Isabelle Braud

Sébastien Zamith
email: sebastien.zamith@irsamc.ups-tlse.fr

Jérôme Cuny

Linjie Zheng

Jean-Marc L'hermite

Size-Dependent Proton Localization in Hydrated Uracil Clusters: A Joint Experimental and Theoretical Study

A collision-induced dissociation study of hydrated protonated uracil (H 2 O) n=1-15 UH + clusters is reported. The mass-selected clusters collide with water molecules and rare gases at a controlled center of mass collision energy. From these measurements, absolute fragmentation cross sections and branching ratios are extracted as a function of the uracil hydration. For small clusters, up to n = 4, we observe that only neutral water molecules are evaporated upon collisions, whereas for larger clusters neutral uracil is also evaporated: this transition in the nature of the evaporation products is interpreted considering the lowest-energy isomers of each species that are obtained from a combination of density-functional based tight-binding (DFTB) and MP2 calculations. The simulations show that in (H 2 O) 1-4 UH + the proton is located on the uracil molecule or on a water molecule strongly bound to uracil whereas, in larger clusters, the proton is bound to water molecules far from uracil. This correlation between the structure of the low-energy isomers and the experimental fragmentation channel suggests that dissociation may occur in a very short time after collisions, so that energy has not enough time to be redistributed among all degrees of freedom and the ground-state geometry of the parent cluster partly determines the nature of the favored fragmentation channels. Of course, thermal dissociations originating from long lived, thus thermalized, collision complexes cannot be ruled out but they are not expected to play the major role since experimental results can be satisfactorily accounted for by assuming that the fragmentation processes are mainly impulsive.

INTRODUCTION

Water is the natural medium of the biological molecules, and the process of hydration is of general interest to chemists and biologists. The study of mixed clusters composed of biological molecules with water is therefore a good workbench to observe how the properties of biological molecules change when going from isolated gas-phase to hydrated species.

One challenging question of great medical interest nowadays is the effect of radiation onto DNA and RNA molecules. The damages on these molecules can be directly caused by the radiations, or indirectly by secondary electrons created by the radiation. Uracil C4H4N2O2 (U) is one of the four nucleobases of RNA that received attention concerning radiation damage. Charged uracil UH + can be formed by radiation damages and has thus deserved some attention [1]. One of the reasons for such degradation can, for example, be due to the interaction with slow electrons as shown by the pioneer work of Boudaiffa et al. [2]. Although several studies have been devoted to the effect of hydration on the electron affinity of DNA bases [3,4,5,6], there is still much to be done to understand the role of aqueous environment on DNA and RNA.

Studying fragmentation of biomolecules through collision induced dissociation (CID) is helpful to understand reactivity and provide access to structural information [START_REF] Hayes | Collision-induced dissociation[END_REF]. Fragmentation of the bare protonated uracil molecule has already been performed under CID with tandem mass spectrometry [START_REF] Nelson | [END_REF]9,10,11,12], but there are only few studies available concerning the effect of hydration on such process. Infrared photodissociation spectroscopy of singly hydrated protonated uracil [13] shows that the most stable tautomeric form of the neutral uracil (di-keto) differs from the most stable one for bare protonated uracil (keto-enol). Some theoretical studies report the structures taken by neutral microhydrated uracil, containing up to 15 water molecules [14,15,16,17,18]. However fragmentation studies of such species under CID conditions has not been reported so far.

We report in this paper both the results of CID experiments performed on hydrated protonated uracil species (H2O)nUH + (n=1-15) and theoretical calculations to determine their lowest-energy structures. In the latter case, we used a methodology combining density-functional based tightbinding (DFTB), for a rough exploration of the potential energy surfaces, and MP2 calculations for accurate characterization of low-lying isomers. In our experiments, the dissociation of mass selected hydrated protonated uracil clusters is induced by collisions with rare gas atoms. After the collisions, the remaining charged species, which have lost one or several neutral subunits, are detected. The resulting inter-molecular dissociation patterns of the (H2O)nUH + clusters show that below n = 5 only water molecules are evaporated whereas for n ≥ 5 a new fragmentation channel appears corresponding to the loss of neutral uracil.

The fragmentation can arise from two distinct mechanisms depending on the life time of the collision complex. On the one hand if fragmentation occurs in a very short time after collision, the dissociation is impulsive (or direct), which mean that molecules are ejected from a parent cluster whose structure is essentially unchanged before evaporation takes place. In this case, the ground state structure of the parent cluster obviously plays a major role in determining the fragmentation channels. On the other hand, in the case of long-lived collision complexes, the structure of the cluster can undergo structural reorganizations before evaporation and the role of the initial structure of the parent clusters is strongly reduced. DFTB/MP2 calculations demonstrate that there is a direct correlation between the location of the excess proton in the lowest-energy isomer of a considered cluster and the fragmentation channel it undergoes. This suggests that direct dissociation upon collision is responsible for the appearance of neutral uracil from n = 5 as statistical dissociation would favor protonation of the uracil. However, an accurate measure of the relative contribution of statistical versus direct dissociation cannot be determined.

Section II of this paper describes the experimental set-up used to determine fragments branching ratios and fragmentation cross sections. The computational method used to determine the lowest-energy structures of hydrated protonated uracil clusters is described in section III. In section IV are reported the experimental cross sections and the fragmentation branching ratios of hydrated protonated uracil clusters. Finally, in section V the calculated structures of mixed uracilwater clusters are presented and the experimental results are discussed in the light of these structures. The main outcomes and perspectives are summarized in the conclusion.

II. EXPERIMENTAL SET-UP

Our experimental set-up enables collisions at a controlled kinetic energy between the molecules of a vapor and mass-selected thermalized charged clusters. It has been described in detail elsewhere [19]. Here we remind of the main stages. Charged clusters are produced in a gas aggregation source [20]. A flow of helium carrier gas and water vapor enters the source in a cell where uracil in solid form (Alpha Aesar, 99%) is heated at 378 K to get a vapor pressure of about 6.6 × 10 -2 mbar [21]. A miniature electron gun located at the cell exit allows to ionize the clusters in the source. The typical kinetic energy of the electrons is 100 eV. The clusters formed in the source at the temperature of liquid nitrogen are carried out of the source by the helium gas flow.

The produced clusters then enter the thermalization chamber where tens of thousands collisions between the helium gas and the clusters cool them down to the helium gas temperature. A thermalization temperature of 25 K is obtained by cooling the thermalization chamber with a closed cycle helium cryostat. This low temperature reduces the amount of internal energy prior to collision compared to experiments usually performed at room temperature. For instance, using the harmonic frequencies ωi calculated for the neutral uracil [22], its internal energy Eint is estimated by:

e / 1 (1)
At 25 K, the internal energy of uracil molecule is about 8 µeV, only the lowest-energy isomers are thus expected to subsequently undergo collision with the target species.

After the thermalization stage, the clusters then enter the high vacuum part of the experiment where an original time of flight device using electrostatic pulses applied to electrodes enables mass-selection and slowing down to a controlled kinetic energy. Laboratory frame collision energies, ranging from 54 to 145 eV, are measured by time of flight measurements [19]. In the present work the corresponding center of mass (CM) collision energy is kept constant at 7.2 eV.

This energy is chosen high enough so that a large number of fragmentation channels are explored.

