Jean Philippe Praene

Vanessa Rakotoson

Environmental sustainability of electricity generation under insular context : An LCA-based scenario for Madagascar and Reunion island by 2050

Keywords: LCA, Electricity, Energy scenario, Reunion Island, Madagascar

Introduction

Because of their geographical isolation it is well known that islands have an high dependence to fossil fuel for their energy requirements. One of the main characteristic of these remote territories is an electricity production that still rely heavily on carbon-based sources. This electricity mix highlights an energy vulnerability to exogenous instabilities on the international market. This high share of fossil fuel lead to the electricity price volatility, [START_REF] Taibi | A framework for technology cooperation to accelerate the deployment of renewable energy in pacific island countries[END_REF] and is the main contributor to the global emissions of greenhouses gases, [START_REF] Góralczyk | Life-cycle assessment in the renewable energy sector[END_REF] [3] [START_REF] Turconi | Life cycle assessment (LCA) of electricity generation technologies: Overview, comparability and limitations[END_REF]. Nonetheless, these territories are generally endowed with high potential for renewable energy sources (RES) . Madagascar has proposed during the COP21 conference an ambitious objective of 14% reduction of GHG by 2020. To achieve this, the government expects international assistance for development of RES for electricity generation. As Reunion island is a french overseas territory, is committed with Europe to reduce its emissions by 40% by 2030. Madagascar and Reunion, two islands located in Indian Ocean, were chosen because of their socio-economic differences and common issues :

-Demographic transition incomplete -Different poverty rate -High dependence to fossil fuels -Ambition to increase RES share In the last decades, ISO 14040 from Life Cycle Assessment (LCA) guidelines has been widely used to evaluate environmental impact of energy production. The objective of this paper is to provide an LCAbased approach to evaluate future plausible energy scenarios under insular context. This study first presents the electricity mix for the two islands.

Electricity overview

Case of Madagascar

According to the Ministry of Energy of Madagascar (MEM), the total energy demand through Madagascar is essentially provided by wood energy (92%), and fossil fuels (7%) [5]. Other renewable energies, besides the wood energy, composed only about 1% of this demand and are mainly constituted by hydropower.

These values refer to electricity, transport and heat consumption. Referring to the Ordinance No. 74-002 of February 4th, 1974 on the orientation of water and electricity policy, the government has the exclusive right to intervene on the electricity sector. Since 1975, this right has been conferred to the national society JIRAMA or Jiro sy Rano Malagasy (Electricity and Water provider of Madagascar), including the exploitation of production, transport and distribution electricity installations through the country. However, activities reporting to electricity have been liberalized by the Act No.98-032 on January 20th, 1999 based on the electricity sector reform. It is based on the following principles: a vertical disintegration of the electricity activities and the implementation of a regulatory agency. The rural electrification will be carried out by private sector, with the support of an autonomous agency, the ADER or Rural Electrification Development Agency. Despite of the competitiveness insertion, JIRAMA remained to be the first electricity production provider almost in its entirety. For this study, the data considered is based only on JIRAMA's statistic, due to the lack of information on rural electrification. Madagascar's electricity mix depends essentially of hydroelectric production 56.56% and thermic production represented 43.43%. Electricity generation includes also photovoltaic (PV) system, but it represented below 1% and was integrated only since 2006 [START_REF] Sy | Evolution annuelle des productions, ventes et nombre d'abonnes[END_REF]. Electricity production based on fossil fuels has increased of an average annual growth rate of 9.79%. On another side, hydraulic production kept his growth on average of 3.69% per year.

Hydroelectric power plants are mainly located in the highlands; the interconnected network of Antananarivo records the maximum power on 112 MW, 87.8% of the total power in 2012 [START_REF] Sy | Evolution annuelle des productions, ventes et nombre d'abonnes[END_REF].

Thermal power plants operating in the national electricity network are divided between 41.6% of diesel steam turbine using heavy fuel oil and 58.4% of combustion turbine engine fueled with diesel [START_REF] Sy | Evolution annuelle des productions, ventes et nombre d'abonnes[END_REF]. Madagascar imports all the petroleum requirements, including heavy fuel oil and diesel necessary for electricity production. Refined oil products are usually delivered to the port of Toamasina, and are spread out the island by different conveyance system, by seaway or by land [5]. These products are mainly imported from South Africa. This study considers the port-to-port distance, which is equal to 3883 km. The unique solar PV system in the JIRAMA production network is located in the southern region of Madagascar, a favorable region for the solar radiation concentration. However, the power granted by this system does not exceed 7 kW [START_REF] Sy | Evolution annuelle des productions, ventes et nombre d'abonnes[END_REF].

Case of Reunion Island

In Reunion Island, the energy supply for heat, transport and electricity dominated by fossil fuels 88.4%, and the rest is provided by renewable energies. The electricity generation in Reunion Island is mainly produced by the EDF or French Electricity Provider, besides the other partners as independent partners.

Figure 2 As same as Madagascar's case, it is necessary to identify the imported raw materials for electricity production, particularly coal, heavy fuel oil and diesel. The fossil products are mainly imported from Singapore and Malta, whose distance from Reunion equals respectively 9500 km and 7000 km, but also from South Africa.

This study considers year 2012 as the base year of the comparison of the life cycle environmental impacts of electricity generation between Madagascar and Reunion Island.

Methodology

This study follows the different guidelines described by the International Standard [START_REF]Environmental management -Life cycle assessment -Principles and framework[END_REF] [10]. The methodology intends to estimate the total amount of the greenhouse gases (GHG) emissions , through electricity generation in Madagascar and Reunion Island. The LCA software GEMIS [START_REF][END_REF] is used to estimate these emissions .

Goal and scope of the study

This study aims to compare and to identify the potential life cycle environmental impacts of the electricity generation mix of Madagascar and Reunion, in the public sector during the year 2012. The impacts of the annual electricity generated and per kilowatt-hour produced are both calculated, to compare the results with other countries in the next sections.

The system boundaries are from 'cradle to gate', which means that network losses are not taken into account. Based on the data collected, the different stages considered are the raw materials acquisition and their transformation into directly usable energy, the transport of these products to the islands, and the production operation for the electricity generation.

Database of LCA

Database of Madagascar

For Madagascar, the data are based only on the statistic collected by JIRAMA, due to the lack of information about the private partners' production and the rural electrification. It is essentially about the total production generated, production from fuels and from renewable resources as hydro and solar power, as outlined in Table 1.

Database of Reunion Island

In another hand, for Reunion Island, the data collected by ARER [START_REF]Bilan énergétique Ile de La Réunion[END_REF] is composed of the total electricity produced by renewable and fossil resources. Table 1 lists also the different technologies used in Reunion for electricity generation. Considering the power plant efficiency, type of fuel and technology, the GEMIS database has been used to estimate the direct emissions from operation power plant.

Assumptions

Regarding to the life cycle of the electricity generation in Madagascar as shown in Figure 3, the processes selected into the GEMIS database reflected the Malagasy conditions in operation power plant, from cradle to gate. Using the LCA software GEMIS, some parameters have been considered in the estimation of the potential impacts:

-power plant infrastructures, which have been included directly by GEMIS -transport, -residues have not been considered in the estimation, -calculation referred to the low heat value.

Reflecting Malagasy conditions and their efficiencies, the different power plants have been classified as the following suggestions in order to compare with GEMIS processes: -the solar photovoltaic system has been considered as solar process used in Algeria, because both countries presented the same solar radiation per square meter.

On the another hand, Figure 4 represents life cycle of the fossil fuel technologies in the electric mix of Reunion Island. Renewable sources, as hydraulic, wind and solar energy are gathered together because their process shaft are similar.

Proceeding in the same way as Madagascar's case and considering that Reunion Island operates power plants -Heavy oil and diesel power plant have been divided into two parts: 54% of dieselmotor-big-generic and 46% of oil-heavy-ST-FR-2000.

