Jorge San

Jean-François Scheid
email: jean-francois.scheid@iecn.u-nancy.fr

Loredana Smaranda
email: smaranda@dim.uchile.cl

Jorge San Martín

Convergence of a discretization scheme

Preliminaries

In this chapter, we present our last results concerning the convergence of a numerical method to discretize the equations modelling the motion of a rigid solid immersed into a viscous incompressible uid using the characteristics technique.

Before stating these results, let us introduce the continuous model of our problem. We assume that the uid-rigid system occupies a bounded and regular domain O ⊂ R 2 and that the solid is a ball of radius 1 whose center, at time t, is denoted by ζ(t). The uid lls the part Ω(t) = O \ B(ζ(t)) at time t. The velocity eld u(x, t) and the pressure p(x, t) of the uid, the center of mass ζ(t) and the angular velocity ω(t) of the ball satisfy the following Navier-Stokes system coupled with Newton's laws:

ρ f ∂u ∂t + (u • ∇)u -µ∆u + ∇p = ρ f f , x ∈ Ω(t), t ∈ [0, T ],
(1.1) div u = 0, x ∈ Ω(t), t ∈ [0, T ],

(1.2)

u = 0, x ∈ ∂O, t ∈ [0, T ], (1.3)
u = ζ (t) + ω(t)(x -ζ(t)) ⊥ , x ∈ ∂B(ζ(t)), t ∈ [0, T ], (1.4) mζ (t) = - ∂B(ζ(t)) σn dΓ + ρ s B(ζ(t))
f (x, t)dx, t ∈ [0, T ],

(1.5)

Jω (t) = - Z ∂B(ζ(t)) (x-ζ(t)) ⊥ •σn dΓ +ρs Z B(ζ(t)) (x-ζ(t)) ⊥ •f (x, t)dx, t ∈ [0, T ]. (1.6)
In the above system, σ = -p Id + 2µD(u) denotes the Cauchy stress tensor with D(u) = (∇u+∇u T )/2 and ∇u T means the transpose of ∇u. The positive constant µ is the dynamic viscosity of the uid and the constants m and J are the mass and the moment of inertia of the rigid body. Throughout this chapter, we will use the notation

x ⊥ = -x 2 x 1 for all x = x 1 x 2 ∈ R 2 . System (1.1)(1.6) is completed with initial conditions: u(x, 0) = u 0 (x), x ∈ Ω(0), (1.7) ζ(0) = ζ 0 ∈ R 2 , ζ (0) = ζ 1 ∈ R 2 , ω(0) = ω 0 ∈ R. (1.8)
One important hypothesis of our problem is that the density ρ f of the uid and the density ρ s of the solid are constant, but dierent, that is

ρ f = ρ s .
The uid-structure interaction problem (1.1)(1.8) is characterized by the strong coupling between the nonlinear equations of the uid and those of the structure, as well as the fact that the equations of the uid are written in a variable domain in time, which depends on the displacement of the structure. Let us now recall some references on the topic. From the numerical point of view, various authors have proposed a number of dierent techniques to solve equations on moving domains, such as the level set method ([OsSe88]), the ctitious domain method [GPHJP00, GPHJP01]), the immersed boundary method ( [START_REF] Peskin | The immersed boundary method[END_REF]) and the Arbitrary Lagrangian Eulerian (ALE) method ([MoGl97], [START_REF] Maury | Direct simulations of 2D uid-particle ows in biperiodic domains[END_REF], [START_REF] Formaggia | A stability analysis for the arbitrary Lagrangian Eulerian formulation with nite elements[END_REF], [START_REF] Gastaldi | A priori error estimates for the arbitrary Lagrangian Eulerian formulation with nite elements[END_REF], [START_REF] Legendre | Convergence of a Lagrange-Galerkin method for a uid-rigid body system in ALE formulation[END_REF], [START_REF] San Martín | Convergence of a nite element/ALE method for the Stokes equations in a domain depending on time[END_REF]). About numerical convergence for Navier-Stokes equations, when the domain is independent of time, we just recall a few references: [START_REF] Pironneau | On the transport-diusion algorithm and its applications to the Navier-Stokes equations[END_REF], [START_REF] Süli | Convergence and nonlinear stability of the Lagrange-Galerkin method for the Navier-Stokes equations[END_REF] and [START_REF] Achdou | Convergence analysis of a nite element projection/Lagrange-Galerkin method for the incompressible Navier-Stokes equations[END_REF]. Concerning the convergence of numerical methods based on nite elements with xed mesh for a two dimensional uid-rigid body problem we recall the works [START_REF] San Martín | Convergence of the Lagrange-Galerkin method for a uid-rigid system[END_REF][START_REF] San Martín | Convergence of the Lagrange-Galerkin method for the equations modelling the motion of a uid-rigid system[END_REF] where the densities of the uid and the solid are equal (i.e. ρ f = ρ s ).

The main novelty presented in this chapter is the convergence of two numerical schemes for the generalized case where the densities of the uid and the solid are not equal (i.e. ρ f = ρ s ). The convergence results are given in Theorem 1 and Theorem 2 below, and they concern with the semi-discretization in time variable, respectively the fully-discretization in time and space variables. The complete proofs of these results could be found in our recent papers [START_REF] San Martín | A time discretization scheme of a characteristics method for a uid-rigid system with discontinuous density[END_REF][START_REF] San Martín | A modied Lagrange-Galerkin method for a uid-rigid system with discontinuous density[END_REF].

Let us now introduce some notation and the functional spaces that we work on. Throughout this chapter, we shall use the classical Sobolev spaces H s (O), H s 0 (O), H -s (O), s 0 and the space of Lipschitz continuous functions C 0,1 (O) on the closure of O. We also dene

L 2 0 (O) = f ∈ L 2 (O) O f dx = 0 .
The usual inner product in L 2 (O) 2 will be denoted by

(u, v) = O u • v dx ∀u, v ∈ L 2 (O) 2 .
(1.9)

If A is a matrix, we denote by A T its transpose. For any 2 × 2 matrices A, B ∈ M 2×2 , we denote by A : B their inner product A : B = Trace (A T B), and by |A| the corresponding norm. For convenience, we use the same notation as in (1.9) for the inner product in L 2 (O, M 2×2 ), that is

(A, B) = O A : B dx ∀A, B ∈ L 2 (O, M 2×2 ).
For ζ ∈ O, we introduce the space of rigid functions in

B(ζ) = {x ∈ R 2 : |x -ζ| ≤ 1}, K(ζ) = u ∈ H 1 0 (O) 2 | D(u) = 0 in B(ζ) , (1.10)
the space of rigid functions in B(ζ) with divergence free in the whole domain

O, K(ζ) = u ∈ K(ζ) | div u = 0 in O (1.11)
and the space of the pressure

M (ζ) = p ∈ L 2 0 (O) | p = 0 in B(ζ) .
(1.12)

Let us consider in the reminder of the chapter that any velocity eld in K(ζ) will be extended by zero outside of O.

According to Lemma 1.1 of [Te83, pp.18], for any u ∈ K(ζ), there exist

l u ∈ R 2 and ω u ∈ R such that u(y) = l u + ω u (y -ζ) ⊥ ∀y ∈ B(ζ).
(1.13)

In addition, we dene the density ρ by the following piecewise constant function

ρ(x) = ρ s if x ∈ B(ζ), ρ f if x ∈ O \ B(ζ).
We notice that, by using the above denitions, for any u, v ∈ K(ζ) we have

(ρu, v) = O\B(ζ) ρ f u • v dx + M l u • l v + Jω u ω v .
(1.14)

The spaces (1.10)(1.11) are specic to our problem. In fact, if the solution u of (1.1)(1.8) is extended by

u(x, t) = ζ (t) + ω(t)(x -ζ(t)) ⊥ ∀x ∈ B(ζ(t)),
then, we easily see that u(t) ∈ K(ζ(t)). In the reminder of this chapter, the solution u of (1.1)(1.8) will be extended as above.

An important ingredient of the numerical method we use is given by the characteristic functions whose level lines are the integral curves of the velocity eld. More precisely (see, for instance, [START_REF] Pironneau | On the transport-diusion algorithm and its applications to the Navier-Stokes equations[END_REF], [START_REF] Süli | Convergence and nonlinear stability of the Lagrange-Galerkin method for the Navier-Stokes equations[END_REF]) the characteristic

function ψ : [0, T ] 2 × O → O is dened as the solution of the initial value problem    d dt ψ(t; s, x) = u( ψ(t; s, x), t) ∀t ∈ [0, T ],
ψ(s; s, x) = x.

(1.15)

It is well-known that the material derivative D t u = ∂u/∂t + (u • ∇)u of u at instant t 0 satises:

D t u(x, t 0 ) = d dt u( ψ(t; t 0 , x), t) |t=t 0 . ( 1
ζ ∈ H 2 (0, T ) 2 , ω ∈ H 1 (0, T ), u ∈ C([0, T ]; K(ζ(t))),
then we have that det J e ψ = 1, (1.17

)
where we have denoted by J e ψ = ∂ e ψi ∂yj i,j the jacobian matrix of the transformation y → ψ(y).

Let us now state the weak formulation of the system (1.1)(1.8) that we use to discretize in time the problem.

Proposition 1. Assume that u ∈ L 2 0, T ; H 2 (Ω(t)) 2 ∩ H 1 0, T ; L 2 (Ω(t)) 2 ∩ C [0, T ]; H 1 (Ω(t)) 2 , p ∈ L 2 0, T ; H 1 (Ω(t)) , ζ ∈ H 2 (0, T ) 2 , ω ∈ H 1 (0, T )
and that u is extended by

u(x, t) = ζ (t) + ω(t)(x -ζ(t)) ⊥ ∀x ∈ B(ζ(t)).
Then (u, p, ζ, ω) is the solution of (1.1)(1.8) if and only if for all

t ∈ [0, T ], u(•, t) ∈ K(ζ(t)), p(•, t) ∈ M (ζ(t)) and (u, p) satises ρ d dt u • ψ (t), ϕ + a(u, ϕ) + b(ϕ, p) = (ρ f (t), ϕ) ∀ϕ ∈ K(ζ(t)), (1.18) b(u, q) = 0 ∀q ∈ M (ζ(t)), (1.19)
where the bilinear forms a(•, •) and b(•, •) are dened as follows:

a(u, v) = 2µ O D(u) : D(v) dx ∀u, v ∈ H 1 (O) 2 (1.20) and b(u, p) = - O div (u)p dx ∀u ∈ H 1 (O) 2 , ∀p ∈ L 2 0 (O). (1.21)
For the proof of Proposition 1 we refer the reader to [QuVa94, Ch.12].

