Pierre Carpentier

Jean-Philippe Chancelier

Guy Cohen

AND Michel De Lara

Pierre Girardeau
email: pierre.girardeau@cermics.enpc.fr

Laetitia Andrieu

Kengy Barty

Anes Dallagi

DYNAMIC CONSISTENCY FOR STOCHASTIC OPTIMAL CONTROL PROBLEMS

Keywords: Mathematics Subject Classification. 93E20, 49L20, 91B70 Stochastic optimal control, Dynamic consistency, Dynamic Programming, Risk measures. This

. We here link this notion with the concept of "state variable" in MDP, and show that a significant class of dynamic optimization problems are dynamically consistent, provided that an adequate state variable is chosen.

Introduction

Stochastic Optimal Control (SOC) is concerned with sequential decision-making under uncertainty. Consider a dynamical process that can be influenced by exogenous noises as well as decisions one has to make at every time step. The decision maker wants to optimize the behavior of the dynamical system (for instance, minimize a production cost) over a certain time horizon. As the system evolves, observations of the system are made; we here suppose that the decision maker is able to keep in memory all the past observations. Naturally, it is generally more profitable for him to adapt its decisions to the observations he makes of the system. He is hence looking for strategies rather than simple decisions. In other words, he is looking for applications that map every possible history of the observations to corresponding decisions. Because the number of time steps may be large, the representation of such an object is in general numerically intractable.

However, an amount of information lighter than the whole history of the system is often sufficient to make an optimal decision. In the seminal work of [START_REF] Bellman | Dynamic Programming[END_REF], the minimal information on the system that is necessary to make the optimal decision plays a crucial role; it is called the state variable (see [START_REF] Whittle | Optimization over time[END_REF], for a more formal definition). Moreover, the Dynamic Programming (DP) principle provides a way to compute the optimal strategies when the state space dimension is not too large (see [START_REF] Bertsekas | Dynamic Programming and Optimal Control[END_REF], for a broad overview on DP). The aim of this paper is to establish a link between the concept of state variable and the notion of time consistency 1 .

The notion of dynamic consistency is well-known in the field of economics (see [START_REF] Hammond | Consistent plans, consequentialism, and expected utility[END_REF] and has been introduced in the context of risk measures (see [START_REF] Artzner | Coherent multiperiod risk-adjusted values and Bellman's principle[END_REF][START_REF] Riedel | Dynamic coherent risk measures[END_REF][START_REF] Detlefsen | Conditional and dynamic convex risk measures[END_REF][START_REF] Cheridito | Dynamic monetary risk measures for bounded discrete-time processes[END_REF], for definitions and properties of coherent and consistent dynamic risk measures). Dynamic consistency has then been studied in the stochastic programming framework by [START_REF] Shapiro | On a time consistency concept in risk averse multistage stochastic programming[END_REF] and for Markov Decision Processes by [START_REF] Ruszczynski | Risk-averse dynamic programming for markov decision processes[END_REF]. In this paper, we rather use the (almost equivalent) definition of time consistency given by [START_REF] Ekeland | Being serious about non-commitment: subgame perfect equilibrium in continuous time[END_REF], which is more intuitive and seems better suited in the framework of optimal control problems. In this context, the property of time consistency is loosely stated as follows. The decision maker formulates an optimization problem at time t 0 that yields a sequence of optimal decision rules for t 0 and for the following time steps t 1 , . . . , t N = T . Then, at the next time step t 1 , he formulates a new problem starting at t 1 that yields a new sequence of optimal decision rules from time steps t 1 to T . Suppose the process continues until time T is reached. The sequence of optimization problems is said to be dynamically consistent if the optimal strategies obtained when solving the original problem at time t 0 remain optimal for all subsequent problems. In other words, time consistency means that strategies obtained by solving the problem at the very first stage do not have to be questioned later on.

The notion of information here plays a crucial role. Indeed, we show in this paper that a sequence of problems may be consistent for some information structure while inconsistent for a different one. Consider for example a standard stochastic optimization problem solvable using DP. We will observe that the sequence of problems formulated after the original one at the later time steps are time consistent. Add now a probabilistic constraint involving the state at the final time T . We will show that such a constraint brings time inconsistency in the sense that optimal strategies based on the usual state variable have to be reconsidered at each time step. This is because, roughly speaking, a probabilistic constraint involves not only the state variable values but their probabilistic distributions. Hence the only knowledge of the usual state variable of the system is insufficient to write consistent problems at subsequent time steps. So, in addition to the usual technical difficulties regarding probabilistic constraints (mainly related to the non-convexity of the feasible set of strategies), an additional problem arises in the dynamic case. We will see that, in fact, this new matter comes from the information on which the optimal decision is based. Therefore, with a well-suited state variable, the sequence of problems regains dynamic consistency.

In §2, we carefully examine the notion of time consistency in the context of a deterministic optimal control problem. The main ideas of the paper are so explained and then extended, in §3, to a sequence of SOC problems. Next, in §4, we show that simply adding a probability constraint (or, equivalently in our context, an expectation constraint) to the problem makes time consistency fall apart, when using the original state variable. We then establish that time consistency can be recovered provided an adequate state variable is chosen. We conclude that, for a broad class of SOC problems, time consistency has to be considered with respect to the notion of a state variable and of DP.

1

We either use the term "dynamically consistent" or "time consistent" to refer to the same notion.

A first example

We introduce sequential deterministic optimal control problems, indexed by time, and derive the notion of time consistency on this instance. We then illustrate the fact that the decision making process may be time consistent or not, depending on the information on which decisions are based. The discussion is informal, in the sense that we do not enter technical details regarding existence of the solutions for the problems we introduce.

Let us consider a discrete and finite time horizon t 0 , . . . , t N = T .2 The decision maker has to optimize (according to a cost function we introduce below) the management of an amount of stock x t , which lies in some space X t , at every time step t = t 0 , . . . , T . Let U t be some other space, for every time step t = t 0 , . . . , T -1. At each time step t, a decision u t ∈ U t has to be made. Then a cost L t is incurred by the system, depending on the values of the control and on the auxiliary variable x t that we call the state of the system. This state variable is driven from time t to time t + 1 by some dynamics f t : X t × U t → X t+1 . The aim of the decision maker is to minimize the sum of the intermediate costs L t at all time steps plus a final cost K.

The problem hence reads:

min x,u T -1 t=t0 L t (x t , u t ) + K (x T ) , (1a)
subject to the initial condition:

x t0 given, (1b) and dynamic constraints:

x t+1 = f t (x t , u t ) , ∀t = t 0 , . . . , T -1. (1c)
Note that here the decision at time t is taken knowing the current time step and the initial condition (the decision is generally termed "open loop"). A priori, there is no need for more information since the model is deterministic.

Suppose a solution to this problem exists. This is a sequence of controls that we denote by u * t0,t0 , . . . , u * t0,T -1 , where the first index refers to the initial time step and the second index refers to the time step for which the decision applies. Moreover, we suppose a solution exists for each one of the natural subsequent problems, i.e. for every

t i = t 1 , . . . , T -1: min x,u T -1 t=ti L t (x t , u t ) + K (x T ) , (2a) s.t. x ti given, (2b) x t+1 = f t (x t , u t ) , ∀t = t i , . . . , T -1. (2c)
We denote the solutions of these problems by u * ti,ti , . . . , u * ti,T -1 , for every time step t i = t 1 , . . . , T -1. Those notations however make implicit the fact that the solutions do generally depend on the initial condition x ti . We now make a first observation.

Lemma 1 (Independence of the initial condition). In the very particular case when the solution to Problem (1) and the solutions to Problems (2) for every time step t i = t 1 , . . . , T -1 do not depend on the initial state conditions, problems are dynamically consistent.

Proof. Let us denote by x * t0,ti the optimal value of the state variable within Problem (1) at time t i . If we suppose that solutions to Problems (2) do not depend on the initial condition, then they are the same as the solutions obtained with the initial condition x * t0,ti , namely u * t0,ti , . . . , u * t0,T -1 . In other words, the sequence of decisions u * t0,t0 , . . . , u * t0,T -1 remains optimal for the subsequent problems starting at a later date.

This property is of course not true in general, but we see in Example 1 hereafter and in §3 that some very practical problems do have this surprising property.

Example 1. Let us introduce, for every t = t 0 , . . . , T -1, functions l t : U t → R and f t : U t → R, and assume that x t is scalar. Let K be a scalar constant and consider the following deterministic optimal control problem:

min x,u T -1 t=t0 l t (u t ) x t + Kx T , s.t. x t0 given, x t+1 = f t (u t ) x t , ∀t = t 0 , . . . , T -1.
Variables x t can be recursively replaced using dynamics f t . Therefore, the above optimization problem can be written:

min u T -1 t=t0 l t (u t ) f t-1 (u t-1 ) . . . f t0 (u t0 ) x t0 + Kf T -1 (u T -1 ) . . . f t0 (u t0 ) x t0 .
Hence the optimal cost of the problem is linear with respect to the initial condition x t0 . Suppose that x t0 only takes positive values. Then the value of x t0 has no influence on the minimizer (it only influences the optimal cost). The same argument applies at subsequent time steps t i > t 0 provided that dynamics are such that x t remains positive for every time step t = t 1 , . . . , T . Now, formulate the same problem at a later date t i = t 1 , . . . , T -1, with initial condition x ti given. By the same token as for the first stage problem, the value of the initial condition x ti has no influence on the optimal controls. Assumptions made in Lemma 1 are fulfilled, so that the time consistency property holds true for open-loop decisions without reference to initial state conditions. Although, for the time being, this example may look very special, we will see later on that it is analogous to familiar SOC problems.

As already noticed, Lemma 1 is not true in general. Moreover, the deterministic formulation (1) comes in general from the representation of a real-life process which may indeed be subject to unmodelized disturbances. Think of an industrial context, for example, in which sequential decisions are taken in the following manner.