-Coal-ST-FR-import-2010 is the corresponding process for coal power plant that had been considered.

-Bagasse-ST-BR-2010 is the only process including the raw material bagasse.

-According to their efficiencies, here are the corresponding processes for the rest of the power plants: windpark-big-DE-2010 biogas-dieselmotor-generic-small-2000, and solar-PV-multi-framedwith-rack-DE-2010.

To note that power plant processes that do not have their corresponding in French facilities are replaced by other processes in GEMIS, generic or from other developed countries.

The following results involve the products transport, as mentioned before. The metadata of the processes including coal, heavy oil and petrol in the electricity production have been revised and data on Table 2 have been integrated in the greenhouse gases (GHG) estimation of electricity production. They were all , on the whole, in range of the emissions order found in literature [START_REF] Turconi | Life cycle assessment (LCA) of electricity generation technologies: Overview, comparability and limitations[END_REF], especially for the SO2 and NOx emissions. As can be seen on figure 5 and figure 6, among the GHG emissions, CO2, CH4 and N2O produce the highest emissions quantity, and SO2 and NOx for the air emission. Those results will be discussed in the following. only less than 1% of the total emission of GHG. Emissions from renewable energies are mainly imputed to the construction of the power plant.

Based on

Interpretation of impact assessment

The life cycle impact assessment is an important phase of the LCA methodology; it aims to classify the potential environmental impacts. The results summarized in Table 5 and in the Figure 7 will be discussed in the next paragraphs.

Global warming potential (GWP)

The GWP includes the main GHG emissions as CO2, CH4 or N2O. For this study, the GEMIS software has also calculated this GWP generated by electricity production. The GWP reported values in GEMIS database are in the range of the emissions order in the literature [START_REF] Turconi | Life cycle assessment (LCA) of electricity generation technologies: Overview, comparability and limitations[END_REF]. During the year 2012, Madagascar recorded 621 kt CO2-eq all technologies combined, 97% are imputed to thermal power plants. According to these results, Madagascar has an emission factor of 464.8 g CO2-eq/kWh (by dividing the total of GWP by the amount of electricity production in 2012).

On the other part, Reunion Island has an emission factor of 673 g CO2-eq/kWh, result that is not far of the value of the ARER report [START_REF]Bilan énergétique Ile de La Réunion[END_REF]. The results of this study indicate a total emission of 1885 kt CO2-eq in 2012, results that differs by 7% compared to the ARER's results which calculated a total emission based on electricity production of 2033 kt CO2-eq [START_REF]Bilan énergétique Ile de La Réunion[END_REF].

Comparing the values, 60% of the total emissions of CO2-eq for Madagascar are imputed to electricity generation from fossil fuels (dieselmotor production) against 13% for Reunion Island, whose coal generation is responsible of 75% of the total emissions.

The total GWP from electricity generation in Madagascar is estimated at about 33% of the Reunion's emissions (Table 5). Regardless coal generation, Madagascar and Reunion Island's emissions are quite similar, even if emissions based on dieselmotor and heavy oil production of Madagascar is higher of 39% than Reunion's results.

Acidification potential (AP)

It can be observed in Table 5 that 59% of the total amount of SO2-eq emissions in Madagascar is imputed to power plants based on diesel generation and the rest is allocated to heavy fuel oil production. The NOx emissions contributed mainly to this high rate.

In Reunion Island, renewable energies occupied 14% of the emissions, which implies a majority part of the fossil energies with 45% by coal generation, 26.1% diesel production and 14.8% by heavy oil production.

As can be seen on the GWP results, Madagascar records approximately the three quarters quantity of the total SO2-eq emissions of Reunion Island (7701 t SO2-eq and 10091 t SO2-eq). Reunion's emission from the heavy fuel oil production represents the half of Madagascar's (1494 t SO2-eq and 3 139 t SO2-eq, respectively), and the diesel production presents the same proportion as heavy fuel oil (2631 t SO2-eq against 4525 t SO2-eq).

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Comparison with other countries

In this section, the electric mix of Madagascar and Reunion will be compared to other countries having a close composition. The main characteristic that will be compared is the GWP generated through the electricity production. To note that the operation process considered does not integer the transport of raw materials, due to the lack of information about the other countries.

Choice and composition mix of the countries

Concerning the repartition mix, Mali and Tanzania on the year 2010 present approximately the same composition mix as Madagascar, about 42-44% of fossil fuels energies against 56-58% of renewable energies; Reunion Island's case will be compared to Japan and Mexico's mix. Mali, Tanzania and Japan are based on the GEMIS database [START_REF][END_REF], and the results for Mexico in 2006 is based on the study of E. Santoyo-Castelazo et al [START_REF] Santoyo-Castelazo | Life cycle assessment of electricity generation in Mexico[END_REF].

To note that the technologies included in the repartition mix are not exactly the same but the study has focused on these countries due to the global repartition between fossil energies and renewable energies, as can be seen on Table 6.

Comparison of the GWP

With a comparable proportion of fossil energies production, Mali's CO2-eq emissions (441 g CO2-eq/kWh)

are lower by 5% than Madagascar's results (464 g CO2-eq/kWh). This difference can be explained by the fact that the diesel production of Madagascar equals 2.5 times of Mali's production. 48% of the fossil energies of Mali's mix is based on gas production, that can also explain the difference between Madagascar and Mali.

About the case of Tanzania, gas-based production dominates 91% of the fossil fuels production, which is remarked on the results on CO2-eq emissions. In fact, the emission factor of Tanzania is reduced by 33% compared to those in Madagascar (309 against 464 g CO2-eq/kWh, seen on Table 6).

According to the values on Table 6, the electric mix of Japan is closest to the energy mix of Reunion Island, in overall distribution. However it generates 24% less emission than Reunion's composition. With gas production at about 40% of the fossil generation and a coal proportion that equals the half Reunion's proportion, the CO2-eq emission generated by electric mix of Japan totals 76% compared to Reunion's result, 511.28 g CO2-eq/kWh against 673 g CO2-eq/kWh.

Compared to the Reunion's energy mix, Mexico includes 20% more on fossil energies production but the results do not reflect this difference. On the contrary, the GWP emissions of Mexico are lower by 15% than those of Reunion, as can be seen on Table 6 (571 g CO2-eq/kWh against 673 g CO2-eq/kWh). The dominance of coal in the Reunion mix can be the main cause of this high emission rate, with 48% for Reunion against 14% for Mexico, however, it is necessary to note that the heavy fuel part of Mexico equals more than twice of Reunion's production (respectively 21.6% and 9.47%). According to the values on Table 6, the thermic production based on diesel combustion in Mexico equals the sixteenth part of the Reunion's total (0.50% and 8.07% respectively).

From these results can be deduced that the coal part in electricity production has a high influence on the GWP emission, as showed in the Reunion's results.

Comparison of the AP

About the AP, Mexico has the highest rate with 6.59 g SO2-eq/kWh, followed by Madagascar (5.77 g SO2-eq/kWh). Reunion equals the half of Mexico's rate (3.60 g SO2-eq/kWh), Japan and Tanzania have a rate 4 to 6 times lower than Mexico's value, with results values ranging from 1.52 to 1.11 g SO2-eq/kWh, respectively.

Proposition of scenarios

The following section proposes some evolution scenarios for the electricity production of both countries, depending on the electrification rate, the population growth and the number of subscribers. The horizon set for this projection is the year 2050. This paragraph aims to evaluate the potential quantity of kWh required per year, including the renewable energy potential for each country. From this evaluation will be estimated the GHG emission, especially the GWP emissions in CO2-eq, valued by the LCA methodology. This section intends to reduce at most the electricity production dependence to fossil energies, by including the renewable energies potentiality. Indeed, the energy mix of reunion is composed by 34% of renewable energies in 2012. However, it has been identified other green energy resources that can provide the electricity demand, as ocean thermal energy conversion (OTEC), wave energy, geothermal or energy pumping transfer station (EPTs). The repartition of energy mix of Reunion Island until 2050 is illustrated on Figure 8. The GEMIS database will be used for the assessment of the environmental impacts [START_REF][END_REF] but for the new technologies, some values have been taken from ADEME [START_REF]Guide des facteurs d'émissions, v 6.1, Chapitre 22-Facteurs associés à la consommation directe d'énergie[END_REF] and study report about ocean energies [START_REF] Dandonneau | Le captage de l'énergie thermique des océas et les échanges de gaz carbonique avec l'atmosphère[END_REF].

