Yves Leroyer

Alois Würger
email: a.wuerger@loma.u-bordeaux1.fr

Soret motion in non-ionic binary molecular mixtures

Keywords:

We study the Soret coefficient of binary molecular mixtures with dispersion forces. Relying on standard transport theory for liquids, we derive explicit expressions for the thermophoretic mobility and the Soret coefficient. Their sign depends on composition, the size ratio of the two species, and the ratio of Hamaker constants. Our results account for several features observed in experiment, such as a linear varition with the composition; they confirm the general rule that small molecules migrate to the warm, and large ones to the cold.

I. INTRODUCTION

The Soret effect describes the non-uniform composition of a complex fluid or molecular mixture in a temperature gradient [START_REF] De Groot | Non-equlibrium Thermodynamics[END_REF]. In the steady state one observes that some components accumulate at the cold side of the sample, whereas others rather migrate in the opposite direction [START_REF] Köhler | Thermal Nonequilibrium Phenomena in Fluid Mixtures[END_REF][3][4][5][6][7][8]. This thermophoresis, or thermal diffusion, is driven by thermodynamic forces that act on the different components.

For charged colloids in an electrolyte solution, several mechanisms have been singled out: The temperature gradient induces a non-uniform pressure and permittivity in the electric double layer, which drive the particle to the cold [9]. On the other hand, the Seebeck effect of the electrolyte solution induces a macroscopic electric field which imposes on a suspended particle an electrophoretic velocity that may take either sign, depending on the electrolyte properties [10]. Standard colloidal transport theory provides an overall satisfactory picture for the thermophoretic velocity, and in particular describes its variation with the salinity and the pH value [11,12].

Surprisingly, the situation is less clear for mixtures of non-ionic molecules and dilute polymer solutions, although dispersion forces are the only molecular interaction. We mention several aspects that add complexity in the case of a binary mixture as illustrated in Fig. 1. First, molecular mixtures generally comprise comparable volume fractions of their components and thus cannot be treated in the low-dilution limit [13][14][15][16][17][18]. Second, in charged systems macroscopic hydrodynamics works well, since both the Debye length and the solute size are large compared to the solvent molecular structure [6][7][8]; this continuum approximation is less obvious for short-ranged dispersion forces [19]. Third, as a related aspect, the interaction energies of each molecular species are comparable; thus it is not suffiicient to consider the forces acting on a "solute" molecule; both components have to be treated on an equal footing, and the Soret motion arises from the competition of their transport velocities [20,21]. Finally we note that, contrary to the case of col-FIG. 1: Schematic view of a binary mixture of spherical beads. In a mean-field approach, the transport coefficients are calculated for each species in a homogeneous liquid. loidal particles, the kinetic energy is important in molecular mixtures, and contributes significantly to the thermal diffusion [22]. These aspects have been addressed by previous authors, mainly in terms of heat-of-transfer models [23][24][25][26] and numerical simulations of the molecular dynamics [27][28][29][30][31][32][33][34] In this paper we study the Soret mobility in binary mixtures. From the condition of mass conservation, we derive in section 2 a formal expression for the Soret coefficient that depends on the thermal transport and diffusion coefficients ξ i and D i of the two components. Using van der Waals potentials and low-Reynolds number hydrodynamics, we calculate in section 3 the ξ i and in particular evaluate their dependence on the molecular size. In Section 4 we discuss our main results in view of the most important parameters and compare with experimental findings.

II. THE SORET COEFFICIENT

We consider a binary system with volume fractions φ 1 = φ and φ 2 = 1φ. For the sake of simplicity we suppose that the mass density does not depend on the composition, in other words, that both components have the same density as the binary mixture. Yet note that the density does depend on temperature.

The diffusion kinetics with respect to composition changes are expressed in terms of the current related to φ [START_REF] De Groot | Non-equlibrium Thermodynamics[END_REF],

J 1 = -D∇φ -φ(1 -φ)D T ∇T, ( 1
)
where D is the mutual diffusion coefficient of the two components; the drift term is proportional to the temperature gradient with the mobility D T . In the case of a closed system in contact with two heat reservoirs at different temperatures, this current vanishes in the stationary state; the spatial variation of the molar fraction is described by the Soret coefficient

S T = D T D . (2)
If both S T and ∇T are constant, Eq. ( 1) can be integrated in closed form. In the dilute limit φ → 0, colloidal or macromolecular dispersions are well described by calculating both the Einstein coefficient and the mobility for a single suspended particle from the solute-solvent interactions.

The above Eq. ( 1) follows from rather general considerations on heat and mass flows in a non-uniform temperature [START_REF] De Groot | Non-equlibrium Thermodynamics[END_REF], yet does not give explicit expressions for D and D T . In order to relate these coefficients to the physical parameters of the liquid, we rewrite the currents of each component as

J i = -D i ∇φ i + φ i u i -φ i ū, (3)
where D i describes the diffusive motion of a given molecule, u i its drift velocity, and ū is the center-of-mass velocity ū. In the simplest case the tracer diffusion coefficient reads as

D i = k B T 6πηR i , (4)
where η is the viscosity of the mixture and R i the hydrodynamic radius. The transport velocity accounts for thermally driven motion in a temperature gradient,

u i = -ξ i ∇T, (5)
with the molecular mobility ξ i of compenent i. The center-of-mass or background velocity ū assures the condition J 1 + J 2 = 0 which results from mass conservation [START_REF] De Groot | Non-equlibrium Thermodynamics[END_REF]; for thermal diffusion in electrolyte solutions its role has been spelt out by Kirkwood and co-workers [35,36].

Here we are intereseted in the steady state where the current of each component vanishes separately, J 1 = 0 = J 2 . Eliminating the gradients ∇φ 1 = -∇φ 2 from (3) and solving the remaining equation for the center-of-mass velocity, we find

ū = u 1 φ 1 /D 1 + u 2 φ 2 /D 2 φ 1 /D 1 + φ 2 /D 2 . ( 6
)
This expression is the average of the quanitities (5), with the weight of each term is given by the volume fraction divided by the diffusion coefficient. Replugging ū in (3) one obtains the current of component 1,

J 1 = -(φ 1 D 2 + φ 2 D 1 ) ∇φ 1 + φ 1 φ 2 (u 1 -u 2 ) ,
and comparing with (1) one readily identifies the quantities D T and D. The thermal diffusion coefficient is given by the difference of the mobilities of the two species,

D T = ξ 1 -ξ 2 . ( 7
)
This implies that the species with the larger mobility moves to the cold, e.g., for ξ 2 > ξ 1 we have D T < 0 for component 1. It turns instructive to consider the particular case ξ 1 = 0. The the thermophoretic mobility D T of component 1 is entirely determined by the transport coefficient ξ 2 . Eq. ( 7) has a simple physical meaning: In general the molecules of component 2 have a tendency to migrate to the cold (ξ 2 > 0); as a consequence, they push those of species 1 in the opposite direction towards higher temperature.

The mutual diffusion coefficient arises as the weighted mean of the molecular coefficients,

D = φ 1 D 2 + φ 2 D 1 . (8)
This corresponds to the expression of a simple model developped for molecular mixtures [37,38]. A more complex result arises when including in the currents (3) additional terms, such as the concentration gradients of other species D ij ∇c j .

Thus we obtain the Soret coefficient

S T = ξ 1 -ξ 2 φ 1 D 2 + φ 2 D 1 . (9)
Except for the sign, this expression is symmetric under exchange of the two species; thus we have -S T for component 2. Eqs. ( 7)-( 9) constitute the main result of the formal part of this paper. In the remainder we calculate the mobility D T .

III. DISPERSION FORCES

In this section we evaluate the mobility ξ for a single solute molecule interacting with solvent through dispersion forces. The main issue is the variation of ξ with the size of the solute particle.

The interaction energy between the particle and the surrounding liquid is obtained by integrating the van der Waals potential over their respective volumes,

ϕ = - H π 2 dV dV ′ |r -r ′ | 6 , (10)
where the Hamaker constant takes values H ∼ 10 -20 J, which at room temperature corresponds to several k B T . This form has been used for calculating the dispersion forces between two macroscopic bodies [START_REF] Russel | Colloidal Dispersions[END_REF].

For the hydrodynamic treatment we rather need the potential energy density in the liquid phase. In turns out convenient to evaluate the integral in ϕ for the effective volume V S occupied by a single liquid molecule at position r. Replacing this volume with the inverse number density of liquid molecules, V S = 1/c, we have

cϕ(r) = - H π 2 dV ′ |r -r ′ | 6 , (11)
where the remaining integral runs over the solute particle.

The van der Waals potential acting on each liquid molecule results in an excess pressure P = -cϕ close to the solid surface. The concentration c of the liquid phase, and thus the pressure P , vary along the solute surface, giving rise to motion of the surrounding fluid. In the following we first consider the simple case of a flat solid boundary and then generalize to a spherical solute particle of finite size.

A. Flat interface

In the case of a large solute, the volume integral in (11) can be taken over an infinite half space. The resulting expression is readily evaluated, and gives the well-known result [START_REF] Russel | Colloidal Dispersions[END_REF]

cϕ(z) = - H 6πz 3 , (12)
where z indicates the distance from the interface. Note that because of the thermal gradient, the concentration of solvent molecules c(x) varies along the surface. The fluid dynamics is governed by Stokes' equation. In the vicinity of a flat surface, it takes a particularly simple form which we discuss in terms of local coordinates x and z as defined in Fig. 2. The vertical velocity component vanishes, whereas a finite velocity v x occurs along the surface and obeys η∂ 2 z v x = ∂ x P . With Stokes boundary conditions this equation is readily integrated [19,[START_REF] Anderson | [END_REF], and gives the velocity well beyond the range of interaction of the van der Waals potential,

v B = - 1 η dc dx ∞ d0 dzzϕ(z). (13)
The lower bound d 0 is required in order to assure convergence of the integral. In physical terms, this cut-off

T ∇ R θ z FIG. 2:
Boundary layer approximation at the surface of a solute particle.

parameter accounts for the minimal distance of atoms of the liquid and the particle. Performing the integral in (13) gives H/(6πd 0 ). In a non-uniform temperature the concentration varies as

∇c = -cβ∇T, (14)
with the thermal expansion coefficient β. Thus we obtain the quasislip velocity of the liquid

v B = Hβ 6πηd 0 dT dx . (15)
In the frame attached to the solid boundary, the liquid flows to higher temperatures.