• At time t 0 , Problem (1) is solved. One obtains a decision u * t0,t0 to apply at time t 0 , as well as decisions u * t0,t1 , . . . , u * t0,T -1 for future time steps. • At time t 1 , one formulates and solves the problem starting at time t 1 with initial condition x t1 = f t0 (x t0 , u * t0,t0 ) + ε t1 , ε t1 being some perturbation of the model. There is no reason not to use the observation of the actual value of the variable x t1 at time t 1 as long as we have it at our disposal.

• Hence a decision u * t1,t1 is obtained, which is different from the initially obtained optimal decision u * t0,t1 (once again, in general). • The same process continues at times t 2 , . . . , T -1.

Let us now state the two following lemmas.

Lemma 2 (True deterministic world). If the deterministic model is actually exact, i.e. if all perturbations ε ti introduced above equal zero, then Problems (2) with initial conditions

x ti = x * ti f ti (x * ti-1 , u * t0,ti-1 ) are dynamically consistent.
Proof. Since decisions u * t0,t0 , . . . , u * t0,T -1 are optimal for Problem (1), it follows that decisions u * t0,t1 , . . . , u * t0,T -1 are optimal for the problem:

min x,u L t x t0 , u * t0,t0 + T -1 t=t1 L t (x t , u t ) + K (x T ) , s.t. x t1 = f t1 (x t0 , u * t0,t0 ), x t+1 = f t (x t , u t ) , ∀t = t 1 , . . . , T -1,
which has the same arg min as Problem (2) at time t 1 . The same argument applies recursively for subsequent time steps.

It is clear that Lemma 2 is not satisfied in real life. Therefore, adding disturbances to the problem seems to bring inconsistency to the sequence of optimization problems. Decisions that are optimal for the first stage problem do not remain optimal for the subsequent problems if we do not let decisions depend on the initial conditions.

In fact, as it is stated next, time consistency is recovered provided we let decisions depend upon the right information.

Lemma 3 (Right amount of information). Suppose that one is looking for strategies (Φ * t0,t0 , . . . , Φ * t0,T -1 ) as feedback functions depending on the variable x. Then Problems (2) are time consistent for every time step t = t 0 , . . . , T -1.

Proof. The result is a direct application of the DP principle, which states that there exists such a feedback function Φ * t0,ti that is optimal for Problem (1) and is still optimal for Problem (2) at time t i , whatever initial condition x ti is.

We thus retrieve the dynamic consistency property provided that we use the feedback functions Φ * t0,t rather than the controls u * t0,t . In other words, problems are dynamically consistent as soon as the control strategy is based on a sufficiently rich amount of information (time instant t and state variable x in the deterministic case).

There is of course an obvious link between these optimal strategies and the controls (u * t0,t0 , . . . , u * t0,T -1 ), namely:

u * t0,t = Φ * t0,t x * t0,t , ∀t = t 0 , . . . , T -1, where x * t0,t0 = x t0 , x * t0,t+1 = f t x * t0,t , Φ * t0,t x * t0,t , ∀t = t 0 , . . . , T -1.
The considerations we made so far seem to be somewhat trivial However, we whall observe that for SOC problems, which may seem more complicated at first sight, the same considerations remain true. Most of the time, decision making processes are time consistent, provided we choose the correct information on which decisions are based.

Stochastic optimal control without constraints

We now consider a more general case in which a controlled dynamical system is influenced by modeled exogenous disturbances. The decision maker has to find strategies to drive the system so as to minimize some objective function over a certain time horizon. This is a sequential decision making process on which we can state the question of dynamic consistency. As in the previous example, the family of optimization problems is derived from the original one by truncating the dynamics and the cost function (the final time step T remains unchanged in each problem), and strategies are defined relying on the same information structure as in the original problem. In the sequel, random variables will be denoted using bold letters.

3.1. The classical case. Consider a dynamical system characterized by state 3 variables X = (X t ) t=t0,...,T , where X t takes values in X t . The system can be influenced by control variables U = (U t ) t=t0,...,T -1 and by exogenous noise variables W = (W t ) t=t0,...,T (U t and W t taking values in U t and W t respectively). All random variables are defined on a probability space (Ω, A, P). The problem we consider consists in minimizing the expectation of a sum of costs depending on the state, the control and the noise variables over a discrete finite time horizon. The state variable evolves with respect to some dynamics that depend on the current state, noise and control values. The problem starting at t 0 writes:

4 min X,U E T -1 t=t0 L t (X t , U t , W t+1 ) + K (X T ) , (3a) s.t. X t0 given, (3b) X t+1 = f t (X t , U t , W t+1 ) , ∀t = t 0 , . . . , T -1, (3c) U t X t0 , W t1 , . . . , W t , ∀t = t 0 , . . . , T -1. (3d)
Noises that affect the system can be correlated through time. A general approach in optimal control consists in including all necessary information in the variable X so that variables W t1 , . . . , W T are independent through time. At most, one has to include all the past values of the noise variable within the variable X. We hence make the following assumption.

Assumption 1 (Markovian setting). Noises variables X t0 , W t1 , . . . , W T are independent.

Using Assumption 1, it is well known (see [START_REF] Bertsekas | Dynamic Programming and Optimal Control[END_REF] that:

• there is no loss of optimality in looking for the optimal strategy U t at time t as a feedback function depending on the state variable X t , i.e. as a (measurable) function of the form Φ t0,t : X t → U t ; • the optimal strategies Φ * t0,t0 , . . . , Φ * t0,T -1 can be obtained by solving the classical DP equation. Let V t (x) denote the optimal cost when being at time step t with state value x, this equation reads:

V T (x) = K(x), V t (x) = min u E L t (x, u, W t+1 ) + V t+1 f t (x, u, W t+1 ) .
3 The use of the terminology "state" is somewhat abusive until we make Assumption 1. 4 We here use the notations ∼ for "is distributed according to" and for "is measurable with respect to".

We call this case the classical case. It is clear while inspecting the DP equation that optimal strategies Φ * t0,t0 , . . . , Φ * t0,T -1 remain optimal for the subsequent optimization problems: min

X,U E T -1 t=ti L t (X t , U t , W t+1 ) + K (X T ) , (4a) s.t. X ti given, (4b) X t+1 = f t (X t , U t , W t+1 ) , ∀t = t i , . . . , T -1, (4c) U t X ti , W ti+1 , . . . , W t , ∀t = t i , . . . , T -1, (4d)
for every t i = t 1 , . . . , T -1. In other words, these problems are dynamically consistent provided the information variable at time t contains at least the state variable X t . While building an analogy with properties described in the deterministic example in §2, the reader should be aware that the case we consider here is closer to Lemma 1 than to Lemma 3, as we explain now in more details. 3) is that the optimal feedback functions do not depend on the initial condition X t0 . The probability law of X t0 only affects the optimal cost value, but not its arg min. In fact, we are within the same framework as in Example 1. Indeed, Problem (3) can be written as a deterministic distributed optimal control problem involving the probability laws of the state variable, the dynamics of which are given by the so-called Fokker-Planck equation. Let us detail this last formulation (see [START_REF] Witsenhausen | A standard form for sequential stochastic control[END_REF].

The distributed formulation. Another consequence of the previous DP equation for Problem (

Let Ψ t be the space of R-valued functions on X t . Denoting µ t0 the probability law of the first stage state X t0 , and given feedback laws Φ t : X t → U t for every time step t = t 0 , . . . , T -1, we define the operator A Φt t : Ψ t+1 → Ψ t , which is meant to integrate cost functions backwards in time, as 5 :

A Φt t ψ t+1 (•) E (ψ t+1 • f t (•, Φ t (•) , W t+1 )) .
Given a feedback function Φ t and a cost function ψ t+1 ∈ Ψ t+1 , for every x ∈ X t the value (A Φt t ψ t+1 )(x) is the expected value of ψ t+1 (X t+1 ), knowing that X t = x and that feedback Φ t is used. Thanks to a duality argument, the Fokker-Planck equation, which describes the evolution of the state probability law (as driven by the chosen feedback laws Φ t ), is obtained:

µ t+1 = A Φt t ⋆ µ t , with (A Φt t ) ⋆ being the adjoint operator of A Φt t . Next we introduce the operator Λ Φt t : X t → R: Λ Φt t (•) E (L t (•, Φ t (•) , W t+1
)) , which is meant to be the expected cost at time t for each possible state value when feedback function Φ t is applied. Let us define, for every ψ t ∈ Ψ t and every probability law µ t on X t , ψ t , µ t as E (ψ t (X t )) when X t is distributed according to µ t . We can now write a deterministic infinite-dimensional optimal control problem that 5 We do not aim at discussing technical details concerning integrability here. We suppose that operators we introduce are well-defined.

is equivalent to Problem (3):

min Φ,µ T -1 t=t0 Λ Φt t , µ t + K, µ T , s.t. µ t0 given, µ t+1 = A Φt t ⋆ µ t , ∀t = t 0 , . . . , T -1.
Remark 1. An alternative formulation is:

min Φ,ψ ψ t0 , µ t0 , s.t. ψ T = K, ψ t = A Φt t ψ t+1 + Λ Φt t , ∀t = T -1, . . . , t 0 .
This may be called "the backward formulation" since the "state" ψ t (•) follows an affine dynamics which is backward in time, with an initial-only cost function (whereas the previous forward formulation follows a forward linear dynamics with an integral + final cost function). Both formulations are infinite-dimensional linear programming problems which are dual of each other. The functions µ(•) and ψ(•) are the distributed state and/or co-state (according to which one is considered the primal problem) of this distributed deterministic optimal control problem of which Φ is the distributed control.

