Bernard Bonnard

Jérémy Rouot
email: jeremy.rouot@inria.fr

Lunar perturbation of the metric associated to the averaged orbital transfer

In a series of previous article we introduced a Riemannian metric associated to the energy minimizing orbital transfer with low propulsion. The aim of this article is to study the deformation of this metric due to the perturbation caused by the lunar attraction. Using Hamiltonian formalism, we describe the effects of the perturbations on the orbital transfers and the deformation of the conjugate and cut loci of the original metric.

Introduction

Recent space missions like lunar Smart-1 mission, Boeing orbital transfer, using electric propulsion are innovative design feature to reduce launch costs and lead to the analyse of the low thrust controlled Kepler equation using averaging techniques in optimal control. Pioneering work in this direction associated to the energy minimization problem are due to Edelbaum [START_REF] Edelbaum | Optimum low-thrust rendezvous and station keeping[END_REF], Epenoy-Geffroy [START_REF] Geffroy | Optimal low-thrust transfers with constraints-generalization of averaging techniques[END_REF], and more recently to Bonnard-Caillau [START_REF] Bonnard | Riemannian metric of the averaged energy minimization problem in orbital transfer with low thrust[END_REF]. Under some simplifying assumption they lead to the definition of a Riemannian distance between Keplerian orbits, and this is a preliminary step in computing the time minimal or find mass maximizing solutions using numerical continuation techniques [START_REF] Cots | Contrôle optimal géométrique: méthodes homotopiques et applications[END_REF].

Main Objectives

The Riemannian metric

From the controlled planar Kepler equation, the ellipse of motion of a satellite can be described by the system

dx dt = 2 i=1 u i F i (x, l) dl dt = w 0 (x, l) + g(x, l, u). (1)
where x = (n, ρ, θ) are the slow orbital elements of the satellite (n is the mean motion, ρ the eccentricity and θ the argument of periapsis), and l is the fast angle pointing out the position of the satellite on its orbit.

The optimal control problem associated to (1) is to find, given two boundary values (x 0 , x f ) and an interval [0, t f ], a control u = (u 1 , u 2 ) such that |u| ≤ 1 and minimizing the cost is [0,t f ] |u(s)| 2 ds.

Applying the Pontryagin Maximum Principle, the averaged Hamiltonian with respect to the true longitude l is given by

H = 1 4n 5 3 18n 2 p 2 n + 5(1 -ρ 2 )p 2 ρ + (5 -4ρ 2 ) p 2 θ ρ 2 .
The Riemannian metric associated to H is

g = 1 9n 1 3 dn 2 + 2n 5 3 5(1 -ρ 2 ) dρ 2 + 2n 5 3 5 -4ρ 2 dθ 2 .

Model for the lunar perturbation

The perturbed dynamic can be written as

dx dt = F 0 (x, l, l ) + 2 i=1 u i F i (x, l) dl dt = w0 (x, l) + g(x, l, u) dl dt = w 1 (l )
where l is the fast angle pointing out the position of the Moon on his orbit. The drift F 0 corresponds to the perturbed vector field induced by the lunar attraction. This perturbation is modelled as the effect of the Moon on the two body system {Earth + satellite} where these three mass points belong to the orbital plane of the Moon. This perturbation acceleration derives from a potential R(x, l, l ) whose double averaged is given by

R(x) = 1 4π 2 2π 0 2π 0 R(x, l, l )dM dM = n 2 4n 4 3 (1 + 3 2 ρ 2 )
where n is the mean motion of the Moon supposed constant and M , M are the mean anomaly respectively of the satellite and the Moon. The double averaged drift vector field is deduced from the Lagrange equations

F 0 (n, p, θ) = 3 4 n 2 n 1 -ρ 2 ∂ ∂θ (n, p, θ).

Hamiltonian from a Zermelo navigation problem

A Zermelo navigation problem on a n-dimensional Riemannian manifold (X , g) is a time minimal problem associated to the system

dx dl = X 0 (x) + n i=1 u i X i (x)
where F i form an orthonormal frame for the metric g and |u| ≤ 1. F 0 represents the current of magnitude |F 0 | g . Applying the PMP, the associated Hamiltonian has the form

G(x, p) = G 0 (x, p) + G(x, p)
where G i (x, p) = p, X i (x) . We consider the following Hamiltonian

H pert (x, p) = H 0 (x, p) + H(x, p) (2)
where H 0 = p, F 0 . To such an Hamiltonian, it corresponds a Zermelo navigation problem.

The geometric concept of conjugate point

Let H pert the Hamiltonian vector field associated to H pert .

-Let z = (x, p) be a reference extremal solution of H pert on [0, t f ]. The variational equation

δz(t) = d H pert (z(t))δz(t) (3)
is called the Jacobi equation. A Jacobi field is a non trivial solution δz = (δx, δp) of (3) and it is said to be vertical at time t if δx(t) = 0. -The first conjugate time t c is a time from which the exponential map p 0 → exp x 0 (t, p 0 ) = x(t, x 0 , p 0 ) associated to the flow of H pert is not an immersion at t = t c . x(t c ) is said to be conjugate to x 0 . This singularity can be characterised by the independence of the Jacobi fields (δx 1 (t), δx 2 (t)) vertical at t = 0 and such that δp i is orthogonal to p 0 (i = 1, 2). In particular, at the first conjugate time t c , the family (δx 1 (t), δx 2 (t)) |t=t c is not of rank 2. The following test condition allow us to compute t c for a given trajectory x(t, x 0 , p 0 ) [START_REF] Bonnard | Second order optimality conditions in the smooth case and applications in optimal control[END_REF] det[δx 1 (t c ), δx 2 (t c ), ẋ(t c )] = 0.

(4)

Computational results

Simulations provided below represent BC-extremals from the Hamiltonian system associated to (2).

The boundary value problem is given by x 0 = (10, 2e -1, 0), x f = (6.16, 7e -2, π 3 ) and t f is free. These extremals correspond to zeros of the shooting mapping

S : (t f , p 0 ) → (x t f (x 0 , p 0 )) -x f , |p(0)| 2 -1).
In order to check the optimality of our trajectories, conjugate points are computed via the verticality test (4). Simulations were performed via the package HAMPATH [START_REF] Cots | Contrôle optimal géométrique: méthodes homotopiques et applications[END_REF] which implements a indirect method (Newton) to find a zero of S. Time evolutions of the extremal components in the perturbed case (dash-dot line) and the unperturbed case (solid line) are illustrated. Rank test condition (4) for the perturbed and unperturbed problem. The following figures represent several trajectories in the coordinates (θ, ψ) starting from (θ 0 , ρ 0 ) = (π, 0.6). Trajectories from the perturbed case.

  1. Compute a double averaged on the lunar perturbation potential. 2. From the averaged Hamiltonian associated to the energy minimization, define a perturbed Hamiltonian related to a Zermelo navigation problem. 3. Using the Pontryagin Maximum Principle (PMP), solve numerically a boundary-value problem via a simple shooting method. 4. Study the second order optimality conditions by computing the conjugate points via an algorithm based on the Jacobi fields. 5. Compare the trajectories and cut loci of the perturbed and unperturbed problem

Acknowledgements

Work supported in part by the French Space Agency the R&T action R-S13/BS-005-012 and by the region Provence-Alpes-Côte d'Azur.


Notations : R is the set of reactions of the form :

m i =1 α i X i y -→ m i =1
β i X i y α i , β i are the stoichiometric coefficients.

/ 32

Chemical Networks with mass action kinetics Graph Model : Species {X 1 , . . . , X m }. Notations : R is the set of reactions of the form :

m i =1 α i X i y -→ m i =1
β i X i y α i , β i are the stoichiometric coefficients. Dynamics for the network

Feinberg-Horn-Jackson graph

ċ(t) = F (c(t), T ) = y→y ∈R K (y → y ) (y -y)
The dynamics is defined by the graph.

Stoichiometric subspace

S = = = span y ---y , y → → → y ∈ ∈ ∈ R Positive class (strict if > 0) (c(0) + S) ∩ R m ≥0 Lemma
The class (c(0) + S) ∩ R m >0 is invariant for the dynamics.

