A Memin

Y Rogister

J Hinderer

M Llubes

E Berthier

J.-P Boy

Ground deformation and gravity variations modelled from present-day ice thinning in the vicinity of glaciers

Keywords: ground tilt, gravity variations, elastic deformations, present-day ice thinning

The solid Earth deforms because of post-glacial rebound due to the viscous relaxation following the last deglaciation but also because of present-day elastic deformation induced by ice thinning. In this paper, we compute elastic loading Green's function associated to the tilt of the ground in the vicinity of glaciers using a Love number formalism for a stratified non-rotating spherical Earth model. We compare this global approach with the plane approximation in terms of height, gravity and tilt changes as a function of the distance from the measurement point to the load. We find that Green's functions for the vertical displacement (resp. horizontal displacement, elastic part of the tilt) agree to within 1% up to ∼ 400 m (resp. 2 km, 5km) from the glaciers.

Two specific cases of ice thinning are considered:1/ the alpine glaciers of the Mont Blanc region (France) where ice-thickness variations are derived from differential digital elevation model analysis for the period 1979-2003; 2/

Introduction

Since the end of the little ice age, most ice masses on Earth have experienced a reduction of their volume [START_REF] Vincent | Solving the paradox of the end of the Little Ice Age in the Alps[END_REF]Rabatel et al., 2008) and, recently, an acceleration of the ice-thinning rates has been observed over many ice-covered areas [START_REF] Meier | Glaciers dominate Eustatic sea-level rise in the 21st century[END_REF]. Rapid ice thinning has been reported on the Greenland [START_REF] Howat | Rapid Changes in Ice Discharge from Greenland Outlet Glaciers[END_REF][START_REF] Stearns | Rapid volume loss from two East Greenland outlet glaciers quantified using repeat stereo satellite imagery[END_REF][START_REF] Barletta | Isolating the PGR signal in the GRACE data: impact on mass balance estimates in Antarctica and Greenland[END_REF][START_REF] Slobbe | Estimating the rates of mass change, ice volume change and snow volume change in Greenland from ICESat and GRACE data[END_REF] and the West Antarctic ice sheets [START_REF] Cazenave | How fast are the ice sheets melting?[END_REF]Rignot et al., 2008;[START_REF] Barletta | Isolating the PGR signal in the GRACE data: impact on mass balance estimates in Antarctica and Greenland[END_REF][START_REF] Horwath | Signal and error in mass change inferences from GRACE: the case of Antarctica[END_REF], large icefields in Patagonia and Alaska [START_REF] Arendt | Rapid wastage of Alaska glaciers and their contribution to rising sea level[END_REF]Rignot et al., 2003;[START_REF] Chen | Alaskan mountain glacial melting observed by satellite gravimetry[END_REF][START_REF] Chen | Patagonia Icefield melting observed by Gravity Recovery and Climate Experiment (GRACE)[END_REF], ice caps in Iceland [START_REF] Magnùsson | Volume changes of Vatnajokull ice cap, Iceland, due to surface mass balance, ice flow, and subglacial melting at geothermal areas[END_REF], as well as on mountain glaciers, for instance in the Alps [START_REF] Berthier | Recent rapid thinning of the 'Mer de Glace' glacier derived from satellite optical images[END_REF], Svalbard [START_REF] Kohler | Acceleration in thinning rate on western Svalbard glaciers[END_REF] or Himalaya [START_REF] Berthier | Remote sensing estimates of glacier mass balances in the Himachal Pradesh (Western Himalaya, India)[END_REF]. Ice-thinning rates range from a few tenths of centimetres per year, in Svalbard for instance [START_REF] Kohler | Acceleration in thinning rate on western Svalbard glaciers[END_REF], to several meters per year such as in the French Alps [START_REF] Berthier | Recent rapid thinning of the 'Mer de Glace' glacier derived from satellite optical images[END_REF] and can reach more than ten meters per year in Greenland [START_REF] Howat | Rapid Changes in Ice Discharge from Greenland Outlet Glaciers[END_REF][START_REF] Stearns | Rapid volume loss from two East Greenland outlet glaciers quantified using repeat stereo satellite imagery[END_REF] A c c e p t e d M a n u s c r i p t Hamilton, 2007).

Past and present-day ice thinning induce a deformation at the Earth surface that has been observed in GPS and gravity measurements close to the shrinking ice bodies (Pagli et al., 2007;[START_REF] Sato | A geophysical interpretation of the secular displacement and gravity rates observed at Ny-Ålesund, Svalbard in the Arctic-effects of post-glacial rebound and present-day ice melting[END_REF][START_REF] Sjöberg | Land uplift near Vatnajökull, Iceland, as observed by GPS in 1992, 1996 and 1999[END_REF][START_REF] Khan | Elastic uplift in southeast Greenland due to rapid ice mass loss[END_REF]. Knowing the current ice-thickness variations, from differential analysis of digital elevation models (DEMs), one can estimate the ground deformations and the gravity changes. Using the World Glacier Inventory database, [START_REF] Barletta | Glacier shrinkage and modeled uplift of the Alps[END_REF] have shown that, in the European Alps, the highest elastic rebound (0.9 mm/yr) due to current ice melting is located in the Mont Blanc area. The reduction in ice volume also induces a tilt of the ground that, close enough to the glaciers, should be detectable by modern tiltmeters, which are already used for monitoring small deformation of the ground due to hydrological loads (e.g. Rerolle et al., 2006) or ocean tide loading (e.g. [START_REF] Llubes | Multi-technique monitoring of ocean tide loading in Northern France[END_REF].

In this paper, we investigate the solid Earth deformation induced by the thinning of three glaciers in the Mont Blanc massif (Mer de Glace, Talèfre, Leschaux) and in Svalbard (Norway) in the Arctic. In the Alps, we consider ice-thinning rates derived from differential DEMs that provide a 24 year-long evolution of the ice thickness [START_REF] Berthier | Recent rapid thinning of the 'Mer de Glace' glacier derived from satellite optical images[END_REF] whereas in Svalbard our analysis is based on the SVAL model [START_REF] Hagedoorn | Pleistocene and Recent deglaciation in Svalbard: implications for tide-gauche, GPS and VLBI measurements[END_REF]. We compute the subsequent Earth deformation, which includes the displacement of the ground and gravity variation, for both a spherical elastic Earth model and a homogeneous elastic half-space. To do so, we convolve Green's functions [START_REF] Farrell | Deformation of the Earth by surface loads[END_REF] obtained for these two models with the variation of ice thickness. A comparison between Green's functions of the spherical and half-A c c e p t e d M a n u s c r i p t space models confirms that the half-space model is a valid approximation at a local scale (i.e. for distances less than 1-10 km). We also model the variation of the tilt of the ground in order to explore the potential use of tiltmeters for monitoring the volume changes of glaciers.

Mass-load Green's functions

Green's functions are largely used to compute the deformation of the Earth due to surface loads [START_REF] Longman | A Green's function for determining the deformation of the Earth under surface mass loads. 1. Theory[END_REF][START_REF] Longman | A Green's function for determining the deformation of the Earth under surface mass loads. 2. Computations and numerical results[END_REF][START_REF] Farrell | Deformation of the Earth by surface loads[END_REF]Peltier, 1974).

They are the response of the Earth to the gravitational and pressure forces exerted by a unit point mass at the surface. The deformation due to an extended surface load is then obtained by convolving the surface mass density describing the surface load with Green's functions. We use the formalism of [START_REF] Farrell | Deformation of the Earth by surface loads[END_REF] to compute Green's functions of the displacement, gravity variation and tilt of the ground for both a homogeneous elastic half-space model and a realistic spherical, elastic, and gravitating Earth model.

The infinitesimal static displacement u of a self-gravitating continuum having a linear and isotropic elastic behaviour obeys the linearized equation of conservation of linear momentum where the derivative with respect to the time has been neglected

∇ • τ + ρ 0 ∇(u • g 0 ) -ρ 0 g 0 ∇ • u + ρ 0 g 1 = 0, (1)
where ρ 0 is the density of the reference configuration, g 0 is the unperturbed radial gravity, g 1 is its Eulerian perturbation, and τ is the elastic stress tensor:

τ = λ∇ • u I + 2µ e, (2)
A c c e p t e d M a n u s c r i p t

I and e being the identity and infinitesimal deformation tensors, respectively, and λ and µ, the Lamé parameters.

In Eq. ( 1), the external body forces have been neglected. We also have the relation between gravity perturbation g 1 and the Eulerian perturbation of the gravity potential, φ 1 :

g 1 = -∇φ 1 . (3)
and Poisson's equation for φ 1

∇ 2 φ 1 = -4πG∇ • (ρ 0 u), ( 4
)
where G is the Newtonian constant of gravitation.

As a boundary condition at the surface of the Earth model, we have that the normal traction is the normal force due to the weight of a unit point mass. The tangential tractions are assumed to be null.

Half-space model

Boussinesq's equation describes the deformation of a homogeneous elastic half-space. As presented in [START_REF] Farrell | Deformation of the Earth by surface loads[END_REF] the initial gravity is not taken into account since it would be infinite for a mass distribution of infinite extent. He computed the displacement u by solving the purely elastic problem described by the following simplified equation for equilibrium:

η∇∇ • u + µ∇ 2 u = 0. ( 5
)
where η = λ + µ. The force exerted by the unit mass point is supposed to be g 0 , which is perpendicular to the surface of the half-space, its norm g 0 being taken as the unperturbed gravity at the surface of a realistic spherical Earth 4) for the perturbation of gravity potential φ 1 , u being the solution of Eq. ( 5). By doing so, we compute the variation of gravity owing to the mass redistribution.