Probability laws µ t are by definition positive and appear only in a multiplicative manner in the problem. Hence we are in a similar case as Example 1. The main difference is rather technical: since we here have probability laws instead of scalars, we need to apply backwards in time interversion theorems between expectation and minimization in order to prove that the solution of the problem actually does not depend on the initial condition µ t0 . Indeed, suppose that µ T -1 is given at time step T -1. Then the most inner optimization problem reads: min

ΦT -1 Λ ΦT -1 t , µ T -1 + K, µ T , s.t. µ T = A ΦT -1 T -1 ⋆ µ T -1 , which is equivalent to: min ΦT -1 Λ ΦT -1 t + A ΦT -1 T -1 K, µ T -1 . The point is that operators Λ ΦT -1 t + A ΦT -1 T -1 K and µ T -1 both take values in X T -1
and that the minimization has to be done "x by x", so that we are in the case of Example 1 for every x. Therefore, the minimizer does not depend on µ T -1 . For a rigorous proof, one needs several technical assumptions concerning measurability, which we do not intend to discuss in this paper (see Rockafellar and Wets, 1998, Theorem 14.60). The same argument applies recursively to every time step before T -1 so that, at time t 0 , the initial condition µ t0 only influences the optimal cost of the problem, but not the argument of the minimum itself (here, the feedback laws Φ * t0,t ). Hence, following Lemma 1, Problems (4) are naturally time consistent when strategies are searched as feedback functions on X t only. It thus appears that the rather general class of stochastic optimal control problems shaped as Problem (3) is in fact very specific. However, such a property does not remain true when adding new ingredients in the problem, as we show in the next subsection.

Stochastic optimal control with constraints

We now give an example in which the state variable, as defined notably by [START_REF] Whittle | Optimization over time[END_REF], cannot be reduced to variable X t as above. Let us make Problem (3) more complex by adding to the model a probability constraint applying to the final time step T . For instance, we want the system to be in a certain state at the final time step with a given probability:

P (h (X T ) ≥ b) ≤ π.
Such chance constraints can equivalently be modelled as an expectation constraint in the following way:

E 1 {h(XT )≥b} ≤ π,
where 1 A refers to the indicator function of set A. Note however that chance constraints bring important theoretical and numerical difficulties, notably regarding connexity and convexity of the feasible set of controls, even in the static case. The interested reader should refer to the work of [START_REF] Prékopa | Stochastic Programming[END_REF], and to the handbook by Ruszczynski and Shapiro (2003, Ch.5) for mathematical properties and numerical algorithms in Probabilistic Programming (see also [START_REF] Henrion | On the connectedness of probabilistic constraint sets[END_REF][START_REF] Henrion | Convexity of chance constraints with independent random variables[END_REF], for related studies). We do not discuss them here. The difficulty we are interested in is common to both chance and expectation constraints. This is why we concentrate in the sequel on adding an expectation constraint to Problem (3) of the form:

E (g (X T )) ≤ a.
The reader familiar with chance constraints might want to see the level a as a level of probability that one wants to satisfy for a certain event at the final time step.

We now show that when adding such an expectation constraint, the dynamic consistency property falls apart. More precisely, the sequence of SOC problems are not time consistent anymore when using the usual state variable. Nevertheless, we observe that the lack of consistency comes from an inappropriate choice for the state variable. By choosing the appropriate state variable, one regains dynamic consistency.

4.1. Problem setting. We now go back to the constrained formulation and introduce a measurable function g : X T → R and a ∈ R. We consider Problem (3) with the additional final expectation constraint:

E (g (X T )) ≤ a.
The subsequent optimization problems formulated at an initial time t i > t 0 are naturally deduced from this problem. The level a of the expectation constraint remains the same for every problem. One has to be aware that this corresponds to a (naive) modelling choice for the family of optimization problems under consideration. Such a choice is questionable since the perception of the constraint may evolve over time.

Suppose there exists a solution for the problem at t 0 . As previously, we are looking for the optimal control at time t as a feedback function Φ * t0,t depending on the variable X t . The first index t 0 refers to the time step at which the problem is stated, while the second index t refers to the time step at which the decision is taken.

One has to be aware that these solutions now implicitly depend on the initial condition X t0 . Indeed, let µ T be the probability law of X T . Constraint (4) can be written g, µ T ≤ a, so that the equivalent distributed formulation of the initial time problem is: min

Φ,µ T -1 t=t0 Λ Φt t , µ t + K, µ T ,
subject to the Fokker-Planck dynamics:

µ t+1 = A Φt t ⋆ µ t , ∀t = t 0 , . . . , T -1,
µ t0 being given by the initial condition, and the final expectation constraint:

g, µ T ≤ a.
Even though this problem seems linear with respect to variables µ t , the last constraint introduces an additional highly nonlinear term in the cost function, namely:

χ { g,µT ≤a} ,
where χ A stands for the characteristic function 6 of set A. The dynamics are still linear and variables µ t are still positive, but the objective function is not linear with respect to µ T anymore, and therefore not linear with respect to the initial law µ t0 either. Hence there is no reason for feedback laws to be independent of the initial condition as in the case without constraint presented in §3.

Let us now make a remark on this initial condition. Since the information structure is such that the state variable is fully observed, the initial condition is in fact of a deterministic nature: X t0 = x t0 , where x t0 is a given (observed) value of the system state. The probability law of X t0 is accordingly the Dirac function δ xt 0 . 7 The reasoning made for the problem initiated at time t 0 remains true for the subsequent problems starting at time t i : an observation x ti of the state variable X ti becomes available before solving Problem (4), so that its natural initial condition is in fact:

X ti = x ti .
Otherwise stated, the initial state probability law in each optimization problem we consider should correspond to a Dirac function. Note that such a sequence of Dirac functions is not driven by the Fokker-Planck equation, but is in fact associated to some dynamics of the degenerate filter corresponding to this perfect observation scheme. In the sequel, we assume such an initial condition for every problem we consider. Now, according to Lemma 2, the subsequent optimization problems formulated at time t i will be dynamically consistent provided their initial conditions are given by the optimal Fokker-Planck equation:

µ * t0,ti = A Φ * t 0 ,t i-1 ti-1 ⋆ . . . A Φ * t 0 ,t 0 t0 ⋆ µ t0 .
However, except for noise free problems, such a probability law µ * t0,ti is always different from a Dirac function, which is, as already explained, the natural initial condition for the subsequent problem starting at time t i . As a conclusion, the sequence of problems is not time consistent as long as we consider feedback laws Φ t depending on X t only.

6 as defined in convex analysis: χ A (x) = 0 if x ∈ A +∞ otherwise 7 The initial law µt 0 in Problem (3) corresponds to the information available on Xt 0 before Xt 0 is observed, but it seems more reasonable in a practical situation to use all the available information when setting the problem again at each new initial time, and thus to use a Dirac function as the initial condition.

Remark 2 (Joint probability constraints). Rather than P (g (X T ) ≥ b) ≤ a, let us consider a more general chance constraint of the form:

P (g t (X t ) ≥ b t , ∀t = t 1 , . . . , T ) ≤ a.
This last constraint can be modelled, like the previous one, through an expectation constraint by introducing a new binary state variable: 4.2. Back to time consistency. We now show that time consistency can be recovered provided we choose the right state variable on which to base decisions. We hence establish a link between time consistency of a family of optimization problems and the notion of state variable.

Y t0 = 1, Y t+1 = Y t × 1 {gt+1(Xt+1
We claim that a better-suited state variable for the family of problems with final time expectation constraint introduced above is the probability law of the variable X. Let us denote by V t (µ t ) the optimal cost of the problem starting at time t with initial condition µ t . Using notations of the distributed formulation of a SOC problem, one can write a DP equation depending on the probability laws µ on X :

V T (µ) = K, µ if g, µ ≤ a, +∞ otherwise,
and, for every t = t 0 , . . . , T -1 and every probability law µ on X :

V t (µ) = min Φt Λ Φt t , µ + V t+1 A Φt t ⋆ µ .
The context is similar to the one of the deterministic example of §2, and Lemma 3 states that solving the deterministic infinite-dimensional problem associated with the constrained problem leads to time consistency provided DP is used. For the problem under consideration, we thus obtain optimal feedback functions Φ t which depend on the probability laws µ t . Otherwise stated, the family of constrained problems introduced in S4.1 is time consistent provided one looks for strategies as feedback functions depending on both the variable X t and the probability law of X t . Naturally, this DP equation is rather conceptual. The resolution of such an equation is intractable in practice since probability laws µ t are infinite-dimensional objects.

Conclusion

We informally introduced a notion of time consistency of a sequence of decisionmaking problems, which basically requires that plans that are made from the very first time remain optimal if one rewrites optimization problems at subsequent time steps. We show that, for several classes of optimal control problems, this concept is not new and can be directly linked with the notion of state variable, which is the minimal information one must use to be able to take the optimal decision.

We show that, in general, feedback laws have to depend on the probability law of the usual state variable for Stochastic Optimal Control problems to be time consistent. This is necessary, for example, when the model contains expectation or chance constraints.