B. Spherical particle

Now we account for a finite solute volume in the van der Waals potential (11). In the case of a homogeneous spherical particle of radius R, the integral is readily performed,

cϕ(r) = - 4H 1 3π R 3 (r 2 -R 2 ) 3 . (16)
In the limit R → ∞ one readily recovers with z = r -R the expression for a macroscopic body, Eq. ( 12). Strictly speaking, Stokes' equation no longer separates in parallel and normal components; using (13) close to a curved surface corresponds to the boundary layer approximation [START_REF] Anderson | [END_REF].

Here we describe finite-curvature corrections that arise from the modified van der Waals potential (16). Inserting the vertical distance z = r -R in (13) and performing the integral one finds where the finite size of the bead is accounted for by

v B = Hβ 6πηd 0 dT dx F d 0 R , (17)
F (x) = 3 2 x ln x x + 2 + 3x 2 + 9x + 4 (x + 2) 2 (18)
with the shorthand notation x = d 0 /R. For large particles (R → ∞) this function takes the value F (0) = 1, and decreases monotonically as the radius R becomes smaller. This is due to the fact that a smaller particle volume exerts a weaker force on the surrounding fluid. The projection of the constant macroscopic temperature gradient ∇T on the particle surface varies with the polar angle θ defined in Fig. 2. The corresponding orientational average of the velocity vector v B results in a factor 2 3 [START_REF] Anderson | [END_REF]; noting moreover that the particle moves in the direction opposite to the surrounding fluid, one finds

ξ = 2Hβ 9πηd 0 F d 0 R . (19)
In the limit of large particles (R ≫ d 0 ) we recover the result given previously in Ref. [19].

C. The cut-off parameter d0

The physical meaning of the cut-off parameter introduced in Eq. ( 13) is twofold. The van der Waals potential (10) is based on a continuum approximation that ignores the molecular structure and thus leads to a divergency in the interaction energy if two beads of volumes V and V ′ are in contact. The common practice of regularization consists in a cut-off parameter that accounts for the finite distance of the two bodies; in a physical picture d 0 may be viewed as the minimum distance of atoms of different beads, and thus is of the order of an Angström.

In Eq. ( 13) the length d 0 takes a somewhat different meaning. The integral gives the solution of the parallel component of Stokes' equation, which describes the balance of viscous and dispersion forces along the particle surface; the integrand is related to the shear stress in the vicinity of the bead under consideration. Thus d 0 accounts for the length scale where continuum hydrodynamics cease to be valid, and is related to the molecular size; the notion of shear flow or velocity gradient is meaningless at shorter distances, as illustrated by the right panel of Fig. 2.

In the case of a large solute particle, R 1 ≫ R 2 , it is save to identify d 0 with the size of a solvent molecule R 2 . Its value is less obvious if both components are of similar size. The length d 0 subsumes the cut-off of macrosccopic hydrodynamics on a molecular scale. Using the relation d 0 ≈ R in the form factor one finds that F takes a value of about 15%.

IV. BINARY SYSTEMS

Here we discuss the above results in view of experimental findinigs on binary molecular mixtures and polymer solutions. The mobilities ξ i are calculated from a mean-field model, where each molecule is considered as a spherical bead that is surrounded by a continuous solvent consisting of molecular species 1 and 2 of volume fractions φ i . Thus the transport coefficients ξ i are given by Eqs. ( 7) and (19), providing the general expression for the thermophoretic mobility,

D T = 2β 9πηd 0 [H 1 F 1 -H 2 F 2 ] , (20)
with the appropriate shape factors

F i = F (d 0 /R i ).
In a simple mean-field picture the Hamaker constants of solute and solvent beads read as

H 1 = φ 1 H 11 + φ 2 H 12 , H 2 = φ 1 H 12 + φ 2 H 22 , (21)
where H ij describes the dispersion forces between materiels i and j.

Experiments on molecular mixtures give the Soret coefficient rather than the mobility D T . Inserting the Stokes-Einstein relation D i = k B T/6πηR i in the mutual diffusion coefficient one finds

S T = β 4R eff 3d 0 H 1 F 1 -H 2 F 2 k B T , (22)
where we have introduced the shorthand notation for the effective radius

1 R eff = φ 1 R 2 + φ 2 R 1 . (23)
Both R eff and the Hamaker constants depend on the volume fractions, thus giving rise to an intricate variation with the composition. The mobility D T and the Soret coefficient S T may take either sign, depending on the relative values of the H ij and F i .

A. Large particles

We start with the case of a dilute suspension of large solute particles P in a molecular solvent S, as illustrated in Fig. 2. With R P ≫ d 0 and φ P ≪ 1 we find that the thermophoretic mobility

D T = 2β 9πηd 0 (H P S -F S H SS ) . ( 24
)
is independent of the solute size R P . This is a particular case of a generally valid statement, which has been shown first for electrophoresis of particles much larger than the Debye length, and applies equally well to chemical and temperature gradients [START_REF] Anderson | [END_REF]. This limit has been discussed previously for thermophoresis of non-ionic particles [5,41] and confirmed experimentally for nanospheres in toluene [42].

The effective radius is that of the particle, R eff = R P , resulting in a Soret coefficient

S T = β 4R P 3d 0 H P S -F S H SS k B T . ( 25
)
The linear variation with the particle radius is related to a constant mobility [START_REF] Anderson | [END_REF] and consitutes one of the few rigorous results for colloidal transport. The first term in ( 24) is due to solute-solvent dispersion forces that attract the particle to regions of higher density and thus to lower temperature. The second one, which describes solvent-solvent interactions, carries a minus sign. Its reduction factor F S = F (d 0 /R S ) accounts for finite integration volume of the potential energy density: The smaller the particle volume, the weaker are the dispersion forces exerted by one solvent molecule on its neighbor. Fig. 3 shows a significant reduction for d 0 /R > 0.2. The above discussion suggests that the cutoff parameter d 0 is comparable to the molecular radius R S and that the shape factor F S is small. Setting F S = 0 we recover the particle mobility to the result obtained previously for a structureless solvent [19].

B. Dilute polymer solutions

At low dilution we set φ 1 = 0 in (20) and thus find where the subscripts indicate the properties of a polymer building unit and of a solvent molecule. Like other transport coefficients, the thermophoretic mobility of high polymers is independent of the molecular weight [43][44][45][46][47][48][49][50][51][52][53].

D T = 2β 9πηd 0 (F P H P S -F S H SS ) , (26)
The mobility may be positive or negative, depending on the form factors and Hamaker constants. Comparison with our previous work reveals a difference concerning the term proportional to βH SS : In the approach of Ref. [54] this contribution is proportional to the inverse gyration radius and thus vanishes for high polymers. The present work treats solute and solvent motion on an equal footing, and leads to the more satisfactory form (26) where the prefactor of βH SS is independent of the molecular weight.

Note that the form factor F P describes a single mer. For polymers made of large and heavy building blocks, such as polystyrene, one expects a positive mobility. If a single mer is smaller than a solvent molecule, one has F P < F S , and a negative mobility. In physicial terms, because of their stronger van der Waals potential, the solvent molecules diffuse more rapidly to the cold and thus push the polymer to regions of higher temperature. This argument explains, at least qualitatively, the mobilities of different polymers in cyclyoctane reported in Ref. [55]; Table 1 shows that the polyethylene (PE) and poly-dimethyl-siloxane (PDMS) are built of small molecular units and diffuse to higher temperatures (D T < 0), whereas the heavier polystyrene has a positive mobility.

An analysis of D T of polystyrene in various solvents in terms of (19) with F = 1, led to values for d 0 that range from 0.6 to 1 nm, and correspond to the size of a solvent molecule [8]. Eq. (26) shows that the sign of the mobility is determined by the ratio R P /R S , independently of the precise value of d 0 . Even if the value of d 0 and the form of the function F should be taken with caution, equation indicates the tendency that the larger molecular units diffuse to lower T . There are additional effects arising from the different Hamaker constants, weak hydrodynamic interactions between neighor beads, and the kinetic energy.

The mutual diffusion coefficient at low dilution reads D = k B T /6πηR h , where R h is the hydrodynamic radius of the polymer chain. With respect to the composition and the molecular radii, the resulting Soret coefficient

S T = β 4R h 3d 0 F P H P S -F S H SS k B T (27)
behaves like the mobility D T . It is proportional to the hydrodynamic radius of the polymer coil and thus increases with the chain length; this dependence has been observed for polystryene in different solvents [44].

C. Molecular mixtures

We briefly discuss the three factors appearing in ( 22) for organic molecules of comparable size. For most liquids, the thermal expansion coefficient β takes values of about 10 -3 K -1 . According to the above discussion of the cut-off parameter, the ratio R eff /d 0 is not very different from unity. Finally, the last factor expresses the effective Hamaker constant in units of the thermal energy; with typical values for H i ∼ 5k B T and F i from Fig. 2, one finds numbers of the order of 1 but hardly larger than 4.

As noted in previous works, S T is proportional to the thermal expansivity [5,41,[56][57][58]; the remaining factors in (22) depend on molecular details and in particular on the composition. Indeed, the Soret coefficient of mixtures of aliphatic and aromatic molecules is mostly hardly exceeds a few 10 -3 K -1 .

Fig. 4 shows the Soret coefficient as a function of the composition φ for three values of the molecular size ratio. In all cases the cut-off parameter d 0 is equal to the smaller radius. If both species are of equal size, the effective radius R eff is constant, and the Hamaker constants result in a linear variation with φ. Unlike molecular radii result in a non-uniform slope, as illustrated by the upper and lower curves. A rather similar behavior has been observed for binary liquids [13,15]. For molecules of equal size, the dependence on the interaction parameters agrees well with numerical simulations [29].

In order to separate the dependencies of ( 22) on composition, size, and Hamaker constants, we consider in the following several special cases.