The clusters cross the collision cell in free flight where they can collide with the molecules or atoms of a vapor at 300 K whose pressure is controlled. The pressure in the cell is measured with a mechanical vacuum gauge (Leybold Ceravac CTR 91). The collision products are then mass analyzed by a reflectron time-of-flight mass spectrometer and detected using micro channel plates. At that stage, it is worth pointing out that an accurate picture of the collision and subsequent fragmentation mechanism cannot be obtained from the present experimental set-up and we are not able to distinguish between direct dissociation and statistical evaporation.

Several target atoms or molecules M were introduced in the collision cell. We have performed experiments with M = H2O, D2O, Ne and Ar. We find essentially the same results whatever the nature of M, and in order to keep things clearer, we only present and discuss results obtained with

Ne in this paper. Figure 1 shows a typical fragmentation mass spectrum obtained here by colliding (H2O)n=7UH + with Neon at a CM collision energy of 7.2 eV. The more intense peak on the right comes from the parent cluster (H2O)n=7UH + , the next 7 peaks at the left of the parent peak correspond to the loss of 1 to 7 water molecules and the next 5 peaks to the left results from the evaporation of the uracil molecule and several water molecules. This figure is obtained at the highest pressure explored in the present experiments. For such a pressure multiple collisions are no longer negligible, thus allowing the evaporation of all water molecules. This is still true for the largest size investigated here, namely n = 15.

From the mass spectrum of the collision products, the branching ratios (BR) of the different charged fragments can be determined. The branching ratio corresponds to the intensity of a specific fragment over the total intensity of fragments. It is important to notice that the fragments considered here are the charged ones.

The total fragmentation cross-section can be deduced from the mass spectrum as: Lcel : The length of the collision cell, namely 5 cm here ;

In order to determine the fragmentation cross-sections, we record the mass spectra after the collision cell as a function of the pressure in the collision cell. Figure 2 gives an example of the evolution of -ln(I/I0) as a function of the product Lcel. The linearity of the curve presented in figure 2 ensures that a single collision is sufficient to induce the fragmentation of the parent cluster.

The fragmentation cross-section for a specific channel i is then given by (3) where BRi is the branching ratio for channel i. In our study we will be interested in two specific channels. Channel 1 corresponds to the loss of only neutral water molecules whereas channel 2 corresponds to the loss of neutral uracil and one or several water molecules: Branching ratios are also determined by varying the collision cell pressure. The branching ratios for channel 1 and 2 are defined as follows:

∑ (5)
Since ∑ and using eq. ( 2), we have :

1 e (6)
From relation ( 6), the branching ratios BRi are obtained as the slope of a linear fit of Ii/I0 plotted as a function of 1 exp , as exemplified in Figure 3 in the case of (H2O)7UH + colliding with Ne atoms. Again the linearity of the curves suggests that single collision events are the predominant processes in our experiment. Indeed if two or more collisions were needed to induce fragmentations, this would lead to a non linear evolution with pressure. We do see such an effect for the largest sizes, n=10-15, for which we took only low pressure points to determine the branching ratio. However, 7.2 eV is only a low estimate of the energy deposited in the clusters.

III. COMPUTATIONAL METHOD

To determine the lowest-energy isomers of the U(H2O)nH + clusters (n = 1-7), we applied a twostep theoretical approach. First, to roughly explore the potential energy surfaces (PES), we conducted parallel-tempering molecular dynamics (PTMD) [23] simulations in combination with a self-consistent-charge density-functional based tight-binding (SCC-DFTB) [24] description of the energies and gradients. In the PTMD algorithm, we used 40 replicas with temperatures going linearly from 50 to 350 K. All the trajectories were 4 ns long, and the integration time step was 0.5 fs. We found that a reasonable time interval for the PT exchanges was 2.5 ps. We used a Nosé-Hoover chain of five thermostats with frequencies of 800 cm -1 to achieve an exploration in the canonical ensemble [25]. The SCC-DFTB calculations were performed with the mio-set for Slater-Koster tables of integrals and repulsive interactions [26]. To improve the description of intermolecular interactions, we used the class IV/charge model 3 (CM3) [27] charges instead of the original Mulliken charges as well as empirical terms to describe dispersion interactions [28]. For the parametrization of the CM3 charges, we used the DOH parametrization proposed by Simon and co-workers (i.e. DOH = 0.129) [29], while all other values were set equal to 0, which corresponds to a Mulliken evaluation of the charges. All SCC-DFTB calculations were performed with the deMonNano code [30]. To avoid any spurious influence of the initial conditions on the PES exploration, three distinct PTMD simulations were carried out. In each one, a distinct initial proton location was set: on the uracil in two cases and on the water molecules in the other one. In the former case, the u178 and u138 isomers of UH + were used as initial geometries (see reference [31] for the isomer numbering and Figure 4 for a representation of those isomers), corresponding respectively to the keto-enol and the di-keto form. 600 geometries per temperature were randomly selected along each PTMD simulation for subsequent geometry optimization which leads to 72000 SCC-DFTB optimized structures for each cluster. The structures were sorted in ascending energy order and identical isomers were discarded. 9, 23, 46, 31, 38, 45 and 63 structures were then selected for U(H2O)H + , U(H2O)2H + , U(H2O)3H + , U(H2O)4H + , U(H2O)5H + , U(H2O)6H + and U(H2O)7H + , respectively, to perform geometry optimizations at the MP2 level of theory in combination with an all-electron Def2TZVP basis-set, [32,33] a tight criteria for geometry convergence and an ultrafine grid for the numerical integration. MP2 calculations were performed with the Gaussian 09 package [START_REF] Frisch | Gaussian 09[END_REF].

IV. FRAGMENTATION OF HYDRATED URACIL CLUSTERS: EXPERIMENTAL RESULTS

A. Fragmentation cross section

The total fragmentation cross sections of mixed clusters U(H2O)n-1H + , pure water clusters (H2O)n=2-6H + [START_REF] Dalleska | [END_REF] and deuterated water clusters (D2O)n=5,10H + [36] are plotted in Figure 5 These experimental data are compared to the geometrical (i.e. hard sphere) cross sections given by:

/ ( 6
)
Where nw is the number of water molecules, nU the number of uracil molecules (nU = 0 or 1 in the present study), rw, rU and rT are the molecular radii of water, uracil and of the target atom or molecule, respectively. The molecular radii are deduced from macroscopic densities that gives rU = 3.2 Å [START_REF] Myers | The 100 Most Important Chemical Compounds, A Reference Guide[END_REF], rw = 1.98 Å. The radii of rare gas target atoms are taken as their Van der Waals radii rNe = 1.54 Å and rXe = 2.16 Å.

The main differences between the curves in Figure 5 can be rationalized as follows: The larger the size of the target atom (or molecule), the larger the fragmentation cross section. The experimental fragmentation cross sections of mixed clusters U(H2O)n-1H + colliding with water molecules are larger than the values obtained for collisions with Ne atoms. In the same vein, for a given number of molecules in the cluster the cross section is larger for clusters containing uracil.

The overall trend of all curves in Figure 5 is the same: The fragmentation cross sections increase with the size and seem to tend towards the geometrical one. The cross sections measured + for mixed clusters are of the same magnitude as the ones previously obtained for deuterated pure water clusters at a similar collision energy [36]. For mixed clusters, fragmentation cross sections are systematically larger than for pure water clusters by an amount of the same magnitude as the one predicted by the geometrical cross sections.

The fragmentation cross sections obtained by Dalleska and coworkers [START_REF] Dalleska | [END_REF] for protonated water clusters are within our error bars for n = 5, 6 and about a factor of 2 lower for n = 3, 4. However their cross-section is notably lower for (H2O)2H + as compared to our measurement for U(H2O)H + .

