Léonard De Izarra
email: leonard.deizarra@cnrs-orleans.fr

Jean-Louis Rouet
email: jean-louis.rouet@univ-orleans.fr

Boujema Izrar
email: boujema.izrar@cnrs-orleans.fr

High order lattice Boltzmann models for gas flow on a wide range of Knudsen number

Keywords: numbers: 47.11.-j, 05.20.Jj, 05.20.Dd, 05.70.Ln, 51.10.+y

 we propose to extend the LBM to those stated, where non-equilibrium effects are obvious and require to include a larger number of distribution function moments.

I. INTRODUCTION

The challenge of modeling low-speed gas flow possessing significant non-equilibrium effects, either due to rarefaction or confinement in small size structures, is well known. Such flows are characterized by a finite Knudsen number and a small Mach number M a = U 0 /c 0 ≤ 0.1, where U 0 is the characteristic velocity of the flow and c 0 the speed of sound. The Knudsen number K n = λ/L, defined as the ratio of the mean free path λ of the particles to the characteristic length L of the flow, characterizes the "distance" from equilibrium. For sufficiently large Knudsen, all assumptions of continuum mechanics collapse. More specifically the Navier-Stokes equations and the no-slip boundary conditions are no longer consistent [START_REF] Cercignani | The Boltzmann Equation and Its Applications[END_REF].

Since the Boltzmann equation is valid to describe fluid flows at any Knudsen, i.e. from hydrodynamic to collisionless regimes, it is a good candidate to model systems with a large range of size scales, namely, where microscopic/rarefied and macroscopic/hydrodynamic scales are connected. Examples of such systems can be found in some natural porous media, such as coal [3], where the size of pores can extend from nanometer to millimeter, or by MEMS [4], which are micro-metric system flows driven by macroscopic pumps.

The Lattice Boltzmann Method (LBM) has recently become a good counterpoint to conventional CFD methods [START_REF] Wolf-Gladrow | Lattice-Gas Cellular Automata and lattice Boltzmann Models[END_REF], especially to simulate hydrodynamic fluid flows in complex geometries, such as porous media [START_REF] Kutay | [END_REF].

Furthermore, this method achieves good results for flows with moderate Knudsen (K n ∼ 0.1), characteristic of the slip regime, when using kinetics boundary conditions [START_REF] Cercignani | The Boltzmann Equation and Its Applications[END_REF]7] or maximizing an entropy [8]. It would be interesting, for many applications, to improve these methods again so as to access the transitional regime, i.e. a Knudsen number of order one. Such an enhancement should help to account for effects related to rarefaction/confinement in porous media, such as the Klinkenberg effect. This has already been studied with standard LBM [9], but dealing with bounce-back or specular boundary conditions which are known to be inefficient at high-Knudsen number when used on their own. For finite Knudsen number, special attention has been given to capture the Knudsen Layer with different kind of LBM models. To keep the computational efficiency of the method, the velocity set has been chosen in accord with a regular lattice (typically the D2Q9 scheme). Nevertheless in order to catch the slip phenomena, effective relaxation time schemes [10,11] or multiple relaxation time schemes [12,13,14,15] associated with appropriate boundary conditions have been developed. For the D 2 Q 9 LBM scheme, Toschi and Succi [16] suggested to add virtual collisions for beams parallels to boundaries, in order to cure the so called "runaway pathology of lattice Boltzmann". Nevertheless, the authors conclude that the standard LBM does not have a sufficient velocity space isotropy. Nie et al. [17] come to the same conclusion. Furthermore, using an important number of beams in the discrete velocity models [18], specifically used to solve flows with high Knudsen number, shows that we need a thinner discretization of the velocity space to access high-Knudsen flows.

From those assessments, we propose to study a family of schemes with a reasonably increasing number of beams and an increasing order of isotropy. This family is built on the systematic procedure of construction described by Shan et al. [1,19] which essentially consists in projecting the distribution function on the basis of Hermite polynomials (as in the approach of Grad [20,21]), and evaluating the moments of this function using the Gauss-Hermite quadrature. Moreover, the present approach may be viewed as a pragmatic alternative to the development given by Shan et al. [19]. The non-regular structure of the velocity space that this quadrature induces requires to interpolate for the transport procedure, as already mentioned by Bardow et al. [22]. We use the Maxwell's boundary conditions [START_REF] Cercignani | The Boltzmann Equation and Its Applications[END_REF]7] with total accommodation because of the wall importance in high-Knudsen regimes, where inter-particle collisions are nearly absent.

This family of schemes is demonstrated through the numerical simulations of a force-driven plane Poiseuille flow. Numerical results are compared with existing semi-analytical theories [START_REF] Cercignani | The Boltzmann Equation and Its Applications[END_REF] and experimental data for various gaseous components [23], which relate the flow rate of the Poiseuille flow to a function of the Knudsen number.

This paper is organized as follows: section II describes the background theory used to build high order lattice Boltzmann models; section III is devoted to the numerical test briefly aforementioned; finally, section IV presents the conclusions and perspectives that can be drawn from this work.

II. HIGH ORDERS LATTICE BGK EQUATIONS

A. The BGK model

The Boltzmann equation describes the evolution of a single particle distribution function, f (x, v, t), where x is the position and v the velocity of the particle at time t. It reads:

∂f ∂t + v • ∇ x f + F m • ∇ v f = ∂f ∂t c , (1)
where ∇ x and ∇ v are respectively the gradients in configurations and velocity spaces, m the mass of a particle and F an external force. In this model, the collision operator (rhs of Eq. ( 1)) is taken in its linearized form given by Bhatnagar-Gross-Krook (BGK) collision term [24]:

∂f ∂t c = - f -f eq τ , (2)
where τ is the relaxation time. This single time is related to both the kinematic viscosity ν (ν = k B T τ /m) and the thermal diffusivity κ (κ = k B T τ /m) of the fluid. This points out that the BGK operator intrinsically describes a fluid for which the Prandt number P r = ν/κ is equal to unity. Finally, the local Maxwell-Boltzmann equilibrium distribution f eq reads:

f eq (x, v, t) = ρ m 2 π k B T D/2 exp - m (v -u) 2 2 k B T , (3)
where k B is the Boltzmann constant and D the space dimension. The equilibrium distribution function shares the three first moments with f : the density ρ, the macroscopic velocity u and the temperature T , which are all functions of position x and time t. Because the BGK collision operator conserves the number of particles, the momentum and the total energy, those macroscopic quantities are given by the first three momenta of the distribution function f , i.e.:

ρ = f dv, (4)
ρ u = v f dv, (5)
ρ D k B T m = (v -u) 2 f dv (6)
B. Discretization procedure

The Lattice Boltzmann Methods (LBM) consist in going back and forth between a kinetic and a macroscopic description. The temporal evolution of the distribution function f is given by (1) where the collisional operator requires to know the equilibrium distribution function f eq . In turn, f eq requires the first three momenta of the distribution function f . The Boltzmann equation is numerically integrated using a splitting scheme [25]. Firstly, the temporal evolution of the distribution function is achieved by solving the linear transport term in the lhs of Eq. ( 1) alone. Different TVD schemes have been experimented and three flux limiters have been retained and compared : MinMod and Superbee limiters [START_REF] Laney | Computational gasdynamics[END_REF] and Koren limiter [START_REF] Koren | A Robust Upwind Discretization Method For Advection, Diffusion And Source Terms[END_REF]. They give very close results apart for very low Knudsen numbers (≤ 10 -3 ) where the advantage goes to the Koren limiter.

The second step implements the local collisional term. That requires to know the equilibrium function using the three first momenta of the distribution function. The same kind of scheme has already been used to integrate the Vlasov equation [28]. Nevertheless, in this context, it has been recognized that the velocity discretization of the distribution function should be precise enough, especially to take into account high velocities.

Here, because the equilibrium is a Gaussian and because the computation of the momenta of the distribution function requires integral calculation which can be performed efficiently by a Gauss-Hermite quadrature method, we propose to decompose the distribution function on Hermite polynomials basis. The decomposition of the equilibrium function given by Eq. ( 3) reads:

f eq = ρ w [θ0] (v) ∞ n=0 u n n! H [θ0] n (v), (7)
where the n-th Hermite polynomial generalized to the same temperature θ 0 (cf. A). That temperature, although arbitrary, will actually be close to the temperature θ of the system. The summation (7) implies an infinite number of terms. From a practical point of view, the summation is performed up to a given order N . So a truncated equilibrium distribution function f eq (x, v, t) is thus introduced:

w [θ0] (v) = 1/ √ 2πθ 0 exp -v 2 /
f eq (x, v, t) = w [θ0] (v) N n=0 a n (x, t) n! H [θ0] n (v), (8)
where the coefficients a n (x, t) are the moments of f eq . Again the distribution function f is given by a decomposition on Hermite polynomials basis up to an order q which is not necessarily equal to N :

f (x, v, t) = w [θ0] (v) q n=0 b n (x, t) n! H [θ0] n (v), (9)
where the b n (x, t) are computed using the orthogonality relation:

b n (x, t) = θ n 0 ∞ -∞ f (x, v, t) H [θ0] n (v) dv (10)
Because the collision operator conserves the first three moments of f , a 0 , a 1 and a 2 are respectively equal to b 0 , b 1 and b 2 . The higher moments of f eq are combinations of these first three moments. It is natural to compute the integral (10) with a Gauss-Hermite quadrature:

b m = θ m 0 ∞ -∞ w [θ0] (v) f H [θ0] m (v) w [θ0] (v) dv = θ m 0 q i=1 f i H [θ0] m (v i ), (11)
with

f i = ω i f (x, v i , t) w [θ0] (v i ) (12)
The velocities v i are the roots of the Hermite polynomial of order q and the ω i are their associated weights:

{ω i = q! q H [θ0] q-1 (v i ) -2 : i = 1, . . . , q}, (13)
where v i is the i-th root H [θ0]
q .

The summation is exact if the order of the polynomial f

H [θ0] m (v)/w [θ0] (v)
is less than 2q. It will then be possible to evaluate the distribution function f up to order q. However, the numerical scheme only needs to construct the equilibrium distribution function f eq explicitly, hence to compute the first three moments of the distribution function. It is consistent with equation ( 9) to take a Gauss summation up to q. Relation ( 11) is indeed exact as soon as the order of f is less or equal to q. It will be the case because f /ω

[θ0] 0 (v) is a polynomial of order q, and H

[θ0]

m is a polynomial of order m (m going from 0 to q).