By using cylindrical coordinates R, ϕ, z centered at the application point of the force, the solution of Eqs. ( 3), (4), and (5) at the surface z = 0 of the half-space is given by

u R (R, 0) = - g 0 4πRη , (6)
u z (R, 0) = - g 0 4πµR σ η , (7)
g 1R (R, 0) = g 0 ρ 0 G 2µR - G R 2 , (8)
and

g 1z (R, 0) = g 0 ρ 0 G 2µR . (9)
where the R-and z-components of the vectors are indicated by the subscripts R and z, respectively. By symmetry, u ϕ = 0, g 1ϕ = 0, and neither u nor g 1 depend on ϕ. The second term on the right-hand side of Eq. ( 8) stems from the direct gravitational attraction of the unit mass point. Because of the symmetry properties of the problem, there is no such term in the z-component of g 1 (R, 0). Two other acceleration terms must be added to g 1 to obtain the gravity variations that would be measured by a gravimeter at the surface of the Earth [START_REF] Farrell | Deformation of the Earth by surface loads[END_REF][START_REF] Dahlen | Theoretical Global Seismology[END_REF]. Indeed, the gravimeter, attached to the surface of the Earth, is displaced in the initial gravity field of the spherical Earth model. Therefore, it experiences a variation of the vertical component of gravity that is the free-air gradient 2g 0 u z /a, where a =6371 km is the mean radius of the Earth. Moreover, the tilt of the Page 7 of 42

A c c e p t e d M a n u s c r i p t

surface is responsible for a variation g 0 ∂u z /∂R of the R-component of the gravity field. Taking those two effects into account, Eqs (8) and ( 9) must be replaced by

g 1 a R = g 0 ρ 0 G 2µR - G R 2 -g 0 ∂u a z ∂R (10)
and

g 1 a z = g 0 ρ 0 G 2µR + 2g 0 a u a z , (11)
respectively. From now on, the superscript a indicates that the quantities are evaluated at the surface of the half-space. Tilt angle t a measured by a tiltmeter is the difference between the tilt of the ground and that of the geoid with respect to their initial horizontal position (Rerolle et al., 2006).

We have

t a = ∂u a z ∂R - g 1 a R g 0 , = - ρ 0 G 2µR + g 0 σ 4πµηR 2 + G g 0 R 2 . ( 12
)
From Eqs (6), (7), and (11), we obtain the ratios A c c e p t e d M a n u s c r i p t

g 1 a z u a z = -2πGρ 0 η σ + 2g 0 a , (13)

Spherical Earth model

We now consider a spherically symmetric, non-rotating, and elastically isotropic (SNREI) Earth model, a system of reference whose origin is at the center of the model, and spherical coordinates r, θ, ϕ. Contrary to the half-space problem where we made ad hoc approximations to compute the gravity variations, there is now a direct coupling, described by Eqs (1)-( 4), between the elastic deformation and gravity variations. Taking advantage of the spherical symmetry, we expand the displacement and stress fields in vector spherical harmonics, and the Eulerian pertubation of the gravity potential in spherical harmonics, to obtain an infinite set of decoupled spheroidal and toroidal systems of ordinary differential equations [START_REF] Alterman | Oscillations of the Earth[END_REF].

We numerically integrate the spheroidal system for the Preliminary Reference Earth Model (PREM) of [START_REF] Dziewonski | Preliminary reference Earth model[END_REF] where we replace the ocean by a solid crust. In the following, we call this model the modified PREM. The density, seismic waves velocities and quality factors of the upper layer of the modified PREM are given in Table 1.

Table 1 At the surface, Green's functions for the vertical and horizontal displace-A c c e p t e d M a n u s c r i p t ments, are respectively given by:

u s z (ψ) = G g 0 a ∞ n=0 h ′ n P n (cos ψ), (15)
u s t (ψ) = G g 0 a ∞ n=1 l ′ n ∂P n (cos ψ) ∂ψ . ( 16
)
where P n is the Legendre polynomial of degree n, h

′ n and l ′ n are the load Love numbers respectively for the vertical and the horizontal displacements, ψ is the angular distance between the observation and loading points, and superscript s indicates that Green's functions are evaluated at the surface.

The Lagrangian perturbation of the gravity is the sum of two terms. One is due to the elastic effect

g s (ψ) = G a 2 ∞ n=0 2h ′ n -(n + 1)k ′ n P n (cos ψ), (17)
where k

′ n is the load Love number for the Eulerian perturbation of the gravity potential. This part of the gravity change includes the correction 2h ′ n for the free air gradient and the effect -(n + 1)k ′ n due to the mass redistribution. The second term is due to the direct attraction of the loading point. If its altitude is h load , the observation point being located at the altitude h obs , the corresponding Green function for the variation of gravity is given by [START_REF] Merriam | Atmospheric pressure and gravity[END_REF][START_REF] Boy | Reduction of surface gravity data from global atmospheric pressure loading[END_REF]:

g s N (ψ) = G (a + h obs ) -(a + h load ) cos ψ [(a + h obs ) 2 + (a + h load ) 2 -2(a + h obs )(a + h load ) cos(ψ)] 3/2 . ( 18
)
Similarly ground tilt Green's function is also the sum of two terms,

t s (ψ) = - G g 0 a 2 ∞ n=1 k ′ n -h ′ n ∂P n (cos ψ) ∂ψ , (19)
A c c e p t e d M a n u s c r i p t due to the elastic deformation, and

t s N (ψ) = G g 0 (a + h load ) sin ψ [(a + h obs ) 2 + (a + h load ) 2 -2(a + h obs )(a + h load ) cos ψ] 3/2 (20)
for the tilt of the geoid due to the Newtonian attraction of the load.

g s N and t s N , given by Eqs ( 18) and ( 20), are plotted in Fig. 1 for h obs = 0 and 7 values of h load .

Figure 1

To cut off the series in Eqs ( 15), ( 16), ( 17), and ( 19) at a finite integer N and avoid Gibbs's phenomenon, we use Kummer's method [START_REF] Farrell | Deformation of the Earth by surface loads[END_REF][START_REF] Meur | A comparison of two spectral approaches for computing the Earth response to surface loads[END_REF][START_REF] Barletta | Glacier shrinkage and modeled uplift of the Alps[END_REF]. We take N = 10000 to guarantee a horizontal resolution of a few kilometers at the surface.

Comparison between half-space and spherical models

For small spatial scales, from some meters to several kilometers, the halfspace model is often adopted to estimate the Earth response to load variations [START_REF] Bevis | Geodetic measurement of the local elastic response to the changing mass of water in Lago Laja, Chile[END_REF][START_REF] Cavalié | Ground motion measurement in the Lake Mead area, Nevada, by differential synthetic aperture A c c e p t e d M a n u s c r i p t radar interferometry time series analysis: Probing the lithosphere rheological structure[END_REF]. For larger spatial scales, it is necessary to take the curvature of the Earth's surface into account as well as the rheology of the layers below the crust. To determine how well the deformation of a SNREI model can be approximated by that of a homogeneous half-space model, we compare Green's functions for the deformation of the two models. We consider a half-space with the same physical properties as A c c e p t e d M a n u s c r i p t the crust of the modified PREM (Table 1). In Figs 2 and 3, we plot various Green's functions and the absolute and relative differences ∆ abs and ∆ rel between Green's functions of the two models as a function of the distance between the observation and loading points. ∆ abs and ∆ rel are given by

∆ abs (R, 0) = G a -G s (21) ∆ rel (R, 0) = ∆ abs /G a (22)
where G a and G s are Green's functions respectively given by Eqs ( 6)-( 12)

and Eqs ( 15)-( 20). In Fig. 2 the amplitude of displacement and gravity

Green's functions decreases by 6 orders of magnitude over 1000 km, the amplitude of tilt Green's functions decreases by 12 orders of magnitude over the same distance. As shown by the ∆ abs 's and ∆ rel 's, Green's functions agree to within 1 % up to ∼ 400 m from the load for the vertical displacement and elastic part of the gravity changes, ∼ 2 km for the horizontal displacement, and ∼ 5 km for the elastic part of the tilt. Further from the loading point, the relative differences increase. As shown in Fig. 3, the 10% relative difference happens at ∼ 2.5 km, ∼ 6 km, and ∼ 10 km from the load for the vertical displacement and elastic part of the gravity changes, the horizontal displacement and elastic part of the tilt variations, respectively. Using Green's functions for the half-space and SNREI models, we investigate the ratios of tangential displacement to vertical displacement and elastic part of the gravity variations to vertical displacement. As noticed at the end of section 2.1 we find that the two ratios are constant for the half-space model. Indeed, as shown in Fig. 4, we have u a t /u a z = 0.304 and -g a 1z /u a z = -0.232 µGal/mm. The ratios u s t /u s z and g s /u s z of the SNREI model are also represented in Fig. 4. The first ratio agrees to within 1 % up to ∼ 400 m from the load and to within 10 % between ∼ 400 m and ∼ 3 km.

The second ratio agrees to within 1 % up to ∼ 4 km from the load and to within 15 % between ∼ 4 and ∼ 1000 km.