D. Composition dependence at equal size

If both molecular species have the same size, the form factors are identical, F = F 1,2 , and simplifiy the mobility

S T = β 4R 3d 0 F H 0 + φ 1 δH k B T , (28)
where we have used φ 2 = 1φ 1 , and the shorthand notation

H 0 = H 12 -H 22 and δH = H 11 + H 22 -2H 12 .
As a remarkable property, this mobility varies linearly with the volume fraction φ 1 . The parameters H 0 and δH may be positive or negative, and may result in a change of sign of S T as a function of φ 1 . This is illustrated by the middle curve of Fig. 4.

A roughly linear dependence on φ 1 has been reported for mixtures of benzene, toluene, and cyclohexane [13]; more complexe variations occur for flexible alkane chains, sugars, and polar molecules such as acetone [14][15][16][17][18]. Both the linear variation with composition and the dependence on the Hamaker constants agree with numerical simulations of a Lennard-Jones binary liquid [32].

E. Size dependence at equal Hamaker constants

If the components have similar chemical properties, their Hamaker constants do not vary much. When setting H = H ij for all pair interactions, the mobility takes a particularly simple form

S T = β 4 (F 1 -F 2 ) 3d 0 (φ 1 /R 2 + φ 2 /R 1 ) H k B T , (29)
that is proportional to the difference of the form factors of the two species. Since F is a mononotically increasing function of the molecular radius, this means that the smaller species migrates to the warm, and the larger one to the cold. The second factor depends on the composition; the Soret coefficient is larger if the smaller species is more abundant. Real molecules are not spherical beads, and their size cannot be reduced to a single radius. Still, the radius dependence of the form factor expresses the dependence on the molecular volume. Since most organic molecules have rather similar densities, R be equally well related to the molecular mass; in the simplest case one has m ∝ R 3 . Then (29) states that the heavier species migrates to the cold, and the lighter one to the warm. This rule is confirmed by Soret data on various binary mixtures [14].

In their numerical simulation results of Lennard-Jones liquids, Galliéro et al. found that the larger species mi-grate to the warm [29], which at first sight seems to contradict the present result (29). Yet in view of the different interaction potentials, this discrepancy is not surprising: The simulations of Ref. [29] are based on a single atomatom Lennard-Jones potential ϕ LJ = ε[(σ/r) 12 -(σ/r) 6 ]; the size dependence is obtained by varying the length σ at constant interaction parameter ε. The present work describes the molecular interactions in terms of the van der Waals potential (10) which reduces to the Lennard-Jones form ∼ 1/r 6 in the limit r ≫ R, but shows a more complex variation at short distances. The Lennard-Jones potential results in a force -∇ϕ LJ ∼ ε/σ that becomes weaker as the parameter σ increases. On the other hand, the force derived from (10) increases with the molecular radius.

F. Kinetic energy

In this paper we have only considered dispersion forces and neglected the thermal agitation of the molecules. That is why the Soret coefficient disappears in the absence of van der Waals interactions. On the contrary, thermal diffusion in gas mixtures and aerosols is well described by kinetic theory. Much numerical work has been done on hard-sphere systems [30,59].

From recent work on a simple hard-bead model it is clear that the kinetic energy contributes significantly to the Soret coefficient in liquids, and may even dominate in the case of molecular mixtures [22]. The isotope effect observed upon deuteration or replacing common carbon 12 C with the heavier isotope 13 C benzene, indicates that the Soret coefficient consists of a "chemical" contribution and a term depending on the molecular masses [13,32].

Taking their sum one finds the total Soret coefficient

S tot T = S T + S mass T , (30)
where the chemical contribution S T is obtained in the present work and the mass-dependent one has been derived in [22]. For small molecules, both may be of comparable size. Thus a quantitative fit of experimental data should include both contributions. Yet so far the kinetic contribution has been derived only for binary mixtures where both components are of equal size [22]; one may expect that a size difference will signficantly affect the mass dependent term.

V. SUMMARY AND CONCLUSION

Starting from the well-known expression for large solute particles at low dilution, we have studied the dependence of the Soret coefficient on the composition and on the molecular size. As a main result, the form factors F account for the fact that smaller beads have a weaker van der Waals potential, and reduce the Soret motion accordingly. As a general law, we find that the smaller species migrates to the warm, due to its weaker dispersion forces; this mechanism is fundamentally different from the mass effect discussed in [22,28,29]. In the limit of large particles, we find that the mobility D T becomes independent of size, in accord with colloidal transport theory [START_REF] Anderson | [END_REF].

A second important aspect concerns the variation of S T with composition. Our findings show a rather complex behavior that arises from the mutual diffusion coefficient (8) and the effective Hamaker parameters, as illustrated in Fig. 4. The change of sign is due to the composition dependence of the Hamaker coefficients. Most of our results agree with previous numerical simulation studies on Lennard-Jones binary liquids [28,29,32].

FIG. 3 :

 3 FIG.3:The function F (d0/R) in the range 0 ≤ d0/R ≤ 1. In the limit x → 0 one recovers with F (0) = 1 the mobility of large particles. The function F strongly decreases as the particle radius R becomes comparable to the cut-off parameter d0.

12 FIG. 4 :

 124 FIG.4: Soret coeffiicient as a function of the composition. The radii are equal to the cutoff parameter d0, or twice d0; the off-diagonal Hamaker constant is H12 = 3kBT , and the thermal expansivity β = 10 -3 K -1 .

TABLE I :

 I Thermophoretic mobility DT of different polymers in cyclooctane C8. The second row compares the mass of a monomer to that of a solvent molecule, m = 104. The data are from Ref.[55].

	Polymer/solvent PE/C8 PDMS/C8 PS/C8
	m (amu)	28/104 74/104 104/104
	DT (µm 2 /sK)	-2	-1.2	2.7


Frank M Ciaramello

Sheila S Hemami
email: hemami@ece.cornell.edu

THE INFLUENCE OF SPACE AND TIME VARYING DISTORTIONS ON OBJECTIVE INTELLIGIBILITY ESTIMATORS FOR REGION-OF-INTEREST VIDEO

Keywords: Region-of-interest coding, sign language video, video quality assessment, video quality database

Objective estimators for video are expected to estimate accurately subjective ratings provided by humans. This work presents a subjective experiment designed to acquire intelligibility ratings for a collection of compressed ASL videos. The distortions present in the experimental database are analyzed in terms of their impact on the performance of objective estimators. Distortions that do not significantly vary across space or time cannot adequately challenge traditional objective estimators, such as PSNR and RMS distortion contrast, and an objective intelligibility measure designed specifically for ASL video provides negligible improvements in prediction accuracy. Distortions that vary across space and time, affecting only localized regions in the video, are considered spatially and temporally diverse. When the distortions present in the experimental database are sufficiently diverse, the objective intelligibility measure estimates subjective ratings more accurately than PSNR and RMS distortion contrast.

INTRODUCTION

Real-time, two-way transmission of American Sign Language (ASL) video over cellular networks provides natural communication among members of the Deaf community. Region-of-interest (ROI) techniques suit ASL video, because the signer is the ROI. Subjective experiments provide an accurate evaluation of the quality of service being delivered by a such a video compression and transmission system. Because of the high cost of subjective studies, objective assessment techniques are developed to estimate the subjective ratings provided by humans and are evaluated in terms of their accuracy on a specific test database.

The experimental test database analyzed in this work is comprised of compressed ASL video, encoded at very low bitrates using region-of-interest encoders designed for ASL content. The subjective experiment that produces the test database is presented in Section 2. Four objective estimators are studied in terms of their ability to estimate subjective intelligibility scores. However, any conclusions regarding the performance of an objective estimator must be conditioned on the content available in the test database. In order to confidently compare objective estimators, the distortions contained in the experimental data must be evaluated in terms of their ability to adequately challenge the objective estimators. Section 3 analyzes the video content and distortions present in the experimental database and studies their impact on the performance of the objective estimators. Concluding remarks are provided in Section 4.

SUBJECTIVE EXPERIMENTAL DATABASE

A subjective experiment was designed to evaluate 4 encoding algorithms at bitrates ranging from 30 kbps to 80 kbps. Sixteen sign language stories told by a fluent signer at her natural signing pace were filmed in two different locations, an indoor studio with a static background and an outdoor location on a busy street having a significant amount of background activity.

A total of 16 fluent ASL users participated in the experiment, consisting of 7 male and 9 female participants, having an average of 28.4 years of experience with ASL. Participants provided their preferred language for communication: 8 reported English, 5 reported ASL, and 3 reported both English and ASL. The subjective experiment followed a single stimulus testing procedure. Following each test video, participants were asked three questions designed to evaluate their comprehension of the story, the intelligibility of the test video, and usability of the test video. Because of the nature of this intelligibility assessment task, no single story is viewed by the same participant twice, eliminating any possible learning effects.

The test set of videos evaluated in this study were generated using 4 different encoding algorithms each operating under both a high bitrate and low bitrate setting. Two different sets of rates were selected such that at each location, the most intelligible videos would be very easy to understand and the least intelligible video would be very difficult to understand. Outdoor videos were encoded at rates of 50 kbps and 80 kbps; indoor videos were encoded at rates of 30 kbps and 45 kbps. Each of the 4 encoding algorithms evaluated in this study operate within the H.264/AVC standard and provide rate control that meets an average target bitrate. Three sign language specific encoders and a general purpose video encoder were evaluated.

x264 Encoder An open-source H.264/AVC encoder, x264 [1], was selected because it offers rate-distortion performance similar to the JM reference encoder at speeds 50 times faster. The ratedistortion optimization in x264 effectively treats all macroblocks equally, minimizing the average MSE over the entire frame, subject to the rate constraint. Rate control is performed by adjusting the quantization parameter on a frame-by-frame basis [START_REF] Merritt | Improved rate control and motion estimation for H.264 encoder[END_REF].

Foveated Encoder In foveated video coding, the video frame is encoded with non-uniform, decreasing quality away from the the observer's point of fixation, attempting to match the visual acuity of the human visual system [START_REF] Kortum | Implementation of a foveated image coding system for image bandwidth reduction[END_REF]. Because an ASL observer primarily gazes at the signer's face, the fixation point is automatically identified using skin segmentation and facial feature detection, and foveated processing is applied to generate a map of priority regions [START_REF] Agrafiotis | A perceptually optimised video coding system for sign language communication at low bit rates[END_REF]. Relative to the location of the face, a foveation model assigns macroblocks to the priority regions, each region having a different quantization parameter, allowing blocks nearest to the face to be coded with more bits than blocks farther away. Rate control is performed by adjusting the quantization parameter assigned to the face macroblocks (on which all the other quantization parameters depend) on a frame-byframe basis.

