examined. An appropriate buffer solution run under the same conditions was taken as a blank and subtracted from the sample spectra. Thermal denaturation experiments were performed by monitoring the ellipticity at 222 nm from 25°C to 75°C and measured every 3°C. Each simple was scanned for 3 times and each spectrum was the average of 3 scans.

ACCEPTED MANUSCRIPT

Fanghua

  Wang, Wuchong Chen, Abdelkarim Abousalham, Bo Yang, Yonghua Wang To cite this version: Fanghua Wang, Wuchong Chen, Abdelkarim Abousalham, Bo Yang, Yonghua Wang. Exploring the influence of phospholipid monolayer conformation and environmental conditions on the interfacial binding of Gibberella Zeae lipase. International Journal of Biological Macromolecules, 2019, 132, pp.1051-1056. 10.1016/j.ijbiomac.2019.03.169. hal-02132750

  mL of 50 mM Tris-HCl (pH 7.0) and disrupted by sonication. To further purify rGZEL, the supernatant was applied to a Ni2+-NTA-agarose column. The target enzyme was eluted with 50 mM Tris-HCl buffer (pH 7.0) containing 200 mM imidazole. Enzyme-containing eluent was further filtered through a Sephadex G-25 column (GE Healthcare, Buckinghamshire, UK) to remove the imidazole. Samples were then loaded into a DEAE Sepharose fast flow column (GE Healthcare, Buckinghamshire, UK) and washed with 50 mM Tris-HCl (pH7.0) that contain 200 mM NaCl. The fractions containing purified enzymes were collected and analyzed by 12% SDS-PAGE. Protein concentrations were determined by the Modified Bradford

Figure 1 .

 1 Figure 1. MIP (A) and Synergy factor 'a' (B) of GZEL (9.08 µg mL -1 , final

Figure 2 .

 2 Figure 2. MIP (A) and Synergy factor 'a' (B) of GZEL (9.08 µg mL -1 , final

Figure 3 .

 3 Figure 3. MIP (A) and Synergy factor 'a' (B) of GZEL (9.08 µg mL -1 , final

Figure 4 .

 4 Figure 4. Circular dichroism of GZEL under various pH buffers. GZEL (0.27 mg

Figure 5 .

 5 Figure 5. Maximum insertion pressure (MIP) (A) and Synergy factor 'a' (B) of GZEL

Figure 4

 4 Figure 4

Figure 5

 5 Figure 5

Table 1 .

 1 Fractions of different secondary structures of GZEL that dissolved in various

	pH buffers
		4.0 (%)	5.0 (%)	6.0 (%)	9.0 (%)
	Helix	31.1	32.5	28.7	24.6
	Sheet	18.4	17.7	20.0	23.0
	Turn	17.2	17.0	17.7	18.5
	Random	33.6	32.7	35.7	39.5

Acknowledgments

This work was made possible with funding provided by the National Key R&D Program of China (2018YFC0311100), National Natural Science Foundation of China (31671791), National Science Fund for Distinguished Young Scholars (31725022), Science and Technology Planning project of Guangdong province (2016B090920082, 2017A050503001), Talent project of scientific and technological innovation in

Guangdong Province (2015TX01N207), Pearl River S&T Nova Program of Guangzhou, China (201610010074).

Conflict of interest

The authors declare that they have no conflict of interest.

stearothermophilus and Potential Applications in the Hydrolysis of Chinese Anchovy (Engraulis japonicus) Proteins, J Agric Food Chem. 60 (2012) 165-172.


Hoang Son Pham

Gwendal Virlet

Dominique Lavenier

Alexandre Termier

Statistically Significant Discriminative Patterns Searching

Keywords: Discriminative patterns, Discriminative Measures, Statistical Significance, Anti-Monotonicity

In this paper, we propose a novel algorithm, named SSDPS, to discover patterns in two-class datasets. The SSDPS algorithm owes its efficiency to an original enumeration strategy of the patterns, which allows to exploit some degrees of anti-monotonicity on the measures of discriminance and statistical significance. Experimental results demonstrate that the performance of the SSDPS algorithm is better than others. In addition, the number of generated patterns is much less than the number of the other algorithms. Experiment on real data also shows that SSDPS efficiently detects multiple SNPs combinations in genetic data.

Introduction

Recently, the use of discriminative pattern mining (also known under other terms such as emerging pattern mining [START_REF] Dong | Efficient mining of emerging patterns: Discovering trends and differences[END_REF], contrast set mining [START_REF] Bay | Detecting group differences: Mining contrast sets[END_REF]) has been investigated to tackle various applications such as bioinformatics [START_REF] Cheng | Direct discriminative pattern mining for effective classification[END_REF], data classification [START_REF] Garca-Borroto | A survey of emerging patterns for supervised classification[END_REF]. In this paper, we propose a novel algorithm, named SSDPS, that discovers discriminative patterns in two-class datasets. This algorithm aims at searching patterns satisfying both discriminative scores and confidence intervals thresholds. These patterns are defined as statistically significant discriminative patterns. The SSDPS algorithm is based on an enumeration strategy in which discriminative measures and confidence intervals can be used as antimonotonicity properties. These properties allow the search space to be pruned efficiently. All patterns are directly tested for discriminative scores and confidence intervals thresholds in the mining process. Only patterns satisfying both of thresholds are considered as the target output. According to our knowledge, there doesn't exist any algorithms that combine discriminative measures and statistical significance as anti-monotonicity to evaluate and prune the discriminative patterns.

The SSDPS algorithm has been used to conduct various experiments on both synthetic and real genomic data. As a result, the SSDPS algorithm effectively deploys the anti-monotonic properties to prune the search space. In comparison with other well-known algorithms such as SFP-GROWTH [START_REF] Ma | An almost exhaustive search-based sequential permutation method for detecting epistasis in disease association studies[END_REF] or CIMCP [START_REF] Guns | Itemset mining: A constraint programming perspective[END_REF], the SSDPS obtains a better performance. In addition the proportion of generated patterns is much smaller than the amount of patterns output by these algorithms.

The rest of this paper is organized as follows: Section 2 precisely defines the concept of statistically significant discriminative pattern, and Section 3 presents the enumeration strategy used by the SSDPS algorithm. In Section 4, the design of the SSDPS algorithm is described. Section 5 is dedicated to experiments and results. Section 6 concludes the paper.

