Cordier Carole

Caroff Martial

Eric C Rannou

 Cordier
email: cordier@unisi.it

M Caroff

C Cordier

Timescale of open-reservoir evolution beneath the south Cleft segment, Juan de Fuca ridge

Keywords: oceanic crust, mid-ocean ridge basalts, magmatic periodicity, open-system reservoir, replenishment melt, residence time

Lavas erupted at the southern end of the intermediate Juan de Fuca ridge (Cleft segment) are mostly cogenetic and their chemical diversity results from melt evolution in an open magma system. In the present study, we apply a theoretical model allowing the time evolution of this periodically recharged and tapped magma chamber to be estimated. In our mathematical procedure, the melt quantity supplied to the reservoir varies through time following a sinusoidal function. The rare earth element concentrations in the refilling melt were calculated on the basis of the REE distribution in lavas. This theoretical composition is akin to that previously estimated for a Mg#70 MORB from mineralogical and chemical data.

Then, we approached the temporal evolution of the reservoir using a set of suitable parameters deduced from the geometry of the crust and magma system beneath the Cleft segment.

Particularly, we considered two end-members scenarios for the melt repartition through the magma reservoir beneath the Cleft segment: the "gabbro glacier" model (crystal nucleation and growth occur within one single melt lens and crystals subside vertically and laterally) and the "sheeted sill" model (crystallization takes place within a network of connected sills located at various depths in the crust). We estimated that the magma chamber is refilled every thousand years and that the melt resides approximately one hundred years within the reservoir.

Introduction

To develop quantitative models for magmatic systems beneath fast-and intermediatespreading ridges, constraints on the timescales of processes such as melting, differentiation, and crystallization are required. Temporal information is still difficult to estimate from geological and geochemical data. For two decades, more and more studies were based on samples collected from holes drilled into the upper oceanic crust [START_REF] Wilson | Drilling to gabbro in intact ocean crust[END_REF], from across-ridge profiles [START_REF] Davis | Geochemistry of basalt from the North Gorda segment of the Gorda Ridge: Evolution toward ultraslow spreading ridge lavas due to decreasing magma supply[END_REF], from crust exposures along slightly tectonized fracture zones or propagating rifts (Karson et al. 2002a;Karson et al. 2002b;[START_REF] Pollock | Temporal and spacial variability in the composition of lavas exposed along the Western Blanco Transform Fault[END_REF][START_REF] Cordier | Bulk-rock geochemistry and plagioclase zoning in lavas exposed along the northern flank of the Western Blanco Depression (Northeast Pacific): Insight into open-system magma chamber processes[END_REF], and from ophiolite exposures [START_REF] Pallister | Samail Ophiolite plutonic suite: Field relations, phase variation, cryptic variation and layering, and a model of a spreading ridge magma chamber[END_REF][START_REF] Smewing | Mixing characteristics and compositional differences in mantle-derived melts beneath spreading axes: evidence from cyclically layered rocks in the ophiolite of north Oman[END_REF][START_REF] Einaudi | Magmatic cycles and formation of the upper oceanic crust at spreading centers: Geochemical study of a continuous extrusive section in the Oman ophiolite[END_REF]. These studies provided constraints on the relative chronology of the volcanics and then on the time-related chemical variations in lavas erupted from a single ridge segment. Further seismological data have shown that, beneath spreading ridges, the melt lens is a dynamic object. Its volume and depth are tied to the eruption and replenishment cycles of the magma reservoir [START_REF] Hussenoeder | Seismic analysis of the axial magma chamber reflector along the southern East Pacific Rise from conventional reflection profiling[END_REF][START_REF] Hooft | Seismic structure and indicators of magma budget along the Southern East Pacific Rise[END_REF][START_REF] Singh | Melt to mush variations in crustal magma properties along the ridge crest at the southern East Pacific Rise[END_REF]. The vertical movements of the melt lens were also documented by petrological evidences of reheating, hydrous partial melting and assimilation of the base of the sheeted dikes [START_REF] Gillis | Anatectic migmatites from the roof of an ocean ridge magma chamber[END_REF][START_REF] Koepke | Petrography of the dike-gabbro transition at IODP Site 1256 (equatorial Pacific): The evolution of the granoblastic dikes[END_REF][START_REF] France | Hydrous partial melting in the sheeted dike complex at fast spreading ridges: experimental and natural observations[END_REF]). On the whole, these results evidence cyclic variations of the thermal state of the axial magma chamber, related to fluctuations of the balance between magma recharge and hydrothermal cooling beneath spreading ridges.

We propose here to characterize the rare earth element (REE) concentrations in melts that evolved in a postulated periodically refilled reservoir and to estimate the REE composition of the replenishment melt, the average crystallization rate, the period of magma recharge and the average magma residence time, using the mathematical procedure developed by [START_REF] Rannou | A geochemical approach to model periodically replenished magma chambers: Does oscillatory supply account for the magmatic evolution of EPR 17-19°S?[END_REF]. We will consider the lavas erupted at the southern end of Juan de Fuca ridge axis: those collected at and near the axis [START_REF] Smith | Petrology and geochemistry of basalts from the southern Juan de Fuca ridge: Controls on the spatial and temporal evolution of midocean ridge basalt[END_REF][START_REF] Stakes | The Cleft revealed: Geologic, magnetic, and morphologic evidence for construction of upper oceanic crust along the southern Juan de Fuca Ridge[END_REF]) and those collected along the northern wall of the Western Blanco Depression, which truncates the crust accreted at the Juan de Fuca axis since 1.4 Ma [START_REF] Cordier | Bulk-rock geochemistry and plagioclase zoning in lavas exposed along the northern flank of the Western Blanco Depression (Northeast Pacific): Insight into open-system magma chamber processes[END_REF]). In addition to chemical data, the model resolution requires the estimation of some geological parameters (Fig. 1) related to the architecture of the crust and to the geometry of the magma reservoir. A broad approach of these parameters has already been discussed by [START_REF] Rannou | A geochemical approach to model periodically replenished magma chambers: Does oscillatory supply account for the magmatic evolution of EPR 17-19°S?[END_REF]. Here, their estimation will be made to consider the specificities of the reservoir beneath fast-and intermediate-spreading ridges. Indeed, it is well-established that beneath these ridges, the axial magma chamber includes one or several thin lens(es) of partially crystallized melt located just below the sheeted dike complex and overlying a partially molten region [START_REF] Detrick | Multichannel seismic imaging of a crustal magma chamber along the East Pacific Rise[END_REF][START_REF] Sinton | Mid-Ocean Ridge Magma Chambers[END_REF][START_REF] Boudier | Magma chambers in the Oman ophiolite: Fed from the top or from the bottom?[END_REF]. However, the role of this (these) melt lens(es) in the storage and differentiation of mid-ocean ridge basalts (MORBs) and in the accretion of the lower crust is still debated. The current models are represented by two endmembers. According to the "gabbro glacier" model (GG, Fig. 1b), crystal nucleation and growth occur within one single melt lens and crystals subside vertically and laterally to form the lower crust as oceanic crust spreads away from the ridge axis [START_REF] Henstock | The accretion of oceanic crust by episodic sill intrusion[END_REF][START_REF] Phipps Morgan | The genesis of oceanic crust: Magma injection, hydrothermal circulation, and crustal flow[END_REF][START_REF] Quick | Ductile deformation and the origin of layered gabbro in ophiolites[END_REF][START_REF] Henstock | Compaction control of melt distribution at fast-spreading mid-ocean ridges[END_REF]. Conversely, the "sheeted sill" model (SS, Fig. 1c) considers that crystallization takes place in situ within a network of connected sills located at various depths in the crust and that the seismically imaged melt lens is simply the shallowest of them [START_REF] Boudier | Magma chambers in the Oman ophiolite: Fed from the top or from the bottom?[END_REF][START_REF] Kelemen | Geochemistry of gabbro sills in the crust/mantle transition zone of the Oman ophiolite: Implications for the origin of the oceanic lower crust[END_REF][START_REF] Korenaga | Melt migration through the oceanic lower crust: A constraint from melt percolation modelling with finite solid diffusion[END_REF][START_REF] Garrido | Variation of cooling rate with depth in lower crust formed at an oceanic spreading ridge: Plagioclase crystal size distributions in gabbros from the Oman ophiolite[END_REF]. The relative efficiency of these two scenarios depends on the cooling rate of the lower oceanic crust and thus on the interplay between heat supply through melt recharge and heat extraction through conduction and hydrothermal circulations. In turn, these models have diverging consequences on the repartition of the amount of crystallization with depth and on the expected degree of differentiation of the melt refilling the upper melt lens. For example, if heat removal by hydrothermal circulations is more efficient from the base of the dyke complex than from deeper in the lower crust, the majority of crystallization probably will occur in the upper melt lens rather than in situ within the gabbroic section. In this case, primitive melts will be delivered to the upper lens. In our modeling, we thus evaluated the role of in situ crystallization and, through the quantity of melt in the magma chamber, the respective contribution of the upper melt lens and of the lower sills during magma differentiation.

Open magma system beneath the southern Cleft segment of the Juan de Fuca ridge

Recent evolution documented by the geochemistry of the Cleft lavas

The Juan de Fuca ridge separates the Pacific and Juan de Fuca plates (Fig. 2a, inset).

Its southern 60 km-long Cleft segment (45°03'N to 44°27'N) spreads at an intermediate rate (56 mm/y, [START_REF] Wilson | Confidence intervals for motion and deformation of the Juan de Fuca plate[END_REF] and is bounded by the Vance segment on the north and the Blanco fracture zone on the south (Fig. 2a). The segment axis is characterized by a dome rifted by a large transient graben [START_REF] Normark | Active hydrothermal vents and sulfide deposits on the southern Juan de Fuca Ridge[END_REF]. Along the southern part of the segment, the graben floor is notched by a central narrow depression, named cleft or axial summit collapse trough, which results from the collapse of volcanic structures, lava lakes or thick volcanic flows [START_REF] Chadwick | Graben formation associated with recent dike intrusions and volcanic eruptions on the mid-ocean ridge[END_REF][START_REF] Stakes | The Cleft revealed: Geologic, magnetic, and morphologic evidence for construction of upper oceanic crust along the southern Juan de Fuca Ridge[END_REF]. The roof of discrete melt lenses has been seismically imaged at ~2 km of depth into the crust and over 10 km-long continuous intervals [START_REF] Canales | Upper crustal structure and axial topography at intermediate spreading ridges: Seismic constraints from the southern Juan de Fuca ridge[END_REF][START_REF] Canales | Seismic evidence for variations in axial magma chamber properties along the southern Juan de Fuca Ridge[END_REF]). In the southern part of the Cleft segment, the melt lens would be 100-m thick and 900-m wide and partially crystallized, comprising only ~ 30 vol. % of melt [START_REF] Canales | Seismic evidence for variations in axial magma chamber properties along the southern Juan de Fuca Ridge[END_REF].