In the remainder of this chapter, we suppose that f and u 0 satisfy

f ∈ C([0, T ]; H 1 (O) 2 ), u 0 ∈ H 2 (Ω) 2 , div (u 0 ) = 0 in Ω, u 0 = 0 on ∂O, u 0 (y) = ζ 1 + ω 0 (y -ζ 0 ) ⊥ on ∂B(ζ 0 ), (1.22)
where

ζ 0 , ζ 1 ∈ R 2 , ω 0 ∈ R and Ω = O \ B(ζ 0 ).
Let us also assume that the corresponding solution (u, p, ζ, ω) of problem (1.1)(1.8) satises We approximate the position of the rigid ball at instant t k+1 by ζ k+1 which is dened by the relation

     u ∈ C([0, T ]; H 2 (Ω(t)) 2 ) ∩ H 1 (0, T ; L 2 (Ω(t)) 2 ), D 2 t u ∈ L 2 (0, T ; L 2 (Ω(t)) 2 ), u ∈ C([0, T ]; C 0,1 (O) 2 ) p ∈ C([0, T ]; H 1 (Ω(t))), ζ ∈ H 3 (0, T ) 2 , ω ∈ H 2 (0, T ) (1.
ζ k+1 = ζ k + u k (ζ k )∆t.
(1.27)

We then dene the characteristic function ψ associated with the semidiscretized velocity eld as the solution of

   d dt ψ(t; t k+1 , x) = u k (ψ(t; t k+1 , x)) -u k (ζ k ) ∀t ∈ [t k , t k+1 ], ψ(t k+1 ; t k+1 , x) = x -u k (ζ k )∆t (1.28)
and we denote

X k (x) = ψ(t k ; t k+1 , x) ∀x ∈ O.
(1.29)

In equation (1.28), the velocity eld u k is extended by zero outside of the domain O.

We next dene u k+1 ∈ K(ζ k+1 ) as the solution of the following Stokes type system

ρ k+1 u k+1 -u k • X k ∆t , ϕ + a u k+1 , ϕ = (ρ k+1 f k+1 , ϕ) ∀ϕ ∈ K(ζ k+1 ), (1.30)
where f k+1 = f (t k+1 ) and ρ k+1 is dened by

ρ k+1 (x) = ρ s if x ∈ B(ζ k+1 ), ρ f if x ∈ O \ B(ζ k+1 ).
The above equation can be rewritten by using a mixed formulation. It is clear that (1.30) is equivalent to the following system

ρ k+1 u k+1 -u k • X k ∆t , ϕ + a(u k+1 , ϕ) + b(ϕ, p k+1 ) = (ρ k+1 f k+1 , ϕ) ∀ϕ ∈ K(ζ k+1 ), (1.31) b(u k+1 , q) = 0 ∀q ∈ M (ζ k+1 ), (1.32) of unknowns (u k+1 , p k+1 ) ∈ K(ζ k+1 ) × M (ζ k+1 ).
It is well-known (see, for example, [GiRa79, Corollary I.4.1., pp.61]) that the mixed formulation (1.31)(1.32) is a well-posed problem, provided that the spaces K(ζ), M (ζ) and the bilinear form b satisfy an inf-sup condition. The fact that this inf-sup condition is satised in our case follows from the result below (for the proof see, for instance [GiRa79, pp.81]):

Lemma 1. Suppose that ζ ∈ O is such that d(ζ, ∂O) = 1 + η, with η > 0.
Then there exists a constant β > 0, depending only on η and on O, such that for all q ∈ M (ζ) there exists

u ∈ K(ζ) with O div (u) q dx ≥ β u H 1 (O) 2 q L 2 (O) .
(1.33)

In addition, we have that u k+1 ∈ C 0 (O) 2 (for more details, see [SMSS10b]).

Let us now state the rst main result concerning the convergence of the semi-discrete scheme (1.31)(1.32) (for the proof of the next theorem, we refer the reader to [START_REF] San Martín | A modied Lagrange-Galerkin method for a uid-rigid system with discontinuous density[END_REF]):

Theorem 1. Suppose that O is an open smooth bounded domain in R 2 , f and u 0 satisfy (1.22) and (u, p, ζ, ω) is a solution of (1.1)(1.8) satisfying (1.23)(1.24).
Then there exist two positive constants C and τ * not depending on ∆t such that for all 0 < ∆t τ * the solution

(u k , p k , ζ k ) of the semi-discretization problem (1.31)(1.32) satises sup 1 k N |ζ(t k ) -ζ k | + u(t k ) -u k L 2 (O) 2
C∆t.

(1.34)

The key ingredients used in the proof of the above result are some properties on the characteristic functions associated with the semi-discretized velocity eld which are given in the following lemma (more details and the complete proof of this result could be found in [START_REF] San Martín | A modied Lagrange-Galerkin method for a uid-rigid system with discontinuous density[END_REF]): Lemma 2. For any k ∈ {0, . . . , N }, the characteristic function ψ dened in (1.28)(1.29) satises the following properties:

i) X k B(ζ k+1 ) = B(ζ k );
ii) If we extend by ρ f the density eld ρ k outside of O, we have

ρ k+1 = ρ k • X k ; iii) For any f ∈ L 2 (R 2 ) such that f = 0 in R 2 \ O, we have f • ψ(t; t k+1 , •) L 2 (O) ≤ f L 2 (O) ∀t ∈ [t k , t k+1 ].
(1.35)

Fully discretization in time and space variables

In order to discretize the problem (1.31)(1.32) with respect to the space variable, let us introduce two families of nite element spaces which approximate the spaces K(ζ) and M (ζ) dened in (1.10) and (1.12). To this end, we consider the discretization parameter 0 < h < 1.

Let T h be a quasi-uniform triangulation of the domain O. We denote by W h the P 1 -bubble nite elements space associated with T h for the velocity eld in the Stokes problem and by E h the P 1 -nite elements space for the pressure. Then, we dene the following nite elements spaces for a conform approximation of the uid-rigid system:

K h (ζ) = W h ∩ K(ζ) ∀ζ ∈ O M h (ζ) = E h ∩ M (ζ) ∀ζ ∈ O.
In order to dene the approximate characteristics, let us denote by F h the P 2 -nite element space associated with the triangulation T h and we introduce the space:

R h (ζ) = {∇ ⊥ ϕ h : ϕ h ∈ F h , ϕ h = 0 on ∂O} ∩ K(ζ) ∀ζ ∈ O,
where we have denoted by

∇ ⊥ ϕ h =    - ∂ϕ h ∂y ∂ϕ h ∂x    .
We denote P(ζ) the orthogonal projection from L 2 (O)

2 onto R h (ζ), i.e. if u ∈ L 2 (O) 2 then P(ζ)u ∈ R h (ζ) such that (u -P(ζ)u, r h ) = 0 for all r h ∈ R h (ζ).
Let N be a positive integer. We denote ∆t = T /N and t k = k∆t for all k ∈ {0, . . . , N }. Assume that the approximate solution (u k h , p k h , ζ k h ) of (1.1) (1.8) at t = t k is known. We describe below the numerical scheme allowing to determinate the approximate solution (u k+1 h , p k+1 h ,

ζ k+1 h ) at t = t k+1 . First, we compute ζ k+1 h ∈ R 2 by ζ k+1 h = ζ k h + u k h (ζ k h )∆t.
(1.36)

We consider the approximated characteristic function ψ k h dened as the solution of 8 > < > :

d dt ψ k h (t; t k+1 , x) = P(ζ k h )u k h (ψ k h (t; t k+1 , x)) -P(ζ k h )u k h (ζ k h ) ∀t ∈ [t k , t k+1 ], ψ k h (t k+1 ; t k+1 , x) = x -u k h (ζ k h )∆t (1.37)
and we dene

X k h (x) = ψ k h (t k ; t k+1 , x) ∀x ∈ O. (1.38)
We observe that since div

P(ζ k h )u k h (ψ k h (t; t k+1 , •)) -P(ζ k h )u k h (ζ k h ) = 0 and ∇(x -u k h (ζ k h )∆t) = Id, we get det J ψ k h = 1. (1.39)
Let us split the mesh into the union of 4 dierent types of triangle's subsets. We rst introduce A h as the union of all triangles intersecting the ball

B(ζ k h ), i.e. A h = T ∈T h • T ∩ • B(ζ k h ) =∅ T.
We also denote by Q h the union of all triangles such that all their vertices are contained in A h . The triangles of T h are then splitted into the 4 following categories:

• F 1 is the subset of T h formed by all triangles T ∈ T h such that T ⊂ B(ζ k h ). • F 2 is the subset formed by all triangles T ∈ T h \ F 1 such that T ⊂ Q h . • F 3 is the subset formed by all triangles T ∈ T h such that T ∩ Q h = ∅ and T ⊂ Q h . • F 4 = T h \ (F 1 ∪ F 2 ∪ F 3 ).
We introduce two approximated density functions ρ k h and ρ k h as follows:

ρ k h (x) = ρ s if x ∈ B(ζ k h ), ρ f if x ∈ O \ B(ζ k h ) (1.40) and ρ k h (x) = ρ s if x ∈ Q h , ρ f if x ∈ F 4 . (1.41)
With these notations, we consider the following mixed variational fully discrete formulation: Find

(u k+1 h , p k+1 h ) ∈ K h (ζ k+1 h ) × M h (ζ k+1 h ) such that ρ k+1 h u k+1 h -u k h • X k h ∆t , ϕ + a(u k+1 h , ϕ) + b(ϕ, p k+1 h ) = (ρ k+1 h f k+1 h , ϕ) ∀ϕ ∈ K h (ζ k+1 h ), (1.42) b(u k+1 h , q) = 0 ∀q ∈ M h (ζ k+1 h ), (1.43)
where

f k+1 h is the L 2 (O) 2 -projection of f k+1 = f (t k+1 ) on (E h ) 2 .
Let us now state the second result of this chapter concerning the convergence of the fully-discrete scheme (1.42)(1.43) (for the proof of this result, we refer the reader to [START_REF] San Martín | A modied Lagrange-Galerkin method for a uid-rigid system with discontinuous density[END_REF]):

Theorem 2. Let O be a convex domain with a polygonal boundary. Suppose that f and u 0 satisfy the conditions (1.22) and that (u, p, ζ, ω) is a solution of (1.1)(1.8) satisfying the regularity properties (1.23) and such that (1.24) holds. Let C 0 > 0 be a xed constant.

