Barbara Petridou

Marie-France Guerin

Franqoise Hayes

Ribosomal proteins of Tetrahymena thermophila. Correlation of one-and two-dimensional electrophoretic migration patterns and characterization of additional small and large subunit proteins

Further analysis of the protein complement of the cytoplasmic ribosome of the protozoon Tetrahymena thermophila has led to the identification and characterization of seven additional proteins, three in the small and four in the large subunit of this ribosome. Several of these proteins are poorly soluble or insoluble in the absence of high concentrations of urea and are not seen in the electrophoretic distribution patterns of ribosomal proteins in two-dimensional polyacrylamide gels unless 6 M urea is added to electrode buffers in contact with protein samples (first dimension) and first-dimension gels (second dimension). The migration patterns of the 40S and 60S subunits of the T. thermophila ribosome in one-dimensional polyacrylamide SDS gels and in two-dimensional gels prepared by means of the basic-acidic system of Kaltschmidt and Wittmann**, and the basic-SDS system of Zinker and Warner*** have been correlated. ....... .

Introduction

Materials and methods

In a previous publication [1] 31 proteins from the small, and 41 from the large subunit of the cytoplasmic ribosome of Tetrahymena thermophila were characterized and their molecular weights were estimated by one-and two-dimensional electrophoresis. This study left in doubt the status of one protein, provisionally designated S1, associated with the small ribosomal subunit, and of several species present in some but not all protein preparations analysed. Further work has produced evidence that confirms the ribosomal status of protein S1 and has led to the identification of three additional proteins in the small ribosomal subunit and of four in the large subunit.

Strains and culture conditions

T. thermophila B1868 mating type IV (Dr D. Nanney, Dept. of Zoology, University of Illinois, Urbana, IL. USA) was grown as described previously [2]. Cells were labelled with [35S]-L-methionine (Amersham, U.K.) sp. act. 30 Tbq/mmol, 18.5 MBq/ml during 6-7 generations of exponential growth in a defined synthetic medium [3] as described in [4].

inhibitor in all cases [1,2]. Protein samples for oneand two-dimensional electrophoresis were prepared as detailed in [1].

Polyacrylamide gel electrophoresis

One-dimensional electrophoretic separations of ribosomal proteins were carried out according to Laemmli [5] with the minor modification that hydrochloric acid in the stacking gel buffer was replaced by orthophosphoric acid. The procedures of Kaltschmidt and Wittmann [6] and Zinker and Warner [7] were used for two-dimensional electrophoresis with the following modifications.

First-dimension electrophoresis

Conditions were identical for both two-dimensional procedures.

Separate first-dimension gels (4 mm x 90 mm) prepared as described by Kaltschmidt and Wittmann [6] were used to fractionate acidic and basic proteins.

Protein samples (200 ~g and 300 ttg, respectively, for separation of basic and acidic proteins) were dissolved in Kaltschmidt and Wittmann first-dimension separation gel solution containing 8 M urea (50/~1). Pyronine red tracking dye, followed by tetramethylethylene diamine, and ammonium persulfate in the quantities specified by Kaltschmidt and Wittman were then added and the mixtures were immediately layered on to first-dimension gels and allowed to polymerise. Electrophoresis was carried out at 6-8oC for 18 h at 10 V/cm with upper electrode buffer (in contact with the protein sample zone) containing 6 M urea.

Second-dimension electrophoresis

Gel slabs (1 mm × 135 mm wide × 230 mm long) for second-dimension electrophoresis according to Kaltschmidt and Wittmann were prepared as described by these authors [6] using an acrylamide concentration of 18% wt/vol. Second-dimension gels (1 mm x 135 mm x 230 mm) for the Zinker and Warner procedure were prepared according to Laemmli [5], with hydrochloric acid replaced by orthophosphoric acid in the stacking gels, as already noted. Firstdimension gels were extruded and shortened by removing the sample zone and the lower 15 mm from gels containing basic proteins and the lower 35 mm from gels containing acidic proteins. The shortened basic and acidic protein-containing gels were then bonded together, in the appropriate orientation, to second-dimension gel slabs. Second-dimension electrophoresis was carried out as follows: Kaitschmidt and Wittmann method, 6-8oC, 1 h at 1 V/cm followed by 16 h at 10 V/cm, upper electrode buffer (in contact with the first-dimension gel) containing 6 M urea; Zinker and Warner procedure, 6-8oC, 1 h at 1 V/cm, followed by 16 h at 8 V/cm. Gel slabs were stained with Coomassie blue and, when necessary, dried for autoradiography.

Elution of proteins from polyacrylamide gels

Proteins were eluted from stained zones taken from one-and two-dimensional polyacrylamide gels by incubation of the gel samples for 72 h at 37°C in 0.5 ml of 10 mM Tris-HC1, 10 mM 2-mercaptoethanol, 0.5% wt/vol sodium dodecyl sulfate (SDS) pH 7.6 and precipitated from the eluates at 0oC overnight in the presence of 10% wt/vol trichloroacetic acid or of 7 vol of acetone with or without addition of carrier proteins (see figure legends for details). Precipitates were dried briefly in a vacuum after first washing trichloroacetic acid precipitated proteins with diethyl ether, and then dissolved in electrophoresis buffers.

Results

Correlation of one-and tw3-dimensional electrophoretic migration patterns of ribosomal proteins

40S subunit proteins

Although its resolving power is lower than that of two-dimension systems, one-dimensional electrophoretic analysis of ribosomal proteins possesses the advantage of rapidity, permits the comparison of numerous preparations in the same gel slab, and can be used for the preliminary characterization of protein samples if the species present in the various bands seen in one-dlm~,n~inn~! ~l~otrmnhnro_arnm~ h~ve heen identiffed.

To do this, radioactive proteins prepared from 40S and 60S ribosomal subunits isolated from cells grown in the presence of [35S]-c-methionine were fractionated by two-dimensional electrophoresis according to Kaltschmidt and Wittmann [6]. Radioactive proteins eluted from each of the 71 spots previously [1] characterized in this seperation system were mixed with total nonradioactive subunit proteins and the mixtures were analysed by one-dimensional electrophoresis according to Laemmli [5]. After electrophoresis gel slabs were stained, dried, and autoradiographed.

In all but two cases a single major radioactive band which comigrated with one of the stained bands in the gel was detected. Fig, 1. Correlation of one-and two-dimensional electrophoretic migration patterns of total proteins of the small and large subunits of the cytoplasmic ribosome of T. thermophila. Preparations of total proteins isolated from 35S-labeled 405 and 605 ribosomal sut-'mits (120/~g protein, sp. act. 105 cpm/tzg) were fractionated by two-dimensional electrophoresis according to Kaltschmidt and Wittmann [6] modified by omission of urea from first-dimension electrode buffers. As reported previously [1], 31 stained spots were observed in the migration pattern of 405 subunit proteins and 40 in that of 605 subunit proteins. Central 4-ram diam circular samples ware taken from each of the 71 stained spots and their protein contents were eluted as described in Materials and methods• Samples of each eluate containing 3000-5000 cpm 355 were mixed with aliquots of solutions or total 405 or 605 subunit proteins in elution buffer (30/zl, 1 tzg protein//xi) and proteins were recovered by acetone precipitation, dried briefly in a vacuum to remove acetone, redissolved in 20/xl of Laemmli sample buffer, and placed in sample wells of one-dimensional gels prepared according to Laemmli [5]. After electrophoresis, gels were stained, dried, and autoradiographed. The results of a series of such analyses are summarized in Fig. 1.

Resolved bands seen reproducibly in stained gels are designated by capital letters. Individual proteins identified in each band are numbered in the original [i] and revised numbering systems. Protein molecular weight estimates are taken from [1] except for those of the seven newly characterized proteins $3, S10, $29, L3, L20, L25, and L43, the molecular weights of which were estimated during the present study.

Prefixes S and L for small and large subunit proteins are omitted to simplify the figure. We note here that the 605 subunit protein numbered L43 in the revised nomenclature was numbered L41 in a recent publication [8], in which proteins released together with 55 rRNA by EDTA treatment of the 605 subunit of 7". thermophila were identified. These proteins numbered L4, L15, L24, L31, and L41 in [8] are, respectively, L5, L16, L27, L34, and L43 in the revised nomenclature. cysteine (methionine is the primary sulfur source for Tetrah~,mena which cannot metabolize inorganic sulfur). The results of a series of analyses of this kind, summarized in Fig. 1,showed: (1) that alI of the 72 previously characterized ribosomal proteins [1] except L39 are assignable to bands in the one-dimensional electrophoresis patterns of 40S and 60S subunit proteins; (2) that two bands, H and U (Fig. 1). in the 40S subunit protein pattern, and two, R and W (Fig. 1) in the 60S subunit protein pattern, do not contain any of these proteins.