ROI Encoders Two region-of-interest (ROI) encoding techniques allocate bits primarily to the face and hands of the signer [START_REF] Ciaramello | Complexity constrained ratedistortion optimization of sign language video using an objective intelligibility metric[END_REF]. Skin segmentation and face detection algorithms identify the macroblocks containing the signer's face and hands and provide a segmentation map to the ROI encoder. Given the segmentation map, different quantization parameters are selected for the macroblocks belonging to the face, hands, or background. Rate control is performed by adjusting the Lagrange multiplier on a frame-by-frame basis, which controls the quantization parameter selection for each region. These two ROI encoders are differentiated by the use of a temporal smoothing of the macroblock segmentation labels. Specifically, for the spatial-temporal ROI encoder, the face and hand labels are held constant for a duration of 1 second, e.g., if a macroblock is labeled as hand in frame 10, that macroblock will retain the hand label until frame 25, at 15 frames per second. The spatial ROI encoder simply uses the segmentation map provided for the current frame.

Verifying the necessity of z-scores

Analysis of variance (ANOVA) is used to identify statistically significant effects on subjective intelligibility and a significant effect was found for the preferred language (F (2, 206) = 28.87, p < 0.01). Participants who reported ASL as their preferred language responded with statistically significantly higher intelligibility ratings than both the group preferring English and the group preferring either ASL or English. Higher fluency is unlikely, as the group reporting both ASL and English has roughly the same mean years of experience with ASL. It is more likely that the ASL group was biased toward higher intelligibility ratings. This is a consequence of the increased desire an ASL user likely has for a mobile phone that offers video communication; making cell phone calls in their preferred language is currently unavailable for only this group of participants.

This phenomenon is confirmed by applying ANOVA to the subjective usability ratings. Similar to the results for intelligibility, the participant's preferred language is a significant effect and those preferring ASL responded significantly higher to the usability question, emphasizing their increased desire for such a technology. In order to eliminate this bias, the subjective intelligibility scores are converted to z-scores, which has the desired consequence of removing information about between subject differences [START_REF] Van Dijk | Subjective quality assessment of compressed images[END_REF]. In this experimental database, the use of z-scores is justified by a thorough analysis of the raw subjective ratings and z-scores necessarily remove a clear bias in a portion of participants. The z-scored intelligibility ratings are used for all further analysis.

Ranking encoders according to intelligibility

The ANOVA identifies a significant effect for the encoding algorithm (F (3, 206) = 3.90, p < 0.01) and encoding bitrate (F (1, 206) = 31.46, p < 0.01). For the high bitrate videos, there is no statistical difference in intelligibility between the x264, foveated, and spatialtemporal ROI encoding algorithms. The mean intelligibility z-scores for these encoders, presented in Table 1, correspond on average to raw intelligibility scores between "easy to understand" and "very easy to understand". Both the x264 encoder and the foveated encoder yield statistically significantly higher intelligibility than the spatial ROI encoder. The reduced performance of the spatial ROI Table 1. Mean and standard deviation for z-scored intelligibility ratings. Each average is computed over 32 individual ratings. A rating of "very difficult to understand" maps to an average z-score of -1.18 while a rating of "very easy to understand" maps to an average z-score of 1.13. In the high bitrate case, the x264, foveated, and temporally smoothed ROI encoders have statistically equivalent mean intelligibility scores. In the low bitrate case, the ASL-specific encoders result in statistically significantly higher intelligibility than the x264 encoder.

Bitrate At low bitrates, all three of the ASL-specific encoding algorithms provide statistically significant improvements over x264 in mean intelligibility scores. The differences in intelligibility between the three ASL-specific encoders are not statistically significant, each having mean intelligibility z-scores corresponding to raw intelligibility ratings between "neither easy nor difficult" and "easy to understand". The mean intelligibility z-scores are provided in Table 1. The subjective experiment demonstrates that encoding algorithms designed specifically for ASL can provide statistically significant improvements in intelligibility over traditional, MSE-based encoding algorithms and can generate intelligible ASL video at bitrates as low as 30 kbps. More importantly, the experimental database affords a detailed analysis of distortions that adequately challenge objective estimators.

INFLUENCE OF SPACE AND TIME VARYING DISTORTIONS ON OBJECTIVE ESTIMATOR PERFORMANCE

While subjective testing is the most accurate method for evaluating distorted video, it is prohibitively costly. Objective estimators are desirable and are evaluated in terms of their ability to predict accurately subjective experimental data. The range of video content and distortion artifacts that occur in an experimental data set can bias conclusions regarding the performance of an objective estimator. In the context of objective intelligibility estimators, it is critical for the subjective test database to challenge the estimators by selecting source videos that vary in brightness and contrast and by applying distortions that vary non-uniformly both spatially, e.g., between the signer and the background, and temporally. This section analyzes the performance of 4 objective estimators on different subsets of the experimental data and demonstrates how the videos and distortions present can bias the conclusions made regarding an objective estimator. Four objective estimators are considered for predicting intelligibility: PSNR, RMS distortion contrast, and an objective intelligibility measure (OIM), with and without appropriate temporal pooling [START_REF] Ciaramello | Quantifying the effect of disruptions to temporal coherence on the intelligibility of compressed American Sign Language video[END_REF]. For a video sequence, both PSNR and RMS distortion contrast are computed in each individual video frame and averaged across all frames. The OIM applies a region-based spatial pooling mechanism that allows for varying importance to be placed on the ROIs contained in sign language video and a temporal pooling mechanism that accounts for the temporal variations in distortions. The spatial only OIM includes only the region-based pooling mechanism.

The performance of an objective estimator is computed in terms of its prediction accuracy and linearity. For a given estimator, a linear fit is applied to map the objective estimate to the subjective ratings. Prediction linearity is measured using Pearson's linear correlation, R, and prediction accuracy is measured using the root mean squared error (RMSE) of the prediction residuals, after applying the linear fit. For this analysis, the experimental data is divided into two sets: the videos encoded using x264 and the videos encoded using the ASL-specific encoders. Within each of these 2 subsets, the prediction accuracy and linearity is computed for 3 additional subsets: the indoor and outdoor videos separately and the indoor and outdoor videos combined, resulting in 6 total data subsets. For all of the objective estimators evaluated, there is at least one experimental data set for which the estimator can accurately predict intelligibility.

PSNR performs well on uniform video content. When con-sidering only the x264 coded set and separating the indoor and outdoor videos, PSNR provides an accurate estimate of subjective intelligibility, having low RMSE (0.96 and 0.46 for indoor and outdoor videos) and high linear correlation (0.899 and 0.980 for indoor and outdoor videos) similar to both RMS distortion contrast and the OIM, as illustrated by Table 2. One way in which energy-based error measures, such as PSNR, fail as objective estimators is with test videos containing varying brightness, because brighter videos yield higher MSE values at perceptually similar levels of distortion. Combining the indoor and outdoor videos into a single data set reveals the inability of PSNR to compare distortions across videos of varying contrast. The RMSE increases to 2.18 and the linear correlation decreases to R = 0.094, demonstrating that PSNR is virtually uncorrelated with the subjective intelligibility ratings when combining both indoor and outdoor video sets. Because it computes errors in contrast and not raw pixel values, RMS distortion contrast performs significantly better than PSNR on the combined data set, having an RMSE of 1.46 and correlation of R = 0.743. RMS distortion contrast performs well for spatially and temporally uniform distortions. distortion contrast provides an accurate estimate of subjective intelligibility for videos without spatially varying distortions, but fails to estimate intelligibility for ASL coded videos, as illustrated by Table 2. The OIM is the most accurate of the 3 objective estimators on the ASL coded set, having an RMSE of 1.23 and linear correlation of R = 0.569. The low correlation is primarily due to the difficulty in estimating intelligibility for the indoor videos. When comparing the ASL coded indoor and outdoor videos separately, the OIM performs well on the outdoor set, having RMSE equal to 0.93 and linear correlation of R = 0.785.

When the test data set includes only distortion artifacts resulting from compression, RMS distortion contrast and the OIM perform similarly and one could incorrectly conclude that applying knowledge of the ROI provides no benefit to an objective estimator. This behavior can be explained by the relationship between the global distortion and the region distortions. For simplicity in computation and discussion, MSE is used as the distortion measure in this comparison. For two sample videos (one indoor, one outdoor), the global MSE and the MSE in the face and hand regions are computed separately in each video frame, providing 3 vectors of per-frame MSEs having length equal to the number of frames. The correlation between the global MSE and each of the region MSEs is computed and presented in Table 3.

For videos coded using x264, which contain only compression artifacts, the global MSE is highly correlated with each of the region MSEs, having RF ace = 0.875, R Hand = 0.837 for indoor videos and RF ace = 0.775, R Hand = 0.711 for outdoor videos. Because of this, measuring distortion globally serves as an accurate predictor of the local distortions, which explains the high performance of RMS distortion contrast on just x264 coded videos. As a result of the high correlation, simply computing the global mean of the distortions can serve as a surrogate for perceptually valid region-based pooling. Knowing that an observer is extracting information from specific regions (e.g. face and hands) provides little improvement in prediction if the video is encoded without any region of interest approach. For videos encoded using the ASL-specific techniques, the distortions are very localized and global distortions are not correlated with the region distortions, having RF ace = 0.028, R Hand = -0.157 for indoor videos and RF ace = -0.154, R Hand = 0.004 for outdoor videos, coded using the spatial-temporal ROI encoder. In these ROI coded video cases, RMS distortion contrast fails to accurately estimate intelligibility. Objective estimators that incorporate regionbased pooling, such as the OIM, are required to differentiate between OIM performs well for spatially and temporally varying distortions. When the average distortion in a single frame is highly correlated with local distortions, the spatial mechanism has little impact on the performance of a particular objective estimator. Similarly for temporal pooling, advanced pooling mechanisms are unlikely to improve the objective estimate when the distortions do not vary across frames. The temporal variation of the distortions in a sequence can be quantified by a measure based on between frame difference in distortions [START_REF] Ninassi | Considering temporal variations of spatial visual distortions in video quality assessment[END_REF]. Videos in which amount of distortion varies significantly between will yield a high measure of temporal variation. The outdoor video sequences coded using either of the ROI encoders have the largest measured temporal variation, having average temporal variation of T V = 250.65, while the indoor video sequences and the x264 coded sequences have very low temporal variation, having average temporal variation of 7.98, as in Table 3. When the temporal variation is low, as is the case with the x264 coded videos, advanced temporal pooling provides negligible improvement over a simple global average in terms of the prediction accuracy. In this case, the spatial only OIM performs similarly to the full spatiotemporal OIM, as illustrated in Table 2. However, when comparing the ASL coded outdoor data subset, which has the highest temporal variation, the spatial OIM, having RMSE of 1.24 and R = 0.563, performs significantly worse than the spatiotemporal OIM, having RMSE of 0.93 and R 0.785.