Figure 4

For the computation of the loading effects, the extension of the load and the distance from the load do really matter. [START_REF] Llubes | Local hydrology[END_REF] showed that the hydrological contributions to gravity can be separated into three scales: a local scale up to 1-10 km, a regional scale from 10 km up to 100 km and a global scale above 100 km. We can clearly see from Figs. 2 and3 that the deformation of the half-space is a very good approximation to the deformation of the SNREI model at the local scale. As Green's functions are rapidly varying functions near the load, especially for the tilt, it is difficult to interpolate them at the local scale. Then the deformation induced by A c c e p t e d M a n u s c r i p t the load variations at short distance from the load can be computed using the analytical Green's functions of the half-space model. This can apply, for example, to the zone near glaciers located in the same massif.

Space convolution

The displacement, gravity variation, and tilt of the ground due to ice thinning are obtained by convolving the ice-thickness variation ∆h with Green's functions G n given by Eqs ( 6)-( 12) or ( 15)-( 20):

E(θ, ϕ) = ρ ice Ω ∆h(θ ′ , ϕ ′ )G n (ψ) dΩ ′ , ( 23
)
where Ω is the surface covered by the ice of density ρ ice .

Gravito-elastic deformation due to ice thinning in the Mont

Blanc region (French Alps)

In this section, we compute the gravito-elastic deformation induced by ice thinning of three glaciers in the Mont Blanc region. We have shown in the previous section that the deformation of a SNREI model at the local scale, up to 1-10 km, can be approximated by the deformation of a homogeneous half-space model. We will show maps of gravity variation and deformation at places located further than 10 km from the glaciers. Therefore, it is necessary to base our calculation on a SNREI model.

Ice-thickness data

Ice-thickness variation ∆h from 1979 until 2003 has been deduced from the differential analysis of two DEMs [START_REF] Berthier | Recent rapid thinning of the 'Mer de Glace' glacier derived from satellite optical images[END_REF]. The first model transverse topographic profiles performed each year [START_REF] Vincent | Un service d'observation des glaciers des Alpes françaises "glacioclim-alpes[END_REF].

Differential DEM elevation changes have an accuracy of 2 m. Although we do not take into account the time variability of the ice-thinning rate, we can mention that, for example, [START_REF] Berthier | Recent rapid thinning of the 'Mer de Glace' glacier derived from satellite optical images[END_REF] give 3 rates for the glacier shrinkage at an elevation comprised between 1600 and 2100 m:

• 1979-1994: 1 ± 0.4 m/yr,

• 1994-2000: 2.9 ± 1.1 m/yr,

• 2000-2003: 4.1 ± 1.7 m/yr.

Therefore, during the period 2000-2003, the ice-thinning rate is four times bigger than the 1979-1994 rate at low elevation. On the average over 24 years, it is approximately 2 m/yr.

In the next 3 subsections, we compute the effects of the ice thinning in the Mont Blanc area on a grid with a resolution of 20 m. We only take into account 3 glaciers, which does not allow us to compare our results with Barletta et al.'s (2006) who consider the ice-mass loss all over the Alps.

But we can study the gravito-elastic deformation due to the spatially nonhomogeneous ice thinning of a small group of glaciers with both a realistic geographical extension and realistic changes for the volume of the ice. Next, assuming that the ice-thinning rate has been constant since 1979, we obtain deformation rates. We take ρ ice = 900 kg/m 3 .

A c c e p t e d M a n u s c r i p t Figures 6 and 7

Gravity changes

Fig. 8 shows the elastic part of the gravity variation. It ranges from -0.2 µGal to approximately -2 µGal over the 24-year period (i.e. from -0.008 to -0.08 µGal /yr). The pattern is the same as that of the rebound but of opposite sign. The uplift and the associated free-air gradient variation effects (decreasing gravity) have a higher amplitude than the mass redistribution effects (increasing gravity). Since the altitude of the glaciers ranges from 1500

A c c e p t e d M a n u s c r i p t m to 3500 m, it is necessary to take into account the difference of altitude between the observation point and the thinning area. Fig. 9 shows the direct attraction due to the loss of ice computed with Eq. ( 18). If we add this to the gravity variation shown in Fig. 8, we obtain a total gravity variation of several hundreds µGal over 24 years, which shows the strong influence of the topography on the gravity measurements in the close vicinity of the glaciers.

Figures 8 and 9

Tilt of the ground

The amplitude of the ground tilt due to 24 years of ice thinning reaches 15 µrad at 20 m from the glaciers, as shown in Fig. 10. The highest amplitude of the tilt outside the glaciers is near the ice tongue of the Mer de glace.

There, the ice-thinning rate is the highest. The Newtonian part of the tilt is one order of magnitude smaller than the elastic part. The annual variation of the tilt reaches 0.63 µrad/yr at 20 m and 0.03 µrad/yr at 2km from the glaciers. It rapidly decreases with the distance from the load variations.

Because of the unrealistic assumption of a constant ice-thinning rate, the displacement, gravity and ground-tilt rates are probably underestimated for thinning. This rate is in agreement with that proposed by [START_REF] Sato | A geophysical interpretation of the secular displacement and gravity rates observed at Ny-Ålesund, Svalbard in the Arctic-effects of post-glacial rebound and present-day ice melting[END_REF].

A c c e p t e d M a n u s c r i p t

The Midtre Lovénbreen glacier is half-way between the station and the nearest ice mass in the SVAL model. Such a rate close to the station suggests that the tilt rates we have obtained from the SVAL model are underestimated. A better estimation of the thinning rates could be computed in the future by considering DEMs from the SPIRIT project [START_REF] Korona | SPIRIT. SPOT 5 stereoscopic survey of Polar Ice: Reference Images and Topographies during the fourth International Polar Year (2007-2009)[END_REF] or ICESAT altimetric profiles [START_REF] Kääb | Glacier volume changes using ASTER satellite stereo and ICESat GLAS laser altimetry. A test study on Edgeøya, Eastern Svalbard[END_REF].

Observations of deformation and gravity variation

The ground displacement near ice masses can be monitored by using GPS and VLBI measurements. [START_REF] Sjöberg | Land uplift near Vatnajökull, Iceland, as observed by GPS in 1992, 1996 and 1999[END_REF] analyzed three epochs of GPS campaigns over a period of 7 years, from 1992 to 1999. They obtained uplift rates comprised between 5 and 19 mm/yr near the Vatnajökull ice cap in Iceland. [START_REF] Sato | A geophysical interpretation of the secular displacement and gravity rates observed at Ny-Ålesund, Svalbard in the Arctic-effects of post-glacial rebound and present-day ice melting[END_REF] derived ground-displacement rates from GPS and VLBI measurements at Ny-Ålesund. They found a rebound of ∼ 5 mm/yr for the periods 1998-2004 and 1994-2004 respectively associated to the GPS and VLBI measurements. [START_REF] Khan | Elastic uplift in southeast Greenland due to rapid ice mass loss[END_REF] glacial rebound and the present-day ice thinning. The small gravity variation signal expected from the latter, about -0.5 µGal/yr (Table 2), suggests that it is difficult to observe far from the thinning area by using gravimeters.

The gravity variation close to the glaciers, which is much bigger (Section 3.3), would give a larger signal that would be easy to observe provided a gravimeter can be installed near the glaciers.

The sensitivity of the tiltmeters depends on the variability of the environment parameters, for instance the temperature, and type of instrument. Indeed, to decrease the influence of the temperature variation, the tiltmeters are often installed in mine galleries. Besides, the long-baseline hydrostatic tiltmeters are less sensitive to the local heterogeneities than the short-baseline tiltmeters and are also more stable [START_REF] Boudin | Développement et validation d'un inclinomètre longue base de subsurface à silice et mercure: Application à des mesures géophysiques de haute résolution sur le chantier pilote du Golfe de Corinthe[END_REF]d'Oreye et al., 2005;[START_REF] Boudin | A silica long base tiltmeter with high stability and resolution[END_REF]. The accuracy of a 100 meter-long tiltmeter is 1 × 10 -4 µrad and its time stability is better than 1 × 10 -1 µrad/yr (Rerolle et al., 2006et al., ). d'Oreye et al. (2005) ) developed and installed their instrument in an underground mine where they obtained a drift rate that did not exceed 5 × 10 -3 µrad/month and a sensitivity of 5 × 10 -6 µrad in the long-period seismic band and 34 × 10 -6 µrad for longer periods. Recently, [START_REF] Boudin | A silica long base tiltmeter with high stability and resolution[END_REF] have shown that the stabilities of two 100 meter-long tiltmeters installed in a mine in the Vosges massif in France are 6.5 × 10 -3 µrad/month and 10 ×10 -3 µrad/month and a low noise level of the order of 1×10 -5 µrad.

They also indicate that such instruments in similar conditions are suitable for the monitoring of long-term tilt rates lower than 1 × 10 -1 µrad/yr. Our computation of ground tilt because of shrinking ice masses in the Alps and A c c e p t e d M a n u s c r i p t

Svalbard shows that the expected signal is well above the instrumental noise and that it should be measurable even if the instrument is not installed in the close vicinity of the glaciers. If the conditions for installing high-precision tiltmeters are fulfilled, then hydrostatic tiltmeter measurements are potentially appropriate to monitor the ice thinning of nearby glaciers.

Conclusion

We have computed Green's functions of the vertical and horizontal displacements, gravity change and ground tilt for a homogeneous half-space model and a realistic spherical Earth model. We have compared Green's functions for the two models and confirmed that the half-space approximation is sufficient to model the Earth deformation at the local scale (1 to 10 km away from the load) .