In dimension 1, the discretization of the velocity space is provided by the Gauss-Hermite quadrature. The q velocity values are given by the q roots of the generalized Hermite polynomial H q (v i ) (cf. A). In higher dimension D, the discretization of the velocity space is obtained by the tensor products of D copies of the 1-dimensional velocity system and the weights are computed as the product of the corresponding 1-dimensional weights. Consequently, the number of velocity beams is q D . Labeling the distribution function with an index associated to the q D beams, the three moments read:

ρ = q D i=1 f i (14)
ρ u = q D i=1 v i f i (15)
D ρ θ + ρ u 2 = q D i=1 v 2 i f i (16)
Those three moments allow us to compute a distribution function

f eq i = ω i f eq (x, v i , t) w [θ0] (v i )
. For example, the truncation of equation ( 8) to N = 2 provides:

f eq i = ω i a 0 (x, t) H [θ0] 0 (v i ) + a 1 (x, t) H [θ0] 1 (v i ) + 1 2 a 2 (x, t) H [θ0] 2 (v i ) = ω i ρ + ρ u • v i θ 0 + ρ (u • v i ) 2 2 θ 2 0 + ρ (θ -θ 0 ) 2 θ 0 v 2 i θ 0 -D -ρ u 2 2 θ 0 (17)
The first three moments of this distribution function are indeed given by a 0 , a 1 and a 2 . Nevertheless we can show that the positivity of this truncated distribution function is no longer guaranteed. A more complete presentation of this method is given by Shan et al. [19]. Here we restrict our study to 2D problems with schemes obtained by 1D composition. So, a scheme called here H q (model with q beams per direction) correspond to the quadrature E q 2 2,2q-1 in [19].

III. NUMERICAL RESULTS

As a benchmark for this method, a transitional-Knudsen-number Poiseuille flows is under study [16]. A force-driven Poiseuille flow was simulated for a large range of Knudsen numbers using schemes based on {H q : q = 3, . . . , 8} and with a second order equilibrium distribution function (N = 2). These simulations are set-up as follows. We apply Maxwell's boundary conditions in the cross-channel direction (y) and a periodic boundary condition in the channel direction (x). In the cross-stream direction L = 100 grid points are employed, and only four grid points are used in the periodic (stream) direction. The Knudsen number is defined as

K n = 5 2 ν L c0
, where ν is the kinematic viscosity and c 0 the speed of sound. Hence, simulations are parametrized using the relation between the kinematic viscosity and the discrete relaxation time τ = ν/c 2 0 -δt/2, with δt = 1 in dimensionless formulation. The flow is driven by an external force F = 8 ν U 0 /L 2 pointing in the positive-x direction, where U 0 is the maximum velocity of the stream in the hydrodynamic limit (i.e. for K n → 0). U 0 is chosen so that every simulation has the same Mach's number: M a = U 0 /c 0 = 10 -4 . Finally, the density, the velocity and temperature are respectively initialized to 1, 0 and θ 0 all over the domain.

For different values of the Knudsen number (0.001 < K n < 10), the mass flow rates across the duct Q = L y=0 ρ(y) u x (y) are calculated when the steady state regime is reached. Figure 1 shows, for each scheme, this mass flow rate normalized to Q 0 = 6 ν U 0 /c 0 as a function of K n . We also give also some experimental values [23] and the low-Knudsen asymptotic value [START_REF] Cercignani | The Boltzmann Equation and Its Applications[END_REF] for comparison:

Q Q 0 = 1 6 K n + C 1 + 2C 2 K n . (18)
In this expression, the term 1/6 K n (also plotted) is associated to the Navier-Stokes solution without slippage while the other terms involving C 1 and C 2 take into account first and second-order slip boundary condition respectively. Different values could be found in the literature (see Tang et al. [9]). Nevertheless C 1 is usually close to 1, while C 2 lives in a wide range of values including negative ones. Here we will take C 1 = 1 and C 2 = .13 (see hereafter for the choice of C 2 ).

Figure 1 points out the following observations. Firstly, in the hydrodynamic regime (i.e. for K n 0.01), all models agree with the theoretical curve given by the Navier-Stokes equations. Even the simplest model H 3 , the well known D 2 Q 9 which only deals with 3 beams per direction, gives good results. When K n is increased, the numerical results deviates from the hydrodynamic asymptote as expected, but all models agree with each other almost up to K n = 0.1, value for which discrepancies between them appear. Hence, all these schemes produce good results up to the slip regime, commonly defined in the range 0.01 < K n < 0.1.

Beyond the slip regime, i.e. in the transitional regime, the flow-rate curves separate, alternating relatively to the experimental curve -our only reference, as no theoretical solution exists in this interval -. This convergence is noticeable because systems with even-order quadrature underestimate the flow-rate, while the odd-order ones overestimate it. However, increasing the order of quadrature improves the result in any case. Physically, the difference between odd and even schemes must be related to the fact that the 0-velocity stream appears in the former but not in the latter. As the 0-velocity particles do not move, they do not collide with boundaries either. They are only sensitive to particle-particle collisions. Unfortunately the influence of this process decreases with increasing Knudsen number and finally, these particles remain in their initial state over a very long time. Although the odd-schemes induce larger errors on the flow-rates, they have the advantage of depicting at least qualitatively a minimum for Kn ∼ 1. Indeed experimental data reported figure 1 show this minimum which is not an artifact and corresponds exactly to the Knudsen paradox behavior.

The alternation suggests the idea of trying to accelerate the convergence of these schemes by combining two different behavior patterns. The natural choice for these schemes is to take two successive orders. We can therefore hope to compensate the overestimation of the flow-rate of the odd-scheme by the underestimation of the lower or higher evenorder, while maintaining the extrema of the curve. These composite schemes are noted H q|q+1 and are simply built by superposition of the H q and H q+1 velocity spaces and by dividing the weights of each ones by 2, so the sum of the weights of the new scheme is again equal to unity. More precisely, the new set of velocities of the composite schemes

Q/Q 0 K n Cercignani Navier-Stokes Experimental values H 3 H 4 H 5 H 6 H 7 H 8
FIG. 1: Q/Q0 obtained with {Hq : q = 3, . . . , 8} (symbols), analytical curve (dashed line) and experimental data (stars).

H q|q+1 is the addition of the q D velocities of H q and the (q +1) D velocities of H q+1 (where D is the spatial dimension). So the transport step of the distribution function is performed for this new set of velocities i.e. on q D + (q + 1) D beams. The equilibrium distribution function is still given by equation ( 17) but the moments are now computed by summation over the q D + (q + 1) D f i 's. Here, the weight of a given beam is the same as for the scheme from which it comes, but divided by two. So the sum of the weights over all the beams remains equal to one. As before, the velocities are normalized to the highest one. On figure 2 are plotted results for the same problem, but obtained with {H 3|4 , H 4|5 , H 5|6 , H 6|7 } composites schemes described in the previous paragraph. Results of schemes based on {H q : q = 7, 8} are also plotted for comparison. In terms of computational cost, the H 3|4 must be compared with H 5 as they both have 25 beams. H 4|5 and H 7 can also be compared as they have respectively 41 and 49 beams. So the combination of two successive order quadratures considerably increases the speed of convergence of the family. Notably, the scheme based on the H 4|5 produces very good results up to K n = 1, with a computational cost of the order of standard high-orders lattice Boltzmann models. Finally, the worst behavior of H 5|6 compared to H 4|5 , may be linked to the fact that the relative weight of the 0velocity stream is more important in the former than in the latter. This suggests to prefer even|odd combination or to give a weight higher then 1/2 to even models.

To have a better insight into the results, the velocity profiles are given figure 3 for H 4/5 and different values of the Knudsen number. The theoretical profiles obtained from an hydrodynamic analysis including a velocity slip is also plotted. Its expression reads :

v(x) = 4U 0 x H (1 - x H ) + C 1 K n + 2C 2 K 2 n ( 19
)
As expected, the agreement is good for low Knudsen numbers while the numerical profile is flatter than the theoretical one for highest Knudsen values. The slip velocities are given on figure 4 for all models including composite ones. The theoretical velocity slip U s = v(x = 0) obtained with the second order approximation in K n is given for comparison.

As for equation (18), C 1 = 1 and C 2 = .13. The value of C 2 has been chosen such that equation ( 19) fits the slip velocity points of H 4|5 . As for the flow curve, the same general picture can be drawn : all the models agree in the hydrodynamic limit, while the slip velocity is higher for odd models than for even models. As q increases, the slip velocities of even and odd models converge toward a single curve. This curve is close to the one obtained for the composite models which do not exhibit huge differences.

The computational time needed for the simulations given here is depicted figure 5. For both families of schemes the CPU time scales as the total number of beams to the power 1.32. For the same number of beams, composite schemes are slightly faster than simple ones. More precisely, the numerical effort for a H q|q+1 is approximatively the same as for H q ′ , with q ′ = int([q D + (q + 1) D ] 1/D ), where the function int(x) maps x to the closest integer (Fig. 5).

IV. CONCLUSION

We have presented a high order lattice Boltzmann model based on the projection of the distribution function on the Hermite's basis. The schemes obtained with that procedure have been tested on a Poiseuille flow for a wide range of Knudsen numbers, ie from the hydrodynamic regime to the rarefied one. All those schemes agree with the theoretical values for small Knudsen numbers. Two successive order schemes show an alternating convergence toward experimental data. However, that convergence seems to be slow. Mixed scheme have been proposed in order to improve it. Qualitatively the good agreement obtained for H q+1 models coupled to the H q ones can be attributed to a finer discretization of the velocity space. For the former, the beams belong to a range around the thermal velocity, while the latter takes into account higher velocities where the probability distribution function is not very significant. Among that family the combination of type H 2q+1|2q should be preferred since the 0-velocity stream is weakly weighted.

In our approach, we used a better velocity space discretization than in the usual LBM scheme. In addition, to be able to use Gauss Hermite quadrature to compute the exact the moments of the distribution function, the velocities are the roots of an Hermite polynomial. The irrationality of these roots demands the use of a more sophisticated propagation step than for a standard lattice method. To that respect, the computational effort is more important. Nevertheless, all the schemes imply the usual relaxation time related directly to the Knudsen number. So there is no need to introduce an effective scheme-dependent relaxation time nor to use a multiple relaxation time scheme. In the former case it appears that it is still a challenge to find a general wall function.

The scheme order is related to the truncation q of the Hermite development of the distribution function (see Eq. ( 7)) which is higher than the truncation N of the equilibrium distribution function toward which the former relaxes. Here, we have taken N = 2, while q runs from 2 to 8. Although it is not explicitly computed, it is important to have a good description of the distribution function, especially for high Knudsen values for which it remains out of equilibrium over long times. It has been numerically verified that, at least for the benchmark presented here, increasing the order N only has minor influence.

  2θ 0 is the weight function for the Hermite polynomials H [θ0] n , c 0 = √ θ 0 = k B T 0 /m the thermal velocity related to an arbitrary temperature θ 0 and H [θ0] n

Hx α x β x γ c 6 0 - x α δ β γ + x β δ α γ + x γ δ α β c 4 0H [c 2 0

 042 Generalized Hermite polynomials with temperature θ 0 = c 2 0 in dimension higher than one. ] n is a tensor of order n.

  Flow rate computed with {Hq : q = 7, 8} and {H 3|4 , H 4|5 , H 5|6 , H 6|7 } (symbols). Experimental data (stars).

		100
			Cercignani
			Navier-Stokes
			Experimental values
			H 7 H 8 H 3|4 H 4|5 H 5|6 H 6|7
	Q/Q 0	10
		1
		0.01	0.1	1
			K n
	FIG. 2:

  Velocity profiles for H 4|5 and Kn=.005, 0.32, 0.64, 1.28 and 2.56. Numerical results are continuous lines. As expected, theoretical curves (dashed lines) are valid for small Knudsen number.