This difference may be explained by the fact that UH + forms a weaker bond with water than H3O + does. Indeed the dissociation energy D[H3O + -H2O] is 1.35 eV [START_REF] Dalleska | [END_REF][START_REF] Hansen | [END_REF] whereas the value for D[UH + -H2O] is estimated between 0.54 eV [1] and 0.73 eV [13]. The same behavior is observed for n = 3, the dissociation energies are D[(H2O)2H + -H2O] = 0.86 eV [START_REF] Dalleska | [END_REF][START_REF] Hansen | [END_REF] > D[U(H2O) + -H2O] = 0.49 eV [1]. Hence the dissociation of water molecules is more favored in the mixed cluster than in the pure water clusters.

B. Inter-molecular fragmentation

The branching ratios for the different dissociation channels (see relation ( 4)) of hydrated uracil are determined for clusters containing one uracil molecule and from 1 to 15 water molecules. The As stated above, both statistical and direct fragmentation processes can occur upon collision. In the former case collision energy is transferred to the parent cluster and is redistributed among all degrees of freedom. This is a slow process and the structures involved during the fragmentation are no longer the lowest-energy isomer. Furthermore, the excess proton can also diffuse in the structure and, for instance, re-combine with the uracil. In the latter case, dissociation is fast upon collision and the energy cannot be statistically redistributed among all degrees of freedom. We thus assume in that case that the nature of the collision products is partly determined by the nature of the lowestenergy isomers of parent clusters and especially by the location of the excess proton in the structure. In figure 6, we focus on the loss of the neutral uracil molecule in the detected fragments since it indicates where the proton lies after collision, namely on the uracil or on a water cluster. A transition in the nature of fragmentation product is clearly seen from n = 5-6. To account for this transition we consider that evaporation originates from a direct fragmentation process. A short discussion about the implications of possible structural rearrangement prior to dissociation, which occurs in a statistical process, will be provided in section V.

The relative proton affinities of each component of the mixed clusters gives a first estimate of which molecule -uracil or water -is more likely to carry the positive charge prior to collisions.

Experimentally, the gas phase proton affinity of uracil is bracketed to 9  0.12 eV [39]. For the water molecule, an experimental value for the proton affinity [40] is reported at 7.31 eV and a theoretical one [41] at 7.5 eV. These last two works also show that the proton affinity of water clusters increases with their size [41]. We report in Figure 7 [40] (black open circles) and from [41] (blue squares). The value of the proton affinity of uracil is also plotted (red dot dashed line [39]).

The proton affinity of uracil PA[U] is hence larger than the one of water monomer PA[H2O].

Thus, for the mono-hydrated uracil, from the energetic point of view, the proton is on the uracil molecule and the only observed fragments are indeed protonated uracil molecules. Moreover, an experimental work [13] confirms that there is no proton transfer from the uracil to the water molecule in mono-hydrated clusters. Proton affinity of the uracil molecule is also larger than that of the water dimer, or even the trimer: PA[U] > PA[(H2O)n], n = 2 or 3 depending on the considered data for water. This is still consistent with our experimental observation of no neutral uracil molecule loss for n = 2 and 3. However from the PA values one would predict that the appearance of neutral uracil should occur for n ≈ 3 -4 . For instance for n=4, assuming a statistical fragmentation for which the end products energies are expected to be of relevance, the channel U + (H2O)4H + is energetically favorable. If one now assumes a direct dissociation, where the parent protonation state remains unchanged, one also expects that neutral uracil evaporates. However, experimentally, for n=4 no neutral uracil evaporation is observed. The loss of neutral uracil starts at n = 5 and becomes significant only at n = 6. This analysis based on PA is however quite crude. Indeed, it assumes that the mixed cluster would be composed of a uracil molecule attached to an intact water cluster. However, one expects that the hydration of uracil may be more complicated than this simple picture. The uracil hydration is explored theoretically in the next section in order to determine the proton location more realistically.

Finally, we note that we have a maximum of only about 20% of neutral uracil loss upon collisions with Neon atoms. For all sizes, the main fragmentation channel remains the loss of neutral water molecules. As the size increases, the proportion of neutral uracil evaporation even decreases. This feature may be explained by a simple entropic effect : The dissociation energy of a water molecule is very close to the dissociation energy of uracil (about 0.5 eV in both cases), thus their evaporation probability is expected to be comparable. Therefore the weak evaporation probability of uracil is merely correlated to the larger number of water molecules likely to evaporate as the cluster size increases.

V. CALCULATED STRUCTURES OF HYDRATED PROTONATED URACIL CLUSTERS -

DISCUSSION

Theoretical works have already been devoted to mixed uracil-water clusters and intended to describe the lowest-energy structures. However, only neutral species were considered [14,15,16,17,18,42]. Those studies showed that for sizes up to n = 3, the water molecules arrange in monomers or dimers in the plane of the uracil molecule [15,16,17,18,42] with no trimer formation. For n>3, very different structures were predicted depending on the considered study.

For instance, Gaigeot et al. [16] predicted that for n = 7 water molecules arrange in dimers and trimers in the plane of the uracil molecule, whereas for n = 11 water molecules form locked chains [14]. 3D configurations were also proposed. In that case, all water molecules lie above the uracil plane as reported in [18] for n = 4, 5. Similarly, for n = 11, Danilov et al. [17] also obtained a structure that consists of a water cluster above the uracil molecule. Such structures are predicted to start with 4 water molecules according to [18] or with 6 water molecules (though 5 has not been calculated) for [15]. Those studies may suggest that, within the frame of the present work, for few water molecules (up to two) the proton should be located on the uracil molecule, whereas when a large number of water molecules surrounds the uracil, the charge is expected to be located on the water molecules. Of course, the excess proton is expected to strongly influence the structure of the lowest-energy isomers of each species, as observed for pure water clusters for instance, so the size at which the proton is transferred from uracil to water cannot be deduced from the aforementioned studies. Moreover, all those theoretical works do not lead to the same low-energy structures as highlighted in [17] and [18]. Consequently, although instructive from a qualitative point of view, the analysis of our experimental data cannot be based on those studies. We have therefore undertaken a theoretical simulation of small hydrated protonated uracil clusters.

The lowest-energy isomers determined theoretically for hydrated uracil protonated clusters U(H2O)nH + are shown in Figure 8 to Figure 11. In the experiments, clusters are produced at a temperature of about 25 K, so only a very few isomers are likely to be populated. Indeed, the clusters are produced in the canonical ensemble at the temperature Tc ≈ 25 K, so only isomers for which the Boltzmann factor exp(-ΔE /kBTc) is larger than ~10 -7 are considered here. In this formula, ΔE represents the relative energy of a considered isomer with respect to the lowest-energy one. For each isomer, we thus only discuss the 3 (6 for U(H2O)H + ) lowest-energy structures obtained from the PES exploration. Additional isomers are reported in the Supplementary Material.

Figure 8 displays the six lowest-energy isomers obtained for U(H2O)H + . Two (1a and 1b) of them contain the u138-like isomer of U (each one with a different orientation of the hydroxyl hydrogen), 3 of them (1c, 1d and 1e) the u178 isomer and 1f contains the u137 isomer with a reverse orientation of the hydroxyl hydrogen. From those 3 isomers, different sites are possible for the water molecule attachment which leads to variety of isomers even for such small size system.