Then there exist two positive constants C and τ * independent of h and ∆t such that for all 0 < ∆t ≤ τ * and for all h ≤ C 0 ∆t 2 we have

sup 1≤k≤N |ζ(t k ) -ζ k h | + u(t k ) -u k h L 2 (O) 2 ≤ C∆t.
The key ingredients in the proof of the previous convergence result are the properties on the characteristic functions associated with the fully-discretized velocity eld given in the following lemma (the proof of this result is analogous to the proof of Lemma 2 and could be found in [START_REF] San Martín | A modied Lagrange-Galerkin method for a uid-rigid system with discontinuous density[END_REF]): Lemma 3. For any k ∈ {0, . . . , N } and h ∈ (0, 1), the characteristic function ψ iii) For any f ∈ L 2 (R 2 ) such that f = 0 in R 2 \ O, we have

f • ψ k h (t; t k+1 , •) L 2 (O) 2 ≤ f L 2 (O) 2 ∀t ∈ [t k , t k+1 ].
(1.45)

  23) and dist(B(ζ(t)), ∂O) > 0 ∀t ∈ [0, T ]. (1.24) Remark 2. The hypotheses (1.23) and (1.24) imply the existence of η > 0 such that dist(B(ζ(t)), ∂O) > 3η ∀t ∈ [0, T ]. (1.25) 1.2 Semi-discretization in time variable By using the weak formulation (1.18)(1.19), let us derive a semi-discrete version of our system. For N ∈ N * we denote ∆t = T /N and t k = k∆t for k = 0, . . . , N . Denote by (u k , ζ k ) ∈ K(ζ k ) ∩ C 0 (O) 2 × O the approximation of the solution of (1.1)(1.8) at the time t = t k . In the sequel, we shall use the notation X(x) = ψ(t k ; t k+1 , x) ∀x ∈ O. (1.26)

kh

  dened in (1.37)(1.38) satises the following properties:i) X k h B(ζ k+1 h ) = B(ζ k h );ii) If we extend by ρ f the density eld ρ k h outside of O, we have

Acknowledgements

J. San Martín was partially supported by Grant Fondecyt 1090239 and BASAL-CMM Project. J.-F. Scheid gratefully acknowledges the Program ECOS-CONICYT (Scientic cooperation project between France and Chile) through grant C07-E05. L. Smaranda was partially supported by Grant RP-2, no. 6/01.07.2009 of CNCSIS-UEFISCSU.


Asier Sáez-Cirión
email: asier.saez-cirion@pasteur.fr

Saez-

Ex vivo T cell-based HIV suppression assay to evaluate HIV-specific CD8+ T cell responses

To advance T cell-based HIV vaccine development it is necessary to evaluate the immune correlates of a protective CD8+ T cell response. We have developed an assay that assesses the capacity ex vivo of HIV-specific CD8+ T-cells to suppress HIV-1 infection of autologous CD4+ T-cells. This assay directly reflects the ultimate effector function of CD8+ T cells, the elimination of infected cells, and accurately differentiates the effective CD8+ T-cell response in spontaneous HIV controllers from ineffective responses in other patients. Here we describe all the steps from cell purification to assessment of viral replication by HIV-p24 ELISA and analysis, along with conditions for cell culturing; and how to choose the viral infectious dose giving the most reliable results. We also depict the conditions of a rapid assay based on flow cytometry analysis of intracellular HIV-Gag products. These procedures take 14 to 17 days when using the p24 ELISA assay or 6 days with the intracellular Gag assay.

INTRODUCTION

Since the identification of HIV-1 as the causative agent of the AIDS pandemic, evidence has been accumulating to support the notion that CD8+ T cells play a central role in restraining HIV/SIV infection in vivo [START_REF] Borrow | Virus-specific CD8+ cytotoxic T-lymphocyte activity associated with control of viremia in primary human immunodeficiency virus type 1 infection[END_REF][START_REF] Jin | Dramatic rise in plasma viremia after CD8(+) T cell depletion in simian immunodeficiency virus-infected macaques[END_REF][START_REF] Kiepiela | CD8+ T-cell responses to different HIV proteins have discordant associations with viral load[END_REF][START_REF] Martinez-Picado | Fitness cost of escape mutations in p24 Gag in association with control of human immunodeficiency virus type 1[END_REF] . These observations have been reinforced by in vitro assays showing the capacity of CD8+ T cells to inhibit HIV-1 infection of CD4+ T cells [START_REF] Mackewicz | CD8+ cell anti-HIV activity correlates with the clinical state of the infected individual[END_REF][START_REF] Tsubota | A cytotoxic T lymphocyte inhibits acquired immunodeficiency syndrome virus replication in peripheral blood lymphocytes[END_REF][START_REF] Yang | Suppression of human immunodeficiency virus type 1 replication by CD8+ cells: evidence for HLA class I-restricted triggering of cytolytic and noncytolytic mechanisms[END_REF] . This has boosted the efforts of the international scientific community to develop an effective HIV-1 vaccine that would be able to induce T-cell responses that could contain the virus, reducing the rate of transmission and the incidence of HIV disease or contributing to protect against infection. However, the failure of Merck's STEP trial showed the limits of the commonly used IFNγ Elispot surrogate assay [START_REF] Walker | Toward an AIDS vaccine[END_REF] . Actually, in the absence of a successful T-cell based vaccine candidate, the definition of what constitutes an effective T-cell response against HIV, and which assay reflects most accurately this efficacy, is still a subject of debate [START_REF] Walker | Toward an AIDS vaccine[END_REF][START_REF] Appay | CD8+ T cell efficacy in vaccination and disease[END_REF][START_REF] Souza | Measuring HIV-1-specific T cell immunity: how valid are current assays?[END_REF] . Much hope has been deposed on identifying new correlates of protection in HIV controllers (HIC), a rare population of HIV-infected individuals who can spontaneously control HIV-1 infection to undetectable levels for over 10 years [START_REF] Deeks | Human immunodeficiency virus controllers: mechanisms of durable virus control in the absence of antiretroviral therapy[END_REF][START_REF] O'connell | Elucidating the elite: mechanisms of control in HIV-1 infection[END_REF][START_REF] Saez-Cirion | HIV controllers: how do they tame the virus?[END_REF] .

Most HIC are characterized by a strong and functional CD8+ T cell response that very likely contributes to their long-term control of infection [START_REF] Gea-Banacloche | Maintenance of large numbers of virus-specific CD8+ T cells in HIV-infected progressors and long-term nonprogressors[END_REF][START_REF] Saez-Cirion | Heterogeneity in HIV suppression by CD8 T cells from HIV controllers: association with Gag-specific CD8 T cell responses[END_REF] . Thus, the CD8+ T cell response in these HIC currently constitutes one of the most appealing examples of a possible goal for new immune therapies or vaccine strategies [START_REF] Baker | Elite control of HIV infection: implications for vaccine design[END_REF] . During the last few years, the analysis of the CD8+ T cell response in HIC has revealed different characteristics of efficient HIV-specific CD8+ T cells in HIV infection, including the capacity to proliferate and generate a multifunctional response [START_REF] Betts | HIV nonprogressors preferentially maintain highly functional HIV-specific CD8+ T cells[END_REF][START_REF] Migueles | HIV-specific CD8+ T cell proliferation is coupled to perforin expression and is maintained in nonprogressors[END_REF][START_REF] Migueles | Lytic granule loading of CD8+ T cells is required for HIV-infected cell elimination associated with immune control[END_REF][START_REF] Sáez-Cirión | HIV controllers exhibit potent CD8 T cell capacity to suppress HIV infection ex vivo and peculiar CTL activation phenotype[END_REF] . However, these characteristics are often only revealed upon in vitro activation of the cells with optimal or overlapping HIV-1 peptides, and the relevance in the control of infection is uncertain [START_REF] Migueles | Defective human immunodeficiency virus-specific CD8+ T-cell polyfunctionality, proliferation, and cytotoxicity are not restored by antiretroviral therapy[END_REF][START_REF] Vojnov | Effective simian immunodeficiency virus-specific CD8+ T cells lack an easily detectable, shared characteristic[END_REF] . Our group has developed an assay that assesses the ex vivo capacity of HIV-specific CD8+ T-cells to suppress HIV-1 super-infection of autologous CD4+ T-cells through cytotoxic activity [START_REF] Sáez-Cirión | HIV controllers exhibit potent CD8 T cell capacity to suppress HIV infection ex vivo and peculiar CTL activation phenotype[END_REF] , this being the ultimate function of CD8 T-cells.

