Elie Hachem
email: elie.hachem@mines-paristech.fr

Hugues Digonnet
email: hugues.digonnet@mines-paristech.fr

T Coupez

STABILIZED FINITE ELEMENT SOLUTION TO HANDLE COMPLEX HEAT AND TURBULENT FLOWS IN INDUSTRIAL FURNACES

Keywords: Stabilized FEM, Turbulent flows, Conjugate heat transfer, Immersed volume method

published or not. The documents may come

Stabilized finite element solution to handle complex heat and turbulent flows in industrial furnaces

INTRODUCTION

The analysis of transient heating characteristics of the steel in an industrial furnace has attracted considerable attention during the past few decades espacially when such processes should have lower energy consumption and pollutant emissions [START_REF] Ishii | Numerical modeling of an industrial aluminium melting furnace[END_REF][START_REF] Nieckele | Numerical modeling of an industrial aluminium melting furnace[END_REF][START_REF] Song | Simulation of fluid flow and gascous radiation heat transfer in a natural gas-fired furnace[END_REF] . In addition, requirement of a uniform temperature distribution inside the volume for the treated workpieces is of great importance to determine the quality of the steel product in terms of hardness, toughness and resistance. Intrinsically, the resulting hot gas flow within the furnace influences the heat transfer process through conduction in the solids, convection, and thermal radiation simultaneously.

However, complex three-dimensional structure of the furnace including the thermal coupling of fluids and solids, turbulent convection, thermal radiation, location of the ingots, the burners, and the given geometry make the problem difficult to analyze accurately and economically. Therefore, models and methods for predicting the furnace behaviour and heat transfer processes of the workpieces are highly demanded. The main objective of this paper is to present a multidomain approach to solve the conjugate heat transfer for which the three modes, convective, conductive and radiative heat transfer interfere simultaneously and in both the fluid part and the solid part [START_REF] Houzeaux | An overlapping Dirichlet/Robin domain decomposition method[END_REF][START_REF] Felippa | Partitioned analysis for coupled mechanical systems[END_REF][START_REF] Principe | A numerical approximation of the thermal coupling of fluids and solids[END_REF] . The proposed numerical method for modelling such multimaterial flows (fluid/solid) will be referred as the immersed volume method (IVM). A complete description and details about this method can be found in [START_REF] Hachem | Immersed Volume for solving threedimensional conjugate heat transfer using stabilized finite element methods[END_REF][START_REF] Hachem | Stabilized finite element method for heat transfer and turbulent flows inside industrial furnaces[END_REF] and will be revisited in this paper. The use of the monolithic formulation with some additional features that could allow a proper resolution is then highlighted. Anisotropic mesh adaptation at the interface between two different materials is used and applied . The proposed mesh generation algorithm allows the creation of meshes with extremely anisotropic elements stretched along the interface, which is an important requirement for conjugate heat transfer and multi-component devices with surface conductive layers [START_REF] Gruau | 3D tetrahedral, unstructured and anisotropic mesh generation with adaptation to natural and multidomain metric[END_REF] . From a numerical point of view, the sudden heating of solid is at the origin of so-called thermal shocks which cause spurious oscillations in the solution. In order to circumvent this issue, a stabilized finite element method is used for both Navier-Stokes [START_REF] Brooks | Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations[END_REF][START_REF] Franca | Stabilized finite element methods: II. the incompressible Navier-Stokes equations[END_REF][START_REF] Codina | Stabilization of incompressibility and convection through orthogonal subscales in finite element methods[END_REF] and the convection-diffusion equations [START_REF] Codina | Stabilized finite element method for the transient Navier-Stokes equations based on a pressure gradient projection[END_REF][START_REF] Brezzi | Choosing bubbles for advection-diffusion problems[END_REF] . As far as the radiative terms are concerned, the radiative transfer equation is solved separately using the so-called P-1 method [START_REF] Modest | Radiative Heat Transfer[END_REF][START_REF] Siegel | Thermal Radiation Heat Transfer[END_REF] .

The outline of the paper is as follows: first, we present the time-dependent, threedimensional, conjugate heat transfer and fluid flow problem. A detailed description of the immersed volume method using both the level set function and the anisotropic mesh adaptation is given in section 3. Section 4 presents in brief the discretization as well as the stabilized finite element method for solving these equations. In section 5, the numerical performance of the presented method is demonstrated by means of a 3D real industrial problem. Comparisons with the experimental results are presented. Finally, conclusions and perspectives are outlined.

GOVERNING EQUATIONS

Navier-Stokes equations

Let Ω ⊂ R d , d, be the spatial computational domain with boundary ∂Ω. In order to compute the motion of an unsteady, viscous, incompressible, non-isothermal flow with buoyancy forces, one has to solve the coupled non-linear system provided by the Navier-Stokes equations including the Boussinesq approximation:

         ∇ • u = 0 in Ω ρ(∂ t u + u • ∇u) -∇ • (2µ ε(u) -p I d ) = ρ 0 β(T -T 0 ) g in Ω ρC p (∂ t T + u • ∇T ) -∇ • (λ∇T ) = f -∇ • q r in Ω ( 1
)
where u is the velocity vector, p the pressure and T the temperature. Equations (1) describe first the momentum conservation features the density ρ, the dynamic viscosity µ, the deformation-rate tensor ε(u) = (∇u + t∇u)/2, the reference density and temperature ρ 0 and T 0 , the thermal expansion coefficient β and the gravitational acceleration g. Eventually, the last equation in (1) denotes the energy conservation and it involves the constant pressure heat capacity C p , the specific thermal conductivity λ, a volume source term f and the heat radiative flux q r .

Turbulence model

The turbulent aspect of flows in furnaces requires the use of dedicated models to compute the flow field. In the present work, we solve the Reynolds-averaged Navier-Stokes problem derived from the system of equations (1) and we resort to the standard k -ε model to close the system. The RANS equations read:

         ∇ • u = 0 in Ω ρ(∂ t u + u • ∇u) -∇ • (2µ e ε(u) -p e I d ) = ρ 0 β(T -T 0 ) g in Ω ρC p (∂ t T + u • ∇T ) -∇ • (λ e ∇T ) = f -∇ • q r in Ω (2)
where the averaged values of the unknowns are the velocity u, the effective pressure p e and the temperature T . The system (2) features the effective viscosity µ e and the effective thermal conduction λ e which are given by:

µ e = µ + µ t and λ e = λ + C p µ t Pr t (3)
with Pr t the turbulent Prandtl number. The turbulent viscosity µ t in expression (3) is a function of the turbulent kinetic energy k and the turbulent dissipation ε that reads:

µ t = ρC µ k 2 ε ( 4
)
with C µ an empirical constant usually equal to 0.09. To assess µ t , the introduced variables k and ε are computed using two transport equations that read:

       ρ (∂ t k + u • ∇k) -∇ • µ + µ t Pr k ∇k = P k + P kb -ρε in Ω ρ (∂ t ε + u • ∇ε) -∇ • µ + µ t Pr ε ∇ε = ε k (C 1ε P k + C 3ǫ P εb -C 2ǫ ρε) in Ω (5)
In equations ( 5), P k represents the production of turbulent kinetic energy due to the mean velocity gradients, P kb is the production due to the buoyancy effects, Pr k and Pr ε are the turbulent Prandtl number for k and ǫ respectively, while C 1ε , C 2ε and C 3ε are model constants. The production terms P k and P kb are modelled as follows:

P k = 2µ t (ε(u) : ε(u)) and P kb = - µ t ρPr g g∇ρ (6)
Finally, it remains to assess the real pressure from the effective pressure and the turbulent kinetic energy, which is carried out in the following manner:

p = p e - 2 3 ρk (7)
2.3 Radiative transfer model

Gray gas assumption

The gray gas model may often be sufficient for furnace applications since, most of the time, surfaces are fairly rough and, as a result, reflect in a relatively diffuse fashion. Furthermore, if the radiative properties do not vary much across the spectrum then the gray gas simplifications may be valid. According to Modest 15 , in the case of a gray medium, the divergence of the heat radiative flux that appears in equation (2) relies on the local temperature and the incident radiation as follows:

-∇ • q r = κ G -4κσT 4 (8)
where G denotes the incident radiation, κ is the mean absorption coefficient and σ the Stefan-Boltzmann constant.

The P-1 approximation

Equation (8) clearly establishes the necessity of getting an expression of G in order to assess the divergence of q r . This can be achieved by considering the radiative transfer equation (RTE) that may be found in [START_REF] Siegel | Thermal Radiation Heat Transfer[END_REF] . In the present study, one resorts to the socalled P-1 radiation model that is the simplest case of the P-N model to express radiation intensity by means of series of spherical harmonics (cf.. Using this approach enables to simplify the RTE into an elliptical partial differential equation in terms of the incident radiation G as follows:

           ∇ • 1 3κ ∇G -κG = 4κσT 4 in Ω ∂G w ∂n = 3κǫ w 2(2 -ǫ w ) (4σT 4 w -G w ) in ∂Ω (9)
where subscript w denotes wall quantities, n is the normal to the wall and ǫ w the emissivity of the wall.