To the best of our knowledge, U(H2O)H + is the most studied protonated uracil water cluster and our results are consistent with previous published works. Indeed, Pedersen and coworkers [31] conducted ultraviolet action spectroscopy on U(H2O)H + and discussed their measurements in the light of theoretical calculations performed on two isomers: ur138w8 (1a in the present study) and ur178w7 (1c) [31]. Their energy ordering at 0K is the same whatever the computational method they used: B3LYP/6-311++G(3df,2p), M06-2X/6-311++G(3df,2p), MP2/6-311++G(3df,2p), CCSD(T)/6-311++G(3df,2p) and CCSD(T)/aug-cc-pVTZ and is similar to what we obtain.

Similarly, Bakker and coworkers [13] considered three isomers: U(DK)H + _W (1a), U(KE)H + _Wa (1c) and U(KE)H + _Wb (1e) at the B3LYP/6-311++G(3df,2p) level of theory and obtained the same energy ordering as we do. Our methodology has thus allowed us to retrieve those isomers and to locate two new low-energy structures (1b and 1d), 1f is too high in energy to be considered in lowtemperature experiments, that are in the same range of relative energies but have never been discussed. To ensure that they are not artificially favored in our computational method, calculations

were also performed at the B3LYP/6-311++G(3df,2p) level of theory. The results are presented in the Supplementary Material and are consistent with the MP2/Def2TZVP ones. This makes us confident in the ability of the present methodology to locate meaningful low energy structures.

Importantly, no isomer with the proton on the water molecule was obtained, neither at the DFTB or MP2 levels.

Figure 9 displays the three lowest-energy isomers obtained for U(H2O)2H + and U(H2O)3H + .

For U(H2O)2H + , the lowest energy structure contains the u138 isomer of uracil while 2b and 2c contain u178 and u138 with reverse orientation of the hydroxyl hydrogen, respectively. This demonstrates that, similarly to U(H2O)H + , a diversity of uracil isomers are present in the lowenergy structures of U(H2O)2H + which makes an exhaustive exploration of its PES all the more difficult. The same behavior is observed for U(H2O)3H + . The configuration of u138 does not allow for the formation of a water dimer which leads to two unbound water molecules in 2a. In contrast, a water-water hydrogen bond is observed for 2b and 2c. The existence of a water dimer was not encountered in the low-energy isomers of the unprotonated U(H2O)2 species due to the absence of hydroxyl group on U. It is worth pointing out that 2a, 2b and 2c are very close in energy which makes their exact energy ordering difficult to determine. However, no isomer displaying an unprotonated uracil (cf. Supplementary Material for additional U(H2O)2H + low-energy isomers)

was located. The lowest-energy structure of U(H2O)3H + is characterized by two water-water hydrogen bond that forms a linear water trimer. Higher energy isomers display only one (3b) or zero (3c) water-water bond (cf. Supplementary Material for additional U(H2O)3H + low-energy isomers). Isomer 3b is similar to 2b with an isolated water molecule linked to the protonated nitrogen of U. Similarly to U(H2O)2H + , no isomer displaying an unprotonated uracil was located for U(H2O)3H + .

Figure 10 displays the three lowest-energy isomers obtained for U(H2O)4H + and U(H2O)5H + which constitute a transition in the behavior of the proton. Indeed, in U(H2O)4H + , two kind of lowenergy structures appear: (i) structures composed of UH + , one water trimer and one isolated water molecule (4b) ; (ii) structures composed of U and a protonated water tetramer (4a and 4c). In the latter case, the hydronium ion is always bounded to an uracil oxygen atom. This U-H3O + bond is always rather strong as compared to U-H2O bonds as highlighted by the corresponding short oxygen-hydrogen distance. Furthermore, speaking of distances, the difference between the U-H3O + and UH + -H2O forms is rather fuzzy and might be sensitive to computational parameters and also to quantum fluctuations of the hydrogen. This suggests that collision with U(H2O)4H + is more likely to induce evaporation of H2O rather than H3O + or a protonated water cluster. The picture is significantly different in U(H2O)5H + where the lowest-energy structure displays a hydronium ion separated by one water molecule from U. Such structures do not appear in U(H2O)4H + due to the limited number of water molecules available to separate H3O + from U. Such separation suggests that, if considering a direct dissociation process, evaporation of neutral uracil can now occurs in agreement with the observations (see discussion above). One sees that 5b, which is only 0.3 kcal.mol -1 higher in energy than 5a, still displays a U-H3O + link. This is in line with the low amount of neutral uracil that is evaporated in the experiment (see Figure 6).

Finally, Figure 11 displays the three lowest-energy isomers obtained for U(H2O)6H + and U(H2O)7H + . Similarly to U(H2O)5H + , the lowest-energy structure we located for both species has the excess proton on a water molecule that is separated by one water molecule the uracil. This appears to be common to the clusters with at least 5 water molecules. This is also observed for higher-energy isomers (6c, 7c) although other characteristics of the proton are observed: proton in a very symmetrical Zundel form bounded to the uracil (6b) or H3O + still bounded to uracil (7b). Of course, for U(H2O)6H + and U(H2O)7H + and also U(H2O)6H + and U(H2O)5H + , the amount of low- energy isomers is expected to be very large and we do not intended to find them all. Furthermore, due to the limited number of MP2 geometry optimization we performed there is few chances that we located the global energy minima for U(H2O)6H + and U(H2O)7H + . However, the general picture we are able to draw from the presently discussed structures fully support the experimental results: from U(H2O)5H + , it exists low-energy structures populated at very low temperature in which the excess proton is not directly bound to the uracil molecule. Upon fragmentation, this allows the proton to remain bounded to the water molecules.

All the aforementioned low-energy structures are relevant to describe the U(H2O)n=1-7H + species at low temperature and to understand the relation between the parent cluster size and the amount of evaporated neutral uracil in the case of direct dissociation. However, as already stated, one has to keep in mind that upon collision statistical dissociation can also occur. In that case structural rearrangements are expected to occur. which are important to understand each individual mass spectra of the (H2O)n=1-15H + clusters and the origin of each collision product.

For instance, the fragment UH + is detected for all cluster sizes (see Figure 1 and time of flight mass spectra presented in the Supplementary Material). This means that for the largest sizes, for which we have shown from the calculation that the proton is located away from the uracil, proton transfer does occur prior to dissociation. One possible scenario is that after collision, water molecules sequentially evaporates. When the number of water molecules is small enough the proton affinity of uracil gets larger than the one of the remaining attached water cluster. Proton transfer is then likely and we therefore end up with protonated uracil.

If one now turns to the neutral uracil evaporation channel it appears that the smaller clusters H3O + and (H2O)2H + are not present in the time of flight mass spectra. This absence might have two origins. First, the dissociation energies of the protonated water dimers and trimers are substantially higher than larger sizes, and they are therefore less prone to evaporation. Second, as already mentioned, for such small sizes, the proton affinity of uracil gets larger than the one of the water dimer or trimer and proton transfer to the uracil is likely to occur.

In order to confirm the above scenario, simulations and/or evaporation rates calculation would have to be conducted to describe the fragmentation channels in details. Such molecular dynamics simulations have already been performed by Spezia and coworkers to understand the collisional induced dissociation of various organic molecules [9,10,43,44]. Although in the present case the initial position of the excess proton appears as a key parameter to explain the evaporation of neutral uracil, such simulations could be additionally conducted to provide a clearer picture on the various evaporation pathways.