The Cleft lavas are normal MORBs resulting from the partial melting of a depleted and quite homogeneous mantle source with constant melting extents [START_REF] Smith | Petrology and geochemistry of basalts from the southern Juan de Fuca ridge: Controls on the spatial and temporal evolution of midocean ridge basalt[END_REF][START_REF] Stakes | The Cleft revealed: Geologic, magnetic, and morphologic evidence for construction of upper oceanic crust along the southern Juan de Fuca Ridge[END_REF]. The lavas display a large range of compositions (3.5 < MgO wt. % < 8, Fig. 2b) that are thought to mostly result from the differentiation of primary tholeiitic melts in open-system magma reservoirs (Fig. 2c). The correlation between lava ages, degrees of differentiation, and latitudes (Fig. 2b, [START_REF] Smith | Petrology and geochemistry of basalts from the southern Juan de Fuca ridge: Controls on the spatial and temporal evolution of midocean ridge basalt[END_REF]) is consistent with the coexistence of several discrete magma chambers along the Cleft segment, as observed in seismic profiles [START_REF] Canales | Upper crustal structure and axial topography at intermediate spreading ridges: Seismic constraints from the southern Juan de Fuca ridge[END_REF], and with the increase of the melt lens crystallinity from north to south inferred from geophysical studies [START_REF] Canales | Seismic evidence for variations in axial magma chamber properties along the southern Juan de Fuca Ridge[END_REF]). In the northern part, young and primitive basalts prevail (Fig. 2b) and would originate from a recently recharged magma reservoir. Southward, lavas are more evolved (Fig. 2b) and would derive from a progressively waned chamber, in response of the decrease of the magma supply [START_REF] Smith | Petrology and geochemistry of basalts from the southern Juan de Fuca ridge: Controls on the spatial and temporal evolution of midocean ridge basalt[END_REF]). Thus, along the segment, the magma chambers are in different stage of evolution, which can be interpreted as reflecting the cyclic evolution through time of the axial magma reservoirs, as already proposed for the East Pacific Rise by [START_REF] Lagabrielle | Formation of large summit troughs along the East Pacific Rise as collapse calderas: An evolutionary model[END_REF] and for the north-south propagating spreading center of the North Fiji Basin by [START_REF] Caroff | The north-south propagating spreading center of the North Fiji Basin. Modeling of the geochemical evolution in periodically replenished and tapped magma chambers[END_REF].

The southernmost magma chamber that we study is interpreted to be in a waning state.

Dacitic glass has been collected at the intersection between the southern Cleft segment and the Blanco fracture zone (Fig. 2). The dacitic melt could correspond to a differentiated product erupted from cooler and distal edges of the melt lens while the composition in the central part of the lens was buffered by replenishment [START_REF] Stakes | The Cleft revealed: Geologic, magnetic, and morphologic evidence for construction of upper oceanic crust along the southern Juan de Fuca Ridge[END_REF]). However, [START_REF] Cotsonika | The occurrence and origin of andesites and dacites from the Southern Juan de Fuca Ridge[END_REF] proposed that dacitic melts might result from contamination of basaltic resident melts by rhyolitic ones issued from the partial melting of the hydrated basaltic crust.

More recently, [START_REF] Wanless | Dacite petrogenesis on Mid-Ocean Ridges: Evidence for oceanic crustal melting and assimilation[END_REF] suggested that MOR dacites result from extensive fractional crystallization combined with partial melting and assimilation of amphibole-bearing altered crust.

Past evolution documented by the Western Blanco Depression lavas

At the southern tip of the Cleft segment, the northern wall of the Western Blanco Depression (Fig. 2a) provides a window through the slightly tectonized upper oceanic crust accreted for 1.4 Ma to the north of the ridge-transform intersection [START_REF] Wilson | Propagation as a mechanism of reorientation of Juan de Fuca Ridge[END_REF][START_REF] Embley | Morphology of the Blanco Transform Fault Zone-NE Pacific: Implications for its tectonic evolution[END_REF][START_REF] Juteau | A submersible study in the Western Blanco Fracture Zone, N.E. Pacific: structure and evolution during the last 1.6 Ma[END_REF]Karson et al. 2002b;Fig. 3a). A thick volcanic unit, made of basaltic pillow-lavas, massive flows, and sparse feeder dikes [START_REF] Juteau | A submersible study in the Western Blanco Fracture Zone, N.E. Pacific: structure and evolution during the last 1.6 Ma[END_REF]Karson et al. 2002b), overlies an intensively hydrothermalized sheeted-dike complex [START_REF] Manac'h G | A fluid inclusion and stable isotope study of hydrothermal circulation in a transform zone: Western Blanco Depression, northeast Pacific[END_REF].

The northern scarp provides an opportunity to study the temporal variations of the lava composition by considering that the vertical succession of the lavas records increasing ages with depth [START_REF] Tivey | Direct measurement of magnetic reversal polarity boundaries in a cross-section of oceanic crust[END_REF][START_REF] Pollock | Temporal and spacial variability in the composition of lavas exposed along the Western Blanco Transform Fault[END_REF][START_REF] Cordier | Bulk-rock geochemistry and plagioclase zoning in lavas exposed along the northern flank of the Western Blanco Depression (Northeast Pacific): Insight into open-system magma chamber processes[END_REF]; Fig. 3a). [START_REF] Cordier | Bulk-rock geochemistry and plagioclase zoning in lavas exposed along the northern flank of the Western Blanco Depression (Northeast Pacific): Insight into open-system magma chamber processes[END_REF] have shown that the lavas outcropping along the Northern Scarp are mostly cogenetic. The conclusions of their petrological and geochemical study confirmed that beneath the southern tip of the Cleft segment: (i) the melt evolution occurs in a complex magma chamber, with differentiated, H 2 O-rich compositions achieved in the cooler solidification zones; (ii) the differentiation mainly results from fractional crystallization, coupled with magma mixing between basaltic and intermediate melts; (iii) the mixing events reveal the periodic recharge of the reservoir by mafic melts (Mg#=70) and this regime has governed the magmatic system over the last ~1.4 Ma (Fig. 3b).

These results on the lavas erupted both at the present time [START_REF] Smith | Petrology and geochemistry of basalts from the southern Juan de Fuca ridge: Controls on the spatial and temporal evolution of midocean ridge basalt[END_REF][START_REF] Stakes | The Cleft revealed: Geologic, magnetic, and morphologic evidence for construction of upper oceanic crust along the southern Juan de Fuca Ridge[END_REF]) and over the last 1.4 Ma [START_REF] Cordier | Bulk-rock geochemistry and plagioclase zoning in lavas exposed along the northern flank of the Western Blanco Depression (Northeast Pacific): Insight into open-system magma chamber processes[END_REF] show that the magma chamber beneath the southern end of the Cleft segment fulfills the conditions required to apply the model of [START_REF] Rannou | A geochemical approach to model periodically replenished magma chambers: Does oscillatory supply account for the magmatic evolution of EPR 17-19°S?[END_REF]: (i) the chemical variations in the collected lavas derive from reservoir differentiation and the chemical effects attributable either to the mantle source heterogeneity or to variations of the melting degree can be considered negligible [START_REF] Smith | Petrology and geochemistry of basalts from the southern Juan de Fuca ridge: Controls on the spatial and temporal evolution of midocean ridge basalt[END_REF], except perhaps for the dacite genesis [START_REF] Wanless | Dacite petrogenesis on Mid-Ocean Ridges: Evidence for oceanic crustal melting and assimilation[END_REF]); (ii) the time evolution of the processes occurring in the reservoir can be approached from the spatial distribution of the lava chemistry, along the length of the Cleft segment (Fig. 2b) or vertically (Fig. 3b) along the Northern Scarp [START_REF] Smith | Petrology and geochemistry of basalts from the southern Juan de Fuca ridge: Controls on the spatial and temporal evolution of midocean ridge basalt[END_REF][START_REF] Pollock | Temporal and spacial variability in the composition of lavas exposed along the Western Blanco Transform Fault[END_REF][START_REF] Cordier | Bulk-rock geochemistry and plagioclase zoning in lavas exposed along the northern flank of the Western Blanco Depression (Northeast Pacific): Insight into open-system magma chamber processes[END_REF]); (iii) the magma chamber has evolved in open system, with periodic melt inputs [START_REF] Cordier | Bulk-rock geochemistry and plagioclase zoning in lavas exposed along the northern flank of the Western Blanco Depression (Northeast Pacific): Insight into open-system magma chamber processes[END_REF].

Geomathematical modeling of the temporal evolution of the magma chamber beneath the southern Cleft segment

Properties and resolution steps of the model

In the next sections, we will approach the variations of melt quantities and compositions during the evolution of a periodically replenished and tapped steady-state magma chamber through differential equations, by using the model developed by [START_REF] Rannou | A geochemical approach to model periodically replenished magma chambers: Does oscillatory supply account for the magmatic evolution of EPR 17-19°S?[END_REF].

Incompatible trace elements (here rare earth elements) are especially suitable for such a modeling. The behavior of compatible elements is too much dependent on both the nature and the proportion of the fractionating minerals. The originality of the model comes from the use of a sinusoidal function to reproduce the continuous and smoothed variations through time of the quantity of melt refilling the reservoir. The volume of resident melt varies in response to the intrusion and controls the crystallized and extruded volumes (Fig. 1a). [START_REF] Rannou | A geochemical approach to model periodically replenished magma chambers: Does oscillatory supply account for the magmatic evolution of EPR 17-19°S?[END_REF] showed that for a steady-state reservoir, the REE concentrations in melts expelled from such a reservoir vary continuously through time following a sinusoidal curve.

Concentrations in incompatible elements are minimal just after the recharge of the system by mafic melts, and they progressively increase due to the fractional crystallization occurring between two recharge events. This approach reconciles both concepts about the open-system magma chambers, usually treated separately: periodic inputs [START_REF] Hara | Geochemical evolution during fractional crystallization of a periodically refilled magma chamber[END_REF][START_REF] Hara | Geochemical evolution in an advancing, periodically replenished, periodically tapped, continuously fractionated magma chamber[END_REF] and continuous inputs [START_REF] Paolo | Trace element and isotopic effects of combined wallrock assimilation and fractional crystallization[END_REF][START_REF] Reagan | Changes in magma composition at Arenal volcano, Costa Rica, 1968-1985 : real-time monitoring of open-system differentiation[END_REF]). Here, indeed, the input is continuous but occurs at different rates. [START_REF] Rannou | A geochemical approach to model periodically replenished magma chambers: Does oscillatory supply account for the magmatic evolution of EPR 17-19°S?[END_REF] demonstrated that this model is especially suitable for modeling the evolution of natural systems since it isolates the signals that are geologically significant.