We have also given the amplitude and geographical extension of the displacements, gravity variations and ground tilt changes induced by the thinning of 3 glaciers in the Mont Blanc region, where ice-thickness variations were previously measured over a 24-years period, and by a homogeneous thinning of the glaciers of Svalbard. We have shown that taking into account the topography of both the surrounding ice-free regions and glaciers is necessary to estimate the magnitude of the gravity variations. We have deduced the tilt rates due to the load variations and compared them with the A c c e p t e d M a n u s c r i p t

Table 1 Density, seismic wave velocities V p and V s and quality factors Q µ and Q κ of the crust that replaces the ocean layer in the PREM model of [START_REF] Dziewonski | Preliminary reference Earth model[END_REF].

Table 2 Deformation induced at the Ny-Ålesund GGP station in Svalbard, Norway, by the SVAL model with an ice-thinning rate of 47 cm/yr and density of 1000 kg/m 3 . Numbers in bold are for the gravity and tilt rates that take into account the topography of the ice masses.

Figure 1 Green functions for the gravity variation g s N and tilt t s N of a spherical Earth model due to the gravitational attraction of the load, given by Eqs ( 18) and ( 20) with h obs = 0 and 7 values for h load . Instead of the angular distance ψ, the abscissa is the distance aψ. [START_REF] Berthier | Recent rapid thinning of the 'Mer de Glace' glacier derived from satellite optical images[END_REF]. The highest and lowest altitudes are also indicated. (1981). t /u a z (dashed red line), u s t /u s z (solid red line), -g a 1z /u a z (dashed black line), and g s /u s z (solid black line) as a function of the distance to the loading point. The last two ratios are in µGal/mm whereas the two first are dimensionless.

Density (kg/m 3 ) V p (m/s) V s (m/s) Q µ Q κ 2600

  , the gravity variation is reintroduced in the problem through Poisson's equation (

  taking λ = 3.29 × 10 10 Pa, µ = 2.56 × 10 10 Pa, and ρ 0 = 2500 kg/m 3 , which correspond to a P-wave velocity of 5800 m/s and a S-wave velocity of 3200 m/s, we have g 1 a z /u a z = 0.235 µGal/mm, in agreement with the ratio found by de Linage et al. (2007) for a self-gravitating spherical elastic Earth model, and u a R /u a z = 0.304.

Figures

  Figures2 and 3

  aerial photographies taken in 1979, the second one, from images acquired by the SPOT 5 satellite in 2003. Detailed explanations can be found in[START_REF] Berthier | Recent rapid thinning of the 'Mer de Glace' glacier derived from satellite optical images[END_REF]. ∆h is shown in Fig.5. The accuracy of these elevation changes has been assessed by comparison with precise (±30 cm)

  Figure 5

  the 1994-2003 period and overestimated for the 1979-1994 period, at least if the ice-thinning rate increased with time everywhere as it did at low elevation

Figure 10 4.

 10 Figure 10

  deduced from two computations. The first one includes neither the topography of the ice masses nor the altitude of the station. We obtain a total gravity variation rate of -0.52 µGal/yr. The 3 nearest ice masses are responsible for 61.54 % of this rate. The second computation includes the effect of the topography of the ice masses and the altitude of the station. The gravity rate due to the 16 ice masses is -0.48 µGal/yr, which is smaller in absolute value than in the first case because the effects of the thinning areas which are above and below the horizontal plane at the station, especially for the surrounding ice masses, act in opposite senses.The surrounding ice masses are responsible for 58.33 % of this rate; the contribution from the other ice masses, which is -0.20 µGal/yr, is the same as in the first computation where we did not take the topography of the ice masses into account. The magnitude of the tilt rates are 70.26 and 37.97 nrad/yr respectively for the West-East (positive in the East direction) and South-North (positive in the North direction) components. The thinning of the 3 nearest ice masses contibute for 90 % to the tilt of the ground.[START_REF] Sato | A geophysical interpretation of the secular displacement and gravity rates observed at Ny-Ålesund, Svalbard in the Arctic-effects of post-glacial rebound and present-day ice melting[END_REF] suggested an ice-thinning rate of ∼ 70 -80 cm/yr to explain the present-day ice-thinning contribution to the rebound observed by VLBI and GPS. But this rate fails to explain the absolute gravity variations associated to the elastic deformation due to present-day ice-thinning.[START_REF] Kohler | Acceleration in thinning rate on western Svalbard glaciers[END_REF] estimated the ice-thinning rate from DEMs for the Midtre Lovénbreen glacier located within 5 km from Ny-Ålesund. For the period 2003-2005, they obtain a rate of ∼ 69 cm/yr, which is almost 1.5 times bigger than the mean rate we used to estimate the effects induced by ice

  observed an elastic uplift of ∼ 35 mm (∼ 7 mm/yr) at the GPS site in Kulusuk, Greenland, due to the rapid thinning of ice between 2001 and 2006 in the southeastern sector of the Greenland ice sheet. These strong uplifts occured in regions where large ice masses experienced high thinning rates. As shown in Section 3.2 the rebound due to 24 years of ice thinning in the Alps over a small area is smaller, at most 9 mm (0.38 mm/yr), and identifying such a small contribution to the total uplift in the GPS measurements remains a difficult task. Sato et al. (2006) also derived gravity variations at Ny-Ålesund from repeated absolute gravity measurements and found a rate of -2.5 µGal/yr A c c e p t e d M a n u s c r i p t for the period 1998-2003. This rate includes different effects such as the post-

  sensitivity and time stability of available long-baseline tiltmeters. For the 3 glaciers of the Mont Blanc massif that we have considered and the glaciers of Svalbard, it should be possible to monitor the local ice-mass variations with hydrostatic tiltmeters, if they were installed at appropriate sites. The A c c e p t e d M a n u s c r i p t seasonal and annual signals could then be extracted. Finally, for the sites where continuous GPS and gravity measurements are already made, such as in the Ny-Ålesund GGP station, tilt measurements would provide a useful complementary information. Moreover, local ground data, often sparse in time and space, would benefit from the integrated view and continuous recording of tiltmeters. N. F. & Zürn W., 2005. Very high resolution long-baseline water-

Figure 2

 2 Figure2Green's functions for a homogeneous half-space model (solid lines) and a spherical model (dashed lines). Black, cyan, red and green curves refer respectively to the vertical and horizontal displacements and non-Newtonian gravity and tilt changes. The dotted dashed lines represent the absolute differences ∆ abs (Eq. 21).

Figure 3 .

 3 Figure3. Relative differences ∆ rel (Eq. 22) between Green's functions of half-space and spherical models with respect to the half-space model. Black, cyan, red and green curves refer respectively to the vertical and horizontal displacements and non-Newtonian gravity and tilt changes.

Figure 4 .

 4 Figure4. Ratios of Green's functions: u a t /u a z (dashed red line), u s t /u s z (solid red line), -g a 1z /u a z (dashed black line), and g s /u s z (solid black line) as a function of the distance to the loading point. The last two ratios are in µGal/mm whereas the two first are dimensionless.

Figure 5 .

 5 Figure 5. Ice-thickness variation (in m) between 1979 and 2003 in the Mont Blanc region that includes the three glaciers of the Mer de Glace, Talèfre and Leschaux[START_REF] Berthier | Recent rapid thinning of the 'Mer de Glace' glacier derived from satellite optical images[END_REF]. The highest and lowest altitudes

Figure 6 .

 6 Figure 6. Vertical displacement (in mm) due to the ice thinning in the Mont Blanc area for the modified PREM. Glaciers are filled in black.

Figure 7 .

 7 Figure 7. Horizontal displacement (in mm) due to the ice thinning in the Mont Blanc area for the modified PREM. The arrows indicate the direction of the motion of the ground and the colored background shows the amplitude of the displacement. Glaciers are filled in black.

Figure 8 .

 8 Figure 8. Elastic part of the gravity effects (in µGal) due to the icethinning in the Mont Blanc area for the modified PREM. Glaciers are filled in black.

Figure 9 .

 9 Figure 9. Newtonian part of the gravity effects (in µGal) due to the ice thinning in the Mont Blanc area for the modified PREM. Glaciers and the region with no topography data are filled in black. Note that the color scale is opposed to that in the former figures.

Figure 10 .

 10 Figure 10. Tilt changes (in µrad) due to the ice thinning in the Mont Blanc area for the modified PREM. The arrows indicate the direction of the tilt of the ground and the colored background shows the amplitude of the tilt variations. To have a clear picture of the area where the tilt is significant, we show the tilt changes up to 3 µrad only. Glaciers are filled in black.

Figure 1 :

 1 Figure1: Green functions for the gravity variation g s N and tilt t s N of a spherical Earth model due to the gravitational attraction of the load, given by Eqs (18) and (20) with h obs = 0 and 7 values for h load . Instead of the angular distance ψ, the abscissa is the distance aψ.

Figure 2 :

 2 Figure 2: Green's functions for a homogeneous half-space model (solid lines) and a spherical model (dashed lines). Black, cyan, red and green curves refer respectively to the vertical and horizontal displacements and non-Newtonian gravity and tilt changes. The dotted dashed lines represent the absolute differences ∆ abs (Eq. 21).

Figure 3 :

 3 Figure3: Relative differences ∆ rel (Eq. 22) between Green's functions of half-space and spherical models with respect to the half-space model. Black, cyan, red and green curves refer respectively to the vertical and horizontal displacements and non-Newtonian gravity and tilt changes.