Notations

Labeling the vertices : y 1 , y 2 , . . . , y n ex :

y 1 y 2 y 3 k 1 k 2 k 3 k 4 5 / 32

Notations

Labeling the vertices : y 1 , y 2 , . . . , y n ex :

y 1 y 2 y 3 k 1 k 2 k 3 k 4
Complex matrix : Y = (y 1 , . . . , y n ) (n : number of vertices).

5 / 32

Notations

Labeling the vertices : y 1 , y 2 , . . . , y n ex :

y 1 y 2 y 3 k 1 k 2 k 3 k 4
Complex matrix : Y = (y 1 , . . . , y n ) (n : number of vertices).

Incidence connectivity matrix : A = = = (a i j ) i j with for instance a 21 = k 1 indicating a reaction with constant k 1 from the first node of the graph to the second :

y 1 -→ k 1 y 2 5 / 32
Notations Labeling the vertices : y 1 , y 2 , . . . , y n ex :

y 1 y 2 y 3 k 1 k 2 k 3 k 4
Complex matrix : Y = (y 1 , . . . , y n ) (n : number of vertices).

Incidence connectivity matrix : A = = = (a i j ) i j with for instance a 21 = k 1 indicating a reaction with constant k 1 from the first node of the graph to the second :

y 1 -→ k 1 y 2
Laplacian matrix :

à = A -diag n i =1 a i 1 , . . . , . . . , n i =1 a i n 5 / 32
One has

ċ(t) = f (c(t), T ) = Y Ã c Y where c Y = (c y 1 , . . . , c y n ) . 6 / 32
Zero deficiency theorem

Definition

The network is weakly reversible if ∀ vertices (i , j ) such that ∃ oriented path joining i to j , there exists an oriented path joining j to i .

If the network is not weakly reversible then for arbitrary kinetics, the differential equation cannot have a positive equilibrium nor a positive periodic trajectory.

2

If the network is weakly reversible, there exists within each strictly positive compatibility class precisely one equilibrium c * , this equilibrium is locally asymptotically stable with (pseudo-Helmholtz) Lyapunov function V (c, c * ) = i c i (ln(c i )ln(c * i ) -1) + c * i . Moreover there are no non trivial periodic orbits.

Assumption δ = = = 0 (Zero deficiency assumption) Theorem 1 If the network is not weakly reversible then for arbitrary kinetics, the differential equation cannot have a positive equilibrium nor a positive periodic trajectory.

2

If the network is weakly reversible, there exists within each strictly positive compatibility class precisely one equilibrium c * , this equilibrium is locally asymptotically stable with (pseudo-Helmholtz) Lyapunov function V (c, c * ) = i c i (ln(c i )ln(c * i ) -1) + c * i . Moreover there are no non trivial periodic orbits.

Application : Test bed cases :

case

1 : A B C k 1 k 2 δ = 3 -1 -2 = 0 : not weakly reversible case 2 : (McKeithan network) T + M A B k 1 k 2 k 3 k δ = 3 -1 -2 = 0 :

Geometric Optimal Control

Optimal Control Problem

dc dt = f (c, T ), dT dt = u, u ∈ [u -, u + ]
u(•) tracked the derivative of the temperature (related to the Goh Transformation).

Single input C ω -control system, affine in u :

q = F (q) + u G(q), |u| ≤ 1, q = (c, T ) ∈ R n Formulation : max c 1 (t f ) t f : (fixed) time batch duration Formulated as min t f (free), |u| ≤ 1 c 1 (t f ) = d is a desired quantity Formulation : max c 1 (t f ) t f : (fixed) time batch duration Formulated as min t f (free), |u| ≤ 1 c 1 (t f ) = d is a desired quantity N : terminal manifold of codimension 1. N = {c 1 = d } c 1 c 1 (0) < d (T, c 2 , . . . , c m ) n n d
Necessary optimality conditions Pontryagin Maximum Principle ( 1956)

Notations : q = F (q) + u G(q), |u| ≤ 1, min t f , q(t f ) ∈ N H (q, p, u) = p • (F (q) + u G(q)), p ∈ R n \ {0} : adjoint vector
H : pseudo-Hamiltonian and the maximized Hamiltonian is M (q, p) = max |u|≤1 H (q, p, u), q, p are fixed

Theorem

Assume (q * (•), p * (•)) is a time minimal solution on [0, t * f ] then there exists p * (•) such that a.e. on [0, t * f ] :

q * (•) = ∂H ∂p (q * (t ), p * (t ), u * (t )), ṗ * (•) = - ∂H ∂q (q * (t ), p * (t ), u * (t )) (1)
the maximization condition is satisfied H (q * (t ), p * (t ), u * (t )) = M (q * (t ), p * (t )).

(2)

Theorem

Assume (q * (•), p * (•)) is a time minimal solution on [0, t * f ] then there exists p * (•) such that a.e. on [0, t * f ] :

q * (•) = ∂H ∂p (q * (t ), p * (t ), u * (t )), ṗ * (•) = - ∂H ∂q (q * (t ), p * (t ), u * (t )) (1)
the maximization condition is satisfied H (q * (t ), p * (t ), u * (t )) = M (q * (t ), p * (t )).

(

) Moreover t → M (q * (t ), p * (t )) is constant and ≥ 0, 2
At the final time one has the transversality condition :

p * (t f ) ⊥ T q * (t f ) N (3)
Computations of singular extremals and properties

Notation : X , Y : two vector fields on R n Lie bracket :

[X , Y ](q) = ∂X ∂q (q)Y (q) - ∂Y ∂q (q)X (q) z = (q, p) and Hamiltonian lift of X : H X (z) = p • X (q) Poisson bracket : {H X , H Y }(z) = p • [X , Y ](q)
Computations of singular extremals and properties

Notation : X , Y : two vector fields on R n Lie bracket :

[X , Y ](q) = ∂X ∂q (q)Y (q) - ∂Y ∂q (q)X (q) z = (q, p) and Hamiltonian lift of X : H X (z) = p • X (q) Poisson bracket : {H X , H Y }(z) = p • [X , Y ](q) Computations H G (z) = p • G(q) = 0 Differentiating twice w.r.t. time gives the two equations d dt H G (z) = dH G • ż = {H G , H F + u H G } = {H G , H F } = 0 {{H G , H F }, H F }(z) + u {{H G , H F }, H G }(z) = 0 Then if {{H G , H F }, H G }(z)
= 0 then we compute û and plug it in H to obtain the true Hamiltonian. Step 1: Take q 0 ∈ N, z 0 = (q 0 , n(q 0 )) where n(q 0 ) is the normal vector of N at q 0 . Find, in a small neighborhood U of q 0 , the time minimal closed loop control u * (q) to reach N starting from q in minimal time.

   min t f |u| ≤ 1 q = F (q) + u G(q) c 1 (t f ) ∈ N = {c 1 = d }
   min t f |u| ≤ 1 q = F (q) + u G(q) c 1 (t f ) ∈ N = {c 1 = d }
N q 0 n    min t f |u| ≤ 1 q = F (q) + u G(q) c 1 (t f ) ∈ N = {c 1 = d }
Tools : Singularity theory N = { f -1 (0)} expand at q 0 with Taylor series : jet spaces. compute : Normal form to estimate W,C near q 0 . Tools are simple but the classification is complicated.

Ex. : Two reactions only. (c, T ) ∈ R 3 , q = F + u G and N = f -1 (0). Generic case z 0 = (q 0 , n(q 0 )). G is tangent to N : Then p • G = 0 so p is normal to N. Using classification of extremals at a point such that p • G(q) = 0, p • [G, F ](q) = 0 : N σ + q 0 n or N σ - q 0 n depending on the sign of p • [G, F ](q 0 ). ...

  Vertices : y = (α 1 , . . . , α m ) , y = (β 1 , . . . , β m ) Orientation :Rate dynamics y → y (Mass kinetics)K (y → y ) = k(T ) c y k(T ) = A exp(-E RT ) : Arrhenius law E , A parameters, T temperature and R is the gas constant K (y → y ) = k(T ) c y k(T ) = A exp(-E RT ) : Arrhenius law E , A parameters, T temperature and R is the gas constant c = (c 1 , . . . , c m ) c i : concentrations of the species X i with c y = c 1 α 1 . . . c α m m⇒ K (y → y ) depends only on y.