Scenarios results and discussion

Referring to these assumptions and the use of the LCA method, the following section discusses about the results generated from the electricity production until the horizon 2050. To compare the results for both islands, Table 7 summarizes the production scenarios according to the high-medium-low assumptions with the corresponding results of GWP.

Based on values on Table 7, the minimal production demand in Madagascar in 2050 equals 8-7 and 6 times the electric consumption of 2012, respectively for high, medium and low scenarios. Considering the GWP, the assumptions taken above engender a significant decrease of the emission factor: a reduction of 39% compared to the value on 2012, 283 g CO2-eq/kWh in 2050 against 464 g CO2-eq/kWh in 2012. The emission factor in CO2-eq per capita, 19.17 kg in 2012, rose of 78% on 2050 and attains a result of 34.05 kg.

Although the total quantity of emission recorded in 2050 equals 5 times the emissions of the year 2012, the gradual increase of the part of renewable energies in the electric mix will allow reducing the emission factor per kWh. About the results of Reunion, the integration of the wave energy and those of geothermal, the electricity production will not depend on fossil energies anymore, and so to reduce considerably the GWP emissions.

Referring to the results of the high scenario, the total emissions in 2050 (178 kt) represent only 10% of the 2012 emissions (1709 kt). These results exceeded the targets of the environmental policy concerning the reduction GHG emissions, fixed by the POPE law [START_REF][END_REF]. This program has set up a goal to reduce to a quarter the GHG emissions generated by the energy mix in 2050.

Comparing the results of Madagascar and Reunion Island, based on Table 7 and Table 9 (see on Appendix B), Madagascar's production in 2012 represent 36% of those of Reunion, and concerning the GWP emissions, 28%. This difference can be explained by the low electricity rate of Madagascar, whereas in Reunion, practically all of their people have access to electricity network.

It can be seen on these values that the total emission quantity of Madagascar kept on rising up over the years, due to the contribution of fossil energies in the electric mix, even if their part has gradually decreased.

On the other side, the Reunion emissions increased until 2030, but the removal of the fossil energies in the energy mix has allowed reducing the GWP emissions.

If in 2012, GWP emissions of Madagascar represent only 25% of those of Reunion as said before, the trend reversed and Reunion Island records only 8% of the Madagascar's results in 2050.

Figure 1

 1 Figure 1 represented the evolution of the electricity production in Madagascar between 2002 and 2012 [6][7],and shows an average annual increase of 5.61%, which means a growth of 71% in ten years, all technology considered.

Figure 1 :

 1 Figure 1: Overview of the electricity production in Madagascar (2002-2012)

Figure 2 :

 2 Figure 2: Overview of the electricity production in Reunion Island (2002-2012)

Figure 3 :Figure 4 :

 34 Figure 3: Life cycle of electricity mix generation in Madagascar

  Figure e and Figure f shows the results of the different emissions generated by electric production in Madagascar and Reunion Island, respectively for the GHG and air emissions.

Figure 5 and Figure 6

 6 Figure 5 and Figure 6 show the results of the different emissions generated by electric production in Madagascar and Reunion Island, respectively for the GHG and air emissions. Values on Table 8 (see on Appendix A) summarized the emissions values from the different life cycle power plants, per kWh electric.

Figure 5 :

 5 Figure 5: Comparison of the GHG emissions from life cycle of electricity mix generation in 2012

Figure 7 :

 7 Figure 7: Impacts expressed on GWP and AP, generated by electric mix in Madagascar and Reunion Island in 2012

1 .Figure 8 :

 18 Figure 8: Repartition of the electric mix of Reunion Island (left part) and Madagascar (right part) 2015-2050

Table 1 :

 1 Overview of the power plant technologies used in Madagascar and Reunion Island for electricity generation in 2012[START_REF] Sy | Evolution annuelle des productions, ventes et nombre d'abonnes[END_REF] [8][START_REF] Sy | Synthèse des performances des installations (Centrales et groupes) -Juin 2012[END_REF]

	Power plant technology Generation	Total capacity
		(GWh)	(MW)
	Madagascar
	Hydropower	755	127.7
	Fuel oil ST	241	201.9
	Diesel CE	339	143.6
	PV system	0.008	0.007
	Total	1335	473.2
	Reunion Island
	Hydropower	488	133.4
	Wind	18.2	16.5
	Biogas	0.96	2.9
	PV system	190.4	152
	Bagasse ST	267.1	210
	Coal ST	1346.3	210
	Fuel oil ST Diesel CE	491.4	120 177.2
	Total	2802.36	210

CE: Combustion engine; PV: Photovoltaic; ST : Steam turbine -the oil power plant have been divided between fuel oil steam turbine and diesel combustible engine, of which technology have been divided as 18.1% of dieselmotor-small-generic, 18.9% of dieselmotormedium-generic, 21.4% of dieselmotor-big-generic and 41.6% of oil-heavy-ST-small-generic; -hydroelectric power combined 54.56% of hydro-dam-mini-generic and 45.44% of hydro-dam-mediumgeneric;

Table 2 :

 2 Amount of the fuels used for electricity generation in 2012 for Madagascar and Reunion Island

		Quantity (t)	Distance (km)
	Madagascar Reunion Madagascar Reunion
	Heavy oil	72 570	77 176	3 883	9500
	Diesel	58 083	399 192	3 883	7000
	Coal	-	659 100	-	10471
	4. LCA results and discussion

4.1. Environmental burdens

According to the GEMIS software, different types of results can be highlighted as GHG emissions, air emissions, solid wastes, water emissions, operating resources.

Table 3

 3 fixes the different gases included in GHG emissions and the gases contributing to acidification in the GEMIS results that will be considered and discussed in the next paragraphs.

Table 3 :

 3 Life cycle impact categories defined by GEMIS

	Emissions type Emissions included by GEMIS Potential impact	Unit
	GHG emission	CO2,CH4,N2O,CF4,		G l o b a l w a r m i n g p o t e n t i a l g C O 2-eq
			perfluorinated ethane
	Air emission		NO2,SO2,HCl, HF, NH2, H2S	A c i d i fi c a t i o np o t e n t i a l	gS O 2-eq
	ueeee
		ulCn	nOIn			0DGDJDVFDU 5HXQLRQ0,VODQG
	ueee	Ino	Cn
	uee				CC	uun
					uO		uo
	ue
	u	h2n0MNWa	h+o0MWa	1n20MWa	ue cu h)o0MNJa	ue cn SHUIOXRULQDWHG0HWKDQH0MNJa

  Table4are due to the fossil energy production, as 59.9% to the diesel production, 36.8% to the heavy oil production and only 3.3% to the renewable energies in Madagascar. Dieselmotor engine has the