For example, in a reservoir that is periodically recharged by melt of near constant composition, the effects of natural disturbances in the replenishment cycles are strongly attenuated and do not perturb significantly the calculated variation through time of the lava composition [START_REF] Rannou | A geochemical approach to model periodically replenished magma chambers: Does oscillatory supply account for the magmatic evolution of EPR 17-19°S?[END_REF]: their Fig. 3). Noises in the input function behave like a high-frequency signal, attenuated by the magmatic system. In the same way, an occasional and short variation of the incompatible trace element composition of the refilling melt, traducing for instance a sudden wall-rock contamination, does not significantly modify the modeled composition of the lavas that evolve in the system. For example, [START_REF] Rannou | A geochemical approach to model periodically replenished magma chambers: Does oscillatory supply account for the magmatic evolution of EPR 17-19°S?[END_REF] have considered a magmatic system assimilating a quantity of rocks (leucosome with 12 ppm Ce) corresponding to 10 % of the incoming melt (MORB with 3 ppm Ce) during a fifth of the period. The difference in output Ce concentrations does not exceed 7% with respect to the assimilation-free model: the lava concentration peak increases from 17.2 to 18.3 ppm of Ce just after the event, then to a damped value of 17.8 ppm at the following cycle.

These properties thus allow considering a smoothed, mathematically simple sinusoid to model the magma recharge. [START_REF] Rannou | A geochemical approach to model periodically replenished magma chambers: Does oscillatory supply account for the magmatic evolution of EPR 17-19°S?[END_REF] divided the resolution procedure in two steps (Fig. 4). The different parameters and their units are listed in Table 1. The first resolution step requires the estimation of:

-the incompatible trace element concentrations in the cogenetic lavas that bound the compositional range of the dataset, regarded as representative of the expelled liquids during the open-system evolution of the reservoir (C E min and C E max for the element E, Table 1);

-the distribution coefficients between the global solid that crystallized and the melt (D E );

-the ratio between expulsion and crystallization rates (r e ).

We introduced an additional parameter with respect to the model of [START_REF] Rannou | A geochemical approach to model periodically replenished magma chambers: Does oscillatory supply account for the magmatic evolution of EPR 17-19°S?[END_REF] to take into account the complexity of the differentiation in the composite magma chambers beneath the spreading ridges. Indeed, the interstitial residual melts of the crystal mush zones can be extracted and mix with the resident melt. The chemical evolution resulting from such a mechanismif existscertainly differs from the pure fractional crystallization process, as considered by [START_REF] Rannou | A geochemical approach to model periodically replenished magma chambers: Does oscillatory supply account for the magmatic evolution of EPR 17-19°S?[END_REF]. Thus, we considered the reinjection into the melt lens of a fraction f of interstitial liquid that has evolved within the partially solidified zones (Table 1). The equations are adapted from [START_REF] Langmuir | Geochemical consequence of in situ crystallization[END_REF] by replacing the bulk distribution coefficient D E by the parameter z E (Table 1 and Eq. 2 of Fig. 4). As expressed, z E models possible chemical exchanges between interstitial liquids and surrounding crystals [START_REF] Langmuir | Geochemical consequence of in situ crystallization[END_REF]. [START_REF] Caroff | Open system crystallization and mixing in two-layers magma chambers[END_REF] named imperfect fractional crystallization this mechanism of solutal convection with mineralogical reactions, the principles of which being close to those of the reactive crystallization model of [START_REF] Collier | The case for reactive crystallization at Mid-Ocean Ridges[END_REF].

The different data are introduced into Eq. 1 of Fig. 4, in which all the parameters are considered constant through time. In a first step, for each REE, we run iteratively the Eq. 1 with different values of C i E and   (internal parameter, see Table 1 and [START_REF] Rannou | A geochemical approach to model periodically replenished magma chambers: Does oscillatory supply account for the magmatic evolution of EPR 17-19°S?[END_REF] until the maximum and minimum concentrations that are modeled match those measured in lavas [START_REF] Rannou | A geochemical approach to model periodically replenished magma chambers: Does oscillatory supply account for the magmatic evolution of EPR 17-19°S?[END_REF]). The replenishment pulsation () is arbitrarily fixed for this first step as it has no effect on the calculated C E values. This is equivalent to model the variations of C E in function of a dimensionless time. The REE concentrations in the replenishment melt (C i E ) and the   value for each REE are estimated. The average of the  values calculated for all the considered REE ( av ) corresponds to the ratio between the replenishment pulsation and the crystallization rate (Table 1). The good reproducibility of the   values, i.e. a low standard deviation on their average  av ), is then used to validate the set of distribution coefficients.

The second step of the modeling requires the estimation of the mean rate of melt injection [q i ] into the reservoir and of the variation of the quantity (here expressed as volume)

of resident melt during a cycle (Q max -Q min ). These parameters are introduced in Eqs. 3-5 (Fig. 4), together with r e and  av , to calculate the fraction of melt crystallized by year (), the period of the replenishment (T), and the mean residence time of the melt within the reservoir (). By introducing these results in Eq. 6 (Fig. 4), we model the temporal variations of the resident melt volume.

The curves of Fig. 5 illustrate the effects of the variation of some parameters introduced into the modeling (C E max , f, Q max -Q min ) on the calculated compositions of melt expelled from the periodically recharged reservoir (from Eq. 1: Fig. 5a,b) and on the volumes of resident melt (from Eq. 6: Fig. 5c,d).

Procedure applied to the magma system beneath the southern Cleft segment

Model parameter estimation

Our calculations are only based on rare earth elements (REE) because (i) these elements have been extensively analyzed in the available samples, (ii) their concentrations have not been 6). We used these two samples to approach C E min and C E max , respectively (Table 2). However, [START_REF] Cordier | Bulk-rock geochemistry and plagioclase zoning in lavas exposed along the northern flank of the Western Blanco Depression (Northeast Pacific): Insight into open-system magma chamber processes[END_REF] found that some ferrobasalts might result from mixing between dacitic residual melts (MgO~1.1 wt.%) and mafic melts (MgO~8.5 wt.%).

Even if such a hypothesis is judged unlikely in recent studies, such as [START_REF] Wanless | Dacite petrogenesis on Mid-Ocean Ridges: Evidence for oceanic crustal melting and assimilation[END_REF], a second set of calculations has been performed using a more evolved C E max end-member, in view to test the response of the model to a variation of the chemical parameters introduced into Eq. 1 of Fig. 4. All along the south Cleft segment, the only dacitic glass has been sampled

by [START_REF] Stakes | The Cleft revealed: Geologic, magnetic, and morphologic evidence for construction of upper oceanic crust along the southern Juan de Fuca Ridge[END_REF] but has not been analyzed for REE by these authors (Table 2, Fig. 2, sample RC10). Consequently, we used the composition of an andesite collected on the Galapagos Spreading Center [START_REF] Fornari | Geochemical studies of abyssal lavas recovered by DSRV Alvin from eastern Galapagos rift, Inca transform and Ecuador rift 1. Major element variations in natural glasses and spacial distribution of lavas[END_REF][START_REF] Perfit | Geochemical studies of abyssal lavas recovered by DSRV ALVIN from Eastern Galapagos Rift, Inca Transform, and Ecuador Rift, 3, Trace element abundances and petrogenesis[END_REF], that has REE pattern parallel to the Northern Scarp ferrobasalts (Table 2 and Fig. 6a).

The next parameter, r e (Table 1), has been approximated following the method proposed by [START_REF] Rannou | A geochemical approach to model periodically replenished magma chambers: Does oscillatory supply account for the magmatic evolution of EPR 17-19°S?[END_REF] as the ratio between the thicknesses of the basaltic and gabbroic layers of the oceanic crust (Figs. 1b andc). Assuming that the gabbros extend from the seismically imaged melt lens to the Moho, the ratio of the melt lens depth (2 km, [START_REF] Canales | Upper crustal structure and axial topography at intermediate spreading ridges: Seismic constraints from the southern Juan de Fuca ridge[END_REF] to the thickness of the plutonic complex (5 km, [START_REF] West | Focused magma supply at the intersection of the Cobb hotspot and the Juan de Fuca ridge[END_REF]) provides a r e ratio equal to 0.4.

The REE bulk distribution coefficients have been calculated by weighting the individual mineral/liquid distribution coefficients of the mineral phases [START_REF] Agee | A new look at differentiation of the Earth from melting experiments on the Allende meteorite[END_REF][START_REF] Fujimaki | Partition coefficients of Hf, Zr, and REE between phenocrysts and groundmasses[END_REF]) by their appropriate proportion in the global crystallizing assemblage. For a differentiation leading to ferrobasalts, the phase proportions are determined for a Fe-Ti oxidefree gabbroic cumulate (D 1 E , Table 2). For an andesitic term, the crystallizing assemblage includes Fe-Ti oxides, as suggested by the drastic drop in the TiO 2 content observed in the Fig. 3 diagram, and apatite (D 2 E , Table 2).

By varying the f value from 0 to 1, we can describe all the cases ranging from perfect equilibrium (restricted to the solidification zone) to perfect fractional crystallization. The procedure described by [START_REF] Rannou | A geochemical approach to model periodically replenished magma chambers: Does oscillatory supply account for the magmatic evolution of EPR 17-19°S?[END_REF] presupposes a f value equal to 1 (z E =D E ). In our calculations, we also tested the model with a value of f of 0.5.

The last parameters to be estimated are the melt quantities, here expressed as volumes.

Beneath the Cleft segment, the distribution of the axial crustal reflector imaging the melt lens shows that the magma chamber is continuous over 5 to 10 km-long intervals, even if its characteristics (depth and crystallinity) vary with shorter wavelength [START_REF] Canales | Upper crustal structure and axial topography at intermediate spreading ridges: Seismic constraints from the southern Juan de Fuca ridge[END_REF]. It is likely that the scale of the magma chamber segmentation has not changed significantly over the last thousands of years. Thus, we calculated the different melt volumes introduced in the model resolution by considering a 10-km long magma chamber.

The mean rate of melt injection [q i ] is regarded as the volume of crust accreted per year. For a 7 km-thick crust [START_REF] West | Focused magma supply at the intersection of the Cobb hotspot and the Juan de Fuca ridge[END_REF]) and a full spreading rate of 56 mm/yr [START_REF] Wilson | Confidence intervals for motion and deformation of the Juan de Fuca plate[END_REF]), [q i ] is equal to 0.004 km 3 /(yr.10km).