Problem Definition

The purpose of discriminative pattern mining algorithms is to find groups of items satisfying some thresholds. The formal presentation of this problem is given in the following:

Let I be a set of m items I = {i 1 , ..., i m } and S 1 , S 2 be two labels. A transaction over I is a pair t i = {(x i , y i )}, where x i ⊆ I, y i ∈ {S 1 , S 2 }. Each transaction t i is identified by an integer i, denoted tid (transaction identifier). A set of transactions T = {t 1 , ..., t n } over I can be termed as a transaction dataset D over I. T can be partitioned along labels S 1 and S 2 into

D 1 = {t i | t i = (x i , S 1 ) ∈ T } and D 2 = {t i | t i = (x i , S 2 ) ∈ T }.
The associated tids are denoted D 1 .tids and D 2 .tids.

For example, Table 1 presents a dataset including 9 transactions (identified by 1..9) which are described by 10 items (denoted by a..j). The dataset is partitioned into two classes (class label 1 or 0). A set p ⊆ I is called an itemset (or pattern) and a set q ⊆ {1..n} is called a tidset. For convenience we write a tidset {1, 2, 3} as 123, and an itemset {a, b, c} as abc. The number of transactions in D i containing p is denoted by |D i (p)|. The relational support of p in class D i (denoted sup(p, D i )), and negative support of p in D i (denoted sup(p, D i )), are defined as follows:

sup(p, D i ) = |D i (p)| |D i | ; sup(p, D i ) = 1 -sup(p, D i )
To evaluate the discriminative score of pattern p in a two-class dataset D, different measures are defined over the relational supports of p. The most popular discriminative measures are support difference, grown rate support and odds ratio support which are calculated by formulas 1, 2, 3 respectively.

SD(p, D) = sup(p, D 1 ) -sup(p, D 2 )
(1)

GR(p, D) = sup(p, D 1 ) sup(p, D 2 ) (2) ORS(p, D) = sup(p, D 1 )/sup(p, D 1 ) sup(p, D 2 )/sup(p, D 2 ) (3)
A pattern p is discriminative if its score is not less than a given threshold α. For example, let α = 2 be the threshold of growth rate support. Pattern abc is discriminative since GR(abc, D) = 2.4. Definition 1. (Discriminative pattern). Let α be a discriminative threshold, scr(p, D) be the discriminative score of pattern p in D. The pattern p is discriminative if scr(p, D) ≥ α.

In addition to the discriminative score, to evaluate the statistical significance of a discriminative pattern we need to consider the confidence intervals (CI). Confidence intervals are the result of a statistical measure. They provide information about a range of values (lower confidence interval (LCI) to upper confidence interval (U CI)) in which the true value lies with a certain degree of probability. CI is able to assess the statistical significance of a result [START_REF] Morris | Statistics in medicine: Calculating confidence intervals for relative risks (odds ratios) and standardised ratios and rates[END_REF]. A confidence level of 95% is usually selected. It means that the CI covers the true value in 95 out of 100 studies.

Let

a = |D 1 (p)|, b = |D 1 | -|D 1 (p)|, c = |D 2 (p)|, d = |D 2 | -|D 2 (p)
|, the 95% LCI and U CI of GR are estimated as formulas 4 and 5 repectively.

LCI GR = e (ln(GR)-1.96 √ 1 a -1 a+b + 1 c -1 c+d ) (4)
U CI GR = e (ln(GR)+1.96

√ 1 a -1 a+b + 1 c -1 c+d ) (5)
Similarly, the 95% LCI and U CI of OR are estimated as formulas 6 and 7 repectively.

LCI ORS = e ln(ORS)-1.96 √ 1 a + 1 b + 1 c + 1 d (6)
U CI ORS = e ln(ORS)+1.96

√ 1 a + 1 b + 1 c + 1 d (7)
For example, consider the pattern abc in the previous example, the 95%CI of GR are LCI GR = 0.37, U CI GR = 16.60. Thus the GR score of abc is statistically significant because this score lies between LCI and U CI values. Problem statement: Given a two-class dataset D, a discriminance score scr and two thresholds α and β, the problem is to discover the complete set of patterns P that are statically significant discriminative for dataset D, discriminative measure scr, discriminative threshold α and lower confidence interval threshold β.

Enumeration Strategy

The main practical contribution of this paper is SSDPS, an efficient algorithm for mining statistically significant discriminative patterns. This algorithm will be presented in the next section (Section 4).

SSDPS owes its efficiency to an original enumeration strategy of the patterns, which allows to exploit some degree of anti-monotonicity on the measures of discriminance and statistical significance. In pattern mining enumeration strategies, anti-monotonicity properties is an important component. When enumerating frequent itemsets, one can notice that if an itemset p is unfrequent (sup(p, D) < min sup), then no super-itemsets p ⊃ p can be frequent (necessarily sup(p , D) < sup(p, D) < min sup). This allows to stop any further enumeration when an unfrequent itemset p is found, allowing a massive reduction in the search space [START_REF] Agrawal | Mining association rules between sets of items in large databases[END_REF]. As far as we know, no such anti-monotonicity could be defined on measures of discriminance or statistical significance.

The enumeration strategy proposed in SSDPS also builds an enumeration tree. However, it is based on the tidsets and not the itemsets. Each node of the enumeration tree is a tidset (with the empty tidset at the root). For example, consider the node represented by 12 : 8 in Figure 1: this node corresponds to the tidset 128 in which 12 ⊂ D 1 .tids, and 8 ⊂ D 2 .tids.

Before presenting details of the enumeration strategy we first explain how to recover the itemsets from the tidsets. This is a well known problem: itemsets and tidsets are in facts dual notions, and they can be linked by two functions that form a Galois connection [START_REF] Pasquier | Discovering frequent closed itemsets for association rules[END_REF]. The main difference in our definition is that the main dataset can be divided into two parts (D = D 1 ∪ D 2 ), and we want to be able to apply functions of the Galois connection either in the complete dataset D or in any of its parts D 1 or D 2 .