VI. CONCLUSION

This article presents the collision induced dissociation of hydrated protonated uracil U(H2O)n=1-

Figure 1 :

 1 Figure 1: Time of flight of mass spectrum obtained by colliding (H 2 O) 7 UH + with Ne at 7.2 eV center of mass collision energy (93.5 eV in the laboratory frame).

  number of clusters that have crossed the cell without undergoing any fragmentation; I0 : The total number of clusters that have crossed the cell ; ρ : The density of the vapor in the collision cell ;

Channel 1 :Figure 2 :

 12 Figure 2: Extraction of the fragmentation cross section from experimental data using relation (2) in the case of (H 2 O) 7 UH + colliding with Neon at 7.2 eV center of mass collision energy (93.5 eV in the laboratory frame).

Figure 3 :

 3 Figure 3: Determination of the branching ratios BRi from the slope of linear fits (full lines) of the experimental data (squares) using relation (6) in the case of (H 2 O) 7 UH + colliding with Ne at 7.2 eV center of mass collision energy (93.5 eV in the laboratory frame). The black curves correspond to the

Figure 4 :

 4 Figure 4: Structure of the two protonated uracil isomers, u178 (ketoenol form) and u138 (di-keto form), used as initial conditions in the PTMD simulations. See reference [31] for the isomer numbering.

  as a function of the cluster size n (here n stands for the total number of molecules in the cluster including, when appropriate, the uracil molecule). Different target molecules or atoms were used in these experiments: Water molecules or Neon atoms in our experiments, Xenon atoms in Dalleska's experiments.

Figure 5 :

 5 Figure 5: Fragmentation cross sections of mixed clusters U(H 2 O) n-1 H + at a collision energy of 7.2 eV plotted as a function of the total number n of molecules in the clusters (including uracil). Experimental results [and geometrical cross sections] are shown for collision with H 2 O (black squares [black full line]) and Ne (red squares [red full line]). The results of Dalleska et al. [35] (using Xe target atoms) on pure protonated water clusters (H 2 O) n=2-6 H + (blue stars) and of Zamith et al. [36] (using water target molecules) on deuterated water clusters (D 2 O) n=5,10 H + (green full circles) are also shown. The geometrical collision cross sections of water clusters (blue dashed line) in collision with Xe atoms (blue dash-dotted line) and water molecules (green dash-dotted line) are also plotted. Error bars represent one standard deviation.

Figure 6 Figure 6 :

 66 Figure 6 shows the percentage of the fragments that have lost a uracil neutral molecule, ie

Figure 7 :

 7 Figure 7: Proton affinities of the water clusters as a function of the number of water molecules n. Proton affinities are taken from[40] (black open circles) and from[41] (blue squares). The value of the proton

Figure 8 :

 8 Figure 8: U(H 2 O)H + lowest-energy structures obtained at the MP2/Def2TZVP level of theory. Relative (E rel ) and binding energies (E bind ) are given in kcal.mol -1 . Important hydrogenbond distances are indicated in bold and are given in Å.

Figure 9 :

 9 Figure 9: The three lowest-energy structures of U(H 2 O) 2 H + (top) and U(H 2 O) 3 H + (bottom) obtained at the MP2/Def2TZVP level of theory. Relative (E rel ) and binding energies (E bind ) are given in kcal.mol -1 . Important hydrogen-bond distances are indicated in bold and are given in Å.

Figure 10 :

 10 Figure 10: The three lowest-energy structures of U(H 2 O) 4 H + (top) and U(H 2 O) 5 H + (bottom) obtained at the MP2/Def2TZVP level of theory. Relative (E rel ) and binding energies (E bind ) are given in kcal.mol -1 . Important hydrogen-bond distances are indicated in bold and are given in Å.

15H+

  clusters and reports their experimental absolute fragmentation cross sections. We demonstrate that the evaporation channels evolve with size: Below n=5, the observed charged fragments always contain the uracil molecule, whereas from n=5 the loss of a neutral uracil molecule becomes significant. To understand this transition, we conducted an exploration of the potential energy

Figure 11 :

 11 Figure 11: The three lowest-energy structures of U(H 2 O) 6 H + (top) and U(H 2 O) 7 H + (bottom) obtained at the MP2/Def2TZVP level of theory. Relative (E rel ) and binding energies (E bind ) are given in kcal.mol -1 . Important hydrogen-bond distances are indicated in bold and are given in Å.

2 O) n-1 H + + H 2 O  geo U(H 2 O) n-1 H + + Ne  geo (H 2 O) n H + + Xe  geo (H 2 O) n H + + H 2 O U(H 2 O) n-1 H + + H 2 O U(H 2 O) n-1 UH + + Ne (H 2 O) n H + : Dalleska et al (D 2 O) n D + : Zamith et al

 geo U(H

ACKNOWLEDGEMENT

This work has been partly funded by the Agence Nationale de la Recherche (ANR) under Grant No. ANR-11-BS04-0028.


Kirsten Koop

Marie-Christine Fourny

Pierre-Antoine Landel

Nicolas Senil

Zsi Dp

Spatial Patterns of Transformative Social Innovation. The example of alternative initiatives in Ardèche, France

This paper discusses spatial patterns of transformative social innovation (TSI), based on an empirical case study of alternative initiatives in

Ardèche, France. It notes that the spatiality of social innovations has been neglected in contemporary social innovation studies and argues that operating with geographical concepts can be particularly instructive when analysing the transformative potential of social innovations. The first section describes TSI in Ardèche as the spatial enactment of alternative values and principles, resulting in the emergence of places of difference. The second part of the paper explores then two distinct dynamics of scaling up that are stimulated by the actors of these places. The first is the dissemination of TSI-related knowledge within transnational alternative networks, encouraging the replication of such alternative initiatives elsewhere in the country and around the world. TSI places act here as nodal points in multi-scale networks. The second dynamic is the spreading of alternative principles into the immediate geographical environment. This happens by directly interacting with the local population and public authorities, but also in an indirect manner: Ardèche has acquired the image of an alternative territory, and public authorities started to act in favour of this image. It is argued that further research on scaling up (or rather scaling deep) of TSI should gain in analyzing such processes of territorialisation of 'alternative' values -in the sense of the spreading of principles with transformative potential in space.

Introduction

The literature on social innovation rarely discusses its spatial patterns. This is not really surprising, as it is an interdisciplinary research field largely dominated by business management and social and economic studies rather than geography [START_REF] Longhurst | Towards an 'alternative' geography of innovation: Alternative milieu, socio-cognitive protection and sustainability experimentation[END_REF]. Analyzing how social innovation shapes space and is disseminated through it, however, is instructive when addressing social innovation that contributes to societal transformation, i.e. transformative social innovation (TSI) (Avelino et al. 2015). TSI actors share principles and values that differ from those of conventional authority. Many TSIs aim at a more balanced articulation between the economy, nature and society, and are part of social economies, transition movements and other initiatives that are often classed as alternative or grassroots. We hypothesize here that such initiatives actually function as pioneers of alter-modernity, indicating 'a decisive break with modernity and the power relations that define it' (Hardt and Negri, 2009, 103) and are 'significant guidelines to potential for future (societal) transformations' [START_REF] Giddens | Consequences of Modernity[END_REF] p. 158). Such initiatives shape space differently by doing things differently. Analyzing the dynamics of place-making and -shaping is instructive about the 'otherness' of underlying intentions, modes of doing and being, and the 'alternative habitus' [START_REF] Vasudevan | The autonomous city: Towards a critical geography of occupation[END_REF] of TSI actors. It thus allows such intended otherness to be explored as the driver of potential societal transformation.