		20
		18
		16
		14	K n =0.005 K n =0.32
		12	K n =0.64
	v	10	K n =1.28 K n =2.56
		8
		6
		4
		2
		0
			10	20	30	40	50	60	70	80	90
							x
	100 FIG. 3: 0.1 1 10 U slip / U 0	Theory H 3 H 4 H 5 H 6 H 7 H 8 H 3|4 H 4|5 H 5|6 H 6|7
		0.01			0.1				1
							K n
	FIG. 4: Slip velocities for Hq (symbols) and theoretical curve (continuous line).

  Normalized CPU time for the different models with Kn = 0.032.

		100	simple scheme nb 1.31
		composite scheme nb 1.33
	computational time	10	H 4	H 5 H 3|4	H 6	H 4|5 H 7	H 8 H 5|6	H 6|7
		H 3
		1
		10						100
				beam number
		FIG. 5:

Acknowledgments

This work is financially supported by the state of Région Centre. The authors benefited from the use of the cluster at the Centre de Calcul Scientifique en Région Centre.


F Cavalieri

P Franchin

P Gehl

B Khazai

Quantitative assessment of socio-economic

Keywords: displaced population, uncertainty, functional interdependence, SYNER-G

Quantitative assessment of socio-economic performance measures accounting for seismic damage to buildings and functional interaction with infrastructural systems at the urban scale

Francesco Cavalieri, Paolo Franchin, Pierre Gehl, Bijan Khazai

To cite this version:

Francesco Cavalieri, Paolo Franchin, Pierre Gehl, Bijan Khazai. Quantitative assessment of socioeconomic performance measures accounting for seismic damage to buildings and functional interaction with infrastructural systems at the urban scale. 15th World Conference on Earthquake Engineering : 15th WCEE, Sep 2012, Lisbon, Portugal. hal-00685462


Emilie Morvant

Stéphane Ayache

Amaury Habrard

Miriam Redi

Claudiu Tanase

Bernard Merialdo

Bahjat Safadi

Franck Thollard

Nadia Derbas

Georges Quenot

VideoSense at TRECVID 2011 : Semantic Indexing from Light Similarity Functions-based Domain Adaptation with Stacking

. This year, we focused on a stacking fusion with Domain Adaptation algorithm. In machine learning, Domain Adaptation deals with learning tasks where the train and the test distributions are supposed related but different. We have implemented a classical approach for concept detection using individual features (low-level and intermediate features) and supervised classifiers. Then we combine the various classifiers with a second layer of classifier (stacking) which was specifically designed for Domain Adaptation. We show that, empirically, Domain Adaptation can improve concept detection by considering test information during the learning process.

Introduction

The High-Level semantic retrieval task concerns features or concepts such as "Indoor/Outdoor", "People", "Speech" etc., that occur in video databases. The TRECVID SIN task [START_REF] Over | Trecvid 2011 -an overview of the goals, tasks, data, evaluation mechanisms and metrics[END_REF] contributes to work on a benchmark for evaluating the effectiveness of detection methods for semantic concepts. The task is as follows: given the feature test collection composed of hundred of hours of videos, the common shot boundary reference for the feature extraction test collection, and the list of feature definitions, participants return for each feature the list of at most 2000 shots from the test collection, ranked according to the highest possibility of detecting the presence of the feature. Each feature is assumed to be binary, i.e., it is either present or absent in the given reference shot.

The VideoSense1 project aims at automatic video tagging by high level concepts, including static concepts (e.g. object, scene, people, etc.), events, and emotions, while targeting two applications, namely video recommendation and ads monetization. The innovations targeted by the project include video content description by low-level features, emotional video content recognition, cross-concept detection and multimodal fusion, and the use of a pivot language for dealing with multilingual textual resources associated with video data.

The first participation of the project to the TRECVID'11 SIN task is based on a stacking fusion with Domain Adaptation. Domain adaptation is a machine learning task consisting in adapting a classifier on new data that come from a distribution different but related to the distribution of the train examples. Since the TRECVID'11 corpus is a real corpus with amount data, the train data could not be representative of all the test data. Our aim is to test a Domain Adaptation algorithm that combines various classifier outputs from individual feature in order to adapt the learned classifier on the test data for improving the performances.

In the following, section 2 lists the features and classifiers we used. Section 3 presents our algorithm for Domain Adaptation namely DASF. Section 4 describes our fusion approach with DASF. Then, in section 5, we show the runs we submitted and discuss about their relative performance.

Feature extraction and individual classifiers

Since the VideoSense members are also members of the IRIM project which participate to TRECVID'11, features and individual classifiers are described in the paper [START_REF] Delezoide | Irim at trecvid 2011: Semantic indexing and instance search[END_REF]. We used the following features from LIG, EURECOM and LIF teams:

DASF: Domain Adaptation with Similarity Functions

Domain Adaptation arises when learning and test data are generated according to two different probability distributions: the first one generating training data is often referred to as the source domain, while the second one for test data corresponds to the target domain. According to the existing theoretical frameworks of Domain Adaptation [START_REF] Ben-David | A theory of learning from different domains[END_REF][START_REF] Mansour | Domain adaptation: Learning bounds and algorithms[END_REF][START_REF] Ben-David | Impossibility theorems for domain adaptation[END_REF] a classifier can perform well on the target domain if its error relatively to the source distribution and the divergence (or distance) between the source and target distributions are together low. One possible solution to learn a performing classifier on the target domain is to find a projection space in which the source and target distributions are close while keeping a low error on the source domain.

In order to illustrate quickly this idea in a formal manner, if err T denotes the error on the target domain (ie our goal here) and err S the error on the source domain where labeled data are available, then for any classifier h belonging to an hypothesis space H, we have from [START_REF] Ben-David | A theory of learning from different domains[END_REF]:

∀h ∈ H, err T (h) ≤ err S (h) + 1 2 d H∆H (D S , D T ) + ν. (1)
The term ν can be seen as a kind of adaptation ability measure of H for the Domain Adaptation problem considered and corresponds to the error of the best joint hypothesis over the two domains: ν = arg min h∈H err S (h) + err T (h). The second term d H∆H (D S , D T ) is called the distance between the two domain marginal probability distributions: D S for the source and D T for the target. Note that both err S (h) and d H∆H can be estimated from finite samples.

Our algorithm addresses Domain Adaptation for binary classification in the challenging case where no target label is available. Following the Domain Adaptation framework of Ben-David et al. [START_REF] Ben-David | A theory of learning from different domains[END_REF], our method looks for a relevant projection space where the source and target distributions tend to be close. Our approach is formulated as a linear program with a 1-norm regularization leading to sparse models.

To improve the efficiency of the method we propose an iterative version based on a reweighting scheme of the similarities to move closer the distributions in a new projection space. Hyperparameters and reweighting quality are controlled by a reverse validation process. Furthermore, our approach is based on a recent framework of Balcan et al. [START_REF] Balcan | Improved guarantees for learning via similarity functions[END_REF] allowing to learn linear classifiers in an explicit projection space based on good similarity functions defined as follows. Roughly speaking, under a criterion of goodness introduced in [START_REF] Balcan | Improved guarantees for learning via similarity functions[END_REF], a good similarity function ensures that a low error linear classifier exists in a space made of similarity scores to a set of prototype examples called reasonable points. The learned linear classifier is of the form:

h(•) = du i=1 α i K(•, x i )
where the examples x i correspond to this so called set of reasonable points. The formulation is close to the one of SVM, except that the framework allows one to use similarity functions K that are more general than kernels in the sense K is not required to be symmetric nor positive semi-definite. The main idea of our Domain Adaptation algorithm, called DASF, consists in automatically modifying the projection space to the similarities (ie φ R (•) =< K(•, x 1 ), . . . , K(•, x i ), . . . , K(•, x du ) >) for moving closer source and target points. For this purpose, we proposed a general method based on the optimization of a regularized convex objective function trying to find reasonable points close both to source and target examples. The objective function proposed in our algorithm is defined as follows:

                     min α F (α) = 1 d l d l i=1 L h, (x i , y i ) + λ α 1 +β (xs,xt)∈C ST t φ R (x s ) -t φ R (x t ) diag(α) 1 , with L h, (x i , y i ) = 1-y i h(x i ) + and h(x i ) = du j=1 α j K(x i , x j ).
(DASF opt )

Examples (x i , y i ) are labeled examples from the source domain, L(•) is the loss function optimized for learning classifiers, x j being the "reasonable" points considered. We have two regularizers, one is a classical L1 norm over the weights α j of the linear classifier α. The complex last one, weighted by a parameter β, corresponds to the term trying to move closer some source instances (x s ) with target examples (x t ) belonging to a set chosen by reverse validation. More details can be found in [START_REF] Morvant | Sparse Domain Adaptation in Projection Spaces based on Good Similarity Functions[END_REF]. Note that we have provided theoretical results with DASF and that our algorithm has been evaluated on a toy problem and on two real image annotation tasks.

We used DASF algorithm as a stacking classifier using outputs from individual classifier on the considered features. Stacking provides a way of combining classifiers together to find an overall system with usually improved generalization performance [START_REF] Smyth | Linearly combining density estimators via stacking[END_REF]. In the context of SIN task, we considered the training set as source domain and the test set as target domain, although they are supposed to be already closed. However, as the challenge is based on real data, the training set could not be representative of the test set. We thus expect DASF to improve further the performance of video indexing.

In order to make good use of the similarity function framework of Balcan et al. we proposed to compare two different similarity function. The first one is a usual Gaussian kernel (which is symmetric and PSD). For the second one we build a new similarity function by normalizing the Gaussian kernel. In order to link the two domains, we consider the information of both of them at the same time by actually renormalizing the Gaussian kernel for all the source and target points relatively to the set of similarities to the reasonable points. By construction, the similarity is then non-symmetric and non-PSD. Our choice is clearly heuristic and our aim is just to evaluate the interest of renormalizing a similarity for domain adaptation problems. Finally, we made a light search of the hyperparameters to accelerate our approach.

Results

In the following, we report our results (infAP) on the full SIN task. We compare DASF with SF as our baseline, SF-classifier is a linear classifier without Domain Adaptation, proposed for leaning with good similarity function ( [START_REF] Balcan | Improved guarantees for learning via similarity functions[END_REF]). Both SF and DASF have been submitted with and without normalization. We can observe that:

-A poor performance of our runs compare to the best run and the median. The stacking process as we implemented seems to overfit data ;

-Normalization was not successful, probably because source and target domains was actually closed: in such a particular case, we lost information by making use of the normalization ; Taking into account target information by using Domain Adaptation has allowed us to improve baseline results which was our main objective. However, we suspect that we actually have overfitted data and unfortunately was not able to generalize as we expected. This can be explained by the following reasons:

-
• We did not consider the goodness of the similarity function used (ie the Gaussian kernel) according to the outputs of the individual classifiers. In particular we are not sure that such a similarity is the best choice with our framework. Optimizing the similarity with some metric learning approaches, for example, would help us to better adapt our framework to the stacking problem considered.