Definition 3 (Galois connection). For a dataset

D = D 1 ∪ D 2 :
-For any tidset q ⊆ {1..n} and any itemset p ⊆ I, we define:

f (q, D) = {i ∈ I | ∀k ∈ q i ∈ t k }; g(p, D) = {k ∈ {1..n} | p ⊆ t k }
-For any tidset q 1 ⊆ D 1 .tids and any itemset p ⊆ I, we define:

f 1 (q 1 , D 1 ) = {i ∈ I | ∀k ∈ q 1 i ∈ t k }; g 1 (p, D 1 ) = {k ∈ D 1 | p ⊆ t k }
-For any tidset q 2 ⊆ D 2 .tids and any itemset p ⊆ I, we define:

f 2 (q 2 , D 2 ) = {i ∈ I | ∀k ∈ q 2 i ∈ t k }; g 2 (p, D 2 ) = {k ∈ D 2 | p ⊆ t k }
Note that this definition marginally differs from the standard definition presented in [START_REF] Pasquier | Discovering frequent closed itemsets for association rules[END_REF]: here for convenience we operate on the set of tids {1..n}, whereas the standard definition operates on the set of transaction {t 1 , ..., t n }.

In Figure 1, under each tidset q, its associated itemset f (q, D) is displayed. For example for node 12:8 , the itemset f (128, D) = bci is displayed. One can verify in Table 1 that bci is the only itemset common to the transactions t 1 , t 2 and t 8 . A closure operator can be defined over the use of the Galois connection.

Definition 4 (Closure operator). For a dataset D and any tidset q ⊆ {1..n}, the closure operator is defined as: c(q, D) = g • f (q, D). The output of c(q, D) is the tidset of the closed itemset having the smallest tidset containing q.

We can similarly define

c 1 (q 1 , D 1 ) = g 1 • f 1 (q 1 , D 1 ) for q 1 ⊆ D 1 .tids and c 2 (q 2 , D 2 ) = g 2 • f 2 (q 2 , D 2 ) for q 2 ⊆ D 2 .tids.
The basics of the enumeration have been given: the enumeration proceeds by augmenting tidsets (starting from the empty tidset), and for each tidset function f of the Galois connection gives the associated itemset. The specificity of our enumeration strategy is to be designed around statistically significant discriminative patterns. This appears first in our computation of closure: we divide the computation of closure in the two sub-datasets D 1 and D 2 . This intermediary step allows some early pruning. Second, most measures of discriminance require the pattern to have a non-zero support in D 2 (GR and ORS). The same condition apply for measures of statistical significance: in both cases we need to defer measures of interest of patterns until it has some tids in D 2 . Our enumeration strategy thus operates in two steps:

1. From the empty set, it enumerates closed tidsets containing only elements of D 1 (case group). 2. For each of those tidset containing only tids of D 1 , augmentations using only tids of D 2 are generated and their closure is computed. Any subsequent augmentation of such nodes will only be allowed to be augmented by tids of D 2 .

More formally, let q ⊆ {1..n} be a tidset, with q = q + ∪ q -, where q + ⊆ D 1 .tids and q -⊆ D 2 .tids. Then the possible augmentations of q are: -(Rule 1) if q -= ∅: q can either:

• (Rule 1a) be augmented with k ∈ D 1 .tids such that k < min(q + ) • (Rule 1b) be augmented with k ∈ D 2 .tids -(Rule 2) if q -= ∅: q can only be augmented with tid k ∈ D 2 .tids such that k < min(q -) This enumeration strategy allows to benefit from an anti-monotonicity property on the measures of statistical significance and discriminance.

Theorem 1 (Anti-monotonicity). Let q 1 and q 2 be two tidsets such as: q + 1 = q + 2 and q - 1 ⊂ q - 2 (we have q + 1 = ∅ and q - 2 = ∅). Let p 1 = f (q 1 , D) and p 2 = f (q 2 , D). Then:

1. scr(p 1 , D) > scr(p 2 , D) with scr a discriminance measure in {SD, GR, ORS}. 2. lci(p 1 , D) > lci(p 2 , D) with lci a lower confidence interval in {LCI ORS , LCI GR }.

Please refer to the full paper at https://arxiv.org/abs/1906.01581 for the detailed demonstration of this part.

This theorem provides pruning by anti-monotonicity in our enumeration strategy: for a node having a tidset with tids both from D 1 .tids and D 2 .tids, if the discriminance or statistical significance measures are below a given threshold, then necessarily its augmentations will also be under the threshold. Hence this part of the enumeration tree can be pruned. For example, node 2:8 has associated itemset bcei, and ORS(bcei, D) = 3/4. Suppose the ORS threshold α = 2 this node can be pruned and its augmentations need not be computed. This allows to significantly reduce the search space.

SSDPS: Algorithm Design

This section presents the SSDPS algorithm which exploits the enumeration strategy presented in the Section 3.

As mentioned in the previous section, our algorithm is based on an enumeration of the tidsets. It discovers statistically significant discriminative closed patterns. The main procedure for enumerating tidsets is given in Algorithm 1. This procedure calls the recursive procedure positiveExpand (Algorithm 2) to find closed frequent itemsets in the positive class. Computing discriminative patterns relies on the recursive procedure negativeExpand (Algorithm 3).

Delving more into details, positiveExpand (Algorithm 2) is based on the principles of the LCM algorithm [START_REF] Uno | Lcm ver. 2: Efficient mining algorithms for frequent/closed/maximal itemsets[END_REF], the state of the art for mining closed frequent itemsets. positiveExpand takes as input the tidset t of a pattern that is closed in D 1 and a tid e ∈ D 1 .tids that can be used to augment t. This augmentation is performed on line 1, and the pattern p associated to the augmented tidset t + = t ∪ {e} is computed in line 2. If p = ∅, there are no items common to all transactions of t + so the enumeration can stop (test of line 3). Else, we can continue the enumeration by applying Rule 1 of enumeration presented in Section 3. Lines 4 to 9 apply the LCM principles of enumerating closed itemsets without redundancies (the interested reader in referred to [START_REF] Leroy | Toppi: An efficient algorithm for item-centric mining[END_REF] Section 3.2 for a recent description of these principles). At this step of the enumeration, the closure is computed in D 1 (line 4). The test of line 5 verifies if the closure actually extends the tidset, requiring a further verification in line 6, and the construction of the new extended tidset (line 7).