Actually, the use of ex vivo (non-stimulated) CD8+ T cells, unlike previous assays which used expanded CD8+ T cell lines, CD8+ T cell clones or in vitro stimulated primary CD8+ T cells [START_REF] Mackewicz | CD8+ cell anti-HIV activity correlates with the clinical state of the infected individual[END_REF][START_REF] Tsubota | A cytotoxic T lymphocyte inhibits acquired immunodeficiency syndrome virus replication in peripheral blood lymphocytes[END_REF][START_REF] Yang | Suppression of human immunodeficiency virus type 1 replication by CD8+ cells: evidence for HLA class I-restricted triggering of cytolytic and noncytolytic mechanisms[END_REF] , allows assessing the antiviral potential of the whole untouched pool of HIV-specific CD8+ T cells in response to infected relevant target cells, which appears as highly important to accurately evaluate the antiviral efficacy of circulating HIV-specific CD8+ T cells. Using this assay, it is possible to differentiate between the effective anti-HIV CD8+ T-cell responses in HIC and ineffective responses in patients with persistent viremia [START_REF] Sáez-Cirión | HIV controllers exhibit potent CD8 T cell capacity to suppress HIV infection ex vivo and peculiar CTL activation phenotype[END_REF] . We have shown that the enhanced capacity of HIV-specific CD8+ T cells from HIC to inhibit HIV-1 infection requires contact and MHC matching with target cells, and is caused by the elimination of infected cells rather than by the secretion of soluble antiviral factors (such as βchemokines or CAF) [START_REF] Sáez-Cirión | HIV controllers exhibit potent CD8 T cell capacity to suppress HIV infection ex vivo and peculiar CTL activation phenotype[END_REF] . Actually, we only observed an effect of anti-viral factors when working with artificially in vitro activated CD8+ T cells, and this effect was, in any case, very modest [START_REF] Sáez-Cirión | HIV controllers exhibit potent CD8 T cell capacity to suppress HIV infection ex vivo and peculiar CTL activation phenotype[END_REF] . Thus, our results point to a preponderant role of cytotoxic mechanisms on the highly efficient antiviral response of HIV-specific CD8+ T cells from HIC, which is in agreement with reports by Migueles et al showing increase lytic granule loading in HIC's CD8+ T cells upon contact with infected target cells [START_REF] Migueles | HIV-specific CD8+ T cell proliferation is coupled to perforin expression and is maintained in nonprogressors[END_REF][START_REF] Migueles | Lytic granule loading of CD8+ T cells is required for HIV-infected cell elimination associated with immune control[END_REF] .

Furthermore, we have found that HIV-suppressive capacity of CD8+ T-cells is strongly correlated with the frequency of HIV-specific CD8+ T-cells in HIC (but not in viremic individuals), and in particular with the frequency of CD8+ T-cells directed against the HIV-1 Gag protein [START_REF] Saez-Cirion | Heterogeneity in HIV suppression by CD8 T cells from HIV controllers: association with Gag-specific CD8 T cell responses[END_REF] . In fact, the depletion of Gagspecific CD8+ T-cells abrogates HIV suppression [START_REF] Saez-Cirion | Heterogeneity in HIV suppression by CD8 T cells from HIV controllers: association with Gag-specific CD8 T cell responses[END_REF] , suggesting that not all cells have the same anti-HIV potential. This is especially relevant considering that no other differences were observed between CD8+ T-cells of different antigen specificity in these experiments (either at the phenotypic level or when other parameters were measured, such as the capacity to secrete cytokines or the potential to proliferate, in response to HIV peptides). The impact of antigen specificity on the capacity of CD8+ T cells to suppress HIV-1 infection may well be due to the different kinetics of antigen presentation on the surface of the CD4+ T cells [START_REF] Sacha | Gag-specific CD8+ T lymphocytes recognize infected cells before AIDSvirus integration and viral protein expression[END_REF] . This underlines the convenience of assessing CD8+ T-cell function in a context closer to that which the cells encounter in vivo, i.e. in response to infected cells rather than to peptide stimulation. In addition, we have shown that the HIV-suppressive capacity of CD8+ T cells is influenced by the antigen sensitivity/functional avidity of the cells [START_REF] Almeida | Antigen sensitivity is a major determinant of CD8+ T-cell polyfunctionality and HIV-suppressive activity[END_REF] . Therefore, the capacity of CD8+

T-cells to suppress HIV-1 infection ex vivo, as measured in our assay, is influenced by the magnitude and the quality of the HIV-specific CD8+ T-cell response, the antigen sensitivity of the cells and even the specificity of the response. Each of these attributes is thought to be important for the generation of an efficient CD8+ T-cell response. Based on these observations, we proposed that the HIVsuppressive assay may be highly relevant to assess the efficacy of CD8+ T-cell responses generated by vaccine candidates (Table 1) and it complements assays that quantify the frequency of HIV-specific CD8+ T cells [START_REF] Saez-Cirion | Heterogeneity in HIV suppression by CD8 T cells from HIV controllers: association with Gag-specific CD8 T cell responses[END_REF] , such as the widely used IFN-γ Elispot assay (see Protocol [START_REF] Streeck | The role of IFN-gamma Elispot assay in HIV vaccine research[END_REF] ).

EXPERIMENTAL DESIGN

The technique used to assess the ex vivo capacity of CD8+ T cells to suppress HIV infection of autologous CD4+ T cells consists of three steps (figure 1):

• Isolation of CD4+ and CD8+ T cells and activation of CD4+ T cells

• Infection in vitro with HIV-1 of CD4+ T cells and CD4+:CD8+ T cell co-cultures with HIV-1

• Determination of viral replication in CD4+ T cells cultured alone or in the presence of CD8+ T cells and calculation of the HIV-1 suppressive capacity of CD8+ T cells Some important points in this schema are depicted

Isolation of cell fractions

We have standardized this technique with fresh blood samples that were recovered using either lithium heparin or EDTA as anticoagulants. [NOTE: Frozen PBMC may also be used. However, the level of CD8+ T cell-mediated HIV-1 suppression is then lower than with fresh cells. Therefore, experiments conducted with fresh samples should not be compared with those using frozen samples].

The blood must be kept at ~20 o C during transport and until "handling" in the laboratory to avoid haemolysis. If properly stored, the blood samples are workable up to 48h after extraction. Because of the drop in CD4+ T cell counts that is associated to HIV-1 progression, it is recommended to start with at least 10 ml of blood from HIV-1 infected individuals to obtain enough target cells (higher volumes might be needed if analyzing severely immunodepleted individuals), whereas 5 ml of blood are enough for most healthy individuals. It is extremely important to ensure the purity of the CD4+ and CD8+ T cell fractions. CD4+ cells are selected by positive selection using anti-CD4 antibody coupled magnetic beads. Although other cells (such as monocytes) are selected along with CD4+ T cells during this step, these are subsequently lost during a 2-3 day activation step with PHA and IL-2. The resulting negative fraction (depleted of CD4+ cells) is used as a source for the isolation of CD8+ T cells. In contrast to CD4+ T cells, it is necessary to isolate the CD8+ T cells by negative selection, to eliminate other cell fractions, especially NK cells, which also express the CD8 molecule and may subsequently interfere with the assay. The cells are incubated with a cocktail of antibodies targeting CD4, CD14, CD16, CD19, CD20, CD56, CD123, TCRγ/δ, Glycophorin A coupled to magnetic beads to eliminate CD4+ T cells (as the prior positive selection does not ensure the total removal of these cells from the negative fraction), B cells, NK cells, dendritic cells, etc. In this way, the CD8+ T cells are recovered untouched in the negative fraction (an alternative approach is to perform a positive selection of CD8β+ cells, but this may result in an undesirable activation of the cells). We use anti-CD4 magnetic beads and CD8+ T cells enrichment kits from either Miltenyi Biotech or StemCell technologies (both for manual or Robosep assisted separation) with excellent results. We routinely get purities above 95% for CD4+ T cells and CD8+ T cells and yields of around 20% of the initial PBMC for CD4+ T cells and 10% for CD8+ T cells, although these last values vary widely in the case of HIV-1 infected individuals.

Choice of viral isolate and infectious dose

The choice of the virus depends on the circumstances of the assay (e.g. subtype prevalence within the study population, strain of interest in a vaccine trial, etc.) and both primary and lab-adapted strains can be used. We routinely assay the HIV-1 suppressive capacity of CD8+ T cells in parallel against an R5

HIV-1 (BaL) and an X4 HIV-1 (NL4.3). Because the assay is carried out using CD8+ T cells ex vivo, we have not observed a significant contribution of soluble inhibitory factors to HIV-1 suppression ( 20 and see above) and the results obtained with both HIV-1 are globally comparable.

For the analysis of the HIV-1 suppression capacity based on an HIV-1 p24 ELISA assay, the choice of the infection dose should be one that regularly gives between 100 and 1000 ng/ml of HIV-1 p24 at the peak of viral replication, using PHA-activated CD4+ T cells from healthy donors (in our hands, using the p24 ELISA Kit from Zeptometrix, an moi = 10 -3.14 of HIV-1 BaL results in levels of infection within these values in >95% of the cases). A value below 100 ng/ml would not allow a good discrimination between high-quality and low-quality CD8+ T cell responses, and infections producing above 1000 ng/ml of HIV-1 p24 in culture supernatants would be too strong even for most high-quality CD8+ T cells.

Similarly, when using intracellular HIV-1 Gag determination, the optimal infectious dose is that which results in infection of between 10 and 30% of CD4+ T cells at day 3 post-infection. However, with this assay it is more complicated to regularly obtain the desired level of infection using a single viral dose than with the p24 ELISA assay because of a higher case-to-case variability in the levels of infection at day 3. We normally use two different viral doses in parallel (moi= 10 -1.15 , 10 -1.84 ) to be sure to achieve the desired level of infection.

When working with cells from HIV-1 patients, the peak level of viral replication that is observed on the CD4+ T cells infected in vitro is generally much higher than viral replication at the same time point in the control cells (activated but non-superinfected, see procedure). However, sometimes it is not possible to distinguish viral replication of the superinfecting virus (the one inoculated in vitro) from that of the infecting virus (the one that is carried ex vivo by CD4+ T cells from the patient). We have observed that the estimated HIV-1 suppressive capacity of CD8+ T cells might be slightly stronger towards infecting viruses than towards "consensus" (lab-adapted) strains, without altering significantly the results ( 15 and unpublished). Nevertheless, caution should be applied when analyzing such results.

Detection of viral replication: p24 ELISA vs intracellular staining for Gag products

Detection of viral replication is one of the key steps in this protocol. Although different approaches may be used to evaluate the level of infection of the cell cultures, we have chosen to monitor the HIV-1 p24 in culture supernatants by ELISA (figure 2A) and to determine the percentage of infected CD4+ T cells by intracellular staining of Gag products (figure 2B). Effectively, these assays are reliable and relatively simple.