Radiative properties

In the context of gray-medium assumption, the mean absorption coefficient κ can be derived from the emissivity ǫ of the material using the Bouguer's law which reads:

κ = - 1 L m ln(1 -ǫ) (10)
where L m is the mean beam length defined as:

L m = 3.6 ∆V ∆S (11)
For unstructured grids, ∆V and ∆S are appropriate measures of volume and surface for each element of the mesh.

Boundary conditions

At the inflow boundary, for a prescribed velocity u, the value of k can be computed using:

k inlet = c bc • |u| 2 (12)
where c bc is fixed to 0.02 as an empirical constant. Once k is computed, the value of ε can be prescribed using:

ε inlet = C µ • k 3/2 L ( 13
)
with L, a fixed constant, known as the characteristic length of the model [START_REF] Jones | The prediction of laminarization with a two-equation model of turbulence[END_REF][START_REF] Launder | The numerical computation of turbulent flows[END_REF] . These computed values of k and ε are extended into the interior domain as initial conditions. At the outflow, the following homogeneous Neumann boundary conditions are applied:

n • ∇k = 0 and n • ∇ε = 0 (14)
On the rest of the computational boundary a combination of Neumann and Dirichlet conditions is imposed by using classical wall function introduced in the asymptotic behaviour of the different variables near the wall. If the boundary mesh nodes are located in the logarithmic region, we impose the wall shear stress given by :

τ w = ρU * 2 (15)
where U * is the friction velocity evaluated by solving the equation:

U U * = 1 k ln ρEδ µ U * ( 16
)
where U is the tangential velocity, δ is the distance to the wall, k is the Von Karman constant (typically equal to 0.41) and E is a roughness parameter taken equal to 9.0 for smooth walls. Imposing the wall shear stress corresponds to a non-homogeneous Neumann boundary condition for the momentum equation in the tangential direction. The normal component of the velocity is set to zero. The turbulent kinetic energy and its dissipation on the boundary of the mesh are given as function of the friction velocity [START_REF] Jones | The prediction of laminarization with a two-equation model of turbulence[END_REF][START_REF] Launder | The numerical computation of turbulent flows[END_REF] :

k w = U * 2 C µ and ε w = U * 3 k w δ (17)
Boundary conditions at a wall for the energy equation are enforced through a temperature wall function similar to that used for the momentum equations. The effective heat flux in the wall function is computed as :

q w = n • q w = ρC p C 1/4 µ k w (T w -T ) T + (18)
where T w is the wall temperature and T + is the normalized temperature given in [START_REF] Han | A temperature wall function formulation for variable-density turbulent flows with application to engine convective heat transfer modeling[END_REF] .

IMMERSED VOLUME METHOD

The immersed volume method (IVM) consists in dealing with only one computational domain for both fluid and solid. Hence, the domain can be viewed as a composite material made of several components. In order to provide very accurate results, such a method must gather three key ingredients: a level set function, an anisotropic mesh adaptation and appropriate mixing laws to describe the properties of the composite material. The following paragraphs aim at detailing these three items.

Level set approach

The so-called level set approach enables to represent the interface between solid and fluid as a zero level of a smooth function. In practice, a signed distance function is used to localize the interface and initialize the material properties on both sides of this latter.

In our context, the solid being fixed, the interface is static. Let Ω f , Ω s and Γ i represent respectively the fluid domain, the solid domain and the interface. They verify:

Ω f ∪ Ω s = Ω and Ω f ∩ Ω s = Γ i (19)
For each node of the computational domain Ω, the level set function α which is the signed distance from the interface reads:

α(x) =        > 0 if x ∈ Ω f 0 if x ∈ Γ i < 0 if x ∈ Ω s (20)
The physical and thermodynamic properties in the domain are then calculated as a function of α; for instance, the mixed density is calculated using a linear interpolation between the values of the density in the fluid and the solid:

ρ = ρ f H(α) + ρ s (1 -H(α)) (21)
where H is a smoothed Heaviside function given by:

H(α) =          1 if α > ε 1 2 1 + α ε + 1 π sin πα ε if |α| ≤ ε 0 if α < -ε (22)
ε being a small parameter such that ε = O(h) and h the averaged mesh size in the vicinity of the interface.

Anisotropic mesh adaptation

Accurate calculation of the temperature distribution along the air-solid interface is critical for a correct modelling of industrial experiments. When the heat flux is directed through the interface, the difficulty arises due to the discontinuity of the properties of the material across the interface. If this latter is not aligned with the element edges, it may intersect the element arbitrarily such that the accuracy of the finite element approach can be compromised. In order to circumvent this issue, the level-set process is thus coupled to an anisotropic mesh adaptation as described in [START_REF] Gruau | 3D tetrahedral, unstructured and anisotropic mesh generation with adaptation to natural and multidomain metric[END_REF][START_REF] Coupez | From a direct to a parallel iterative solver in 3D forging simulation[END_REF][START_REF] Digonnet | Object-oriented programming for fast and easy development of parallel applications in forming processes simulation[END_REF][START_REF] Coupez | Génération de maillage et adaptation de maillage par optimisation locale[END_REF] .

The idea of this method is to gradually refine the mesh when approaching the interface. In this way, the mesh becomes locally refined which enables to sharply define the interface and to save a great number of elements with respect to classical isotropic refinement. This anisotropic adaptation is performed by constructing a metric map that allows the mesh size to be imposed in the direction of the distance function gradient. Let us briefly described the main principles of this technique. First of all, one has to resort to a socalled metric which is a symmetric positive defined tensor representing a local base that E. Hachem, H. Digonnet and T. Coupez modify the distance computation, such that:

||x|| M = √ t x • M • x , < x, y > M = t x • M • y . ( 23
)
The metric M can be regarded as a tensor whose eigenvalues are related to the mesh sizes, and whose eigenvectors define the directions for which these sizes are applied. For instance, using the identity tensor, one recovers the usual distances and directions of the Euclidean space. In our case the direction of mesh refinement is given by the unit normal to the interface which corresponds to the gradient of the level set function: x = ∇α/||∇α||. A default mesh size, or backround mesh size, h d is imposed far from the interface and it is reduced as the interface comes closer. A likely choice for the mesh size evolution is the following: Eventually, at the interface, the mesh size is reduced by a factor m with respect to the default value h d .

Then this size increases until equalling h d for a distance that corresponds to the half of a given thickness e. The unit normal to the interface x and the mesh size h defined above, lead to the following metric:

M = C (x ⊗ x) + 1 h d I with C =      0 if |α(x)| ≥ e/2 1 h 2 - 1 h 2 d if |α(x)| < e/2 ( 24
)
where I is the identity tensor. This metric corresponds to an isotropic metric far from the interface (with a mesh size equal to h d for all directions) and to an anisotropic metric near the interface ( with a mesh size equal to h in the direction x and equal to h d in the others).

In practice, the mesh is generated in several steps using, through the CIMLIB librairy, the MTC mesher developed by T. Coupez 32,[START_REF] Gruau | 3D tetrahedral, unstructured and anisotropic mesh generation with adaptation to natural and multidomain metric[END_REF] . This mesher is based on a topological optimisation technique available in [START_REF] Coupez | From a direct to a parallel iterative solver in 3D forging simulation[END_REF][START_REF] Digonnet | Object-oriented programming for fast and easy development of parallel applications in forming processes simulation[END_REF] for the anisotropic case. At each step of the refinement process, the mesh size converges locally toward the target size whereas the rest of the domain keeps the same backround mesh size.