The variation of the volume of resident melt during a cycle (Q max -Q min ) is the least precisely estimated, because it requires assumptions on the quantity of melt expellable from the magmatic system and thus on the melt distribution over the crust thickness beneath the ridge axis. Beneath the southern part of the Cleft segment, given the lens size and crystallinity deduced from seismic data [START_REF] Canales | Upper crustal structure and axial topography at intermediate spreading ridges: Seismic constraints from the southern Juan de Fuca ridge[END_REF][START_REF] Canales | Seismic evidence for variations in axial magma chamber properties along the southern Juan de Fuca Ridge[END_REF], the quantity of melt that can be expelled from the uppermost, seismically imaged and partially crystallized lens (gabbro glacier model GG1, Fig. 1b) during the time interval of inflation and deflation of the magma chamber is ca. 0.45 km 3 (Table 3). We also run the calculations with a higher volume of melt (0.63 km 3 /10 km, GG2, Fig. 1b and Table 3) to consider the partial draining of the interstitial melt from the mushy solidification zones to the melt lens during compaction of the magma chamber [START_REF] Lagabrielle | Formation of large summit troughs along the East Pacific Rise as collapse calderas: An evolutionary model[END_REF]. Finally, we made an attempt to estimate the volume of melt expellable from several sheeted sills distributed all over the crust thickness (SS model, Fig. 1c). However, no geophysical results can be actually used to decide how many sills lie in depth and how these sills contribute to the magma chamber tapping. We arbitrarily considered that no more than a second melt lens is affected by the melt tapping, assigning a value of 0.9 km 3 /10 km to the parameter Q max -Q min (Table 3).

Results

The geochemical and temporal results of the modeling applied to the magma system beneath the southern Cleft segment are shown in Table 3 and in Figs 5-6. The consistency of the set of D E (and z E ) coefficients, and consequently the validity of the calculated C i E , is attested by the good reproducibility of the   values calculated for the different REE (Table 3), as shown by the low  av ) values (ranging from 0.119 to 0.200, Table 3). For a f value of 1, the C i E values calculated from the ferrobasalt and andesite composition to approach C E max are fairly similar (Table 3 and Fig. 6b). The C i E patterns have lower REE contents and are slightly more depleted in light REE relative to lavas. The pattern of the primary melt with Mg#=70 determined by [START_REF] Cordier | Bulk-rock geochemistry and plagioclase zoning in lavas exposed along the northern flank of the Western Blanco Depression (Northeast Pacific): Insight into open-system magma chamber processes[END_REF] is very close to and bracketed by the two theoretical refilling melt compositions (Fig. 6b). This similarity confirms that the modeled replenishment liquid can be regarded as a primary melt.

The differentiation sequence leading to andesites cannot be reproduced using a low f value to model a low melt flow from the solidification zones to the main magma lens [START_REF] Langmuir | Geochemical consequence of in situ crystallization[END_REF][START_REF] Caroff | Open system crystallization and mixing in two-layers magma chambers[END_REF]. Indeed, for most of the REE (except La and Nd), the modeled composition of expelled melts does not match the observed composition range. This result might support that andesite/dacite compositions cannot be achieved by pure MORB fractional crystallization, consistently with the [START_REF] Wanless | Dacite petrogenesis on Mid-Ocean Ridges: Evidence for oceanic crustal melting and assimilation[END_REF] conclusions. For the differentiation leading to ferrobasalts, introducing a f value of 0.5 results in C i E values slightly higher than for perfect fractional crystallization (f=1, Fig. 5b), without significant increase of the  E variability ( av )=0.124, Table 3).

When calculating the temporal data, the only varying parameters are  av and Q max -Q min (Eqs 3-5, Fig. 4). Low  av , resulting either from high C E max or from low f values (Table 1,

Step 1), produces high average crystallization rate , high replenishment period T, and low average melt residence time  (Fig. 5a, b and Table 3, Step 2). Conversely, an increase of the variation of the magma chamber volume during a cycle (Q max -Q min ) results in a diminution of  and an increase of both T and (Fig. 5c, d and Table 3, Step 2). Thus, considering a reservoir with a well-established thermal regime, the more the volume of interconnected (i.e. expellable) liquids is high the more the time required for magma differentiation is long. As the temporal results are very sensitive to the Q max -Q min value (Fig. 5 and Table 3), they strongly depend on the assumptions about the quantity of expellable melt.

The volume of melt in the reservoir oscillates through time with inflation plus deflation cycles of 550 to 2250 years, in function of the values ascribed to the chemical and geological parameters (Table 3 and Fig. 5). In average, melts reside 60 to 150 years in the magma chamber (Table 3). The variation range of the calculated magma residence times is close to that determined using Ra-Th disequilibria (tens to thousands years) for basaltic to andesitic magmas that have evolved in steady-state, well mixed, open-reservoirs [START_REF] Pyle | The volume and residence time of magma beneath active volcanoes determined by decay-series disequilibria methods[END_REF].

However, the temporal results of this modeling can hardly be validated by direct comparison with radiochronological data measured on the studied samples. First, we cannot estimate the cycle period by dating the mafic samples that bracket a chemical cycle. Current datation methods have not a sufficient time resolution (e.g. magnetic isochrones, Fig. 3), they are difficult to apply to tholeiites (e.g. K/Ar and 40 Ar/ 39 Ar methods), or they are not suitable for the considered lavas that are older than about 300 Ka (e.g. 230 Th/ 238 U, Fig. 2). Second, our samples are too old (> 8,000 years) to still record the 226 Ra-230 Th or 210 Pb-226 Ra disequilibria, which are generally used to estimate the magma residence time in spreading ridge context [START_REF] Cooper | Uranium-series chronology of Gorda ridge volcanism: new evidence from the 1996 eruption[END_REF][START_REF] Goldstein | 231 Pa and 230 Th chronology of mid-ocean ridge basalts[END_REF][START_REF] Rubin | Dating of neovolcanic MORB using ( 226 Ra/ 230 Th) disequilibrium[END_REF][START_REF] Rubin | Minimum speed limit for ocean ridge magmatism from 210 Pb-226 Ra-230 Th disequilibria[END_REF][START_REF] Volpe | 226 Ra-230 Th disequilibrium in axial and off-axis mid-ocean ridge basalts[END_REF].

Conclusions

In this study, we attempted to model the time evolution of the periodically recharged magma chamber beneath the southern tip of the Cleft spreading segment. First, [START_REF] Rannou | A geochemical approach to model periodically replenished magma chambers: Does oscillatory supply account for the magmatic evolution of EPR 17-19°S?[END_REF] developed a realistic mathematical procedure to model the geochemical evolution of changing volume magma chambers, periodically recharged and tapped. Subsequently, in their study on the lavas exposed along the northern wall of the Western Blanco Depression, Cordier et al.

(2007) highlighted a complex chemical evolution with depth, interpreted as the result of periodic replenishment of the southernmost magma reservoir of the Cleft segment.

We applied here the procedure of [START_REF] Rannou | A geochemical approach to model periodically replenished magma chambers: Does oscillatory supply account for the magmatic evolution of EPR 17-19°S?[END_REF] to this zone of the Cleft segment. The composition of the replenishment melt that we modeled is consistent with that obtained from mineralogical and chemical data for a Mg#=70 melt [START_REF] Cordier | Bulk-rock geochemistry and plagioclase zoning in lavas exposed along the northern flank of the Western Blanco Depression (Northeast Pacific): Insight into open-system magma chamber processes[END_REF]). This reproducibility between theoretical and experimental compositions, already shown by [START_REF] Rannou | A geochemical approach to model periodically replenished magma chambers: Does oscillatory supply account for the magmatic evolution of EPR 17-19°S?[END_REF] in their application to North Fiji Basin lavas, validates the first step of the modeling. In addition, by introducing geological parameters in the modeling procedure, we estimated that the magma chamber is refilled every 1,100 ± 500 years and that the melt resides ~ 100 years within the reservoir beneath the southern Cleft segment. These temporal results are close to those calculated in a same way for the ultra-fast spreading East Pacific ridge (period T = 750 years and magma residence time  = 300 years; [START_REF] Rannou | A geochemical approach to model periodically replenished magma chambers: Does oscillatory supply account for the magmatic evolution of EPR 17-19°S?[END_REF]).

This study demonstrates the applicability of the model of [START_REF] Rannou | A geochemical approach to model periodically replenished magma chambers: Does oscillatory supply account for the magmatic evolution of EPR 17-19°S?[END_REF] to magma reservoirs beneath spreading ridges. Once the periodic evolution of the magma chamber demonstrated, it can be used to approach the composition of the replenishment melt.

Besides, its application to sites where conventional dating methods are not relevant is an auxiliary approach to access the periodicity of the magmatic cycles and the melt residence time. The result accuracy depends on the precision when estimating the variable parameters, from geological and geochemical data. Inversely, for sites where our theoretical approach could be combined with radiochronological data, such a combination could bring new constraints on some of the data used for the model resolution and consequently on the subjacent assumptions about the magma system. For example, the volume of melt expellable from the magmatic system (Q max -Q min ) could then be stated and the models of lower oceanic crust accretion be discriminated.

Figure captions:

Figure 1. Theoretical magma chamber considered in the mathematical modeling (a) and its adaptation to fit with the different mechanisms proposed for the accretion of the lower oceanic crust and for the related geometry of the magma chamber beneath fast to intermediate spreading ridges (b and c). In the ""Gabbro glacier"" model (b), crystallization takes place in a thin sill at the base of the sheeted dike complex from which cumulates subside down [START_REF] Henstock | Compaction control of melt distribution at fast-spreading mid-ocean ridges[END_REF][START_REF] Henstock | The accretion of oceanic crust by episodic sill intrusion[END_REF][START_REF] Phipps Morgan | The genesis of oceanic crust: Magma injection, hydrothermal circulation, and crustal flow[END_REF][START_REF] Quick | Ductile deformation and the origin of layered gabbro in ophiolites[END_REF]. GG1 and GG2 refer to the two scenarios envisioned when discussing in the text the volume of melt expellable from the reservoir (with or without the contribution of the interstitial melt of the crystal mush, respectively). In the ""Sheeted sill"" model (c), the lower oceanic crust is formed through in situ crystallization of multiple sills [START_REF] Boudier | Magma chambers in the Oman ophiolite: Fed from the top or from the bottom?[END_REF][START_REF] Garrido | Variation of cooling rate with depth in lower crust formed at an oceanic spreading ridge: Plagioclase crystal size distributions in gabbros from the Oman ophiolite[END_REF][START_REF] Kelemen | Geochemistry of gabbro sills in the crust/mantle transition zone of the Oman ophiolite: Implications for the origin of the oceanic lower crust[END_REF][START_REF] Korenaga | Melt migration through the oceanic lower crust: A constraint from melt percolation modelling with finite solid diffusion[END_REF]. The volume of expellable melt is then approached by considering the contribution of two melt lenses. The different parameters are defined in Table 1: Q refers to melt volumes, C to element concentrations, and the subscripts i, c and e to injected, crystallized and expelled, respectively. The wide arrows show the main melt fluxes through the magmatic system. 2. Chemical data are from the literature [START_REF] Smith | Petrology and geochemistry of basalts from the southern Juan de Fuca ridge: Controls on the spatial and temporal evolution of midocean ridge basalt[END_REF][START_REF] Cotsonika | The occurrence and origin of andesites and dacites from the Southern Juan de Fuca Ridge[END_REF][START_REF] Cordier | Bulk-rock geochemistry and plagioclase zoning in lavas exposed along the northern flank of the Western Blanco Depression (Northeast Pacific): Insight into open-system magma chamber processes[END_REF]. Figure 4. Resolution procedure of the model of [START_REF] Rannou | A geochemical approach to model periodically replenished magma chambers: Does oscillatory supply account for the magmatic evolution of EPR 17-19°S?[END_REF]. Parameters are defined in Table 1. In the step 1, Eq. 1 is modified after Eq. 12 of [START_REF] Rannou | A geochemical approach to model periodically replenished magma chambers: Does oscillatory supply account for the magmatic evolution of EPR 17-19°S?[END_REF].  is fixed arbitrarily to 2. f and z E are new parameters with respect to the model of [START_REF] Rannou | A geochemical approach to model periodically replenished magma chambers: Does oscillatory supply account for the magmatic evolution of EPR 17-19°S?[END_REF] and are used to model the mixing between the interstitial residual melts of the crystal mush zones and the melt residing in the lens. b The z E values are calculated from the bulk partition coefficients D E (Table 1), considering two f values (1 and 0.5) and two cumulate modal compositions: 0.10 ol + 0.35 cpx + 0.55 plag for z 1 E [START_REF] Rannou | A geochemical approach to model periodically replenished magma chambers: Does oscillatory supply account for the magmatic evolution of EPR 17-19°S?[END_REF]) and 0.043 ol + 0.447 cpx + 0.452 plag + 0.055 tmt + 0.003 ap for z 2 E [START_REF] Perfit | Geochemical studies of abyssal lavas recovered by DSRV ALVIN from Eastern Galapagos Rift, Inca Transform, and Ecuador Rift, 3, Trace element abundances and petrogenesis[END_REF]. Note that when f = 1, z E and D E are equivalent. c Bas. = basalt; Fe-bas. = ferrobasalt; And. = andesite; Dac. = dacite. d Location: NS = Northern Scarp; Galap. = Eastern Galapagos rift; Cleft = south Cleft segment. e WR = whole-rock analysis (ICP-AES); GL = glass analysis (EPMA). f References: 1. [START_REF] Cordier | Bulk-rock geochemistry and plagioclase zoning in lavas exposed along the northern flank of the Western Blanco Depression (Northeast Pacific): Insight into open-system magma chamber processes[END_REF]; 2. [START_REF] Fornari | Geochemical studies of abyssal lavas recovered by DSRV Alvin from eastern Galapagos rift, Inca transform and Ecuador rift 1. Major element variations in natural glasses and spacial distribution of lavas[END_REF] and [START_REF] Perfit | Geochemical studies of abyssal lavas recovered by DSRV ALVIN from Eastern Galapagos Rift, Inca Transform, and Ecuador Rift, 3, Trace element abundances and petrogenesis[END_REF]; 3. [START_REF] Stakes | The Cleft revealed: Geologic, magnetic, and morphologic evidence for construction of upper oceanic crust along the southern Juan de Fuca Ridge[END_REF]. g All Iron as Fe 2 O 3 tot . h Mg# is calculated using a Fe 2 O 3 /FeO ratio of 0.2, 0.3 and 0.4 for basalt/ferrobasalt, andesite, and dacite, respectively. 1 C max : composition of the most evolved lava considered in our calculations.

2  av ):standard deviation of the  E values deduced from the different REE.

3 GG: gabbro glacier model for the magma chamber, by ignoring or considering the partial draining of the crystal much lying beneath the melt lens; SS: sheeted sill model. See text for the estimation of the different volumes.

  significantly modified during subsequent seawater alteration, and (iii) their individual mineral/liquid distribution coefficients are quite well constrained from literature data. Along the Northern Scarp, Cordier et al. (2007) defined a cogenetic suite that extends from the mafic basalt BV2960-7 (MgO~8.1 wt.%) to the ferrobasalt BN02-12 (MgO~4.32 wt.%), both aphyric (Figs 2c and

Figure 2 .

 2 Figure 2. Chemical evolution of the lavas collected along the Cleft segment and the Northern

Figure 3 .

 3 Figure 3. Chemical evolution with depth in the extrusive unit of the Northern Scarp for two

Figure 5 .

 5 Figure 5. Effect of the variation of the parameters C E max , f and Q max -Q min on the REE

Figure 6 .

 6 Figure 6. Chemical compositions used for the model resolution and results of the first step of the modeling. (a) The range of REE compositions of the Northern Scarp lavas, the C E min and C E max used in the modeling (listed in Table 2) and the Mg#70 melt composition deduced by

Table 3

 3

			) together with the lava range (see text). C E	i are calculated
	graphically for each REE by introducing into Eq. 1 of Fig. 4 the following parameters: r e =
	0.4; C E	max = REE contents in Fe-basalt and andesite, respectively (Table 2); f=0.5 and f=1.
	The theoretical C E	i patterns have lower REE contents than the lavas and are slightly more
	depleted in LREE. The spectrum of the Mg#=70 primary melt is very close to and bracketed
	by our theoretical refilling melts. The model does not give suitable C E	i pattern for f = 0.5 and
	C E	max (andesite).

Table 1 .

 1 Definition of the model parameters.Average magma residence time a Values introduced into the resolution procedure are stated here when constant for the different REEs. Otherwise, they are listed in Table2. b Parameters adapted from the equations of in situ crystallization of[START_REF] Langmuir | Geochemical consequence of in situ crystallization[END_REF]. c Units are expressed for a 10 km-long magma chamber, as typically observed beneath the Cleft segment. See text.

	Parameters	Values a	Definition
	C E C E E (µg/g) max (µg/g) min (µg/g) C i D E	Table 2 Table 2 Table 2	Concentration of the rare earth element E in the most evolved lava Concentration of E in the most mafic lava Concentration of E in the refilling melt Bulk distribution coefficient of E
	f b	0.5 and 1	Fraction of melt evolving in the solidification zones and reintroduced in the melt lens
	z E b	Table 2	Coefficient accounting for melt differentiation due to fractional crystallization and
			possible chemical exchanges between melt and crystals in crystal mush
	[q i ] (km 3 /yr.10km) c	0.004	Average rate of melt input in the reservoir
	 (yr -1 )		Average crystallization rate: fraction of melt crystallized per time unit
	Hz		Frequency of the replenishment, with  the pulsation of the replenishment
	 E		Internal parameter iteratively estimated for each E, the average of which gives  av
	 av		Ratio between pulsation (ω) and crystallization rate (α), average of the  E values
	r e Q (km 3 /yr.10km) c	0.4	Mean ratio between average extrusion and crystallization rates Volume of melt residing (i.e. expellable) in the reservoir
	Q max -Q min (km 3 /10km) c 0.45 to 0.90 Amplitude of the variations of the melt volume in the reservoir
	T (yr)		Period of the replenishment
	(yr)

Table 2 .

 2 Chemical input parameters.

	Sample	2960-7 BN02-12 999-1B RC-10
	Parameter a C E Type c Bas. min C E Fe-bas. And. max C E max	Dac.	z 1 Fe-bas. And. Fe-bas. And. E b z 2 E b z 1 E b E b z 2
	f					1	1	0.5	0.5
	Loc. d	NS	NS	Galap.	Cleft
	Analysis e	WR	WR	GL	GL
	Ref. f	1	1	2	3
	SiO 2 (wt. %) 49.50	48.85	56.70	63.15
	TiO 2	1.36	3.61	1.91	1.29
	Al 2 O 3 Fe 2 O 3 tot g	15.15 10.80	11.62 19.10	11.42 17.98	12.47 11.84
	MnO	0.19	0.26	0.29	0.18
	MgO	8.05	4.27	1.80	1.13
	CaO	12 .00	7.78	6.90	4.52
	Na 2 O	2.30	3.10	3.48	4.43
	K 2 O	0.15	0.34	0.39	0.98
	P 2 O 5	0.14	0.52	0.65	-
	LOI	-0.15	1.08	-	-
	Total	99.49 100.53	101.52	99.99
	Mg# h	64.85	35.62	22.07	23.95
	La (µg/g)	3.1	13.3	20.6		0.06	0.09	0.11	0.16
	Ce	9.6	42	61		0.06	0.10	0.11	0.19
	Nd	8.3	40	58		0.11	0.18	0.20	0.30
	Sm	3.05	-	18.2		0.17	0.27	0.30	0.42
	Eu	1.09	3.30	4.82		0.21	0.29	0.35	0.45
	Gd	4.25	-	23.5		0.22	0.32	0.35	0.49
	Dy	5.25	16.2	27.0		0.22	0.33	0.37	0.50
	Er	3.10	10.7	18.8		0.23	0.33	0.37	0.49
	Yb	3.10	9.65	17.6		0.22	0.30	0.36	0.46

a Parameters are defined in Table

1

.

Table 3 .

 3 Results of the modeling for the Cleft segment magma system in function of different values of C E max , f and Q max -Q min but similar values of C E min (Table2), r e (0.4) and [q i ] (0.004 km3/yr.10km). Crystallization rate (, period (T), residence time ( GG 3 , Q max -Q min = 0.45 km 3 /10km

	C E	max 1	Fe-bas	Fe-bas	Andesite Mg#=70
	f		1	0.5	1
	Step 1: Composition of the modeled replenishment melt
		La (µg/g)	1.42	1.54	1.52	1.35
		Ce	4.41	4.82	4.85	4.37
		Nd	4.19	4.75	4.67	4.13
		Sm			1.90
		Eu	0.62	0.72	0.70	0.69
		Gd			2.80
		Dy	3.03	3.56	3.50	3.08
		Er	1.82	2.13	2.05	1.90
		Yb	1.78	2.09	2.02	1.83
		 REE	0.930-1.285 0.715-1.048 0.141-0.730
		 av	1.137	0.899	0.467
		 av ) 2	0.119	0.124	0.200
	Step 2: yr -1 )	0.0099	0.0107	0.0121
		T (yr)	561	654	1118
	72 GG 3 , Q max -Q min = 0.63 km 3 /10km 67 (yr)	59
			0.0070	0.0076	0.0086
		T	785	916	1565
	101 SS 3 , Q max -Q min = 0.9 km 3 /10km 94 	83
			0.0049	0.0053	0.0060
		T	1122	1308	2235
			145	134	119

Acknowledgments:

We acknowledge Johann G. Raith for editorial assistance and Wendy Bohrson for reviewing this work.


Gabriel Sargent
email: gabriel.sargent@irisa.fr

Stanisław A Raczy Ński

Frédéric Bimbot
email: frederic.bimbot@irisa.fr

Emmanuel Vincent
email: emmanuel.vincent@inria.fr

Shigeki Sagayama
email: sagayama@hil.t.u-tokyo.ac.jp

A MUSIC STRUCTURE INFERENCE ALGORITHM BASED ON SYMBOLIC DATA ANALYSIS

. The segments are then clustered according to their similarity, through the minimization of an adaptive model selection criterion.

FEATURE EXTRACTION

The considered music piece is transformed into a sequence of estimated chord symbols thanks to the system of Ueda et al. [START_REF] Ueda | HMM-based Approach for Automatic Chord Detection Using Refined Acoustic Features[END_REF]. It considers 7 chord types for each of the 12 semitones : minor, major, augmented, diminished and seventh (plus the "no chord" type).