  Feinberg and Horn-Jackson : articles in Archive Rational Mechanics Graph concept : deficiency : δ = = = n --l --s where n : number of vertices l : number of connected components s : dimension of the stoichiometric subspace

  time minimal syntheses near the terminal manifold

  FIGURE-Dotted line : elliptic, red line : hyperbolic.

The dynamics is defined by the graph.

Extremals : solutions of (1)-(2). BC-extremal : Extremals & transversality condition (3) satisfied.

Maximization condition

Finite number of switches : Bang-Bang singular :

⇒ necessary optimality condition (High Order Maximum Principle, Krener).

Strict generalized Legendre-Clebsch condition

⇒ necessary optimality condition (High Order Maximum Principle, Krener).

Classification of regular extremals (Ekeland -IHES, Kupka -TAMS) Denote :

σ + : bang arc with u = +1 σ -: bang arc with u = -1

Classification of regular extremals (Ekeland -IHES, Kupka -TAMS) Denote :

σ + : bang arc with u = +1 σ -: bang arc with u = -1

σ 1 σ 2 is the arc σ 1 followed by σ 2 .

Switching surface :

Classification of regular extremals (Ekeland -IHES, Kupka -TAMS) Denote :

σ + : bang arc with u = +1 σ -: bang arc with u = -1

σ 1 σ 2 is the arc σ 1 followed by σ 2 .

Switching surface :

Let t be a switching time.

Ordinary Switching time :

In the parabolic case |u 0 | > 1 and the singular arc is not admissible.

Theorem (Kupka TAMS)

In the neighborhood of z(t ) every extremals projects onto :

Elliptic case : every extremal is of the form σ + σ -σ + σ -. . . (Bang-Bang) but the number of switches is not uniformly bounded.

FIGURE -Fold case in the hyperbolic case and the turnpike phenomenon

Application to Chemical Networks

Computations : q = F (q) + u G(q), q(t f ) ∈ N Synthesis : it means determine the switching locus Ex. : N σ + σ -

W : switching locus

Computations : q = F (q) + u G(q), q(t f ) ∈ N Synthesis : it means determine the switching locus Ex. : N σ + σ - W : switching locus determine the splitting locus or the cut locus C where two distinct optimal trajectories occur. Ex. : N C :cut locus Tools : Singularity theory N = { f -1 (0)} expand at q 0 with Taylor series : jet spaces.

compute : Normal form to estimate W,C near q 0 . Tools are simple but the classification is complicated.

Define :

S the singular locus : {q ∈

S the singular locus : {q ∈

For S : from the classification near a fold point one has :

Hyperbolic case Elliptic case

Parabolic case To make the analysis we construct a semi-normal form : q = (x, y, z) near 0

Synthesis : There exists a C 0 -foliation by planes such that in each plane the synthesis is :

Note that the synthesis is σ ± σ s σ ± hence the temperature is not constant.

Synthesis : There exists a C 0 -foliation by planes such that in each plane the synthesis is :

Note that the synthesis is σ ± σ s σ ± hence the temperature is not constant.

Case : Parabolic. For instance, a synthesis is

Switching locus

Bridge phenomenon

Local (planar) simplified model (inspired from the saturation problem in Magnetic Resonance Imaging) :

and is not bounded.

Trajectories : bridge

Bridge connecting two switching points of the singular set.


Marc Deneire

The British Leave, but European Englishes will Remain

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

Brexit will no doubt be remembered as pivotal in European politics in the first part of this century. It has come as a surprise to most political and economic actors and observers; as a result, its impact is difficult to predict. As of today (February 2017), some of the effects are already being felt, especially in Britain. For example, universities are already worried about a 14 percent drop in international enrolments and job centers are experiencing a shortage of workers due to the return home of a sizeable number of Eastern European expatriates.

However, it remains highly uncertain how Brexit will affect the European Union in general, and the development of English in that context. Any speculation will partly depend on the analysis of the present political situation. In that respect, my own analysis seems to be at the opposite ends of the spectrum to Marko Modiano's and, consequently, as are my conclusions concerning the spread of English in Europe.

BREXIT AND EUROPE

First, today's European Union is not a "global village" as Modiano seems to argue; rather it is dominated by all forms of divisions, by economic and political protectionism, not only in Britain of course, where the Northern Irish fear that the civil war might flare up again, but also everywhere in Europe where right and left-wing parties share varied forms of nationalism and populism marked by xenophobia and racism, and an adamant protection of culture and language at the national and regional levels (see e. Second, Modiano falls in the traditional trap of comparing so-called "pro-English" and "anti-English" countries, somewhat predictably using Germany as an example of the first, and France to illustrate the latter. For that purpose, he uses quotations by German European Commissioner Gunther Ottinger on the one hand, and left-wing and right-wing French politicians Jean-Luc Mélanchon and Marine Le Pen on the other. Had he taken German nationalists and mainstream French politicians, he might have come out with a very different picture. For example, French finance minister Michel Sapin has been criticized for using English with French economic commissioner Pierre Moscovici; Foreign Policy presents presidential candidate Emmanuel Macron as "the English-speaking, German-loving French politician Europe has been waiting for" (http://foreignpolicy.com/2017/01/17/the-englishspeaking-german-loving-french-politician-europe-has-been-waiting-for-emmanuel-macron/), and most French politicians and business leaders have received the (in)famous "carpette anglaise" for "deserting the French language" and "promoting the domination of the Anglo-Saxon language" (http://www.languefrancaise.org/Articles_Dossiers/Carpette_historique.php) On the other hand, Ulrich Ammon (2006) gives us a number of instances where German educational and cultural institutions actively resisted the spread of English in Germany. More recently, following the adoption of English as a company language by Volkswagen (17 years after Renault), Walter Krämer of the German language foundation deplored the fact that: "The words Volkswagen and the German language no longer go together" and added: "I am dismayed at how thoughtless our elites are giving up their own language and culture" (https://qz.com/875425/volkswagen-ischanging-its-official-language-from-german-to-english/).

In fact, 2011 Eurostat figures show that only 16% of the Germans claim to be fully proficient in English against 13% for the French. This may explain why when I spend my holidays in large German cities such as Köln or Munich outside university circles, I am often more successful communicating in a "germanized" version of one of my native languages, Dutch, rather than in English.

Finally, Modiano's paper may give the impression that most Europeans eagerly embrace globalization and "freely" adopt English as a result. This may be true for a small segment of the population, but not for the much larger part for whom globalization has meant lowering life conditions, and increased poverty, and unemployment. Brexit and other elections in Europe reflect the discontent and the frustration of the majority. Those who benefit from English proficiency are few, and even among them, many only reluctantly accept to use English when/because it is forced upon them (see e.g., https://www.youtube.com/watch?v=P8qIc_kLuek). As language economists have shown, proficiency in English may translate into a ten or twenty percent salary increase in certain jobs [START_REF] Grin | L'enseignement des langues étrangères comme politique publique[END_REF], but for the 85 % who are not proficient, it often means worsening life conditions, demotion, downgrading, or job loss.

Further, as Michael Hartman and Klarissa Lueg (2017) explain, Brexit is in part due to the decline in the homogeneity of European Elites. So far, Europeans Elites were usually drawn from the same national elite institutions, Oxbridge in Britain, The Ecole Nationale d'Administration (ENA) in France, etc., and dominate all spheres of society -economic, social, and cultural. However, globalization and internationalization have eroded the collusion between national elites and led to the creation of a new international Englishspeaking elite. As noted by A.-C Wagner (2011: 6):

The capital produced and legitimized by the State is now in competition with new sources of legitimacy that rely on a new form of international capital; this capital, which is inextricably cultural, linguistic, social, inherited to a large extent, and reinforced through international curricula and professional experience in several countries, appears to be particularly well-suited for the changing economic sphere. This reminds us that English never comes alone, and in the present situation, it is clear that it primarily serves a form of class habitus that leads to the increasing isolation of a smaller and smaller elite. This may explain why Volkswagen, which became the number one auto-maker worldwide using German, now adopts English to attract international talent to high-level positions. The company clearly possesses plenty of industrial talent, but its development now depends on management by members of that small international elite.

In the 1930s and 1940s, the Marxist linguist Nikolaj Marr argued that economic revolutions produced linguistic revolutions and that all languages were class languages. For him, the speech of a French worker had more in common with that of a German worker than with that of a French capitalist. Paradoxically, his dream of a true international language may have become true, but it is that of a capitalist/financial class, not that of the proletariat.