Mixing laws

The immersed volume technique implies that the material which is treated in the equations is a composite one. Hence, it is necessary to define the physical and thermodynamic properties of such a material. To achieve this, linear interpolations are mainly used between the values of the properties in the fluid and the solid as previously evoked in expression (21). The smoothed Heaviside function defined in (22) enables to assign the right properties on each side of the interface. The material properties introduced in systems of equations (1-9), such as density, initial temperature, dynamic vicosity, constant E. Hachem, H. Digonnet and T. Coupez pressure heat capacity and mean absorption coefficient, are defined as:

ρ = ρ f H(α) + ρ s (1 -H(α)) µ = µ f H(α) + µ s (1 -H(α)) ρC p = (ρ f C pf H(α) + ρ s C ps (1 -H(α))) ρC p T = ρ f C pf T f H(α) + ρ s C ps T s (1 -H(α)) κ = κ f H(α) + κ s (1 -H(α)) (25)
However, as far as the thermal conductivity is concerned, linear interpolation would lead to inaccurate results. According to the reference [START_REF] Patankar | Numerical Heat Transfer and Fluid Flow[END_REF] , one has to resort to the following law to ensure the conservation of the heat flux:

λ = H(α) λ f + 1 -H(α) λ s -1 (26)

STABILIZED FINITE-ELEMENT METHOD

In this section, the Galerkin finite-element approximation and the corresponding stabilization methods for the resulting discrete system of equations (2) are briefly described. Based on a partition T h of Ω into set of N el elements K, the functional spaces for the velocity V := H 1 0 (Ω) d and the pressure P := C 0 ( Ω) ∩ L 2 0 (Ω) are approached by the following finite dimensional spaces spanned by continuous piecewise polynomials:

V h = u ∈ (H 1 0 (Ω)) d | u |K ∈ P 1 (K) d , ∀K ∈ T h P h = p ∈ C 0 ( Ω) ∩ L 2 0 (Ω) | p |K ∈ P 1 (K), ∀K ∈ T h (27)
The weak formulation of the incompressible Navier-Stokes equations reads:

                  
Find u ∈ V h and p ∈ P h such that:

∀w ∈ V h , q ∈ P h , B(u; u, p; w, q) = 0 B(v; u, p; w, q) = ρ (∂ t u, w) + ρ (v • ∇u, w) + (2µε(u) : ε(w)) -(p, ∇ • w) -(f, w) + (∇ • u, q) ( 28
)
where f is the given force vector. It is well known that the classical finite element approximation for the flow problem may fail because of two reasons: the compatibility condition known as the inf-sup condition or Brezzi-Babuska condition which required an appropriate pair of the function spaces for the velocity and the pressure [START_REF] Brezzi | Stabilized mixed methods for the Stokes problem[END_REF][START_REF] Franca | Two classes of mixed finite element methods[END_REF][START_REF] Arnold | A stable finite element for the Stokes equations[END_REF] ; and when the convection dominates [START_REF] Brooks | Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations[END_REF][START_REF] Franca | Stabilized finite element methods: II. the incompressible Navier-Stokes equations[END_REF][START_REF] Codina | Stabilization of incompressibility and convection through orthogonal subscales in finite element methods[END_REF][START_REF] Hughes | A new finite element formulation for computational fluid dynamics: V. circumventing the Babuska-Brezzi condition: A stable Petrov-Galerkin formulation of the Stokes problem accommodating equal-order interpolations[END_REF] . Therefore, we employ stable finite element formulation based on the enrichment of the functional spaces with space of bubble functions known as Mini element [START_REF] Brooks | Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations[END_REF][START_REF] Arnold | A stable finite element for the Stokes equations[END_REF] . The special choice of bubble functions enables us to employ static condensation procedure giving rise to a stabilized formulation for equal-order linear element. A detailed description on the implementation of the finite element solver using the P1+/P1-based mixed finite element method can be found in [START_REF] Hachem | Immersed Volume for solving threedimensional conjugate heat transfer using stabilized finite element methods[END_REF][START_REF] Hachem | Stabilized finite element method for heat transfer and turbulent flows inside industrial furnaces[END_REF][START_REF] Coupez | From a direct to a parallel iterative solver in 3D forging simulation[END_REF] . Scalar equations in (2), ( 5) and ( 9) can be represented by a single scalar transient convection-diffusion-reaction equation which reads:

∂ t ϕ + u • ∇ϕ + ∇ (α∇ϕ) + rϕ = f ( 29
)
where ϕ is the scalar variable, u the velocity vector, α the diffusion coefficient, r the reaction coefficient and f a source term. The solution strategy for solving such an equation is similar to that used for the equations of motion. Again, the spatial discretization is performed using approximation spaces. Thus, the Galerkin formulation is obtained by multiplying these equations by an appropriate test functions, applying the divergence theorem to the diffusion terms and integrating over the domain of interest. Following the lines on the use of stabilisation methods for transient convection-diffusion-reaction equations as discussed in [START_REF] Codina | Stabilized finite element method for the transient Navier-Stokes equations based on a pressure gradient projection[END_REF][START_REF] Galeao | A consistent approximate upwind Petrov-Galerkin method for convection-dominated problems[END_REF] , the stabilized weak form of equation ( 29) reads:

                     Find ϕ ∈ S h such that, ∀w ∈ W h (∂ t ϕ + u • ∇ϕ, w) + (α∇ϕ, ∇w) + (rϕ, w) + K (R(ϕ), τ SUPG u • ∇w) K streamline upwind + K (R(ϕ), τ SCPG ũ • ∇w) K discontinuity-capturing = (f, v) (30)
where S h and W h are standard test and weight finite element spaces (the scalar counterpart of the vector space defined in ( 27)) and R(ϕ) is the appropriate residual of equation (29).

In equation (30), two additional stabilizing terms have been introduced; the first controls the oscillations in the direction of the streamline (SUPG) [START_REF] Brooks | Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations[END_REF][START_REF] Franca | Stabilized finite element methods: II. the incompressible Navier-Stokes equations[END_REF] and the other controls the derivatives in the direction of the solution gradient (SCPG) [START_REF] Galeao | A consistent approximate upwind Petrov-Galerkin method for convection-dominated problems[END_REF] . This can improve the result for convection dominated problems while the shock-capturing technique precludes the presence of overshoots and undershoots by increasing the amount of numerical dissipation in the neighborhood of layers and sharp gradients. The evaluation of the τ SUPG and τ SCPG stabilizations terms follows the definition described in [START_REF] Brooks | Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations[END_REF][START_REF] Franca | Stabilized finite element methods: II. the incompressible Navier-Stokes equations[END_REF][START_REF] Codina | Stabilization of incompressibility and convection through orthogonal subscales in finite element methods[END_REF][START_REF] Codina | Stabilized finite element method for the transient Navier-Stokes equations based on a pressure gradient projection[END_REF] . The time derivatives are approximated by the Euler forward difference scheme. The algebraic problems resulting from the finite element formulation are assembled and solved using the conjugate residual method associated to the incomplete LU preconditioner from the PETSc (Portable Extensive Toolkit for Scientific Computation) library. A master-slave parallel strategy was used [START_REF] Digonnet | Object-oriented programming for fast and easy development of parallel applications in forming processes simulation[END_REF] , involving SPMD (Single Program, Multiple Data) modules and the MPI (Message Passing Interface) library standard. The computations of the 3D conjugate heat transfer presented in the next section have been obtained using 32 2.4 Ghz Opteron cores in parallel (linked by an Infiniband network).

E. Hachem, H. Digonnet and T. Coupez

NUMERICAL SIMULATION OF A 3D INDUSTRIAL FURNACE

In this section, we aim to present several minutes of heating process for an industrial furnace given by an industrial partners. The furnace was modelled as a rectangular section duct, 1.5x1.3x1.1 m 3 forming one heat transfer zone. The hot gas is pumped into the furnace through two burners located on the vertical wall at 75m/s each having a constant temperature of 1100 o C. By applying the IVM method, the levelset function first detects and defines the treated objects. The second step consists in deriving the anisotropic adapted mesh that describes very accurately the interface between the workpieces, the walls and the surrounding air. Recall that the mesh algorithm allows the creation of extremely stretched elements along the interface, which is an important requirement for multimaterial problem with surface conductive layers. The additional nodes are added only at the interface region keeping the computational cost low. Note that although the support is made by six different cylindrical objects and one flat grid, however, as shown in figure 3, the shape of these treated objects is well captured and respected by applying the proposed anisotropic mesh adaptation.

The algorithm progressively detects and refines the support grid and the walls leading to a well respected shape in terms of curvature, angles, etc. All the small details in this given geometry can be captured accurately (see figure 4). Note that the the final mesh used for the numerical simulation consists of 155015 nodes and 896539 linear tetrahedral elements as shown in figure 5. Once the mesh is well adapted along the interfaces between the walls, the support grid and the volume of the furnace, the material distribution between each physical domain can be described by means of the level set function. Consequently, the same set of equations; momentum equations, energy equation, the turbulent kinetic, dissipation energy equations, and radiative transport eqautions are simultaneously solved over the entire domain including both fluid and solid regions with variable material properties (see figure 6).

Recall that the interface between the solid and the fluid is rendered by the zero isovalue of the distance function; hence the calculations of the classical boundary conditions to ensure the heat exchange between the subdomains (air-solid and air-walls) are no longer applicable on their interfaces. The state of art in the proposed thermal coupling analysis lies in that the heat transfer at any interfaces has been treated naturally", i.e. without the use or a previous knowledge of any heat transfer coefficient. Usually, the heat transfer coefficient between two subdomains can be obtained through experimental tests or empirical rules, but in the presence of complex geometries and flows, different configurations Summing up, for any different geometry, even if we consider a new studied solid, it is shown that the proposed method only requires to define the composite material properties to ensure the corresponding heat transfer.