	Rrrrr	neor	nerr	i r	iunr		uIRr	5HXQLRQ5,VODQG 0DGDJDVFDU
							Ruor
	Rrrr
								uli
								eRl
	Rrr
						u
						Rusu
	Rr							gisei
		62 e 54W7	12[5477	+CO5477	+)54NJ7	+ e 654NJ7	1+ u 54NJ7
	highest results on CO2, CH4, NO2 and NOx emissions (respectively 360 kt, 343 t, 9.85 t and 4332 T),
	followed by heavy oil results (221 kt of CO2, 194 t of CH4, 7.90 t of N2O and 664 t of NOx). Heavy
	oil steam turbine has the highest SO2 rate with 11.08 g/kWh, so the total emission of SO2 amount to 2
	672 t and represented about 64% of the total emission. In another hand, renewable energies production
	represented only 0.2% of the SO2 emissions. For the NOx emissions, 86% of the total emissions are due to
	dieselmotor production.
	For Reunion , 64% of the total emissions are attributed to coal steam turbine production: 74% of CO2
	(1321 kt), 89% of CH4 (2646 t), 78% of N2O (68 t), 40% of SO2 (1752 t) and 49% of NOx (4006 t). The
	second main contributor is heavy oil combined to Dieselmotor production, and renewable energies occupied

Figure 6: Comparison of the air emissions from life cycle of electricity generation in 2012

Table 4 :

 4 Total amount of emissions by power plant categories for Madagascar and Reunion Island

	Technology				Emissions
			CO2	CH4	N2O	S O 2	NOx
			(kt)	(t)	(t)	(t)	(t)
	Renewable energy MDG	19.63	21.86	0.43	6.83	42.32
		RUN	27.49	68.17	5.48	366.35 1 484.24
	Diesel	MDG	360.27	343.39	9.85 1500.57	4332.22
		RUN	240.67	228.61	6.56 1018.63	2308.45
	Heavy oil	MDG	221.39	194.17	7.90 2672.52	663.73
		RUN	194.30	44.80	7.31 1202.94	417.12
	Coal	RUN 1321.24 2646.14 68.09 1752.97	4006.57
	Total	MDG	601.29	559.42 18.18 4179.92	5038.27
		RUN 1783.71 2987.72 87.43 4340.89	8216.38

Table 5 :

 5 Total environmental impacts per country in 2012

	Technology	GWP(kt CO2-eq)	AP(t SO2-eq)
		MDG	RUN	MDG	RUN
	Renewable energy	20.30	31.80	36.41	1401.55
	Dieselmotor engine 371.79	248.34 4525.23	2631.44
	Heavy oil ST	228.60	197.60 3139.47	1493.72
	Coal ST	-	1407.72	-	4564.84
	Total	620.70	1885.45 7701.11 10091.55
	GWP : Global warming potential; AP: Acidification potential

Table 6 :

 6 Comparison of environmental impacts [5] [8][11] [13]

		Electricity mix(%)
	Energy source	Madagascar Reunion	Mali Tanzanie Japan Mexico
		(2012)	(2012) (2010)	(2010) (2010)	(2006)
	Fossil fuels	43.43	65.58	42	42.5	63.44	78.7
	RES	56.57	34.42	58	57.5	36.56	21.3
	Hydro	56.56	17.41	58	57.5	7.02	13.50
	Biomass	-	-	-	-	1 . 9 8	-
	Bagasse	-	9 . 5 3	-	-	-	-
	Wind	-	0 . 6 5	-	-	-	0 . 0 2
	Biogas	-	0 . 0 3	-	-	-	-
	PV system	0.01	6.80	-	-	0.25	-
	Geothermal	-	-	-	-	0 . 3 1	3
	Nuclear	-	-	-	-	2 7	4 . 8 0
	Heavy oil	18.07	9.47	12	-	10.09	21.60
	Diesel	25.36	8.07	10	1	-	0.50
	Coal	-	4 8 . 0 4	-	2 . 5	2 7 . 9 9	1 4
	Gas	-	-	2 0	3 9	2 5 . 3 5	4 2 . 6 0
	Total	100	100	100	100	100	100
	GWP (g CO2-eq/kWh)	464	673	441	309	511	571
	AP (g SO2-eq/kWh)	5.77	3.60	3.45	1.11	1.52	6.59

Table 7 :

 7 Results of production and GWP emissions from scenarios for Madagascar and Reunion Island 2012-2050

			High scenario(%)	Medium scenario(%)	Low scenario(%)
			Production	GWP Production	GWP Production	GWP
	Year Country	GWh kt CO2-eq	GWh kt CO2-eq	GWh kt CO2-eq
	2012	Madagascar	926	430	926	430	926	430

Table 10 (

 10 see Appendix B) shows the evolution of the emission factors of both islands, in parallel. These values reflect the contrast of the consumption per person in each country, and the environmental impacts generated until 2050, based on the assumptions. The consumption evolution for each country, between 2012 and 2050, is respectively 193% and 55% for Madagascar and Reunion. Although Madagascar has improved its electricity consumption ratio, it represents only 2% of the average consumption per year of one person in Reunion in 2050.

Table 10 :

 10 Emission factors from scenario results

		kWh/capita	g CO2-eq/kWh kg CO2-eq/capita
		MDG RUN MDG	RUN MDG	RUN
	2012	41	3031	464	673	19	2040
	2015	71	3498	450	640	32	2240
	2030	93	4154	378	573	35	2381
	2050	121	4692	283	30	34	139
	Evolution 2012/2050 193%	55%	-39%	-96%	78%	-93%

voltage subscriber (LV) and small and medium industries to high/medium voltage subscriber (MV/HV), the total number of subscribers amounted to 456422 in 2012, of which 99% is dedicated to LV (455,409) for a consumption equals to 584 GWh and 1% to MV/HV (1,013) for a consumption of 345 GWh, as shown in JIRAMA's report [START_REF] Sy | Evolution annuelle des productions, ventes et nombre d'abonnes[END_REF].

Through the ten current years, between 2002 and 2012, there was an average increase of production of 6% per year, and 3% for the number of subscribers to electricity consumption, so an average consumption of 1.282 MWh/LV sub and 341 MWH/HV sub.

In the following, the population growth is defined by the United Nations report, in the World Population Prospects [START_REF]World Population Prospects: The 2012 Revision[END_REF], it will show three degrees of evolution: low, medium and high scenario.

Referring to the International Energy Agency's value [16], this study will take as assumption an electrification rate of 14% with a decennial increase of 3%. The electricity consumption is estimated based on the number of subscribers and the electrification ratio on the year 2012. The consumption is considered as the minimal electricity production quantity, required for each year.

Concerning the renewable energies potential of Madagascar, the hydropower has the highest potential through the country. Referring to the sites identified by the "Office de Régulation de l'Electricité" (ORE) [START_REF]Madagascar hydroelectric sites[END_REF], Madagascar has numerous sites with potential power superior to 60 MW. On the other hand, the Japan New JEC Inc study [START_REF]Preliminary study for expansion of Manandona Hydroelectric power plant in Madagascar[END_REF] has identified a potential up to 3500 GWh of annual production, if all the sites are operating.

In the framework of this study, it is more coherent to fix a gradual increase until 2050, assuming a regular introduction of new hydropower plants. The solar energy has also an interesting potential, with a solar radiation about 2000 kWh/m 2 /year throughout the island [START_REF] Ramarojaona | Madagascar face aux défis du changement climatique[END_REF] .

The potential environmental impacts generated by the electricity production will be estimated from the assumptions above. The hydropower will reach from 56% to 70% in 2050, so an average annual growth of 0.35%; solar energy will attain 5% of the energy mix. This situation will imply a progressive decrease in production based on fossil energies. Figure 8 shows the evolution of the contribution of each power plant in the electricity mix.

Case of Reunion Island

Proceeding as for the case of Madagascar, here are the key values for the electricity production of Reunion Island until the horizon set 2050.

The assessment of the consumption evolution will depend on the population growth. With a high electrification rate and a total population of 837 870, Reunion records an electric rate of 3.344 MWh/habitant [START_REF]Bilan énergétique Ile de La Réunion[END_REF].