On the basis of its known molecular weight [1], protein L39 could plausibly be assigned to 60S subueit band R and this conclusion was confirmed by one-dimensional electrophoretic comparison of nonradioactive protein L39 eluted from spot L39 taken from a heavily loaded Kaltschmidt and Wittmann seconddimension gel slab and total 60S subunit proteins (results not shown). Identification of the proteins present in 40S subunit bands H and U and 60S subunit band W was then undertaken. From the positions in the one-dimensional analysis in Fig. 1 and the known molecular weights of the 72 previously characterized ribosomal proteins [1], those of the proteins present in 40S subunit bands H and U and 60S subunit W can be estimated as 22 000, 11 000, and 15 000, respectively. Absence in two-dimensional electrophoretie analyses of spots corresponding to these proteins could be explained: (1) by loss of material during the extraction of proteins for twodimensional analyses; (2) by exceptionally high first-or second-dimensional electrophoretic mobilities leading to loss of these proteins under standard conditions of two-dimensional electrophoresis; (3) by retention of material in the sample zone of two-dimensional analyses.

The first explanation was eliminated by the presence of these three bands in normal amounts in one-dimensional electrophoretic analyses of acetic acid-extracted proteins, and the second by failure to observe additional high mobility spots in two-dimensional electrophoretic analyses carried out with first-and second-dimension migration times reduced to one-third of the standard values (results not shown). To test the third explanation, the electrophoretic properties of material eluted from 40S band H, and concentrated from the eluate by precipitation with trichloroacetic acid after addition of pancreatic RNase as carrier were examined.

As expected, the recovered material migrated as two bands in one-dimensional gels, one at the position of band H, the other at that expected for pancreatic RNase (Fig. 2, track B). Twodimensional electrophoresis of the same material was then carried out according to Kaltschmidt and Wittmann. Two Coomassie bluestained regions were observed after seconddimension electrophoresis, namely the firstdimension sample zone, and a spot at the position expected for pancreatic RNase (result not shown). To confirm that the material present in

A :? B C Q ~~ ~--H t RNase Fig. 2.
Eletrophoretic behavior of the protein present in 40S band H (Fig. 1). One-dimensional SDS-polyacrylamide gel electrophoresis was carried out as described by Laemmli [5]. A, Total 40S subunit proteins. B, Protein eluted from band H. Protein was eluted as described in Materials and methods from 40S band H removed from a heavily loaded one-dimensional gel similar to that shown in Fig. 1. After addition of pancreatic RNase (5/xg) as carrier, proteins were recovered from the eluate by acetone precipitation. One-third of the product was dissolved in Laemmli sample buffer and used to obtain the result shown in lane B.

C, Protein present in the sample gel after two-dimensional electrophoresis according to Kaltschmidt and Wittmann [6]. The remaining two-thirds of the material eluted from 40S band H was subjected to two-dimensional electrophoresis according to Kaltschmidt and Wittmann using urea-free first-dimension electrode buffer. The first-dimension sample zone was removed from the stained second-dimension gel slab and a 1 mm thick slice from its center was dialysed briefly against Laemmli sample buffer and then immersed in the same buffer in well C the first-dimension sample zone was the protein in band H, the stained sample zone was removed from the gel slab and placed in one sample well of a one-dimensional SDS-containing gel slab. After electrophoresis a single Coomassie bluestained band was seen at the position of band H (Fig. 2,track C).

These results show that the material eluted from band H possesses unaltered migration properties in one-dimensional SDS polyacrylamide gel electrophoresis, and migrates in neither dimension of two-dimensional electrophoresis according to Kaltschmidt and Wittmann.

Repetition of the preceding experiment using total 40S subunit proteins in place of the material extracted from band H gave similar results. The first-dimension sample zone recovered from the second-dimension gel slab was found to contain large amounts of material which migrated at the position of band H in a one-dimensional SDScontaining gel together with smaller amounts of components migrating at the positions of several other 40S proteins (results not shown). Further experiments were therefore carried out with total 40S subunit proteins.

Nonmigration of band H material in the first dimension of the Kaltschmidt and Wittmann procedure could be caused either by a pl value close or identical to that of the first-dimension electrode buffer (pH 8.6) or by low solubility under the conditions of first-dimension electrophoresis; nonmigration in the secon6 electrophoretic dimension could be readily accounted for only by low solubility.

Total 40S subunit proteins dissolve rapidly and apparently completely in the first-dimension sample buffer of Kaltschmidt and Wittmann which contains 8 M urea. However, according to the practice of other investigators [9][10][11][12][13], urea was routinely omitted from first-dimension electrode buffers which are in contact with firstdimension sample zones. Under such conditions diffusion of urea from the sample zones would be rapid and could lead to precipitation of proteins possessing low solubility in its absence. Urea (6 M) was therefore added to the firstdimension upper electrode buffer (in contact with the sample zone) in Kaltschmidt and Wittmann, and Zinker and Warner two-dimensional procedures as originally specified by these authors. In addition, the second-dimension upper electrode buffer of Kaitschmidt and Wittmann was modified by addition of 6 M urea.

The results of electrophoretic analyses of total 40S subunit proteins using urea-containing upper electrode buffers are shown in Fig. 3A,B. They differ in several respects from those obtained [1] with urea-free upper electrode buffers:

(1) Spot S1 observed previously in small amounts now appears as a relatively strongly stained spot, confirming its status as a ribosomal protein;

(2) An additional strongly stained spot with significant first-and second-dime,ision mobilities appears in the acidic side of two-dimensional separations ($3, Fig. 3A,B, revised numbering of 40S proteins). The spot is not seen if urea-free upper electrode buffers are used for both dimensions of electrophoresis according to Kaltschmidt and Wittmann (see Fig. 4A in [1]) or for he first dimension of electrophoresis according to Zinker and Warner (see Fig. 5A in [1]). It is also not seen if 6 M urea is added to the firstdimension but not to the second-dimension upper electrode buffer in the Kaltschmidt a~ld Wittmann procedure, but in this case a stained zone with the same first-dimension mobility as spot $3 in Fig. 3A remains in the first-dimensic, n gel (results not shown). To locate the migration position of protein $3 in the one-dimensional SDS gel electrophoresis migration pattern of 40S subunit proteins, spots containing proteins $3, $5, $7, and $8 (revised numbering of40S subunit proteins) were removed from a two-dimensional gel slab and their protein contents were eluted and examined by one-dimensional SDS gel electrophoresis, rrlg,,r,~ a ~h ...... ,h.,, protein ~ migrates in 40S subunit protein band D with protein $7. Its molecular weight is estimated to be 43 000.

(3) A tail of stained material ending in a distinct, more strongly stained region (Sill, Fig. 3A, revised numbering of 40S subunit proteins) appears in the Kaltschmidt and Wittmann second-dimension gel slab vertically below the first-dimension sample zone. This trail is not seen if second-dimension electrophoresis is carried out with urea-free upper electrode buffer (e.g., Fig. 4A in [1]). After two-dimensional electrophoresis according to Zinker and Warner using urea-free electrode buffers, a trail of stained material appears in the final gel slab vertically below the first-dimension sample zone (see Fig. 5A in [1]). A similar but less intense trail is seen when first-dimension upper electrode buffer contains 6 M urea (Fig. 3B). To identify the protein or proteins present in these trails, they were excised from two-dimensional gels prepared with upper electrode buffer containing 6 M urea and cut into sections as indicated in Fig. 3A these were subjected to electrophoresis in onedimensional SDS-containing gels with control total 40S subunit proteins. Figure 5 shows the results obtained with the stained central trail taken from a Kaltschmidt and Wittmann gel. All sections of the trail contained a major component migrating at the position of band H together with smaller amounts of other materials, and the concentration of the major component was greatest in the more strongly stained zone at the lower end of the trail.