Future works will focus on three main directions. The first concern will be to better formalize the state notion in the vein of the works by [START_REF] Witsenhausen | On information structures, feedback and causality[END_REF]

  )≥bt+1} , ∀t = t 0 , . . . , T -1, and considering constraint E (Y T ) ≤ a.

wheret i + 1 = t i+1

1973) and [START_REF] Whittle | Optimization over time[END_REF]. The second will be to establish the link with the literature concerning risk measures, in particular the work by [START_REF] Ruszczynski | Risk-averse dynamic programming for markov decision processes[END_REF]. Finally, the last DP equations we introduced are in general intractable. In a forthcoming paper, we will provide a way to get back to a finite-dimensional information variable, which makes a resolution by DP tractable. E-mail address: delara@cermics.enpc.fr


Claude Colomer

Luis A Olivos-Oré

Anne Vincent

Michael Mcintosh

Antonio R Artalejo

Nathalie C Guérineau
email: nathalie.guerineau@univ-angers.fr

J Michael Mcintosh

Drs M G Desarménien

Norbert Chauvet

P Didier

A Carrette

E Galibert

D Haddou

Functional characterization of alpha9-containing cholinergic nicotinic receptors in the rat adrenal medulla: implication in stress-induced functional plasticity

Keywords: synaptic cholinergic neurotransmission, chromaffin cell synapses, nicotinic receptors, stress, cold exposure, rat acute adrenal slices

Introduction

Catecholamines are one of the primary mediators for many of the physiological consequences of the organism's response to stressors. Once delivered into the blood circulation in response to stress, these mediators exert multiple actions enabling an organism to cope with a changing environment and to respond efficiently to a threat for its survival. Since chromaffin cells are the main source of circulating epinephrine, it is of interest to investigate how they ensure increased secretion upon stressful situations. Catecholamine secretion is regulated by both synaptic release of acetylcholine from splanchnic nerve terminals synapsing onto chromaffin cells [START_REF] Douglas | Stimulus-secretion coupling: the concept and clues from chromaffin and other cells[END_REF][START_REF] Wakade | Studies on secretion of catecholamines evoked by acetylcholine or transmural stimulation of the rat adrenal gland[END_REF] and local gap junction-mediated communication between chromaffin cells [START_REF] Martin | Gap junctions mediate electrical signaling and ensuing cytosolic Ca 2+ increases between chromaffin cells in adrenal slices: a role in catecholamine release[END_REF][START_REF] Colomer | Revisiting the stimulus-secretion coupling in the adrenal medulla: role of gap junction-mediated intercellular communication[END_REF]. It is noteworthy that the cholinergic synaptic activity exerts a tonic inhibitory control on gap junctional coupling [START_REF] Martin | Evidence for long-lasting cholinergic control of gap junctional communication between adrenal chromaffin cells[END_REF]. Additionally, the two commands are upregulated in stressed rats (Colomer et al., 2008a). Whilst the mechanisms underlying upregulation of junctional coupling have been investigated (Colomer et al., 2008b), nothing is known regarding the increased neurotransmission.

At rat splanchnic nerve-chromaffin cell synapses, postsynaptic nicotinic receptors (nAChRs) dominantly contribute to acetylcholine-mediated excitatory responses and ensuing secretion [START_REF] Douglas | Mechanism of nicotinic action at the adrenal medulla: calcium as a link in stimulus-secretion coupling[END_REF]Wakade and Wakade, 1983). Whilst most nAChRs contain α and β subunits, some contain only α subunits, as examplified by α7, α9 and α9/α10 nAChRs. Multiple α and β subunits have been identified in rat chromaffin cells (Di [START_REF] Angelantonio | Molecular biology and electrophysiology of neuronal nicotinic receptors of rat chromaffin cells[END_REF][START_REF] Sala | Nicotinic acetylcholine receptors of adrenal chromaffin cells[END_REF]. Although the α3 subunit constitutes a major component of nAChRs activated in response to synaptically released acetylcholine [START_REF] Criado | Primary structure of an agonist binding subunit of the nicotinic acetylcholine receptor from bovine adrenal chromaffin cells[END_REF][START_REF] Nooney | Inhibition by cyclothiazide of neuronal nicotinic responses in bovine chromaffin cells[END_REF][START_REF] Barbara | Quantal release at a neuronal nicotinic synapse from rat adrenal gland[END_REF], α7-built receptors are also involved in acetylcholine-mediated responses [START_REF] López | Unmasking the functions of the chromaffin cell alpha7 nicotinic receptor by using short pulses of acetylcholine and selective blockers[END_REF][START_REF] Martin | Evidence for long-lasting cholinergic control of gap junctional communication between adrenal chromaffin cells[END_REF][START_REF] Martin | Agrin mediates a rapid switch from electrical coupling to chemical neurotransmission during synaptogenesis[END_REF].

The expression of α9 and α10 subunits in rat chromaffin cells (L. A. Olivos-Oré, L. Solís, C. Montiel and A. R. Artalejo, personal communication) extends the tissular distribution of α9/α10 nAChRs to a neuroendocrine tissue and raises the question of their role. α9/α10 nAChRs display an unusual pharmacological profile as they can be activated by both nicotinic and muscarinic agonists [START_REF] Verbitsky | Mixed nicotinic-muscarinic properties of the alpha9 nicotinic cholinergic receptor[END_REF] and are highly permeable to Ca 2+ [START_REF] Katz | High calcium permeability and calcium block of the alpha9 nicotinic acetylcholine receptor[END_REF]. This prompted us to hypothesize that they may play unexpected roles in stimulussecretion coupling in the adrenal medulla. In particular, whether they contribute to synaptic neurotransmission and whether they are modulated upon increased synaptic activity remains unknown.

To address the functional role of α9-containing nAChRs in the adrenomedullary tissue, we took advantage of its potent and selective blockade by the α-conotoxin RgIA (Ellison et al., 2006;[START_REF] Vincler | Molecular mechanism for analgesia involving specific antagonism of alpha9alpha10 nicotinic acetylcholine receptors[END_REF][START_REF] Olivera | Subtype-selective conopeptides targeted to nicotinic receptors: Concerted discovery and biomedical applications[END_REF][START_REF] Pérez | Molecular modeling of the alpha9alpha10 nicotinic acetylcholine receptor subtype[END_REF]. Our results obtained in rat acute adrenal slices show that α9-containing nAChRs are involved in the excitatory neurotransmission at the splanchnic nerve-chromaffin cell synapse and in the tonic inhibitory control exerted by cholinergic activity on gap junctional coupling. In addition, α9 subunit expression level is upregulated in cold stressed rats, making α9-containing nAChR a major determinant in acetylcholine-induced current.

Material and methods

All procedures in this study conformed to the animal welfare guidelines of the European Community and were approved by the French Ministry of Agriculture (authorization no.

34.247).

Adrenal slice preparation

Acute slices were prepared from 8-to 12-week-old Wistar male rats (Janvier, Le Genest-St-Isle, France) as reported previously [START_REF] Martin | Gap junctions mediate electrical signaling and ensuing cytosolic Ca 2+ increases between chromaffin cells in adrenal slices: a role in catecholamine release[END_REF]. After removal, the glands were kept in ice-cold saline for 2 min. A gland was next glued onto an agarose cube and transferred to the stage of a vibratome (DTK-1000, D.S.K, Dosaka EM CO. LTD, Kyoto, Japan). Slices of 200 μm thickness were cut with a razor blade and transferred to a storage chamber maintained at 37°C, containing Ringer's saline (in mM): 125 NaCl, 2.5 KCl, 2 CaCl 2 , 1 MgCl 2 , 1.25 NaH 2 PO 4 , 26 NaHCO 3 , 12 glucose and buffered to pH 7.4. The saline was continuously bubbled with carbogen (95% O 2 / 5% C0 2 ).

Stress paradigm

In some experiments, rats were subjected to a cold stress paradigm (Colomer et al., 2008a(Colomer et al., , 2008b)). Upon entrance to the colony, rats were allowed to acclimatise to the animal facility for a minimum of 7 days before use. They were housed initially three per cage and then singly housed during the conduct of the experiments. Rats were randomly assigned to a coldexposed or control group. Cold stressed rats were kept in clear plastic cages with bedding and continuously exposed to an ambient temperature of 4°C for 5 days in a temperature-controlled cold chamber. Control rats were housed in similar conditions but at 22°C. For each series of experiments, and to avoid an additional stress due to isolation, we made sure that at least two rats underwent the same protocol (control or cold exposure) at the same time. The rooms were maintained on a 12-hour light/dark cycle (light on from 8 a.m. to 8 p.m.). Food and water were available ad libitum.

Electrophysiology

All experiments were performed in the whole-cell configuration of the patch-clamp technique [START_REF] Hamill | Improved patch-clamp techniques for high-resolution current recording from cells and cell-free membrane patches[END_REF]. Patch pipettes were pulled to a resistance of 5-8 MΩ from borosilicate glass and filled with the following internal solution (in mM): 140 potassium-gluconate, 2 MgCl 2 , 1.1 EGTA, 5 Hepes, that was titrated to pH 7.2 with KOH. Adrenal slices were transferred to a recording chamber attached to the stage of an upright microscope (Axioskop FS, Zeiss, Le Pecq, France) and continuously superfused with Ringer's saline at 34°C. Spontaneous EPSCs (sEPSCs) were recorded in chromaffin cells voltage-clamped at -80 mV using an EPC-9 patch-clamp amplifier (HEKA Electronik, Lambrecht/Pfalz, Germany) and were filtered at 1 kHz. Signals were acquired and analyzed using Pulse and PulseFit softwares (version 8.50,HEKA Electronik). In some cells, a quantal analysis of sEPSCs was performed.

Note that sEPSCs are independent of presynaptic action potentials at the splanchnic nervechromaffin cell synapse [START_REF] Barbara | Quantal release at a neuronal nicotinic synapse from rat adrenal gland[END_REF][START_REF] Kajiwara | Functional organization of chromaffin cells and cholinergic synaptic transmission in rat adrenal medulla[END_REF]. sEPSCs were analysed by using Clampfit 9.0 (Axon Instruments, Inc., Foster city, CA). Only single events were selected for construction of amplitude histograms. These histograms were then inspected for the presence of peaks and a corresponding number of Gaussians was then fitted by nonlinear regression using Igor Pro 5.04.8 (Wavemetrics Inc., Lake Oswego, OR). Quantal size was estimated from the mean value of the first Gaussian curve fitted to the amplitude distribution histogram.

Dye transfer assay

The fluorescent dye LY (Lucifer yellow-CH, lithium salt, 0.5 mM in the above-mentioned internal solution) was introduced into chromaffin cells using patch pipettes. Cells were viewed with a 63x 0.9 NA achroplan water immersion objective (Zeiss). Dye transfer between gap junction-coupled cells was visualized with a real-time confocal laser scanning microscope equipped with an Ar/Kr laser (Odyssey XL with InterVision 1.5.1 software, Noran Instruments Inc., Middleton, WI). LY diffusion was imaged using the 488 nm-centered wavelength of the laser beam. The largest detection slit (100 μm) of the confocal microscope was used, giving images with a 3.1 μm axial resolution. The extent of LY diffusion was estimated by counting the number of neighboring cells that received dye in 30 min. The probability of LY diffusion was expressed as a ratio corresponding to the number of injected cells that show dye transfer to adjacent cells over the total number of injected cells.