• The renormalization of the kernel function used in our approach is simple but we know that it works well when the two domains are very different. The fact that this renormalization does not increase the performance shows that the train and test data are not that different here. By combining an information on the distance domains and some metric learning approaches, as evoked before, we may drastically improve the results.

• In domain adaptation, the estimation of the hyperparameters is difficult and costly. In our runs, we simplified a bit the search of the parameters which may explain why we tend to overfit.

• We did not take into account some second order (ie variance/covariance) information from the outputs of the classifiers and we think that it may be useful to find a better combination.

Our first attempt shows that Domain Adaptation could bring some improvement. However, to be competitive with the state of the art, we have to take into account more accurately the diversity of the data and classifiers. It appears especially important in the case of multiple source of annotations. Under this condition, we think that Domain Adaptation approaches can lead to significant improvement of the results. Using some correlations between labels is in particular an interesting direction.

  Global features: LIG/hg104 (Color histogram + Gabor filters) Local features: LIG/opp sift, LIG/stip (SIFT and STIP) Shape features: EUR/sm462 (Saliency Moments) Intermediate features: LIF/percepts (Mid-level concepts based on 15 concepts). We used two types of classifiers from LIF team: KNN: LIG KNNB (multiclass KNN) SVM: LIG MSVM (for imbalanced data).

  As expected Domain Adaptation runs both outperformed our baseline. Even if train and test set are similar, we can still take advantage of Domain Adaptation approach by considering (test) target information during the learning process.Our main focus for TRECVID'11 SIN task is on the exploration of Stacking with Domain Adaptation to combine individual classifiers.

	Videosense 1 0.067	DASF with normalization
	Videosense 2 0.040	SF with normalization
	Videosense 3 0.080	DASF
	Videosense 4 0.072	SF
	Best run	0.1731 -
	Median	0.1083 -

The french project VideoSense ANR-09-CORD-026 of the ANR and the IST Programme of the European Community.

Acknowledgment

This work was supported in part by the french project VideoSense ANR-09-CORD-026 of the ANR.


Christèle Maison

Delphine Bailly

Danièle Roche

Rocio Montes De Oca

Aline V Probst

Isabelle Vassias

Florent Dingli

Damarys Bérengère Lombard

Rocío Montes De Oca

Damarys Loew

Jean-Pierre Quivy

Geneviève Almouzni
email: genevieve.almouzni@curie.fr

SUMOylation promotes de novo targeting of HP1α to pericentric heterochromatin

Keywords: HP1α, sumoylation, non-coding centromeric RNAs, pericentric heterochromatin 2

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.

Heterochromatin at pericentric domains represents a paradigm for understanding how a functional nuclear domain is established and maintained. Studies in S. pombe and Drosophila have advanced our knowledge concerning basic mechanisms and conserved components in the organization of the domain [START_REF] Grewal | Heterochromatin revisited[END_REF] .

In particular HP1 proteins which accumulate in these domains are highly conserved from S. pombe to mammals. However in mammalian cells, how HP1 is specifically targeted de novo to initiate formation of a domain of accumulation as found in pericentric heterochromatin [START_REF] Guenatri | Mouse centric and pericentric satellite repeats form distinct functional heterochromatin[END_REF][START_REF] Probst | Epigenetic inheritance during the cell cycle[END_REF] remains mysterious. The recognition of H3K9me3 by HP1 [START_REF] Bannister | Selective recognition of methylated lysine 9 on histone H3 by the HP1 chromo domain[END_REF][START_REF] Lachner | Methylation of histone H3 lysine 9 creates a binding site for HP1 proteins[END_REF] which exemplifies the paradigm of the reader model in the histone code hypothesis [START_REF] Strahl | The language of covalent histone modifications[END_REF][START_REF] Jenuwein | Translating the histone code[END_REF] does not necessarily provide on its own a de novo specific targeting mechanism. One should also consider other HP1 binding partners [START_REF] Peng | Epigenetic gene silencing by the SRY protein is mediated by a KRAB-O protein which recruits the KAP1 co-repressor machinery[END_REF][START_REF] Quivy | A CAF-1 dependent pool of HP1 during heterochromatin duplication[END_REF] , potential post-translational modifications [START_REF] Lomberk | Evidence for the existence of an HP1-mediated subcode within the histone code[END_REF] and the elusive RNA that has been linked to the presence of HP1 at pericentric heterochromatin [START_REF] Maison | Higher-order structure in pericentric heterochromatin involves a distinct pattern of histone modification and an RNA component[END_REF][START_REF] Muchardt | Coordinated methyl and RNA binding is required for heterochromatin localization of mammalian HP1alpha[END_REF] . While transcripts from major satellite DNA repeats have been identified [START_REF] Rudert | Transcripts from opposite strands of gamma satellite DNA are differentially expressed during mouse development[END_REF][START_REF] Lu | Proliferation-dependent and cell cycle regulated transcription of mouse pericentric heterochromatin[END_REF] , a functional connection between specific RNAs and HP1 has not yet been established. Taken together, these data prompted us to explore further the HP1-RNA connection and particular post-translational modifications or partners that could provide a means for the de novo targeting of HP1 to pericentric heterochromatin, thereby helping to define this specific subnuclear compartment.

We first verified that repetitive DNA sequences in mouse centromeres, known as major and minor satellites in pericentric and centric heterochromatin respectively [START_REF] Kalitsis | Centromere DNA of higher eukaryotes[END_REF] , can be transcribed in both orientations.

All these transcripts detected by RT-PCR analysis with strand-specific primers for major or minor satellites showed various sizes corresponding to multiple repeats of their basic units (Fig. 1a). We next examined whether some of these transcripts could be stably found in the nucleus. As a reference for comparison, we used the well-defined organization of chromocenters with major satellite repeats surrounded by minor satellite DNA (Fig. 1b, left, DNA FISH) [START_REF] Guenatri | Mouse centric and pericentric satellite repeats form distinct functional heterochromatin[END_REF] . For this, we exploited fluorescently labelled locked nucleic acid (LNA) probes for RNA FISH that detect specifically major and minor transcripts in either forward or reverse orientation. While minor RNAs were barely detectable, LNA probes for major RNAs in both orientations revealed a significant number of nuclear spots frequently associated or close to chromocenters (Fig. 1b,middle). These signals were not a result of DNA cross-hybridization, since they were undetectable after RNase treatment (Supplementary Fig. 1). With some variations from cell to cell suggesting cell cycle modulation, reverse major RNAs were usually detected as fewer and larger spots (Fig. 1b, middle, red) and forward major RNA signals were smaller in size and present in higher numbers (green). Interestingly, these forward major RNAs were consistently at the periphery of HP1α domains (Fig. 1b, right, immuno-RNA FISH and Supplementary Fig. 2a). Since active transcription occurs frequently in the external part of chromosomal domains by DNA looping out [START_REF] Heard | The ins and outs of gene regulation and chromosome territory organisation[END_REF] , they may represent primary transcripts stably maintained at the site of transcription. Notably, HP1α accumulated at major satellite domains, away from minor satellites which were juxtaposed (Fig. 1c and Supplementary Fig. 2b, Immuno-DNA FISH) [START_REF] Guenatri | Mouse centric and pericentric satellite repeats form distinct functional heterochromatin[END_REF] . We then examined further the possible in vivo association of major RNAs with major satellite domains by other methods.

Under conditions that preserved RNAs, we immunoprecipitated heterochromatin-associated material with a specific HP1α antibody. We found a significantly higher amount of forward major transcripts compared to reverse transcripts (Fig. 1d). Taken together, our data highlight a particular link between major RNA in the forward orientation and pericentric heterochromatin. While HP1α can bind RNA in vitro [START_REF] Muchardt | Coordinated methyl and RNA binding is required for heterochromatin localization of mammalian HP1alpha[END_REF] , a specific binding to a given transcript has been reported so far only for TERRA RNA [START_REF] Deng | TERRA RNA binding to TRF2 facilitates heterochromatin formation and ORC recruitment at telomeres[END_REF] . Using GST-tagged HP1α full-length protein or fragments thereof and radioactively labelled centromeric RNA probes (Fig. 2a), we find that the hinge domain (H) of HP1α strongly recognized both forward and reverse centromeric RNA probes, while the chromo-hinge (CD+H) and the hinge-chromoshadow (H+CSD) domains showed a lower binding capacity. Under these conditions, we did not detect binding between full-length HP1α and RNAs (Fig. 2a). These results suggest that the central hinge domain may adopt a different conformation in the full-length protein, possibly constrained by the CD and/or the CSD. This raised the possibility that HP1α could actually bind RNA in vivo and that this interaction can be regulated. To investigate this hypothesis, we aimed to identify proteins from nuclear cell extracts that associated with centromeric RNAs, using in vitro transcribed biotin-labelled forward major or minor RNAs immobilized on streptavidin beads (Fig. 2b and Supplementary Fig. 3a). Mass spectrometry analysis of the RNA-associated proteins identified mainly hnRNPs and proteins involved in RNA processing (Supplementary Fig. 3b and Supplementary Table 1) including vigilin, RNA helicase A (RHA) and Ras-GAP SH3 domain binding protein (G3bp), which were all validated by Western blotting (Fig. 2c). Vigilin and the Drosophila RHA ortholog, maleless (MLE), are thought to play roles in heterochromatin formation and X-chromosome dosage compensation, respectively [START_REF] Wang | Vigilins bind to promiscuously A-to-Iedited RNAs and are involved in the formation of heterochromatin[END_REF][START_REF] Kuroda | The maleless protein associates with the X chromosome to regulate dosage compensation in Drosophila[END_REF] , while G3bp may be involved in RNA metabolism [START_REF] Irvine | more promiscuous than ever: a review of G3BP[END_REF] . Surprisingly, under these experimental conditions, we did not detect any significant association between HP1α and major or minor RNAs, neither by mass spectrometry (Supplementary Fig. 3b) nor by Western blotting (Fig. 2c). Given our in vitro observations (Fig. 2a), we wondered whether post-translational modification of HP1α could promote in vivo HP1α binding to RNA. Indeed, HP1 can be phosphorylated [START_REF] Lomberk | Evidence for the existence of an HP1-mediated subcode within the histone code[END_REF] and in fission yeast, Swi6/HP1 is sumoylated in vivo [START_REF] Shin | SUMO modification is involved in the maintenance of heterochromatin stability in fission yeast[END_REF] . Furthermore, defective sumoylation of Swi6 results in significantly reduced heterochromatin stability. This prompted us to repeat our RNA pull down strategy with nuclear extracts prepared in the presence of a cocktail of phosphatase inhibitors and N-ethylmaleimide (NEM), a strong inhibitor of SUMO isopeptidases [START_REF] Aagaard | Functional mammalian homologues of the Drosophila PEV-modifier Su(Var)3-9 encode centromere-associated proteins which complex with the heterochromatin component M31[END_REF] . Remarkably, Western blotting with an anti-HP1α antibody revealed a slower migrating band in the input for HP1α that was not detected in absence of NEM and that then was specifically enriched in precipitates with forward major RNAs corresponding to either one or two satellite repeats length (Fig. 2d; Maj1 F or Maj2 F). This band, with an approximate additional molecular mass of ~11 kDa compared to HP1α, might represent an ubiquitin or a SUMO moiety. We confirmed that this slower-migrating form was modified by SUMO-1, but not SUMO-2/3, using specific antibodies (Fig. 2d). We obtained similar results with antibodies specific of HP1β and HP1γ (Supplementary Fig. 3c) indicating that all HP1 isoforms can potentially be sumoylated in vivo and are specifically retrieved with forward major RNAs. While the forward major RNA pulls down SUMO-1-HP1α, we estimated that only a small percentage of HP1α was SUMO-1 modified in vivo (less than 1% of total protein from nuclear extracts, Fig. 2d). This low representation is in agreement with rapid cycles of sumoylation and desumoylation as reported for other proteins weakly detected in a SUMO-modified state in vivo [START_REF] Hay | SUMO: a history of modification[END_REF][START_REF] Meulmeester | Cell biology: SUMO[END_REF] .