ON THE QUESTION OF EURO-ENGLISH

Modiano is right to point out that English is making inroads into all walks of life in the European Union. However, for the following reasons, this does not make it "a variety in development": (1) it is mostly used in fairly closed communities of practice that are functionally and socially identifiable; in other words, English lacks both range and depth (Kachru 1986: 95) to qualify as a variety; (2) English has not been institutionalized in the way it has been in the Outer Circle. On the contrary, institutionalizing English in the European institutions for example would irremediably lead to the political breakup of the European Union (E. Roseau, Linguist at the European Council, personal communication); (3) it does not rely on an identifiable European culture and identity. The latest political and economic developments have shown over and over again that such a culture dos not exist. In fact, Modiano's range of features which, according to him, characterize the manner in which English is used in Europe are all formal features; they are not "culture-specific" in any way.

Moreover, most of them are also used in non-native varieties of English. In my experience, the English used by Germans is "very German", that used by the Polish is "very Polish", etc., and indeed, the English used by people who have studied in the United States or Britain is "very international", but in no way European. All we may hope is that, following recent events and the present political reactions by the numerous casualties of globalization, this small international elite will come to an understanding that in a multilingual Europe, plurilingualism is the only option.

  g. the Front National in France, the Alternative für Deutschland in Germany, the Freiheitliche Partei Österreichs in Austria, the Movimento 5 Stelle in Italy, Geert Wilders' Partij voor de Vrijheid in the Netherlands, Viktor Orban's Fidesz in Hungary, and also the Flemish movement in Belgium and the movement of Catalan independence in Spain.


Tassa Dit Issaadi-Hamitouche

Colette Besombes

Karim Allaf

Instant autovaporization as intensification way of classic distillation processes: fundamental and industrial applications

Keywords: Intensification, Instant Autovaporization, Volatility, Instant Controlled Pressure Drop DIC, Distillation, Paradoxical Stage

In the present work, the new extraction process of Détente Instantanée Contrôlée DIC was studied, developed, optimized and compared to the conventional hydrodistillation method for the extraction of essential oils of sandalwood. DIC was used as a thermomechanical treatment, DIC subjecting the product to a high-pressure saturated steam. The DIC cycle ends with an abrupt pressure drop towards vacuum, and this instantly leads to an autovaporization of sandalwood volatile compounds. An immediate condensation in the vacuum tank produced a micro-emulsion of water and essential oils. Thus, an ultra-rapid cooling of residual leaves occurred, precluding any thermal degradation. Response surface methodology RSM was used with a 2-parameter 5-level Design of Experiments (DoE). The structure with a slight destruction of cell walls after DIC treatment. The operating parameters (independent variables) were the treatment time t, and the number of pressure drops C, whilst the main response was the extraction of extraction efficiency EE of volatile compounds. RSM Statistical analysis allowed comparing this process with conventional hydrodistillation unit operation in terms of total yields of essential oil. The most important differences between the two essential oils were reflected in the yields, with 1.14 as against 1.23 g EO/100 g of raw matter, and in the extraction time, with 5 min as against 24 hours for respectively the DIC and the hydrodistillation operations. These differences have been previewed through the fundamental analysis based on both concept of thermodynamics of instantaneous transformations and calculation of the volatility as well as on Darcy similar transfer law was used to explain the main results.

[Tapez ici]

Introduction

Sandalwood is considered one of the most valuable trees in the world [START_REF] Fox | The royal tree[END_REF], Sandalwood oil is an essential oil obtained by the distillation of the heartwood and roots of the plant Santalum album (family -Santalaceae). S. album is a hemiparasitic tree of great economic value, growing in Southern India, Sri Lanka, Australia and Indonesia. Its trunk contains resins and essential oils particularly the α and β santalols, santalenes and many other minor sesquiterpenoids [START_REF] Jones | Non-destructive sampling of Indian sandalwood (Santalum album L.) for oil content and composition[END_REF].These sesquiterpenoids are responsible for the unique sandalwood fragrance. A number of aromatic and phenolic compounds have also been identified in the oil S. album [START_REF] Kim | Aromatic constituents from the heartwood of Santalum album L[END_REF] . The quantity of oil produced in a tree varies considerably according to location (environmental factors) and age of the tree, even in nearly identical growing conditions [START_REF] Jones | Non-destructive sampling of Indian sandalwood (Santalum album L.) for oil content and composition[END_REF]. It should also be noted that santalol composition can vary depending on the method of oil extraction, sections of a single tree. The international standard (ISO 3518, 2002) for sandalwood oil and similar authorities stipulate a minimum of 90% w/w santalol (as free alcohol) in the oil [4]. Sandalwood oils are essential oils commonly used as fragrances for body oils and incense as well as in medicines and cosmetics. Sandalwood oils have many well-known health benefits in traditional medicinal systems such as Ayurveda, as antiseptic, antipyretic, antiscabietic, diuretic, expectorant, stimulant, and for the treatment of bronchitis, dysuria, urinary infection, and in gonorrheal recovery. Sandalwood oils are usually extracted by steam distillation [START_REF] Misra | Differential Extraction and GC-MS based Quantification of Sesquiterpenoids from Immature Heartwood of East Indian Sandalwood Tree[END_REF]. However, solvent extraction can be performed on chips of sandalwood [START_REF] Hasegawa | Isolation of new constituents with a formyl group from the heartwood of Santalum album L[END_REF]. It would present numerous disadvantages [START_REF] Misra | Differential Extraction and GC-MS based Quantification of Sesquiterpenoids from Immature Heartwood of East Indian Sandalwood Tree[END_REF]. Therefore, various other alternatives were tested. Thus Marongiu and al. [START_REF] Marongiu | Extraction of Santalum album and Boswellia carterii Birdw. volatile oil by supercritical carbon dioxide: influence of some process parameters[END_REF], Piggott and al [START_REF] Piggott | Western Australian Sandalwood Oil: Extraction by Different Techniques and Variations of the Major Components in Different Sections of a Single Tree[END_REF] used supercritical or subcritical fluid for extracting and fractioning essential oils. Microwave-assisted extraction was also used as new innovative techniques [START_REF] Tran | Sandalwood Microwave Characterisation and Oil Extraction[END_REF]. They offer some advantages regarding kinetics and preservation of the chemical composition, but as far as we know, no industrial development has been achieved and all applications are still at the laboratory or pilot scale. In this context, it was proposed to carry out a comparative study of the extraction of the essential oils of the sandalwood using two different methods: traditional hydrodistillation and the innovative technology of Détente Instantanée Contrôlée DIC (French, for instant controlled pressure drop). DIC was defined in 1988 [START_REF] Allaf | Feasibility study of a new process of drying/swelling by instantaneous decompression towards vacuum[END_REF] and has been studied, developed, optimized and used at industrial scale for various applications such as drying and decontamination, texturing, the extraction of non-volatile molecules such as flavonoids [START_REF] Amor | Effect of instant controlled pressure drop treatments on the oligosaccharides extractability and microstructure of Tephrosia purpurea seeds[END_REF] and of volatile compounds [START_REF] Allaf | Thermal and mechanical intensification of essential oil extraction from orange peel via instant autovaporization[END_REF][START_REF] Besombes | Instant controlled pressure drop extraction of lavandin essential oils: Fundamentals and experimental studies[END_REF]. In the present work, we studied DIC, as essential oil extraction process. A preliminary thermodynamic study allowed us to determine the relative or absolute volatility of each compound versus temperature. The hydrodistillation was performed as references to compare the DIC extraction yields and kinetics.

Materials and methods

Raw Material

The bark of the sandalwood tree used in this study. Was provided by the company BAHAVE (Nantes, France). Its was originally from Australia and harvested in avril 2013. Its initial moisture content was 11 g H 2 O/100 g dry matter, with average diameter of 2 mm.

Assessment protocol

In the present study we had examine the effects of the total heating time (t) and the number of cycles (C) as DIC operating parameters (independent parameters), regarding the extraction efficiency EE considered as the main response parameter (dependent variable). The principle objective was to identify separately the impacts of evaporation and autovaporization phenomena. An experimental design was built intervening t and C; the first must be correlated to the evaporation process while the second one must reveal the effect of the autovaporization by itself. This investigation was achieved according to the protocol shown in Fig.