All the given parameters used for the numerical simulations do not reflect the true measurements from the experimental tests, due to the complexity of the materials, the gas composition and other technical issues. However, we made sure that the chosen parameters have at least the real physical representations and are appropriate to simulate E. Hachem, H. Digonnet and T. Coupez the real test.

Figure 7 and 8 shows the evolution of the isotherms and the streamlines at different time steps (t= 1.25s, 9.61s, 27.08s, 58.77s, 116.57s and 222s). The temperature distribution clearly indicates the expected flow pattern. At the solids level, we observe also that the injected air from the bottom burner is slowed down and slightly influence the main air circulation in the lower part of the domain. This explains the difference in the flow pattern between the two burners. When the hot fluid passes across the volume of the furnace, it induces a turbulent and recalculating motion within the geometry. This forced convection is caused by the interaction of the moving stream and the stationary fluid inside the furnace. The air movement around the workpieces is interesting; i.e. it allows studying the influence of different arrangements and positions to optimize the heat treatment. A number of vortices between the objects and the surroundings can be observed due to the turbulence dissipation and mixing between the hot and cold air. spurious oscillations (high undershoots or overshoots) which are frequently observed in the presence of high temperature gradients at the interface or in convection dominated problems across the enclosure. This can be attributed to the stabilization finite element discretization applied on the system of equations. However, there is still some regions where the solution (temperature, turbulent kinetic energy or the dissipation rate energy) exhibits some overshoots or undershoots. But they are very localized and will not affect the overall solution and do not lead to global instability. It could be avoided by refining and adapting the grid in these regions using for example a posteriori error estimator coupled to an anisotropic mesh adaptation strategy. A point that needs also further investigations.

Recall that the contribution of the radiations to the heat transfers is assessed by solving the radiative transfer equation (RTE) over the whole domain and by computing volumetric terms that acts as an energy source terms via divergence of radiative heat flux. These source terms, rendered by the discontinuity of both the temperature and the emissivity E. Hachem, H. Digonnet and T. Coupez across the interfaces, replace the classical boundary conditions that usually are applied at the interface between two subdomains.

The amount of energy required to increase the temperature of the loads by a few hundred degrees is considerable both in real application and computational studies. The immersed solids gain only few degrees above their initial temperature. Such a 3D computation has yet required 5 days on 32 cores. Hence, a great effort is still necessary to supply fast algorithms in order to calculate this kind of full heating sequences in reasonable reducing time. These numerical results indicate that the IVM approach is suitable for the parallel numerical simulation of industrial furnaces with different loads. Future investigation will be concerned with experimental comparisons and time reducing models. Finally, the time history of the temperature captured at the centres of the sidewalls is shown in figure 9 and compared to the experimental results given by an industrial partner. According to the analysis made, it is shown that during the first 150s the average temperature inside the volume and on the walls is approximately the same. At this stage, the temperature of 250 o C was recorded and used as initial temperature for the numerical computations.

The walls were instrumented with many thermal sensors at different locations as shown in figure 1. Data were acquired via a computer controlled data acquisition system, tabulated and then reported by our industrial partner. All the experimental results on the walls (resp. inside the volume) were approximately the same. Therefore, only their average temperature was plotted. The average temperature on the walls was referred as the Zone 1 while the average temperature in the centre was referred as Zone 2.

As can be seen, the agreement is generally good for all stations. However, the difference respect to the experimental results may be due to different factors. We will state here only the important one. First, the use of the correct physical properties as well as the appropriate initial conditions can play an important role on the final results. From the numerical point of view, we can say that the use of a fine enough grid could be more appropriate to simulate accurately such complex fluid phenomena. Moreover, such discrepancies in the results clearly indicate that a more sophisticated radiative transfer model may be needed to improve the solution and account for a better directional influence. This issue will be the subject of further investigations.

CONCLUSION

This paper presents the CFD simulation of the heating process of a loaded industrial furnace. The methods presented in this work has provided a useful tool to predict the temperature evolution at the same time in the furnace and within the walls and the support grid. The 3D stabilized finite element methods developed in this work was used to solve the turbulent flows, the conjugate heat transfer and the thermal radiation problem. The fluid-solid interactions were treated using the immersed volume method (IVM). Temperature measurement data on the walls and inside the volume was the used to validate the present CFD model. The heating profile was reasonably predicted by the simulation. As

E

  . Hachem, H. Digonnet and T. Coupez

E

  . Hachem, H. Digonnet and T. Coupez

Figure 1 :Figure 1

 11 Figure 1: 1m3 furnace (left) and the support grid (right)

Figure 2 :

 2 Figure 2: Materials properties and initial temperature

E

  . Hachem, H. Digonnet and T. Coupez

Figure 3 :

 3 Figure 3: Two verticals cuts in the volume at different heights of the support grid

Figure 4 :

 4 Figure 4: Detailed view of the anisotropic mesh adaptation along the treated walls

Figure 5 :

 5 Figure 5: Two cuts in the final mesh at different position. Locations of the burners, the outlet and the support grid

Figure 6 :

 6 Figure 6: A top view of the density distribution along the walls, the atmosphere and the support grid

Figure 7 :

 7 Figure 7: The evolution of isotherms and streamlines at different time step (side view)

Figure 8 :

 8 Figure 8: The evolution of isotherms and streamlines at different time step (top view)

E

  . Hachem, H. Digonnet and T. Coupez

Figure 9 :

 9 Figure 9: Temperature-time profile at different locations in the furnace


Marián Mazáň

Enrico Ragni

Laura Popolo

Vladimir Farkas

Vladimír Farkaš

Catalytic properties of the Gas family β-(1,3)glucanosyltransferases active in fungal cell wall biogenesis as determined by a novel fluorescent assay

Keywords: Catalytic properties of yeast β-(1,3)-glucanosyltransferases Gas proteins, GH72 family, transglycosylation, cell wall, yeast, cell wall BGT, β-1,3-glucanosyl transglycosylase, LamOS, laminarioligosaccharides, L6, laminarihexaose, SR, sulforhodamine, L6-SR, sulforhodamine-labeled laminarihexaose, HPAEC, high-performance anion exchange chromatography, GPI, glycosyl phosphatidylinositol, GFP, green fluorescent protein

HAL is

INTRODUCTION

The cell wall is an external envelope which is essential for fungal viability. It consists of a matrix of cross-linked glucose polymers (β-glucans), mannoproteins and a small amount of chitin. A balance between the biosynthesis of the constituents and hydrolysis/transglycosylation reactions is crucial for cell wall homeostasis, which is essential for both cell integrity and proper morphogenesis.

Family 72 of glycoside hydrolases (GH72), annotated in the carbohydrate active enzyme (CAZy) database, include endo-ß-(1,3)-glucanases that are endowed with significant transglycosylase activity [START_REF] Henrissat | Structural and sequence-based classification of glycoside hydrolases[END_REF][START_REF] Henrissat | Glycoside hydrolases and glycosyltransferases. Families, modules, and implications for genomics[END_REF]. Due to this activity these enzymes are also referred to as ß-(1,3)-glucanosyltransferases. To date, 157 proteins have been identified in this family [http://www.cazy.org/, 3]. The presence of GH72 enzymes is restricted to yeast and fungal species indicating a highly specialized role in fungal wall biogenesis.

ß-(1,3)-Glucan is the most abundant glucose polymer of the yeast cell wall. It is synthesized by plasma membrane enzyme complexes -glucan synthases with Fks proteins as their catalytic components [START_REF] Mazur | Differential expression and function of two homologous subunits of yeast 1,3-beta-D-glucan synthase[END_REF]. On the cytoplasmic side of the cell membrane, UDP-glucose serves as a substrate for the vectorial synthesis of the polymer. In the extracellular space, GH72 enzymes catalyze the linear elongation of the polymers. Moreover, they contribute to the formation of lateral branches by elongating branching points -ß-(1,6)-linked glucose residueswhich are created by branching enzymes [START_REF] Gastebois | Characterization of a new beta(1-3)-glucan branching activity of Aspergillus fumigatus[END_REF]. All these reactions occur through transglycosylation due to the lack of availability of small energy-exchange molecules such as ATP in the extracellular space.