A similar analysis (results not shown) of a stained trail taken from a Zinker and Warner gel revealed the presence, as expected, of band H protein at a position corresponding to its molecular weight and to traces of several larger and smaller 40S subunit proteins. We conclude that protein S10 (revised numbering) present in 40S H (Fig. 1A) has a pI of or close to 8.6, is insoluble in the absence of urea, and is poorly soluble and displays a tendency to aggregate even in the presence of high concentrations of urea. These properties cause its retention in the first-dimension sample zone of two-dimensional electrophoresis according to Kaltschmidt and Wittmann, unless urea is added to electrode buffers.

(4) A weakly stained spot previously seen nonreproducibly in two-dimensional separations of 40S subunit proteins (dotted outlines in the verticals through spots $4 and $29 at positions southwest of $21:3f Fig. 4B in [1], and north of $29 in Fig. 5B in [i], protein numOering as in [1]) appears reproducibly as a relatively strongly stained spot ($29 in Fig. 3A,B, revised numbering of 40S subunit proteins). The similarity of the electrophoretic mobilities of 40S band U in Fig. 1 and of spot $29 in Fig. 3B (second-dimension mobility) suggested that they contained the same Fig. 3. Two-dimensional electrophoretic analysis of total proteins of the 40S ribosomal subunits of T. thermophila according to Kaltschmidt and Wittmann [6] and Zinker and Warner [7]. Ribosomal proteins were prepared for analysis and two-dimensional electrophoresis was carried out as described in Materials and methods.

A, 40S subunit proteins separated by electrophoresis according to Kaltschmidt and Wittmann.

B, 40S subunit proteins separated by electrophoresis according to Zinker and Warner.

Bold numbers: Revised protein numbering. Light numbers: Original protein numbering [1]. The prefix S (small) is omitted to simplify the figure. Formation of double spots by proteins $4, $29, and $33 (revised numbering) in the Zinker and Warner two-dimensional procedure, which is evident in Fig. 7B, is frequently observed in the case of $29 but rarely in that of $4 and $33. None of these proteins forms a double spot in the Kaltschmidt and Wittmann two-dimensional procedure (Fig. 3A).

protein. This was confirmed by removing band U from a one-dimensional SDS-polyacrylamide gel in which [35S]methionine-labeled 40S subunit proteins had been separated, eluting its protein content, and examining the eluted material by two-dimensional electrophoresis according to Kaltschmidt and Wittmann. Figure 6 shows that the [35S]methionine-labeled material eluted from band U migrates with spot $29.

60S subunit proteins

Figure 7A, B shows the results obtained by two-dimensional electrophoresis of total 60S subunit proteins using urea-containing upper electrode buffers. Comparison with the results obtained previously (Fig. 4C, 5C in [1]) reveals three differences:

(1) The appearance of an additional weakly basic protein with low electrophoretic mobilities in both dimensions (L3, Fig. 7A,B, revised numbering of 60S subunit proteins). To identify this protein in the one-dimensional SDS polyacrylamide gel electrophoretic pattern of 60S subunit proteins, spots L3 and L5 (revised numbering) The stained trail below the first-dimension sample zone in the gel slab shown in Fig. 3A was removed in six sections as indicated. Protein was eluted from each section and concentrated by precipitation with trichioroacetic acid (Materials and methods) without addition of carrier proteins. The products were analyzed by one-dimensional SDS-polyacrylamide gel electrophoresis according to Laemmli [5].

a, b, e, d, e, f, Material eluted from sections a-f indicated in Fig. 3A. The position of 40S subunit protein band H is indicated.

were removed from a two-dimensional gel similar to that shown in Fig. 7A and their protein contents were eluted and examined by onedimensional SDS polyacrylamide gel electrophoresis. Figure 8 shows that protein L3 migrates in 60S band D already known to contain proteins L6 and L7 (revised numbering of 60S subunit proteins). Its molecular weight is therefore • --..32 31 ......33 Fig. 6. 40S subunit protein $29 (Fig. 3A,B, revised numbering) migrates in band U of the one-dimensional SDS-polyacrylamide gel electrophoresis pattern of 40S subunit proteins. Band U (Fig. 1) was removed from a one-dimensional SDS-polyacrylamide gel in which 35S-labeled 40S ribosomal subunit proteins (20/~g protein, sp. act. 105 cpm//zg) had been separated, and its protein content was eluted and recovered by precipitation with trichloroacetic acid after addition of 120/~g of total unlabeled 40S subunit proteins (Mate-rial~ and methods). The product was analyzed by two-dimens.ional electrophoresis according to Kaltschmidt and Wittmann ( [6] basic proteins only) and the gel slab was stained, dried, and autoradiographed. Fig. 6 shows the autoradiograph upon which the spot contours of stained 40S subunit proteins have been added. Protein numbering as in fig. 3A; prefix S omitted to simplify the figure .   approximately 40 000. It may be noted that no additional acidic spots and no ct...tral stained zones are visible in Figure 7A,B.

(2) Two weakly stained spots seen nonreproducibly in previous analyses of 60S proteins by the Zinker and Warner procedure (dotted outlines below spot L22, and above and to the left of spot L30 in Fig. 5D in [1], protein numbering as in [1]) appear as strongly stained spots, L25 ar:d L20 in Fig. 7B (revised protein numbering). Analysis of the same 60S subunit protein preparation by the Kaltschmidt and Wittmann procedure using 6 M urea-containing upper electrode buffers (Fig. 7A) does not reveal additional spots corresponding to L25 and L20 in Fig. 7B, suggesting that the materials present in these two spots comigrate with other 60S subunit proteins in this procedure. Spots with the same first-dimension mobility as spots L25 and L20 in Fig. 7B were therefore removed from a gel slab similar to that shown in Fig. 7A (spots numbered L14, L19 + L20, L24 + L25, and L29 in Fig. 7A, and L13, L18, L22, and L26 in our earlier report [1]) and their protein contents were examined by one-dimensional SDS polyacrylamide gel electrophoresis [5]. The results of this analysis showed that two of the excised spots each contained one extra protein in addition to those detected in earlier analyses (see above) of the same spots taken from gel slabs in which two-dimensional electrophoresis of total 60S subunit proteins was carried out with urea-free electrode buffers. These two spots are those designated L19 + L20 and L24 + L25 in Fig. 7A. The molecular weights of the additional proteins that they contain, i.e L25 in spot L24 + L25 and L20 in spot L19 + L20, estimated from their seconddimension migration in Fig. 7B are 21 500 and 17 500, respectively.

(3) Improved resolution of low molecular weight basic proteins in the Zinker and Warner procedure led to partial resolution of the spot previously numbered L36 (Fig. 5D, in [1]) into two spots. Reexamination of earlier results shows that evidence suggesting the binary nature of this spot was present in Fig. 5C of our previous report [1]. When proteins were eluted from the two partly resolved zones of this spot, (excised from a gel slab similar to that shown in Fig. 7B) and ree~tamined by electrophoresis according to Kaltschmidt and Wittmann, they were found to correspond to the species previously numbered L36 and L38 (Fig. 4C,D in [1]) now revised to L39 and L41 (Fig. 7A, this report). Since the spot numbered L36 in Fig. 5C in [1] contained two proteins identified as L36 and L38 (earlier nomenclature), it was necessary to establish the identity of the protein present in the spot numbered L38 in Fig. 5C in [1] and L43 in Fig. 7B of the present report. To do this, proteins were eluted from spots L42, L43, and L44 (revised nomenclature) taken from a gel slab similar to that shown in Fig. 7B and reexamined by electrophoresis according to Kaltschmidt and Wittmann (Figure 8).

Material eluted from spot L42 (Fig. 7B) migrated, as expected, with the front at the position previously numbered L39 (Fig. 4D in [1]); those eluted from spots L43 and L44 (Fig. 7B) also migrated at the front, both at the position previously numbered L40 (Figure 4D in [1]). It can be concluded that the spot previously numbered L40 in Kaltschmidt and Wittmann gels [1] contains two proteins which are well separated in the Zinker and Warner system (L43 and L44 in Fig. 7B). The second-dimension mobility of spot L43 in this system, very close to that of spot L40 (Fig. 7B) suggested that protein L43 was the species present in 60S band W of Fig. lB. This was verified by removing spot L43 from a Zinker and Warner gel, eluting its protein content, and comparing its mobility and that of total 60S subunit proteins by a one-dimensional SDS gel electrophoresis (Fig. 8D

B Conclusions

The present report increases the number of proteins in the cytoplasmic ribosome of 1_ thermophila from 72 to 79 and, we believe, completes the catalogue of these proteins. Inclusion of the additional proteins does not significantly modify 4 Fig. 7. Two-dimensional electrophoretic analysis of total proteins of the 60S ribosomal subunit of T. thermophila according to Kaltschmidt and Wittmann [6] and Zinker and Warner I71. Ribosomal proteins were prepared and twodimensional electrophoresis was carried out as described in Materials and methods. A, 60S subunit proteins scparated according to Kaltschmidt and Wittmann.