For this study, the projection has been calculated through the ANN's methodology, taken account of the production between the years 1980 and 2011. The results follow three evolution curves: low, medium and Appendix A. Lists of emissions in GEMIS


Didier

Phylogenetic Tools in Astrophysics

Keywords:

Multivariate clustering in astrophysics is a recent development justified by the bigger and bigger surveys of the sky. The phylogenetic approach is probably the most unexpected technique that has appeared for the unsupervised classification of galaxies, stellar populations or globular clusters. On one side, this is a somewhat natural way of classifying astrophysical entities which are all evolving objects. On the other side, several conceptual and practical difficulties arize, such as the hierarchical representation of the astrophysical diversity, the continuous nature of the parameters, and the adequation of the result to the usual practice for the physical interpretation. Most of these have now been solved through the studies of limited samples of stellar clusters and galaxies. Up to now, only the Maximum Parsimony (cladistics) has been used since it is the simplest and most general phylogenetic technique. Probabilistic and network approaches are obvious extensions that should be explored in the future.

Introduction

Extragalactic astronomy is a good illustration of the new era that is opening. Galaxies were discovered by Hubble one century ago, and the only data he had was images at visible wavelengths. He classified the morphologies of his observed galaxies by eye into four classes, and a few years later, from a physical argument, he depicted the evolutionary relationships between three of them on the famous Hubble Tuning Fork Diagram. This classification, slighly refined, is still made by eye and used as a general classification of galaxies despite the fact that the technology provides us with much more information (different wavelengths, spectra) on millions and millions of objects. However, a few multivariate unsupervized classification (stat06490.pub2, stat05127.pub2, stat05612) studies have begun to appear in the extragalactic literature at the turn of the XXIst century [START_REF] Fraix-Burnet | Multivariate Approaches to Classification in Extragalactic Astronomy[END_REF] . The phylogenetic approach is one of them [START_REF] Fraix-Burnet | Towards a Phylogenetic Analysis of Galaxy Evolution : a Case Study with the Dwarf Galaxies of the Local Group[END_REF][START_REF] Fraix-Burnet | Astrocladistics: a phylogenetic analysis of galaxy evolution I. Character evolutions and galaxy histories[END_REF][START_REF] Fraix-Burnet | Astrocladistics: a phylogenetic analysis of galaxy evolution II. Formation and diversification of galaxies[END_REF] .

Phylogenetic tools are heavily used in evolutionary biology (stat05446.pub2, stat07642), even though linguists (stat00088) have probably invented the principles of the methodology. The idea is strongly based on the darwinian process of transmission with modification: two entities are said to be close if they share a same trait inherited from a common ancestor. This explains the hierarchical organization of the diversity of living organisms. The simplest and most general technique to build a phylogenetic tree is cladistics (stat05363), also called Maximum Parsimony (stat01733, stat05770).

In unsupervized classification, the most common approach is to aggregate objects into clusters. The origin of these clusters is better understood through their relationships. The phylogenetic approach con-versely looks for these relationships and then defines families and sub-families depending on the inheritance scheme depicted by the tree [START_REF] Fraix-Burnet | Concepts of Classification and Taxonomy Phylogenetic Classification in Statistics for Astrophysics: Clustering and Classification[END_REF] (stat06461).

Why and how is it possible to use the phylogenetic approach in astrophysics where the diversification process is not comparable to sexuation or duplication? There are at least two answers to this question.

Firstly, the role of evolution in the tree-like representation provided by cladistics is debated [START_REF] Pécaud | Three roles that evolutionary theory has played in cladistics[END_REF] . For instance, is darwinian evolution really a prerequisite for cladistics, or are the relationships interpretable in terms of evolution? Indeed, this may not be so important in practice, since the key point for the hierarchical structure is the transmission with modification as illustrated by the success of the phylogenetic approach in linguistics. Very generally, the evolution of any single object can be seen as a transmission with modification process. However, the evolution of an ensemble of objects is not necessarily represented by a hierarchical tree if there are too many parallel or regressive evolution of some properties, or hybridization as for bacteria. In any case, a phylogenetic tree depict the shortest path to transform an object into another one, and this transformation can be virtual, like in the example of volcanoes [START_REF] Hone | Cladistic analysis applied to the classification of volcanoes[END_REF] .

Secondly, all astrophysical objects evolve, and we can nearly always identify a transmission with modification process. For instance, stars form from clouds of gas. This gas is enriched into heavier chemical elements inside the more massive stars, which then explode and eject this new gas that will later form new stars. For galaxies, when two galaxies merge, the new object inherits from all the material of its progenitors (stars, gas and dust) but with many modifications (formation of new stars, modified kinematics, and global distinct chemical composition). Do we expect a hierarchical organization of the diversity of astrophysical entities? This is a priori difficult to guarantee, but the increase of the metallicity of stars and gas due to the previous generations, and the complexity of the transformation processes for galaxies that very probably induced an increase of diversity with time, seems to open this possibility. In any case, nothing prevents the use of phylogenetic algorithms on astrophysical data as exploratory tools. And this has now been done on several kinds of astrophysical objects, with great success.

Phylogenetic Algorithms

The most natural phylogenetic algorithm is cladistics, or Maximum Parsimony (stat05363). It can be readily applied to any kind of data since there are a very minimal assumptions. The idea is to look for all the possible arrangements of the objects in study on a tree, and select the most parsimonious one as the best evolutionary scenario. The objects are called taxa which can be individuals or species.

The parsimony criterion is based on the total evolutionary cost. To go from an object to another on the tree, some properties must be changed by certain amounts. The total cost of the tree is the sum of all these changes which are called steps.

Let us illustrate this point with the Hubble Tuning Fork Diagam mentioned above. Let us consider two parameters that describe the rough morphology of galaxies: the presence/absence of a disk, the presence/absence of a bar. Elliptical galaxies have no disk and no bar (0,0), spiral ones have a disk and no bar (0,1) and barred spiral ones have both (1,1). Since there is only one possible arrangement on a tree with three objects, the simplest scenario is to put one change for the disk property on the branch connected to the ellipcal galaxies, and one change for the bar property on the branch for the barred spiral galaxies. According to Hubble, the elliptical galaxies should flatten in a disk with time. Hence the absence of a disk (value 0) is an ancestral state and its presence (value 1) a derived state acquired by the two groups of spiral galaxies [START_REF] Fraix-Burnet | Concepts of Classification and Taxonomy Phylogenetic Classification in Statistics for Astrophysics: Clustering and Classification[END_REF] .

To perform the computation of the number of steps of a tree, discrete data are necessary, each discrete value is called an evolutionary state. The parameters to use are called characters and are the ones that can be given at least two evolutionary states, one being called ancestral and the other one derived. The parameters are observables or properties describing the objects, the characters being supposed to keep a trace of the history. In astrophysics, all quantities are quantitative and continuous, so that discretization is required. This is a complicated subject in statistics (see stat02713), but we have found that about 20 to 30 equal bins is a good compromize between objectivity, stability and the continuous nature of the parameters.

Some additional hypothesis can be imposed to the cost between two evolutionary states. Probably the most general one is the Wagner optimization criterion which is a l1-norm and allows for reversals. But irreversibility can be imposed or any more or less complicated hypothesis through a cost matrix.

A rather unique feature of the cladistics algorithm is its ability to take into account uncertainties and even missing values (stat03968). By providing a range of possible states instead of a single one, the Maximum Parsimony procedure selects the state which minimizes the total evolutionary cost, value which can be regarded as a prediction. This feature can be quite appreciable in astrophysics where uncertainties are omnipresent.

At this point it should be clear that the minimization process of Maximum Parsimony is very similar to the Mimimum Spanning Tree technique (stat06487) with the l1-norm. The big difference is that in a phylogeny, internal nodes are added and represent hypothetical ancestors. Formally, it is postulated that the ancestors be unknown to allow for future discoveries. These internal nodes widen considerably the possible topologies of the trees, at the expense of the computing time (NP-hard problem).