Figure 4 :

 4 Figure4: Ratios of Green's functions: u a t /u a z (dashed red line), u s t /u s z (solid red line), -g a 1z /u a z (dashed black line), and g s /u s z (solid black line) as a function of the distance to the loading point. The last two ratios are in µGal/mm whereas the two first are

Table 2

 2

	. We see

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Table 1 :

 1 Density, seismic wave velocities V p and V s and quality factors Q µ and Q κ of the crust that replaces the ocean layer in the PREM model of Dziewonski and Anderson

Table 2 :

 2 Deformation induced at the Ny-Ålesund GGP station in Svalbard, Norway, by the SVAL model with an ice thinning rate of 47 cm/yr and density of 1000 kg/m 3 . Numbers in bold are for the gravity and tilt rates that take into account the topography of the ice-masses.

		16	3	13	16 ice-masses
		ice-masses	ice-masses	ice-masses	Sato et al. (2006)
	Vertical
	displacement	2.04	1.27 (62.26 %)	0.77 (37.74 %)	2.04
	(mm/yr)
	Gravity	-0.52	-0.32 (61.54 %)	-0.20 (38.46 %)	-0.53
	(µGal/yr)	-0.48	-0.28 (58.33 %) -0.20 (41.67 %)	-
	Tilts (nrad/yr)
	West-East	-70.26	-32.14 (88.44 %) -8.12 (11.56 %)	-
	South-North	37.97	37.90 (99.82 %)	0.07 (0.18 %)	-

Acknowledgements

A. Memin acknowledges financial support from the Centre National d'Etudes Spatiales. We thank T. Sato for providing the SVAL model and two anonymous reviewers for their suggestions and constructive comments.

 [START_REF] Berthier | Recent rapid thinning of the 'Mer de Glace' glacier derived from satellite optical images[END_REF]. The highest and lowest altitudes are also indicated.

A c c e p t e d M a n u s c r i p t


Mohammed A Aleskandarany

Emad A Rakha

Mohammed A Ahmed

Des G Powe

Ian O Ellis

Dr Andrew R Green
email: andrew.green@nottingham.ac.uk

Clinicopathologic and Molecular Significance of phospho-Akt expression in Early Invasive Breast Cancer

Keywords: pAkt/PKB, oncogene, immunohistochemistry, Breast cancer

Akt/PKB serine/threonine kinase is a leading signalling modulator for several cellular processes including metabolism, growth, proliferation, and survival. However, complexity and diversity in the upstream/downstream arms of Akt pathway, as recent genetic studies reported, challenge considerably the evolvement of effective targeted therapies.

Aim: To study the expression of phospho-Akt1 (pAkt) in breast cancer (BC), with respect to different component proteins upstream/downstream of Akt pathway activation, clinicopathologic parameters, and patients' outcome. pAkt (ser473) was evaluated by immunohistochemistry, on tissue microarrays containing 1,202 early invasive BC with long term clinical follow-up.

Seventy six percent of the studied tumours overexpressed pAkt, where it was associated with expression of estrogen and androgen receptors, PIK3CA, cytokeratin (CK)18, CK19 and PTEN. Loss of pAkt was correlated with high grade, CK5/6, p53 and high Ki67 labelling index. Higher proportions of luminal tumours were pAkt positive relative to triple negative/basal subtypes. However, pAkt overexpression was not associated with breast cancer specific (BCSS) or metastasis free survival (MFS).

Four tumour phenotypes were identified based on PIK3CA and pAkt expression, with substantial proportions being PIK3CA -/pAkt + or PIK3CA + /pAkt -. These four combinatorial phenotypes were significantly associated with BCSS (p=0.001) and MFS (p=0.002).

Although pAKT is an oncogene correlated with poor prognostic variables, it was not a prognostic marker. Combinatorial phenotypic groups of PIK3CA/pAkt denoted functional complexity, at translational level, within the upstream and downstream arms of Akt activation with significant impact on patients' outcome. These findings may help development more adequate therapeutic regimens for specific subgroups of this key cancer pathway.

Introduction

Akt (also termed Protein Kinase B, PKB), a serine/threonine kinase, is an important signalling mediator between extracellular stimuli and the modulation of diverse cellular processes including metabolism, cell growth, proliferation, and survival [START_REF] Chin | Function of Akt/PKB signaling to cell motility, invasion and the tumor stroma in cancer[END_REF][START_REF] Song | The activation of Akt/PKB signaling pathway and cell survival[END_REF]. Akt is a major downstream target of the phosphoinositide 3-kinase (PI3-K) signalling pathway [START_REF] Arcaro | The phosphoinositide 3-kinase pathway in human cancer: genetic alterations and therapeutic implications[END_REF]. Recent studies have revealed that the PI3-K/Akt signalling network harbours some of the most prevalent genetic derangements in cells and tissues derived from almost all human solid cancers [START_REF] Altomare | Perturbations of the AKT signaling pathway in human cancer[END_REF]. Therefore, PI3K/Akt has emerged as a key target for cancer treatment strategies [START_REF] Engelman | Targeting PI3K signalling in cancer: opportunities, challenges and limitations[END_REF] Activation of Akt1 is a multistep process initiated primarily through the binding of exogenous growth factors to receptors having intrinsic tyrosine-kinase activity. Such binding phosphorylates, and activates the intracellular tyrosine-kinasecontaining moiety of the receptor [START_REF] Jiang | PI3K/PTEN signaling in angiogenesis and tumorigenesis[END_REF]. One of the several proteins recruited to and activated by the tyrosine phosphorylated growth factor receptor is PI3-kinase, which converts phosphatidyl inositol-4, 5-bisphosphate (PIP2) at the 3′ position of the inositol ring to PIP3, leading to recruitment of Akt1 via its pleckstrin homology (PH) domain to the plasma membrane. Akt1 phosphorylation is mediated by phosphatidyl inositol-3-phophate dependent kinases; PDK1 which phosphorylates Akt1 at Threonine (Thr) 308, and another kinase that phosphorylates it at Serine (Ser) 473 [START_REF] Jiang | PI3K/PTEN signaling in tumorigenesis and angiogenesis[END_REF][START_REF] Vogt | A random walk in oncogene space: the quest for targets[END_REF][START_REF] Woodgett | Recent advances in the protein kinase B signaling pathway[END_REF]. In addition, other Akt1 activators have been reported including DNA-PK, oxidative stresses, HSP90 (heat shock protein-90KDa), PKC-β (protein kinase C-Beta), integrins via focal adhesion kinase (FAK), and others [START_REF] Matheny | Current perspectives on Akt Aktivation and Akt-ions[END_REF][START_REF] Sarbassov | Phosphorylation and Regulation of Akt/PKB by the Rictor-mTOR Complex[END_REF] Phosphorylated Akt, pAkt, exerts its effects in the cell by phosphorylating a wide variety of downstream substrates including; caspase9, MDM2, Androgen receptor (AR), p21, p27, GSK (Glycogen Synthase Kinase), and others [START_REF] Paez | PI3K/PTEN/AKT pathway. A critical mediator of oncogenic signaling[END_REF]. These alterations culminate in pleiotropic biological events, including cell growth, survival and migration, which contribute not only to oncogenesis but also to tumour progression [START_REF] Chin | Function of Akt/PKB signaling to cell motility, invasion and the tumor stroma in cancer[END_REF][START_REF] Song | The activation of Akt/PKB signaling pathway and cell survival[END_REF].

Constitutive activation of Akt1 occurs in human cancer through different mechanisms. Firstly, deletion and mutation of PTEN (Phosphatase and Tensin Homolog); the phosphatase that dephosphorylates PI3-K and hence negatively regulating Akt [START_REF] Jiang | PI3K/PTEN signaling in tumorigenesis and angiogenesis[END_REF]. Secondly, through amplification of the Akt gene [START_REF] Staal | Molecular cloning of the akt oncogene and its human homologues AKT1 and AKT2: amplification of AKT1 in a primary human gastric adenocarcinoma[END_REF], or PH domain mutation of Akt1 leading to increased its affinity for phosphoinositides and membrane localisation [START_REF] Carpten | A transforming mutation in the pleckstrin homology domain of AKT1 in cancer[END_REF], and thirdly through amplification or mutation of the PIK3CA [START_REF] Yuan | PI3K pathway alterations in cancer: variations on a theme[END_REF].

Currently, an abundance of basic and pre-clinical studies have been conducted to elucidate implications of pAkt pathway derangements in breast cancer using different detection systems and tissue platforms [START_REF] Al-Bazz | Immuno-analysis of phospho-Akt in primary human breast cancers[END_REF][START_REF] Blanco-Aparicio | PTEN, more than the AKT pathway[END_REF]. The use of immunohistochemistry (IHC) has been collectively considered as a useful means of identifying the Akt status in a wide range of human cancers including BC with most studies reporting that increased pAKT expression correlates with clinical aggressiveness and progression [START_REF] Shtilbans | Current overview of the role of Akt in cancer studies via applied immunohistochemistry[END_REF][START_REF] Wu | Clinical significance of Akt and HER2/neu overexpression in African-American and Latina women with breast cancer[END_REF], while others find no such associations [START_REF] Frogne | Determination of HER2 phosphorylation at tyrosine 1221/1222 improves prediction of poor survival for breast cancer patients with hormone receptor-positive tumors[END_REF].