CONCLUSION

Depending on the presence of varying video content and the homogeneity of the spatial and temporal distortions, several possible conclusions regarding the performance of objective intelligibility estimators can be incorrectly reached. Four objective estimators were evaluated in terms of their subjective intelligibility prediction accuracy. For each of the tested estimators, there exists a subset of videos on which the estimator can accurately predict subjective intelligibility. If the distortions present in a test set do not contain spatially or temporally localized errors, objective estimators that incorporate an ROI pooling mechanism cannot reliably improve the estimation accuracy, even in cases such as ASL video, when an ROI is unequivocally known to exist. This highlights the importance of both designing a diverse experimental data set and verifying that a proposed objective estimator is adequately challenged by the experimental data set on which it is tested.

In future work, the methodology of analyzing a subjective experimental database will be extended to other image and video quality databases. In the domain of quality assessment, many techniques have been proposed for improving objective quality estimators by incorporating visual attention data [START_REF]Does where you gaze on an image affect your perception of quality? Applying visual attention to image quality metric[END_REF][START_REF] Engelke | Framework for optimal region of interest-based quality assessment in wireless imaging[END_REF]. Typically this is done by applying a spatially-varying weight to the errors prior to spatial pooling, wherein the weights are proportional to the relative importance of each region or pixel. Care must be taken to ensure that the distortions present in the subjective database effectively challenge the objective estimators. As demonstrated by this work, compression artifacts alone are insufficient for evaluating region-based pooling mechanisms.

Table 2 .

 2 Objective estimator performance comparison. PSNR performs well for x264 coded videos at a single location, but fails to predict intelligibility when the locations are combined. RMS distortion contrast can predict intelligibility across the combined locations, but only for the compression artifacts.

			The objective intelligibility
	measure (OIM) offers improvements over both PSNR and RMS dis-
	tortion contrast for videos containing spatially varying distortions.
	For the outdoor videos containing temporally varying distortions, the
	spatiotemporal OIM outperforms the spatial only OIM.
	Source Videos	Measure	Data Set	RMSE	R
			Indoor	0.96	0.899
		PSNR	Outdoor	0.46	0.980
	x264 Coded	RMS	Combined Indoor	2.18 1.01	0.094 0.886
		Distortion	Outdoor	0.98	0.908
	Spatially	Contrast	Combined	1.46	0.743
	Uniform	OIM	Indoor	1.01	0.886
	Distortions	Spatial	Outdoor	0.68	0.956
		Only	Combined	1.14	0.853
			Indoor	0.98	0.894
		OIM	Outdoor	0.63	0.964
			Combined	1.06	0.875
			Indoor	1.54	0.090
		PSNR	Outdoor	1.15	0.638
	ASL Coded	RMS	Combined Indoor	1.49 1.53	0.056 0.141
		Distortion	Outdoor	1.09	0.688
	Spatially	Contrast	Combined	1.47	0.190
	Varying	OIM	Indoor	1.34	0.499
	Distortions	Spatial	Outdoor	1.24	0.563
		Only	Combined	1.29	0.509
			Indoor	1.36	0.480
		OIM	Outdoor	0.93	0.785
			Combined	1.23	0.569

Table 3 .

 3 Comparison of spatial and temporal variations in distortions. Correlation between global MSE and MSE in face and hand regions is given by RF ace and R Hand , respectively. When considering only compression artifacts, such as those resulting from x264, the global MSE is highly correlated with distortion in the ROI. When the distortions vary spatially, global MSE and the ROI distortions are uncorrelated and a global distortion measure is unable to predict accurately the distortion in the ROI. T V measures the temporal variation of the distortions. Temporal distortions are relatively uniform for the indoor videos but vary substantially for the outdoor videos coded using the ROI encoders.

	Location	Encoding Algorithm	RF ace R Hand	T V
		x264	0.875	0.837	3.5
	Indoor	Foveated Spatial-Temporal ROI	0.261 0.028	0.714 -0.157	5.0 9.7
		Spatial ROI	0.069	-0.066	12.3
		x264	0.775	0.711	9.0
	Outdoor	Foveated Spatial-Temporal ROI -0.154 0.166	-0.001 0.004	8.4 233.1
		Spatial ROI	-0.096	0.042	268.2
	distortions in the background and in the signer.

Proc. IEEE International Conference on Image Processing (ICIP),Sept. 2010


Michail Nomikos

Khalil Elgmati

Maria Theodoridou

Athena Georgilis

Raul Gonzalez-Garcia

George Nounesis

Karl Swann

F Anthony Lai
email: lait@cf.ac.uk

Novel regulation of PLCζ activity via its XY-linker

Keywords: phospholipase C, PLC, phospholipase C-zeta, PLCζ, XY-linker, XYl, phosphatidylinositol 4,5-bisphosphate, PIP 2, inositol 1 device, CCD, human chorionic gonadotrophin, hCG, glutathione-Stransferase, GST phospholipase C zeta, enzyme regulation, calcium oscillations, egg activation, fertilization

4,5-trisphosphate, IP 3 ; open reading frame, ORF; charge-coupled

INTRODUCTION

The activation of a mammalian egg by a fertilizing sperm is effected by a characteristic series of cytoplasmic Ca 2+ oscillations following sperm-egg fusion. This fundamental activation event provides the stimulus for the initiation of embryo development [START_REF] Miyazaki | Essential role of the inositol 1,4,5trisphosphate receptor/Ca2+ release channel in Ca2+ waves and Ca2+ oscillations at fertilization of mammalian eggs[END_REF][START_REF] Stricker | Comparative biology of calcium signaling during fertilization and egg activation in animals[END_REF]. A sperm-specific phospholipase C isoform, PLC-zeta (PLC), is widely considered to be the physiological stimulus that triggers these intracellular Ca 2+ oscillations at fertilization [START_REF] Saunders | PLC zeta: a sperm-specific trigger of Ca(2+) oscillations in eggs and embryo development[END_REF][START_REF] Cox | Sperm phospholipase Czeta from humans and cynomolgus monkeys triggers Ca2+ oscillations, activation and development of mouse oocytes[END_REF][START_REF] Kouchi | Recombinant phospholipase Czeta has high Ca2+ sensitivity and induces Ca2+ oscillations in mouse eggs[END_REF][START_REF] Knott | Transgenic RNA interference reveals role for mouse sperm phospholipase Czeta in triggering Ca2+ oscillations during fertilization[END_REF][START_REF] Yoon | Human sperm devoid of PLC, zeta 1 fail to induce Ca(2+) release and are unable to initiate the first step of embryo development[END_REF]. Sperm-delivered PLC is responsible for catalysing phosphatidylinositol 4,5-bisphosphate (PIP 2 ) hydrolysis within the fertilized egg to stimulate the inositol 1,4,5-trisphosphate (IP 3 ) signaling pathway leading to Ca 2+ oscillations [START_REF] Swann | PLCzeta(zeta): a sperm protein that triggers Ca2+ oscillations and egg activation in mammals[END_REF][START_REF] Saunders | PLCzeta, a sperm-specific PLC and its potential role in fertilization[END_REF]. The phosphoinositide-specific PLC family comprises thirteen isozymes grouped into six different subfamilies (, , , , , ), each activated by different stimuli to catalyze PIP 2 hydrolysis yielding IP 3 , which in turn mediates intracellular Ca 2+ release. All known mammalian PLCs possess homologous X and Y catalytic domains separated by a charged XY-linker (XYl) region. Likewise, all isoforms have four tandem EF hand domains and a single C2 domain that flank the core X and Y domains, respectively [10].

Notably, the sperm-specific PLC is unique in displaying a positively-charged XYl region whereas in the somatic cell PLC,  and  isoforms, this region is negatively-charged. Recently, the XYl within PLC,  and  was shown to specifically mediate auto-inhibition of PIP 2 hydrolytic activity, suggesting that the negatively-charged residues of the XYl directly prevent access of PIP 2 to the enzyme active site via steric exclusion and electrostatic repulsion of the negatively-charged PIP 2 substrate [11]. The PLC XYl, which comprises additional regulatory domains including two SH2 domains and an SH3 domain, regulates PLC via tyrosine phosphorylation [START_REF] Ozdener | Activation of phospholipase Cgamma2 by tyrosine phosphorylation[END_REF][START_REF] Sekiya | Mechanism of tyrosine phosphorylation and activation of phospholipase C-gamma 1. Tyrosine 783 phosphorylation is not sufficient for lipase activation[END_REF]. Identification of the critical determinant for PLC inhibition at one of the SH2 domains has led to a proposed general mechanism of PLC auto-inhibition mediated by the XYl region [START_REF] Gresset | Mechanism of phosphorylation-induced activation of phospholipase C-gamma isozymes[END_REF].