B, 60S subunit proteins separated according to Zinker and Warner.

Bold numbers: Revised protein numbering. Light numbers: Original protein numbering [1]. The prefix L (large subunit) is omitted to simplify the figure. It may be noted that protein L34 (revised protein numbering) forms double spots in both two-dimensional electrophoresis systems. The intensities of staining of the two components of this double spot vary widely when different preparations of 60S subunit proteins are analyzed and, in some cases, only a simple spot is seen. The stained spot containing protein L42, which does not appear in Fig. 7A, was weak but evident in the original stained gel slab. This protein appears as a relatively strongly stained spot in Fig. 7B. the overall composition of this ribosome or the average molecular weight of its proteins now estimated to be 23 200 (previously 23 100, [1]), and leaves unaltered our earlier conclusion [1] that the value of this parameter is closer to that found for cytoplasmic ribosomes of higher than of lower eukaryotic organisms.

The presence of a high molecular weight basic protein comparable in these respects to protein S1 of the Escherichia coli ribosome [14] has not been observed in studies of other eukaryotic ribosomes (rabbit reticulocytes, [15,16]; rat, rabbit, mouse, and chicken liver [15,[17][START_REF] Wool | Ribosomes: Structure, Function and Genetics[END_REF][START_REF] Madjar | [END_REF]; Bombyx mori [START_REF] Madjar | 1~81[END_REF]; Saccharomyces carlsbergensis [21], S. cerevisiae [22]; etc.).

Reproducible observation of 40S band A spot S1 in one-and two-dimensional analyses of a very large number of different preparations of ribosomes of T. thermophila, and a significant increase in the staining intensity of spot S1 when urea-containing electrode buffers are used in two-dimensional analyses, leave no doubt that the protein in spot S1 is a component of the small subunit of this ribosome.

Three of the seven additional proteins of the Tetrahymena ribosome, $3, S10, and L3, are not observed in the Kaltschmidt and Wittmann twodimensional gel electrophoresis procedure unless both first-and second-dimension electrode buffers in contact with protein samples and first-dimension gels contain a high concentration of urea. These proteins are also not observe J "n the pH 8.6-SDS t"ocedure of Zinker and war ner if urea is omitted from the first-dimensit a, upper electrode buffer, and :wo orb ~" additional proteins L20 and L30 do ,or ap[. ,,, repr~,ducibly in significant amounts under these cor.ditons.

These results emphasize the importance, particularly in the case of the initial characterization of ribosomal proteins, of using the urea-containing first-dimension electrode buffer originally specified by Kaltschmidt and Wittmann, and, in addition, of adding urea to their second-dimension plat-trnrlo h],~er We "'*~ .h,~, lOW ~_l..k:~:,..

LIIClL

:~UlUUillty of at least one protein of the large subunit of the E. coli ribosome (L20) has been observed in the first dimension of the Kaltschmidt and Wittmann procedure when urea-free electrode buffer is used [12,[START_REF] Kaltschmidt | Proc. Natl. Acad. Sci[END_REF]. Proteins were eluted from spots L3, L5, and L43 of a gel slab similar to that shown in Fig. 7A, concentrated from the eluates by precipitation with trichloroacetic acid without added carrier proteins, and analyzed by one-dimensional SDS-polyacrylamide gel electrophoresis according to Laemmli, [5].

A, Total 60S subunit proteins. B, C, D, Material eluted from spots L3, L5, and L43. Selected bands are identified on the left side of the figure.

Fig. 4 .

 4 Fig.4. Additional 40S subunit protein $3 (revised numbering) migrates in band D of the migration pattern of 40S subunit proteins obtained by one-dimensional SDS-polyacrylamide gels. Proteins were eluted as described in Materials and methods from spots $3, $5, and $7+$8 taken from a heavily loaded gel slab similar to that shown in Fig.3A(twodimensional separation according to Kaltschmidt and Wittmann; spots $7 and $8 are poorly resolved and were eluted together) and concentrated from the eluates by precipitation with trichloroacetic acid without added carrier proteins.A, Total 40S subunit proteins. B, Material eluted from spot $5. C, Material eluted from spots $7+$8. D, Material eluted from spot $3.

Fig. 5 .

 5 Fig. 5. One-dimensional SDS.-polyacrylamide gel electrophoresis of material eluted from the stained trail extending vertically below the first-dimension sample zone in twodimensional Kaltschmidt and Wittman analyses of total 40S subunit proteins.The stained trail below the first-dimension sample zone in the gel slab shown in Fig.3Awas removed in six sections as indicated. Protein was eluted from each section and concen-

Fig. 8 .

 8 Fig. 8. Additional 60S subunit proteins L3 and L43 (revised nomenclature) migrate in bands D and W, respectively, of the migration pattern obtained by separation of 60S subunit proteins in one-dimensional SDS polyacrylamide gels.Proteins were eluted from spots L3, L5, and L43 of a gel slab similar to that shown in Fig.7A, concentrated from the eluates by precipitation with trichloroacetic acid without added carrier proteins, and analyzed by one-dimensional SDS-polyacrylamide gel electrophoresis according to Laemmli,[5].A, Total 60S subunit proteins. B, C, D, Material eluted from spots L3, L5, and L43. Selected bands are identified on the left side of the figure.

Band 405 Protein Number Mr original revised ~kD) Ba nd 605 Protein Number Mr original revised (kD)

	1	71	2 4	5~ 56
			1	45
			5	45
			3	40
			6	41
	2 4 6	48 48 48	7 • 9 14	39 25 25
	7 3	43 40	8 13	25 24.5
	5 8 !1 10 9 14 13 12 21 22 15 16 18 20 26 31 24 28 30 17 27 23	40 40 24 22 21.5 21-5 19 20 18G 18 20 18 17.5 175 18 17 17 1~t5 176 17 16 15G	10 12 15 24 18 25 19 28 16 21 26 30 26' 20 23 29 33 31 35 36 311 39	22 22.5 22-5 22,5 21-5 21-5 20 21 19,5 17-$ 17-5 16 17.5 17-5 17-5 1~5 17-5 17-5 17 17 17.5 15
	33 19 25 29 34 32	!6 14 12 11 95 8,5	34 11 17 27 37 22	15.5 • 15 15 15"5 IS,,S . 14"5
			41	I S'5
			40	15
			43	15
			42	11.5
			44	10
				Exceptions were
			the spot containing 60S subunit proteins L26 and
			L26' (revised numbering) which yielded, as
			expected, two radioactive bands, and the spot
			containing 60S subunit protein L39 (revised
			numbering) which gave no radioactive spot, show-
			ing that it contained neither methionine nor

  ).

		43+44;40 ---		-,
	A	42,39 ~.	\	Q	"	'~\ ,
				o
	1: 1: 11 li
	31+26:28
	16
	21
	29

Acknowledgments

The work described here was supported by grants from the Centre National de la Recherche Scientifique and the Fondation Nationale pour la Recherche Mrdicale Fran~aise.


Josefa Bleu
email: josefa.bleu@gmail.com

Ivar Herfindal

Anne Loison

Anne M G Kwak

Mathieu Garel

Carole Toïgo

Thomas Rempfler

Flurin Filli

Bernt-Erik Saether

Age-specific survival and annual variation in survival of female chamois differ between populations

Keywords: age-specific survival, capture-mark-recapture, environmental variability, Rupicapra rupicapra, senescence

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INTRODUCTION

Demographic parameters of many long-lived species are strongly structured by age (e.g. [START_REF] Gaillard | Temporal variation in fitness components and population dynamics of large herbivores[END_REF]. This has important implications for population dynamics [START_REF] Benton | Complex population dynamics and complex causation: devils, details and demography[END_REF][START_REF] Saether | How life history influences population dynamics in fluctuating environments[END_REF]) through age-specific contribution to the population growth rate [START_REF] Coulson | Decomposing the variation in population growth into contributions from multiple demographic rates[END_REF]. Age-structure has been shown to influence how the population is affected by harvesting (e.g. [START_REF] Milner | Demographic side effects of selective hunting in ungulates and carnivores[END_REF]) and its response to environmental variation.