Lines 8 to 10 implement Rule 1a of enumeration, allowing to grow the positive part of the tidset. Lines 11 to 12 implement Rule 1b of enumeration, stopping the growth of the positive part and starting to grow the negative part of the tidset. The same logic is followed in lines 14 to 18, in the case where the tidset is not extended by the closure (test of line 5 is false).

Algorithm 2: positiveExpand Function

1 t + ← t ∪ {e} 2 p ← f (t + , D) 3 if p is not empty then 4 t ext + ← c1(t + , D1) 5 if t ext + = t + then 6 if max(t ext + ) < e then 7 q ← t + ∪ t ext + 8
for each e + in D1.tids \ q do 9 if e + < e then 10 positiveExpand(q, e + , D, α, β)

11
for each e -in D2.tids do The final expansion of the tidset is handled by negativeExpand (Algorithm 3), that can only perform augmentations with negative tidsets. It is very similar to positiveExpand, with several key differences. The first obvious one is that the closure is this time computed in D 2 (line 4). The second one is that only Rule 2 of enumeration can be applied (lines 13 and 20). The third and most important difference is that because we have tidsets with positive and negative tids, we can compute discriminance as well as statistical significance measures. Hence, Theorem 1 can be applied to benefit from pruning by anti-monotonicity. This is done in line 3.

Algorithm 3: negativeExpand Function

1 t -← t ∪ {e} ; p ← f (t -, D) 2 if p is not empty then 3 if check signif icance(p, D, α, β) is true then 4 t ext -← c2(t -, D2) 5 if t ext -= t -then 6
if max(t ext -) < e then 7 q ← t -∪ t ext -; q ext ← c(q, D); p ← f (q, D)

Experimental Results

This section presents various experiments to evaluate the performance of the SSDPS algorithm. In addition, we apply the SSDPS to discover multiple SNPs combinations in a real genomic dataset. The details of the result was presented in the full paper which was published at https://arxiv.org/abs/1906.01581. All experiments have been conducted on a laptop with Core i7-4600U CPU @ 2.10GHz, 16GB memory and Linux operating system. A synthetic two-class data was created to evaluate the pruning strategy as well as compare SSDPS with other algorithms. This dataset includes 100 transactions (50 transactions for each class). Each transaction contains 262 items which are randomly set by value 0 or 1. The density of data is set up to 33%.

Pruning Efficiency Evaluation

To evaluate the pruning efficiency of the SSDPS algorithm, we executed 2 setups on the synthetic dataset.

-Setup 1: use OR as discriminative measure; the discriminative threshold α = 2. -Setup 2: use OR as discriminative measure and LCI of OR as statistically significant testing; the discriminative threshold α = 2, and LCI threshold β = 2.

As the result, the running time and the number of output patterns significantly reduce when applying LCI ORS . In particular, with the setup 1, the SS-DPS algorithm generates 179,334 patterns in 38.69 seconds while the setup 2 returns 18,273 patterns in 9.10 seconds. This result shows that a large amount of patterns is removed by using statistically significant testing.

Comparison with Existing Algorithms

We compare the performance of the SSDPS algorithm with two well-known algorithms: CIMCP [START_REF] Guns | Itemset mining: A constraint programming perspective[END_REF] and SFP-Growth [START_REF] Ma | An almost exhaustive search-based sequential permutation method for detecting epistasis in disease association studies[END_REF]. Note that these algorithms deploy discriminative measures which are different from the measures of SSDPS . In particular, CIMCP uses one of measures such as chi-square, information-gain and gini-index as a constraint to evaluate discriminative patterns while SFP-GROWTH applies -log(p value). For this reason, the number of output patterns and the running times of these algorithms should be different. It is hence not fair to directly compare the performance of SSDPS with these algorithms. However, to have an initial comparison of the performance as well as the quantity of discovered patterns, we select these algorithms.

We ran three algorithms on the same synthetic data. The used parameters and results are given in Table 2. As the result, the SSDPS algorithm finds 49,807 patterns in 73.69 seconds; CIMCP discovers 5,403,688 patterns in 143 seconds. The SFP-GROWTH runs out of storage memory after 172 seconds. Hence the number of patterns isn't reported in this case.

In comparison with these algorithms the SSDPS gives a comparable performance, while the number of output patterns is much smaller. The reason is that the output patterns of SSDPS are tested for statistical significance by CI while other algorithms use only the discriminative measure. However, this amount of patterns is also larger for real biological analysis. Thus, searching for a further reduced number of significant patterns should be taken into account.

Conclusion and Perspectives

In this paper we propose a novel algorithm, called SSDPS, that efficiently discover statistically significant discriminative patterns from a two-class dataset. The algorithm directly uses discriminative measures and confidence intervals as anti-monotonic properties to efficiently prune the search space. Experimental results show that the performance of the SSDPS algorithm is better than other discriminative pattern mining algorithms. However, the number of patterns generated by SSDPS is still large for manual analysis. To reduce the amount of patterns our first perspective is to investigate a heuristic approach. Another perspective is to apply statistical techniques such as minimum description length or multiple hypothesis testing in order to further remove uninteresting patterns.

Definition 2 .

 2 (Statistically significant discriminative pattern). Given a discriminance score scr ∈ {GR, ORS}, a discriminative threshold α and a lower confidence interval threshold β, the pattern p is statistically significant discriminative in D if scr(p, D) ≥ α and lci scr (p, D) > β.