The molecular mechanisms involved in physiological regulation of sperm PLC activity, which plays a crucial role in mammalian fertilization, remain unknown. To examine whether the XYl-mediated auto-inhibition observed in somatic cell PLC isoforms also applies to PLC activity regulation, we specifically removed this unique PLC XYl region and monitored consequent changes in the in vivo Ca 2+ oscillation-inducing and in vitro PIP 2 hydrolysis activity relative to the wild-type sperm PLC. For comparative analysis, we also generated the corresponding XYl deletion within PLC1, as well as a chimaeric PLC construct, in which the last 12 amino acids from the XYl region (residues 374-385) were replaced with those of PLC1 (residues 480-491). Our studies show that in contrast to somatic cell PLCs, the XYl of PLC does not confer enzymatic auto-inhibition, indicating a disparate regulatory mechanism may apply to this distinctive, gamete-specific PLC isozyme.

MATERIALS AND METHODS

Plasmid construction and cRNA synthesis

To prepare the PLCζ XYl-deletion construct, mouse PLCζ 1-307 (GenBank #AF435950) was amplified by PCR, using Phusion polymerase (Finnzymes) using appropriate primers to incorporate a 5'-KpnI and 3'-EcoRI site to generate pCR3-PLCζ 1-307 . Similarly, PLCζ 386-647 with a 5' EcoRI site and a 3' primer that ablated the stop codon to create a NotI site, was cloned into the pCR3-PLCζ 1-307 to generate pCR3-PLC 1-307/386-647 . The luciferase ORF amplified from pGL2 (Promega) to incorporate flanking NotI sites was then cloned into the NotI site of pCR3-PLC 1-307/386-647 to generate PLC 1-307/386-647 -luciferase. The PLC 1-307/386-647 was further amplified from pCR3-PLC 1- 307/386-647 to incorporate a 5'-SalI and 3'-NotI site and subcloned into a modified pET vector (pETMM30) to enable bacterial expression.

Rat PLC1 (GenBank #M20637) with a 5'-SalI site and a 3'-NotI site was cloned into pGEX-5X2. To generate pCR3-PLC1-luciferase, PLC1 amplified from pGEX-5X-2-PLC1 to incorporate a 5'-EcoRV and 3'-NotI site and cloned into pCR3, was ligated in-frame with luciferase containing 5'-NotI and 3'-NotI sites. To prepare the PLC1 XYl-deletion construct, pCR3-PLC1 1- 440/491-756 -luciferase, PLC1 1-440 with a 5'-EcoRI and 3'-EcoRV site cloned into pCR3 was ligated inframe to PLC1 491-756 with a 5'-EcoRV site and a 3'-NotI site. Luciferase was then inserted via the NotI site of pCR3-PLC1 1-440/491-756 . The PLC1 1-440/491-756 , via the 5'-SalI and 3'-NotI sites was further subcloned into pETMM30 for bacterial expression.

The PLC/XYlδ1 480-491 chimaeric construct was prepared using a long primer strategy that utilised primers comprising nucleotides corresponding to XYl residues 480-491 of PLCδ1. These primers also contained a short sequence from the XYl region of PLC. Amplification of the two halves of PLC with these long primers enabled replacement of the PLC XYl residues 374-385 (KKRKRKMKIAMA) with the corresponding PLCδ1 XYl residues 480-491 (KPKEDKLKLVPE) to be achieved. Four silent mutations in the PLCδ1 XYl sequence were introduced to circumvent nonspecific annealing of the primers. The PLC/XYlδ1 pCR XL TOPO and then subcloned into pCR3. The luciferase ORF amplified from pGL2 as above was then ligated in-frame into the NotI site of pCR3-PLC/XYlδ1 480-491 to generate PLC/XYlδ1 480- 491 -luciferase. The PLC/XYlδ1 480-491 was further amplified from pCR3-PLC/XYlδ1 480-491 to incorporate a 5'-SalI and 3'-NotI site and subcloned into a modified pET vector (pETMM30) to enable bacterial expression.

Following linearization of wild-type, XYl-excised and chimaeric PLC plasmids, cRNA was synthesized using mMessage Machine T7 kit (Ambion) and the poly(A) tailing kit (Ambion), as per the manufacturer's instructions.

Preparation and handling of gametes

Experiments were carried out with mouse eggs in Hepes-buffered saline (H-KSOM) as described previously [START_REF] Saunders | PLC zeta: a sperm-specific trigger of Ca(2+) oscillations in eggs and embryo development[END_REF][START_REF] Cox | Sperm phospholipase Czeta from humans and cynomolgus monkeys triggers Ca2+ oscillations, activation and development of mouse oocytes[END_REF]. Female mice were superovulated by injection of human chorionic gonadotrophin (hCG; Intervet). Eggs were collected 13.5-14.5 h later and maintained in 100 μl H-KSOM under mineral oil at 37 °C. Egg microinjection was carried out 14.5-15.5 h after hCG administration [START_REF] Swann | Use of luciferase chimaera to monitor PLCzeta expression in mouse eggs[END_REF].

Microinjection and measurement of intracellular Ca 2+ and luciferase expression

Mouse eggs were microinjected with cRNA encoding the particular PLC(s) mixed with an equal volume of 1 mM Oregon Green BAPTA-dextran (Molecular Probes) in injection buffer (120 mM KCl, 20 mM Hepes, pH 7.4). All injections were 3-5 % of the egg volume. Eggs were then maintained in H-KSOM containing 100 μM luciferin and imaged on a Nikon TE2000 microscope equipped with a cooled intensified-CCD camera (Photek Ltd, UK). Ca 2+ was monitored for 4 h after injection by measuring Oregon Green BAPTA-dextran fluorescence with low-level excitation light from a halogen lamp. Luminescence was measured with the same camera alongside fluorescence by switching, every 10 seconds, between light collection in the presence and the absence of excitation light. Fluorescence signals were 10-100 times that for luminescence. The luminescence, measured as the light emission in the absence of excitation light, was quantitatively converted into luciferase protein using a standard luminescence calibration curve generated by microinjection of eggs with known amounts of luciferase protein (Sigma) [START_REF] Swann | Use of luciferase chimaera to monitor PLCzeta expression in mouse eggs[END_REF]17].

Protein expression and purification

For GST-PLC fusion protein expression, E.coli (Rosetta (DE3), Novagen) transformed with the appropriate plasmid, was cultured at 37 °C until A 600 of 0.6 then protein expression induced for 18 h, 16°C with 0.1 mM isopropyl β-d-thiogalactopyranoside (Promega). Cells were centrifuged at 6000 × g for 10 min, resuspended in phosphate-buffered saline (PBS: 137 mM NaCl, 2.7 mM KCl, 4.3 mM Na 2 HPO 4 •7H 2 O, 1.4 mM KH 2 PO 4 , pH 7.4) containing 2 mM dithiothreitol and protease inhibitor mixture (Roche) then sonicated 4 x 15 s on ice. After centrifugation at 15,000 × g, 15 min, 4 °C, soluble GST-PLC fusion proteins were purified by affinity chromatography using glutathione-Sepharose™ 4B following standard procedures (GE Healthcare). Eluted proteins were dialyzed overnight (Pierce; SnakeSkin 10,000 MWCO) at 4 °C in 4 litres of PBS, and concentrated with centrifugal concentrators (Sartorius, 10,000 MWCO).

PLC activity assay, PAGE and Western blotting

PIP 2 hydrolytic activity of PLC constructs was assayed as described previously [17]. The assay mixture final volume was 50 μl containing 100 mM NaCl, 0.4% sodium cholate (w/v), 2 mM CaCl 2 , 4 mM EGTA, 20 μg of bovine serum albumin, 5 mM 2-mercaptoethanol, and 20 mM Tris-HCl buffer, pH 6.8. The PIP 2 concentration in the reaction mixture was 220 μM, containing 0.05 μCi of [ 3 H]PIP 2 . Assay conditions were optimized for linearity, requiring a 10 min, 25 °C incubation with 20 pmol protein. Recombinant proteins were separated by SDS-PAGE and immunoblot analysis performed as described previously [START_REF] Nomikos | Male infertility-linked point mutation disrupts the Ca2+ oscillation-inducing and PIP(2) hydrolysis activity of sperm PLCzeta[END_REF]. Proteins were probed with anti-GST polyclonal antibody (1:10,000 dilution).

RESULTS

To understand the regulatory role of the short linker region separating the catalytic X and Y domains, the XYl of both PLC (308-385aa) and PLC1 (441-490aa) were excised from the wild-type PLCs to create the XYl-deletion constructs, PLC XYl and PLC1 XYl , respectively (Fig. 1). The PLC XYl notably contains a unique cluster of basic residues that may be involved in enzyme function [START_REF] Swann | PLCzeta(zeta): a sperm protein that triggers Ca2+ oscillations and egg activation in mammals[END_REF][START_REF] Saunders | PLCzeta, a sperm-specific PLC and its potential role in fertilization[END_REF]. To further examine the potential role of this short, positively-charged XYl segment in regulation of PLC activity, a chimaeric PLC construct was prepared in which these 12 amino acids of PLC (aa374-385, KKRKRKMKIAMA; +7 charged residues) were replaced with the corresponding stretch from PLC1 (aa480-491, KPKEDKLKLVPE; +4/-3 charged residues), generating PLC/XYlδ1 480-491 (Fig. 1). The XYl-deletion and chimaeric constructs, along with the corresponding wild-type PLCs, were each tagged at the C-terminus with luciferase to enable realtime monitoring of relative protein expression by luminescence quantitation [START_REF] Swann | Use of luciferase chimaera to monitor PLCzeta expression in mouse eggs[END_REF]. Consistent with previous reports [17,20], prominent Ca 2+ oscillations (25 spikes/2h) are observed in unfertilized mouse eggs microinjected with PLCζ cRNA (Fig. 2), with the first Ca 2+ spike appearing at a luminescence of 0.52 counts per second (cps) for the expressed PLC-luciferase fusion protein (Table 1). In contrast, microinjecting cRNA encoding the XYl-deletion construct, PLCζ XYl , produces Ca 2+ oscillations in mouse eggs with a significantly lower frequency (3.4 spikes/2h) relative to PLCζ, and with the first Ca 2+ spike only appearing after luminescence had reached 3.6 cps. Similarly, microinjection of cRNA corresponding to the XYl chimaera, PLC/XYlδ1 480-491 , also triggered relatively low frequency Ca 2+ oscillations (5.3 spikes/2h) with the first Ca 2+ spike appearing at a luminescence of 4.0 cps (Fig. 2; Table 1).