Immunostaining

To process for immunolabeling, the adrenal glands from control and cold stressed rats were removed and fixed by immersion in 4% PFA in 0.1 M phosphate buffer (4 hours at RT). They were then cut using a vibratome (Leica VT1000S, Leica Microsystems, Rueil-Malmaison, France) into 50 μm-thick sections. Sections were incubated 48h at 4°C with a goat polyclonal antibody raised against α9 nAChR (1:250, Santa Cruz Biotechnology, Inc, Heidelberg, Germany) and a mouse monoclonal antibody against the presynaptic protein synaptophysin Primary and secondary antibodies were diluted in PBS containing 2% BSA and 0.1% Triton X100. Stained sections were imaged with a Biorad MRC 1024 confocal laser scanning microscope equipped with a krypton-argon mixed gas laser emitting at 488 and 568 nm. The specificity of the commercial antibodies has been assessed by absorption tests. Negative controls were carried out by omitting primary antibodies. Quantitative analysis of colocalization between synaptophysin and α9 nAChR was performed using Image J software, as previously described [START_REF] Chauvet | Distribution of p120 catenin during rat brain development: potential role in regulation of cadherin-mediated adhesion and actin cytoskeleton organization[END_REF]. Briefly, a fixed threshold for the fluorescent intensity was set to remove background and include only labeled puncta. The thresholded images were then converted to binary images, pseudocolored and the lookup table was inverted so that binary images showed a green labeling for α9 nAChRs and a red labeling for synaptophysin-positive presynaptic terminals. After superimposition of binary images, synaptophysin puncta co-distributed with α9 nAChRs were counted and results were expressed as a percentage of co-localization of synaptophysin staining over α9 nAChR staining.

Western blotting

After decapsulation of the adrenal gland, medullary tissue was separated from the cortex. To remove remaining cortical cells, samples were incubated for 10 min at 0-4°C in Ringer's saline containing 1 mg/ml collagenase type I. Membrane proteins were then isolated using lysis buffer (10 mM Tris-HCl, pH 7.4, 5 mM EDTA, 1 mM sodium orthovanadate and 10 mM NaF as phosphatase inhibitors, 10 mM β-glycerophosphate and 1% Triton X-100), supplemented with Mini complete protease inhibitors (Roche Applied Science, Laval, Quebec). Proteins were centrifuged once for 5 min at 5,000 rpm and supernatants were collected. Proteins were centrifuged for 30 min at 13,200 rpm and concentrations were determinated using the Dc Protein Assay Kit (Bio-Rad Laboratories, Hercules, CA). Protein samples (40 µg) were heated for 5 min at 95°C and separated on a 10% polyacrylamide gel in parallel with molecular weight markers. Electrophoresed proteins were transferred onto a nitrocellulose membrane (80 V, 75 min) using a semi-dry blotting system (Bio-rad, Hercules, CA). Blots were then blocked with 10% Blocking Reagent (BM Chemoluminescence Blotting Substrate kit, Roche Applied Science) in TBS (pH 7.4, 0.1% Tween 20) for 1 h at room temperature with gentle agitation. Blots were then incubated with the same α9 nAChR polyclonal antibody as that used for immunofluorescence in TBS-Tween 0.1% containing 10% Blocking Reagent at 4°C overnight. Following washout, blots were incubated with a peroxydase conjugated-secondary antibody for 1 h at room temperature. This was followed by 1 min incubation in BM Chemoluminescence Blotting substrate. Labeled blots were then exposed to Fujifilm Medical X-Ray Film to visualize antibody binding. To ensure equal loading of protein samples, blots were stripped of the α9 nAChR antibody and reprobed with an actin-specific monoclonal antibody (actin, pan Ab-5, clone ACTN05, 1:1000, Interchim, Montluçon, France). Intensities of α9 nAChR bands were normalized to those of actin and quantified using ImageJ software.

Quantification of mRNA expression levels by real-time PCR

Total RNA was extracted from macrodissected adrenal medulla and treated with DNase I using the RNeasy Micro extraction kit (Qiagen, Courtaboeuf, France). RNA (1 μg) was first reverse transcribed using Superscript III reverse transcriptase (Invitrogen) and 250 ng of random hexamer (Amersham Biosciences Europe, Orsay, France) in a final volume of 20 μl.

Real-time PCR analyses of α3nAChR, α7nAChR, α9nAChR and housekeeping genes were performed using SYBR Green PCR master mix (Applied Biosystems, Foster City, CA) with 1:10 of the reverse-transcription reaction, and were carried out on an ABI 7500 Sequence Detector (Applied Biosystems). Primer sequences for rat α3nAChR, rat α7nAChR, rat α9nAChR and housekeeping genes are given in Table 1. The concentration of the primers used was 300 nM for α3nAChR, α7nAChR, α9nAChR and housekeeping genes. After an initial denaturation step for 10 min at 95°C, the thermal cycling conditions were 40 cycles at 95°C for 15 s and 60°C for 1 min. Each sample value was determined from triplicate measurements. The selection of appropriate housekeeping genes was performed with geNorm [START_REF] Vandesompele | Accurate normalization of real-time quantitative RT-PCR data by geometric averaging of multiple internal control genes[END_REF]. Expression of α3, α7 and α9 nAChR transcripts was normalized to the geometric mean of the expression levels of three housekeeping genes, Hprt (hypoxanthine-guanine phosphoribosyltransferase), GAPDH (glyceraldehyde-3-phosphate dehydrogenase) and Gus (Glucuronidase), according to the formula Cx/geometric mean (R1, R2, R3) = 2 -(Ct[Cx]-arithmetic mean [Ct(R1),Ct(R2),Ct(R3)]) , where Ct is the threshold cycle, and R1, R2, R3 are the three reference genes.

Solutions and chemicals

The α3-built nicotinic receptor blocker hexamethonium (hexamethonium chloride), Lucifer yellow (LY), collagenase type I, acetylcholine chloride and the gap junction blocker carbenoxolone were purchased from Sigma. Primers for qPCR were purchased from MWG-Biotech AG (Ebersberg, Germany). The α-RgIA conotoxin was synthesized by previously described methods [START_REF] Cartier | A new alphaconotoxin which targets alpha3beta2 nicotinic acetylcholine receptors[END_REF]. To investigate the blocking effect of hexamethonium and α-RgIA on acetylcholine (ACh)-evoked inward current, the pharmacological blockers were continuously pressure-ejected (during 4 min before ACh stimulation) from an extracellular micropipette (tip diameter 2-5 µm) that was positioned in the vicinity of the recorded chromaffin cell. Cells were briefly stimulated (1 s) by the cholinergic agonist ACh that was also pressure-applied. To examine the effect of α-RgIA on sEPSCs, the toxin was pressure-applied for 4 min at the vicinity of the voltage-clamped cell before recording of synaptic currents.

Statistics

Numerical data are expressed as the mean ± SEM. Differences between groups were assessed by using the non-parametric Mann-Whitney U test. Unpaired or paired Student's t-test was used to compare means when appropriate. Percentages were compared using a contingency table and the chi-square test. Differences with P<0.05 were considered significant.

Results

In the absence of specific cholinergic agonists acting at α9 subunit-built nAChR channels, the functional role of these nicotinic receptors in the rat adrenal medulla was assessed by using a recently discovered toxin isolated from the Western Atlantic species Conus regius, αconotoxin RgIA (α-RgIA). α-RgIA specifically and potently antagonizes α9-and α9/α10built nAChRs [START_REF] Ellison | Alpha-RgIA: a novel conotoxin that specifically and potently blocks the alpha9alpha10 nAChR[END_REF][START_REF] Ellison | Alpha-RgIA, a novel conotoxin that blocks the alpha9alpha10 nAChR: structure and identification of key receptor-binding residues[END_REF]. In all experiments, we used the toxin at a concentration that is effective to block rat α9-containing nAChR channels and without any effect on the closely related α7-built nAChRs [START_REF] Ellison | Alpha-RgIA: a novel conotoxin that specifically and potently blocks the alpha9alpha10 nAChR[END_REF][START_REF] Vincler | Molecular mechanism for analgesia involving specific antagonism of alpha9alpha10 nicotinic acetylcholine receptors[END_REF].

α9-containing nAChRs are involved in synaptic neurotransmission between splanchnic nerve terminals and chromaffin cells

To determine whether α9-containing nAChRs contribute to cholinergic synaptic transmission at the splanchnic nerve-chromaffin cell junction, spontaneous excitatory post-synaptic currents (sEPSCs) were recorded in whole-cell voltage-clamped chromaffin cells, in the absence or in the presence of the α-RgIA conotoxin (Figure 1A). The effect of α-RgIA on synaptic events was examined after a 4-min continuous application of the toxin. α-RgIA (200 nM) led to a decreased synaptic activity (right panel) when compared with control condition (left panel). This result strongly suggests that α9-containing nAChRs are activated in response to in situ synaptically released ACh. To determine whether α9 nAChRs have a synaptic distribution, their co-localization with the 38kDa presynaptic vesicle protein synaptophysin (Wiedenmann and Franke, 1985) was assessed using double immunostaining.

As illustrated in figure 1B, labeling of α9 nAChRs matches closely that of synaptophysin, supporting the hypothesis of a synaptic/perisynaptic localization. Altogether, these results consistently fit with an activation of α9-containing nAChR channels upon ACh release in the synaptic cleft and represent the first documentation of a functional role of α9-containing nAChRs in the adrenal medullary tissue. This finding also extends available data on the expression of nAChR subtypes at the cholinergic synapse between splanchnic nerve endings and chromaffin cells and their activation in response to synaptically release ACh.