For example, the effects of weather on dynamics of wild soay sheep (Ovis aries) were different between populations of equal size but differing in age-and sex-structures [START_REF] Coulson | Age, sex, density, winter weather, and population crashes in soay sheep[END_REF]. The importance of age-structure in shaping the responses to environmental changes can be explained by age-specific sensitivity to environmental conditions among ageclasses, resulting in differences in the variation in survival among age-classes. Understanding these mechanisms is essential in order to predict how climate change will affect populations, particularly in populations experiencing rapid environmental changes [START_REF] Hansen | Climate, icing, and wild arctic reindeer: past relationships and future prospects[END_REF][START_REF] Engler | 21st century climate change threatens mountain flora unequally across Europe[END_REF].

In ungulates, prime-aged females have a high survival with low variance [START_REF] Gaillard | Temporal variation in fitness components and population dynamics of large herbivores[END_REF]. However, individuals belonging to age-classes with lower survival (young and senescent individuals) may be more sensitive to environmental variation with a corresponding higher temporal variation in survival suggesting high environmental stochasticity in these ageclasses. Accordingly, the age at which individuals are in the more vulnerable age classes (i.e. young or senescent stages) may affect how environmental variation affect population dynamics [START_REF] Pfister | Patterns of variance in stage-structured populations: evolutionary predictions and ecological implications[END_REF][START_REF] Saether | Avian life history variation and contribution of demographic traits to the population growth rate[END_REF][START_REF] Gaillard | Temporal variation in survival of mammals: a case of environmental canalization?[END_REF]. As the senescent stage normally is considerably longer than juvenile stage, and senescent individuals also contribute by reproduction, variation in the characteristics of senescence is of particular importance for population dynamics: we can expect that the later the onset of senescence (and hence the longer the prime-age stage) and/or the smaller the rate of senescence, the lower the impact of environmental variation on population dynamics. Senescence has been described in many wild animals from very diverse taxa [START_REF] Nussey | Senescence in natural populations of animals: widespread evidence and its implications for bio-gerontology[END_REF], but see also [START_REF] Jones | Diversity of ageing across the tree of life[END_REF].

A large part of the inter-specific variation in senescent rates can be explained by life history variation along a slow-fast continuum [START_REF] Jones | Senescence rates are determined by ranking on the fast-slow life-history continuum[END_REF]. However, variations at the intraspecific level also exist (see below). The evolutionary theories of senescence (antagonistic pleiotropy theory, disposable soma theory) rely on the fact that selection is weak at late ages and converge on the idea that there is a trade-off between early performance/somatic maintenance and late survival [START_REF] Kirkwood | Why do we age?[END_REF]. In accordance with these theories, it has been shown that early environmental conditions or investment in reproduction affected senescence both within populations [START_REF] Nussey | Environmental conditions in early life influence ageing rates in a wild population of red deer[END_REF][START_REF] Péron | Age at the onset of senescence in birds and mammals is predicted by early-life performance[END_REF]) and, in a handful of studies, between populations of the same species [START_REF] Austad | Retarded senescence in an insular population of Virginia opossums (Didelphis virginiana)[END_REF][START_REF] Bronikowski | The aging baboon: comparative demography in a non-human primate[END_REF][START_REF] Bryant | Comparative studies of senescence in natural populations of guppies[END_REF]. At the intra-specific level, studies comparing survival patterns and also age-specific variation in this vital rate between populations are rare. The difficulty is that such studies require long-term studies of marked individuals of known age in several wild populations of the same species, a requirement which is rarely met.

Based on long-term longitudinal datasets and capture-mark-recapture methods in three populations of the same species, we could estimate age-specific survival patterns and agespecific inter-annual variation in survival rates in females in three contrasted populations of an alpine ungulate, the chamois (Rupicapra rupicapra). We assessed the among-populations differences in (1) average survival rates per age-classes, and more specifically senescence patterns; (2) inter-annual variation in survival rates. This allowed us to examine at the intraspecific level, whether temporal variation in survival rates may be used as a proxy of the agespecific sensitivity to environmental stochasticity.

MATERIAL AND METHODS

We used longitudinal data from long-term monitoring of female chamois from three populations. Chamois were trapped annually, marked and then visually monitored. Age at capture was determined by counting horn annuli (Schröder and von Elsner-Schack 1985).

French study site

Chamois were monitored since the early 1980s in the Game and Wildlife Reserve of the Bauges massif (45°40'N 6°13'E), in the northern French Alps (e.g. [START_REF] Loison | New insight on survivorship of female chamois (Rupicapra rupicapra) from observation of marked animals[END_REF]. We studied the chamois from the Armenaz site (227.4 ha, Table S1), which has a continental climate with oceanic influence (weather station at 595 m: mean annual temperature = 9.22 ± 0.46°C, mean annual rainfall = 1361.8 ± 210.6 mm). The area is characterized by sub-alpine meadows (e.g., Carex sp. and Sesleria caerulae) with shrublands (e.g. Rhododendron ferrugineum and Vaccinium sp.), mountain hay meadows, and screes [START_REF] Duparc | Co-variation between plant above-ground biomass and phenology in sub-alpine grasslands[END_REF]. In this site, chamois have no natural predators and are not in sympatry with other wild ungulates [START_REF] Darmon | Do ecologically close species shift their daily activities when in sympatry? A test on chamois in the presence of mouflon[END_REF]. Chamois are trapped below falling nets baited with salt (May to September) and are marked with a collar. Between 1991 and 2012, 238 females, aged 1 to 12 years old, were captured (see detailed sample sizes in Table S2). The mean estimated probability of observation of an individual is 0.70 (SE=0.27) (estimates from model M4).

Individuals that died from non-natural causes (e.g. hunting) were right-censored to estimate natural survival probabilities [START_REF] Lebreton | Modeling survival and testing biological hypotheses using marked animals: a unified approach with case studies[END_REF]) (Table S2).

Swiss study sites

In the Swiss national park (SNP, 46°40'N 10°12'E), two populations of chamois are monitored, one in Val Trupchun (ca. 2 000 ha in the SNP and 4 000 ha in Italy) and one in Il Fuorn (ca. 5 025 ha in the SNP) (Filli and Suter 2006, Table S1). The SNP has a continental climate with low annual precipitation (weather station at 1800 m: mean annual temperature = 0.98 ± 0.48°C, mean annual rainfall = 882.5 mm ± 213.2 mm). Hunting is prohibited and visitors must stay on designated footpaths. Val Trupchun is dominated by screes, sub-alpine meadows (nutrient poor: Elyno-Seslerietea, nutrient rich: Poion alpinae grasslands), whereas Il Fuorn is dominated by screes, sub-alpine meadows (nutrient poor: Seslerio-Sempervirentum meadows and Carex firma-turfs) and mountain pine Pinus mugo. In both sites, predation is very rare but Golden eagle, Aquila chrysaetos, may attack kids. Interspecific competition may occur from red deer, Cervus elaphus, and ibex, Capra ibex (more pronounced in Val Trupchun). Chamois are captured all year round using box or sling traps and are marked with ear tags (Filli and Suter 2006). Between 1995 and 2012, 89 females were captured in Il Fuorn and 40 in Val

Trupchun. Age at capture ranged from 0 to 23 years old (see detailed sample sizes in Table S2). The mean estimated probability of observation of an individual is 0.58 (SE=0.39) (estimates from model M9). Some females were captured between January and April, but were considered as if they had been captured in the following May (and thus belonged to the following age class). The results were qualitatively similar if these individuals were considered as captured the preceding December (analyses not shown).