In addition to GH72 and branching enzymes active on β-(1,3)-glucan, other transglycosylases are involved in fungal cell wall formation [START_REF] Latgé | The cell wall: a carbohydrate armour for the fungal cell[END_REF]. Remarkably, in S. cerevisiae it has been demonstrated that Crh enzymes (Crh1, Crh2 and Crr1 of family GH16) cross-link chitin both to the ß-(1,6)-glucan, which in turn tethers GPI-trimmed mannoproteins to the wall, and to the ß-(1,3)-glucan [START_REF] Cabib | Crh1p and Crh2p are required for the cross-linking of chitin to beta(1-6)glucan in the Saccharomyces cerevisiae cell wall[END_REF][START_REF] Cabib | Assembly of the yeast cell wall. Crh1p and Crh2p act as transglycosylases in vivo and in vitro[END_REF]. Crh1p and Crh2p are required to covalently link a pool of the yeast Gas1 protein molecules to the bud scars [START_REF] Rolli | Immobilization of the glycosylphosphatidylinositol-anchored Gas1 protein into the chitin ring and septum is required for proper morphogenesis in yeast[END_REF]. The in vivo role of other glycanases/transglycosylases such as Dcw1p and Dfg5p (putative mannanases of family GH5) and Scw10/Scw4 proteins (putative glucanases of family GH17) is still unclear.

Hydrolases/transglycosylases also play a role in plant cell wall growth and modification and are the object of intense biochemical investigation. An example is provided by the xyloglucan-endotransglycosylase/hydrolase (XET/XTH), ubiquitous plant enzyme involved in the loosening and reformation of xyloglucan tethers between cellulose microfibrils in the cell walls [START_REF] Fry | Xyloglucan endotransglycosylase: a new wall-loosening enzyme activity from plants[END_REF][START_REF] Nishitani | Endo-xyloglucan transferase, a novel class of glycosyltransferase that catalyzes transfer of a segment of xyloglucan molecule to another xyloglucan molecule[END_REF][START_REF] Farkaš | Cleavage of xyloglucan by nasturtium seed xyloglucanase and transglycosylation to xyloglucan subunit oligosaccharides[END_REF][START_REF] Hrmova | A Barley xyloglucan xyloglucosyl transferase covalently links xyloglucan, cellulosic substrates, and (1,3;1,4)-beta-D-glucans[END_REF]. Thus, the creation of an interwoven texture of polymers in the cell wall shares some common principles both in fungal and plant cells.

The first clues to the activity of the GH72 enzymes came from biochemical studies on Gel1p from A. fumigatus [START_REF] Hartland | A novel beta-(1-3)-glucanosyltransferase from the cell wall of Aspergillus fumigatus[END_REF]. When Gel1p was incubated with borohydride-reduced laminarioligosaccharides of 10 or more glucose residues (rG ≥10 ), both shorter and longer products were obtained. This was consistent with a double-inversion transglycosylating reaction mechanism of the so-called retaining glycoside hydrolases [START_REF] Sinnott | Catalytic mechanism of enzymatic glycosyl transfer[END_REF]. In the first step, the enzyme cleaves an internal ß-(1,3)-glycosidic linkage in the donor substrate molecule, the non-reducing part is released and the newly created reducing-end portion of the donor molecule is linked via an ester bond to the catalytic acid residue in the enzyme, thus forming a covalent glycosyl-enzyme intermediate. In the next step, the glycan portion is transferred from the intermediate to a molecule of water (hydrolysis) or to C3(OH) of non-reducing end glucose residue in the acceptor molecule with formation of a ß-(1,3)-glycosidic linkage (transglycosylation). Consequently, a disproportionation of the substrate takes place and a series of oligosaccharide products with DP both higher and lower than that of the donor are formed. High-performance anion-exchange chromatography (HPAEC) was used to analyze the reaction mixture and to detect the transglycosylation activity [START_REF] Hartland | A novel beta-(1-3)-glucanosyltransferase from the cell wall of Aspergillus fumigatus[END_REF][START_REF] Mouyna | Glycosylphosphatidylinositol-anchored glucanosyltransferases play an active role in the biosynthesis of the fungal cell wall[END_REF]. The GH72 enzymes are not pure transglycosylases but also possess a significant hydrolytic activity. The ratio of transferase versus the hydrolytic activity depended on the substrate concentration; for Gel1p from Aspergillus fumigatus it was 100% at high substrate concentration but dropped to 35% at low concentration [START_REF] Hartland | A novel beta-(1-3)-glucanosyltransferase from the cell wall of Aspergillus fumigatus[END_REF]. The term ß-(1,3)-glucan elongase was also coined to indicate the ability of these enzymes to elongate the substrate molecules [START_REF] Lesage | Cell wall assembly in Saccharomyces cerevisiae[END_REF].

The HPAEC method used in the previous studies to detect transglycosylation activity of the Gas proteins enables both qualitative and quantitative characterization of the reaction products, but determination of overall transglycosylation activity is complicated. Moreover, the HPAEC assay is rather cumbersome and does not permit simultaneous measurements of multiple enzyme samples. Of considerable importance may also be the fact that the HPAEC instrumentation is quite sophisticated and hence expensive. It was our aim to design a simple, rapid and cost-effective method to test the transglycosylating activity of GH72 enzymes. The new assay of ß-(1,3)-glucanosyl transglycosylase activity exploits laminarin as the donor and fluorescently labeled laminarioligosaccharides as the acceptors. The assay was used to determine the basic biochemical properties of heterologous yeast Gas proteins and to map the distribution of ß-(1,3)-glucanosyl transglycosylase activity in the yeast cell fractions.

EXPERIMENTAL

Substrates and chemicals

Laminarin [β(1,3)-glucan] was purchased from Sigma and pustulan [β [START_REF] Henrissat | Structural and sequence-based classification of glycoside hydrolases[END_REF][START_REF] Latgé | The cell wall: a carbohydrate armour for the fungal cell[END_REF]-glucan] from Calbiochem. Laminarioligosaccharides and N-acetyl chito-oligosaccharides were from Megazyme. Oligosaccharides derived from pustulan (DP 2-7), were prepared by partial acid hydrolysis of pustulan with 4M trifluoroacetic acid and fractionated on a Biogel P4 column (1.7 x 120 cm) eluted with water. Lissamine™ rhodamine B sulfonyl chloride (LRSC) was purchased from Anaspec or from Acros Organics. All other chemicals used were of p. a. quality, mostly from Merck or Fluka.

Protein purification

Pichia pastoris strains expressing and secreting tail-less and 6x His-tagged Gas1p, Gas2p, Gas3p, Gas4p and Gas5p proteins from Saccharomyces cerevisiae were previously described [START_REF] Carotti | Characterization of recombinant forms of the yeast Gas1 protein and identification of residues essential for glucanosyltransferase activity and folding[END_REF]19]. Recombinant proteins were purified from the supernatants of P. pastoris cultures as previously described [START_REF] Carotti | Characterization of recombinant forms of the yeast Gas1 protein and identification of residues essential for glucanosyltransferase activity and folding[END_REF]19]. Protein concentration was determined by Quant-iT TM Protein Assay Kit (Invitrogen) using BSA as a standard. Fractions of the purified preparations were checked for purity by SDS-PAGE using 10% polyacrylamide gels. Proteins were stained with Coomassie Blue R-250 or silver nitrate.

Cell fractionation

Diploid strain Saccharomyces cerevisiae CCY 21-4-13 from the Culture Collection of Yeasts, Institute of Chemistry, Slovak Academy of Sciences, Bratislava, Slovakia) was grown in YPD medium containing 1% each yeast extract, bacto-peptone and glucose at 30 °C on an orbital shaker. The cells were harvested in middle logarithmic phase of growth by centrifugation, washed twice with cold water, suspended in the homogenization buffer (0.1 M citrate, pH 5.0, containing 1 mM each EDTA, PMSF and DTT) and disintegrated with ballotini beads (0.2 mm diameter) in a rotatory disintegrator cooled from the outside with an ice-bath. All subsequent steps were carried out at 0 -4 °C. The progress of the cell disintegration was checked microscopically. When more than 97 % cells had ruptured, the beads were decanted with the homogenization buffer and the suspension was centrifuged at 1,500 g for 10 min. The sediment containing the cell walls and unbroken cells was washed twice with the buffer and suspended in the 0.1 M citrate buffer, pH 5.0 (buffer A), in a volume corresponding to one tenth of the wet weight of the starting cells. The supernatant from the first centrifugation was centrifuged at 20,000 g for 15 min, the sediment washed twice with the homogenization buffer, suspended in a small volume of the buffer A so as to obtain thick suspension, and used as the plasma membrane-enriched fraction. The 20,000 g supernatant was spun at 100,000 g for 30 min, the sediment washed once with the buffer A, suspended in an equal volume of the same buffer and used as the microsomal fraction. The 100,000 g supernatant was considered as the cytosolic fraction. The prepared subcellular fractions could be stored at -70 °C for more than one week before the assays, without appreciable loss of activity.