Microinjection of PLC1 cRNA into mouse eggs caused very low frequency Ca 2+ oscillations (1.8 spikes/2h) that commenced only when the PLC1-luciferase protein expression produced a luminescence value of 20.4 cps. However, the PLC1 XYl deletion construct cRNA effected a 2 fold increase in Ca 2+ oscillation frequency (3.3 spikes/2h) compared to PLC1, with the first Ca 2+ spike manifest at a luminescence of 17.2 cps. These mouse egg microinjection results show that absence of the PLC XYl region dramatically attenuates Ca 2+ oscillation-inducing activity (Fig. 2), yielding a 7fold reduction in spike frequency (25 versus 3.4 spikes/2h) and requiring a 7-fold increased level of PLCζ XYl expression (3.6 versus 0.52 cps) to initiate the first Ca 2+ spike (Table 1). In addition, replacing the cluster of basic residues in the PLC XYl (7 of 12 residues are positively-charged, overall +7) with the corresponding amino acids from the XYl of PLC1 (4 +ve, 3 -ve residues; overall +1), also dramatically reduces by 5-fold the Ca 2+ oscillation-inducing activity of PLCζ with requirement for an 8-fold increased level of PLC/XYlδ1 480-491 expression to initiate the first spike compared to wild type PLC (4.0 versus 0.52 cps). Conversely, the XYl deletion from PLC1 increased its Ca 2+ oscillation-inducing activity in mouse eggs with a doubling of the Ca 2+ spike frequency (3.3 versus 1.8 spikes/2h).

The effect of removing or replacing part of the XYl on the in vitro PIP 2 hydrolysis activity of PLC, PLC1, PLC XYl , PLC1 XYl and PLC/XYlδ1 480-491 constructs was examined following their expression in bacteria and purification as GST-fusion proteins. Figure 3A shows the affinitypurified fusion proteins displayed the predicted molecular masses for GST-PLCζ, GST-PLC XYl , GST-PLC1 ,GST-PLC1 XYl and PLC/XYlδ1 480-491 recombinant proteins of 100, 94, 111, 107 and 102 kDa, respectively, as also confirmed by immunoblot analysis with anti-GST antibody. The specific PIP 2 hydrolytic enzyme activity values obtained for each protein (Fig. 3B) reveals a 30% reduction in PLC XYl enzyme activity relative to PLC (30258 vs 42551 nmol/min/mg), and a 20% reduction in the chimaera PLC/XYlδ1 480-491 enzyme activity (34238 vs 42551 nmol/min/mg), indicating the presence of the XYl region and the highly positively-charged cluster are required for maximal PLC activity. In contrast, PLC1 XYl displayed a 2.3-fold increase in enzymatic activity compared to PLC1 (286554 vs 124940 nmol/min/mg). These differential results for XYl-deleted PLCs suggest that there are disparate regulatory roles for the XYl of PLC1 and PLC with respect to enzyme hydrolytic activity. Calculation of the Michaelis-Menten constant, Km, for these proteins yielded comparable values for PLC1 (93 M) and PLC1 XYl (63 M). However, for PLC XYl (3936 M) the Km was 36-fold higher than that of PLC (110 M) (Table 2), indicating that deletion of the XYl has a major effect by dramatically reducing the in vitro affinity of PLC for the PIP 2 substrate. Similarly, the Km value for the XYl chimaeric protein (1909 M) was 17-fold higher than that of PLC (Table 2), highlighting the importance of the cluster of basic residues in the XYl region of PLC for the in vitro affinity of this enzyme for PIP 2 .

Further, the impact of XYl deletion or replacement on the relative Ca 2+ sensitivity of PLC and PLC1 enzyme activity [START_REF] Kouchi | Recombinant phospholipase Czeta has high Ca2+ sensitivity and induces Ca2+ oscillations in mouse eggs[END_REF]17,[START_REF] Kouchi | The role of EF-hand domains and C2 domain in regulation of enzymatic activity of phospholipase Czeta[END_REF] was determined at Ca 2+ concentrations ranging from 0.1 nM to 0.1 mM. The resulting EC 50 value obtained for PLC was near identical to the corresponding XYltruncated protein (91 nM vs 84 nM) and the XYl-chimaeric protein (91 nM vs 76 nM) (Fig. 3C, Table 2). Likewise, removing the XYl from PLC1 marginally altered the EC 50 value from 6.3 to 7.0 M. These results suggest that loss of the XYl or replacement of the cluster of basic residues in this region does not significantly alter the Ca 2+ sensitivity of PIP 2 hydrolysis for both PLC and PLC1.

DISCUSSION

Although the precise regulatory mechanism remains unclear, PLC has become established as the primary sperm-derived candidate factor that activates the egg at mammalian fertilization. Upon sperm-egg fusion, PLC is proposed to be delivered by the sperm into the ooplasm and catalyses PIP 2 hydrolysis to generate IP 3 , which induces the cytoplasmic Ca 2+ oscillations that initiate embryo development. Sperm-specific PLC is the smallest mammalian PLC isoform with the most elementary domain organization and it is the only one not found in somatic cells [START_REF] Saunders | PLC zeta: a sperm-specific trigger of Ca(2+) oscillations in eggs and embryo development[END_REF]. PLC is most structurally similar to PLC1 with the notable exception that it lacks a PH domain at the Nterminus (Fig. 1). One further important and unique functional feature of PLC is the relatively low Ca 2+ concentration (nanomolar) required for enzymatic activity, exhibiting ~100-fold higher Ca 2+ sensitivity than PLC1 which requires micromolar Ca 2+ concentration for optimal PIP 2 hydrolysis. Thus, at the basal cytosolic Ca 2+ concentration of 50-80 nM likely present within eggs, the PLC isoform but not PLC1 would be strongly activated. The molecular determinants that confer PLC's high Ca 2+ sensitivity are unknown, although previous studies suggest both EF hand and C2 domains are required for a functional PLC in the egg [17,[START_REF] Kouchi | The role of EF-hand domains and C2 domain in regulation of enzymatic activity of phospholipase Czeta[END_REF].

Another important question that remains unresolved is how PLC activity is intrinsically regulated. Recent structural and biochemical studies have convincingly demonstrated that the XYl region of the PLC, ,  and  isozymes can mediate potent auto-inhibition of enzyme function [11,[START_REF] Gresset | Mechanism of phosphorylation-induced activation of phospholipase C-gamma isozymes[END_REF]. This is consistent with the negatively-charged XYl of these isoforms conferring electrostatic repulsion of the negatively-charged PIP 2 substrate, as well as providing steric hindrance by occluding the enzyme catalytic active site. However, the sperm PLC in this regard is very distinct from somatic PLCs in possessing a positively-charged XYl region. It was therefore important to investigate whether this putative general mechanism of XYl auto-inhibition observed in various somatic PLC isoforms also applies to the sperm-derived PLC.

In the present study, a truncated PLC lacking the XYl region, as well as a chimaeric PLC in which the cluster of basic residues at the C-terminal end of the XYl was replaced by the homologous region of PLC1 were prepared. These two novel PLC constructs enabled the specific examination of how these targeted XYl changes might alter the in vivo Ca 2+ oscillation-inducing and in vitro PIP 2 hydrolysis activity relative to wild-type PLC. Parallel studies were simultaneously performed using the corresponding construct derived from the most closely-related PLC isoform, PLC1. Notably, PLC1 is absent from differentiated spermatids and is not believed to play a role in mammalian fertilization [START_REF] Lee | Molecular cloning and expression analysis of a mouse phospholipase C-delta1[END_REF], but it provides a useful comparative PLC isoform control. The bacterially-expressed and purified PLC1 exhibited a much higher in vitro PIP 2 hydrolytic activity than PLC (Fig. 3B), although the in vivo Ca 2+ oscillation-inducing activity observed for PLC1 in mouse eggs was much lower than that of PLC (Fig. 2). This is consistent with a previous study showing PLC1 was capable of inducing only low frequency Ca 2+ oscillations in mouse eggs, even at a 20-fold higher concentration than PLC [START_REF] Kouchi | Recombinant phospholipase Czeta has high Ca2+ sensitivity and induces Ca2+ oscillations in mouse eggs[END_REF]. Interestingly, deletion of the XYl from PLC1 resulted in a 2-fold increase in Ca 2+ oscillation-inducing activity in eggs (Fig. 2), which correlates with the in vitro PIP 2 hydrolysis assays showing a 2.3-fold increased enzymatic activity relative to wild-type PLC1 (Fig. 3B, Table 1). In contrast, the deletion of XYl from PLC decreased both the in vitro enzymatic activity (Fig. 3B) and the PIP 2 substrate affinity (Table 2), which was consistent with the observed 7-fold reduction in Ca 2+ oscillation-inducing activity in eggs (Table 1). The XYl appears not to be directly involved in Ca 2+ -dependent regulation of enzyme activity, as the Ca 2+ sensitivity of in vitro PIP 2 hydrolysis was essentially unchanged between the wild-type and XYldeleted PLC constructs (Fig. 3C, Table 2). Significantly, replacement of only the PLC XYl cluster of basic residues (overall charge +7) by the homologous twelve amino acids of the XYl region of PLC1 (overall charge +1) also resulted in decrease of both the in vitro enzymatic activity (Fig. 3B) and the PIP 2 substrate affinity (Table 2). These in vitro results are consistent with the observed 5-fold reduction in Ca 2+ oscillation-inducing activity in eggs with this chimaeric PLC (Table 1), whereas the Ca 2+ sensitivity remained comparable to the wild-type enzyme (Fig. 3C, Table 2).