Statistical analyses

We kept the observations between May and December, in order to have similar periods between the sites and to estimate winter survival (the period of highest mortality for chamois ; [START_REF] Jonas | Mortality pattern of the Alpine chamois: the influence of snow-meteorological factors[END_REF]. We first analyzed the Bauges population and the SNP populations separately (pooling Il Fuorn and Val Trupchun). Survival estimates were obtained independently of re-sighting probabilities using capture-mark-recapture (CMR) modeling based on the open population model of Cormack-Jolly-Seber [START_REF] Clobert | A general approach to survival rate estimation by recaptures or resightings of marked birds[END_REF]. This model produces apparent survival estimates resulting from mortality and emigration. We used the program E-surge (version 1.9.0) to fit models [START_REF] Choquet | Program E-Surge: a software application for fitting multievent models[END_REF]. For all populations we found no transience in the data but a strong trap-happiness (details in ESM). The best model to account for trap-happiness was a two-state mixture model with transitions between the states (see details in Table S3). From this model, we selected the best model describing the effect of the year in re-sighting probabilities (Table S4). Finally, we fitted models on the survival probabilities. We compared models with different age class and/or with a continuous effect of age (see Table 1 for candidate models). The different models were built from typical age-classes already described in ungulates: juveniles, yearlings, prime-aged adults (2-7 years old), old adults (8-12 years old) and senescent individuals (after 12 years old) [START_REF] Gaillard | Temporal variation in fitness components and population dynamics of large herbivores[END_REF][START_REF] Gaillard | Assessing senescence patterns in populations of large mammals[END_REF]). We also tested models with a continuous effect of age as senescence can also be realistically described by a linear decrease of survival with age on a log scale (Gompertz models) (e.g. [START_REF] Loison | Age-specific survival in five populations of ungulates: evidence of senescence[END_REF][START_REF] Gaillard | Assessing senescence patterns in populations of large mammals[END_REF]). Models were implemented with a logit link, which has been shown to be a good approximation of the Gompertz model [START_REF] Loison | Age-specific survival in five populations of ungulates: evidence of senescence[END_REF]Viallefont 2011). In those models, the rate of senescence was the slope from the linear function between survival rates and age with a logistic link. For the SNP populations, we also tested the effect of site on the initial state, transition, re-sighting and survival probabilities.

In a next step, we examined differences between the Bauges and SNP populations by analyzing all the data together, using the best model structure selected in the separate analyses. Finally, we examined the variation of survival between years by allowing survival to vary among years and calculated the age-and population-specific standard deviation (SD) in survival from the annual survival rates. However, concern have been raised regarding the comparison of variances from estimates that are limited between 0 and 1 [START_REF] Morris | Buffering of life histories against environmental stochasticity: accounting for a spurious correlation between the variabilities of vital rates and their contributions to fitness[END_REF]. We therefore also calculated scaled variances, Pmax, following [START_REF] Morris | Buffering of life histories against environmental stochasticity: accounting for a spurious correlation between the variabilities of vital rates and their contributions to fitness[END_REF]. Results did not differ qualitatively between estimates of SD and Pmax (Table 3).

Model selection was based on AICc (Akaike Information Criterion corrected for small sample size ; [START_REF] Burnham | Model selection and multi-model inference: a practical information-theoretic approach[END_REF]. In the results we report the estimates of survival from the models (back-transformed from the logit scale) and the parametric 95% confidence interval (CI), unless otherwise noted.

RESULTS

The age-specific survival of the Bauges population was best described with a linear decrease of survival with age (logit-scale) from 1 years onwards (model M12 in Table 1, AICc = 1660.43, estimates in Table S5). Survival was relatively stable and high until 7 years of age, when a more pronounced decrease in survival occurred (Figure 1a). In the second best model (ΔAICc = 1.73), the linear decrease starts at 2 years old (model M14, Tables 1 andS5). The best model where age was grouped in classes included the following age-classes: 1-7, 8-12 and > 12 years old (ΔAICc = 9.28, model M4 in Tables 1 andS5, Figure 1a) and was consistent in term of pattern with the model with a linear trend. The estimates of a classic 4 age-classes model (model M5 in Table 1) are given in Table S5 (ΔAICc = 11.30).

In the SNP populations, two models had almost similar AICc-value and both supported a senescence starting after age 12. The best model with age grouped to classes had three age-classes: 0-1 years old, 2-12 years old and > 12 years old (model M9, AICc = 1030.97, Tables 1 andS5, Figure 1b). A model with equal support (ΔAICc = 0.08) had similar survival as the previous model for 0-1 and 2-12 years old, but a linear decrease in survival after age 12 (model M20 in Tables 1 andS5, Figure 1b). Model M5, the second best model with age-classes (ΔAICc = 1.94, Table 1), considered two distinct age-classes for prime-aged females (2-7 and 8-12 years old) (Table S5). All the highest ranked models grouped 0 and 1 years old females together, as supported from the similar survival estimates shown in Figure 1B (and model M6 in Table S5).

The two populations in the SNP were similar in terms of survival probabilities (Table S6 and Figure S1). Indeed, while the model with lowest AICc included an additive effect of site, suggesting overall higher survival in Il Fuorn, the ΔAICc with the model with no effect of site was only 1.21 (Table S6). We therefore pooled these two populations in further analyses.

We then examined further the differences in survival pattern and corresponding variation between the Bauges and SNP populations. As a base model, we used the four ageclasses model (model M5 in Table 1) which was the most parsimonious model when considering both study areas simultaneously. Age-specific survival differed between the SNP and Bauges populations (Table 2, ΔAICc to other models >= 3.88). The survival estimates from this model confirmed the differences observed on Figure 1 A and B: survival is lower in the Bauges population than in the SNP populations except for the first age-class (Figure 1c).

In adults, the difference is largest for the 8-12 years old females (Figure 1c).

Finally, we compared the annual variation in age-specific survival in each population by including temporal (i.e. annual) variation in the CMR models. We allowed survival to vary with year differently for each population and each age-class (Figures S2 andS3). Overall, survival is more variable in the Bauges population than in the SNP population (SD (Bauges) = 0.2638 vs. SD (SNP) = 0.2017), even if we account for the overall lower survival in the Bauges population (Pmax (Bauges) = 0.4238 vs. Pmax (SNP) = 0.3297). In both populations, the females from the age-class with the lowest survival (young and senescent females) showed also the highest variation of their survival (SD and Pmax, Table 3), with an effect more pronounced for old females in the Bauges and for young females in SNP. Conversely, the variation of survival of females with the highest survival (> 0.94: age-class 2-7 in Bauges and 2-7 and 8-12 in SNP) is low (SD < 0.093 and Pmax < 0.155).

DISCUSSION

Thanks to similar monitoring of individuals of known age for >16 years in 3 populations of the same species, we found evidence of clear differences in age at occurrence and rate of senescence at the intra-specific level, along with differences in age-specific annual variation in survival. In most large herbivores comparable to chamois the senescent stage is expected after approximately 7 years of age (Gaillard et al. 2003;[START_REF] Péron | Age at the onset of senescence in birds and mammals is predicted by early-life performance[END_REF].

Accordingly, the onset of senescence at 7 years old in the Bauges population is typical whereas the onset at 12 years old in the SNP populations is later than expected. Our evidence for inter-population differences in senescence supports the idea that senescence patterns are not fixed within species and can be influenced by, for instance, environmental conditions [START_REF] Loison | Age-specific survival in five populations of ungulates: evidence of senescence[END_REF][START_REF] Ricklefs | Comparison of aging-related mortality among birds and mammals[END_REF][START_REF] Lemaître | Comparing free-ranging and captive populations reveals intra-specific variation in aging rates in large herbivores[END_REF]. The difference in senescence between the Bauges population and the SNP populations could be caused by contrasting environmental conditions resulting in a faster life history strategy in the Bauges population compared to the SNP populations. A faster life history strategy could be selected by hunting (which is permitted in the Bauges but not in the SNP populations) (e.g. [START_REF] Hutchings | Measuring marine fish biodiversity: temporal changes in abundance, life history and demography[END_REF] or by harsher environmental conditions [START_REF] Promislow | Living fast and dying young: a comparative analysis of life-history variation among mammals[END_REF].

However, we have no evidence that climatic or general environmental conditions are harsher in the low-altitude population of the Bauges compared to SNP (Table S1). Future studies need to compare age at maturity and reproductive effort of females in each population to address the hypothesis that different survival rates and senescent patterns correspond to different life history strategies [START_REF] Nussey | Senescence in natural populations of animals: widespread evidence and its implications for bio-gerontology[END_REF].

Since age-specific survival patterns differed between the two study sites, we expected differences in annual variation in survival. This can occur because environmental variability (e.g. changes in weather conditions, habitat quality, population density) have a larger impact on individuals of lower quality, i.e. that have a lower survival (e.g. for climate effects, Willisch et al. 2013). Moreover, it has been suggested that in prime-aged female ungulates survival is partly buffered against environmental variations through an adjustment of the reproductive effort [START_REF] Gaillard | Temporal variation in fitness components and population dynamics of large herbivores[END_REF][START_REF] Gaillard | Temporal variation in survival of mammals: a case of environmental canalization?[END_REF]. In agreement with the interspecific comparisons of [START_REF] Gaillard | Temporal variation in survival of mammals: a case of environmental canalization?[END_REF], we supported, at the intra-specific level, that the lower the overall survival (in the Bauges vs the SNP population) during primeage, the higher annual variation in survival. This can again reflect a faster life-history strategy (Saether et al. 2004) and/or more variable environmental conditions in the Bauges. A shorter length of the prime-age stage and longer senescence stage in the Bauges population suggest that this population may be more vulnerable to environmental variation such as climate change, compared to the SNP population where females spend more years in a stage with high survival and low variation.