Fig. 1 :

 1 Fig. 1: Tidset-itemset search tree

Algorithm 1 :

 1 SSDPS algorithm input : D, α, β output: a set of statistically significant discriminative patterns 1 t = ∅ 2 for each transaction id e in positive class do 3 positiveExpand(t, e, D, α, β)

12 negativeExpand

 12 (q, e -, D, α, β) 13 else 14 for each e + in D1.tids do 15 if e + < min(t + ) then 16 positiveExpand(t + , e + , D, α, β) 17 for each e -in D2.tids do 18 negativeExpand(t + , e -, D, α, β)

Table 1 :

 1 Two-class data example

	Tids		Items			Class
	1 a b c		f	i j	1
	2 a b c	e	g	i		1
	3 a b c		f	h	j	1
	4	b	d e	g	i j	1
	5		d	f g h i j	1
	6	b c	e	g h	j	0
	7 a b c		f g h		0
	8	b c d e		h i		0
	9 a		d e	g h	j	0

Table 2 :

 2 Used parameters and results of 3 algorithms

	Algorithms	Measure	Threshold #Patterns	Time(seconds)
	SSDPS	OR, LCI ORS α = 2, β = 2	49,807	73.69
	CIMCP	Chi-square	2	5,403,688	143
	SFP-GROWTH -log(p value)	3	* > 172 (out of memory)


P Berthod

C Vebert

L Aranda

Effect of dendritic orientation of the high temperature oxidation kinetic of tantalum-containing nickel-base alloys

Keywords: High Temperature Oxidation, Cast Ni-base alloys, Dendritic Orientation

The aim of this work is the study of the possible effect of surface dendritic orientation on the high-temperature oxidation behavior of two chromia-forming Ni-base alloys with two tantalum contents (3 and 6% wt ). Samples were prepared by special cutting orientation with regard to the external surface. Thermogravimetry tests were run at 1000, 1100 and 1200°C and parabolic oxidation constants were considered. The mathematical process of the raw data was performed taking into account the effect of the transient oxidation. When the sample surface is mainly parallel to the dendritic network, the oxidation parabolic constant is higher than for a surface perpendicular to dendrites. The situation is contrary for the transient oxidation linear constant.

Introduction

When obtained by a classical foundry way, the microstructure of metallic alloys depends on their chemical composition but also on the solidification conditions. For example the thermal gradient existing during the solidification governs the general direction of crystals growth, then dendrites and grain boundaries orientations. The latter are to be considered as special diffusion paths for species involved in the oxidation mechanisms [START_REF] Kofstad | High Temperature Corrosion[END_REF]. Then it can be thought that the kinetics of high-temperature oxidation of superalloys could locally depend on dendrites orientation, as it was previously seen for different complex Co-base and Ni-base cast superalloys [START_REF] Berthod | [END_REF]. This possible effect was studied here at different high temperatures in the specific case of two chromia-forming Ni-base cast alloys which also contain tantalum.

Effect of the thermal gradient on the dendrite orientation

A microstructural evolution usually exists in alloys obtained by a classical foundry way, from the external surface towards the last point to solidify [START_REF] Kurz | Fundamentals of solidification[END_REF][START_REF] Lesoult | [END_REF]5]. Near the mold wall (Fig. 1), among the first numerous very small crystals that appeared here, only a little number of them pursue their growth in the next zone. They are the ones which are favorably oriented with regard to the local thermal gradient, which is generally perpendicular to the mold wall. Thus, after a skin zone containing very small and randomly oriented grains, a columnar zone develops with an oriented microstructure. Here columns or dendrites (e.g. in the case of Ni-base alloys) are mainly perpendicular to the mold wall. The third zone, where solidification is finished, contains coarser dendrites that are randomly oriented again, because of the absence of any very marked gradient. After machining, a cast piece can present locally external surfaces with different grain sizes and also different orientations with regard to the subsurface dendritic network. Even if dendrites are not all either parallel or perpendicular to such surfaces, as it could be encountered for directionally solidified (DS) alloys, a global effect on the local oxidation kinetic may exist. The latter will be better studied with specially machined equiaxed alloys than with DS alloys.

Materials and methods

Synthesis of the alloys

Two Ni-base alloys were elaborated using a high frequency induction furnace under argon gas, and solidified in a water-cooled copper crucible (cone-shaped ingots of about 100g and height = maximal diameter = 30mm). They were synthesized from pure elements (more than 99.9%): Ni (supplier: Eramet), Cr (supplier: Alfa Aesar), Ta (supplier: Aerometal) and C (graphite). The obtained chemical compositions are given in Table I.

High temperature oxidation tests and mathematical processing

Samples were parallelepipeds of approximately 10mm x 10mm x 2mm. Cutting orientation was chosen in order to obtain square faces that are either parallel or perpendicular to dendrites (Fig. 2). For each sample, the total mass gain kinetic is the sum of two contributions which can be uncoupled. The oxidation rates of the parallel surface S // and of the perpendicular surface S ⊥ exist together in the global mass gain (Eq. 1). Then, the two parabolic constants Kp // and Kp ⊥ , that describe the two local oxidation rates, appear as the two unknown values of a linear equation (Eq. 2), in which they are related to the measured global constant Kp. For a same alloy and a same temperature, solving the two linear equations (Eq. 2) written for the two types of samples gives both Kp // and Kp ⊥ . (2) Oxidation runs were performed using a Setaram TGA92 thermobalance. Alloys were exposed at 1000°C, 1100°C and 1200°C for 100 hours under a flow of synthetic air (80%N 2 -20%O 2 ) of about 1,5l/min. The heating rate, until reaching the targeted temperature, and the cooling rate, for the return to room temperature, were 20°C/min and 10°C/min respectively. The recording of the mass gain was made every 74 seconds.

) t ( S m ∆ = ⊥ ⊥ + ∆ + ∆ S S ) t ( m ) t ( m
All the obtained mass gain curves showed an initial linear part (of the (Eq. 3) type) and a following parabolic part (of the (Eq. 5) type) by which it was possible to determine a parabolic Kp constant. The oxide thickness obtained before the beginning of the parabolic oxidation must be taken into account for the determination of Kp. Then, to process the obtained files, we applied the following procedure.

S m

∆ = t . K l (3) l K = T . R Q l e . K o - (4) S m ∆ = t Kp . 2 (5)
Oxidation during heating and linear isothermal oxidation each induced a first mass gain before parabolic oxidation took place. The initial mass gain is the sum (Eq. 6) of a heating part (first term) and a linear isothermal part (second term):

S m o ∆ = dt . e . K test o T K 273 ) t ( T . R Q l ∫ - + L S m       ∆ ≈ ( ) t . e . K N 1 n t . n . R K 273 . R Q l H o ∆           ∑ = ∆ + - + L S m       ∆ (6)
where:

-K lo and Q, the Arrhenius constants of the linear constant K l (Eq. 4), were deduced from the K l values obtained for 1273, 1373 and 1473K, -R H is the heating rate, -∆t the recording time increment (74s), -N the number of recording paths during the heating

N = t . R K 273 T H test ∆ - ), - and L S m       ∆
is the mass gain during the isothermal linear oxidation.