Synthesis of sulforhodamine-labeled oligosaccharides

The oligosaccharides were labeled with sulforhodamine B according to a previously published protocol [START_REF] Kosik | One-pot fluorescent labeling of xyloglucan oligosaccharides with sulforhodamine[END_REF]. The purity of individual SR-labeled oligosaccharides derived from laminarin and from pustulan was checked by TLC on silica gel plates using the solvent system 1-butanol/ethanol/water (5/3/2, by vol.) whereas for the resolution of SR-N-acetyl-D-chito-oligosaccharides the solvent system 2-propanol/water/25% aq. ammonia (7/2/1, by vol.) was used. The chromatograms were viewed under a UV lamp. Molar concentrations of the labeled oligosaccharides were calculated on the basis of the molar absorption coefficient for LRSC, ε 566 = 85,000 M -1 cm -1 [Certificate of Analysis for Lissamine rhodamine B sulfonyl chloride, Lot No. CM16-027 Anaspec, Inc., San José, CA].

Assay of β-(1,3)-glucanosyl transglycosylase (BGT) activity

The standard assay mixture contained 2.5 mg/ml laminarin, 30 -45 µM of appropriate SR-labeled oligosaccharide, 50 mM citrate-phosphate buffer pH 2.5-7.5; and 0.9-3.0 μg of the respective purified Gas protein (or 0.05-0.12 mg protein in case of subcellular fractions) in the total volume of 20 µl. Incubations were carried out at 30 to 37 °C for 30-60 min. The reaction was stopped by addition of 20 µl of 40 % (v/v) formic acid. Aliquots of 5 μl were applied in quintuplicate from the stopped reaction mixture onto a chromatographic paper (Whatman 3MM) template into positions exactly fitting the positions of wells in a 96-well ELISA microtiter plate and dried. The paper was then washed with several changes of 66 % (v/v) aqueous ethanol containing 5 % (v/v) formic acid to remove the unreacted SR-oligosaccharides, and left overnight in 66 % ethanol. After drying, the paper was sandwiched between two glass plates and fluorescence was measured in a Synergy HT Multi-Detection Microplate Reader (BioTek Instruments) at excitation wavelength 530 nm and emission 575 nm.

RESULTS

Setup of a fluorescent assay for ß-(1,3)-glucanosyl transglycosylase

In designing the novel fluorescence-based approach to test the BGT activity, we took advantage of the previous demonstration that laminarioligosaccharides of 7 glucose residues and shorter were able to function as the acceptor molecules but not as the donors [START_REF] Hartland | A novel beta-(1-3)-glucanosyltransferase from the cell wall of Aspergillus fumigatus[END_REF]. Therefore, laminarioligosaccharides of DP 2-7 (L2 -L7) were labeled with sulforhodamine (Fig. 1) and used as glucanosyl acceptors with laminarin as the donor substrate. To prove their transglycosylating activity, individual Gas proteins were incubated with laminarin and L6-SR and at time intervals aliquots were taken and applied onto the cellulose filter paper Whatman 3 MM and dried. Washing the paper with 66% aqueous ethanol removed the low-Mr reaction products and the unused fluorescent substrate while the high-Mr transfer products remained adsorbed to the paper. The binding of the labeled L6-SR to the polymer fraction was indicated by an increase in fluorescence adsorbed to the filter paper and resistant to washing with 66% ethanol (Fig. 2). The transfer of the label was specifically due to the enzyme activity, since the sample of L6-SR incubated under the same conditions but without enzyme showed no changes (not shown). Gas3p was not tested since it is an inactive member of the Gas family [START_REF] Rolli | GAS3, a developmentally regulated gene, encodes a highly mannosylated and inactive protein of the Gas family of Saccharomyces cerevisiae[END_REF].

In order to analyze multiple protein samples simultaneously, the incubations were performed in 1.5 ml conical Eppendorf tubes and multiple 5 μl aliquots from the stopped reaction mixtures were applied as dot blots onto the filter paper, dried and subsequently washed with 66% ethanol. The quantification of the transglycosylase activity was accomplished in a high-throughput mode using a fluorescent ELISA plate reader. High sensitivity of the fluorescence measurement (less than picomole amounts of sulforhodamine could be determined) enabled miniaturization of the assay and measurement of multiple parallel applications from one sample ensured high precision and reproducibility of the results. When required, a calibration curve constructed by measuring the fluorescence of a series of known quantities of the oligosaccharide acceptor was used to convert the fluorescence units into the absolute amounts of the products.

The novel fluorescent method could also be applied for the determination of BGT activity in isolated cell walls and membrane fractions prepared from vegetative yeast cells. The highest specific activity was found in the fraction of plasma membranes, although a significant BGT activity was detected also in microsomes and in the cell walls (Table 1).

Time-course of the reaction and the effect of enzyme concentration on activity

Progress curves of the reactions catalyzed by Gas proteins exhibited typical hyperbolic shapes characteristic for pseudo-first order reactions (Fig. 3). With Gas4p, the reaction rate was constant throughout the 2-h assay, presumably due to the low initial activity of the enzyme. Furthermore, the dependence of activity on the enzyme concentration was linear with all the Gas proteins (Fig. 4).

pH-and temperature optima of transglycosylase reactions

The dependence of ß-(1,3)-glucanosyl transglycosylase activity of Gas proteins on pH was tested in the pH range 2.5-7.5. The amount of transfer products produced after 30 min reaction time (after 3h in the reaction with Gas4p) was determined. As shown in Fig. 5, all the Gas proteins showed approximately symmetrical bell-shaped dependences of activity on pH. There was a rather broad maximum with Gas1p. The curve showed a plateau in the pH range between 3.5 and 6 and the Gas1 enzyme still retained over 60 % of its maximal activity at pH 6. Gas5p activity was maximal at pH 3.5-4.5, decreased sharply at pH values higher than 4.5 and was <10% at pH 6. By contrast, Gas2p activity reached its maximum at pH 6 and was still over 50% at pH 7. Gas4p had a similar curve but with its maximum shifted towards pH values 5.0-6.0. In conclusion, the pH optimum of Gas5p protein was acidic, whereas the pH optima for Gas2p and Gas4p were closer to neutral (Fig. 5). Gas1p had the broader range of pH optimum. Interestingly, these values are consistent with the functional interplay among the Gas isoforms during yeast life cycle (see the Discussion).

In the temperature assay, the incubation temperature varied between 20 and 55 °C. The temperature optima for the individual Gasps were found to be in the range between 30 and 37 °C (not shown).

Donor and acceptor substrate specificities of the Gas proteins

In order to determine the preferred donor substrate, individual Gas proteins were incubated with polysaccharides similar to or identical with those present in the yeast cell wall. Of the polysaccharides tested, only laminarin was active as the donor substrate with all the Gas enzymes. Pustulan, carboxymethyl-chitin and/or yeast αmannan did not yield detectable amounts of transfer products.

The acceptor specificity was tested using equimolar concentrations of SR-labeled hexamers derived from laminarin, pustulan and chitin representing the potential interpolymeric linkage pairs occurring in the yeast cell wall [22]. It was found that with all Gas proteins, only the glucooligosaccharides of the β-(1,3)series were active as acceptors, whereas the formation of products with SR-pustulooligosaccharides or SR-N-acetyl-D-chitooligosaccharides was negligible.

To determine the effect of oligosaccharide chain length (expressed as degree of polymerization, DP) on the acceptor efficiency, the purified Gas proteins were incubated with a series of SR-labeled laminarioligosaccharides containing from one up to 7 glucose residues (L1-SR to L7-SR). As can be seen from Fig. 6, their capability to serve as the acceptor increased with increasing number of glucosyl units in the β-(1,3)oligosaccharide moiety, the smallest active acceptor being laminaripentaose L5-SR with all Gasps.

DISCUSSION

The assay

In the initial studies reporting the enzymatic activity of recombinant fungal β-(1,3)glucanosyl transferases, the activities were assayed using a reduced G 13 laminarioligosaccharide (rG 13 ) as the substrate. A short incubation generated products compatible with the following reaction scheme: E + rG 13 ↔ E-G x + rG 13-x E-G x + rG 13 ↔ E + rG 13+x where 4 < x < 7 and E denotes the enzyme. An incubation time of several hours produced longer oligosaccharides which themselves became either donors or acceptors, resulting in a wide range of products with increasing chain length (DP>30) which gradually became water-insoluble. Monitoring the progress of the reaction and analysis of the reaction products were accomplished by high-pressure anion-exange chromatography, HPAEC [START_REF] Hartland | A novel beta-(1-3)-glucanosyltransferase from the cell wall of Aspergillus fumigatus[END_REF][START_REF] Mouyna | Glycosylphosphatidylinositol-anchored glucanosyltransferases play an active role in the biosynthesis of the fungal cell wall[END_REF]19]. While the HPAEC is suitable for characterization of the reaction products, its usefulness for quantitative determinations of transglycosylase reactions is limited. In this work we describe a new, highly sensitive fluorescent method to assay the β-(1,3)-glucanosyl-transglycosylase activity of yeast Gas proteins and of GH72 enzymes in general. The method employs principles previously applied successfully to the study of plant transglycosylases such as xyloglucan endotransglycosylase, XET [START_REF] Fry | Novel 'dot-blot" assays for glycosyltransferases and glycosylhydrolases: optimization for xyloglucan endotransglycosylase (XET) activity[END_REF][24][START_REF] Kosík | Effect of the label of oligosaccharide acceptors on kinetic parameters of nasturtium seed xyloglucan endotransglycosylase[END_REF].