As seen in figure 1, both sEPSC frequency and amplitude were affected by the toxin α-RgIA. A more detailed analysis is presented in figures 2, 3 and 4. In the presence of α-RgIA, sEPSC frequency was significantly decreased (0.36 ± 0.17 Hz, n = 17 in control conditions versus 0.04 ± 0.03 Hz, n = 17 in the presence of α-RgIA, P<0.05, Figure 2A). On average, α-RgIA reduced sEPSC frequency by 62 ± 8% (n = 17). α-RgIA-induced decrease in sEPSC frequency was reversible after 5 min washout (in 9 out of the 9 cells tested for reversibility, Figure 2B, P<0.05). Not only sEPSC frequency was affected by α-RgIA, but also sEPSC amplitude although to a lesser extent (Figure 3). In the presence of α-RgIA, sEPSC amplitude was significantly decreased (147 ± 29 pA, n = 17 in control conditions versus 100 ± 26 pA, n = 17 in the presence of α-RgIA, P<0.05, Figure 3A). On average, α-RgIA reduced sEPSC amplitude by about 36% (n = 17). As illustrated by the plot of sEPSC amplitude variance (Figure 3B), α-RgIA reduced the amplitude variance value, supporting the finding that the toxin acts by homogeneizing sEPSC amplitudes. Accordingly, the distribution of cumulative probability plotted from sEPSC amplitude recorded in one representative cell exhibited a bimodal distribution including both low and high amplitude (over 400 pA) events in control condition, and a decreased proportion of these high amplitude events in the presence of α-RgIA (Figure 3C). To go further, we next performed a quantal analysis of sEPSCs (Figure 4).

In control saline, the mean quantal size of sEPSCs was 20 ± 2.4 pA (n = 5). This value does not differ from those previously reported [START_REF] Barbara | Quantal release at a neuronal nicotinic synapse from rat adrenal gland[END_REF][START_REF] Kajiwara | Functional organization of chromaffin cells and cholinergic synaptic transmission in rat adrenal medulla[END_REF].

As shown in figure 4Ab, α-RgIA diminished the relative contribution of larger events to amplitude histograms, leading to a switch from a bimodal to an unimodal amplitude distribution. This effect is consistent with a decrease of release probability at splanchnic nerve terminals. Additionally, in α-RgIA-containing saline, the quantal size was reduced (Figure 4A), as evidenced by a leftward shift of the first Gaussian peak. This is consistent with an action on postsynaptic α9-containing nAChRs receptors. This effect was observed in 4 out of 5 recorded cells (Figure 4B, mean decrease of 34 ± 6.7%; n = 4). We noticed that the effect of α-RgIA on sEPSC quantal size and sEPSC frequency differed from one cell to another. In the majority of cells, α-RgIA reduced both the quantal size and the frequency, whereas in others it reduced either one or the other. This suggests that the toxin may affect independently the frequency and the quantal size, implying separate modulatory effects of presynaptic and postsynaptic α9-containing nAChRs.

α9-containing nAChRs tonically inhibit gap junction-mediated cell-to-cell communication

As previously reported [START_REF] Martin | Evidence for long-lasting cholinergic control of gap junctional communication between adrenal chromaffin cells[END_REF], nAChRs exert a tonic inhibitory control on gap junctional communication between chromaffin cells. To investigate the ability of α9containing nAChRs to modulate gap junctional coupling, we imaged Lucifer yellow diffusion by real-time confocal microscopy during 30 min with an image acquisition every 5 min (Figure 5). A 30 min bath-application of α-RgIA significantly increased the probability of LY diffusion from the patched cells to 1-2 adjacent cells (P<0.05 for time ≥ 15 min). By contrast, in control slices, the number of fluorescent cells did not change during the recording time and was preferentially restricted to the patched cells, as recently reported (Colomer et al., 2008b).

As expected for a gap junction-mediated effect, α-RgIA did not affect LY diffusion when applied after 15 min incubation in the presence of the uncoupling agent carbenoxolone [START_REF] Ishimatsu | Synchronous activity in locus coeruleus results from dendritic interactions in pericoerulear regions[END_REF]. Altogether, these results show that α9-containing nAChRs are involved in the tonic inhibitory control exerted by cholinergic signaling on gap junctionmediated cell-cell communication in the adrenal medulla, as previously reported for α3 and α7-built nAChRs [START_REF] Martin | Evidence for long-lasting cholinergic control of gap junctional communication between adrenal chromaffin cells[END_REF].

Altogether, our findings showing the contribution of α9-containing nAChRs to synaptic transmission and to regulation of gap junctional communication strengthen the hypothesis that these nAChRs may be functionally relevant for stimulus-secretion coupling in the adrenal medulla.

Upregulation of α9 nAChR channel protein expression level in cold stressed rats

Our finding showing the involvement of α9-containing nAChRs in synaptic transmission between splanchnic nerve endings and chromaffin cells prompted us to investigate the expression level of these receptors in a condition associated with an increased synaptic transmission. Besides its well-described effects on expression of genes and proteins involved in the catecholamine biosynthesis [START_REF] Baruchin | Effects of cold exposure on rat adrenal tyrosine hydroxylase: an analysis of RNA, protein, enzyme activity, and cofactor levels[END_REF][START_REF] Kvetnansky | Stress-induced changes in tyrosine hydroxylase and other catecholamine biosynthetic enzymes[END_REF][START_REF] Sabban | Stress-triggered activation of gene expression in catecholaminergic systems: dynamics of transcriptional events[END_REF], cold stress also triggers long lasting anatomical and functional remodeling of intercellular communication in the rat adrenal medulla. In particular, synaptic activity is upregulated (Colomer et al., 2008a). Do α9-containing nAChRs play a role in cold stress-induced increased synaptic activity? Because nAChR function can be regulated at the transcriptional, translational and post-translational level [START_REF] Laufer | Activity-dependent regulation of gene expression in muscle and neuronal cells[END_REF][START_REF] Fornasari | Transcriptional regulation of neuronal nicotinic receptors subunit genes[END_REF][START_REF] Albuquerque | Mammalian nicotinic acetylcholine receptors: from structure to function[END_REF], we first examined the expression level of both α9 nAChR protein and transcript in cold exposed rats.

The membrane content of α9 nAChRs was measured by western blot. As illustrated in figure 6A, α9 nAChRs protein level was upregulated in stressed rats. The level of α9 nAChR expression being normalized to that of actin, the quantitative analysis showed a significant upregulation (1.8-fold increase) of α9-built nAChRs in cold stressed rats as compared to unstressed animals (mean ratio α9 nAChR/actin of 0.45 ± 0.04, n = 6 for control rats versus 0.82 ± 0.05, n = 6 for cold exposed rats, P<0.05).

As a first step towards the characterization of the mechanisms involved in increased α9 nAChR expression in cold exposed rats, we examined by real-time PCR whether the expression level of its transcript was modified. Total RNA was extracted from macrodissected adrenal medulla from 13 control and 12 cold exposed rats. Expression of nAChR subtype mRNA was normalized to the geometric mean of the expression levels of Hprt, GAPDH and Gus mRNA. α9 nAChR mRNA relative expression level was 5.2-fold higher in stressed rats (23.6 ± 7.9 versus 4.5 ± 1.2 in stressed and control rats, respectively, P<0.05, Figure 6Ba). Interestingly, no change was observed for α3-and α7-built nAChR transcripts (relative expression 249 ± 48 versus 186 ± 51 for stressed and control rats, respectively, P>0.05 for α3 nAChRs and 159 ± 18 versus 118 ± 16 for stressed and control rats, respectively, P>0.05 for α7 nAChRs, Figure 6Bb).

Major contribution of α9-containing nAChRs in mediating acetylcholine-evoked inward currents in cold stressed rats

What could be the functional consequence of the upregulation of α9 nAChR subunit in cold stressed rats? We addressed this issue by investigating the effects of α-RgIA on acetylcholine-evoked inward current in acute slices from unstressed and cold stressed rats (Figure 7). Chromaffin cells were voltage-clamped at -40 mV and briefly stimulated by pressure-applied acetylcholine (ACh, 100 µM, 1 s). The recorded cell was then bathed during 4 min in saline, or α-RgIA, or hexamethonium, or a mixed solution containing the two drugs.

The cell was then re-stimulated with ACh. Density of ACh-triggered inward currents was compared between the different perfusing conditions. The reversibility of the observed effect was examined 5 min later upon a third ACh application. In the absence of a nicotinic receptor blocker, ACh-induced currents did not rundown, either in unstressed (left panel, upper trace) or in cold stressed (right panel, upper trace) rats. In addition, the current density did not significantly differ between control and stressed animals (30.0 ± 1.6 pA/pF, n = 52 versus 33.4 ± 1.0 pA/pF, n = 57 for control and stressed rats, respectively, P>0.05, data not shown).

As expected for nicotinic receptor blockers, both α-RgIA (200 nM) and hexamethonium ( 200µM) reduced ACh-induced inward current (Figures 7A for raw data and Figure 7B for pooled data). However, their blocking effect significantly differed between control and stressed rats, pointing to a differential contribution of α9-containing nAChRs and other nAChRs to AChmediated currents. α-RgIA (200 nM) reduced ACh currents in stressed rats by 75.5% (n = 26) while reducing them by only 39.3% (n = 22) in unstressed rats (P<0.05, Figure 7C).

Conversely, hexamethonium (200 µM) mainly reduced ACh-evoked currents in control rats (76.2% reduction, n = 11) but decreased them by only 44.6 % (n = 13, P<0.05, Figure 7C) in cold stress rats. When applied together, α-RgIA and hexamethonium had comparable effects on cholinergic currents (90.8%, n = 6 versus 90.5%, n = 12, in unstressed and stressed rats, respectively, P>0.05, Figure 7C). Note that the blocking effect was not complete, indicating that other nAChRs are likely involved in the current generation. Altogether, these results show a major contribution of α9-containing nAChR channels in ACh-evoked current in cold stressed rats.