Ideally, this protocol should result in a broad range of levels of infection: strong for CD4+ T cells and very weak or even undetectable for co-cultures with highly efficient CD8+ T cells (figure 2). We use a kinetic ELISA assay for HIV-1 p24 because it offers a wider range standard curve than do endpoint assays, reducing the number of manipulations and dilutions needed to quantify the different culture conditions in a single experiment. Culture supernatants need to be diluted before testing by ELISA (e.g. we often use 1/625 for 7 days post-infection supernatants from CD4+ T cells cultured alone, or 1/5 for supernatants from CD4+ T cells cultured in the presence of highly inhibitory CD8+ T cells).

Some experience is required to judge by how much the supernatants should be diluted. The quantification of viral replication by the determination of the number of infected cells (intracellular staining of Gag products) is a convenient method (faster, cheaper and consumes less cells than the p24 ELISA assay) to distinguish CD8+ T cells with weak and strong HIV-1 suppressive capacities (Table 2 and figure 3). However, it is not as sensitive/quantitative as the p24 ELISA and it is probably less well-adapted to "categorize" CD8+ T cell responses.

MATERIALS

Reagents

Blood

CAUTION: Blood should be obtained according to an ethical committee approved protocol andfollowing patient consent. When obtained from an HIV-1 infected patient it should be treated as infectious material.

HIV

Reagent setup

Separation buffer: PBS 1X supplemented with EDTA 2mM and FBS 0.5% (vol/vol). Can be stored at 4°C for up to 3 weeks.

Culture medium: RPMI 1640 supplemented with Glutamine, Pen/Strep and FBS 10% (vol/vol). Can be stored at 4°C for up to 3 weeks.

Activation medium: Culture medium supplemented with PHA (1 μg/ml*) and IL-2 (100 uI/ml*). Should be freshly prepared or stored no longer than 3 days at 4°C. *these values are indicated as a reference. You need to choose PHA and IL-2 concentrations that induce an optimal activation of CD4+ T cells after three days of culture.

IL-2 medium: Culture medium supplemented with IL-2. Can be stored at 4°C for up to 2 weeks.

Labelling buffer: PBS 1X supplemented with FBS 1% (vol/vol). Can be stored at 4°C for up to 2 months.

Equipment setup

Configure ELISA microplate reader as follows: 15 minutes run time, 30 seconds of time interval to read at 405 nm wavelength.

PROCEDURE Isolation of PBMC * TIMING 1h30 for Ficoll gradient separation

1-Transfer fresh blood from peripheral vein into a sterile 50-ml plastic tube and dilute with an equal volume of PBS.

CRITICAL STEP: It is recommended to start with at least 10 ml of blood to ensure that enough CD4+

T cells are recovered, especially when blood from HIV-1 infected individuals is analysed. For healthy individuals 5 ml of blood should be enough.

2-Gently add 20 ml of diluted blood to the top of 10 ml of Lymphocyte Separation medium in a 50-ml tube.

3-Centrifuge at 1200g (2000 rpm/min) for 20 minutes at room temperature CRITICAL STEP: do not use brake, because a sudden stop will disrupt the density gradient.

4-Remove top plasma phase (yellow) through gentle aspiration with a 10 ml pipette and discard (or store for further analysis)

5-Recover the mononuclear cell-containing interface (white) with a 5 ml pipette and transfer to a new 50-ml tube.

6-Add PBS to fill up the tube, and centrifuge at 400 g for 10 minutes at room temperature. Discard the supernatant, loosen the pellet and repeat PBS-wash twice. ii. Collect positive fraction, count CD4+ cells and centrifuge cells at 400 g for 5 minutes at room temperature.

CRITICAL STEP: also collect negative fraction that will be used in step 9.

iii. Remove supernatant and resuspend cell pellet in activation medium to a final concentration of 10

TROUBLESHOOTING

Evaluation of the capacity of CD8+ T cells to suppress HIV-1 infection of autologous CD4+ T cells * TIMING = 3h for infection and washings; 10 to 14 days for culture (depending on the peak of viral replication (option A)) or 3 days (option B); 4h for p24 ELISA (option A) or 2h30 for intracellular labelling of Gag products (option B).

10-Aspirate CD4+ and CD8+ T cells from wells with 5 ml pipettes and put cells to 15-ml conical tubes.

Fill up the tubes with culture medium.

11-Centrifuge at 400 g for 5 minutes at room temperature. Aspirate medium and resuspend cell pellets in 1 ml of IL-2 medium (for CD4+ T cells) or culture medium (for CD8+ T cells).

12-Count cells with haemocytometer and adjust concentration to 10 6 cells/ml with suitable medium.

CRITICAL STEP: It is important to count the cells accurately to allow different experiments to be compared. An automated cell counter is preferable.

13-Evaluate HIV-1 suppression by HIV-1 p24 ELISA (option A) or by quantification of intracellular

HIV-1 Gag products (option B).

A. Determination of the capacity of CD8+ T cells to suppress HIV

TROUBLESHOOTING

B. Determination of the capacity of CD8+ T cells to suppress HIV-1 infection of autologous CD4+ T cells by analysis of the percentage of infected CD4+ T cells using flow cytometry.

i. Add 50 μl of CD4+ T cells to wells in 96-well-round bottom-well plate. Allow one well for a non-infected in vitro control, two wells for in vitro HIV-1 infected CD4+ T cells, two additional wells for co-culture with CD8+ T cells at a 1:1 ratio.

CRITICAL STEP: you may want to provide for additional cells for proper monolabelled compensation controls for flow cytometry analysis (step xviii). Alternatively you can use compensation beads for this purpose.

CRITICAL STEP: the use of 96-well-round bottom-well plates is mandatory to ensure that no cells are lost during washing steps (steps iii, viii and ix)

ii. Add 50 μl of CD8+ T cells (10 6 cells/ml) to two wells containing 5x10 4 CD4+ T cells for co-culture at a 1:1 CD4+:CD8+ T cell ratio.

iii. Centrifuge plate at 400 g for 5 minutes at room temperature and remove 50 μl of supernatant from CD4+:CD8+ T cell co-cultures-containing wells.

iv. Add 50 μl of IL2 medium to well destined to non-infected in vitro control. viii. Remove 90 μl of supernatants using an 8-channel pipette, add 90 μl of culture medium and centrifuge at 400 g for 5 minutes at room temperature. Repeat twice. Use 90 μl of IL2 medium after the last wash.

CRITICAL STEP: after centrifugation the cells are concentrated at the bottom of the well. Place the tips on the border of the well, well above the cell pellet, to avoid loss of cells.

ix. Incubate the plate for three days at 37 o C in a humidified incubator under 5% CO 2 . Centrifuge the plate at 400 g for 5 minutes at room temperature and discard supernatants.

x. Harvest cell pellets with 100 μl of labelling buffer and transfer to 5 ml cytometry tubes. Add 500 μl of labelling buffer to each tube and centrifuge at

TROUBLESHOOTING

Troubleshooting advice can be found in Table 3.

ANTICIPATED RESULTS

The peak of viral replication when using the p24 ELISA assay will usually be observed at day 7 or 10 after infection. Ex vivo CD8+ T cells from healthy donor controls should not have any significant effect on viral infection of CD4+ T cells. Highly efficient HIV-specific CD8+ T cells with strong abilities to suppress HIV-1 infection, such as those from HIV controllers, should be able to reduce viral infection by more than 2 logs of p24 when using the ELISA assay, or more than 1 log of infected cells when using the intracellular assay (figure 3). However, it is necessary to keep in mind that HIV-1 infection is also generally inhibited to some extent when CD4+ T cells are cultured in presence of less efficient HIV-specific CD8+ T cells, such as those from HIV-infected viremic individuals [START_REF] Saez-Cirion | Heterogeneity in HIV suppression by CD8 T cells from HIV controllers: association with Gag-specific CD8 T cell responses[END_REF] (although in less than 1 log of p24 assayed by ELISA or less than 0.5 logs of infected cells with the intracellular assay) (figure 3).

7 - 3 days for the activation of CD4+ T cells 8 -

 738 Resuspend PBMC in separation buffer and count them in a haemocytometer.Cell fractionation and culture * TIMING 2h00 to obtain CD4+ and CD8+ T cell fractions and 2-Purify CD4+ cells i. Concentrate PBMC (typically to 10 7 cells/ml) in chilled separation buffer after centrifugation at 400 g for 5 minutes and perform positive selection of CD4+ cells with anti-CD4+ antibody coupled to magnetic beads as recommended by the manufacturer.

  100 μl of CD4+ T cells to wells in 96-well-round bottom-well plate. Allow three wells for non-infected in vitro control, three wells for HIV-1 infected in vitro CD4+ T cells, three additional wells for co-culture with CD8+ T cells at a 1:1 ratio and, optionally, three wells for each co-culture at additional CD4+:CD8+ T cell ratios (see step ii) CRITICAL STEP: the use of 96-well-round bottom-well plates is mandatory to ensure that no cells are lost during washing or recovery of supernatants (steps iii, viii and x)ii. Add 100 μl of CD8+ T cells at 10 6 cells/ml to each of three wells containing 10 5 CD4+ T cells for co-culture at a 1:1 CD4+:CD8+ T cell ratio. Dilute CD8+ T cells 1/3 and 1/10 in culture medium and add (3x) 100 μl of the different dilutions to additional CD4+ T cell-containing wells for 1:0.3 and 1:0.1 CD4+:CD8+ T cell ratios (optional).iii. Centrifuge plate at 400 g for 5 minutes at room temperature and remove 100 μl of supernatant from CD4+:CD8+ T cell co-culture-containing wells. iv. Add 100 μl of IL-2 medium to each of three wells destined as non-infected in vitro controls. v. Dilute viral stocks to a 2x assay viral dose in IL2 medium and add 100 μl of viral suspension to the three wells containing CD4+ T cells and to wells containing CD4+:CD8+ T cell co-cultures. CRITICAL STEP: viral dose needs to be determined by the user vi. Centrifuge plate at 1200 g for 1 hour at 22 o C in a refrigerated centrifuge to improve infection efficiency 27

  v. Prepare two viral dilutions at a 2x assay viral dose in IL-2 medium and for each viral suspension add 50 μl to one well containing CD4+ T cells and 50 μl to one well containing CD4+:CD8+ T cell co-cultures. CRITICAL STEP: viral dose needs to be determined by the user vi. Centrifuge plate at 1200 g for 1 hour at 22 o C in a refrigerated centrifuge to improve infection efficiency 27 . CAUTION: to ensure biocontainment and to avoid exposure to aerosols, use a centrifuge with sealed plate carriers vii. Incubate plate for 1 hour at 37 o C in a humidified incubator under 5% CO 2 .