The fluorescent assay has several advantages over the HPAEC method previously applied to assess transglycosylating activity of GH72 proteins. Among them is the high , the ability to express the overall reaction rates in quantitative terms, the possibility to perform multiple assays simultaneously, and finally the simplicity which results in low price per assay. Theoretically, every catalytic event leads to a transfer of the label from the pool of acceptor molecules to the pool of donor molecules. It should be taken into account, however, that the fluorescent assay records only those labeled transfer products that are insoluble in 66% ethanol, and not the portions of donor molecules that are split off from the reducing-end and released during the first step of the transglycosylation reaction [START_REF] Sinnott | Catalytic mechanism of enzymatic glycosyl transfer[END_REF]. Since the solubility of SR-laminarioligosaccharides in 66% ethanol decreases with increasing oligosaccharide chain length, it is advantageous to use acceptors having their carbohydrate moiety composed of at least five glucosyl units. In such case, any lengthening of the sugar chain caused by the oligoglucosyl transfer would result in the formation of a product insoluble in 66% ethanol. However, in contrast to HPAEC, the new fluorescence-based method does not yield information about the qualitative composition of the reaction products.

Using the new fluorescence-based method, it was possible to detect β-(1,3)glucanosyl-transglycosylase also in yeast subcellular fractions. The highest specific activity of BGT was found in the plasma membrane-enriched fraction but the presence of significant activity was detected also in microsomes and cell wall fractions (Table 1). Such distribution seems to map the typical maturation and transport pathway of GPIproteins from the site of their synthesis in the ER to their final destination. It should be kept in mind, however, that the measured quantities may be distorted by the presence of β-1,3-glucan hydrolyzing enzymes that could degrade the product as it is being synthesized. Since for the isolation of subcellular fractions, the cells were taken from the logarithmic growth phase, the detected activity presumably belonged to Gas1 and Gas5 proteins which are expressed during vegetative growth, although we cannot exclude the contribution of other enzymes catalyzing a transglycosylase reaction in the conditions used [27].

It is perhaps noteworthy to point out to a potential versatility of the described fluorescent assay method. Namely, by selecting suitable combinations of donor/acceptor pairs, similar fluorescent assays could be devised also for other types of transglycosylases that possibly are present in fungal cell walls. As an example could serve the demonstration of transglycosylating activity of CRH1 and CRH2 gene products linking chitin to β-(1,3)/β- [START_REF] Henrissat | Structural and sequence-based classification of glycoside hydrolases[END_REF][START_REF] Latgé | The cell wall: a carbohydrate armour for the fungal cell[END_REF] glucan in the yeast cell walls [START_REF] Cabib | Assembly of the yeast cell wall. Crh1p and Crh2p act as transglycosylases in vivo and in vitro[END_REF].

Enzymatic properties of Gas proteins

From the previous studies, Gas1p, Gas2p, Gas4p and Gas5p were known to be endowed with a similar type of enzymatic activity but no further analysis of their biochemical properties has been performed hitherto [START_REF] Hartland | A novel beta-(1-3)-glucanosyltransferase from the cell wall of Aspergillus fumigatus[END_REF][START_REF] Mouyna | Glycosylphosphatidylinositol-anchored glucanosyltransferases play an active role in the biosynthesis of the fungal cell wall[END_REF]19]. The fluorescent assay described here enabled us to ascertain the basic biochemical parameters of the Gas proteins and to establish optimal conditions for determination of their activity. All reactions catalyzed by Gas proteins exhibited attributes characteristic for an enzymatic reaction. The progression curves of the reactions were typical for pseudo first order reactions (Fig. 3), and there was a linear dependence between enzyme concentration and the transglycosylating activity (Fig. 4).

Substrate specificity

The results obtained using the fluorescent method essentially confirmed the previous findings that all Gas proteins are specific to β-(1,3)-linked glucan and β-(1,3)oligoglucosides [START_REF] Hartland | A novel beta-(1-3)-glucanosyltransferase from the cell wall of Aspergillus fumigatus[END_REF][START_REF] Mouyna | Glycosylphosphatidylinositol-anchored glucanosyltransferases play an active role in the biosynthesis of the fungal cell wall[END_REF]19]. The acceptor effectivity of SR-laminarioligosaccharides increased with increasing oligoglucoside chain length, starting with DP 5. This result corroborates well the finding of Hartland et al. [START_REF] Hartland | A novel beta-(1-3)-glucanosyltransferase from the cell wall of Aspergillus fumigatus[END_REF] that laminaripentaose was the smallest possible acceptor when using the purified β-(1,3)-glucanosyltransferase from A. fumigatus. Interestingly, the recently published 3D-structure of Gas2p revealed binding of laminaripentaose in the active site both in the donor and acceptor position [START_REF] Hurtado-Guerrero | Molecular mechanisms of yeast cell wall glucan remodelling[END_REF]. With regard to the donor specificity, our results are in agreement with previous data indicating that ß-(1,3)-glucan is the preferred substrate for Gel proteins of A. fumigatus [START_REF] Hartland | A novel beta-(1-3)-glucanosyltransferase from the cell wall of Aspergillus fumigatus[END_REF] and further extend this conclusion to the complete Gas protein family of Saccharomyces cerevisiae.

pH-optima and their biological significance

Our previous studies on the biological role of Gas proteins revealed that a Gas1/Gas5 protein pair is required for proper cell wall formation during vegetative growth, whereas Gas2 and Gas4 proteins are essential for spore wall formation [27]. In accordance with this, GAS1-GAS5 and GAS2-GAS4 pairs have different expression patterns. GAS1-GAS5 is expressed during vegetative growth and repressed during sporulation, whereas the GAS2-GAS4 pair exhibits the reverse pattern. As the Gas proteins are anchored through GPI in the outer layer of the yeast plasma membrane or spore membrane, they are exposed to changes of external pH. This probably is the reason why Gas1p and Gas5p, which are expressed in vegetative cells, are most active between pH 3.5 and 5. This is consistent with the fact that the vegetative growthspecific isoforms face the culture medium that is usually acidic due to the proton efflux occurring during yeast growth. The external pH drops from about 5.5 to almost 3 in late exponential phase. Interestingly, the defective phenotype of cells lacking GAS1 gets worse in media buffered at pH 6.5 and pH 6.7 is a semi-lethal condition for growth of the mutant [START_REF] Vai | Candida albicans homologue of GGP1/GAS1 is functional in Saccharomyces cerevisiae and contains determinants for glycosylphosphatidylinositol attachment[END_REF]. On the basis of the results described in this work, we can hypothesize that the auxiliary function of Gas5p is less effective at pH 6.5 since its activity decreases to less than 10% and therefore cell wall defects could be aggravated due to the lack of sufficient β-(1,3)-glucanosyltransferase activity. Thus, during vegetative growth the more extended optimum pH range of Gas1p compared to Gas5p could guarantee the presence of BGT activity over a wide range of extracellular pH whereas the auxiliary function of Gas5p could be effective only in a narrow range of pH's which is more typical of the initial phases of vegetative growth in unbuffered media. On the other hand, the sporulation-specific Gas2 and Gas4 proteins, which are synthesized in a narrow temporal window coincidentally with the assembly of the spore wall, face the cytoplasmic pH of the diploid cell inside which the spores develop [29]. The optima between pH 5 and 6 suggest that Gas2 and Gas4 proteins work better at pH values closer to the intracellular pH of the yeast cytoplasm, which is between 6.5 and 6.9 depending on the strain [START_REF] Marešová | New applications of pHluorin-measuring intracellular pH of prototrophic yeasts and determining changes in the buffering capacity of strains with affected potassium homeostasis. Yeast 27, 317-325 of GEL2 encoding for a beta(1-3)glucanosyltransferase affects morphogenesis and virulence in Aspergillus fumigatus[END_REF]. It should be also taken into account that alkalization of the medium by accumulation of bicarbonate is essential for sporulation (together with respiratory competency and high cell density) and may induce an increase of intracellular pH [31].