When the external oxide scale becomes continuous, the Wagner's differential equation describes the parabolic mass gain kinetic ∆m P /S (Eq. 7). Its integration leads to (Eq. 8).

Knowing the values of ∆m o /S and of t o (instant at which the parabolic oxidation took place) the value of Kp can be obtained without any error caused by the mass gain obtained before.

For 1100 and 1200°C, the volatilization of the external Cr 2 O 3 scale (partly oxidized into gaseous CrO 3 ) was taken into account by adding the Kv . t quantity (Eq. 9), in order to get a value closer to the real Kp constant. The volatilization constant Kv is the rate of mass loss per surface unit area due to the volatilization of re-oxidized chromia. The values of Kv for 1100°C and 1200°C used here were the ones that were directly determined in a previous work [6] for similar alloys: Kv = 2.4 . 10 -10 g.cm -2 .s -1 (1100°C) and 46 . 10 -10 g.cm -2 .s -1 (1200°C).

Kp = ( ) ( ) ( ) ( ) [ ] 2 o 2 o p o S / m S / m t . Kv S / m . t t . 2 1 ∆ - ∆ + + ∆ - (9)
To finish, on the time range where oxidation is linear on both the part parallel to dendrites and the perpendicular one, the global K l is a linear combination of two contributions (Eq. 10), like for the parabolic constants (Eq. 2). The uncoupling (Eq. 10) leads to the K l// and K l┴ constants.

⊥ ⊥ + l // l // K . S S K . S S = l K (10)

Examination of the oxidized samples

After testing, the surface of the oxidized samples became electrically conductive by a gold layer deposited by cathodic plasma pulverization. Then the external chromia layer was mechanically protected by a sufficiently thick electrolytic nickel coating. Thereafter samples were cut, embedded in resin, polished and examined using a Philips XL30 Scanning Electron Microscope (SEM), under a 20kV acceleration voltage. Spot analysis and concentrations profiles were performed using Energy Dispersive Spectroscopy (EDS) coupled with the SEM. Identification of phases like carbides and oxides and Cr and Ta contents profiles were performed with a Cameca SX100 WDS microprobe.

Results

Initial microstructures of the alloys

The bulk microstructures of the as-cast alloys are illustrated by the SEM photographs presented in Fig. 3. The two alloys own first an austenitic matrix which solidified with the form of dendrites. They also contain two types of carbides in the grain boundaries. Chromium carbides and tantalum carbides precipitated at the end of solidification forming an eutectic with matrix, with the Cr 7 C 3 and TaC stoechiometries. These carbides are known to be very useful for strengthening at high temperatures [START_REF] Bradley | Superalloys : A technical guide[END_REF][START_REF] Sims | The superalloys[END_REF]. Carbides are obviously more present in the high carbon alloy (H alloy) than in the low carbon one (L alloy).

Oxidation rates

Oxidation runs were performed on the two alloys for the two main dendrites orientations and for the three temperatures 1000, 1100 and 1200°C. All curves started by a linear part when temperature reached the targeted one. Thereafter parabolic oxidation acted and led to a more or less long parabolic part of curve. Indeed, in some cases detachments of the external and continuous oxide scale obviously occurred and induced jumps of the mass gain. Some of thermogravimetry tests were started again but detachments still existed; fortunately the parabolic part was always sufficiently long (about 50 hours) to allow the determination of the parabolic constants. Fig. 4 shows all the obtained curves from the beginning of the parabolic oxidation (i.e. after isothermal transient linear is finished), and after addition of the Kv.t linear term to correct from the mass loss by chromia volatilization for 1100 and 1200°C. The two mass gain curves corresponding to a same alloy and a same temperature but for the two cutting orientations, were plotted together in a same graph.

It already appears on this example that dendrite orientation seems have an effect on the oxidation rate. Indeed, for 1200°C the mass gain curve of L alloy for the parallel orientation is above the other one. Everywhere along the curves, the slope is also higher for the first one than for the other. For H alloy at the same temperature it is especially the slope that shows a lightly faster oxidation for the parallel orientation than for the other one. For the two other temperatures the comparison is more difficult, especially for H alloy at 1000°C for which the perpendicular orientation seemed to favor detachment of the oxide scale during thermogravimetry tests.

Thereafter it was mathematically proceeded as previously explained. Table II shows the values of K l obtained for all the oxidation tests and the calculated S m o ∆ mass gains already existing before the parabolic oxidation. For each sample, as is to say each alloy and each main orientation, the linear constant logically increases with temperature and, effectively follows an Arrhenius law (example in Fig. 5). The activation energies presented in the last column are those which were employed to estimate the initial mass gains by oxidation during heating before test. One also can see that the linear constants seem to be higher for H alloy than for L alloy (except for 1000°C), and when the external surface is mainly perpendicular than parallel to dendrites (at all temperatures). The same observations can be done for the mass gains before parabolic oxidation. This tendency is enhanced after uncoupling as shown in Table III in which it clearly appears that the orientation has directly an influence of the linear oxidation rate.

After having exploited the values of the global linear constants, the global parabolic constants were obtained. Table IV displays their values. They also increase with temperature and showed a dependence of the orientation, especially at 1200°C. Indeed, the global Kp values are almost equals between the two orientations for 1000°C and 1100°C (except for the L alloy at 1100°C). But at 1200°C, it appears that the samples mainly parallel to dendrites oxidized faster than the samples mainly perpendicular to dendrites. Like for the linear constants, the uncoupling enhances the differences. For 1200°C the parabolic oxidation rate of the surface elements parallel to dendrites are sensibly higher than the perpendicular ones. For the two lowest temperatures the differences that appeared after uncoupling are only due to the calculation. However, the opposite difference observed for L alloy at 1100°C still exists and is increased after uncoupling. The parabolic constant of each type of surface also follows an Arrhenius law (Fig. 6), the activation energies of which are given in Table V.