Hydrodistillation

The hydrodistillation equipment used was a modified Clevenger, in accordance with conventional hydrodistillation protocols, 50 g of raw material was immersed in 500 mL of distilled water in a 1 L distillation flask. The extraction of essential oils was performed out from the first drop of distillate until no more essential oil was obtained. The essential oil yield (Y) is defined as the ratio of the mass of the essential oil obtained (M EO ) to the dry of sandalwood chips (M dm ):

Y(%) = (1)

Laboratory scale (DIC) process

The reactor we used was a 18 l processing vessel with a heating jacket; thermal treatment in this vessel was achieved using saturated steam with a pressure varying from 0,1 MPa up to 0,6 MPa, which means a temperature between 100 and 160°C. A 1600 l vacuum tank with cooling water jacket is connected with a water ring vacuum pump allowing the vacuum to be to be maintained at 5 kPa. A pneumatic valve ensures an "instant" connection between the vacuum tank and the processing vessel; it can open in less than 0.2 s. Some other valves control the flow of steam and compressed air within the processing vessel (Fig. 2).

DIC treatment

In the present study, the raw sandalwood was directly put in the DIC reactor-processing vessel. After placing the raw material in the treatment vessel and closing it, a first vacuum stage (about 5 kPa) was

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established in order to remove the air presented in the vessel and, thus to assure close contact between the surface of the sample and the steam to be injected just after (Figure 3. phase c).

High pressure saturated steam used in our case was 0.6 MPa according to the experiment design (Table 1), and the product temperature to 160 °C. This stage lasted 10-300 s and ended by an abrupt pressure drop towards a vacuum (5 ± 0.2 kPa) by opening the pneumatic valve V3 (Fig. 2), which assured a decompression rate higher than 1 MPa s -1 In our case, several DIC-cycles were carried out and atmospheric pressure was estabilished after the final pressure drop. Fig. 3 gives the flow-sheet of this treatment. In our case, during the total thermal treatment time (phases d of various cycles), a part of essential oils must evaporate; the instant pressure drops towards a vacuum would normally simultaneously provoke an autovaporization of a part of water and volatile molecules (essential oils), and an instantaneous cooling of the product immediately stoppes its thermal degradation.

Statistical and experimental design protocol

Response surface methodology (RSM) method with a five-level central composite rotatable experimental design method was adopted. In the present study, the saturated steam pressure used kept constant at 0.6 MPa and the two DIC operating parameters we studied were the total heating time t, and the number of pressure drops C, (Table 1). Moisture content just before DIC treatment was maintained constant (11±0.3 g H 2 O/100 g dry matter). DIC treatment experiments were then carried out using the operating conditions described in Table 2.

The statistical treatment of results was executed using the analysis design procedure of Statgraphics Plus software for Windows (1994, version 4.1, Levallois-Perret, France). Variance (ANOVA) was performed to determine significant differences between independent variables, and Pareto charts were introduced as well as general trends, response surface, empirical model coefficients, and R 2 were determined. The dependent variables had concerned process performances: the response was expressed with a second order polynomial model of independent variables :

where Y was the response, were the regression coefficients, C, t were the independent variables, ε was random error. Response surface methodology could be used to optimize the operating parameters by coupling various studied responses. The extraction efficiency EE considered as the main response parameter (dependent variable) was calculated from SPME analysis by summing the areas, carried out on untreated sandalwood chips (raw material) and residual solid after DIC treatments, as:

EE (%) =

Analysis by GC/MS with solid-phase microextraction (SPME)

The volatile molecules present in the untreated solid samples, as well as in DIC treated samples were analyzed through SPME system (model CombiPal, CTC Analytics AG, Zwingen, Switzerland) connected with a GC-MS system. Comprising a Varian GC 3800. equipped with a capillary column VARIAN, with an apolar phase (polydimethylsiloxane) model VF-5ms (30m× 0,25 mm× 0,25 mm), was connected to a mass spectrometer Saturn 2100T, equipped with a sample tray of the CombiPaL ( Cie Varian, Les Ulis, France).

In this study, a 75µm CAR/PDMS Fuses Sillica fiber was used.The SPME parameters including the sample mass, extraction temperature, extraction time, and desorption time were respectively: 1 g, 70 °C, 30 min and 10 min. GC analysis conditions were optimized, with helium used as carrier gas, at a constant rate of 1 ml/min. The column temperature was 70 °C for 6 min; it increased to 120 °C at 15°C/min, from 120 to 200 at 3 °C/min, and 25 °C/min up to 250 °C. The detection, and transfer temperature was 230 °C and 250 °C respectively. Compounds were identified by comparing their mass spectral fragmentation patterns with those stored in the data bank MS from National Institute of Standards and Technology (NIST). For each compound on the chromatogram, percentage of peak area relative to the total peak areas from all compounds was determined and reported as the relative amount of that compound.

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Results and discussion

Hydrodistillation

The study of the kinetics of extraction of essential oil by hydrodistillation reveals extraction increases with time to reach after 160 hours of extracting a level of stability (Fig. 4).

The partial pressures of water and other volatile compounds inside the holes of the plant considered as porous material closely depend on the temperature through the thermodynamic liquid/gas equilibrium of the mixture of the volatile molecules. Therefore, we sought to determine the thermodynamic properties of liquid-vapor equilibrium of each compound of sandalwood. The vapor pressure at various temperatures of the various compounds was determined using the ACD / I-Lab (ACD / Labs 2010-2014). These data then plot the relative volatility of each compound relative to the water Fig. 5. The results show a relative volatility whose evolution is significant depending on the temperature. Thus, in the field of hydrodistillation, the temperature is 100 °C, and the relative volatility is less than 0.004. This aspect of very low relative volatility explains the low kinetic evaporation extraction.

Comparative extraction yields of hydrodistillation extraction and DIC

These both values of hydrodistillation and DIC yields were sub-estimated, the first would be due to the condenser problems whereas the second would concern some amount of essential oils linked on the vacuum tank wall. However, these values were able to prove the ability of DIC to extract very quickly much higher yields of sandalwood essential oils (Table 3).

DIC optimization statistical and experimental design protocol

As shown in Table 2, we performed a central composite experimental design. The number of DIC cycles and total heating time were taken as independent parameters it allowed analyzing and determing the importance of the Autovaporisation and evaporation respectively. The extraction efficiency EE% determined on each solid residue after DIC experimental design by SPME was considered as the main response parameter. The mathematical relationship obtained with the statistical package Statgraphics was a polynomial equation representing the quantitative effect of process variables and their interactions on the measured response EE.

The response surfaces allowed us to represent the total effect of operative parameters. RSM optimization was used to show the impact of the operative factors in terms of extraction efficiency EE (Fig. 6). Thus, it was possible to identify the highest and the quickest DIC extraction process through the operation efficiency. Here, it was clear that the number of cycles (revealing the impact of the pressure drops) was the only factor to have a profound effect. The values of the coefficients of C and t were related to the effect of these variables on the response EE (Fig. 7). A positive value represented an effect that favors the operation, while a negative value indicated an antagonistic effect.

This mathematical relationship is listed below: EE (%) = 15.6644 -0.0218008t + 4.54692C + 0.0000199396t 2 -0.000341237tC -0.0729185C 2 With R 2 = 87.62% (4) The optimized operative conditions with the goal to maximize the extraction efficiency EE was calculated as an optimum value of 77.17%, for 120 s as a total thermal treatment time t, and 22 as a theoretical value of the number of cycles C. These t and C optimized values were substituted and used in experimental trials carried out at 0.6 MPa as saturated steam pressure P, total thermal treatment time t = 330 s, and C = 22 cycles, which means 15 s of thermal treatment time for each cycle.

Conclusion

The present research work confirmed the high relevance of DIC treatment as extraction process. At both fundamental and experimental points of view, this study allowed the DIC extraction process to be defined as a mainly autovaporization phenomenon; the contribution of evaporation to the extraction of essential oils was established to be very weak even negligible in the usual DIC processes. The natural structure of some plants such as sandalwood prevents an easy conventional essential oil extraction. The extraction performed by hydrodistillation (HD) showed that a slow process.

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1 .

 1 The treatments by hydrodistillation were performed as references to compare the DIC extraction yields and kinetics. An adequate statistical treatment of the data issued from the experimental work carried out in the present article allowed us to study, analyze, optimize and model the DIC extraction of essential oils.