Although factors other than pH of the epiplasm and spore wall, such as different types of β-(1,3)-glucan chains or the presence of small molecules, may explain the requirement for a specialized pair of enzymes during sporulation, pH appears to be an important parameter that affects the activity of Gas2-Gas4 proteins. In previous studies GAS2 and GAS4 genes were ectopically expressed in vegetative gas1cells by fusion to the GAS1 promoter. GAS4 fully complemented the defective phenotype of gas1Δ mutant in vegetative growth even in media buffered at pH 5.5, whereas GAS2 could partially suppress the defects of the mutant only when ambient pH was 6.5 [32]. These findings are consistent with the pH optima for the isolated enzymes reported in this work. The character of dependence of activity on the ambient pH may help explain the presence of a specialized pair of Gas enzymes during sporulation. It should be noted that in the human pathogen C. albicans the GAS1-homologous genes, PHR1 and PHR2, are differently regulated by ambient pH being PHR1 expressed at pH values of 5.5 and higher and PHR2 at pH values of 5.5 or lower [33,34]. C. albicans colonizes niches of the human body at very different pHs, slightly alkaline in the bloodstream (pH7.3) close to neutrality in organs like the kidney, liver and duodenum or acidic as in the stomach (pH ~ 2) or vagina (pH 4.5), Thus, we speculate that the existence of these two genes may meet the requirement to express at the cell surface glucanosyltransferase activities that work optimally in a wide range of ambient pH's. As pH affects the ionization of the aminoacid residues in the active site, the molecular models built on the basis of the recently resolved 3D-structure of Gas2p may provide further information [START_REF] Hurtado-Guerrero | Molecular mechanisms of yeast cell wall glucan remodelling[END_REF].

Several studies indicate that the GH72 family of fungal enzymes plays a crucial role in fungal morphogenesis [35,[START_REF] Gastebois | beta(1-3)Glucanosyltransferase Gel4p is essential for Aspergillus fumigatus[END_REF]. The lack of these enzymes reduces ß-(1,3)glucan incorporation into the expanding cell wall and induces cell wall changes aimed to counteract the damage and prevent lysis [37]. The evoked changes cause defects in morphology and impairment in developmental processes such as sporulation or conidiogenesis [27,35]. The fundamental role of GH72 in fungal biology is further testified by the recent finding that GEL4 is an essential gene for A. fumigatus [START_REF] Gastebois | beta(1-3)Glucanosyltransferase Gel4p is essential for Aspergillus fumigatus[END_REF], a major human fungal pathogen. In addition, GAS4 + and the GAS2/GAS4 pair are essential for spore viability in Schizosaccharomyces pombe and S. cerevisiae, respectively [27,32]. Furthermore, fungal pathogens lacking GH72 enzymes exhibit reduced virulence. An example is provided by the PHR1 null mutant of C. albicans that is avirulent in a mouse model of systemic infection but uncompromised in its ability to cause vaginal infections in rats whereas the virulence phenotype of Phr2 null mutant is the inverse, consistently with the pH-dependent expression of PHR1 and PHR2 genes [38]. Moreover, PHR1 null mutant manifests defects in adhesion to and invasion of reconstituted human epithelia, two processes required for the establishment of infections [38,[START_REF] Calderon | PHR1, a pH-regulated gene of Candida albicans encoding a glucan-remodeling enzyme, is required for adhesion and invasion[END_REF]. Despite the existence of a high degree of redundancy, it is envisaged that the active site of most GH72 members could have sufficient similarity to be targeted by inhibitors of the same type.

The armamentarium of drugs to fight fungal infections is still limited to a few compounds. The new fluorescent assay for β-(1,3)-glucanosyltransferases could provide a simple tool for the detection, identification and characterization of GH72 family enzymes in diverse fungal species as well as for screening and identification of potential inhibitors of BGT activity, which may lead to the development of new antifungal drugs and to new therapeutic strategies. Ohkuni, K., Hayashi, M. and Yamashita, I.( 1998 Standard reaction mixtures (see Experimental section) were incubated with individual Gas proteins under the respective optimal conditions. After indicated time intervals, 5 μl aliquots were taken from the reaction mixtures, applied onto the chromatographic paper Whatman 3MM and dried. The paper was washed overnight in 66% ethanol and photographed under UV light. In the case of reactions catalyzed by Gas4p, the incubation times were four times longer than indicated.

Figure 3 Progress-curves of reactions catalyzed by individual Gas proteins

Standard reaction mixtures were incubated under conditions optimal for the respective Gas protein. The transglycosylation was monitored by the fluorescent method as described in the Experimental section, F. u., arbitrary fluorescence units. The error bars denote standard deviation calculated from quintuplicate dot blots.

Figure 4 Dependence of β-(1,3)-glucanosyltransferase activity on enzyme concentration

The standard incubation mixtures were incubated at 37 °C for 30 min except the reaction with Gas4p where the incubation was extended to 2 h. Conditions were as in Fig. 3, but the amounts of enzyme proteins in the reaction mixtures varied as indicated. The significance of the error bars and units is the same as in Fig. 3.

Figure 5 Dependence of β-(1,3)-glucanosyltransferase activity on pH

The standard incubation mixtures were buffered with 0.05 M McIlvaine citratephosphate buffers and incubated at their respective optimal temperatures for 30 to 180 min. The significance of the error bars and units is the same as in Fig. 3.

Figure 6 Effect of oligosaccharide chain length on acceptor effectivity

The reaction mixtures contained equimolar (40 μM) concentrations of the respective SR-laminarioligosaccharides containing 1 to 7 glucosyl units, and the reactions were carried out with the individual Gas proteins under the respective optimal conditions for 1 h (5 h in the case of the reaction with Gas4p). The significance of units is the same as in Fig. 3.

Biochemical

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Biochemical

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Biochemical

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  sensitivity

Biochemical

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BiochemicalFigure 1

 1 Figure 1Structure of sulforhodamine-labeled laminaritriose (L3-SR)

Figure 2

 2 Figure 2Transfer of the fluorescent label from L6-SR into high-M r fractions adherent to filter paper and insoluble in 66% ethanol

Figure 1 Biochemical

 1 Figure 1

  Figure 2

  Figure 4

20

 20

  Figure 5

  Figure 6

  Morelle, W., Vai, M., Monod, M., Léchenne, B., Fontaine, T., Beauvais, A., Sarfati, J., Prévost, M.-C., Henry, C. and Latgé, J.-P. (2005) Deletion

		) Bicarbonate-mediated
	social communication stimulates meiosis and sporulation of Saccharomyces
	cerevisiae. Yeast 14, 623-631
	32	Ragni, E., Coluccio, A., Rolli, E., Rodriguez-Peña, J. M., Colasante, G., Arroyo,
	J., Neiman, A. M. and Popolo, L. (2007) GAS2 and GAS4, a pair of developmentally
	regulated genes required for spore wall assembly in Saccharomyces cerevisiae.
	Eukaryot. Cell 6, 302-316
	33	Saporito-Irwin, S. M., Birse, C. E., Sypherd, P. S. and Fonzi, W. A. (1995)
	PHR1, a pH-regulated gene of Candida albicans, is required for morphogenesis. Mol.
	Cell Biol. 15, 601-611
	34	Fonzi, W. A. (1999) PHR1, a pH-regulated gene of Candida albicans, is
	required for morphogenesis. J. Bacteriol. 181, 7070-7079
	35	Mouyna, I.,

Table 1 Distribution of β-1,3-glucanosyltransferase activity in subcellular fractions

 1 The incubation mixtures contained 0.05 M citrate buffer, pH 5; 10 mg ml -1 laminarin; 20 μM L7-SR; 0.05-0.11 mg protein in a total volume of 60 μl. The incubation was carried out at 37 °C for 3 h. The data are from a representative experiment. Biochemical Journal Immediate Publication. Published on 08 Jun 2011 as manuscript BJ20110405 THIS IS NOT THE VERSION OF RECORD -see doi:10.1042/BJ20110405 A c c e p t e d M a n u s c r i p t

	Fraction	Specific activity
		(pkat mg protein -1 )
	Cell walls	0.21
	Plasma membrane	0.46
	Microsomes	0.22
	Cytoplasm	0.04

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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

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

Biochemical Journal Immediate Publication. Published on 08 Jun 2011 as manuscript BJ20110405 THIS IS NOT THE VERSION OF RECORD -see doi:10.1042/BJ20110405 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

© 2011 The Authors Journal compilation © 2011 Portland Press Limited

ACKNOWLEDGEMENTS

The technical assistance of L. Fischerová and T. Lipka is gratefully acknowledged. We thank Eva Stratilová for drawing Fig. 1 and Michael J. Bailey for correcting the English style.

FUNDING

This work was supported in parts by grant no. 2/0011/09 from the Grant Agency for Science VEGA (Slovakia) to V. F. and by grant P. U. R. 2009 from Universitá degli Studi di Milano to L. P. Enrico Ragni was a recipient of a type A contract from Universitá degli Studi di Milano.