Observation of the oxidation front

After oxidation tests all samples were metallographically prepared and examined using a Scanning Electron Microscope. Unfortunately, the chromia layer had totally quitted the surface of the samples, then could not be examined. On the contrary it was possible to study the sub-surface deterioration of the alloy due to oxidation (Fig. 7).

From the external surface, all samples exhibit a first zone having lost its initial carbides. For each alloy the depth of this carbide-free zone increases with temperature. Its depth also seems to be higher for the L alloy than for the H alloy, the carbide network of which is more dense.

On a thin outer part this zone also contains internal oxides, which were identified as being CrTaO 4 by WDS microanalysis. These oxides seem to be more present for the H alloy than for the L alloy which contains less tantalum. These oxides almost form a continuous layer along the external surface of the H alloy. Between the carbide-free zone and the bulk we often encounter an intermediate zone in which carbides are different compared to the bulk: darker, coarser or having precipitated in the matrix. These phenomena were explained in previous works [9 to 11] in others alloys also reinforced by carbides, as resulting from an inwards diffusion of carbon atoms released by the dissolving carbides.

Concerning the dendritic orientation, one does not see real differences on both the carbide-free zone and the internal oxides between the main faces of the two types of samples for a same alloy and a same temperature.

WDS profiles

The evolution of contents of both chromium and tantalum were analyzed from the external surface towards the bulk until the values remain constant. Two profiles were performed by sample and the results that are presented respectively in Table VI The chromium profiles show two successive gradients for all samples at 1000°C and 1100°C, the first one corresponding to the carbide-free zone for 1000 and 1100°C, while the second one exists more deeper in the bulk where carbides remained. However the second gradient is almost negligible for 1200°C and it can be considered that it does not exist (Fig. 9). For all alloys, when the temperature increases, the depths of the two gradients also increase while the values of the gradient decrease. Between the alloys the gradients are higher and their depths are smaller for the L alloy than for the H alloy at 1000°C while these tendencies disappear for the two highest temperatures. Between the two orientations, some differences can be pointed out. Indeed, for 1000°C and for the two alloys Cr gradients seems to be greater for the parallel orientation than for the perpendicular one, while such an order does not exist for 1100°C. However the first tendency as 1000°C seems to be found again for 1200°C.

The tantalum profiles often present two successive gradients, especially in the case of L alloy. Like for chromium the gradients decrease and their depths increase when temperature increases. Their gradients are more accentuated for H alloy than for L alloy, because of the higher Ta content of the first one. The total depletion is deeper for the L alloy than for H alloy. Except for the H alloy at 1000°C, the orientation does not sensibly influence the Ta gradients.

Discussion

Thermogravimetry results showed that the dendritic orientation can have an effect on the oxidation rate of these two nickel alloys. This was already seen on samples, at all temperatures for linear oxidation constants but only at 1200°C for the parabolic constant, but it appeared more marked by considering the two uncoupled contributions. We saw first that the transient linear oxidation is faster when dendrites are mainly perpendicular to the local external surface, than when they are parallel. The same observation can be made for the total mass gain obtained before the parabolic oxidation takes place.

To explain that, one can say that perpendicular orientation is probably favorable to a more exposed position of emerging sub-surface carbides (i.e. their very oxidable Cr and Ta constitutive elements) to oxidation, in terms of density as well as of homogeneity. Then transient oxidation and early linear mass gain can be faster in this case than for the other orientation for which the presence of primary dendrites arms can act, here and there, as oriented barriers between interdendritic carbides and the external surface. The general nucleation of chromia (average number of nucleus per surface unit) could be also greater for the perpendicular orientation than for the parallel one, for the same reasons. The first lateral growth of the chromia can be accelerated until all these Cr 2 O 3 crystals meet one another, leading to a faster mass gain during the transient oxidation for the perpendicular orientation than for the parallel one. On the contrary, the Wagner's parabolic oxidation tends to be lower when dendrites are perpendicular to surface than when they are parallel. The same effect of the dendritic orientation on the values of the parabolic constant Kp was already found [START_REF] Berthod | [END_REF], but more marked, for a similar alloy (Ni-30Cr-0.7C-7.5Fe-7.5W) for which a sample with a surface mainly parallel to dendrites exhibited a higher Kp than a sample mainly perpendicular to dendrites (Kp // ~ 3.Kp ⊥ at 1000°C and Kp // ~ 2 Kp ⊥ at 1100°C). Here, the real differences that were observed in this work are at 1200°C for the two alloys (but more marked for L alloy). The parabolic constant for the parallel orientation is twice the one for the perpendicular orientation for L alloy, while, for H alloy, the parallel parabolic constant is greater than the perpendicular one, of 25% only.

The faster oxidation for the parallel orientation could be explained by a less homogeneous chromia scale structure due to the dendrites orientation. Indeed grain boundaries are parallel to surface and then may induce an anisotropy (or orientation along the external surface) for the conditions of formation of external oxides. Thus one can think that the quality of external chromia scale can depend on this special texture, then the chromia scale is less protective for the alloy, i.e less favorable to a better resistance to the diffusion of the species involved by oxidation. Despite of a greater difficulty due to diffusion paths not well oriented, chromium then diffuses faster towards the oxidation front. This can be more accentuated in the case of L alloy, for which the emerging interdendritic carbides are less dense and the primary dendrite arms coarser, than for H alloy for which this heterogeneity is less marked because of a lower surface fraction of emerging matrix. When one sees to the chromium depletion of the parallel L alloy sample, it appears that more chromium was concerned by oxidation at 1200°C (greater gradients and lightly deeper depletion zone) than for the perpendicular one.

Unfortunately, no analysis was done on the chromia scale since this one systematically quitted the alloy during cooling. Like for all chromia-forming alloys this phenomenon is possible since the average thermal expansion coefficient (about 7.10 -6 °C-1 ) is sensibly lower than our alloys' one (10.10 -6 °C-1 ), but the chromia exfoliation is worsen by the inner development of CrTaO 4 oxide just under chromia that obstruct the adhesion of chromia of the substrate. Slower cooling rates obviously were not able to prevent this loss of the external oxide scale for these tantalum-rich alloys. Concerning the sub-surface CrTaO 4 . One can also remark that the inner development of the CrTaO 4 has maybe also decreased the effect of dendritic orientation when the results of this study are compared to previous ones [START_REF] Berthod | [END_REF] obtained for a nickel alloy without tantalum.