This study exemplifies that age, a factor already known to affect demographic rates, also relates to the variability in survival, and thus is an important factor to understand the sensitivity to environmental changes [START_REF] Pardo | Evidence for an age-dependent influence of environmental variations on a long-lived seabird's life-history traits[END_REF]. Further studies on differences in agespecific survival and variation in survival between populations of the same species could be important to understand population-specific impact of environmental changes (e.g. [START_REF] Grøtan | Effects of climate on population fluctuations of ibex[END_REF]. 1). Dotted lines are the estimates from the best linear models (models M12 and M20 in Table 1 in panels a and b respectively), and solid lines are estimates from the best age-class models (models M4 and M9 in Table 1 in panels a and b respectively). Panel c shows the estimates of a direct comparison between the two sites based on a model with 4 age-classes (Table 2). Juveniles (0 year old) are only in the SNP dataset.

Figure legends Figure 1 .

 legends1 Figure legends

ACKNOWLEDGEMENTS

We thank the Office National de la Chasse et de la Faune Sauvage (ONCFS), and in particular Jean-Michel Jullien and Thibaut Amblard, and the Swiss National Park for collecting and managing data with the help of many volunteers. This research was conducted on the Long-Term Ecosystem Research (LTER) site Zone Atelier Alpes, a member of the ILTER-Europe network. The study received support from the European Research Council (STOCHPOP research grant to B.-E.S.). SUMMARY STATEMENT Funding: European Research Council (STOCHPOP research grant to B.-E.S.)

Conflict of interest:

The authors declare that they have no conflict of interest Ethical statement: All applicable national guidelines for the care and use of animals were followed.


Van Cuong Nguyen

Gilney Damm

Modeling and Conditional Integrator Control of an Unmanned Aerial Vehicle for Airlaunch

A satellite launching procedure known as airlaunch is modeled and simulated at the staging phase, where a reusable unmanned aerial vehicle airlaunches a second (rocket) stage. This allows to study the effects of the split phase on the stability of the airlaunch system. A robust conditional integrator controller is designed with the objective of stabilizing the system during and after the airlaunch. The controller is indeed able to assure system stability for rather large disturbances. Performance of the proposed control algorithm is illustrated through simulations.

I. INTRODUCTION

Satellites launching is a strategical activity today. Launchers are able to carry from micro-satellites of some tens of kilograms up to 10 tons in the case of French Ariane 5 launcher. Recently new applications have called upon very small satellites, named nano-satellites, mostly used in groups (see [START_REF] Burlacu | An analysis of the nanosatellites launches between 2004 and[END_REF]). These nano-satellites need a new class of launchers since launching implies in many fixed costs that are independent of the size and weight of the launched device. For this reason, the ratio price-per-kilogram launched in space becomes too high. A quite logical solution in this case would be to pack many small devices to be launched together. Unfortunately this implies many additional risks in the split phase and is not envisaged. A more efficient solution in this case is to use the procedure of airlaunch (see [START_REF] Sarigul-Klijn | Selection of a carrier aircraft and a launch method for air launching space vehicles[END_REF], [START_REF] Gary | Quickreach responsive launch system[END_REF]). It consists of using a two stages launching system (see Fig. 1). The first stage is composed of an air vehicle (manned or unmanned) that carries (inside, beneath or above) a launcher which constitutes the second stage. There are many advantages in airlaunch, mainly because there is no need for specific large non populated launching areas. The aerial vehicle takes-off from a standard runway and fly to open ocean, avoiding Van Cuong Nguyen is with IBISC -Université d'Evry Val d'Essonne, Evry, France vancuong.nguyen@ibisc.fr Gilney Damm is with IBISC -Université d'Evry Val d'Essonne, Evry, France gilney.damm@ibisc.fr populated areas or ship and airplane paths. For this reason there is also a minimization of weather constraints, since the vehicle can fly to open sky, and as consequence the launch delay can be significantly shortened. Similarly, instead of waiting for specific launch windows (to attain desired orbits), the vehicle may be flown to a better suited launch point, with a better alignment with the desired orbit. The fact that the first stage is a reusable aerial vehicle allows a much smaller launching delay. In the same way, launching reuse time may be very short (one or two days). These characteristics provide great flexibility, and allow to deploy small satellites designed for specific tasks of communication or data gathering in real time for urgent situations.

Airlaunch provides the advantages of two stage launchers. The second (dropped) stage may use specific nozzles and propellants for the low outside atmospheric pressure at altitude (20 000 meters or 60000 feet). This is obtained without the complex, expensive and relatively dangerous high pressure ground-launched first stage that is replaced by the aerial vehicle. Most current airlaunch projects use standard or lightly modified airplanes as first stage. For example, there has been tests using F15, C17, B52, L-1011 in Rascal, QuickReach, Proteus, Pegasus projects.

It is important to remark that airplanes use the wing's lift force to fly. For this reason, higher (low altitude) air density benefit the flight while the aircraft uses standard fuel to keep flying. A first stage rocket would use a much more complex, dangerous and expensive fuel while in this higher air density. From a certain altitude, air density is too low to be useful for an airplane, while not representing anymore a drawback for rockets.

For all these reasons, French space agency, Center National d'Etudes Spatiales (CNES), started the project PERSEUS (Projet Etudiant de Recherche Spatiale Europen Universitaire et Scientifique), PERSEUS intends to use an unmanned aerial vehicle to fly the launcher to the desired drop point. There are many advantages in doing so, in first place safety since no human lives are involved during the delicate launching phase. In addition, since there is no need for life supporting devices, weight is restricted to the strict minimum. Finally, mission may take as long as necessary without human restrictions as tiredness.

That project aims in developing an airlaunch system that uses an Unmanned Aerial Vehicle (UAV) instead of a standard aircraft with a human pilot inboard. The current paper addresses its launching phase. It intends to introduce modeling and a robust controller for this delicate procedure. In fact, airlaunch may be very challenging since the rocket may be almost as heavy as the UAV. This means that the aircraft will instantaneously lose almost half of its mass. Current airlaunch systems present a much smaller ratio launcher/aircraft and rely on human pilot to stabilize the aircraft during and immediately after the launching instant. Unlike those systems, our airlaunch uses an UAV, and as consequence, the stabilization task is much more complex during and after the launching phase with a much more adverse mass ratio. In the best knowledge of authors, it does not exist an equivalent research line, and then there is no results in the literature considering this problem (modeling and control).

The paper is organized as follows: in section II, we describe the nonlinear mathematical system model, we illustrate some cases of non perfect separations during staging phase. A conditional integrator control design and its application to the full system model is discussed in section III. The paper is completed by computer simulations and conclusions. Modeling an air launch system and its separation phase is a difficult task which requires many data and informations about the real system. Since the UAV and launcher are yet not available, as well as its wind tunnel measurements, we have based our work on a F-16 aircraft (that already has been tested for manned airlaunch). We have also used it to verify in simulations the reactions of the system when modeling the air launch phase.

II. MODELING

There are some authors studying related topics. In [START_REF] Bandu | Simulation and analyses of staging maneuvers of next generation reusable launch vehicles[END_REF] and [START_REF] Naftel | Analysis of the staging maneuver and booster glideback guidance for a two-stage, winged, fully reusable launch vehicle[END_REF], it is studied the stage separation of a reusable booster from its down stage. The booster allows a stage separation at a high angle of attack and at supersonic speed. In this study, the aerodynamic inference effects are included. An aerodynamic separation of booster from the down stage vehicle is simulated by a private software SepSim.

In [START_REF] Bandu | Simulation and analyses of staging maneuvers of next generation reusable launch vehicles[END_REF] and [START_REF] Bandu | Simulation and analyses of stage separation of two-stage reusable launch vehicles[END_REF], a two stage reusable launch vehicle is studied at the stage separation by a new ConSep simulation tool. The ConSep tool is applied to simulation and analysis of stage maneuver of two stage to orbit Bimese reusable launch vehicle with aerodynamic database from the data of wind tunnel tests at the NASA Langley Research Center. In this simulation, the effects of variations in mass and inertia from their nominal values at staging are evaluated. The effects of the variations in mass and inertia on the aerodynamic coefficients of the launch vehicle are an important topic for study.