However, the complexity and diversity in the upstream and downstream arms of this pathway, reinforced by recent genetic studies [START_REF] Vasudevan | AKT-independent signaling downstream of oncogenic PIK3CA mutations in human cancer[END_REF][START_REF] Stemke-Hale | An integrative genomic and proteomic analysis of PIK3CA, PTEN, and AKT mutations in breast cancer[END_REF], bear considerable challenges and limitations that might confront the clinical evolvement of effective targeted therapies [START_REF] Engelman | Targeting PI3K signalling in cancer: opportunities, challenges and limitations[END_REF]. This retrospective study adheres to REMARK criteria [START_REF] Mcshane | REporting recommendations for tumor MARKer prognostic studies (REMARK)[END_REF].

This study was conducted to determine the pAkt status in a large series of human invasive breast cancer to study the relationship of its expression with different upstream/downstream component proteins, as well as correlations with clinicopathological parameters and disease outcome.

Material and Methods:

Patients and tumours

This study was conducted on a well-characterised series of early stage (pT1 & pT2) primary operable invasive breast carcinoma from patients enrolled into the Nottingham Tenovus Primary Breast Carcinoma Series that presented at Nottingham City Hospital between 1990 and 1998. Patients were under the age of 70 years and managed in a uniform manner. Patients' clinical history and tumour criteria, information on therapy and outcomes were available and prospectively maintained.

Outcome data included survival status (whether alive, or deceased), survival time (in months), cause of death (died from breast cancer, other cause, or lost to follow-up), disease free interval (DFI), time to loco-regional recurrence, and/or distant metastasis.

The Breast Cancer Specific Survival (BCSS) is defined as the time (in months) from the date of primary surgery to the date of breast cancer-related death. DFI is defined as the duration (in months) from the date of primary surgery to the appearance of loco-regional recurrence or distant metastasis. Data on a wide range of biomarkers of known clinical and biological relevance to breast cancer were available [START_REF] El-Rehim | High-throughput protein expression analysis using tissue microarray technology of a large wellcharacterised series identifies biologically distinct classes of breast cancer confirming recent cDNA expression analyses[END_REF]. These include, hormone receptors [estrogen receptor (ER), progesterone receptor (PR), androgen receptor (AR)], epidermal growth factor receptor family members [HER1 (EGFR), HER2, HER3 and HER4], cytokeratins (CKs); basal CKs (CK5/6 and CK14), and luminal CKs (CK18 and CK19), tumour suppressor genes (p53 and PTEN), the Akt pathway activator PIK3CA, proliferation-related and cell cycle regulator markers (Ki-67, p21, p27, Bcl2 and cyclin D1), and cadherin family members (E-cadherin and P-cadherin) [START_REF] El-Rehim | High-throughput protein expression analysis using tissue microarray technology of a large wellcharacterised series identifies biologically distinct classes of breast cancer confirming recent cDNA expression analyses[END_REF][START_REF] Rakha | Triple-negative breast cancer: distinguishing between basal and nonbasal subtypes[END_REF].

The patients had a median age at diagnosis of 54 years (range 18-70 years) with a median overall survival of 125 months (range 4-243 months) and the median time of event-free survival of 112 months (range 2-239 months). Distant recurrence occurred in 375 cases (31%), while 313 (26%) patients died from breast cancer, while 689 (59%) patients were alive at the end of follow-up.

This study was approved by Nottingham Research Ethics Committee 2 under the title of "Development of a molecular genetic classification of breast cancer".

Immunohistochemistry

Expression of pAkt1 in breast cancer was assessed using immunohistochemistry. Four-μm sections were cut from paraffin processed block of previously prepared tissue microarrays (TMAs) and mounted on Superfrost slides (Surigpath). Sections were deparaffinised and heat induced retrieval of antigen epitope was performed in citrate buffer (pH 6.0). Endogenous peroxidase activity was blocked with 0.3% hydrogen peroxide for 10 minutes. The sections were incubated at room temperature for 60 minutes with polyclonal antibody against S473pAkt1 (RB-10369-P1, Neomarkers, Fremont, CA) optimally diluted 1:150, Following wash in TBS , sections were for 60 minutes in Strept AB complex (Dako, Denmark) diluted in 1:100 in normal swine serum/TBS, followed by chromagen for visualisation [3-3'Diaminobenzidine tetrahydrochloride (Dako liquid DAB Plus, K3468; Dako, Denmark)]. Sections were counterstained with Mayer's haematoxylin. Negative (primary antibody replaced by TBS) and positive (a known pAkt positive full-face BC tissue section) controls were included in the staining run.

Validation of anti Phospho-AKT (S473) antibody specificity:

For validation of anti Phospho-AKT (S473) antibody specificity, Western blotting was performed on whole cell lysates of MCF-7 and MDA-MB231 human breast cancer cell lines (obtained from the American Type Culture Collection; Rockville, MD, USA) using 1:100 dilution of the primary antibody dilution, and 1:2000 of the HRP labelled secondary anti-rabbit antibody. BSA was used for blocking. ECL was used to visualize the membrane as previously described [START_REF] Albasri | C-terminal Tensin-like (CTEN) is an oncogene which alters cell motility possibly through repression of E-cadherin in colorectal cancer[END_REF].

TMA IHC scoring

Stained TMAs sections were scored using the semi-quantitative H-score (Histochemical score) visual approach, taking into consideration the intensity of staining and the percentage of stained cells [START_REF] Mccarty | Estrogen receptor analyses. Correlation of biochemical and immunohistochemical methods using monoclonal antireceptor antibodies[END_REF] within each tissue core. Staining intensity was scored as 0, 1, 2 or 3 for negative, weak, moderate and strong, respectively. The proportion (percentage) of positive cells for each intensity were subjectively estimated. Final scores were obtained by the sum of multiplying each staining intensity by its proportion, producing an H-score ranging from 0-300. All cases were scored without prior knowledge of the patients' pathologic or outcome.

Statistical analysis

Statistical analysis was performed using SPSS 16.0 statistical software (SPSS Inc., Chicago, IL, USA). Cut-off values for the different biomarkers included in this study were chosen before statistical analysis. Standard cut-offs were used for established prognostic factors and were the same as for previously published patient series [START_REF] El-Rehim | High-throughput protein expression analysis using tissue microarray technology of a large wellcharacterised series identifies biologically distinct classes of breast cancer confirming recent cDNA expression analyses[END_REF][START_REF] Rakha | Triple-negative breast cancer: distinguishing between basal and nonbasal subtypes[END_REF]. Determination of the optimal pAkt cut-offs for pAkt staining was obtained using pAkt H-score frequency distribution histogram. Analysis of categorical variables was performed using the appropriate statistical test. Survival estimates were analyzed by Kaplan-Meier method with significance determined by the Log Rank test.

Multivariate analysis was performed by Cox proportional hazard analysis. A p-value

<0.05 (two sided) was considered significant.

Results

pAkt expression in stained TMA sections (n=1,202) showed homogenous cytoplasmic immunoreactivity in invasive tumour cells (Figure 1A&B). The specificity of the antibody was confirmed using a Western blotting analysis of MCF-7 and MDA-MB231 human breast cancer cell lines, which showed a specific band at the correct predicted size (~ 60 KDa) of the pAkt protein confirming the specificity of the antibody used in the IHC staining (Figure 1C). The distribution of pAkt H-score did not display normal distribution (median =100). Using the pAkt H-score frequency distribution histogram, the optimal cut-off point for pAkt positivity was set at 65 (taken at the mid-point of the observed trough in the distribution histogram of pAkt), that dichotomised the cohort into two categories: pAkt negative (H-score<65), and pAkt positive expression (H-score ≥65). Therefore, 914/1202 (76%) cases were positively stained with pAkt, with the remaining cases 288 (24%) were negative.

Association of pAkt with clinico-pathologic parameters

Table 1 summarises the associations between pAkt expression and clinicopathological variables. pAkt overexpression showed significant positive association with patients' age (p= 0.003) and menopausal status (p= 0.002), while a significant negative association was observed with tumour grade (p= 0.005). Interestingly, a trend toward significant negative associations was observed between pAkt and grade components; mitosis, tubule formation and pleomorphism (p= 0.07). In addition, pAkt was associated with histologic tumour type (p= 0.008). Importantly, special types such as pure tubular and lobular carcinomas showed high proportions of pAkt overexpression compared with medullary-like carcinomas. pAkt expression was not significantly associated with tumour size, axillary nodal involvement, Nottingham Prognostic Index (NPI), or with lympho-vascular invasion (LVI); p> 0.05). Similar associations were obtained when the pAkt (H-score) expression was used as a continuous variable (data not shown).

Correlation between pAkt expression and the expression of other biomarkers and molecular classes of breast cancer:

A significant positive association was found between pAkt and expression of ER, androgen receptor (AR), luminal CKs, HER4, PIK3CA, and PTEN. In addition, loss of pAKT expression was associated with p53 positive, basal CKs positive, and tumour growth fraction as assessed by the Ki-67/MIBLI. However, no associations were found between pAkt and the expression of PR, the adhesion molecules Ecadherin and p-cadherin, or with the cell cycle regulators p21, p27, and Bcl-2.