The downbeat estimator by Davies et al. [START_REF] Davies | Towards Automatic Rhythmic Accompaniment[END_REF] is tuned so as to consider 4 beats per bar. For more information about the beat tracker used, please refer to the description of the non-causal system in [START_REF] Stark | Real-Time Beat-Synchronous Analysis of Musical Audio[END_REF].

The estimations of beats and downbeats allow to build the beat scale whose beat period is closer to 1 second, and synchronous to the downbeat scale. The temporal units obtained are referred as "snaps" and used for structural analysis in [START_REF] Bimbot | Decomposition into autonomous and comparable blocks : a structural description of music pieces[END_REF].

This document is licensed under the Creative Commons Attribution-Noncommercial-Share Alike 3.0 License. http://creativecommons.org/licenses/by-nc-sa/3.0/ c 2011 The Authors.

We associate to each snap the symbol of the chord which appears the most in the time frame limited by this snap and the next one. Then, the set of features used by the structure inference system is a sequence of chords symbols expressed at the snap scale.

MUSIC STRUCTURE INFERENCE SYSTEM

Viterbi-based structural segmentation under regularity constraints

This system seeks for the best structural segmentation through a cost optimization process. Let S = {s k } 1≤k≤n be a segmentation of the sequence of features X describing a music piece. We assume that the cost function can be written :

C(S) = n k=1 Γ(s k ) (1) with
Γ(s k ) = Φ(s k ) + λΨ(s k ) (2)
• Φ(s k ) is a data-based segmentation cost which assign a low value to segments made of sequences of features repeated elsewhere in the song.

• Ψ(s k ) is a regularity cost which takes a low value when the segment size is close to a particular value τ .

• λ is a balance parameter between these two costs.

The minimization of this cost is achieved by means of a Viterbi algorithm. This system corresponds to "System2" described in [START_REF] Sargent | A regularityconstrained Viterbi algorithm and its application to the structural segmentation of songs[END_REF], with the following regularity cost :

Ψ(s k ) = m k τ -1 (3)
m k is the length of segment s k . The typical segment size is set to τ = 16 snaps, and λ = 0.15 according to a former experiment on the RWC popular database.

http://www.quaero.org/

http://versamus.inria.fr/

ACKNOWLEDGEMENTS

The authors would like to thank Yushi Ueda and Nobutaka Ono for their help in the collection of chord transcriptions used in this article. This work was partly supported by the Quaero project 2 funded by Oseo and by the associate team VERSAMUS 3 funded by INRIA.

Structural segment clustering through automaton modeling

We consider that the set of features of a music piece can be interpreted as a sequence of states of an automaton. Segments modeled by the same branch are considered as a cluster, i.e. they typically correspond to similar sequences of symbols. The probability of the observed song is therefore modeled as the product of two types of transition probabilities: transitions between the automaton branches (between two successive segments) and between the automaton states (between two successive symbols in a segment).

As a lot of automata can model a single music piece, let's precise the automaton space we consider and the selection criterion used.

Automaton space :

We consider a set of automata with different number of branches. A first automaton is built by associating one branch to each structural segment. Additional automata are recursively built by fusing pairs of branches into a single branch, until only a single branch is left.

Here, the order of fusion of the branches is set according to their similarity : considering the automaton with i branches, the automaton with (i -1) branches is obtained by fusing the two branches with lowest distance.

The distance between the two branches, which model respectively two sets (A and B) of structural segments, is the minimum of the edit distance between each segment of A and each segment of B (i.e. the number of symbol addition, deletion and substitution errors) 1 .

Adaptive criterion for automaton selection :

To each automaton is associated its probability to produce the sequence of symbols describing the whole song. Let i be the number of automaton branches and P i this probability, we have :

P Bi is the probability of the observed sequence of segment clusters (branches), P Si is the probability of the observed sequence of symbols given the clustering of segments.

In information theory, searching for the automaton with highest P i is equivalent to searching for the automaton with the lowest quantity of information -log(P i ). As we observe in pop music pieces that the number of labels rarely reaches one, or the number of segments, we add a penalty term y that is affine in the number of branches and that gives the same quantity of information to the smallest and largest automata (with respectively one branch, and n branches if the song is made of n segments).

We then search for the automaton which minimizes the following criterion : y -log (P ) = {y i -log (P i )} 1≤i≤n

(5) 1 we currently use the edit distance script by Miguel Castro, available at http://www.mathworks.com/matlabcentral/fileexchange/213editdist-m where

Former experiments showed that the performances obtained with this criterion were close to the ones obtained with BIC or AIC criteria.

Each cluster is then associated to a segment label (A, B, C...) which is returned with the segment borders by the structure inference system.


PhD Roland P Kuiper
email: r.kuiper@antrg.umcn.nl

Lisenka E L M Vissers

Ramprasath Venkatachalam

Danielle Bodmer

Eveline Hoenselaar

Monique Goossens

Aline Haufe

Eveline Kamping

Renée C Niessen

Frans B L Hogervorst

Bodmer

C Niessen

Johan J P Gille

Bert Redeker

Carli M J Tops

Marielle E Van Gijn

Ans M W Van Den Ouweland

Nils Rahner

Verena Steinke

Kahl

Elke Holinski-Feder

Monika Morak

Matthias Kloor

Susanne Stemmler

Beate Betz

Pierre Hutter

David J Bunyan

Sapna Syngal

Julie O Culver

Graham

Tsun L Chan

Iris D Nagtegaal

J Han

J M Van Krieken

Hans K Schackert

Nicoline Hoogerbrugge

Ad Geurts Van Kessel

Marjolijn J L Ligtenberg

Recurrence and variability of germline EPCAM deletions in Lynch syndrome

Keywords: HNPCC, TACSTD1, NAHR, Alu-mediated recombination, genomic deletion, Lynch Syndrome, NHEJ Lynch syndrome, TACSTD1, NAHR, Alu-mediated recombination, genomic deletion 18

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

ABSTRACT: Recently, we identified 3' end deletions in the EPCAM gene as a novel cause 1 of Lynch syndrome. These truncating EPCAM deletions cause allele-specific epigenetic 2 silencing of the neighboring DNA mismatch repair gene MSH2 in tissues expressing EPCAM. 3

Here we screened a cohort of unexplained Lynch-like families for the presence of EPCAM 4 deletions. We identified 27 novel independent MSH2-deficient families from multiple 5 geographical origins with varying deletions all encompassing the 3' end of EPCAM, but 6 leaving the MSH2 gene intact. Within the Netherlands and Germany, EPCAM deletions 7 appeared to represent at least 2.8% and 1.1% of the confirmed Lynch syndrome families, 8 respectively. MSH2 promoter methylation was observed in epithelial tissues of all deletion 9 carriers tested, thus confirming silencing of MSH2 as the causative defect. In a total of 45 10 families, 19 different deletions were found, all including the last two exons and the 11 transcription termination signal of EPCAM. All deletions appeared to originate from Alu-12 repeat mediated recombination events. In 17 cases regions of microhomology around the 13 breakpoints were found, suggesting non-allelic homologous recombination as the most likely 14 mechanism. We conclude that 3' end EPCAM deletions are a recurrent cause of Lynch 15 syndrome which should be implemented in routine Lynch syndrome diagnostics. 16

INTRODUCTION 1
The most frequently diagnosed colorectal cancer (CRC) syndrome is Lynch syndrome, also 2 known as hereditary non-polyposis colorectal cancer (HNPCC) (MIMs 120435, 609310), 3 which accounts for up to 5% of CRCs. Mutation carriers exhibit a high risk to develop CRC 4 (60-90%), endometrial cancer (20-60%), as well as several other cancers [Lynch and de la 5 Chapelle, 2003; [START_REF] Watson | The risk of extra-colonic, extra-endometrial cancer in the Lynch syndrome[END_REF]. Lynch syndrome is caused by a germline mutation in 6 one of the DNA mismatch repair (MMR) genes MSH2, MLH1, MSH6 or PMS2 [Aaltonen et 7 al., 1998;Lynch and de la Chapelle, 2003;Hampel et al., 2005; [START_REF] Barnetson | Identification and survival of carriers of mutations in DNA mismatch-repair genes in 7 colon cancer[END_REF] ( MIM 8 120436, 609309, 600678, 600259). MSH2 and MLH1 account for the majority of the 9 identified mutations, whereas PMS2 mutations explain only a few percent of the confirmed 10 cases [Lynch and de la Chapelle, 2003; [START_REF] Barnetson | Identification and survival of carriers of mutations in DNA mismatch-repair genes in 7 colon cancer[END_REF]. [START_REF] Batzer | Alu repeats and human genomic diversity[END_REF] Increasing evidence suggests that also epigenetic modifications may play a role in cancer 12 predisposition in Lynch syndrome. Several groups have reported the occurrence of mono-13 allelic methylation of the MLH1 gene promoter in peripheral blood cells of individuals that 14 meet the criteria for Lynch syndrome, but lack germline mutations in the MLH1 gene [Gazzoli 15 et al., 2002;[START_REF] Suter | Germline epimutation of MLH1 in individuals with multiple 26 cancers[END_REF]Hitchins et al., 2007]. Occasionally, these so-called 16 epimutations were found to be transmitted over several generations, but the mechanism 17 underlying this phenomenon remains to be elucidated [Hitchins et al., 2007;Morak et al., 18 2008;Hesson et al., 2010]. [START_REF] Chan | Heritable germline epimutation of MSH2 in a family with hereditary nonpolyposis 14 colorectal cancer[END_REF] for the first time reported an inherited germline 19 MSH2 epimutation in a family presenting with Lynch-associated tumors and a mosaic MSH2 20 hypermethylation pattern in normal tissues. Recently, we demonstrated that these families 21 carry 3' end deletions in the epithelial cell adhesion molecule gene EPCAM (MIM 185535), 22 previously known as TACSTD1, which is located upstream of the MSH2 gene. EPCAM is 23 highly expressed in epithelial tissues and carcinomas [START_REF] Winter | The epithelial cell adhesion molecule 22 (Ep-CAM) as a morphoregulatory molecule is a tool in surgical pathology[END_REF], and these 24 deletions were found to result in transcriptional read-through into the MSH2 gene and 25 subsequent hypermethylation of its CpG island promoter in EPCAM-expressing tissues 26 [START_REF] Ligtenberg | Heritable somatic methylation 28 and inactivation of MSH2 in families with Lynch syndrome due to deletion of the 3' exons of 29 TACSTD1[END_REF], thereby providing an explanation for the origin of the epimutation 27 and its mode of inheritance. The identification of several additional families with 3' EPCAM 28 Germany (n=11), USA (n=4), UK (n=1), and Canada (n=1) were identified through targeted 5 genomic screens in cohorts of unexplained Lynch-like families, using variable inclusion 6 criteria, i.e., unexplained patients with MSH2-deficient and/or microsatellite-instable tumors 7 (Supporting Table S1). In addition, 18 EPCAM deletion families of various origins from earlier 8 studies were included in the breakpoint analyses (Supporting Table S1). All patient material 9 was obtained with informed consent. 10 11