400 g for 5 Steps 1 - 9 ,

 519 minutes at room temperature. Discard supernatants. xi. Prepare a mix of anti-CD4-ECD, anti-CD8-PE-Cy5 and anti-CD3-PE-Cy7 antibodies for cell surface staining. Dilute pre-titered antibodies in a final volume of 50 μl of labelling buffer for each tube. Loosen cell pellet in tubes and add antibody mixes. Vortex the tubes, wrap in aluminium foil and incubate at room temperature for 20 minutes. CRITICAL STEP: other than the sample tubes, you need to include a tube with non-labelled cells (cultured in the same condition as the experimental sample) and 4 tubes with single labelled compensation controls (either cells expressing the appropriate molecule or compensation beads). xii. Add 1 ml of staining buffer to each tube, centrifuge tubes at 400 g for 5 minutes at room temperature. Discard supernatants. xiii. Loosen pellets and add 250 μl of cytofix/cytoperm solution to all tubes and incubate in the dark at 4 o C for 20 minutes. xiv. Add 1 ml of 1X cytofix/cytoperm wash solution to each tube, centrifuge tubes at 400 g for 5 minutes at room temperature. Discard supernatants. xv. Prepare anti-Gag KC57-FITC antibody mix (3 μl of antibody and 47 μl of cytofix/cytoperm wash solution for each tube). Loosen pellets, add 50 μl of mix to tubes and incubate at 4°C for 30 minutes in the dark. xvi. Add 1 ml of 1X cytofix/cytoperm wash solution to each tube, centrifuge tubes at 400 g for 5 minutes at room temperature. Discard supernatants and resuspend cell pellet in 400 μl of staining buffer. xvii. Keep samples at 4 o C in the dark while setting up the flow cytometer with nonstained control and compensation controls. xviii. Proceed to flow cytometer acquisition of experimental data. TROUBLESHOOTING 14-Calculate HIV-suppressive capacity of CD8+ T cells from HIV-1 p24-ELISA (A) or intracellular Gag (B) results. A. Calculate HIV-suppressive capacity of CD8+ T cells using HIV-1 p24 ELISA assay i. Express the level of secreted p24 (ng/ml) for each sample at the different time points as the mean and standard deviation of triplicate wells (figure 2A). ii. Calculate HIV-1 suppressive capacity of CD8+ T cells at the peak of viral replication in the CD4+ T cell cultures infected in vitro with HIV-1 (typically day 7 or 10), as the Log of p24 production lost when CD8+ T cells are present in the culture at a 1:1 ratio (see figure 2A). HIV-suppressive capacity of CD8+ T cells (log p24 decrease) = Log10 mean p24 ng/ml in cultures of HIV-1 infected in vitro CD4+ T cells at peak of viral replication mean p24 ng/ml in infected in vitro-CD4+:CD8+ (1:1) co-cultures at the same time point B. Calculate HIV-suppressive capacity of CD8+ T cells using intracellular HIV-1 Gag assay i. Because HIV-1 infection downregulates surface expression of CD4+ molecules, gate on CD3+CD8-cells to calculate the percentage of infected CD4+ T cells. ii. Calculate HIV-1 suppressive capacity of CD8+ T cells as the logarithmic fold decrease in the percentage of HIV-infected CD4+ T cells when CD8+ T cells are present in the culture at a 1:1 ratio (see figure 2B). HIV-suppressive capacity of CD8+ T cells (log fold decrease in % kc57+CD4+ T cells) = Log10 % of Kc57+ CD3+CD8-cells in culture of CD4+ T cells infected in vitro % of Kc57+ CD3+CD8-cells in infected CD4+:CD8+ (1:1) co-cultures TIMING Isolation of PBMC and cell fractioning: 3-4h; and 2-3d of culture for activation of CD4+ T cells Steps 10-13.A-B. viii, Infection in vitro with HIV-1 and washings: 3h Steps 13.A.ix-13.A.x, Culture of infected cells for ELISA assay: 10-14d Steps 13.A.xi-13.A.xx, Analysis of viral replication by p24 ELISA: 4h Step 13.B.ix, Culture of infected cells for flow cytometry assay: 3d Steps 13.B.x-xviii, Analysis of viral replication by intracellular labelling of Gag products: 2h30

Figure 1 .Figure 2 .

 12 Figure 1. Schema outlying the ex vivo CD8+ T cell-based HIV suppression assay

Figure 3 .

 3 Figure 3. Correlation between the values of HIV-suppressive capacity of CD8+ T cells as obtained by ELISA-monitoring of HIV-1 p24 in culture supernatants and those obtained by flow cytometry analysis of the percentage of infected CD4+ T cells. Each circle represents experiments performed in parallel with cells from a single individual. The black line represents the linear regression. Blue lines and red lines are the 95% confidence intervals and 95% prediction intervals, respectively. Statistics were calculated by SigmaPlot with SigmaStat software (Systat Software Inc).

Table 1 .

 1 Advantages and disadvantages of using the CD8+ T cell based HIV-1 suppression assay to determine the efficacy of HIV-specific CD8+ T cell responses Advantages Disadvantages Reliable quantification of the ultimate function of cytotoxic CD8 T-cells, i.e. the killing of infected cells Labour-intensive handling of sample Takes into account the infection dynamics: response to infected cells instead of to peptides Donor-dependent variability in the susceptibility of CD4+ T cells to HIV-1 infection Reflects the magnitude and quality of the HIVspecific CD8+ T-cell response, the antigen sensitivity of the cells and even the antigenic specificity of the response Dissection of specificities contribution requires additional, heavier, experiments involving sorting of cell subpopulations 15,22Easy and low-cost adaptability to different HIV-1 strains (tropism, subtype)

  careful to always place tips on the border of the well, well above cell pellets, and remove less than 90% of the volume of the supernatant

  CRITICAL: positive selection of CD4+ cells followed by negative selection of CD8+ T cells optimizes the yield of recovery of the cell fractions, and ensures obtaining untouched CD8+ T cells (see isolation of cell fractions on experimental design section).

	5 ml round bottom cytometer tube (BD Bioscience, cat n o 352005)
	6, 12 and 96-well tissue culture plate. Flat bottom
	96-well tissue culture test plates. Round bottom
	RoboSep® Buffer (StemCell, cat n o 20104) Sterile 5, 10 and 25 ml disposable pipets
	CAUTION: This product is a potential irritant to eyes, respiratory system, and skin. Wear suitable Pipette (0.5-10, 2-20, 20-200, 100-1000 μl)
	protective clothing, glasses and gloves. Multichannel pipette (50-200 μl)
	-1 isolate (see Protocol 26 ) Benchtop centrifuge with sealed buckets and plate carriers
	CAUTION: HIV-1 is a class 3 human pathogen and it should be handled in a BSL3 facility HIV-1 P24 Antigen Elisa Bulk (ZeptoMetrix, cat n o 0801200) Flow cytometer
	Dulbecco's PBS 1x (Gibco, cat n o 14190) HIV-1 P24 Extended range Kit (ZeptoMetrix, cat n o 0801137) Mini vortex
	Lymphocyte Separation Medium LSM 1077 (PAA, cat n o J15-004) o-Phenylenediamine dihydrochloride tablets (OPD) (Sigma-Aldrich, cat n o P8412) Optical microscope
	CAUTION: May cause sensitization by inhalation and skin contact. Wear suitable protective clothing Microbiological safety cabinet
	and gloves Plate shaker
	RPMI 1640 (Gibco, cat n o 31870-025) Dry Incubator
	Foetal bovine serum (FBS) (PAA, cat n o A15-073) CO 2 cell incubator
	Elisa Microplate reader (with kinetic reading capabilities, suggested)
	Countess Automated Cell Counter (Invitrogen, cat n o C10227) or similar
	LSR II Flow Cytometer (BD bioscience) or similar
	Equipment
	RoboSep (Stemcell technologies, cat n o 20000)
	MidiMACS™ Separator (Miltenyi Biotec, cat n o 130-042-301)
	LS Columns (Miltenyi Biotec, cat n o 130-042-301 130-042-401)
	25 and 75cm² Cell Culture Flask with Vent Cap
	15 and 50 mL Centrifuge Tubes
	14 ml Falcon Polystyrene Round-Bottom Tubes (BD Biosciences, cat n o 352057)
	1.5 and 2 ml screw cap micro tubes

CAUTION: Harmful by inhalation and in contact with skin. Toxic if swallowed. Irritating to eyes. Limited evidence of a carcinogenic effect. Very toxic to aquatic organisms, may cause long-term adverse effects in the aquatic environment. Possible risk of irreversible effects. Wear suitable protective clothing, glasses and gloves. This material and its container must be disposed of as hazardous waste. KC57-FITC antibody (Beckman Coulter, cat n o 6604665) CD4-ECD antibody (Beckman Coulter, cat n o 6604727) CD8-PC5 antibody (Beckman Coulter, cat n o A07758) CD3-PE-Cy7 antibody (BD Pharmigen, cat n o 557749) Fixation and Permeabilization Solution (BD bioscience, cat n o 554722) CAUTION: Limited evidence of a carcinogenic effect. It may cause sensitization by skin contact. Wear suitable protective clothing and gloves.

  [START_REF] Tsubota | A cytotoxic T lymphocyte inhibits acquired immunodeficiency syndrome virus replication in peripheral blood lymphocytes[END_REF] cells/ml. iv. Place cells into a well of a 12-well plate (or of a 6-well plate if more than 3x10 6 cells are recovered) and culture them for 2-3 days at 37 o C, under 5% CO 2

	with humidified atmosphere.
	TROUBLESHOOTING
	9-Purify CD8+ T cells
	i. Concentrate negative cellular fraction from step 8 (typically to 10 7 cells/ml) in
	chilled separation buffer after centrifugation at 400 g for 5 minutes, and
	perform indirect magnetic cell sorting of untouched CD8+ T cells with a CD8+
	T cell enrichment kit as recommended by the manufacturer.
	ii. Collect negative fraction, count CD8+ T cells and centrifuge them at 400 g for
	5 minutes at room temperature.