To confirm independently that HP1α gets sumoylated in vivo, we co-transfected HA-tagged HP1α (e-HP1α) and GFP-SUMO-1 into NIH3T3 cells to prepare total cell extracts and carried out immunoprecipitations with anti-HA beads under conditions that preserved the SUMO modification [START_REF] Park-Sarge | Detection of sumoylated proteins[END_REF] .

Western blot analysis using anti-GFP antibodies clearly revealed a band corresponding to GFP-SUMO-e-HP1α (Supplementary Fig. 4a), demonstrating unambiguously that HP1α can be sumoylated in vivo. To determine which region of HP1α was SUMO-modified, we next used an in vitro sumoylation assay with either wildtype (W) or mutant (M) SUMO-1 protein, in the presence of E1 activating and E2 conjugating (Ubc9) SUMO enzymes and various GST-HP1α domains (Fig. 3a). Western blot analysis using anti-GST antibodies showed SUMO-modification on the full-length HP1α, the chromo-hinge, the hingechromoshadow and the hinge domains, the latter domain showing the highest level of sumoylation (Fig. 3b and Supplementary Fig. 4b,asterisks). This is also true when using SUMO-2 or SUMO-3 (Supplementary Fig. 4c). These results revealed that the hinge, the same domain of HP1α that displayed RNA binding activity (Fig. 2a), is a target for sumoylation. Since the fusion of Ubc9 to a substrate provides a convenient way to increase its sumoylation [START_REF] Jakobs | Ubc9 fusion-directed SUMOylation (UFDS): a method to analyze function of protein SUMOylation[END_REF] , we also verified with a GST-HP1α-Ubc9 fusion protein that we could enhance SUMO-1-modification of HP1α in vitro without adding the E2 enzyme (Fig. 3c). Then, using the GST-HP1α hinge and SUMO-1 proteins as above (Supplementary Fig. 5a), we further identified specific sumoylated residues on HP1α by mass spectrometry. In the hinge domain, among the 13 lysines (K) as potential targets for sumoylation, we found that K84 of HP1α in the peptide, "EKSEGNK", was unequivocally identified as sumoylated by mass (with high accuracy in the orbitrap; Fig. 3d, right spectra, arrow) and sequence (by MS/MS in the Qstar mass spectrometer; Fig. 3d; shown y and b ions). However, we also found other potentially sumoylated lysines in HP1α (e.g., KMoxK, SKK, KYK or YKK; Supplementary Fig. 5b andc) indicating alternative usage of various lysine residues. We thus mutated successively each of the individual 13 lysines to arginine and performed in vitro sumoylation assays as above and in vivo co-transfections as in Supplementary Figure 4a. We observed in all cases that once we mutated one residue an alternative sumoylation site was used (data not shown), showing the usage of more than one sumoylation site and corroborating our mass spectrometry data. This suggests a lack of a strict requirement for a "specific" SUMO modified residue.

Since the fusion of Ubc9 to HP1α increases sumoylation efficiency in vitro (Fig. 3c), we thus generated an HP1α-Ubc9-HA fusion construct (e-HP1α-Ubc9) for in vivo expression and further analysis in a cellular context. Transfection of e-HP1α-Ubc9 or e-HP1α into NIH3T3 cells lead to comparable levels of proteins being expressed (Supplementary Fig. 6a andb; anti-HA). Interestingly, a significantly higher amount of SUMO-modified e-HP1α-Ubc9 could be detected. In total cell extracts, we found that e-HP1α-Ubc9 was mainly SUMO-2/3-modified reflecting the readily available endogenous SUMO-2/3 proteins compared to the limited amount of free endogenous SUMO-1 protein in cells (compare SUMO-1 vs SUMO-2/3 inputs in Fig. 2d) [START_REF] Hay | SUMO: a history of modification[END_REF] . This could be compensated for by providing exogenous SUMO-1 by transient transfection (Supplementary Fig. 6c). These in vivo results underline the fact that HP1α can be modified by SUMO-1 or SUMO-2/3 depending on the available substrate, as shown in vitro (Fig. 3b&c and Supplementary Fig. 4b&c). We verified that the catalytic activity of the fused Ubc9 was directly involved in HP1α sumoylation enhancement using a Ubc9 catalytic mutant fused to HP1α (e-HP1α-Ubc9C93S). In comparaison with e-HP1α-Ubc9wt, we detected a strongly reduced sumoylation of e-HP1α-Ubc9C93S (Supplementary Fig. 6c). Next, we examined e-HP1α-Ubc9 and e-HP1α localization in NIH3T3 cells. Both of them could accumulate at pericentric domains where endogenous HP1α is already located (Fig. 3e). Thus under these conditions, promoting HP1 sumoylation did not give a particular advantage for the recruitment and maintenance of exogenous HP1 to preexisting HP1 domains of accumulation. Next, we wondered whether HP1α sumoylation could be required more specifically for a de novo targeting of HP1α to heterochromatin domains. To test this hypothesis we used MEFs derived from Suv39h double-null (dn) mice, in which the H3K9me3 mark and HP1α are no longer enriched at pericentric heterochromatin [START_REF] Maison | Higher-order structure in pericentric heterochromatin involves a distinct pattern of histone modification and an RNA component[END_REF][START_REF] Peters | Loss of the Suv39h histone methyltransferases impairs mammalian heterochromatin and genome stability[END_REF] (Fig. 4). Transfection with exogenous Myc-SUV39H1 can restore the proper localization of these marks (Fig. 4b) [START_REF] Lachner | Methylation of histone H3 lysine 9 creates a binding site for HP1 proteins[END_REF][START_REF] Loyola | PTMs on H3 variants before chromatin assembly potentiate their final epigenetic state[END_REF] . Since we postulated that the interaction between major RNAs and sumoylated HP1α targets HP1α to pericentric domains, we first verified that we could detect major RNAs by RNA-FISH in Suv39h dn MEFs (Supplementary Fig. 7a). We then transiently transfected Suv39h dn cells with e-HP1α or e-HP1α-Ubc9 in the absence of Myc-SUV39H1 and verified that the proteins were expressed at comparable levels (Fig. 4c). We could not detect the typical localization to chromocenters in cells transfected with e-HP1α (Fig. 4c). In contrast, in about 10% of cells transfected with e-HP1α-Ubc9 cells, we found a faint but detectable pericentric localization 6h post-transfection.

Remarkably, in the latter case, we could not detect H3K9me3 accumulation at pericentric heterochromatin (Fig. 4c and Supplementary Fig. 7b) while H3K9me1 was clearly visible at these domains in all Suv39h dn cells (Supplementary Fig. 7c). Thus, a targeting of e-HP1α-Ubc9 to pericentric heterochromatin could occur in the absence of SUV39H1-dependent H3K9me3. However, while e-HP1α-Ubc9 was more efficiently targeted than e-HP1α, the low fraction of cells showing this staining suggested that following this initial recruitment, retention at pericentric domains was rather inefficient. We thus modified our assay to monitor the localization of e-HP1α or e-HP1α-Ubc9 to pericentric chromatin in the presence of Myc-SUV39H1 assuming that H3K9me3 could promote stabilization (Fig. 4d). Immunofluorescence analysis revealed that e-HP1α, e-HP1α-Ubc9C93S and e-HP1α-Ubc9wt accumulated at pericentric heterochromatin when co-transfected with Myc-SUV39H1, in contrast to a negative control protein e-hnRNPC (Fig. 4e). Remarkably, e-HP1α-Ubc9wt localized to these domains more efficiently than e-HP1α and e-HP1α-Ubc9C93S (62% vs 37% and 39% of positive cells, respectively 6h post-transfection) for comparable levels of expressed proteins (Supplementary Fig. 8a). Also, the e-HP1α and e-HP1α-Ubc9C93S overall staining in the nucleus was rather diffuse compared to e-HP1α-Ubc9wt staining suggesting that a significant fraction of e-HP1α and e-HP1α-Ubc9C93S is not localized at pericentric heterochromatin (Fig. 4e, Supplementary Fig. 8b and supplemental legend for details). Taken together, these results indicate that enhancing sumoylation on HP1α promotes a more efficient accumulation at pericentric heterochromatin. We then performed a time course analysis to compare the appearance of HP1α at pericentric heterochromatin, in Suv39h dn cells co-transfected with Myc-SUV39H1 and e-HP1α or e-HP1α-Ubc9 (Fig. 4f). We found that e-HP1α-Ubc9 always localized more efficiently to pericentric heterochromatin compared to e-HP1α (52% vs 31% of positive cells, respectively, 4h post-transfection) for comparable levels of expressed proteins along the time course analysis (Fig. 4f). The different efficiencies with which these proteins localized to pericentric heterochromatin support the hypothesis of sumoylation acting as a limiting step to promote HP1α targeting. In support of this hypothesis, although toxic, the direct fusion of SUMO-1 to HP1α showed an even more efficient accumulation compared to e-HP1α-Ubc9 (Supplementary Fig. 9 and supplemental legend for details). The simplest interpretation is that a higher amount of sumoylated protein provided by HP1α-Ubc9 fusion would allow a rapid targeting to pericentric domains whereas HP1α alone would be delayed by the time needed to undergo an entire cycle of sumoylation. Overall our data underline the importance of the HP1α SUMO modification prior to HP1α targeting to pericentric heterochromatin.