Multiplex ligation-dependent probe amplification (MLPA) 12

EPCAM deletion screening was performed with MLPA using SALSA MLPA kits P072-B1 13 MSH6 or P008 MSH2/PMS2 (MRC-Holland, Amsterdam, The Netherlands). For fine-14 mapping of the identified deletions we used two custom-designed probe sets as previously 15 described [START_REF] Ligtenberg | Heritable somatic methylation 28 and inactivation of MSH2 in families with Lynch syndrome due to deletion of the 3' exons of 29 TACSTD1[END_REF], in which two additional probes targeting the EPCAM 16 promoter region (probe O) and intron 4 of the EPCAM gene (probe P) were included (Fig. 1). 17 Based on the MLPA results, long range PCR across the deletion was applied using a 22 TAKARA LA PCR kit (TaKaRa Bio Inc., Otsu, Shiga, Japan) or the Expand Long Range kit 23 (deletions 8, 9, 13, and 14; Roche Applied Sciences, Mannheim, Germany). To identify the 24 exact breakpoints, the PCR products were directly sequenced at various positions in both 25 orientations. Primers used for these analyses are available upon request. 26 Methylation-specific multiplex ligation-dependent probe amplification (MS-MLPA) analyses 1 were performed using SALSA MS-MLPA kit ME011 Mismatch Repair genes (MMR) (MRC-2 Holland) as previously described [START_REF] Ligtenberg | Heritable somatic methylation 28 and inactivation of MSH2 in families with Lynch syndrome due to deletion of the 3' exons of 29 TACSTD1[END_REF], using 200 ng DNA isolated from 3 formalin fixed paraffin embedded material. Samples with known MGMT, MLH1 or MSH2 4 hypermethylation levels were used as positive controls. 5 6

Bioinformatic analysis of SINE density 7

The density of short interspersed nuclear elements (SINEs), which include Alu repeats, in the 8 maximal deletion region was compared to the remainder of the genome by random sampling 9 of 10,000 genomic sequences of 25 kb in size. These sequences were obtained from hg18 10 (http://genome.ucsc.edu/) by random selection of autosomal chromosomes and subsequent 11 locations. Centromeres and gaps in the sequence alignment were excluded. These 25 kb 12 regions were annotated for the presence of all repeat masked elements, and the number of 13 SINE elements was calculated. Next, the 95% confidence interval for the presence of SINEs 14 within these 10,000 genomic regions was determined. In a search for novel germline EPCAM deletion cases we performed a multicenter screen of 4 unexplained Lynch-like families using multiplex ligation-dependent probe amplification 5 (MLPA) and/or deletion PCR, which yielded 27 novel EPCAM deletion families (Supporting 6 Table S1). Through the participation of all clinical genetic centers in The Netherlands, we 7 have now identified 17 unrelated Dutch families with EPCAM deletions, thus representing 8 2.8% of all explained Lynch syndrome families and 6.9% of all explained MSH2-deficient 9 families in this country, respectively (Table 1). Additionally, 11 German EPCAM deletion 10 families were found in a systematic screen of 146 families with MSH2-deficient tumors in 11 which no MSH2 mutations were found (7.5%). Therefore, in Germany the frequency of 12 EPCAM deletion families in explained Lynch families is at least 1.1%, which is 2.3% of all 13 explained MSH2-deficient families. (Table 1). 14

In addition to these 27 families, we included 18 EPCAM deletion families that were previously 15 reported by us and others (Supporting Table S1). Together, these screens and searches 16 resulted in 45 independent families with EPCAM deletions originating from eight different 17 countries (Supporting Table S2). Using long-range PCR we precisely localized and 18 sequenced the breakpoints in all EPCAM deletion families (Table 2). In total, 19 different 19 deletions were identified, varying in size from 2.6 to 23.8 kb. All deletions were located 20 upstream of the MSH2 gene promoter and encompassed at least the last two exons of the 21 EPCAM gene, leaving its 5' exons intact (Fig. 1A). Our breakpoint mapping data indicate that 22 a wide variety of EPCAM deletions does occur in these Lynch syndrome families. [START_REF] Stankiewicz | Structural variation in the human genome and its role in disease[END_REF]

24

EPCAM deletion carriers show MSH2 promoter hypermethylation 25

We previously showed for two different deletions (deletions 1 and 5, Table 2) that they result 26 in allele-specific hypermethylation of the MSH2 gene promoter in tissues expressing EPCAM 27 [START_REF] Ligtenberg | Heritable somatic methylation 28 and inactivation of MSH2 in families with Lynch syndrome due to deletion of the 3' exons of 29 TACSTD1[END_REF]. Here, we analyzed the methylation status of the MSH2 gene 28 2, Supporting Table S2). 3 MSH2 promoter hypermethylation was detected in all tissues tested. One of the patients in 4 our cohort also developed a benign dermatofibroma, which was not MSH2-deficient and, in 5 contrast to the colorectal tumor, indeed was found to lack hypermethylation of the MSH2 6 gene promoter. Therefore, we conclude that hypermethylation of the MSH2 gene promoter in 7 tissues expressing EPCAM is a general phenomenon in the deletion carriers, thereby 8 explaining the concomitant cancer predisposition in these families. 9 10

EPCAM founder deletions 11

Several EPCAM deletions appeared to be widespread both within and between different 12 populations. The 4.9-kb EPCAM founder deletion, thus far observed in seven Dutch families 13 [START_REF] Ligtenberg | Heritable somatic methylation 28 and inactivation of MSH2 in families with Lynch syndrome due to deletion of the 3' exons of 29 TACSTD1[END_REF]Niessen et al., 2009], was found to be present in nine out of ten 14 additional families from The Netherlands, but in none of the families from other geographic 15 origins, thus confirming its founder nature. Furthermore, this founder deletion appears to 16 represent a considerable fraction (~6.5%) of the explained MSH2-deficient Lynch syndrome 17 families in this population (Table 1). In addition, six EPCAM deletions were identified in more 18 than one family originating from Germany (deletions 2 and 14, n=2 and n=4, respectively), 19 Switzerland (deletion 3, n=2), and the USA (deletion 6, n=2) or from multiple origins 20 (deletions 5 and 10, n=3; Table 2). Although we cannot rule out with certainty that these 21 deletions have occurred independently, we anticipate that most of them will have an 22 ancestral origin. 23 Indeed, all EPCAM deletion breakpoints characterized in this study were located within Alu 2 elements (Table 2 and Fig. 1). Together, the 19 different deletions involved 11 Alu repeats at 3 the distal intragenic breakpoints (within EPCAM), and 13 at the proximal breakpoints (in the 4 intergenic region between EPCAM and MSH2), of which several were involved in different 5 deletions (Fig. 1B and1C). As expected, the two recombined Alu elements were always 6 directed in the same orientation, being either sense (deletions [START_REF] Barnetson | Identification and survival of carriers of mutations in DNA mismatch-repair genes in 7 colon cancer[END_REF][6][7][START_REF] Bastepe | Deletion of the 9 NESP55 differentially methylated region causes loss of maternal GNAS imprints and 10 pseudohypoparathyroidism type Ib[END_REF][9][10][START_REF] Batzer | Alu repeats and human genomic diversity[END_REF] or antisense (deletions 7 1-4 and 12-19). For 17/19 (89%) of the deletions, sequence alignment of the distal and 8

proximal Alu repeats revealed the presence of stretches with microhomology at the 9 breakpoint, ranging from 6 to 32 bp in size (Table 2 and Supporting Fig. S1), which is in line 10 with Alu-Alu mediated non-allelic homologous recombination (NAHR). Interestingly, two 11 deletions of exactly the same size (deletions 7 and 8) appeared to originate from 12 recombination events at different positions within the same Alu repeat pair with high 13 sequence homology, further illustrating the homology-based mechanism driving these 14 genomic deletions (Fig. 2). 15 The remaining two deletions (9 and 12) appear to have arisen by a mechanism different from 16 NAHR. Deletion 9, of which the breakpoints are near those of deletions 7 and 8 (Table 1), 17 contains a 2-nt interstitial sequence (AG) and lacks microhomology at the breakpoint 18 junction. Similarly, the sequences surrounding the breakpoint junctions of deletion 12 do, 19 with only 3 bases, not contain sufficient homology in order to be explained by NAHR. In 20 these cases, classical non-homologous end-joining (NHEJ) or microhomology-mediated 21 break-induced repair (MMBIR) may serve as better explanations for the origin of the deletion 22 MSH2 locus in a genome-wide context. To this end, we randomly sampled 10,000 genomic 1 regions of 25 kb. This yielded a median Alu element density of 10 [95%CI: 0-39], which is 2 significantly lower than the density of 55 Alu elements that we observed within the 25-kb 3 EPCAM-MSH2 locus (Supporting Fig. S1). This local enrichment is also observed in other 4 regions with recurrent Alu-mediated rearrangements (e.g. the VHL locus in von Hippel-5 Lindau disease patients), but is absent in the locus encompassing the DNA mismatch repair 6 gene MLH1 (Supporting Fig. 2). These observations may explain the wide variety of 7 deletions observed within the EPCAM-MSH2 locus. 8 The presence of a mono-allelic EPCAM deletion results in a highly efficient silencing of the 13 MSH2 gene in target tissues such as colonic mucosa. This observation is in full agreement 14 with the lifetime risk for colorectal cancer in these families, which appears to be similar to 15 Upon analysis of the genomic region encompassing the Lynch-associated DNA mismatch 24 repair gene MLH1, we found that the above described characteristics do not apply to this 25 locus. Consequently, we postulate that in the previously reported families with germline 26 methylation of the MLH1 gene promoter, which in some families was found to be transmitted 27

8 F

 8 by others [van der Klift et al., 2005; Kovacs et al., 2009; Niessen et al., 2009; 1 Nagasaka et al., 2010; Guarinos et al., 2010] has underscored the notion that these 2 abnormalities indeed represent a common cause of Lynch syndrome. 3Here, we report the characterization of EPCAM deletions in 45 independent Lynch syndrome 4 families, including hypermethylation of the MSH2 gene promoter. The incidence of EPCAM 5 deletions appeared to vary between populations and was found to represent at least 1-3% of 6 the explained Lynch syndrome families. Detailed analysis of the EPCAM deletions uncovered 7 their range of variability as well as their Alu-repeat-mediated origin. 27 families with EPCAM deletions originating from The Netherlands (n=10), 4

  Primers were designed using the MeltIngeny program according to guidelines provided by 18 MRC-Holland and are available upon request. 19 20 Long range PCR and breakpoint sequencing 21

2

  Identification of novel EPCAM deletions in MSH2-deficient Lynch families 3

  and/or normal colon mucosa tissues of at least one index patient from 1 each of 27 different families (encompassing 11 different deletions) using methylation-specific 2 multiplex ligation-dependent probe amplification (MS-MLPA, Table