CRITICAL STEP: in contrast to CD4+ cells, the CD8+ T cells are not magnetically labelled and are recovered in the negative fraction iii. Remove supernatant and resuspend cell pellet in culture medium to a final concentration of 10 6 cells/ml. CRITICAL STEP: do not add cytokines to the culture medium of CD8+ T cells to preserve ex vivo activation status iv. Put cells into a well of a 12-well plate (or of a 6-well plate if more than 3x10 6 cells are recovered) and culture in a humidified incubator at 37 o C and 5% CO 2 during activation of CD4+ T cells.

  .CAUTION: to ensure biocontainment and to avoid exposure to aerosols, use a centrifuge with sealed plate carriers. vii. Incubate plate for 1 hour at 37 o C in a humidified incubator under 5% CO 2 .viii. Remove 190 μl of supernatants using an 8-channel pipette, add 190 μl of culture medium and centrifuge at 400 g for 5 minutes at room temperature.Repeat twice. Use 190 μl of IL2 medium after the last wash.CRITICAL STEP: after centrifugation the cells are concentrated at the bottom of the well. Place the tips on the border of the well, well above the cell pellet, to avoid loss of cells. ix. Incubate plate at 37 o C in a humidified incubator under 5% CO 2 . . Add 20 μl of lysing buffer to all wells except blank and standard. Cover plate with an adhesive plate sealer and incubate at 37 o C for 2 hour in a dry

	incubator.
	PAUSE POINT: You can also incubate the plate overnight at this point.
	xv. Decant liquid and add 300 μl of assay wash buffer to each well and decant
	liquid. Repeat this step 6 times. Tap inverted plate gently but firmly on a pad
	of absorbent towels to remove all liquid and bubbles.
	xvi. Add 100 μl of HIV-1 p24 detector antibody (anti-p24 biotin reagent) to each
	well except the blank, cover plate with adhesive plate sealer and incubate at
	37 o C for 1 hour.
	Tap inverted plate gently but firmly on a pad of absorbent towels to remove
	liquid and bubbles.
	CRITICAL STEP: Do not allow washed plates to dry completely. Proceed immediately to sample
	addition.
	xiii. Leave one well empty (substrate blank), and add 200 μl of culture medium to
	two other wells, 200 μl of standard dilutions (4 to 0.08 ng/ml) and 50 μl of

x. At day 3 post-infection, centrifuge the plate at 400 g for

5

minutes at room temperature. Remove 190 μl of supernatants and transfer them to a new 96 well plate and store it. Replenish cell cultures with 190 μl of IL-2 medium and put the 96-well plate containing the cell cultures back to the incubator. Repeat at days 7, 10 and 14. PAUSE POINT: Store plates with culture supernatants at 4 o C if p24 ELISA is to be performed within 15 days or at -80 o C if it will be done later or if further analyses are planned. xi. If frozen, allow culture supernatants to thaw at room temperature. Dilute supernatants with assay diluent and proceed with HIV-1 p24 antigen ELISA determination. xii. Allow antibody-coated strips to reach room temperature. Add 300 μl of assay's wash buffer to each well and decant liquid. Repeat this step 6 times. diluted samples plus 150 μl of culture medium to strips. xivxvii. Decant liquid from plate and wash the wells as in step xv. xviii. Add 100 μl of Streptavidin-Peroxidase solution into each well except the blank, cover plate with adhesive plate sealer and incubate at 37 o C for 30 minutes. xix. Decant liquid from plate and wash the wells as in step xv. CRITICAL STEP: removal of air bubbles is critical at this point as they interfere with the signal during reading. xx. Place plate on plate reader and add 100 μl of OPD-substrate solution. Start reading immediately on pre-configured plate reader.

Table 2 . Comparison of p24 ELISA vs intracellular Gag assay. HIV-1 p24 ELISA assay Intracellular HIV-1 Gag assay

 2

	Time	14-17 days (10-14 days of	6 days (3 days of infection)
		infection)
	Sample required	10 million PBMCs	1-2 million PBMCs
	Reproducibility	Good	Good
	Range	Excellent	Limited

Table 3 . Troubleshooting table

 3

	Step Problem	Possible reason	Solution
	8,9	Poor cell recuperation

ACKNOWLEDGMENTS

We thank Olivier Lambotte, Alain Venet, Martine Sinet for helpful discussions. We thank the French National Agency for Research on AIDS and Viral Hepatitis (ANRS) HIV Controllers EP36 observatory.

We thank Katherine Kean for the English editing of the manuscript. We especially thank the subjects who participate in the studies developed in the laboratory for their cooperation.

This work was financially supported by ANRS. SYS was supported by Korea Science and Engineering Foundation and the Institut Pasteur Korea.

AUTHOR CONTRIBUTION

ASC designed the protocol, performed experiments, analyzed the data and wrote the manuscript; SYS performed experiments and analyzed the data; PV performed experiments and gave technical support; FBS gave conceptual advice; GP designed the protocol and edited the manuscript. All authors discussed the results and commented on the manuscript.

COMPETING FINANCIAL INTERESTS

The authors declare that they have no competing financial interests


Guido Vanham

Anne Buvé

Carole Seguin-Devaux

Vic Arendt

Sylvie Delhalle

Asier Sáez

What is the significance of post-treatment control of HIV infection vis a vis functional cure?

. This PTC status may provide additional information to develop a functional cure.

. Within the French ANRS PRIMO cohort, 164 patients interrupted cART, initiated during PHI 3) : VL remained <50 copies/mL in 14 subjects for a

median of 4.5 years [START_REF] Goujard | HIV-1 control after transient antiretroviral treatment initiated in primary infection: role of patient characteristics and effect of therapy[END_REF] and additional PTC were described in the European seroconverter CASCADE cohort 4) [START_REF] Lodi | Immunovirologic control 24 months after interruption of antiretroviral therapy initiated close to HIV seroconversion[END_REF].

In most of these studies, pretreatment VL had been documented, but, since cART was started very soon after infection, it is not excluded that at least some of these apparent PTC could in fact have been ECs, who would have controlled viremia even if they had been left untreated. Moreover, these clinical studies did not provide insight in underlying immune or viral mechanisms.

The French VISCONTI study analyzed 14 PTC, who had been treated with cART in the acute 5) phase and did not show viral rebound or showed intermittent blips only for 48-113 months after TI. The HLA profile of these PTC was different from that of EC. In the acute phase (before treatment), the PTC also had a higher VL and a lower CD4 T count than EC. Conversely, in the post-treatment aviremic state, PTC had lower immune activation and much lower CD8 T cell suppressor activity as compared to EC. The cellular proviral DNA of PTC after TI was very low, it was mainly associated with transitional memory CD4 T cells and, remarkably, tended to further decrease over time in the absence of treatment in some PTC. Nevertheless, in all cases, HIV could be cultured, but fitness of these viruses was not evaluated. [START_REF] Saez-Cirion | Post-Treatment HIV-1 Controllers with a Long-Term Virological Remission after the Interruption of Early Initiated Antiretroviral Therapy ANRS VISCONTI Study[END_REF].

Recently, four patients were described, who had been treated in the chronic viremic phase of the infection for several years, interrupted treatment for a variety of reasons and maintained controlled viremia. Whereas their T cell responses were largely unremarkable and no HLA association was found, all four PTC had a low viral reservoir as assessed by proviral DNA and no intracellular viral mRNA species could be measured. Moreover, virus cultivation from CD4 T cells repeatedly failed in 1 patient and showed delayed kinetics and low fitness in two others. After 5 years of follow up, two PTC with low CD4 T cell counts were restarted on cART in the absence of viral rebound, whereas the two others, with high CD4 T cells, maintained viral control (with intermittent blips) without treatment [START_REF] Van Gulck | Immune and Viral Correlates of "Secondary Viral Control" after Treatment Interruption in Chronically HIV-1 Infected Patients[END_REF].

In conclusion, a small proportion of HIV-1 infected subjects can maintain viral suppression after stopping cART.

They seem to challenge the common wisdom that antiretroviral treatment needs to be taken lifelong to prevent rebound and disease progression [START_REF] Siliciano | Long-term follow-up studies confirm the stability of the latent reservoir for HIV-1 in resting CD4+ T cells[END_REF]. Most of these PTC were originally treated in the acute phase, but there is emerging evidence that, in rare instances, patients, who started treatment in the chronic progressive stage, can also control viremia after TI. PTC patients are distinct from EC e.g. host genetics are different and CD8 T cell responses do not seem to be involved in viral control in PTC, while they do play a role in EC. Importantly, although the few PTC described until now are a heterogeneous group, they all have a very low proviral reservoir, which is even lower than in long-term non-progressors [START_REF] Lewin | HIV cure and eradication: how will we get from the laboratory to effective clinical trials?[END_REF].

Obviously, all these studies have included few patients, with rather limited pre-and on-treatment data. Therefore,

ANRS (French National Agency for Research on AIDS and Viral Hepatitis) has recently launched a first initiative to study PTC in a larger international cohort (visconti@anrs.fr). This cohort aims to identify mechanisms underlying control of infection in PTC and factors that may help to predict PTC outcome after TI in patients receiving

antiretroviral treatment. Patients who initiated antiretroviral treatment with viral loads above 2,000 copies/ml, kept viremia suppressed under treatment for at least one year and have documented viral loads below 400 copies/ml for more than one year after treatment interruption will be eligible to participate in this cohort.

It has repeatedly been argued that analytical treatment interruption (ATI) in selected patients (with high CD4 T counts) may be acceptable to evaluate interventions aimed at functional cure [START_REF] Routy | Assessing risk of a short-term antiretroviral therapy discontinuation as a read-out of viral control in immune-based therapy[END_REF][START_REF] Machado | Long-term outcome of patients after a single interruption of antiretroviral therapy: a cohort study[END_REF]. To gain more definitive insight into possible mechanisms and predictors of PTC, prospective studies are needed, but candidates should be selected carefully. The data, summarized above, suggest that some patients with elevated CD4 T cell numbers and an exceptionally low proviral load after a prolonged period on cART, who consider treatment interruption, might control the virus after TI. In depth studies of pre-, on and post-treatment clinical, immunological but especially (pro)viral characteristics, including viral fitness evaluation, in those who control the virus after TI versus noncontrollers might provide clues to understand the nature of PTC. A possible mechanism of PTC is that drug (and immune) pressure has resulted in crippling mutations in the virus. Obviously very strict monitoring, with prompt reinitiation of cART, according to preset viral rebound criteria, would be a prerequisite for such a study.