To go further, we next compared the kinetics of α-RgIA-and hexamethonium-induced blocking effect in both control and cold stressed rats. ACh-evoked current density was calculated 1, 4 and 5 min after nicotinic receptor antagonist application (Figure 8). In control rats, the blocking effect of α-RgIA was complete after 1 min, while it took 4 min in cold stressed rats. Regarding hexamethonium, its blocking effect on ACh-evoked current was complete within 4 min in control animals and was still under process after 5 min in stressed rats. Assuming that receptor antagonists sequentially reach their extrasynaptic and synaptic targets, blocking kinetics may be used as indicator of synaptic and extrasynaptic nAChRs localization. Our results are in favor of a preferential synaptic localization of α9-containing nAChRs versus α3-built nAChRs in cold stressed rats. Conversely, in control rats, α9containing nAChRs would be preferentially extrasynaptic and α3 nAChRs would be the dominant nAChR channels expressed at the splanchnic nerve-chromaffin cell synapse. To test the hypothesis that α9-containing nAChRs preferentially localize close to the synaptic sites in stressed rats, a dual immunodetection of synaptophysin and α9-containing nAChRs was carried out in stressed and unstressed rats. The percentage of co-distribution of synaptophysin over α9-containing nAChRs was assessed quantitatively by using confocal microscopy, as previously decribed [START_REF] Chauvet | Distribution of p120 catenin during rat brain development: potential role in regulation of cadherin-mediated adhesion and actin cytoskeleton organization[END_REF]. As illustrated in figure 9, the co-distribution of synaptophysin with α9-containing nAChRs was significantly higher in cold stressed rats, as compared with controls (40.5 ± 4.1%, n = 12 versus 23.9 ± 3.9, n = 12, respectively, P<0.05).

Altogether, these results suggest a recruitment of α9-containing nAChRs at synaptic sites in cold stressed rats.

Discussion

This study documents for the first time functional roles of α9-containing nAChR channels in the rat adrenal medulla. We report that i) these receptors are activated upon synaptic transmission between splanchnic nerve endings and chromaffin cells and ii) they tonically inhibit gap junctional coupling between chromaffin cells. Additionally, our findings provide evidences that α9 nAChR subunit is upregulated in cold stressed rats, consistent with a dominant contribution of α9-containing nAChRs to ACh-evoked currents.

Activation of α9-containing nAChRs in response to synaptic release of ACh

Both electrophysiological data showing reduced sEPSC amplitude and frequency in the presence of α-RgIA and the distribution of α9 nAChRs close to the synaptic marker synaptophysin suggest that α9 nAChR channels contribute to cholinergic synaptic transmission. Since α10 subunit conferes functionality to α9 nAChRs [START_REF] Sgard | A novel human nicotinic receptor subunit, alpha10, that confers functionality to the alpha9-subunit[END_REF][START_REF] Vetter | The alpha10 nicotinic acetylcholine receptor subunit is required for normal synaptic function and integrity of the olivocochlear system[END_REF], it is likely that the functional nAChRs are composed of both α9 and α10 subunits. Taking into consideration i) the apparent affinity of α9 and α9/α10 nAChRs for ACh (EC 50 of ~27 µM and ~30 µM, respectively, [START_REF] Sgard | A novel human nicotinic receptor subunit, alpha10, that confers functionality to the alpha9-subunit[END_REF] and ii) the concentration of ACh in the synaptic cleft (up to 1 mM during quantal response, [START_REF] Matthews-Bellinger | Distribution of acetylcholine receptors at frog neuromuscular junctions with a discussion of some physiological implications[END_REF], activation of α9-containing nAChRs in response to synaptically released ACh is highly plausible. In this context, our report extends previous contributions showing the involvement of α9-containing nAChRs receptors in neuronal synaptic transmission. Indeed, they mediate cholinergic synaptic transmission between olivocochlear fibers and cochlear outer hair cells [START_REF] Elgoyhen | Alpha 9: an acetylcholine receptor with novel pharmacological properties expressed in rat cochlear hair cells[END_REF][START_REF] Elgoyhen | alpha10: a determinant of nicotinic cholinergic receptor function in mammalian vestibular and cochlear mechanosensory hair cells[END_REF][START_REF] Vetter | The alpha10 nicotinic acetylcholine receptor subunit is required for normal synaptic function and integrity of the olivocochlear system[END_REF] and are involved in synaptogenesis [START_REF] Vetter | Role of alpha9 nicotinic ACh receptor subunits in the development and function of cochlear efferent innervation[END_REF].

Regarding cholinergic neurotransmission at rat splanchnic nerve-chromaffin cell synapses, we provide evidence that, in addition to α3 and α7 nAChRs [START_REF] Barbara | Quantal release at a neuronal nicotinic synapse from rat adrenal gland[END_REF][START_REF] Martin | Evidence for long-lasting cholinergic control of gap junctional communication between adrenal chromaffin cells[END_REF], nAChRs built by assembly of α9 and/or α9/α10 subunits are activated during synaptic release of ACh. Additionally, our data describing an α-RgIAinduced decrease of both sEPSC frequency and amplitude fit with the presence of synapses containing pure α9-containing nAChRs and synapses containing a mixture of α9-containing and other nAChRs (such as α3 and/or α7). The respective contribution of α9 and/or α9/α10, α3 and α7 nAChR channels to sEPSCs still remains to be quantified. Based on the blocking effects of α-RgIA and hexamethonium, α3 nAChRs appear to preferentially mediate sEPSCs in control rats, as reported [START_REF] Barbara | Quantal release at a neuronal nicotinic synapse from rat adrenal gland[END_REF] whilst α9-containing nAChRs predominantly mediate sEPSCs in cold stressed rats. The contribution of α7 nAChRs would need further investigation, keeping in mind that α7 and α10 subunits can be spatially associated [START_REF] Lips | Coexpression and spatial association of nicotinic acetylcholine receptor subunits alpha7 and alpha10 in rat sympathetic neurons[END_REF]. The involvement of α7 nAChRs in adrenal synaptic transmission has been evidenced by the blocking effect of α-bungarotoxin (α-Bgt) on sEPSCs [START_REF] Martin | Evidence for long-lasting cholinergic control of gap junctional communication between adrenal chromaffin cells[END_REF]. However, α-Bgt antagonizes not only α7 nAChRs (IC 50 1.6 nM, Lopez et al., 1998) but also α9 and α9/α10 nAChRs (IC 50 2.1 nM and 14 nM, respectively, [START_REF] Sgard | A novel human nicotinic receptor subunit, alpha10, that confers functionality to the alpha9-subunit[END_REF]. Although other data support the presence of α7 nAChRs in adrenal chromaffin cells [START_REF] Rust | Expression of neuronal nicotinic acetylcholine receptor subunit genes in the rat autonomic nervous system[END_REF][START_REF] Criado | Differential expression of alpha-bungarotoxin-sensitive neuronal nicotinic receptors in adrenergic chromaffin cells: a role for transcription factor Egr-1[END_REF][START_REF] Mousavi | Expression of nicotinic acetylcholine receptors in human and rat adrenal medulla[END_REF], their contribution to synaptic transmission merits re-examination, by using for example the highly selective α7 nAChR antagonist α-conotoxin ArIB[V11L,V16D] ( Whiteaker et al., 2007).

Functional relevance of α9-containing nAChRs in the stimulus-secretion coupling

Since i) α9 nAChRs are highly permeable to Ca 2+ [START_REF] Katz | High calcium permeability and calcium block of the alpha9 nicotinic acetylcholine receptor[END_REF][START_REF] Jagger | Calcium signalling mediated by the 9 acetylcholine receptor in a cochlear cell line from the immortomouse[END_REF][START_REF] Fucile | Ca 2+ permeability through rat cloned alpha9containing nicotinic acetylcholine receptors[END_REF] and ii) an increase in cytosolic Ca 2+ , ([Ca 2+ ]i), is a prerequisite for chromaffin cell exocytosis [START_REF] Cheek | Calcium signalling and the triggering of secretion in adrenal chromaffin cells[END_REF], it is likely that α9 nAChR activation by ACh would trigger instructive signaling cascades contributing to catecholamine release from chromaffin cells.

Consistent with their high Ca 2+ permeability [START_REF] Jagger | Calcium signalling mediated by the 9 acetylcholine receptor in a cochlear cell line from the immortomouse[END_REF], α9-containing nAChRs have been reported to interact with the small conductance Ca 2+ -dependent K + (SK) channels [START_REF] Nie | Cloning and expression of a small-conductance Ca 2+ -activated K + channel from the mouse cochlea: coexpression with alpha9/alpha10 acetylcholine receptors[END_REF]. So, SK channel-mediated currents can be gated by α9 nAChRs [START_REF] Kong | Fast cholinergic efferent inhibition in guinea pig outer hair cells[END_REF] and SK channels are required for expression of functional α9/α10 nAChRs [START_REF] Kong | Expression of the SK2 calcium-activated potassium channel is required for cholinergic function in mouse cochlear hair cells[END_REF]. Since activation of SK channels by ACh negatively regulates cell excitability [START_REF] Nenov | Acetylcholine response in guinea pig outer hair cells. II. Activation of a small conductance Ca 2+ -activated K + channel[END_REF][START_REF] Nakajima | Functional interactions between the SK2 channel and the nicotinic acetylcholine receptor in enteric neurons of the guinea pig ileum[END_REF], it is tempting to speculate that SK channels shorten the depolarizing action of synaptically released ACh, thereby preventing the formation of a depolarizing plateau in case of high frequency synaptic activity at the splanchnic nerve-chromaffin cell junction. On the other hand, one could propose that α9containing nAChRs modulate SK channel trafficking and remove them from synapses, as described for beta adrenoceptors [START_REF] Faber | Modulation of SK channel trafficking by beta adrenoceptors enhances excitatory synaptic transmission and plasticity in the amygdala[END_REF]. Thus, cholinergic neurotransmission at the splanchnic synapses would initially be more robust. The discrimination between these two hypotheses would need further studies.