To alleviate this computing limitation of cladistics, other methods have been developed. Among the other character-based approaches, the Maximum Likelihood algorithm is quite popular in biology. It is a probabilistic method which selects the most probable tree according to some evolutionary model [START_REF] Williams | An investigation of phylogenetic likelihood methods in Third[END_REF] . This technique has not yet been applied in astrophysics since it requires a good knowledge of the evolutions for the characters. However this should be certainly investigated in the future.

The other big category of methods uses pairwize distances between the taxa (stat02470, stat02231). These distances are computed from the characters and the algorithms are generally extremely fast and efficient. It has always been somewhat surprising that character-and distance-based approaches yield similar results since the mathematical connection is still not obvious [START_REF] Thuillard | Phylogenetic Applications of the Minimum Contradiction Approach on Continuous Characters[END_REF][START_REF] Thuillard | Phylogenetic Trees and Networks Reduce to Phylogenies on Binary States: Does It Furnish an Explanation to the Robustness of Phylogenetic Trees against Lateral Transfers?[END_REF] . This might be due at least partly to the fact that the characters have an evolutionary information (the phylogenetic signal) that is not entirely lost when computing distances. The most popular algorithm is the Neighbor Joining Tree Estimation [START_REF] Saitou | The neighbor-joining method: a new method for reconstructing phylogenetic trees[END_REF][START_REF] Gascuel | Neighbor-Joining Revealed[END_REF] which is a bottom-up hierarchical clustering method (stat02449.pub2). It would sound like an interesting choice in astrophysics, however it is not easy to assess the robustness of the result tree without comparing with cladistics analyzes.

Applications

Up to now, the Maximum Parsimony method has been used for galaxies [START_REF] Fraix-Burnet | Towards a Phylogenetic Analysis of Galaxy Evolution : a Case Study with the Dwarf Galaxies of the Local Group[END_REF][START_REF] Fraix-Burnet | Structures in the fundamental plane of early-type galaxies[END_REF][START_REF] Fraix-Burnet | A six-parameter space to describe galaxy diversification[END_REF] , globular clusters [START_REF] Fraix-Burnet | The environment of formation as a second parameter for globular cluster classification[END_REF] , stellar populations [START_REF] Fraix-Burnet | Application of Phylogenetic Networks in Evolutionary Studies[END_REF] , Gamma Ray Bursts [START_REF] Cardone | Hints for families of GRBs improving the Hubble diagram[END_REF] and the Jovian satellites [START_REF] Holt | Cladistical Analysis of the Jovian Satellites[END_REF] . In all cases, cladistics provides the identification of families of objects that are characterized by an interpretation in terms of formation and evolution that could not have been discovered otherwize. For instance, the analysis finds three families of Globular Clusters of our Galaxy together with their evolutionary relationships. The average properties of each family is found to be specific of a certain formation environment, such as the chemical content of the gas and its dynamics. The three families thus correspond to three stages in the assembly of our Galaxy [START_REF] Fraix-Burnet | The environment of formation as a second parameter for globular cluster classification[END_REF] . The phylogenetic approach in astrophysics was initially thought for galaxies because of their intrinsic complexity and the complexity of the diversification throughout the evolution of the Universe [START_REF] Fraix-Burnet | Astrocladistics: a phylogenetic analysis of galaxy evolution I. Character evolutions and galaxy histories[END_REF][START_REF] Fraix-Burnet | Astrocladistics: a phylogenetic analysis of galaxy evolution II. Formation and diversification of galaxies[END_REF] . The demonstration of this idea was given [START_REF] Fraix-Burnet | A six-parameter space to describe galaxy diversification[END_REF] with the first evolutionary tree showing how the transformation processes of galaxies shaped their diversity. This was also the first multivariate classification of galaxies, even though it is based on a limited sample of less than one thousand individuals. Ongoing studies are tackling bigger samples.

There is a fundamental difficulty in phylogenetic approaches, that is indeed true also for any multivariate classification, and biologists have been struggling for several centuries for this problem: which set of parameters should be used for multivariate classification (stat05615)? It may depend on the goal of the classification, but if the understanding of the entire diversity and its origin is desired, then an objective selection of the parameters is required. Taking blindly all available observables or properties would probably lead to a negative result, either because of the curse of dimensionality that smears out structures in the parameter space (stat00408), or because of dominant or conflicting parameters.

Phylogenetic approaches are particularly sensitive to the quality of the characters since they should be the tracers of the relationships between the species. Synapomorphies are characters for which innovations are transmitted to all descendant branches of a given node (the hypothetical ancestor) and are maximized by the Maximum Parsimony procedure. Conversely the homoplasies are minimized since they tend to destroy this transmission behavior and consequently the hierarchical structure. Reversals, convergent and parallel evolutions are homoplasies.

Despite some mathematical rules that would probably help [START_REF] Thuillard | Phylogenetic Applications of the Minimum Contradiction Approach on Continuous Characters[END_REF] , it remains difficult to find the best parameter set without trial-and-error computations. Statistical analyzes like Principal Component Analysis (stat06472) give some insight on the parameters and their correlations, but it may not always be obvious to distinguish a size effect from a confounding correlation (stat06786, stat06194) due to evolution [START_REF] Fraix-Burnet | The Fundamental Plane of early-type galaxies as a confounding correlation[END_REF] . The first one is probably not very informative while we are clearly looking for the second one. For illustration, a cladistic analysis reveals that the origin of the correlation in galaxies between the central velocity dispersion and the metallicity is certainly evolutionary, i.e. the two properties independantly and statistically evolve monotically [START_REF] Fraix-Burnet | A six-parameter space to describe galaxy diversification[END_REF] . Other statistical investigations can be performed, and with the multiplication of phylogenetic studies, a better idea of the parameters to use will emerge.

The Future

The application of phylogenetic methods is rather recent in astrophysics, and many conceptual, technical and philosophical questions had to be first addressed. We are however now in a position to use these approaches more widely, explore, adapt or develop new algorithms which can be specifically more efficient for the analyzes of astrophysical entities. Maximum Parsimony will probably remain a reference because of its conceptual and practical relative simplicity to implement. Its main limitation is to be a NP-hard problem. We have to build the phylogenies piece by piece, much like the Tree of Life. Other approaches, like distance-based phylogenetic methods or multivariate clustering techniques, could probably be used in parallel to build classes or sub-classes before finding their relationships with Maximum Parsimony.

Probabilistic methods like the Maximum Likelihood is also promising since the basic physics of the astronomical objects and their evolution is in principle well known. Their complexity prevents precize prediction through heavy numerical simulations, but it seems reasonable to think that some probabilistic laws could be found at least for some characters. Also bayesian phylogenetic methods would deserve some attention in the future.

The network (stat02300) representations of the diversification of the astrophysical entities is a promising direction. It has now been shown that the tree-like representation of different species of astrophysical objects is physically reasonable, but it appears, especially for galaxies, that a more complex scheme could be required [START_REF] Fraix-Burnet | Multivariate Approaches to Classification in Extragalactic Astronomy[END_REF] . Firstly, a network representation can synthetize conflicting trees [START_REF] Huson | Application of Phylogenetic Networks in Evolutionary Studies[END_REF] in a more informative way than consensus trees. These conflicts may arize from a lack of information on the population of objects, which is probably often, if not always, the case. Secondly, hybridization, or parallel or convergent evolution of some characters, certainly occur in galaxy evolution. This is known to destroy the tree-like structure by creating perpendicular branches, making what biologists call reticulograms. In any case, networks are a more general representation of evolutionary relationships than trees. They are also more difficult to read and to use for a physical interpretation.