A second argument in favor of exploring spatial patterns of TSI is its usefulness when analyzing TSI's potential for systemic change. Literature on social innovation has generally addressed its growth and dissemination as scaling up [START_REF] Murray | The Open Book of Social Innovation NESTA/The Young Foundation[END_REF][START_REF] Mulgan | Social innovation. What it is, why it matters and how it can be accelerated[END_REF] -thus mobilizing a geographical concept designating the scalar. Here again, we note that the small amount of literature addressing scaling-up processes uses the concept more as a metaphor for the proliferation of social innovation than for spatial analysis (see Dees at al. 2004, Davies and[START_REF] Davies | How to grow social innovation: A review and critique of scaling and diffusion for understanding the growth of social innovation[END_REF][START_REF] Westley | Five Configurations for Scaling Up Social Innovation: Case Examples of Nonprofit Organizations From Canada[END_REF]. Analyzing the scales and spatial patterns of organizational growth, networking, multiplication and other forms of scaling up, and focusing on the spread of alternative norms and principles in space can provide insights into the transformational dynamics induced by social innovations. This paper aims to help initiate discussion on the spatial patterns of transformative social innovation by describing a concrete case study on alternative initiatives in Ardèche, a rural region in southeast France. This study is part of a four-year program of the French Research Agency (ANR) on innovation in marginalized regions around the Mediterranean (ANR Med-Inn-Local) and is based on 26 qualitative interviews with actors of 15 alternative initiatives on their values and views, work-and lifestyles, and their innovations and innovationrelated knowledge transfer.

Since the 1970s, Ardèche has been attracting communities that question capitalist society and endeavour to live outside the dominant system. There are currently more than 30 initiatives sharing similar visions of economic, social and energy transition. Many of these communities have created place-based life projects combining accommodation, work and leisure. The first section of this paper analyses how these communities produce places of 'alternativity'. Taking their alternative values and principles as a starting point, we describe their activities as the spatial enactment of these values. Their concretization and materialization is here understood as a process of creative (re)appropriation of space. This has resulted in the emergence of more or less confined 'places of difference' in the Ardèche region, characterized by modes of doing and being and normative views that these communities consider as differing from the dominant conventional system 2 .

The second part of the paper discusses two distinct dynamics of 'scaling up'. First, it describes the transfer of specific knowledge about innovative and transformative practices towards like-minded individuals and communities from outside Ardèche. Places here act as nodal points within transnational alternative networks, stimulating the replication of such alternative initiatives elsewhere in the country and around the world. Links with the immediate environment are not relevant here. The spatial pattern taken by this type of 'scaling up' informs about a distinct process of societal transformation, resulting in the multiplication of widely-scattered alternative places, while transformative processes in the immediate geographical environment are less stimulated. Alongside this, we observed direct and indirect impacts on local Ardèche communities and public authorities. Actions intending to integrate the local community as well as the local authorities' growing interest in innovative techniques and principles indicate that transformative dynamics affect/ing the dominant conventional regime are at work in Ardèche.

The enactment of places of difference within the dominant conventional system

Alternative initiatives engaging in agroecology, eco-construction, renewable energy, recycling and the social economy have been mushrooming in Ardèche, especially since 2000 (see Figure 1). While the first generation of alternative 'settlements' in the 1970s aimed more at retreating from the mainstream system than transforming it, more recent ones explicitly express their vision of contributing to the transition of Ardèche, as testified by the adherence of most of them to the oui-transition07 regional community comprising around 30 member organizations. We address them as transformative social innovations here.

TSI drivers: Resistance to fundamental characteristics of modernity

The analysis of the interviewees' discourse reveals that these initiatives are based on values that challenge not only neoliberal capitalism, a current narrative, but also other fundamental characteristics of (high-)modern society. As shown below (Figure 2), living with nature, sharing, conviviality, frugality and autonomy are central issues for Ardèche's alternativity actors. In this way they question progress, accumulation, overuse of natural resources, the division of labor and other key features of modernity, as described by Durkheim, Weber, Giddens and other scholars.

2 'Conventional regime' is here defined and the societal system were individuals behave « according to a certain number of principles, which orient individual's behaviours within that society. These principles, of a conventional nature, rest upon common values shared by the individuals of that society » [START_REF] Buclet | Principles for sustainability: the need to shift to a sustainable conventional regime[END_REF] Principles for sustainability: the need to shift to a sustainable conventional regime. Environment, Development and Sustainability Science Online first: 20. Reflexive ordering and reordering of social relations 13 Humanized technology Technology * 1-9: mentioned by the interviewees; 10-13: as analyzed by the research team ** According to [START_REF] Durkheim | The Division of Labour in Society[END_REF][START_REF] Giddens | Consequences of Modernity[END_REF][START_REF] Scott | Seeing like a State. How Certain Schemes to improve the Human Condition Have Failed[END_REF]Weber, 2003Weber, [1921]]); [START_REF] Werlen | Sozialgeographie alltaeglicher Regionalisierung, Band 1. Zur Ontologie von Gesellschaft und Raum[END_REF] Source: [START_REF] Koop | Innovation sociale, improvisation et développement territorial: l'expérience ardéchoise[END_REF] It should be noted that he interviewees emphasize that they do not want to be considered as returning to the past. In fact, the analysis of their modes of doing shows that they do not refuse high technology or global networking, as they also are reflexive and apply linear thinking. They consider their principles as guidelines for a necessary transition towards enhanced individual wellbeing and a collective sustainable future. We propose here to consider these principles as an overall framework shaping the intention behind the action [START_REF] Giddens | Social Theory and Modern Sociology[END_REF] or, with reference to improvisation in music, as a collectively shared code [START_REF] Koop | Innovation sociale, improvisation et développement territorial: l'expérience ardéchoise[END_REF]. There are more or less concrete ideas about housing, farming and producing goods and services, there is motivation and enthusiasm, but no master plan exists for such transformative dynamics. Improvisation and experimentation are thus essential characteristics of the way ideas are put into practice, as will be illustrated below.

Filling space with new sense: the emergence of places of difference

We will describe here the emergence of places of diverseness by analyzing three dimensions: the acquisition of space, its modes of appropriation and the creation of collective identity. The first step by communities who have decided to set up an alternative project is the acquisition of a convenient place to settle. Having space is an essential precondition for putting their value system into practice and living their heterotopia. Many of the communities said they had chosen the ruins of an abandoned hamlet and tried to acquire the land legally. Unlike actors of Temporary Autonomous Zones (TAZ), official recognition is a crucial issue for them, as it gives the right to exist within the dominant system. However, it is also the first conflict with the conventional regime: how to set up a framework that is legally recognized by a societal system based on individual property rights but is compatible with the idea of collective use? Some groups took several years to reach a financial and legal arrangement in line with both their principles and the official norms. A frequent solution is acquisition of property through the Civil Real Estate Company scheme admitting plural ownership. In most cases, up to three or four people acquired the collective property rights. In order to avoid unequal power relations caused by ownership, the formal owners then granted heritable building right to the other project members -who specifically adopted an official status (e.g., association or cooperative). Another interesting example of reconciling alternative values with the formal system is the detection and reactivation of an old existing law: shares are distributed to the members, not according to their financial input but to the work time invested by each. In-depth knowledge of formal regulations is thus necessary to combine or bypass them.

The second step is then the appropriation of the acquired space, i.e. actions to fill it with the intended meaning.

Our case study revealed life worlds characterized by improvisation: shared motivation, creativity, flexibility, learning by doing, assembling known elements to create something new, mixing intuition and inspiration and spontaneous coordinating with the other members -the same as in musical improvisation [START_REF] Soubeyran | Pensée aménagiste et improvisation[END_REF].