Fig. 1 .

 1 Fig. 1. Protocol treatment of sandalwood chips oil extraction.

Fig. 2 .

 2 Fig. 2. Schematic diagram of DIC system. (1: boiler; 2: processing vessel; 3: quick pneumatic motion valve; 4: vacuum tank; 5: vacuum pump; 6: tank of liquid).

Fig. 3 .

 3 Fig. 3. Temperature and pressure history of a cycle of DIC extraction: (a) Sample at atmospheric pressure; (b) initial vacuum; (c) saturated steam injection to reach the selected pressure; (d) constant temperature corresponding to saturated steam pressure; (e) abrupt pressure drop towards vacuum; (f) vacuum; (g) releasing tothe atmospheric pressure.[START_REF] Allaf | Instant controlled pressure drop (D.I.C.) in food processing : from fundamental to industrial applications[END_REF].

Fig. 4 . 5 .

 45 Fig. 4. Kinetics of hydrodistillation of sandalwood. Fig. 5. Relative volatility of sandalwood volatile compounds vs water.

Table 1 .

 1 Independent variables used in response surface methodology at a fixed steam pressure value

Table 2 .

 2 DIC extraction trials with extraction efficiency.

		1	2	3	4	5	6	7	8	9	10	11	12	13
	Total time (s) 600 1080 600 600 960 960 600 240 240 600 120 600 600
	Time per cycle	50	90 27	50	51	192	50	48	13	50	10	300	50
	(s)
	Number of	12	12	22	12	19	5	12	5	19	12	12	2	12
	cycles
	Efficiency (%) 47.54 48.32 69.51 40.97 71.03 38.06 63.22 31.28 67.69 55.34 59.92 15.43 50.12

Table 3 .

 3 Yield of essential oils obtained using DIC extraction in comparison with conventional hydrodistillation.

		DIC Hydrodistillation
	Yields (g EO/100	1.14	1.23
	g dm)
	Total heating time 5min	24h

Acknowledgements

The authors wishes to thank la Communauté d'Agglomération de La Rochelle for financial support for this research.


MD Bruce R Conklin
email: bconklin@gladstone.ucsf.edu.

Edward C Hsiao

Sylvie Claeysen

Aline Dumuis

Supriya Srinivasan

John R Forsayeth

Jean-Marc Guettier

W C Chang

Ying Pei

Ken D Mccarthy

Robert A Nissenson

Jürgen Wess

Joël Bockaert

MD Bryan L Roth
email: bryan_roth@med.unc.edu

Engineering GPCR signaling pathways with RASSLs

We are creating families of designer G-protein-coupled receptors (GPCRs) to allow for precise spatiotemporal control of GPCR signaling in vivo. These engineered GPCRs, called receptors activated solely by synthetic ligands (RASSLs), are unresponsive to endogenous ligands but can be activated by nanomolar concentrations of pharmacologically inert, drug-like small molecules. Currently, RASSLs exist for the three major GPCR signaling pathways (G s , G i , G q ). These new advances are reviewed here to help facilitate the use of these powerful and diverse tools. G-protein-coupled receptors (GPCRs) are an ideal vehicle for engineering synthetic signaling systems. These receptors function as signaling switches throughout the body and regulate virtually every physiological response 1-3 . GPCRs are also the largest gene family targeted for drug discovery 4 . GPCRs stimulate a variety of G protein pathways; for example, G s stimulates

cAMP production, G i inhibits cAMP production, and G q stimulates phospholipase C and releases intracellular calcium stores. Since GPCRs have a relatively simple modular design and are encoded by small genes (usually <1.5 kb), engineered GPCRs can be easily transferred without loss of their functionality into different tissues and species. Finally, designer GPCRs could be useful for regulating physiologic processes and engineering tissues with stem cells and other technologies.

Attempts to engineer GPCRs that are activated solely by pharmacologically inert drug-like molecules have met with varying degrees of success (Table 1). Engineered receptors and engineered receptor/ligand pairs have been created by several approaches and bear different names-receptors activated solely by synthetic ligands (RASSLs) 5 , therapeutic receptoreffector complexes (TRECs) 6 , neoceptors 7 , and designer receptors exclusively activated by designer drugs (DREADDs) 8 . Here we will refer to them as RASSLs, and we propose a consensus nomenclature (Table 1) for those in widespread use or in development. This nomenclature links the name of the parent receptor to the major G-protein signaling pathway activated by the receptor.

Engineering RASSLs by directed mutagenesis

In the first attempt to make a designer GPCR, Strader and colleagues developed a series of compounds to selectively activate a mutant version of the ••-adrenergic receptor (••-AR) that was unresponsive to its natural hormone 9 . This group focused on D113 3.32 , which is conserved among all biogenic amine GPCRs and is critical for binding terminal amine groups (Fig. 1). Mutating D113 3.32 to Ser greatly reduced activation of the •2-AR by biogenic amines. Remarkably, this mutation enabled the newly synthesized butanone derivative, 1-(3',4'dihydroxyphenyl)-3-methyl-1-butanone (L-185,870), to activate the mutant receptor but not the wildtype (WT) receptor, albeit with relatively low potency (EC 50 =118 •M) 9 . Although this original report was inspiring, the synthetic agonist had low affinities and unknown pharmacokinetics that rendered it impractical for in vivo use.

The first engineered receptor or RASSL activated by an agonist with nanomolar affinity suitable for in vivo use was reported by Coward et al. 5 , who took advantage of potent synthetic drugs originally developed as potential analgesics, such as •-opioid receptor (KOR) agonists (e.g., spiradoline). The first RASSL was created by introducing mutations in the KOR that abrogated signaling via the natural peptide ligands, yet preserved stimulation by spiradoline 5 . This engineered human RASSL (hRO-i; h=human, R=RASSL, O=Opioid, i=G i ; referred to as Ro1 5 , a G i -coupled receptor, has been expressed in at least six tissues (Fig. 2) in transgenic animals. Diverse phenotypes were induced, including ligand-dependent heartrate modulation 10 , bitter and sweet taste sensations 11,12 , and ligand-independent cardiomyopathy 13 , hydrocephalus 14 , and osteopenia 15 . These exciting results fueled efforts to develop RASSLs with improved ligand pharmacology and a greater range of signaling responses.

Once scientists understood that RASSLs could be designed to work with existing drugs, new RASSLs soon emerged from studies of a wide variety of receptors, including the 5-HT 4 serotonin 16 , •2-adrenergic 6 , H 1 -histamine 17 , A3 adenosine 7 , 5-HT 2A -serotonin 18 , and MC4melanocortin 19 receptors. In most, key residues essential for binding the native ligand were targeted by site-directed mutagenesis. For example, introduction of the D100 3.32 A mutation (analogous to the D113 3.32 A mutation in the •2-AR 9 ) into the G s -coupled human 5-HT 4 serotonin receptor abolished the ability of 5-HT to activate the receptor but did not affect the activity of many synthetic agonists, including carbazimidamides, benzamides, benzimidazolones, and aryl ketones; this RASSL, previously known as Rs1, will be referred to as hRS-s 16 . Many of these synthetic agonists have drug-like properties, nanomolar affinities, and readily penetrate the central nervous system and can therefore be used effectively in vivo 16,20 . In addition, hRS-s is activated by antagonists of the 5-HT 4 receptor, which have fewer in vivo side effects than 5-HT 4 receptor agonists. Intriguingly, when expressed in osteoblasts of young mice, hRS-s dramatically alters bone growth in vivo 21 , presumably due to constitutive activation of the G s pathway. These experiments provide valuable insights into the specific cellular and temporal factors that allow G s signaling to induce bone growth. This same mutagenesis approach of replacing conserved residues of the binding pocket with alanines has been applied to other biogenic amine receptors. Thus, mutation of a conserved serine residue in the fifth transmembrane region (S204 5.46 A) led to a sizeable loss of affinity and efficacy of (-)-adrenaline at • 2A -adrenoceptors (G i/o -coupled receptors), while the mutated receptor could still be activated by synthetic agonists (UK14304, clonidine) or even by antagonists of the WT receptor (atipamezole, SKF86466) 22 . Similarly, a G q/11 -coupled RASSL was obtained by introducing the F435 6.55 A mutation into the histamine H 1 receptor 17 . This RASSL could be activated by high concentrations of endogenous histamine and had improved affinity and potency for 2-phenylhistamines, a class of synthetic H 1 R agonists (2-[3-chlorophenyl]histamine). Interestingly, alternative substitutions at this position (F435 6.55 ) resulted in RASSLs with different levels of constitutive activity; F435 6.55 A (hRHs) had the lowest level of constitutive signaling.