5 Related Articles Statistics in Astrophysics, 2014, E. Feigelson, stat00155 Ultrametric trees, 2014, F. Murtagh, stat06461


O Ronsin

C Caroli

T Baumberger

Preferential hydration fully controls the renaturation dynamics of collagen in water-glycerol solvents

Glycerol is one of the additives which stabilize collagen, as well as globular proteins, against thermally induced denaturation -an effect explained by preferential hydration, i.e. by the formation, in water/glycerol solvents, of a hydration layer whose entropic cost favors the more compact triplehelix native structure against the denatured one, gelatin. Quenching gelatin solutions promotes renaturation which, however, remains incomplete, as the formation of a gel network gives rise to growing topological constraints. So, gelatin gels exhibit glass-like dynamical features such as slow aging of their shear modulus and stretched exponential stress relaxation, the study of which gives us access to the re(de)naturation dynamics of collagen. We show that this dynamics is independent of the bulk solvent viscosity and controlled by a single parameter, the undercooling ∆T below the glycerol-concentration dependent denaturation temperature. This provides direct proof of (i) the presence of a nanometer thick, glycerol-free hydration layer (ii) the high locality of the kinetically limiting process governing renaturation.

I. INTRODUCTION

Glycerol has been for decades one of the most widely used additives that stabilize the native structure of proteins against denaturation induced by e.g. thermal stresses. Extensive work by Timasheff and collaborators [START_REF] Timasheff | Linkage Thermodynamics of Macromolecular Interactions[END_REF] on globular proteins led them to explain this effect in terms of the so-called preferential hydration effect: in a stabilizing binary solvent, the protein interacts more favorably with water than with the cosolvent. This results in the formation of a hydration shell out of which the cosolvent is excluded, at the expense of a mixing entropy cost. The resultant increase in chemical potential of the protein acts as a driving force to minimize the protein-solvent interfacial area, leading to stabilization of the (more compact) native conformation. This interpretation was later shown [2][3][4] to be valid as well for collagen. Collagen molecules are constituted of the wrapping into a right-handed helix of three left-handed single strand α-like (polyproline II) helices. When heating a collagen solution above T denat , denaturation of this H-bond stabilized structure results in a so-called gelatin solution of single-stranded chains in the coil configuration -hence an increase of the polymer/solvent area of contact. It has been found [2,4] that the increase ∆T denat upon addition of glycerol grows linearly with its concentration φ, up to φ 40 wt%.

Renaturation of collagen from a gelatin solution occurs via nucleation and growth of triple-helix segments [START_REF] Nijenhuis | Gelatin," in Thermoreversible Networks: Viscoelastic Properties and Structure of Gels, Advances in Polymer Science[END_REF][START_REF] Djabourov | Physical gels from biological and synthetic polymers[END_REF], a process kinetically controlled by the unusually slow cistrans isomerisation of the prolyl peptide bonds present in large proportion along the chains [START_REF] Bächinger | [END_REF]. However, except for very small gelatin concentrations ( 1%) renaturation is only partial. Indeed, each chain is engaged in the formation of several triple-helix nuclei, each of which connects it with different partners. The nucleation and growth of these cross-links leads to the formation of a percolating thermoreversible gelatin gel network. This process is revealed by the growth with time t of the shear elastic modulus G. After a lapse time t 0 associated with percolation of the polymer network, G first exhibits a rapid increase due to further nucleation and growth of cross-links [8,9]. It then crosses over to a slow regime in which G grows logarithmically with time, without any measurable trend towards saturation [10]. In this glass-like aging stage, increasingly strong topological constraints prevent the formation of new cross-links, and logarithmic strengthening can be assigned to network rearrangements taking place via thermally activated Hbonds fluctuations resulting in zippings and unzippings of the existent triple-helix segments [START_REF] Nijenhuis | Gelatin," in Thermoreversible Networks: Viscoelastic Properties and Structure of Gels, Advances in Polymer Science[END_REF]11].

The same type of rearrangements also control the stress relaxation dynamics of gelatin gels [12]. In such experiments it is found that, upon applying a shear deformation step, which biases the glass-like complex energy landscape of the network, the macroscopic shear stress exhibits a slow, stretched exponential decrease à la Kohlrausch [13] with a characteristic time growing as a power of the gel age t w , i.e. the time elapsed since the beginning of the thermal quench.

In short, monitoring the aging of the elastic modulus and/or the stress relaxation of gelatin gels yields information about the dynamical scale of the processes which control the re(de)naturation of collagen.

In this article we study gelatin gels formed in waterglycerol solvents and assess the evolution of their slow dynamics with glycerol concentration. We show that this dynamics is by no means slaved by the viscosity of the bulk solvent but fully controlled by the presence of the water shell associated with Timasheff's preferential hydration effect. Conversely, this result confirms the locality of the zipping-unzipping processes responsible for gelatin aging and stress relaxation.

II. MATERIALS AND METHODS

Samples are prepared by dissolving, at 55 • C, 5 wt % gelatin (300 Bloom, from porcine skin, Sigma) in either pure water or mixtures of water and glycerol at concentration φ = 40 or 60 wt %, of viscosity η(φ) (see Fig. 4). Gelatin solutions in pure water have a pH = 5.1 ± 0.05 at 40 • C.

The pregel solution is poured into the sand-blasted cone-plate cell of a stress-controlled rheometer (Anton-Paar, MCR 501) protected against solvent evaporation by a paraffin oil rim. The sample temperature is first set at 55 • C and then ramped at 7. The early advancement of the gelation process is monitored by measuring the growth of the storage shear modulus G at frequency 1 Hz versus the time t elapsed after reaching the working temperature T . For this particular set of experiments we use a strain amplitude of 4%, a relatively large value which we choose in order to optimize the signal-to-noise ratio while remaining in the linear mechanical response domain.

Successive runs are performed at increasing temperatures spaced by 1 • C. After each run, the sample is reinitialized by reheating it up to 55 • C and shearing at the constant rate 1 s -1 for 200 s before performing a new quench. We have checked that this protocol ensures that mechanical measurements are reproducible to within 1%, over 20 cycles at least. At low enough temperatures, after an initial induction period t 0 during which it remains below the detection threshold, a gel network percolates and G starts growing. As seen on Fig. 1, t 0 increases with temperature. We define T gel as the lowest temperature at which G(t = 2×10 4 s) does not exceed 2 Pa, a threshold value much smaller than the typical moduli (several hundred Pa) used in this study. With this protocol T gel is thus determined to within 1 • C.

B. Mechanical measurements

For a given value of φ, time evolution of the modulus and stress relaxation experiments are performed on a single sample, reinitialized between various runs as described above.

The time-dependent storage modulus G(t) is measured at frequency 1 Hz with a strain amplitude 1%.

Stress relaxation experiments are performed as follows. We first let gelation proceed freely for a time t w (defined as the age of the gel) after the end of the quench, then apply a 5% strain step and monitor the subsequent evolution of the shear stress σ(t). Such measurements have been performed for t w = 200, 10 3 and 10 4 s.

III. RESULTS AND DISCUSSION

In order to get some insight into the effect of glycerol on the dynamics of collagen re(de)naturation, we first performed the following preliminary experiments, in which we compare the transient mechanical behavior of gels with φ = 0 (pure water) and φ = 60% solvents, at room temperature T = 20 • C where gelatin gelation is known to proceed rapidly.

A simple macroscopic argument leads to expect the characteristic time scale(s) of relaxation processes to scale as the viscosity η φ of the solvent [14]. Such a guess is in particular suggested by two groups of previous results which have both shown this scaling to hold for :

(i) the linear viscoelastic loss angle measured in a frequency range chosen so as to probe the mobility of individual strands of the gel network [15].

(ii) the rate dependence of the gel fracture energy. For gelatin gels, this process occurs without any scission of the polymer chains, but via their stress-induced disentanglement and pull-out [16,17].