Nature preservation and frugality clearly appear as major guiding principles. They are specifically tangible when analyzing the construction of dwellings. The greatest possible use of local resources, adaptation to the landscape and preservation of the environment lead the communities to assemble and hybridize local or external vernacular knowledge with modern technologies. Inspiration comes from contacting local craftsmen as well as from information exchanges with other social movements at local and global scales. The buildings thus have an amazing mix of styles and materials: a timber house might be inspired by Canadian techniques, but only locally available resources are used (such as caissons filled with crushed recycled cork to isolate walls). Houses might have green roofs of lichen and glass-bottle floors (a technique dating back to ancient Rome and very fashionable in contemporary ecological housing). Mongolian yurts are sometimes taken as source of inspiration and adapted to local climate conditions, using wood instead of felt. The (re)construction of traditional stone houses might be inspired by a Japanese style and built in a round form for maximum light; insulation techniques are improved by putting movable glass panes in front of a wall to maximize heat, the so called 'captive wall' -a local innovation at Hameau des Bois. The principle of frugality is also present in the construction of machines and infrastructure for everyday life: homemade solar water heaters, washing machines powered by human energy (by pedaling a bicycle connected to the machine), toothpaste produced with local plants, the examples are numerous.

The principles of solidarity and cooperation are also fundamental for all activities, including economic ones. These values are always prioritized over efficiency, productivity and profit. They even influence the choice of techniques and production material. At Viel Audan, for instance, the community intentionally chose not to purchase a modern oven for bread production because their traditional oven obliges them to work collaboratively. At Hameau des Buis, intergenerational activities are a guiding principle. Production that exceeds the needs of the community is always a relevant issue, and its market use is discussed collectively.

The principle of autonomy leads to self-production and construction, using local resources as much as possible.

It is also a means for responding to the community's own ecological and esthetic values that break with conventional standards. The search for personal fulfillment and the control of one's own life, linked to the idea of autonomy, opens ways to dispense with the division of labor, felt as being alienating. The labor force is activated collectively according to the desires and skills of each member. The goal of work is not efficiency, but self-fulfillment. Most of the interviewees said they had chosen various jobs and tasks from the beginning of their project according to their evolving personal interests. It is clear that such a mode of living together requires adequate forms of governance. Such communities are characterized by horizontal organization, participatory democracy or, sometimes, anarchic principles (the community trusts people who propose a project and gives them the responsibility for implementing it).

These examples should have given some insight into how alternative principles are enacted in space. The collective organization of alternative living based on improvisation leads to what some interviewees called a particular 'esprit de lieu' (spirit of place). Sites are imbued with a specific meaning, with culture and materiality that differ from the dominant conventional system. We call this the enactment of places of difference. They might also be called 'alternative life worlds' or, in line with Arturo Escobar, as 'territories of difference' -in the sense that they are appropriated, shaped and governed in a different way, with different means, giving them a different meaning [START_REF] Escobar | Territories of Difference. Place, Movements, Life, Redes[END_REF]. Following John Law, we could assert that they are 'different realities being done in different practices' (Law, 2011) (p. 2). If these spaces of difference are to be understood from an epistemological or ontological standpoint, this could be a future field for research. 3ZSI DP 36 July 2016 10

Concerning their 'otherness', such initiatives have similarities with indigenous movements claiming their right to live according to their values, with Temporary Autonomous Zones and other (spatial) forms of what is often called 'resistance' or counter-culture in the globalized world -not as the negation of modernity as such, but as other, alternative modernities [START_REF] Hardt | [END_REF].

Spatial patterns of scaling up

At first sight, social innovation and transformation in Ardèche seem to concern only the alternative communities and 'their' places. We might therefore be tempted to consider these places as confined, with an inside (the places) and an outside (the environment embodying the dominant conventional regime). However, other dynamics clearly document that interactions with the 'outside' are at work, thus indicating the dissemination of these social innovations. The processes can best be analyzed with the conceptual tool of scaling up. The scaling up of social innovation has many forms, such as organizational growth, increased target group reach, replication, differentiation and/or institutional change. Undertaking a comprehensive discussion of its types and taxonomies [START_REF] Dees | Scaling Social Impact. Strategies for spreading social innovations[END_REF][START_REF] Westley | Five Configurations for Scaling Up Social Innovation: Case Examples of Nonprofit Organizations From Canada[END_REF][START_REF] Uvin | Fighting Hunder at the Grassroots: Paths to Scaling Up[END_REF][START_REF] Moore | Scaling Out, Scaling Up, Scaling Deep. Strategies of Non-profits in Advancing Systemic Social Innovation[END_REF][START_REF] Davies | How to grow social innovation: A review and critique of scaling and diffusion for understanding the growth of social innovation[END_REF] would go beyond the scope of this paper. What is of interest in our research on social innovation considered as transformative is the question of what scaling-up processes reveal about its potential to contribute to wider social transformation [START_REF] Avelino | Game Changers and Transformative Social Innovation. The Case of the Economic Crisis and the New Economy[END_REF]. Attention should therefore not only be paid to the multiplication of such 'places of difference', but above all to the processes whereby alternative principles and norms are disseminated into the dominant conventional regime.

Scaling out: Dissemination and multiplication processes within alternative networks

When asked what they are doing in favor of dissemination, the majority of Ardèche's TSI actors state that they are engaged in knowledge transmission. Many of the communities regularly organize workshops and periodic training sessions, and they host volunteers, trainees and visitors throughout the year. Some are part of a nationwide alternative and solidarity economy apprenticeship network (Réseau d'Echanges et de Pratiques Alternatives et Solidaires -REPAS). The Terre et Humanisme and Viel Audan communities have even established training centers for school classes, university students and team leaders, using education on sustainable development, on social economy and on agroecology as a source of income.

All initiatives have a website and are part of translocal national and international networks. Some actively coordinate national or international programs, internet sites and/or newsletters. A case study on the modes and contents of knowledge transfer at Terre et Humanisme, an association engaged in agroecology, revealed that the individuals they attract are mostly young people sharing the communities' principles and searching for in-depth knowledge on how to put their ideas into practice. Most declared they were 'in a transition stage in their lives', and were 'interested in alternative ways of doing things', considering 'the current dominant system as incoherent and unsustainable' (Lopez, 2015, 85). It is worth examining exactly what is being transmitted here. Much of it is practical and technical knowledge, but as such activities rely heavily on the local context (soil, climate, available resources), practical knowledge is considered less relevant than savoir-être (literally, knowing how to be). In fact, visitors, trainees and trainers all agree that the dissemination of the place's philosophy, its principles and ethics is of primary importance [START_REF] Lopez | Agroecology -A potential for social transformation? A discussion based on a field study in the Ardèche department[END_REF].

Here scaling up means disseminating techniques and core values within the alternative global network community and outside the dominant conventional regime. This leads to the replication of similar projects -and thus places -at all scales, from regional to international, including the Global South4 , leaving learners to adapt principles to local conditions when trying to replicate them elsewhere. This type of scaling up is often referred to as scaling out [START_REF] Moore | Scaling Out, Scaling Up, Scaling Deep. Strategies of Non-profits in Advancing Systemic Social Innovation[END_REF][START_REF] Westley | Five Configurations for Scaling Up Social Innovation: Case Examples of Nonprofit Organizations From Canada[END_REF], in the sense of impacting greater numbers and covering a larger geographical area through replication and disseminating principles (Moore et al. 2015, p. 77) -thus circumventing direct confrontation with the dominant conventional system.

Scaling up and deep: Towards an alternative territory?