The correlation between pAkt status and expression of the HER family members was investigated. Although there was a positive association between pAkt expression and the expression of HER4, no associations were found between pAkt and the expression of EGFR, HER2 or HER3. Tumours were profiled based on their HER family members expression into three groups; a) HER2 -/HER1,3&4 -(i.e. all negative), b) HER2 + /HER1 + and/or HER3 + and/or HER4 + , and c) HER2 -/ HER1 + and/or HER3 + and/or HER4 + . However, no correlations were noticed between these groups and the pAkt status ( 2=3.028, p= 0.220).

pAkt expression was significantly associated with the molecular BC subtypes as defined by their immunohistochemical profiles; luminal-like (ER + and/or PR + ), HER2 + (HER2 positive), triple negative basal-like BC (BLBC; ER -, PR -, HER2 -, and positive for CK5/6, and/or CK14 and/or EGFR) and triple negative non-basal BC (TNnon-B; ER -, PR -, HER2 -, CK5/6 -, and/or CK14 -and/or EGFR -), ( 2=28.6, p<0.001). Interestingly, BLBC and TNnon-B subtypes displayed significantly higher proportions (38.4%, and 42%, respectively) of pAkt negativity, compared to the luminal-like tumours and HER2 over-expressing BC (21.6% and 20.2%, respectively), Table 2.

Association of pAkt with patients' outcome

Although univariate survival analyses showed that there was no significant difference between patients with pAkt positive and negative tumours for BCSS and metastasis free-survival, MFS, (log rank, (LR) =2.643, p=0.104, and LR=2.265, p=0.132, respectively), patients with pAkt positive tumours showed a trend towards a relatively shorter BCSS and MFS when compared to those showing pAkt negativity, Figure 2 A&B.

PIK3CA/pAkt combinatorial groups

To address interactions between pAkt and PIK3CA expression and its correlation with clinicopathological parameters and patients' outcomes, tumours were re-defined based on their expression of both pAkt and PIK3CA, resulting in four phenotypic groups; PIK3CA -/pAkt -, PIK3CA -/pAkt + , PIK3CA + /pAkt -, and PIK3CA + /pAkt + . Table 3 displays the resulting numbers and percentages of this combination. The majority of tumours showed PIK3CA + /pAkt -phenotype while PIK3CA -/pAkt + was the least common phenotype.

Significant positive association was found between these phenotypic groups and patient age (p=0.001), menopausal status (p=0.001), tumour grade (p<0.001), LVI (p<0.001), NPI (p<0.001), and molecular subtype (p<0.001). Importantly, PIK3CA + groups showed more aggressive features regardless of the expression of pAkt (PIK3CA + /pAkt -and PIK3CA + /pAkt + ). These groups showed association with higher histological grade, LVI positivity and were in the moderate and poor NPI categories (p>0.05).

Using the Kaplan-Meier survival plots and log rank statistics, significant differences were noticed between these phenotypes for patients' BCSS and MFS, (LR=15.5, p=0.001, HR=1.319, 95% CI=1.140-1.526, and LR=14.4, p=0.002, HR=1.271, 95% CI=1.115-1.449, respectively, Figure 2A&B) independently of patients' age, menopausal status, LVI, molecular subtypes, and adjuvant therapy (p=0.034, HR=1.184, 95% CI=1.013-1.483 for BCSS, and p=0.024, HR=1.173, 95% CI=1.021-1.348 for MFS). However, inclusion of the grade into Cox proportional hazard models for BCSS and MFS left the PIK3CA/pAkt combinations as a gradedependant prognostic variable (p>0.05). Importantly, tumours positive for PIK3CA showed worse outcome regardless of the expression of pAkt and no significant survival difference was observed between patients having PIK3CA + /pAkt -and PIK3CA + /pAkt + tumours.

Discussion

The expression of pAkt in this study, as determined by IHC, demonstrated that 914/1202 (76%) of investigated tumours overexpressed pAkt. This relatively high prevalence of may be a reflection of pAkt oncogenetic role that was reported to occur early during the cascade of carcinogenic events, seen in the in-situ stage carcinomas prior to their progression to invasive carcinomas [START_REF] Bose | The Akt pathway in human breast cancer: a tissue-array-based analysis[END_REF].

A significant inverse association was found between pAkt and tumour grade, with a trend toward significance with individual grade components especially mitosis, which is reinforced by the significant negative association with proliferative fraction as assessed by MIB1-LI and are in accordance with previous studies [START_REF] Panigrahi | The role of PTEN and its signalling pathways, including AKT, in breast cancer; an assessment of relationships with other prognostic factors and with outcome[END_REF]. However, other investigators reported direct association of pAkt with tumour grade [START_REF] Gershtein | Phosphatidylinositol 3-kinase/AKT signalling pathway components in human breast cancer: clinicopathological correlations[END_REF][START_REF] Florena | Associations between Notch-2, Akt-1 and HER2/neu expression in invasive human breast cancer: a tissue microarray immunophenotypic analysis on 98 patients[END_REF]. In line with others [START_REF] Al-Bazz | Prognostic significance of Akt, phospho-Akt and BAD expression in primary breast cancer[END_REF], a direct association was revealed between pAkt expression and patients' age and menopausal status. Moreover, histologic tumour types of favourable outcome (invasive tubular, lobular, and invasive papillary carcinomas) displayed high proportions of pAkt overexpression, relative to medullary carcinomas; a type with relatively less favourable prognosis; which is inverse to the expression of PIK3CA in the same cohort [START_REF] Aleskandarany | Growth fraction as a predictor of response to chemotherapy in node negative breast cancer[END_REF].

Importantly, pAkt expression was positively associated with ER status, a further demonstration of previous reports of Akt activation downstream of ER [START_REF] Basu | Molecular targets of breast cancer: AKTing in concert[END_REF].

However, of the HER family; (EGFR, HER2, HER3 and HER4), which are wellknown Akt upstream activators, only HER4 showed positive association with pAkt, while no associations were found with EGFR, HER2 status, or HER3. The cooperation between the HER receptors with HER2 to produce a more aggressive tumour phenotype is well-evidenced [START_REF] Zaczek | The diverse signaling network of EGFR, HER2, HER3 and HER4 tyrosine kinase receptors and the consequences for therapeutic approaches[END_REF]. Therefore, we profiled our tumour series based on their HER2 status with respect to the other HER family members. Interestingly, no association was found between the resulting subgroups and the pAkt status. These findings may point to other mechanisms of constitutive Akt activation, other than growth factor stimulation via receptor tyrosine kinase [START_REF] Staal | Molecular cloning of the akt oncogene and its human homologues AKT1 and AKT2: amplification of AKT1 in a primary human gastric adenocarcinoma[END_REF][START_REF] Carpten | A transforming mutation in the pleckstrin homology domain of AKT1 in cancer[END_REF][START_REF] Yuan | PI3K pathway alterations in cancer: variations on a theme[END_REF]. In line with this hypothesis is the significant positive association between pAkt and PTEN expression, which was available in only a subset of tumours of this series, despite the expected and reported inverse relationship between the two [START_REF] Shi | Dysregulated PTEN-PKB and negative receptor status in human breast cancer[END_REF].

In addition, pAkt overexpression was directly correlated to the expression of AR, a known downstream pAkt target. Lin et al demonstrated that AR phosphorylation via pAkt abrogates AR-induced apoptosis resulting in increased cell survival [START_REF] Lin | Akt suppresses androgen-induced apoptosis by phosphorylating and inhibiting androgen receptor[END_REF]. On the other hand, pAkt was inversely associated with the IHC expression of p53 in our series, where p53 negative/wild cases showed higher proportions of pAkt positivity than p53 positive cases. However, this could not solely be explained through the action of pAkt on the p53 degradation mediator Mdm2, which showed no correlation with pAkt expression. In this respect, growing evidence challenge the conventional simplistic view that proposes Mdm2 as the principal mediator for p53 turnover, where many other factors are integral members of the multi-faceted p53 pathway [START_REF] Brooks | p53 ubiquitination: Mdm2 and beyond[END_REF].

Of utmost interest is the correlation seen between pAkt expression and the BC molecular subtypes, where the luminal-like subtype displayed a higher frequency of pAkt positivity than the basal-like and TN subtypes. This association might mirror the positive association between pAkt with ER, luminal CK18, 19 and the negative association with basal CK14 found in our series; and on the other hand supports other reports attributing the resistance to adjuvant hormonal therapy to the activation of Akt in hormone receptor positive cases [START_REF] Tokunaga | The association between Akt activation and resistance to hormone therapy in metastatic breast cancer[END_REF].

Despite the strong correlation with histologic grade, hormonal receptor status and BC molecular subtypes, the association of pAkt expression with patients' BCSS or MFS during the period of follow-up did not reach statistical significance. These findings might not be surprising, firstly because of the dependency of pAkt status in our series on ER expression whose its prognostic significance is reported to be dependant on age, lymph node status and length of follow up time [START_REF] Collett | Prognostic role of oestrogen and progesterone receptors in patients with breast cancer: relation to age and lymph node status[END_REF]. Secondly, it may be due to the high proportion of tumours showing pAkt expression implying an early activation of Akt pathway in these cases, rather than a feature of tumour progression [START_REF] Bose | The Akt pathway in human breast cancer: a tissue-array-based analysis[END_REF].