Fig. 2 displays the stress relaxation curves of the two gels, the compositions of which was chosen so that they exhibit the largest viscosity contrast (η 60 /η 0 = 11, see inset of Fig. 4). Since it is known that the characteristic time of the stretched exponential stress relaxation of pure water gels scales as a power of the gel age t w , both measurements have been performed at the same t w = 10 4 s. In order to assess the above scaling expectation, we also plotted on the same figure the normalized stress σ/σ 0 (with σ 0 the stress immediately after loading) vs. the scaled time (η 0 /η 60 ) t. Obviously, our naive guess is not correct. On the contrary, visual inspection suggests that the stress relaxation dynamics is but very weakly slowed down by the presence of glycerol. A second piece of information is provided by comparing the growth dynamics of the moduli of the two gels (Fig. 3). Strikingly, G is seen to grow noticeably faster for the more viscous gel -an effect which is dramatically enhanced when scaling the time variable. Clearly, a hydrodynamic description of the dissipation associated with the movements of the network responsible for aging and stress relaxation in terms of the viscosity of the bulk solvent is inappropriate to account for our observations. We must therefore consider the possibility for the microscopic structuration of the solvent to be of crucial importance. This is strongly suggested by the nature of the gelation process: it involves the formation of triple helix cross-links exhibiting the structure of native collagen which, as mentioned above, induces preferential hydration as revealed by the dependence of the denaturation temperature T denat on the glycerol content. Since gelation means renaturation, T gel should be a good indicator of T denat . In order to test this for our gels, we have measured T gel (φ) (see Materials and Methods). Fig. 4 shows that T gel grows linearly with the glycerol content with a slope

dT gel dφ = 0.14 • C/wt%
Both the large extent of the linear behavior (which we extend here up to 60 wt%) and the slope value are fully compatible with the results of Gekko and Koga [2] and Penkova et al [4] for the φ-dependence of the denaturation temperature T denat (dT denat /dφ = 0.12 ± 0.01 • C/wt% for calf skin collagen). From now on we will therefore use T gel as an approximant for T denat . We now want to identify the parameters which controls the modulus build up and stress relaxation dynamics at various temperatures and glycerol concentrations. These mechanical responses are governed by the dynamics of the microscopic motions of network constituents involved in the de(re)naturation transition. We note that in the temperature range ( (T gel -T )/T 1) relevant to our experiments, the thermodynamic force which drives these motions is controlled, not by temperature itself, but by the undercooling ∆T = T gel (φ) -T .

In order to determine to which extent ∆T is effectively a relevant control parameter for the dynamics, we have compared the early build up of the shear modulus a φ = 40 wt% gel at 30 • C (i.e with ∆T = 6 • C) and of a φ = 0 one at temperatures T ranging from 22 to 26 • C (∆T from 8 to 4 • C). As can be seen on Fig. 5, the five φ = 0 curves are widely splayed and the one among them which lies closest to the φ = 40 one corresponds to the same ∆T = 6 • C value. Results for the evolution of G are shown on Fig. 6. Strikingly, for each value of ∆T , the curves for the three solvent compositions collapse very nicely over the full time range. That is, ∆T controls the modulus build up dynamics not only in the early stage of gelation corresponding to nucleation and initial cross-link growth but, as well, in the late logarithmic aging regime resulting from cross-link rearrangements via zipping-unzipping of the collagen segments. Each of the three panels of Fig. 7 displays stress relaxation curves measured, for a given ∆T , at different stages of gel aging (t w = 200, 10 3 and 10 4 s). Again, for each value of ∆T and t w , the data for the three solvent compositions exhibit excellent collapse over 5 time decades.

These two groups of results clearly demonstrate that, in a substantial temperature range of biological relevance, the de(re)naturation dynamics of collagen is controlled by a single parameter, namely the undercooling ∆T below the denaturation temperature. This dynamics is affected by the presence of glycerol exclusively via the φdependent upward shift of T denat , and is completely insensitive to the value of the bulk solvent viscosity.

IV. CONCLUSIONS

This behavior entails the following conclusions. (i) The time-dependent network structure of gelatin gels formed in water/glycerol mixtures is uniquely determined, at all stages of its evolution, by the undercooling ∆T below the glycerol-concentration dependent gelation temperature.

(ii) Renaturation in a water-glycerol mixture proceeds as it would in pure water. This dynamical behavior directly confirms the presence of a hydration layer and indicates that glycerol is fully expelled out of it.

(iii) At a given value of ∆T , i.e. for a fixed chemical potential difference between the native and denatured states, the probability of the zipping-unzipping elementary events, i.e. of the (triple helix)↔(three coils) thermally activated transition, is glycerol-insensitive. Hence the free energy barrier height is φ-independent. The same is true of the frequency of the vibration modes which control the prefactor of the Eyring activation exponential. In view of the fact that the kinetically limiting process is known to be the cis-trans isomerisation of Gly-Pro bonds [START_REF] Bächinger | [END_REF], we are led to suggest that the thickness of the glycerol-free hydration layer should range close to one nanometer.

Finally, putting these conclusions in regard with the above-mentioned results about the viscoelastic loss angle and the rate dependence of the fracture energy leads us to formulate a last, more general, remark.

Note that, on the one hand, the dynamics which we have studied here is controlled by the ultra local, subnanometric, motions which trigger network rearrangements. On the other hand, in ref [15] the authors chose to probe preferentially the frictional dynamics of the flexible inter-crosslink strands, which involve motions on the scale of the mesh size ξ of the gel network. Similarly, ξ is the spatial scale relevant to dissipation associated with crack propagation. Indeed, the velocity dependence of the fracture energy is due to the viscous dissipation induced by the pull out of gelatin chains out of the poroelastic network [16,17]. In this process, the solvent is sheared on a space range on the order of the gel mesh size. For commonly used gels, ξ lies in the 10 nm range -i.e. extends much beyond the hydration range. This explains why the dissipation measured in the the two latter experiments is controlled by the bulk solvent viscosity rather than by that of the hydration layer.

In summary, from the results of our study of the effect of glycerol on the macroscopic dynamic elastic responses of gelatin gels, we conclude, in agreement with Frauenfelder's views about protein motions [18], to the primary importance of the space scale of the motions on protein dynamics.

FIG. 1 .

 1 FIG. 1. Early time evolution of the shear modulus for a φ = 0 (pure water) gel at temperatures (in • C) as specified by the labels. The dashed line indicates the G = 2 Pa threshold chosen to define the gelation temperature. Here, T gel = 30 • C.

FIG. 2 .

 2 FIG. 2. Stress relaxation curves at 20• C for gels with age tw = 10 4 s and glycerol content φ = 0 (red, thick line) and φ = 60 wt% (blue, thin line). The blue, dashed line shows the φ = 60 wt% data plotted vs. scaled time (η0/η60) t. Arrows indicate the corresponding shift.

FIG. 3 .

 3 FIG. 3. Shear modulus vs. time after quench for gels at 20 • C with φ = 0 (red, thick line) and φ = 60 wt% (blue, thin line). The blue, dashed line shows the φ = 60 wt% data plotted vs. scaled time (η0/η60) t. Arrows indicate the corresponding shift.

FIG. 4 .

 4 FIG. 4. Gelation temperature of 5 wt% gelatin gels in aqueous solvents with glycerol weight fraction φ. The insert shows the solvent viscosity η φ at T = 20 • C and T gel (φ) values.

FIG. 5 . 15 FIG. 6 .

 5156 FIG. 5. Early growth of the shear modulus G of a φ = 40 gel at T = 30 • C (∆T = 6 • C): black, thick line, as compared with a φ = 0 gel at various temperatures in • C, as labelled: color, thin lines.

4 FIG. 7 .

 47 FIG. 7. Stress relaxation curves for solvents with glycerol contents φ = 0 (full lines), 40 (dotted lines) and 60 wt% (dashed lines). Each panel corresponds to a fixed value of ∆T , as indicated. Each group of curves corresponds (see labels) to a common age value: tw = 200 s (blue), 10 3 s (red) and 10 4 s (black). Note the absence of tw = 200 s data in the lower panel, due to the fact that at this value of ∆T (6 • C), network percolation has not yet occurred.

ACKNOWLEDGMENTS

We are grateful to M. Djabourov for an enlightening discussion.