Two distinct dynamics reveal the beginning of more profound changes in the immediate geographical environment of Ardèche's alternative places. The first one is closely linked to changes in vision and attitudes between the first and the second generation of initiators. Whereas the generation of the 1968 era aimed more at autonomous living outside the consumer society [START_REF] Hervieu-Léger | Le Retour à la nature : au fond de la forêt[END_REF][START_REF] Pruvost | L'alternative écologique Terrain[END_REF] and created isolated, insular places, the younger one seeks to make its alternative projects visible and spread its ideas among the Ardèche population.

Several examples illustrate the initiators' determination to interact with the local population and public authorities, to make their values known and thus act in favor of social transformation. The association Changement de Cap rented a plot of land near a roundabout on a main thoroughfare in front of the local supermarket, and created types of open spaces: a 'material area' (selling secondhand clothes and furniture), a 'plant area', based on the agroecology model, a 'reading area', a 'catering area' and so on. These spaces evolve according to the desire and wishes of new adherents and partners. Recycl'Art made contract with the local waste management authority in order to recover useful waste, repair, transform and resell it. Autopia, a solidarity garage, offers training for autonomous car repairing, supplying tools and knowhow, as well as public debates and concerts in order to spread ideas into the immediate vicinity.

This search for contact with the local population is clearly seen in the new geographical patterns of recently emerged 'alternative' sites: they are located along the main road which crosses Ardèche from north to south, and are close to central villages and towns (Figure 2), thus showing a geographical shift from the Ardèche margins to the center. Intended to activate system change, these projects seek geographical and social proximity, with the boundaries between the places of difference and the 'outside' becoming more porous.

A second dynamic that indicates that alternative values are beginning to spread into the dominant regime is the changing attitude of local authorities. Due to its long history of alternative places and their spatial distribution,

Figure 2. Location and year of creation of alternative projects in Ardèche

Source: [START_REF] Koop | Innovation sociale, improvisation et développement territorial: l'expérience ardéchoise[END_REF] Ardèche has acquired a reputation of divergence or 'alternativity'. The region is actually referenced as a hotspot in alternative networks and is known as an attractive space for experimentation, thus attracting like-minded visitors as well as people from outside willing to settle there [START_REF] Koop | Innovation sociale, improvisation et développement territorial: l'expérience ardéchoise[END_REF]. Public authorities have started to become aware of the alternative image 'their' territory has acquired and seem to be opening their minds to the idea. 5 In the last few years, town councils and other public institutions have begun supporting alternative projects actively by co-financing the local social economy network (Initiatives Territoriales de l'Economie Sociale et Solidaire -ITESS), and creating a network of actors operating in favor of eco-housing and other actions. Ardèche department has even dedicated a specific budget to the social economy since 2012. Some town councils seek concrete inspirations and contact associations in order to obtain technical knowhow on frugal and sustainable solutions (such as dry toilets for public spaces) and even to associate them in collective thinking on future territorial development.

Such dynamics can be interpreted as signs for ongoing transformational processes in Ardèche, stimulated by the places of difference. The growing geographical proximity with the local population and the efforts to involve citizens in alternative actions, recognition by official institutions and changing local policies do in fact indicate scaling-up processes [START_REF] Westley | Five Configurations for Scaling Up Social Innovation: Case Examples of Nonprofit Organizations From Canada[END_REF][START_REF] Moore | Scaling Out, Scaling Up, Scaling Deep. Strategies of Non-profits in Advancing Systemic Social Innovation[END_REF]. However, transformation in the sense of systemic change is a more profound process than the fields generally covered by the literature via the concept of scaling up. [START_REF] Moore | Scaling Out, Scaling Up, Scaling Deep. Strategies of Non-profits in Advancing Systemic Social Innovation[END_REF] argue that achieving systemic impacts also involves processes of scaling deep, defined as changes in 'social relationships, cultural values and beliefs' and 'impacting cultural roots' (Moore et al. 2015, 75). Our examples are not sufficient to confirm systemic change in Ardèche, and further research needs to be carried out on how and how far new principles and values are spreading and transforming the region.

Dynamics of scaling up and scaling deep in the immediate vicinity of place-based social innovations should be paid further attention in studies on the transformative potential of social innovation for system change. The concept of territorialisation for the spatial analysis of such processes appears to be an appropriate conceptual tool for this. Territorialisation signifies socio-symbolic construction of territory [START_REF] Debarbieux | Le territoire: histoire en deux langues/ A bilingual (his)-story of territory. In: Chivallon C, Ragouet[END_REF], embracing socio-cultural, economic, political and spatial dimensions equally. It produces collective identity and common references. This actor-oriented concept allows the spatial spread of a specific set of alternative ideas, beliefs and habitus, to be analyzed, focusing on its modes of appropriationor notby the actors of the dominant conventional system. It can provide information on the modalities of appropriation, as well as on the limits to dissemination (refusal, denial, repression or mainstreaming while changing the original meaning).

Conclusion

We have argued in this paper that the analysis of spatial patterns of transformative social innovations helps reveal major characteristics of social innovation and patterns of transformative processes. By drawing attention to the intentions behind action, we have taken the specific set of values and principles of Ardèche actors of alternative initiatives as a starting point and interpreted it as the driver for action. The spatial enactment of these principles presupposes the acquisition of suitable spaces that are then appropriated according to the alternative values. As no master plan exists for putting their views into practice, experimentation and improvisation are major features of the way the actors fill these places with the intended meaning. The outcome is places with a specific 'esprit de lieu' (spirit of place), differing from the dominant conventional system. Such 'places of difference' have been multiplying all over Ardèche in recent decades.

They are boosting transformative processes in two distinct manners. Some communities are actively involved in transferring their norms and skills within alternative national and international networks. Such dynamics of scaling out have a reticular patternthe places function as nodal points within wider networks at different scales. Benefitting from the alternative image of Ardèche in the world of alternative movements, they attract the like-minded and impel such networks. Actor-network theory, most frequently used in the social movement literature, is suitable for analyzing such processes.

Other places aim more at system transformation through impacting their direct geographical environment, disseminating their values by proposing alternative services and goods to the local population and involving them in their activities. These initiatives have also induced policy changes, even without directly interacting with public institutions. In fact, the alternative image acquired by Ardèche territory has made public authorities start to act in favor of alternative ideas and actions. Such dynamics in the immediate vicinity of place-based social innovations can be interpreted as transformative. Further spatial analysis of such dynamics, focusing on the territorialisation of alternative norms, could be instructive as to the potentials and limits of social innovation for system change.

Figure 1 :

 1 Figure 1: Types of transformative social innovations in Ardèche

Figure 2 :

 2 Figure 2: Alternative values challenging fundamental principles of (high-)modern society

In his article "What's Wrong with a One-World", John Law states that postcolonial studies have the potential to help Western scholars to distance themselves from "One World" thinking and understand that different realities exist. Concerning the Global North, he further states that 'it becomes urgent, too, to pick through the practices within the north that multiply realities, even as they insist on a universe rather than a fractiverse'(Law, 2011, p. 3). Further research in this direction could be fruitful for transformative social innovation studies.

Terre et Humanisme, for instance, has a specific training program for actors in the Global South.

Even statistical data are beginning to show the importance of the regional social economy: in 2014, the social economy (SE) employed 15% of the Ardèche active population (12,850 people in employment), thus making Ardèche the leading SE employer of the 13 departments of the Rhône-Alpes-Auvergne region. (http://www.ardeche.fr/162-economie-sociale-et-solidaire.htm)