Given that the hinge domain, which shows RNA-binding properties [START_REF] Muchardt | Coordinated methyl and RNA binding is required for heterochromatin localization of mammalian HP1alpha[END_REF] is the target for sumoylation at multiple sites (Fig. 3b), we generated mutants of e-HP1α and e-HP1α-Ubc9 lacking the hinge domain and assayed whether they could specifically localize de novo to pericentric heterochromatin in Suv39h dn cells. After transfection of e-HP1αΔH and e-HP1αΔH-Ubc9 constructs in NIH3T3 cells, we found that the hinge domain was perfectly dispensable to localize HP1α at pre-existing HP1 domains in a 'maintenance assay' (Fig. 5a andb) as reported in Drosophila Kc167 cells [START_REF] Smothers | The hinge and chromo shadow domain impart distinct targeting of HP1-like proteins[END_REF] . Remarkably, when using Suv39h dn cells for our 'de novo' localization assay, after co-transfection with Myc-SUV39H1, the e-HP1α mutant lacking the hinge domain did not localize at pericentric heterochromatin, in contrast to the wild type protein which did accumulate at these domains (44% positive cells, Fig. 5c). We verified that all transfected proteins were expressed at comparable levels (Fig. 5d). Even when Ubc9 was fused to the mutant protein, we did not detect localization of e-HP1αΔH-Ubc9 at pericentric domains. These data clearly show that the hinge domain, the SUMO modification and the association with major RNAs are critical for de novo localization of HP1α at pericentric heterochromatin.

Based on our data, we propose a model for the de novo targeting and local accumulation of HP1α at pericentric heterochromatin by a multistep mechanism involving initial SUMO-dependent targeting as a "seeding" step (Fig. 6; "1"). This SUMO modification imposed in the hinge domain of HP1 would leave the CD and CSD available for other interactions with heterochromatin proteins (as represented in Fig 6).

Subsequent "chromatin marking" steps would follow, including SUV39-dependent H3K9me3 to ensure HP1 stabilization (Fig. 6; "2") and accumulation through a self-enforcing loop (Fig. 6; "3") [START_REF] Grewal | Heterochromatin revisited[END_REF] . Our identification of a specific association between SUMO1-HP1α and major RNAs in the forward orientation (Fig. 2) provides a molecular basis for the "seeding" step. Such association may help to guide SUMO-HP1α specifically to pericentric heterochromatin. The specificity of the interaction promoted by sumoylation, either by the sequence, by particular structures formed by these RNAs or by know HP1 partners [START_REF] Quivy | A CAF-1 dependent pool of HP1 during heterochromatin duplication[END_REF] , remains to be determined. Importantly, the HP1-RNA interaction is specific for the forward strand, which is purine rich and may thus adopt a distinct structure. Furthermore, It will be interesting to examine potential SUMO-binding protein candidate [START_REF] Kerscher | SUMO junction-what's your function? New insights through SUMO-interacting motifs[END_REF] . Following the "seeding" event, coordination with SUV39-mediated H3K9 methylation would be key for HP1α stabilization. While this step could formally be independent of sumoylation, it is possible that SUMO-HP1 and RNA interaction may promote additional interactions with other partners (such as SUV39) and enhance SUV39 enzymatic activity. In this way, the seeding event might favor further stabilization steps to establish a robust system for the maintenance of heterochromatin domains. Given that several proteins involved in heterochromatin stability have been shown to bind SUMO conjugates [START_REF] Ouyang | Direct binding of CoREST1 to SUMO-2/3 contributes to gene-specific repression by the LSD1/CoREST1/HDAC complex[END_REF] , it is tempting to speculate that they could also bind SUMO-HP1. Future work should address how and where HP1 gets sumoylated and which enzymes trigger both its sumoylation and desumoylation as well as the impact on centromere function. Given the conserved importance of HP1 from fission yeast to mammals [START_REF] Probst | Epigenetic inheritance during the cell cycle[END_REF][START_REF] Allshire | Epigenetic regulation of centromeric chromatin: old dogs, new tricks?[END_REF] , further investigation of these issues in various organisms should help to define some general principles.

We detected forward RNAs as long species (several repeat lengths, Fig. 1a), and showed that they localize at the periphery of pericentric domains (Fig. 1b and Supplementary Fig. 2a), however we did not detect small dsRNA corresponding to major satellites, as described for the maintenance of heterochromatin in S. pombe [START_REF] Grewal | Heterochromatin revisited[END_REF][START_REF] Moazed | Small RNAs in transcriptional gene silencing and genome defence[END_REF] . It is intriguing that even in S. pombe primal RNAs have been reported to be important for heterochromatin formation [START_REF] Blankenship | Two new roles for the Drosophila AP patterning system in early morphogenesis[END_REF] . Although we do not exclude an RNAi pathway in connection with heterochromatin in mammalian cells [START_REF] Kanellopoulou | Dicer-deficient mouse embryonic stem cells are defective in differentiation and centromeric silencing[END_REF][START_REF] Murchison | Characterization of Dicer-deficient murine embryonic stem cells[END_REF] , the fact that we detected long non-coding RNA that are stably located in the nucleus just at the periphery of major satellite domains is very compelling. This is reminiscent of other long nuclear non-coding RNA like the lincRNA HOTAIR, proposed to serve as a modular scaffold for histone modification complexes involved in Polycomb function [START_REF] Tsai | Long Noncoding RNA as Modular Scaffold of Histone Modification Complexes[END_REF] or Xist, which is critical to establish the silent state of the inactive X in mammals. Moreover, Xist RNA is known to be critical in setting up a de novo silent domain at specific times during development [START_REF] Savarese | Hematopoietic precursor cells transiently reestablish permissiveness for X inactivation[END_REF][START_REF] Agrelo | SATB1 defines the developmental context for gene silencing by Xist in lymphoma and embryonic cells[END_REF] . In this respect, the situation of early development in mice [START_REF] Santos | Dynamic chromatin modifications characterise the first cell cycle in mouse embryos[END_REF][START_REF] Puschendorf | PRC1 and Suv39h specify parental asymmetry at constitutive heterochromatin in early mouse embryos[END_REF] is particularly interesting, since a burst of transcription of major RNAs occurs just prior to the formation of HP1 domains of accumulation on the paternal genome [START_REF] Probst | A strand-specific burst in transcription of pericentric satellites is required for chromocenter formation and early mouse development[END_REF] . Thus, it is tempting to speculate that sumoylation could be critical also at this time and perhaps during other developmental time windows. This mechanism could apply to certain cell types when major rearrangements of the genome occur as observed during spermatogenesis [START_REF] Haaf | Higher order nuclear structure in mammalian sperm revealed by in situ hybridization and extended chromatin fibers[END_REF] , differentiation [START_REF] Mayer | Common themes and cell type specific variations of higher order chromatin arrangements in the mouse[END_REF][START_REF] Terranova | The reorganisation of constitutive heterochromatin in differentiating muscle requires HDAC activity[END_REF] , reprogramming in the mouse germ line [START_REF] Hajkova | Chromatin dynamics during epigenetic reprogramming in the mouse germ line[END_REF] , in specialized cell types like Rod photoreceptor cells [START_REF] Solovei | Nuclear architecture of rod photoreceptor cells adapts to vision in mammalian evolution[END_REF] , or even in the formation of Senescence Associated Heterochromatin Foci (SAHF) [START_REF] Narita | Rb-mediated heterochromatin formation and silencing of E2F target genes during cellular senescence[END_REF] .

Beyond HP1, the concept that a modification like SUMO imposed on a chromatin protein could promote localization guided by a particular transcript in the nucleus, should be explored. One may wonder whether similar mechanisms also apply to the formation of other local domains of accumulation or nuclear compartments such as polycomb or insulator bodies. c. RNA pull down using forward major (Maj2 F) or minor (Min F) RNAs, or no RNA as negative control, in the absence of NEM. We show Western blot analysis with anti-vigilin, anti-RHA, anti-G3bp or anti-HP1α antibodies. Input is 10% of nuclear extracts. d. RNA pull down using forward (F) and reverse (R) major (Maj2 F, Maj1 F, Maj2 R) or minor (Min F, Min R) RNAs as baits, or no RNA control, in the presence of NEM. Western blot analysis using anti-HP1α, anti-SUMO-1 and anti-SUMO-2/3 antibodies revealed endogenous unmodified HP1α (HP1α), modified-HP1α, SUMO-HP1α (S-HP1α) and free SUMO-2/3. Input is 10% of nuclear extracts. Asterisk (*) marks SUMO-HP1α in the input. A schematic representation of a nucleus with pericentric domains enriched in HP1 (red) is depicted showing the nuclear non-coding forward major RNA (green) at the periphery. HP1 (red) most likely as part of a complex becomes sumoylated. This SUMO-modified form of HP1α recognizes and binds to major RNAs (green) at pericentric heterochromatin, providing specificity to the initial targeting of HP1α to these domains (1). HP1α stabilization is then ensured by the recognition of H3K9me3 (blue) introduced by SUV39 (light brown) (2). Further HP1α accumulation involves a "self-enforcing" loop in which new HP1α directly binds to chromatin by multimerizing with other HP1α molecules, or by associating with other proteins and/or newly methylated H3K9 (3).

ONLINE METHODS

Mouse cell lines. We cultured wild type and Suv39h double-null MEFs (provided by T. Jenuwein) [START_REF] Peters | Loss of the Suv39h histone methyltransferases impairs mammalian heterochromatin and genome stability[END_REF] and NIH3T3 cells (ATCC #CRL-1658) as described [START_REF] Guenatri | Mouse centric and pericentric satellite repeats form distinct functional heterochromatin[END_REF] . We transfected MEFs and NIH3T3 cells with Nucleofector Kit 2 (Amaxa) and Lipofectamine 2000 (Invitrogen) respectively, according to manufacturer instructions.

Plasmids. We obtained plasmids encoding GFP-SUMO-1 from R. Hay, Myc-SUV39H1 from T.

Jenuwein [START_REF] Aagaard | Functional mammalian homologues of the Drosophila PEV-modifier Su(Var)3-9 encode centromere-associated proteins which complex with the heterochromatin component M31[END_REF] and GST-HP1α full-length protein and fragments thereof (CD, CD+H, H and CSD) from R.

Losson [START_REF] Nielsen | Heterochromatin formation in mammalian cells: interaction between histones and HP1 proteins[END_REF] . We carried out cloning using standard PCR-based techniques. We made e-HP1α, e-Ubc9 and e-SUMO-1Δ6 constructs by inserting HP1α (gift of R. Losson), Ubc9 (gift of J. Seeler) and SUMO-1Δ6 (from pEGFP-SUMO-1) fused to a HA-tag in C-terminus into pcDNA5 vector (Invitrogen). We generated e-HP1α-Ubc9 and e-HP1α-SUMO-1 constructs by inserting the HP1α cDNA at the N-terminus of the e-Ubc9 and the e-SUMO-1Δ6 plasmids, respectively. To avoid conjugation of e-HP1α-SUMO-1 into other proteins, we removed the last six C-terminal amino acids of SUMO-1, which contain the diglycine motif required for isopeptide bond formation. We generated HP1α and e-HP1α-Ubc9C93S point mutants using the QuickChange site-directed mutagenesis kit (Stratagene). To generate e-HP1αΔH and e-HP1αΔ-Ubc9 mutants, we made truncation contructs of e-HP1α and e-HP1α-Ubc9 in which amino acids M67 to R117 forming the hinge domain were deleted and replaced by a linker of 2 amino acids (ID). These truncation contructs led to the fusion of the chromo domain to the chromoshadow domain. We generated GST-HP1αhinge-chromoshadow domain and GST-HP1α-Ubc9 by subcloning from GST-HP1α full-length and e-HP1α-Ubc9, respectively. Each mutation and truncation was verified by sequencing.