24

  Alu-mediated recombination as a mechanism of origin25 It is well-established now that repetitive DNA sequences, such as Alu repeats, can act as 26 facilitators of chromosomal rearrangements [Stankiewicz et al., 2010]. Previous reports have 27 already suggested Alu repeat-mediated recombination as a likely mechanism for some of the 28 deletions [van de Klift et al., 2005; Kovacs et al., 2009; Ligtenberg et al., 2009]. 1

[

  McVety et al., 2005; Vissers et al., 2009]. 23 Partial or complete deletion of the MSH2 gene represents a relatively frequent cause of 24 Lynch syndrome [van der Klift et al., 2005; Li et al., 2006]. These germline deletions appear 25 to originate almost exclusively from Alu-mediated recombination, which is in accordance with 26 the relatively high local density of repetitive Alu elements [Li et al., 2006]. We have extended 27 this analysis by determining the relative Alu element density throughout the entire EPCAM-

  and characterization of 3' EPCAM gene deletions in Lynch 2 syndrome families, we show that these deletions explain a considerable fraction (at least 1-3 3%) of all families with this syndrome, thus legitimating standard clinical testing. In total, we 4 have identified and characterized 19 different EPCAM deletions in 45 Lynch syndrome 5 families. These deletions turned out to be highly variable in size and location, but always 6 encompassed the last two exons of the EPCAM gene, including its polyadenylation signal. In 7 concordance with previous studies[START_REF] Ligtenberg | Heritable somatic methylation 28 and inactivation of MSH2 in families with Lynch syndrome due to deletion of the 3' exons of 29 TACSTD1[END_REF] Niessen et al., 2009; Nagasaka 8 et al., 2010], all available tumor and normal colonic tissues showed hypermethylation of the 9 MSH2 gene promoter, thus confirming a direct correlation between these two aberrations. 10 Detailed localization of the deletion breakpoints at the sequence level revealed Alu-mediated 11 recombination as the major mechanism underlying the occurrence of EPCAM deletions.[START_REF] Chan | Heritable germline epimutation of MSH2 in a family with hereditary nonpolyposis 14 colorectal cancer[END_REF]

  those observed in families with other MSH2 alterations [Kempers et al, 2010]. This efficient 16 MSH2 inactivation may be associated with one or more of the following structural 17 characteristics of this locus: (i) the close vicinity of a neighboring gene (EPCAM) that is 18 oriented towards MSH2, and (ii) the high level of expression of EPCAM in targeted tissues 19 instilling MSH2 promoter methylation. Together with the relative high density of Alu repeat 20 elements in this genomic region, which increases the chance of Alu-mediated recombination, 21 these characteristics may explain the recurrent nature of variable EPCAM deletions in Lynch 22 syndrome families. 23

8 Page

 8 Figures Legends 1 2

Figure 1 . 12 13Figure 2 .

 1122 Figure 1. EPCAM deletions in Lynch syndrome patients. A: Schematic outline of the 3 genomic region around EPCAM and MSH2, showing 19 different deletions (grey bars) 4 identified in 45 families. All deletions include at least exons 8 and 9 of EPCAM. Deletions 5 identified in multiple (apparently) unrelated families are indicated in dark grey. Positions of 6 the MLPA probes used for deletion mapping are indicated by triangles. All intragenic (B) and 7 intergenic (C) breakpoints are located in Alu repeats (referred to as SINEs: short 8 interspersed nuclear elements, red bars), of which eight are involved in several different 9 deletions (indicated by arrows and numbers of the deletion). Arrowheads above the bars 10 denote the orientation of the repeats. 11 12 13 Figure 2. Sequence alignment of two Alu repeats involved in two distinct EPCAM deletions. 14 A distal intragenic repeat (AluSp, in green) and a proximal intergenic repeat (AlusSx, in blue) 15 show high local sequence homology. The microhomology around the breakpoint in deletions 16 7 and 8 are marked by shaded boxes. Deletion 9 involves the same intragenic repeat, 17 including a directly downstream located intergenic Alu repeat sequence (FLAM-C), with a 18 lack of local microhomology around the breakpoint. The position of the breakpoints and the 19 insertion of a di-nucleotide sequence AG are indicated by triangles. 20

Figure S1 .

 S1 Figure S1. Distribution of short interspersed nuclear elements (SINEs), which includeAlu repeats, for 10,000 random genomic loci of 25 kb. A total number of 10,000 loci of 25 kb in size were randomly generated from the UCSC genome browser to represent a random sampling of the genome. The size of 25 kb was chosen to mimic the genomic size interval in which all EPCAM deletions occur (total locus: 25,484 bp). For all regions, SINE elements were annotated to determine their frequency per genomic region of 25 kb. The 95% confidence interval indicates 0 to 39 SINE elements per 25 kb region. The EPCAM locus contains 55 such SINE elements, indicating that the number of SINEs located in the EPCAM locus is significantly higher than elsewhere in the genome.

Figure S2 .

 S2 Figure S2. Local genomic SINE density surrounding the EPCAM/MSH2 locus, the MLH1 locus and the VHL locus. Comparison of local SINE (Alu) densities of the EPCAM/MSH2 locus (A) and the MLH1 locus (B). The local SINE density of the VHL locus (C), another locus frequently targeted by Alu-Alu mediated recombination, is shown as a reference. Local SINE density per 10 kb interval (1kb moving window) were determined for a total region of ~2 Mb surrounding these loci. The total number of SINEs (gray lines) as well as the moving averages (black lines) are plotted. The exact position of the genes and their orientations are indicated by black arrows. Blue dotted lines depict the average level of SINEs in a 10-kb region. The data indicate that the local SINE density surrounding the MLH1 is not significantly elevated compared to the local genomic background. A drastic drop in Alu density within the MSH2 gene may explain why genomic deletions are usually restricted the 5' end and rarely affect the 3' end of the gene.

Table 1 . Relative incidence of EPCAM deletions in The Netherlands and Germany

 1 Amsterdam, and the Free University of Amsterdam), Utrecht, and Groningen. 2 includes all unique families that are known by the German HNPCC consortium. 3 all cases known thus far are reported in this study.4 Including MSH2 deletions and EPCAM-MSH2 deletions.5 The total number of families with MSH2-deficient tumors is composed of families carrying MSH2 mutations or deletions and EPCAM deletions.

	Cohort	no. of	% of explained MSH2-	% of explained
		families	deficient families 5	Lynch families
	The Netherlands 1
	EPCAM deletions 3	17	6.9%	2.8%
	EPCAM founder deletions 3	16	6.5%	2.6%
	MSH2 mutations 4	230		37.2%
	Explained Lynch families	618
	Germany 2
	EPCAM deletions	11	2.3%	1.1%
	MSH2 mutations 4	458		47.9%
	Explained Lynch families	957
	1 includes all unique families that are known in one of the DNA diagnostic laboratories in
	Nijmegen, Rotterdam, Leiden, Amsterdam (Netherlands Cancer Institute, University of

Table 2 . EPCAM deletions in 45 MSH2-deficient Lynch syndrome families

 2

	deletion	Country of Origin 1	number of families	deleted EPCAM exons	size deletion (bp)		Nomenclature 2	microhomology (bp)	repetitive element distal 4	repetitive element proximal 4	max sequence homology (%)	MSH2 methylation (families) 5	reference
	1	NL	16	8+9	4,909	c.859-1462_*1999del	6 bp	AluSx	AluSq	84% for 211/250	yes (12)	Ligtenberg et al, 2009; Niessen et al., 2009
	2	D	2	5-9	11,660	c.491+529_*874del	25 bp	AluSg	AluSg/x	78% for 156/198	yes (1)
	3	CH	2	5-9	23,829	c.492-509_*13721del	24 bp	AluSp	AluSg	79% for 232/292	yes (1)	Van der Klift et al., 2005
	4	H	1	6-9	10,355	c.555+402_*1220del	12 bp	AluSx	AluSx	77% for 241/309	NA	Kovacs et al., 2009
	5	CN/USA	3	6-9	22,836	c.555+927_*14226del	32 bp	AluY	AluSc	79% for 237/300	yes (2)	Ligtenberg et al., 2009
	6	USA	2	6-9	13,128	c.555+901_*4492del	15 bp	AluY	AluSx	79% for 225/282	yes (2)
	7	NL	1	8+9	9.963	c.858+1244_*4562del	18 bp	AluSp	AluSx	85% for 243/284	NA
	8	D	1	8+9	9,963	c.858+1212_*4521del	8 bp	AluSp	AluSx	82% for 240/291	yes (1)
	9	D	1	8+9	10,074	c.858+1364_*4793del	-	AluSp	FLAM-C Alu	85% for 243/284	yes (1)
	10	D/H	3	8+9	8,674	c.858+2478_*4507del	14 bp	AluSp	AluSx	83% for 232/278	NA	Kovacs et al., 2009
	11	H	1	8+9	14,734	c.859-2524_*10762del	15 bp	AluSp	AluSp	86% for 137/159	NA
	12	UK	1	8+9	2,419	c.859-353_*618del	3 bp	AluSx	AluSg	78% for 222/282	yes (1)
	13	D	1	8+9	2,648	c.859-670_*530del	18 bp	AluSx	AluSg	78% for 246/312	yes (1)
	14	D 3	4	8+9	16,834	c.859-689_*14697del	24 bp	AluSx	AluSx	82% for 246/299	yes(4)
	15	H	1	8+9	6,058	c.859-696_*3914del	19 bp	AluSx	AluJo	75% for 114/151	NA	Kovacs et al., 2009
	16	D	1	8+9	5,246	c.859-1682_*2116del	13 bp	AluJb	AluSq	78% for 180/229	NA
	17	USA	1	8+9	8,879	c.859-1605_*5862del	10 bp	AluJb	AluSq	79% for 153/193	yes (1)
	18	USA	1	8+9	13,004	c.859-645_*10911del	14 bp	AluSx	AluSx	91% for 73/80	NA	Van der Klift et al., 2005
	19	D	1	4-9	16,500	c.423-545_*3903del	7 bp	AluSq	AluJo	80% for 183/227	NA
	1 Families originate from The Netherlands (NL), Germany (D), Switzerland, (CH), Hungary (H), China (CN), USA, and UK.	2 Nomenclature is based on mRNA
	sequence with Genebank Accession Code NM_002354.	3 Includes one family from unknown European origin [van der Klift et al., 2005]. See also Supporting
	Table 1.	4 Alu-subfamily identified at each each breakpoint [Batzer and Deininger, 2002].

5

Methylation specific-MLPA on normal colon mucosa and/or colorectal tumor tissues. NA, not assessable (no material left or DNA of too poor quality).

Table S1 . Screening of EPCAM deletions in unexplained MSH2-deficient families Country of origin Detection method 1 EPCAM deleted Reference The Netherlands 2

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MLPA 11

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