For further scrutiny of the results of pAkt expression in our series relevant to the upstream Akt activator PI3K, tumours were redefined according to their combined pAkt and PIK3CA IHC status, resulting in four phenotypic groups; PIK3CA -/pAkt - (double negative), PIK3CA -/pAkt + , PIK3CA + /pAkt -, and PIK3CA + /pAkt + (double positive). Significant differences were noticed between these combinatorial phenotypic groups for patients' BCSS and MFS, independently of other prognostic parameters except grade; a similar pattern to that previously reported for PIK3CA expression in this cohort [START_REF] Aleskandarany | Growth fraction as a predictor of response to chemotherapy in node negative breast cancer[END_REF]. Interestingly, a substantial proportion (~16%) of tumours was PIK3CA -/pAkt + , meaning that the Akt was activated whereas the main upstream PI3K activator was inactive. The activation of Akt in this subset of tumours may be an indication of other mechanisms of Akt activation other than PI3K [START_REF] Jiang | PI3K/PTEN signaling in tumorigenesis and angiogenesis[END_REF][START_REF] Staal | Molecular cloning of the akt oncogene and its human homologues AKT1 and AKT2: amplification of AKT1 in a primary human gastric adenocarcinoma[END_REF][START_REF] Carpten | A transforming mutation in the pleckstrin homology domain of AKT1 in cancer[END_REF].

In addition, a comparable subset of tumours was PIK3CA + /pAkt -, indicating diminished pAkt levels in the presence of PI3K over-activity. A growing body of evidence has recently reported a diminished Akt activation in breast tumours and cell lines harbouring the activating PIK3CA mutations, denoting an Akt-independent execution of downstream oncogenic signals of PI3K [START_REF] Vasudevan | AKT-independent signaling downstream of oncogenic PIK3CA mutations in human cancer[END_REF][START_REF] Stemke-Hale | An integrative genomic and proteomic analysis of PIK3CA, PTEN, and AKT mutations in breast cancer[END_REF]. Furthermore, the largest subset of tumours was the double positive tumours (~60%), in which both PI3K/Akt was active. In this subset, the activation of Akt is most probably a downstream effect of PI3K activation, although other Akt activators might also have contributed. This phenotype displayed a 10 year BCSS and MFS of 72% and 68% respectively, nearly equal to these displayed by the PK3CA + /pAkt -phenotype. In other terms, the outcome of patients relative to pAkt status has been mostly driven by PIK3CA status, thus when the later was positive, the prognosis was more or less the same to that of PIK3CA + /pAkt -phenotype, but was dramatically poorer than PIK3CA - /pAkt + tumours.

It is noteworthy that the PIK3/Akt pathway inhibitors, as specific cancer therapies, are currently in their early phase of clinical trials [START_REF] Engelman | Targeting PI3K signalling in cancer: opportunities, challenges and limitations[END_REF]. In addition, current research strategies to limit PI3K/Akt signalling focus primarily on inhibitors of the PI3K catalytic subunit, which would not be as effective in cases of constitutively active Akt [START_REF] Vasudevan | AKT-independent signaling downstream of oncogenic PIK3CA mutations in human cancer[END_REF][START_REF] Yap | Targeting the PI3K-AKT-mTOR pathway: progress, pitfalls, and promises[END_REF]. With the findings of the current study in mind, specific inhibitors that target Akt should be considered within the specific context of Akt activation whether it is a result of an upstream stimulation, genetic mutation, or gene amplification [START_REF] Jiang | PI3K/PTEN signaling in tumorigenesis and angiogenesis[END_REF][START_REF] Staal | Molecular cloning of the akt oncogene and its human homologues AKT1 and AKT2: amplification of AKT1 in a primary human gastric adenocarcinoma[END_REF][START_REF] Carpten | A transforming mutation in the pleckstrin homology domain of AKT1 in cancer[END_REF]. For instance, the prevalence and importance of Akt pathway activation with or without PI3K activation, represented in our series by the double positive and PIK3CA -/pAkt + phenotypes respectively, might warrant the clinical effectiveness of specific Akt inhibitors. However, the pervasiveness of Aktindependent effectors of PI3K signalling, represented in our series by the PIK3CA + /pAkt -phenotype, might therefore substantially limit the clinical effectiveness of Akt inhibitors in this subset of tumours.

Therefore, to develop effective new cancer therapeutics that could limit constitutively active Akt signals, it will be important to gain a more complete insight of the precise upstream and downstream members of this complex kinase pathway, and the specific PI3K/Akt axis in particular, in more specific rather than general signalling terms.

Figure legends

Figure 1 :

 1 Figure 1: pAkt (Ser473) immunohistochemical expression in invasive breast carcinoma TMA cores and Western blotting of MCF-7 and MDA-MB231 cell lysates. (A) Negative IHC expression, (B) Positive IHC expression; (200x magnification). C: Western blotting analysis using anti Phospho-Akt (S473) rabbit monoclonal antibody showing band at the expected size (56 KD), lane (1)-MCF-7 lysates and lane (2)-MDA-MB231 lysates.

Figure 2 :

 2 Figure 2: Kaplan-Meier survival plot for patients' BCSS showing the association between pAkt expression and: Breast cancer specific survival (A) and the probability of distant recurrence (B).

Figure 3 :

 3 Figure 3: Kaplan-Meier survival plot for patients' BCSS showing the association between the patients' subsets resulted from PIK3CA and pAkt expression: Breast cancer specific survival (A); the probability of distant recurrence (B).

Table Legends :Table 1 : Correlation between pAkt expression and the clinicopathologic parameters in the studied cohortTable 2 : Table 2: Correlations between pAkt expression and the expression of other biomarkerTable 2 (continued): Correlations between pAkt expression and the expression of other biomarkersTable 3 : Numbers and percentages within each subset of PIK3CA/pAkt combinations:Table 3 : Correlation between pAkt expression and the clinicopathologic parameters in the studied cohort pAkt Expression Significance Negative No. (%) Positive No. (%)

 Legends12233

				2	p value
	Patients' Age
	≤ 50 yrs > 50 yrs	131 (28.9) 157 (21.1)	323 (71.1) 588 (78.9)	9.358	0.003

Table 2 : Correlations between pAkt expression and the expression of other tissue markers

 2

	Total	288	911
	Menopausal Status
	Premenopausal Postmenopausal Total Tissue marker	135 (28.8) pAkt Expression 333 (71.2) 153 (20.9) 578 (79.1) 288 911 Negative No. (%) Positive No. (%)	9.797 Significance 0.002 2 p value
	Grade ER
	1 2	Negative Positive	47 (22.7) 73 (18.9) 101 (31.5) 158 (22)	160 (77.3) 314 (81.1) 220 (68.5) 561 (78)	10.509 10.685	0.005 0.001
	3		167 (27.8)	434 (72.2)
	Total	287	908
	LN Stage
	1 (Negative)	176 (23.7)	566 (76.3)
	2 (1-3 LN involved)	91 (25.8)	262 (74.2)	1.620	0.445
	3 (>3)	20 (19.8)	81 (80.2)
	Total	287	909
	Tumour size
	≤2cm >2cm	170 (23.3) 117 (25.2)	559 (76.7) 348 (74.8)	0.527	< 0.488
	Total	287	907	907
	Nottingham Prognostic Index
	Good NPI (<3.4)	76 (20.2)	301 (79.8)
	Moderate NPI (3.41-5.4)	157 (25.3)	463 (74.7)	4.717	0.09
	Poor NPI (5.41-5)	54 (27.1)	145 (72.9)
	Total	287	909
	Vascular Invasion
	Negative Definite	154 (23.1) 104 (26.9)	512 (76.9) 2835 (73.1)	1.861	0.181
	Total	258	795
	Local recurrence
	Negative Positive	255 (24.8) 25 (17.7)	755 (75.2) 116 (82.3)	3.366	0.073
	Total	280	891
	Regional recurrence
	Negative Positive	253 (23.9) 27 (23.7)	804 (76.1) 87 (76.3)	0.004	0.995
	Total	280	891
	Distant metastases
	No Yes	208 (25.3) 78 (20.9)	614 (74.7) 295 (79.1)	2.719	0.099

Table 2 (continued): Correlations between pAkt expression and the expression of other biomarkersTable 3 : Numbers and percentages within each subset of PIK3CA/pAkt combinations:

 23

	Positive	152 (21.6)	553 (78.4)
	MIB1
	Low proliferative	67 (21.2)	249 (78.8)
	Moderately proliferative	83 (21.1)	310 (78.9)	9.104	0.011
	Highly proliferative	77 (30.6)	175 (69.4)
	PTEN
	Negative Positive	21 (35.6) 99 (22.1)	38 (64.4) 349 (77.9)	5.255	0.033
	p21
	Negative Positive	70 (21.7) 147 (23.5)	252 (78.3) 476 (76.5)	0.111	0.765
	p27
	Negative Positive	19 (25) 77 (17.7)	62 (75 313 (80.3)	3.152	0.089
	Bcl-2
	Negative Positive	69 (25.3) 124 (20.7)	204 (47.4) 474 (793)	2.239	0.136
	Mdm2
	Negative Positive	75 (21.7) 12 (28.6)	271 (78.3) 30 (71.4)	1.024	0.328
	Molecular subtype
	Luminal-like	161 (21.6)	586 (78.4)
	HER2 over-expressing Tripe negative	34 (20.2) 21 (42)	134 (79.8) 29 (58)	28.603	< 0.001
	Triple negative basal	56 (38.4)	90 (61.6)

Group PIK3CA/pAkt status Number Percentage 1 PIK3CA -/pAkt -

			75	7.9
	2	PIK3CA -/pAkt +	158	16.6
	3	PK3CA + /pAkt -	149	15.7
	4	PIK3CA + /pAkt +	567	59.7
		Total	949	100%

Acknowledgements M. Aleskandarany and M. Ahmed are funded by the Ministry of Higher Education (Egypt).