The increased LY diffusion between chromaffin cells in the presence of α-RgIA indicates that activation of α9-containing nAChRs negatively modulate gap junctional coupling, thus extending data showing that cholinergic synaptic inputs play a tonic inhibitory control on gap junction-mediated communication [START_REF] Martin | Evidence for long-lasting cholinergic control of gap junctional communication between adrenal chromaffin cells[END_REF]. Since coordination of cellular and intercellular responses is crucial in maintaining tissular syncytial function (Ramanan et al., 1998), we hypothesize that negative modulation of gap junctional coupling by synaptic transmission in basal condition acts as a shield to protect the organism against a huge catecholamine release potentially harmful or even lethal. Conversely, upon a reduced synaptic transmission, it may act as a compensation lever to sustain catecholamine release by maintaining communication within the chromaffin cell network. Dominant expression and function of α9-containing nAChRs in cold stressed rats: an added value?

The major contribution of α9-containing nAChRs to ACh-evoked currents in stressed rats parallels an upregulation of α9 nAChR transcript expression level, consistent with the fact that the α9 nAChR gene undergoes transcriptional regulation [START_REF] Valor | Transcriptional regulation by activation and repression elements located at the 5'-noncoding region of the human alpha9 nicotinic receptor subunit gene[END_REF]. The associated upregulation of α9 nAChR protein expression level is also in agreement with posttranslational regulation and a possible mechanism would involve receptor trafficking, as observed for other nAChR subypes [START_REF] Gaimarri | Regulation of neuronal nicotinic receptor traffic and expression[END_REF].

With regard to changes in adrenal nAChR expression levels in stressed rats, data are sparse and only a recent study reports a decrease in α7 nAChR messenger in response to longterm hypoxia [START_REF] Ducsay | Long-term hypoxia modulates expression of key genes regulating adrenomedullary function in the late gestation ovine fetus[END_REF]. By contrast, as reported here in cold stressed rats, the expression level of transcripts encoding α3 and α7 nAChR subunits remained unchanged, indicating that the regulation of nAChR expression is stressor-specific. This specific regulation of nAChRs exhibiting different intrinsic properties (gating, Ca 2+ permeability, ...) may allow chromaffin cells to appropriately respond to a variety of environmental changes.

The preponderant blockade of ACh-induced current by α-RgIA (>70%) and the preferential localization of α9-containing nAChRs at synaptic sites observed in cold exposed rats led us to propose that α9-containing nAChRs play a dominant role in the postsynaptic detection of cholinergic inputs in stressed animals. By contrast, in unstressed rats, α9containing nAChRs contribute to a lesser extent to ACh-evoked current, the major contribution being that of α3 nAChRs, consistent with a dominant expression of α3/β4 nAChRs in chromaffin cells [START_REF] Criado | Primary structure of an agonist binding subunit of the nicotinic acetylcholine receptor from bovine adrenal chromaffin cells[END_REF][START_REF] Campos-Caro | Neuronal nicotinic acetylcholine receptors on bovine chromaffin cells: cloning, expression, and genomic organization of receptor subunits[END_REF][START_REF] Sala | Nicotinic acetylcholine receptors of adrenal chromaffin cells[END_REF].

We propose that under resting conditions, in which expression level of α9 subunit is low, the synaptic response of chromaffin cells would be dominated by α3 subunit-containing nAChRs [START_REF] Barbara | Quantal release at a neuronal nicotinic synapse from rat adrenal gland[END_REF][START_REF] Martin | Evidence for long-lasting cholinergic control of gap junctional communication between adrenal chromaffin cells[END_REF][START_REF] Martin | Agrin mediates a rapid switch from electrical coupling to chemical neurotransmission during synaptogenesis[END_REF] that exhibit low Ca 2+ permeability [START_REF] Fucile | Ca 2+ permeability of nicotinic acetylcholine receptors[END_REF]. Interestingly, transmural electrical stimulation of bisected adrenals intermittently failed to evoke action potentials when the stimulus frequency was >10Hz [START_REF] Holman | Synaptic transmission from splanchnic nerves to the adrenal medulla of guinea-pigs[END_REF]. Moreover, the few action potentials fired in this condition arose from a depolarized membrane potential and appeared somewhat inactivated, thus suggesting a depolarization block. These observations are consistent with that of Iijima and colleagues (1992), who reported that action potentials in rat chromaffin cells began to fail when the stimulus frequency was >20 Hz. This suggests that chromaffin cells are not adequately prepared to increase their electrical and their secretory responses when the firing rate of preganglionic neurons increases above 10 Hz, although such frequencies are commonly observed in animals under prolonged-asphyxia or even in resting conditions [START_REF] Iggo | Preganglionic sympathetic activity in normal and in reserpine-treated cats[END_REF]Beacham and Pearl, 1964). The upregulation of α9 nAChR expression level reported here in cold exposed rats associated with the fact that these receptors exhibit a higher Ca 2+ permeability than other nAChRs would provide a mechanism by which enhanced synaptic Ca 2+ entry through this receptor subtype and the ensued activation of SK channels would shape excitatory synaptic potentials in a way that would enable chromaffin cells to repetitively and faithfully discharge action potentials to cope with stressful situations as manifested by a high frequency of splanchnic nerve firing. nAChR expression level was significantly increased (1.8-fold) in stressed rats. *, P<0.05 as compared with unstressed rats. B, Expression levels of α9-, α3-and α7 nAChR subunits were determined by quantitative PCR. Total RNA was extracted from macrodissected adrenal medulla from 13 control and 12 cold stressed rats. Expression of nAChR mRNA was normalized to the geometric mean of the expression levels of Hprt, GAPDH and Gus mRNA.

A significant increase in relative expression level was observed for α9 nAChR (Ba) but not for α3 nAChR and α7 nAChR transcripts (Bb). *, P<0.05 as compared with unstressed rats.

( 1 :

 1 1000, clone SVP-38, Sigma). Sections were then incubated (3 hours at RT) with appropriate secondary antibodies conjugated to Alexa 488 (1:2000, Molecular Probes, Eugene, OR) or Cy3 (1:2000, Jackson ImmunoResearch Laboratories, Inc., West Grove, PA).

  Wakade AR, Wakade TD (1983) Contribution of nicotinic and muscarinic receptors in the secretion of catecholamines evoked by endogenous and exogenous acetylcholine. Neuroscience 10:973-978. Whiteaker P, Christensen S, Yoshikami D, Dowell C, Watkins M, Gulyas J, Rivier J, Olivera BM, McIntosh JM (2007) Discovery, synthesis, and structure activity of a highly selective alpha7 nicotinic acetylcholine receptor antagonist. Biochemistry 46:6628-6638. Wiedenmann B, Franke WW (1985) Identification and localization of synaptophysin, an integral membrane glycoprotein of Mr 38,000 characteristic of presynaptic vesicles. Cell 41:1017-1028.

Figure legends Figure 1 :

 legends1 Figure legends

Figure 2 :

 2 Figure 2: Effect of α9-containing nAChR blockade on sEPSC frequency

Figure 3 :

 3 Figure 3: Effect of α9-containing nAChR blockade on sEPSC amplitude

Figure 4 :

 4 Figure 4: Effect of α9-containing nAChR blockade on sEPSC quantal size

Figure 5 :

 5 Figure 5: Increased Lucifer yellow diffusion after α9-containing nAChR blockade

Figure 6 :

 6 Figure 6: Upregulation of α9 nAChR protein and transcript expression levels in cold

Figure 7 :

 7 Figure 7: Dominant contribution of α9-containing nAChRs in acetylcholine-evoked

Table 1 : Primer sequences used for quantitative PCR

 1

		forward sequence (5'-3')	reverse sequence (5'-3')
	rα3nAChR TATAGAACTCCAACCACAC	CCGTAGAAGGTCCTCGTC
	rα7nAChR AGCCATACCCAGATGTCACCTAC	GCAGCAAGAATACCAGCAGAGC
	rα9nAChR AGCAAGAGCAGATTAGCAG	AAGCATACGCAACCTATCC
	rGus	CACCACTGAGAGTAACAGGAAACAA	TCGTTGGCAATCCTCCAGTATCT
	rHprt	TGACTATAATGAGCACTTCAGGGATT TCGCTGATGACACAAACATGATT
	rGAPDH	ATGATTCTACCCACGGCAAG	CTGGAAGATGGTGATGGGTT
	r, rat.

plateform (IFR3). This work was supported by grants from Centre National de la Recherche Scientifique, Institut National de la Santé et de -Roussillon, and grants from the Ministerio de Ciencia e Innovación (BFU2005-06034; CSD2008-00005) and the Comunidad de Madrid (S-SAL-0253-2006).

A, Individual chromaffin cells from control and cold stressed rats were voltage-clamped at -40 mV and stimulated by a 1 s-application of ACh (100 µM). A, Representative AChtriggered current recorded in the absence of toxin and 4 min after α-RgIA (200 nM), hexamethonium (200 µM) or α-RgIA+hexamethonium applications. Note that the stronger blockade of ACh-evoked current is observed for hexamethonium in control rats and for α-RgIA in cold stressed rats. B, Histograms illustrating the blockade efficiency of α-RgIA, hexamethonium and α-RgIA+hexamethonium on ACh current density, in control and cold stressed rats. Note that in each condition, toxins effects are fully reversible. C, Histogram illustrating the percentage of inhibition of the ACh-evoked inward current by α-RgIA, hexamethonium and α-RgIA+hexamethonium in control and cold stressed rats. ACh current density was calculated before, 1, 4 and 5 min after blocker application and after 1 and 5 min washout, in control (A) and cold stressed rats (B). ACh-evoked current did not rundown over the 10 min recording (insets). In control rats, the blocking effect of α-RgIA was complete after 1 min, whilst it required at least 4 min in cold stressed rats. Regarding hexamethonium, the blocking effect was complete within 4 min in control animals and was still under process after 5 min in stressed rats.