Antibodies. We used: mouse monoclonal anti-HP1α (2HP-1H5-AS for immunofluorescence and 2HP-2G9-AS for Western blot; 1:1,000), anti-HP1β (1MOD-1A9-AS; 1:1,000), and anti-HP1γ (2MOD-1G6-AS; 1:1,000) all from Euromedex, rabbit polyclonal anti-vigilin (from D. Shapiro 50 ; 1:3,000), rabbit polyclonal anti-RHA (PA-001, Vaxron; 1:10,000), mouse monoclonal anti-SUMO-1 (#33-2400; 1:500) and rabbit polyclonal anti-SUMO-2/3 (#51-9100; 1:250) both from Zymed, rat monoclonal anti-HA (#1867423, Roche; 1:2,000 for Western blot and 1:250 for immunofluorescence), mouse monoclonal anti-G3bp (#611126, BD Biosciences; 1:1,000), mouse monoclonal anti-Myc (ab32, Abcam; 1:500), rabbit polyclonal anti-GST (ab9085 Abcam; 1:1,000), rabbit polyclonal anti-GFP (sc-8334, Santa-Cruz; 1:500), rabbit polyclonal anti-H3K9me3 (#07-442, Upstate; 1:500), mouse monoclonal anti-β actin (#A5441 Sigma; 1:20,000). For chromatin immunoprecipitations we used a rabbit polyclonal anti-HP1α antibody generated against the full length GST-HP1α protein (Agro-Bio).

Nuclear extracts. After incubation in hypotonic buffer A (20 mM Hepes-KOH pH 7.8, 5 mM potassium acetate, 0.5 mM MgCl 2 , 0.5 mM DTT) for 10 min at 4°C, we disrupted NIH3T3 cells by 25 strokes with a dounce homogenizer and separated nuclei from the soluble proteins by centrifugation at 1600 g. After incubation of nuclear pellets in buffer A containing 615 mM NaCl for 1.5 h at 4°C, followed by centrifugation at 14 000g for 20 min, we collected supernatant as the nuclear extract that we aliquoted and flash froze in liquid nitrogen. All buffers contained protease and phosphatase inhibitors (10 µg/ml pepstatin, 10 µg/ml leupeptin, 100 μM PMSF, 5 mM sodium fluoride, 10 mM β-glycerophosphate, plus or minus 20 mM N-ethylmaleimide [NEM; Sigma] when indicated).

Centromeric RNA pull down. The Maj9-2 and Min5-1 pCR4 plasmids contain 542-bp of the mouse major satellite DNA and 162-bp of minor satellite DNA, respectively (provided by T. Jenuwein) [START_REF] Lehnertz | Suv39h-mediated histone H3 lysine 9 methylation directs DNA methylation to major satellite repeats at pericentric heterochromatin[END_REF] . We subcloned a cDNA encoding a 234-bp repeat unit of the mouse major satellite DNA from pUC19-Sat15 (provided by A. Bird) into the pBS vector (Stratagene). We obtained biotinylated major (Maj1 from Sat15-pBS and Maj2 from Maj9-2 pCR4) and minor (Min from Min5-1 pCR4) RNAs by in vitro transcription with T7 or T3 RNA polymerases (Promega) in the presence of biotin RNA labelling mix (Roche), at 37°C for 2 h. After DNA digestion by RNase-free DNase I (Promega), we removed unincorporated rNTPs by a Sephadex G-50 quick spin column (Roche). For RNA pull down, we incubated 2 µg of biotinylated RNA with nuclear extracts in binding buffer (20 mM Hepes pH 7.6, 100 mM KCl, 2 mM EDTA, 0.01% Nonidet P-40, 1% gelatin) with 200 µg/ml tRNA, 4 mg/ml heparin, 80 U RNasin, plus or minus 20 mM NEM as indicated, for 30 min at room temperature. For each binding reaction we used 100 µl of streptavidin-coated magnetic beads (Dynabeads; Invitrogen) for 1 h at room temperature, on a rotating wheel. After 4 washes with binding buffer containing 20 µg/ml tRNA and 0.1% Tween-20, followed by one more wash with 20 mM Hepes pH 7.6, plus 50 mM KCl, we eluted bound proteins with SDS-PAGE loading buffer and ran samples on NuPAGE 4-12% Bis-Tris gels (Invitrogen) with MOPS running buffer (Invitrogen). We stained gels with Coomassie brilliant blue.

Immunoprecipitations and Western blotting. We lysed NIH3T3 cells 48 h post-transfection, with lysis buffer (50 mM Tris-HCl pH 7.5, 150 mM NaCl, 5 mM EDTA, 15 mM MgCl 2 , 1% Nonidet P-40, and 0.75% sodium deoxycholate) supplemented with protease and phosphatase inhibitors, and 20 mM NEM (Sigma). We incubated cell lysates corresponding to 4x10 6 cells with 40 µl of monoclonal anti-HA agarose-conjugated beads (Roche) for 2 h at 4°C. After washing the beads with lysis buffer, we eluted the immunocomplexes with SDS-PAGE loading buffer, and resolved proteins by 4-12% Bis-Tris NuPAGE gels (Invitrogen), and transferred to nitrocellulose membranes (Protran). For visualization of proteins after Western blots with the indicated antibodies we used the Super Signal detection kit (Pierce).

Northwestern blotting. We resolved recombinant full-length GST-HP1γ and GST-HP1α full-length and fragments thereof by SDS-PAGE and transferred them to nitrocellulose. We incubated the membranes with in vitro transcribed radioactively labelled RNAs in buffer containing 20 mM Hepes pH 7.6, 100 mM KCl, 2 mM EDTA, 0.01% Nonidet P-40, overnight at 23°C. After 3 washes with the same buffer, we visualized bound radioactively labelled RNAs by autoradiography.

Immunofluorescence microscopy. We processed cells for immunostaining as described [START_REF] Maison | Higher-order structure in pericentric heterochromatin involves a distinct pattern of histone modification and an RNA component[END_REF] . We used an epifluorescence photo-microscope (DM6000B, Leica) piloted with Metamorph software, an x63 (NA 1.32) objective lens and an HQ2 CoolSnap camera (Photometrics) for image acquisition. For all time course studies, we performed three independent experiments. For spot formation analysis, after image acquisition, we draw a scan line across the nucleus and measured the relative intensity of fluorescence across this line for signals corresponding to e-HP1α and Myc-SUV39H1 (ImageJ software). For Immuno-RNA FISH, we acquired 50 optical sections separated by 0.2 μm with an Imager.Z1 microscope (Zeiss) piloted with Metamorph software and made Z projections. We quantified the localization of forward major transcripts at the periphery of pericentric heterochromatin domains from 3D image series (z-step 0.2 μm) of major RNA FISH/DAPI staining acquired on a Delta Vision system (Applied Precision, 100x objective). For each nucleus, we manually scored the total number of RNA foci (f tot ) and the number of RNA foci at the periphery of DAPI dense pericentric domains (f per ) using ImageJ software and the Image 5D plugin to allow co-visualization in 3D of the RNA FISH and DAPI signals. We determined the volume of the nuclei (V nuc ) and the volume of the individual pericentric domains (V dom , DAPI dense) using the ImageJ software and the 3D Object Counter plugin. We calculated the volume of peripheral pericentric domain (V per ) as the difference between the volume corresponding to the pericentric domain with an increase of 20% of the radius of the domain (V dom20% , assuming a spherical form) and the volume of the domain (V per =V dom20% -V dom ). We obtained the concentration of RNA foci (foci/ μm 3 ) at the periphery from the ratio f per /V per and in the nucleus from the ratio f tot /(V nuc -V dom ). We removed the volume of the pericentric domains from total volume given that RNA foci are never found within domains.

RNA and DNA FISH. For RNA FISH, after extraction with 0.5% Triton X-100 in CSK buffer (10 mM Pipes pH7, 100 mM NaCl, 300 mM sucrose, 3 mM MgCl2, supplemented with 10 mM Vanadyl ribonucleoside complex (VRC)) for 5min on ice, we fixed cells in 3% paraformaldehyde in PBS for 12 min and stored them in 70% EtOH at -20°C overnight. Following dehydration in 80%, 95% and 100% EtOH, we carried out hybridization with 0.4 µM locked nucleic acid (LNA) fluorescent probes (Exiqon) in 50% formamide (Sigma), 2x SSC (Sigma), 10% dextran sulfate (Fluka), 10 mM VRC (NEB) and 2 mg/mL BSA (NEB) in a humid chamber for 35 min at 37°C. After 3 washes in 0.1x SSC for 5 min at 60°C, we stained DNA with DAPI staining and mounted the cells in Vectashield (Vector Laboratories).

For Immuno-RNA FISH, we performed RNA FISH as described above. After post-hybridization washes, we post-fixed cells in 3% paraformaldehyde in PBS for 12 min and processed them for immunostaining.

DNA FISH and Immuno-DNA FISH were performed as described 2 , except that the hybridization mix contained LNA fluorescent probes (0.1 µM) and we performed post-hybridization washes in 0.1X SSC (3 times for 5 min) at 60°C. The sequences of the LNA fluorescent probes are listed in Supplementary Table 2.

RT-PCR analysis. We performed RT-PCR analysis on HP1α-associated RNAs and on total RNA extracted from 3T3 cells with Trizol (Invitrogen). We digested genomic DNA by incubation with DNase 1 (Sigma). We synthesized first strand cDNA from 1 µg RNA in 20 µl buffer containing 1 µM forward (For) or reverse (Rev) specific primers for major or minor satellites, 0.5 mM dNTPs, 40 U/µl RNasin and 10 U/µl of SuperScript II reverse transcriptase (Qiagen). We then amplified the generated cDNA by PCR using 1/2000 and 1/250 dilutions of major and minor cDNA respectively, and a PCR Master Kit (Roche) supplemented with 0.5 µM specific primers during 45 cycles. Primer sequences are listed in Supplementary Table 2.

Chromatin Immunoprecipitation (ChIP).

We extracted NIH3T3 cells with Triton X-100 to remove soluble proteins as previously described [START_REF] Martini | Recruitment of phosphorylated chromatin assembly factor 1 to chromatin after UV irradiation of human cells[END_REF] and cross-linked them with 1.5% formaldehyde in PBS for 20 min at room temperature. We then added 125 mM glycine for 20 min to quench any residual formaldehyde. After one wash with PBS, we collected the cells by scraping and resuspended them in ChIP buffer (20 mM Tris-HCl at pH 7.5, 200 mM NaCl, 0.2% Nonidet P-40, 1% gelatin and 80 U RNasin). We then sonicated the cells seven times for 30 seconds on high intensity (Bioruptor sonicator, CosmoBio Inc.) and centrifuged at 10 000g for 5 min. We incubated approximately 200-300 µg of supernatant containing the soluble chromatin with 20 µl of sera against HP1α raised in the laboratory for 3 h at 4°C. We used preimmune sera as negative control. Then, we added 100µl of Protein-A sepharose slurry (50% W/V, Amersham Biosciences) and incubated for 3 h at 4°C on a rotating wheel. We recovered the immunoprecipitated chromatin by centrifugation, washed it five times with 1 ml of ChIP buffer and resuspended it in 10 mM Tris-HCl at pH 7.5, 1 mM EDTA, 0.2% SDS. We reversed the crosslink by incubation at 65°C overnight. We then extracted the HP1α-associated RNAs with Trizol (Invitrogen) and we performed RT-PCR analysis.