Creating RASSLs by directed molecular evolution

Despite these noteworthy advances, first-generation RASSLs were not ideal for experimentation. The ligands of first-generation RASSLs activated endogenous receptors (e.g., •-opioid, H1-histamine, 5-HT4-serotonin, MC4-melanocortin), and had low affinities for the mutated receptor (A3-adenosine neoceptor; ••-AR TREC; 5-HT 2A serotonin RASSL). Moreover, profound phenotypes induced by constitutive activity were observed upon RASSL overexpression in vivo (RO-i and RS-s). Finally, development of new RASSLs by repeated cycles of directed mutagenesis was labor intensive and did not consistently yield receptors with ideal agonist affinities or controlled levels of constitutive signaling. To overcome these inherent difficulties, we developed a generic approach to create a new class of RASSLs that have low constitutive activity and respond specifically to drug-like, pharmacologically inert small molecules 8 .

We used a well-established yeast mutagenesis system to produce hundreds of thousands of mutant hM 3 muscarinic receptors and screened them for signaling characteristics of an "ideal" RASSL 8 . After multiple rounds of mutagenesis and iterative screening, we isolated mutants that had lost the ability to respond to the natural ligand (acetylcholine) but gained the ability to respond with nanomolar potency to clozapine-N-oxide (CNO), a pharmacologically inert, bioavailable 23 synthetic compound (Fig. 3). This new class of RASSLs was designated DREADDs (ref. 6). We will refer to this first DREADD as "hRMD-q" (RASSL M 3 DREADD, G q -coupled; referred to as hM3-D in ref. 6 ). The RMD-q receptor is insensitive to acetylcholine but activates the G q pathway to induce calcium mobilization upon binding of CNO. Analogous mutations in the closely related M 4 muscarinic receptor, which is Gi-coupled and inhibits cAMP accumulation, led to another RASSL/DREADD that we call hRMD-i (referred to as hM4D 8 ). Intriguingly, when activated by CNO, hRMD-i silenced hippocampal neurons via G••-mediated activation of G-protein inwardly rectifying K + (GIRK) channels 8 . It is likely that hRMD-i will be widely used to induce neuronal silencing in vivo via indirect activation of GIRKs. More recently, (Guettier, J.M., et al abstract, International Group on Insulin Secretion, St. Jean Cap-Ferrat, France; 2007), made chimeras of the rat equivalent of the hRMD-q that incorporates the second and third intracellular loops of the G s -coupled •1 adrenergic receptor to create a G s -coupled RASSL (rRMD-s, see table 1). Thus, CNO can be used to activate the G s , G i , or G q signaling pathways, depending on which of the new RASSLs is utilized.

With the current DREADD-type RASSLs, only two point mutations were required to create hRMD-I and hRMD-q. By contrast, the rRMD-s required two point mutations and swapping of two intracellular loops. Creating other DREADD-type RASSLs by directed molecular evolution will likely require at least multiple point mutations based on our own unpublished experience (Pei et al, in preparation). Thus far, all of the point mutations have been found in or near predicted binding sites for orthosteric ligands.

The general method we devised evolves GPCR ligand specificity toward pharmacologically `inert" ligands (e.g., drug-like compounds without known molecular targets). This technique is likely to be widely used to create designer GPCRs, owing to the availability of strains of yeast (Saccharomyces cerevisiae) engineered to express and respond to human GPCRs 24,25 . When these GPCR-expressing yeast are activated by an agonist, the signal induces the expression of a variety of selectable markers under control of a Fus-1 promoter. This system allows for the facile screening and optimization of millions of mutant GPCRs in a relatively short time 26 . Dozens of human GPCRs have been expressed in yeast 27 , thereby opening up the potential to create families of designer GPCRs activated by specific small molecules.

RASSLs as molecular switches for tissue engineering

RASSLs may be valuable in controlling growth and ensuring appropriate control of function for experimental or therapeutic tissue engineering. GPCR signaling is essential for the growth and differentiation of many tissues 2 . For example, the 5-HT 2B serotonin receptor is required for cardiac development and cell-cycle progression 28-30 . Ectopic signaling via GPCRs can promote abnormal growth 3 , leading to human disease. For instance, drug-induced valvular heart disease may be caused by excessive stimulation of cardiac 5-HT 2B receptors 31 . One can envision the use of RASSLs to activate discrete signaling pathways to promote the proper growth and differentiation of engineered tissues.

Another potential use of RASSLs is to gain precise control of signaling in neurons and other tissues. Currently, this control in defined neuronal populations can be facilitated by expressing RASSLs in a neuron-specific manner. We reported that CNO-mediated activation of the G icoupled hRMD-i induces neuronal silencing when expressed in hippocampal neurons 8 . When expressed in hippocampal neurons, hRMD-q induces neuronal excitation and intracellular Ca ++ release in CNO-dependent fashion (Rogan and Roth, manuscript in preparation). Using these two engineered muscarinic receptors, one could gain precise bi-directional control of neuronal firing in vitro and in vivo. These modified receptors could also be used in other excitable tissues, such as cardiac pacemaker cells, where G s stimulation speeds diastolic depolarization and accelerates heart rate, and G i stimulation slows heart rate. Expression of different G s (e.g., hRS-s or rRMD-s) and G i (e.g., RO-i or hRMD-i) RASSLs in pacemaker cells could allow for the precise regulation of heart rate without affecting cardiac muscle function.

The importance of constitutive signaling by RASSLs

In studies of first-generation RASSLs expressed in vivo, constitutive signaling (constitutive activity) has often produced the most profound effects. Overexpression of a G i -coupled RASSL (hRO-i) in cardiomyocytes led to cardiomyopathy 13 , while overexpression in osteoblasts led to osteoporosis 15 . Recently a G s RASSL (hRS-s) expressed in osteoblasts induced marked bone growth 15 . Constitutive activity is a common property of native GPCRs 32,33 and is essential for the normal function of certain GPCRs 34 . Therefore, RASSLs with different levels of constitutive activity (high and low) will be needed to recapitulate normal GPCR functions. Because of the potential ligand-independent effects, RASSL expression ideally should be controlled through conditional expression systems (e.g., Tet or Cre). With these systems, a single RASSL transgenic line can be used to drive expression in diverse tissues with tighter temporal control. The second-generation RASSLs (hRMD-q, hRMD-i, rRMD-s) were created to lack constitutive activity 8 , and thus far, their overexpression in mice has not elicited baseline phenotypes (Rogan, Roth, Guettier and Wess, unpublished observations). These secondgeneration RASSLs will be most useful for studies in which ligand-dependent effects (rather than baseline phenotypes) are sought.

Future directions

The RASSL field has undergone dramatic growth in the past decade, but many more challenges lie ahead. For instance, the ideal family of RASSLs would respond to a clinically approved, biologically inert drug (e.g., antibiotic or antiviral) that has no intrinsic effect on human cells, allowing tissue engineering without the drug safety studies needed for relatively new compounds such as CNO. The optimal series of RASSLs would also selectively couple to each of the GPCR pathways, including noncanonical pathways, such as those involving arrestins, GRKs, and intracellular kinases 29 . Furthermore, each RASSL would have different constitutive responses, desensitization properties, and subcellular targeting that could be finetuned with simple mutations. For many of these goals, we will need spatiotemporal control of RASSL expression to allow for direct comparisons of RASSL actions that could be applicable to virtually any tissue. Several groups are now testing a variety of approaches (BAC transgenics, knock-ins, and inducible systems) to meet these new challenges and provide new tools to RASSL researchers. With these highly refined tools, biologists will have a better understanding of how to use RASSLs and GPCR signaling pathways for tissue engineering.

The cross-disciplinary nature of RASSL-related research fosters a highly collaborative community that makes protocols, reagents, and transgenic animals publicly available whenever possible. Even though individual members of the RASSL community initially created tools specifically for their own research, the potential uses of these tools go well beyond any individual project. Indeed, precisely because GPCR signaling is important to such a wide swath of biology, it is impossible for us to accurately predict how and where RASSLs will be ultimately used.