Our findings suggest that the XYl of PLC serves a different regulatory role to that of the XYl in PLC1. A critical determinant for this disparity may be the high density of basic amino acids in the XYl of PLC that is absent from PLC1 and other somatic PLC isoforms. Previously, we have proposed that this unstructured cluster of positively-charged residues at the C-terminal end of the PLC XYl may play a role in facilitating interaction with biological membranes, particularly the negatively-charged substrate, PIP 2 [20,21]. Direct involvement of the XYl positively-charged residues in PIP 2 interaction was recently examined by sequentially substituting three XYl lysine residues, K374, K375 and K377, for alanine to produce single (K374A), double (K374,5AA) and triple (K374,5,7AAA) substitutions [21]. The Ca 2+ oscillation-inducing activity in mouse eggs, PIP 2 binding and enzymatic hydrolysis measurements of these K-A mutants revealed that the cumulative reduction of the PLCζ XYl net positive charge progressively abated both the in vivo Ca 2+ oscillations and in vitro PIP 2 interaction/enzyme function of mouse PLCζ [21]. These results indicate that the XYl cluster of positively-charged residues may perform a central role in the interaction of PLCζ with the substrate, PIP 2 [20,21]. Such a proposed role for the XYl of PLCζ in PIP 2 binding is entirely consistent with the present study in which excision of the complete XYl or exchanging a discrete XYl segment, and thereby removing the entire cluster of basic residues, causes significant diminution of both PLCζ functional properties and PIP 2 interaction without altering Ca 2+ sensitivity.

Although the specific amino acid sequence of the XYl in PLC is poorly conserved across species, the presence of positively-charged residues is a common feature of the PLC sequences currently available [START_REF] Swann | PLCzeta(zeta): a sperm protein that triggers Ca2+ oscillations and egg activation in mammals[END_REF][START_REF] Saunders | PLCzeta, a sperm-specific PLC and its potential role in fertilization[END_REF]. The significance of this sequence diversity, albeit with charge conservation, might explain the different rates of PIP 2 hydrolysis observed for PLC isoforms from different species and thus the species-specific frequency of sperm-induced Ca 2+ oscillations observed in the eggs of different mammals [START_REF] Saunders | PLCzeta, a sperm-specific PLC and its potential role in fertilization[END_REF]. Interestingly, a study of bovine PLC has found that it remains functionally active even after proteolytic cleavage occurs specifically within the XYl region [22]. Further investigation is required to delineate the precise molecular mechanism of action of the various PLC domains and this may lead to important implications in the therapeutic approach to PLC-mediated male infertility [START_REF] Nomikos | Male infertility-linked point mutation disrupts the Ca2+ oscillation-inducing and PIP(2) hydrolysis activity of sperm PLCzeta[END_REF]. Fluorescence and luminescence recordings reporting the Ca 2+ changes (red traces; Fluorescence, arbitrary units (a.u.)) and luciferase expression (black traces; Luminescence, counts per second (cps)), respectively, in unfertilized mouse eggs following microinjection of cRNA encoding luciferase-tagged PLCζ, PLC1, their corresponding XY-linker deletions and the PLC/XYlinker1 chimaera (left panels). Panels on the right show the integrated luminescence image of a field of mouse eggs following cRNA microinjection of each PLC construct (see Table 1).

Figure 3 Expression, purification and enzyme activity of PLC and XY-linker/chimaera proteins

(A) Glutathione affinity-purified GST-PLC fusion protein (1 μg) was analyzed by 8% SDS-PAGE followed by either Coomassie Brilliant Blue staining (left panel) or immunoblot analysis using anti-GST antibody (middle panel). Lanes 1-4 show PLCζ, PLC XYl , PLC1 and PLC1 XYl , respectively. The pair of single lane panels on the right shows Coomassie gel and immunoblot analysis of the PLC/XYlinker1 chimaera. (B) PIP 2 hydrolysis enzyme activity assay of PLC, PLC1 their XY-linker deletions and chimaera (20 pmol) obtained with the standard [ 3 H]PIP 2 cleavage assay, n 3 ±S.E., using two different preparations of recombinant protein and with each experiment performed in duplicate. (C) Effect of varying [Ca 2+ ] on the normalized activity of PLC, PLC1 and their XY-linker deletions and chimaera. For these assays n = 2 ± S.E., using two different batches of recombinant proteins and with each experiment performed in duplicate (see Table 2).

TABLE LEGENDS Table 1 Properties of PLC-luciferase and deletion/chimaera constructs expressed in mouse eggs

Ca 2+ oscillation-inducing activity (Ca 2+ spike number in 2 hours) and luciferase luminescence levels (Peak luminescence; Luminescence at 1 st spike) are summarized for mouse eggs microinjected with each of the PLC-luciferase constructs, PLCζ, PLCζ XYl , PLC1, PLC1 XYl and PLCζ XYl1 (see Fig. 2). Each egg was microinjected with a pipette cRNA concentration of 1.6 g/l. The data are expressed to 2 significant figures, with means ± s.e.m.

Table 2 [ 3 H]PIP 2 hydrolysis activity and Km of purified GST-PLC fusion proteins

Specific enzyme activity values obtained for the various GST-PLC fusion proteins showing the EC 50 of Ca 2+ -dependent enzyme activity and the Michaelis-Menten constant, Km, determined by nonlinear regression analysis (GraphPad, Prism 5) for the GST-fusion proteins PLCζ, PLCζ XYl , PLC1, PLC1 XYl and PLCζ XYl1 (see Fig. 3C).

20

  Nomikos, M., Mulgrew-Nesbitt, A., Pallavi, P., Mihalyne, G., Zaitseva, I., Swann, K., Lai, F.A., Murray, D. and McLaughlin, S. (2007) Binding of phosphoinositide-specific phospholipase C-zeta (PLC-zeta) to phospholipid membranes: potential role of an unstructured cluster of basic residues. J. Biol. Chem. 282: 16644-16653 21 Nomikos, M., Elgmati, K., Theodoridou, M., Nounesis, G., Swann, K. and Lai, F.A. (2011) Phospholipase Cζ binding to PtdIns(4,5)P 2 requires the XY-linker region. J Cell Sci. (in the press) 22 Kurokawa, M., Yoon, S.Y., Alfandari, D., Fukami, K., Sato, K. and Fissore, R.A. (2007) Proteolytic processing of phospholipase Czeta and [Ca2+]i oscillations during mammalian fertilization. Dev. Biol. 312: 407-418 Biochemical Journal Immediate Publication. Published on 18 Jul 2011 as manuscript BJ20110953 THIS IS NOT THE VERSION OF RECORD -see doi:10.1042/BJ20110953A c c e p t e d M a n u s c r i p t Licenced copy. Copying is not permitted, except with prior permission and as allowed by law.

Figure 1

 1 Figure 1 Domain organisation of PLCζ, PLC1 and deletion/chimaera constructs Schematic representation of the domain organisation of wild-type PLCζ and PLC1, their corresponding XY-linker deletions PLCζXYlinker and PLC1XYlinker, and the PLC/XYlinker1 chimaera. Note the similar presence in PLCζ and PLC1 of the EF, X, XY-linker, Y and C2 domains, but absence of the PH domain in PLCζ. The various amino acid lengths and respective XY-linker coordinates are also indicated for each construct.

Figure 2 Ca

 2 Figure 2Ca 2+ oscillation-inducing activity of PLC and XY-linker deletion/chimaera expressed in mouse eggs Fluorescence and luminescence recordings reporting the Ca 2+ changes (red traces; Fluorescence, arbitrary units (a.u.)) and luciferase expression (black traces; Luminescence, counts per second (cps)), respectively, in unfertilized mouse eggs following microinjection of cRNA encoding luciferase-tagged PLCζ, PLC1, their corresponding XY-linker deletions and the PLC/XYlinker1 chimaera (left panels). Panels on the right show the integrated luminescence image of a field of mouse eggs following cRNA microinjection of each PLC construct (see Table1).

Biochemical

  Journal Immediate Publication. Published on 18 Jul 2011 as manuscript BJ20110953 THIS IS NOT THE VERSION OF RECORD -see doi:10.1042/BJ20110953A c c e p t e d M a n u s c r i p t Licenced copy. Copying is not permitted, except with prior permission and as allowed by law.

Fig. 1 Biochemical

 1 Fig. 1

Fig. 2 Biochemical

 2 Fig. 2

Fig. 3A Biochemical

 3A Fig. 3A

Fig. 3B Biochemical

 3B Fig. 3B

Fig. 3C Biochemical

 3C Fig. 3C

  480-491 chimaera thus generated was cloned into Licenced copy. Copying is not permitted, except with prior permission and as allowed by law.

		Biochemical Journal Immediate Publication. Published on 18 Jul 2011 as manuscript BJ20110953
	THIS IS NOT THE VERSION OF RECORD -see doi:10.1042/BJ20110953	A c c e p t e d M a n u s c r i p t

Table 2 PLC-luciferase injected Ca 2+ oscillations (spikes/2 hour) Peak luminescence (cps) Luminescence at 1 st spike (cps)

 2 Biochemical Journal Immediate Publication. Published on 18 Jul 2011 as manuscript BJ20110953 THIS IS NOT THE VERSION OF RECORD -see doi:10.1042/BJ20110953 A c c e p t e d M a n u s c r i p t

	No.
	of
	eggs

Licenced copy. Copying is not permitted, except with prior permission and as allowed by law.

© 2011 The Authors Journal compilation © 2011 Portland Press Limited

Licenced copy. Copying is not permitted, except with prior permission and as allowed by law.© 2011 The Authors Journal compilation © 2011 Portland Press Limited

A c c e p t e d M a n u s c r i p t Licenced copy. Copying is not permitted, except with prior permission and as allowed by law. © 2011 The Authors Journal compilation © 2011 Portland Press Limited

ACKNOWLEDGEMENTS

We are grateful to Matilda Katan, Institute of Cancer Research, London, UK for providing the PLCδ1.

FUNDING This work was supported by the Wellcome Trust [080701]. KE and MT hold research scholarships supported by the Libyan Government and NCSR Demokritos, respectively. Biochemical Journal Immediate Publication. Published on 18 Jul 2011 as manuscript BJ20110953 THIS IS NOT THE VERSION OF RECORD -see doi:10.1042/BJ20110953

A c c e p t e d M a n u s c r i p t Licenced copy. Copying is not permitted, except with prior permission and as allowed by law.

AUTHOR CONTRIBUTIONS

Michail Nomikos, J. Raul Gonzalez-Garcia, George Nounesis, Karl Swann and F. Anthony Lai devised the project strategy, MN and FAL designed the experiments, which were performed by MN, Khalil Elgmati, Maria Theodoridou, Athena Georgilis and JRG. MN, KS and FAL prepared the manuscript.