The greater differences about oxidation rates (linear and parabolic), and also subsurface microstructure and concentration profiles, were also seen between the two alloys: on the one hand lower transient and parabolic oxidation kinetics, and on the other hand deeper carbide-free zone, higher Cr gradients at 1000°C but deeper Ta depletions, were clearly found for the L alloy compared to the H alloy. Such results were already found in previous studies concerning other carbides-strengthened cast alloys.

Conclusions

The dependence of the local oxidation rate on the dendritic orientation was found again in the case of tantalum-containing nickel alloys, but essentially for 1200°C. A second effect was also seen on the transient oxidation. The quantification of the latter, allowed by the determination of the linear K l constants and of their law of variation with temperature, led to see also a dependence of this first stage of oxidation on the dendritic orientation.

These results confirm others obtained in previous works on other equiaxed cast alloys. The dendritic orientation obviously influences the oxidation behavior. But the mechanisms remain to be more clearly explained, since it was not possible to examine the structure of the external chromia layer, a problem which is probably due to inner oxidation of tantalum. Future works, on alloys which can more easily conserve their external oxide until return to room temperature, will certainly allow to better understand the phenomena responsible of this influence of the dendritic orientation on the oxidation behavior.

Figure 1

 1 Figure1The three different microstructure zones which can be met from the mold wall in a metallic piece obtained by a classical foundry way

Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9

 23456789 Figure 2 Cutting modes for samples mainly parallel or mainly perpendicular to dendrites

  and Table VII, are the obtained average values.

TABLE I

 I

	Chemical compositions of the two studied nickel-base alloys
			Weight contents (%)
	Alloys
		Ni	Cr		C	Ta
	H alloy	Bal.	30		0.40	5.4
	L alloy	Bal.	30		0.20	2.0
	TABLE II Global oxidation linear K l constants (10 -8 g.cm -2 .s -1 ) and values of the calculated S m o ∆ mass gains already existing before the parabolic oxidation (in mg/cm 2 )
	Temperature	1000°C	1100°C		1200°C	Activation
						energy
	Alloy					(kJ.mol -1 )
	//	1.12	8.84		33.3	265
	H alloy	(0.651mg/cm2)	(1.25mg/cm2)	(4.82mg/cm2)
	⊥	1.29	11.8		41.7	272
		(1.06mg/cm2)	(1.32mg/cm2)	(5.52mg/cm2)
	//	2.65	3.58		14.2	129
	L alloy	(0.113mg/cm2)	(2.08mg/cm2)	(4.18mg/cm2)
	⊥	2.63	4.13		20.6	158
		(0.096mg/cm2)	(2.52mg/cm2)	(4.59mg/cm2)
	TABLE III Uncoupled oxidation K l constants (10 -8 g.cm -2 .s -1 )
	Temperature				Activation
		1000°C	1100°C	1200°C	energy
	Alloy					(kJ.mol -1 )
	K l //	1.02			8.20	27.2	257
	H alloy
	K l ⊥	1.60			13.4	48.4	267
	K l //	2.65			3.14	11.7	113
	L alloy
	K l ⊥	2.63			4.53	23.5

TABLE IV

 IV Global oxidation parabolic Kp constants (10 -12 g 2 .cm -4 .s -1 ) Temperature

		1000°C	1100°C	1200°C
	Alloy
	//	3.24	24.9	137
	H alloy
	⊥	3.20	24.8	126
	//	2.46	13.3	117
	L alloy
	⊥	2.21	16.1	81.5

TABLE V

 V

	Uncoupled oxidation parabolic constants (10 -12 g 2 .cm -4 .s -1 )
	Temperature				Activation
		1000°C	1100°C	1200°C	energy
	Alloy				(kJ.mol -1 )
	Kp //	3.26	24.9	145	296
	H alloy
	Kp ⊥	3.12	24.7	117	283
	Kp //	2.49	11.2	133	308
	L alloy
	Kp ⊥	2.15	18.2	67.5

TABLE VI

 VI Mean values of chromium gradients from the external surface Temp.

		1000°C	1100°C	1200°C
	Alloy	external	internal	external	internal	external	internal
		0.110%/µm	0.017%µm	0.038%/µm	0.008%/µm	0.025%/µm
	//	over	over	over	over	over	too light
		24µm	120µm	76 µm	203µm	260µm
	H alloy
		0.062%/µm	0.015%/µm	0.050%/µm	0.010%/µm	0.020%/µm
	⊥	36µm over	101µm over	66µm over	174µm over	270µm over	too light
		0.200%/µm	0.075%/µm	0.046%/µm	0.007%/µm	0.031%/µm
	//	over	over	over	over	over	too light
		20µm	50µm	95µm	150µm	275µm
	L alloy
		0.113%/µm	0.029%/µm	0.047%/µm	0.004%/µm	0.018%/µm
	⊥	40µm over	70µm over	90µm over	220 µm over	265µm over	too light

TABLE VII

 VII

	Mean values of tantalum gradients from the external surface
	Temp.
		1000°C	1100°C	1200°C
	Alloy
				0.028%/µm over 130µm
	H alloy //	0.054%/µm over 70µm	0.038%/µm over 130 µm	then 0.008%/µm over 80µm
			0.062%/µm over 45µm
	⊥	0.095%/µm over 40µm	0.014%/µm over 65µm then	0.010%/µm over 160µm
		0.049%/µm over 45µm	0.037%/µm over 35µm	0.011%/µm over 135µm
	//	then	then	then
	L alloy	0.020%/µm over 40µm	0.013%/µm over 105µm	0.004%/µm over 195µm
			0.038%/µm over 40µm	0.009%/µm over 155µm
	⊥	0.045%/µm over 40µm	then 0.009%/µm over 95µm	then 0.004%/µm over 165µm

Acknowledgements

The authors thank J. Demange, Y. Ravaux and A. Kohler, of the Microanalysis Common Service of the Faculty of Science of Nancy for their contribution at this work.