We anticipate that our RASSL delivery systems will be deployed for a wide range of tissue engineering applications in neurological disease, pain perception, immunology, bone metabolism, and diabetes. In each case, our efforts will provide enabling technologies to rapidly advance those fields. For instance, in many neurological diseases (e.g., Parkinson's disease), RASSLs may be useful for correcting the imbalance of neural pathways, in a manner that could complement the surgical/electrical approaches in current clinical practice. Similarly, many groups envision using tissue-engineering approaches to study pain perception pathways. RASSLs, which selectively modulate neuronal firing, should be ideal for this application. Although GPCRs are clearly important in bone metabolism, many key receptors signal via multiple pathways and exhibit constitutive signaling. RASSLs allow researchers to stimulate discrete signaling pathways in bone metabolism. Finally, in diabetes, GPCRs play a role in the growth, development, and function of insulin-secreting pancreatic •-cells 35 . Dissecting the precise roles of different G-protein signaling pathways in •-cell function should be of considerable therapeutic interest.

Perhaps most importantly, the use of RASSL technology may shed light on relatively unknown aspects of GPCR signaling. For instance, many researchers are investigating nonclassical signaling responses of GPCRs, such as signaling by G 12/13 , arrestins, receptor kinases, regulators of G protein signaling, Wnt receptor signals, and scaffolding proteins 29 . It should be of interest to create two RASSLs that only differ in their ability to activate the arrestin pathways. Expression of these two RASSLs in the same spatial and temporal pattern would then allow determination of the true physiological roles of arrestin signaling. Some of these non-G-protein signaling pathways could prove essential for robust tissue engineering and for uncovering the pathways responsible for stem cell differentiation. One can envision scenarios in which RASSLs are selectively expressed in different stem cell lineages and then activated (with an exogenous ligand or by overexpression) to determine which pathways are responsible for lineage choices and tissue differentiation. Creating RASSLs by targeted mutagenesis. A conserved residue(s) in the canonical binding pocket of biogenic amine receptors (e.g., adrenergic, serotonin, histamine) is mutated to eliminate the binding and activation of the receptor for the native ligand. A model using the coordinates of the ••-adrenergic receptor structure 30 is used to illustrate this. In all biogenic amine GPCRs, the binding pocket is composed of a conserved aspartic acid (D113 3.32 in the •2-AR model; SIDE VIEW) and conserved aromatic and polar residues (TOP VIEW). Mutation of the highly conserved Asp to Ser (D113S) renders the •2-AR insensitive to •-AR exogenous and endogenous agonists, such as isoproterenol, epinephrine, and norepinephrine. However, the D113S mutant receptor could be activated by the synthetic ligand L-185, 870. Such a targeted mutagenesis approach was used to create both peptidergic RASSLs (e.g., •-opioid, MC4-melanocortin) and nonpeptidergic RASSLs (H1-histamine, 5-HT2A serotonin, 5-HT4 serotonin, •2-adrenergic) (see text for details). Directed molecular evolution to create novel RASSLs. Shown is a generic scheme for obtaining RASSLs via directed molecular evolution. In brief, a large library of randomly mutated GPCRs is obtained by error-prone PCR and used to efficiently transform the appropriate yeast strain. Yeast with functional GPCRs is grown in histidine-deficient medium in the presence of the inert ligand (in this case clozapine-N-oxide, CNO), and surviving colonies are expanded and characterized pharmacologically. GPCRs with the appropriate pharmacological profiles are subjected to iterative rounds of additional mutagenesis and selection until the ideal RASSL is obtained. Candidate RASSLs are subjected to growth assays in the presence and absence of candidate ligands to screen out those with elevated levels of constitutive activity. Typically several candidate inert ligands are used in the initial screens to determine which are most suitable for directed molecular evolution and then one or more chosen for further testing. The final choice of the candidate ligand is based on its potency and drug-like properties.

Figure 1 .

 1 Figure 1.

Figure 2 .

 2 Figure 2. Myriad ligand-dependent and -independent phenotypes are induced by tissue-specific expression of a single RASSL. Ligand-induced phenotypes are noted in red; constitutive signaling-induced phenotypes are in blue. Asterisks indicate tissues in which RO1 expression results in embryonic or perinatal lethality. Conditional expression allows RASSL researchers to avoid embryonic lethality and analyze adult phenotypes.

Figure 3 .

 3 Figure 3.

Table 1

 1 Commonly used RASSLs

	Name	Alternative names:	Signaling notes	Agonist and antagonists	In vivo phenotypes
		major versions		(relative affinities in nM)
	hRO-i	Ro1 5,10 : human kappa opioid receptor with delta opioid extracellular loop,	G i signaling, with constitutive signaling in heart,	Agonists	Cardiac, neurological, sweet taste, bitter taste, bone. See Figure 1.
		and N-terminal FLAG	but not no apparent
		epitope tag	constitutive
			signaling in cultured
			cells
				Spiradoline (low nM)
				Salvinorin A (low nM)
				Antagonist:
		hRO3-i (RO3 or Rog) 36 :		Nor-binaltorphimine-
		same as Ro1, but with		dilhydrochloride (Nor-BNI)
		point mutation and N-		(low nM)
		terminal GFP tag
	hRS-s	Rs1 16,20,21 : human serotonin 4 receptor with	G s -signaling, with high level of	Agonist	Massive increase in bone formation
		D100A mutation with N-	constitutive activity
		terminal FLAG epitope
		tag
				RS67333, RS39604, Cisapride,
				ML10375, GR113808 (all nM)
		hRS2-s (Rs2) 20 : has N-		Antagonist None known
		terminal GFP tag
	hRMC-s	RM1 19 : human	G s -signaling	Antagonist	None known
		melanocortin 4 receptor	constitutive
		with point mutations	signaling essential
			for native receptor
			function
				None known
	hRMD-q	DREADD hM3D 8 :	G q signaling	Agonist	None known
		human M 3 muscarinic
		receptor with point
		mutations
				CNO (low nM)
				Antagonist
				Atropine (reduced affinity vs.
				WT; high nM)
	hRMD-i	DREADD hM4D 8 :	Gi signaling	Agonist	Inhibits electrical
		human M 4 muscarinic			signaling in brain slices
		receptor with point
		mutations M 2 receptor
		RASSL is also Gi coupled
				CNO (low nM)
				Antagonist
				Atropine (reduced affinity vs.
				WT; high nM)
	rRMD-s	DREADD RASSL2: rat M 3 receptor with point	G s signaling	Agonist	None known
		mutations and
		intracellular loops from
		the turkey •1-AR
				CNO (low nM)

Antagonist

Nat Methods. Author manuscript; available in PMC 2009 June 29.

Nat Methods. Author manuscript; available in PMC 2009 June 29.

ACKNOWLEDGMENTS

We would like to thank our funding agencies and the members of our labs who have contributed to the RASSL projects. In particular, we appreciate support by the US National Institutes of Health; HL60664-07 (BRC), DK072071 (RAN), U19MH82441 (BLR), a NARSAD Distinguished Investigator Award (BLR), the American Heart Association predoctoral fellowship program (0415005Y to WCC), and the Veterans Affairs Merit Review Program (to BPH), the California Institute of Regenerative Medicine, Gladstone Institute CIRM Fellowship Program (Grant T2-00003 to ECH). The Gladstone Institutes received support from National Center for Research Resources Grant RR18928-01. The authors thank J. Ng, T. Nguyen, D. Srivastava, R.W. Mahley, H. Zahed, B. Phillips, M. Spindler, G. Howard, and S. Ordway for providing valuable technical assistance and discussions.

Name

Alternative names: major versions

Signaling notes Agonist and antagonists (relative affinities in nM)

In vivo phenotypes

Atropine (reduced affinity vs. WT; high nM)

This table only includes RASSLs that are actively used in transgenic animals and have a commercially available ligand with low side effects. A uniform RASSL naming system is used. For instance hRMD-q stands for: h=human, R=RASSL, M=Muscarinic, D=DREADD, q=signaling via G q . The shortest possible name is used. For the parent RASSL we do not add a number but numbers can be added, to indicate versions. For instance hRO3-i, is a GFP tagged version of hRO-i.