In vitro sumoylation assays. We produced recombinant proteins in E. coli by expressing constructs corresponding to the GST-HP1α full-length protein and fragments thereof and GST-HP1α-Ubc9. We utilized the recombinant proteins in in vitro sumoylation reactions, using the SUMOlink kits (Active Motif), using manufacturer instructions. We validated sumoylation of HP1α and HP1α-Ubc9 by Western blot with anti-GST antibodies. For analysis of the sumoylated GST-HP1α hinge fragment by mass spectrometry, we used a total of 5 µg of GST-HP1α hinge and 10 µg of SUMO-1 protein. We ran 90% of the reaction mixture on a 4-12% Bis-Tris NuPAGE gel (Invitrogen) and stained the gel overnight with LabSafe GEL Blue stain (Biosciences) for later mass spectrometry analysis. We used the remaining 10% of the sumoylation mixture for Western blotting with rabbit anti-GST and rabbit anti-SUMO-1 (Active Motif; 1:4,000 dilution) antibodies.

Mass Spectrometry. We reduced, alkylated and trypsin digested slices (1 mm wide) cut out from Coomassie blue-stained gels as previously described [START_REF] Fevrier | Cells release prions in association with exosomes[END_REF] . We dried extracted peptides, resolubilized them in solvent A (95/5 water/acetonitrile, 0.1% formic acid) prior to liquid chromatography tandem mass spectrometry (LC-MS/MS) analysis. We concentrated and separated them on a LC-Packings system (Dionex S.A.) coupled to the nano-electrospray II ionization interface of a QSTAR Pulsar i (Applied Biosystems/MDS Sciex). HPLC mobile phases contained solvent A and solvent B [20/80: water/acetonitrile, 0.085% formic acid]. We eluted bound peptides with a gradient of 5-50% of solvent B.

We used information-dependent acquisition (IDA) to acquire MS/MS data, with experiments designed such that the two most abundant peptides were subject to collision-induced dissociation (CID). We analyzed twice the data from the IDA experiments by using MASCOT software (Matrix Science, London) on an internal server, first without taxonomic restriction to reveal the presence of proteins of interest and mammalian contaminants, then again the "Mus musculus" (mouse) database of the National Center for Biotechnology Information nr (National Library of Medicine, Bethesda, 2005 05 02, 2 452 561 and 41 362 protein entries). We converted the RAW files to the Mascot Generic Format (MGF) and submitted them to the Mascot search engine (version 1.0). We used the following parameters in the database search: Full trypsin enzyme specificity; Missed cleavages allowed = 1, Peptide mass tolerance = 0.8 Da; Fragment ion tolerance = 1 Da; Monoisotopic molecular weight for both peptide and fragment ion masses, b/y ion search, and fixed carbamidomethyl cysteine modification. We manually validated all data using myProMS [START_REF] Poullet | a web server for management and validation of mass spectrometry-based proteomic data[END_REF] .

For SUMO-1 LC-MS/MS experiments, we used two different MS platforms in parallel. We achieved peptide concentration and separation using an actively split capillary HPLC system (Ultimate 3000, Dionex, Germering, Germany) connected to each MS platform. The first platform was a quadrupole timeof-flight (Q-TOF) mass spectrometer (QSTAR Elite, Applied Biosystems/MDS Sciex). We acquired a TOF-MS survey scan for 1 sec over a mass range of 800-1200 m/z. We used an IDA method to acquire product ion scans on the three most intense 3+ ions per cycle over a mass range of 65-2000 m/z, excluding previously gated ions for 60 sec. We used a Smart setting of 2.0. The second platform was an LTQ-Orbitrap XL mass spectrometer (Thermo Fisher Scientific, Bremen, Germany) equipped with a nanospray source using a Pico-Tip (10 µm i.d., New Objectives). We set the spray voltage to 2.2 kV and the temperature of the heated capillary to 200°C. The mass spectrometer was operated in data-dependent mode to automatically acquire MS and MS/MS spectra. We acquired full scan survey spectra (m/z 615-1200) in the Orbitrap with a resolution of 100,000 at m/z 400 after accumulation of 1,000,000 charges. We sequentially isolated the five most intense ions and fragmented them in the linear ion trap by collisioninduced dissociation after accumulation of 30,000 ions (normalized collision energy 35%). Maximum inject times were 500 msec for full scans and 200 msec for MS/MS scans. Dynamic exclusion was enabled with exclusion duration of 120 sec. We calculated and used the monoisotopic m/z values for SUMO-1-GST-HP1α hinge branched precursor peptides as described [START_REF] Matic | In vivo identification of human small ubiquitin-like modifier polymerization sites by high accuracy mass spectrometry and an in vitro to in vivo strategy[END_REF] to search for the corresponding ions (assignment was confirmed by manually interpreting all MS/MS spectra). We manually validated all reported MS/MS spectra. We considered only branched peptides having an extensive coverage of b and/or y ions. It was assumed that modified (sumoylated) lysines cannot be cleaved by trypsin, and one trypsin missed cleavage was allowed.

Figure 1 .

 1 Figure 1. Strand-specific localization of centromeric RNAs. a. Transcription from both strands of major and minor satellite repeats. Top: schematic representation of mouse major and minor satellite repeats and strand specific primers (forward [For], reverse [Rev]) used for analysis by RT-PCR. Bottom: corresponding results for RNAs isolated from NIH3T3 mouse cells. We show PCR reactions in the presence (+RT) or absence (-RT) of reverse transcriptase, or primers, as controls. b. Nuclear localization of centromeric RNA compared to major and minor satellite DNA in NIH3T3 cells. Left: DNA FISH. Scheme of an acrocentric mouse chromosome with telomeres (black), major (red) and minor (green) satellites. Major (red) and minor (green) satellites are shown along with a merged image of major and minor satellites and DAPI stained DNA. Middle: RNA FISH. We localized major (forward in green, reverse in red) and minor (forward in red, reverse in green) RNAs with strand-specific LNA probes and show a merged image of DAPI and centromeric RNA staining. Insets show magnifications of chromocenters. Right: Immuno-RNA FISH. Forward major RNAs (green) and anti-HP1α antibodies (red) staining are shown along with a merged image of DAPI and major RNA staining. Scale bar, 10 μm. c. HP1α accumulation at major satellite DNA domains. Immuno-DNA FISH with anti-HP1α antibodies (green) and major or minor satellite DNA (red) probes. Insets as in b. Scale bar, 10 μm. d. RNAs associated with HP1α. ChIP experiments using pre-immune serum (Ctr) or anti-HP1α antibodies (HP1α) analysed by strand-specific RT-PCR as indicated. We show PCR reactions with (+RT) or without (-RT) reverse transcriptase, and without cDNA (mock), as controls. The input corresponds to the soluble chromatin prior to ChIP.

Figure 2 .

 2 Figure 2. SUMO-1-modified HP1α interacts specifically with forward major RNAs.

Figure 3 .

 3 Figure 3. Sumoylation of HP1α occurs at its hinge domain in vitro. a. Experimental scheme. b. HP1α sumoylation in vitro. Left: Schematic representation of full-length HP1α and fragments thereof. Right: Western blot analysis of the sumoylation reaction mixture with anti-GST antibodies revealed the positions of SUMO-1-modified full-length HP1α (S-HP1α) or fragment domains (S-CD+H and S-H) marked by an asterisk (*). c. HP1α-Ubc9 sumoylation in vitro. Western blot analysis of the sumoylation reaction mixture with anti-GST antibodies revealed the positions of SUMO-1-modified HP1α-Ubc9 (S-HP1α-Ubc9) and unmodified HP1α-Ubc9. Arrow indicates a degradation product of GST-HP1α-Ubc9. d. Mass spectrometry analysis of the in vitro SUMO-1-modified HP1α hinge fragment. Shown are the MS (right) and MS/MS (left) fragmentation spectra of the tryptic peptide corresponding to residues 79-97 of SUMO-1 (top right, black) and 83-89 of HP1α (EKSEGNK; red) where K84 is sumoylated. The precursor ion mass was fragmented and acquired in Qstar (m/z 981.8 [3+]; left) and Orbitrap (m/z 981.77563, mass deviation 2 ppm; right, arrow) mass spectrometers. The majority of the fragment ions could be assigned to the y or b ion series, as annotated in the spectra and peptide sequence (top right). e. Localization of e-HP1α and e-HP1α-Ubc9 in Triton extracted NIH3T3 cells. Left: Experimental scheme. Right: Immunofluorescence using anti-HA (red) and anti-HP1α (green) antibodies. Scale bar, 10 μm.

Figure 4 .

 4 Figure 4. Sumoylation of HP1α promotes its targeting and accumulation at pericentric heterochromatin.

Figure 5 .

 5 Figure 5. The hinge domain is required for de novo localization of HP1α at pericentric heterochromatin. a. Experimental scheme. b. Localization of wild type (WT) or mutant (ΔH) e-HP1α and e-HP1α-Ubc9 in NIH3T3 cells by immunofluorescence using anti-HA antibodies (red) 24 h after transfection. Scale bar, 10 μm. c. de novo localization of wild type (WT) or mutant (ΔH) e-HP1α and e-HP1α-Ubc9 in Suv39h dn cells co-transfected with Myc-SUV39H1 by immunofluorescence using anti-HA (red) and anti-Myc (green) antibodies 6 h after transfection. For each condition, we calculated the percentage of cells with HA signal enriched at pericentric domains (positive cells). Scale bar, 10 μm. d. Comparison of protein expression corresponding to experiment in c by Western blot using anti-HA and anti-β actin antibodies. Arrows indicate degradation products of e-HP1α-Ubc9 and e-HP1αΔH-Ubc9 .

Figure 6 .

 6 Figure 6. Model for a de novo HP1α targeting to pericentric heterochromatin.

ACKNOWLEDGMENTS

We thank A. Bird, D. Shapiro, R. Hay, T. Jenuwein, R. Losson and J. Seeler for constructs and reagents. We thank W. Faigle for Mass Spectrometry support, G. Cappello for helpful discussions, A. Cook for critical reading and P. Le Baccon at the Curie Imaging Platform. GA's Laboratory is funded by la Ligue Nationale contre le Cancer (Equipe labellisée la Ligue), Curie PIC Programs, the European Network of Excellence Epigenome (LSHG-CT-2004-503433), ACI-2007-Cancéropôle IdF "Breast cancer and Epigenetics", ANR "ECenS" ANR-09-BLAN-0257-01, INCa "GepiG", ERC Advanced Grant 2009-AdG-20090506 and DL's Laboratory by le Cancéropôle Ile-de-France and l'INCA.

COMPETING FINANCIAL INTERESTS

The authors declare no competing financial interests.

SUPPLEMENTARY DATA