Clearly, this type of larger observational cohorts and well-designed ATI studies might reveal modifiable factors that could inspire novel treatment strategies aiming at functional cure.

Note on PHI definition: 1) PHI was defined as having a negative or indeterminate western blot for HIV-1 antibodies in combination with a positive test for either p24 antigen or a detectable HIV-1 RNA concentration, or a negative result on an HIV screening test within 6 months before seroconversion. 2) PHI was defined as a negative/incomplete HIV-1 western blot and a p24 Ag positive test, and/or a current positive HIV antibody test with a negative one within the previous 3 months. 3) PHI was diagnosed in the basis of a negative or incomplete western blot with detectable HIV-1 RNA or an interval of < 3 months between a negative and a positive ELISA. 4) Patients initiated cART within 3 months after seroconversion. 5) Primary infection was defined as symptoms associated with an incomplete HIV-1 Western blot and a positive p24 antigen test or detectable plasma HIV RNA, and/or seroconversion documented by a positive HIV antibody test that was preceded by a negative test less than 3 months before.


Lamine Aouad

Tahar Kechadi

Justin Trentesaux

Nhien-An Le- Khac

AN OPEN FRAMEWORK FOR SMARTPHONE EVIDENCE ACQUISITION

Keywords: Mobile phone forensics, evidence acquisition, open framework

The forensic processes and procedures for performing a bit-for-bit copy of computer memory and media are well established and documented. However, most commercially-available tools for smartphone data acquisition and analysis have unspecified implementations and do not provide technical documentation about the acquisition process. A detailed understanding of the acquisition process is important in criminal cases because the technique that was used may be questioned in courtroom proceedings. To address the gap, this paper proposes an open framework for documenting and implementing the acquisition and analysis of digital evidence from smartphones.

Introduction

Smartphones have become an integral part of the daily lives of an increasing number of people from around the world. Smartphones are essentially pocket computers and, as such, contain a large amount of information. Information stored on smartphones such as the details of communications (calls, text and email messages), user locations, contacts, photographs and videos are all potentially relevant in forensic investigations.

Given the variety of devices and the lack of standards, there is no unified data acquisition method for smartphones. Data acquisition is one of the most important steps in a forensic investigation. Unfortunately, the majority of tools retrieve the baseline of extractable evidence (e.g., address book data, call details, text messages, photographs), but omit important evidence, especially deleted data. Additionally, because of the variety of communication protocols and proprietary interfaces, acquisition methods have yet to be formalized for many models of smartphones.

This paper attempts to address these issues by proposing an open and flexible framework designed to facilitate forensic investigations of mobile devices while supporting add-ons and mappings to existing protocols. The paper also presents an implementation of the framework that supports the capture of bit-for-bit copies of the memory and media of several Android smartphone models.

Background

In recent years, there has been increasing interest in mobile device forensics. Several studies have evaluated techniques and tools for acquiring digital evidence from Android and iPhone smartphones [START_REF] Hoog | Android forensics[END_REF][START_REF] Hoog | iPhone Forensics, White Paper, viaForensics[END_REF][START_REF] Jansen | Guidelines on Cell Phone Forensics: Recommendations of the National Institute of Standards and Technology[END_REF][START_REF] Thing | Live memory forensics of mobile phones[END_REF]. Given the variety of devices -the Android operating system for instance is compliant with more than 300 smartphone models -it should come as no surprise that no standardized or generalized methods exist for acquiring and analyzing digital evidence from smartphones.

The tools analyzed in the studies include .XRY, EnCase Neutrino, CelleBrite UFED and Oxygen Forensic Suite. The studies have considered tool performance in terms of the support for and the accuracy of targeted data such as call logs, text messages, email, multimedia, maps, cookies and deleted data. However, practically all the tools that have been analyzed are commercial products with unspecified implementations and little or no documentation of their logical and physical acquisition methods. One of the keys goals of this work and, indeed, current research in mobile phone forensics, is to document the fundamentals of acquiring and analyzing evidence from smartphones.

Evidence Acquisition Methods

There are two main evidence acquisition methods: logical acquisition and physical acquisition. Logical acquisition methods interact with devices to extract storage objects such as directories or files using protocols such as AT commands, OBEX (OBject Exchange) or vendor interfaces. These methods typically extract data that is accessible via the operating system and interfaces; they cannot extract deleted data.

Physical acquisition methods extract the memory contents via the bit-by-bit imaging of the flash memory of a device. The method used depends on the manner in which a device stores data in its memory structures and can be performed using system access to the flash mem- ory or using communications ports based on standards such as JTAG. However, the connections and interface specifications are not available for many smartphone models. Also, many vendors disable or lock access to device memory. Physical acquisition can also be done via direct memory chip access, but this requires specialized equipment and knowledge about the raw data structures. Also, the approach is very invasive and can damage the device and its memory. While the forensic tools mentioned above can extract a variety of data from smartphones, a bit-by-bit copy of the original media is the most accurate representation of evidence on a device [START_REF] Jansen | Guidelines on Cell Phone Forensics: Recommendations of the National Institute of Standards and Technology[END_REF]. This memory image can be analyzed by a forensic investigator using ad hoc and/or standard techniques and tools.

GUI

Open Framework

Figure 1 presents a schematic diagram of the open framework. The basic functionality is provided by the acquisition, storage and parsing packages, all of which are implemented in C++. The basic methods in the packages are defined in a manner that permits the extension and/or re-definition of the core functionality. This is motivated by the desire to have a generic framework that would allow other programmers to add support for new devices and data sources.

Currently, application databases and memory images from a supported Android smartphone can be extracted only after rooting the device. Depending on the operating system version running on the smartphone, various exploits, such as psneuter or gingerbreak, may be used to gain root access. After the data is extracted, it is parsed into an XML format in order to define standard metadata.

Future versions will employ content providers to extract databases without rooting smartphones. Note, however, that content provider methods do not extract deleted data, so recovering deleted data would still require rooting a smartphone.

Logical Recovery of Databases

Depending on the operating system variant, the framework browses folders in its search for databases and proceeds to recover them. In the case of a Nexus One device running OS version 2.1, the list of the database files includes (among others): The current version of the framework is able to query seven of these databases to extract contacts, call details, text messages, emails and pictures. Deleted data corresponding to contacts and calls are also recoverable. Future versions will be able to extract evidence from additional databases, including SQLite.

/data/

Physical Recovery of Images

The Android filesystem has a number of partitions that potentially hold data of interest in forensic investigations. These partitions are located in /dev/mtd. For example, a Nexus One device running OS version 2.1 has six partitions: mtd0: "misc" mtd1: "recovery" mtd2: "boot" mtd3: "system" mtd4: "cache" mtd5: "userdata"

The current implementation images all six partitions. Most of the data of interest resides in mtd3 and mtd5. Note, however, that the partition order can vary for different smartphone models. The current version does not support the mounting and reading of images. However, investigators can use commercially-available forensic tools such as the Forensic ToolKit (FTK) to mount and browse images.

Experimental Tests

The current implementation of the framework has been tested on several Android phones and emulators with different operating system versions. After setting up a smartphone and choosing the extraction mode (Figure 2), the framework displays a summary and the status of the extraction process (Figure 3). The results are then displayed as shown in Figure 4. Functionality for browsing the extracted memory images and searching for data of interest will be implemented in a future version.

Forensic Recovery of iPhone Data

As part of the implementation effort, we have also investigated the hardware and system specifications of the iPhone. The iPhone has two partitions, root and user, which are mounted at / and /private/var, respectively.

The root partition is 300 MB in size and stores the operating system and pre-loaded applications. It is mounted as read-only and remains in a factory state by default. No user data of value to a forensic investigation can be retrieved from this partition, but it can be used to safely install forensic toolkits without affecting user data. The user partition contains data of interest to forensic investigations.

Various utilities can be used to access iPhone data depending, of course, on the firmware version. For firmware versions 1.0.2 to 1.1.4, the iLiberty+ utility may be used. This free toolkit includes a basic Unix world, OpenSSH, netcat, md5 and dd. It can also be used to remove the operating-system-level passcode.

In the case of iPhones with newer firmware versions, the Pwnage and Xpwn recovery tools may be used. The recovery is then performed using ssh, dd and nc. More details about recovering the media partition and deleted data can be found in [START_REF] Le-Khac | iPhone Forensics[END_REF]. Future versions of the open framework will incorporate these and other tools.

Conclusions

The open framework for evidence acquisition from smartphones is designed to facilitate forensic investigations of a variety of mobile devices while supporting add-ons and mappings to existing protocols. The implementation of the framework supports the capture of bit-for-bit copies of the memory and media of several Android smartphone models. Our future research will focus on implementing evidence extraction and anal- ysis functionality for other Android models and other smartphone platforms.

Figure 1 .

 1 Figure 1. Open framework.

Figure 2 .

 2 Figure 2. Selecting the extraction mode.

Figure 3 .

 3 Figure 3. Performing the extraction.

  data/com.android.browser/databases/browser.db /data/data/com.android.browser/databases/webviewCache.db /data/data/com.android.browser/databases/webview.db /data/data/com.android.providers.settings/databases/settings.db /data/data/com.android.providers.calendar/databases/calendar.db /data/data/com.android.providers.contacts/databases/contacts2.db /data/data/com.android.providers.downloads/databases/downloads.db /data/data/com.android.email/databases/EmailProviderBody.db /data/data/com.android.email/databases/EmailProvider.db /data/data/com.android.providers.telephony/databases/telephony.db /data/data/com.android.providers.telephony/databases/mmssms.db /data/data/com.google.android.gm/databases/gmail.db /data/data/com.google.android.apps.maps/databases/friends.db /data/data/com.google.android.apps.maps/databases/search history.db