Unlike these authors, we suppose that the studied system is a set of a reusable launch vehicle and a down stage, whose mass is equivalent to half of the reusable launch vehicle's own mass. For the sake of simplicity, this set form a complete aircraft before air launching.

Depending on the position of the the down stage on the reusable airlaunch vehicle, the system will possibly changes its mass, inertia matrix, abscissa of center of the gravity and aerodynamic coefficients. For the following study, we take assumptions:

Assumption 2.1: The abscissa of center of the gravity of the down stage is identical to that of the reusable airlaunch vehicle. For this reason, there is no change in abscissa of center of the gravity after the airlaunch phase.

Assumption 2.2: The change in aerodynamic coefficients only affects drag and moments.

Airlaunch can be modeled as an hybrid system composed by two (or three) continuous models that are switched. These models represents the system before, (possible during) and after the separation phase. In the present work we have adopted this strategy, we have considered three phases, using two aircraft models.

1) before the separation → The first aircraft model (representing the UAV and the rocket) is in an stable operating condition 2) during the separation → a second aircraft model representing only the UAV, starting on the previous operating condition is disturbed by impulses on forces and moments. These disturbances are inside a time interval T int and represent a not perfect separation. Furthermore the initial conditions, inherited from the first phase, are not an equilibrium point for the second aircraft model. 3) after the separation → the disturbances stop (UAV and rocket are not in physical contact anymore). It can be shown that the effect of launching the rocket from the UAV impacts most the lift force, and the roll and pitch moments. We suppose that these perturbing force and moments are constant during interval T int , and we represent then F zp , L p and M p for the perturbations on the lift force, on the roll moment and pitch moment respectively.

In the present work we will study a worst case of disturbance. We consider that the separation phase is not simultaneous in all links that attach the rocket and the UAV. For this reason, the rocket remains attached to one end of the UAV during T int . We have then studied how long the disturbance could last and that the control algorithm could still stabilize the aircraft back.

We have then assumed that:

• the perturbation on lift force during T int is equal the rocket's mass (times gravity), that means F zp = mg.

• the perturbation on pitch moment during T int is M p = mgl r /2 where l r is the rocket length. • the perturbation on roll moment during T int is small, because of the geometry of the rocket (thin and long). • the model following the launch phase is that of an F-16. Its initial condition is the equilibrium point of the model previous the launch phase. This is taken as the F-16 model with twice the F-16's mass. The model of the dynamic airlaunch after the split phase is described by the Newton-Euler's law in the aerodynamic axes OX W Y W Z W in Fig. 2 (see [START_REF] Lee | Nonlinear adaptive flight control using backstepping and neural networks controller[END_REF], [START_REF] Sonneveldt | Nonlinear F-16 Model Description[END_REF], [START_REF] Peter | Modeling and Simulation of Aerospace Vehicle Dynamics[END_REF]) i.e. the reference frame attached to the airspeed vector (V ), because of the measurability of its state variables.

                                                               α = -cos α tan βp + q -sin α tan βr -sin α mV cos β (T + F x ) + cos α mV cos β F z + g V cos β [sin α cos θ + cos α cos φ cos θ] β = sin αp -cos αr -cos α sin β mV [T + F x ] + cos β mV F y -sin α sin β mV F z + g V [cos α sin β sin θ + cos β cos θ sin φ -sin α sin β cos φ cos θ] V = cos α cos β m [T + F x ] + sin β m F y + sin α cos β m F z + g[cos α cos β sin θ + sin β sin φ cos θ + sin α cos β cos φ cos θ] ṗ = 1 IxxIzz-I 2 xz [(I yy I zz -I 2 zz -I 2 xz )rq -I xz (I xx +I zz -I yy )pq + I zz L -I xz N ] q = 1 Iyy [(I zz -I xx )pr + I xz (p 2 -r 2 ) + M ] ṙ = 1 IxxIzz-I 2 xz [(-I xx I yy + I 2 zz + I 2 xz )pq +I xz (I xx + I zz -I yy )rq + I xx N -I xz L] φ = p + tan θ(q sin φ + r cos φ) θ = q cos φ -r sin φ ψ = q sin φ+r cos φ cos θ                                                                (1)
In (1), I xx , I yy , I zz , I xz are the moments of inertia, m is the mass of the system (kg) and g the gravity constant.u, v, w are translational velocities of the system in body fixed axes in m/s. α, β, V, p, q, r, φ, θ, ψ are the state variables of the airlaunch aircraft model, they are the angle of attack, sideslip, airspeed, roll rate, pitch rate, yaw rate, roll angle, pitch angle and yaw angle respectively. α, β, φ, θ, ψ are expressed in rad, p, q, r in rad/s and V in m/s. T is the thrust force, F x , F y , F z and L, M, N are aerodynamic forces and moments respectively. All forces and moments are expressed in N and Nm.

These aerodynamic forces and moments are function of all considered states. In this model, these aerodynamic forces and moments are under look-up table from wind tunnel data measurements as may be found in [START_REF] Nguyen | Simulator study of fighter airplane with relaxed longitudinal static stability[END_REF]. Finally, the control inputs are respectively the aileron (δ a ), rudder (δ r ) and elevator (δ e ) angles.

This model is based on wind tunnel data from NASA, considering the following conditions:

• angle of attack is in the range of [-10 • all actuators are modeled as a first order model (τ = 1/0.0495s) with limit rates 60 • /s for aileron and elevator, and 120 • /s for rudder.

In particular, we use the low quality mode of the F-16 model, and the aerodynamic data is interpolated and extrapolated linearly in simulation from tables found in [START_REF] Nguyen | Simulator study of fighter airplane with relaxed longitudinal static stability[END_REF].

The system was considered starting on an equilibrium point of the first model (V, h) = (154m/s, 6500m), that corresponds to the trimmed angle of attack α 0 = 12.5 • , pitch angle θ 0 = 12.5 • sideslip β 0 = 0 • , φ 0 = 0 • and to control surface states: aileron δ a = 0 • , elevator δ e = -4.0 • and rudder δ r = 0 • . At first, we take an interval of perturbation T int = 0.2s, a simulation of this model with fixed control signals can be seen in Fig. 3. There one can see that the angle of attack and the sideslip are stabilized after the impulsional disturbances on the aerodynamic force and moments. However, Fig. 4 shows that roll angle and pitch angle even if remaining bounded, are not asymptotic stable to their equilibrium at the origin. If we increase T int to 0.227s, the system will be completely unstable as shown in Fig. 5.

III. CONTROL DESIGN A. Conditional integrator control design

The MIMO conditional integrator controller design for the output regulation of a class of minimum-phase nonlinear systems in case of asymptotically constant references is studied in [START_REF] Hassan | On the design of robust servomechanisms for minimum phase nonlinear systems[END_REF], [START_REF] Seshagiri | Robust output feedback regulation of minimum-phase nonlinear systems usingconditional integrators[END_REF] and [START_REF] Seshagiri | Robust output regulation of minimum phase nonlinear systems using conditional servocompensators[END_REF]. These papers concern a servocompensator performing as a sliding mode controller outside the boundary layer, and performing as a conditional one that provides servo-compensation only inside the boundary layer. First results have studied the SISO case with a scalar sliding surface and the asymptotic stability of the system inside a boundary layer. These results were extended in [START_REF] Seshagiri | Robust output feedback regulation of minimum-phase nonlinear systems using conditional integrators[END_REF] and [START_REF] Attaullah | Output regulation of nonlinear systems using conditional servocompensators[END_REF] for linearized MIMO systems under some additional assumptions. Our present work is dedicated to use a nonlinear extension of these results developed in [START_REF] Damm | Mimo conditional integrator control for a class of nonlinear systems[END_REF], for stabilizing an unmanned aircraft after the airlaunch phase.

Consider the system:

ė1 = e 2 ė2 = f (e 1 , e 2 ) + g(e 1 , e 2 )u (2)
where e 1 (t) ∈ R n is an output error vector, e 2 = ė1 , u ∈ R n control input and f (e 1 , e 2 ) ∈ R n , g(e 1 , e 2 ) ∈ R n×n are continuous functions. Let us define the sliding surface as:

s = k 0 σ + K 1 e 1 + e 2 (3)
where σ ∈ R n is the output of the conditional servo-

compensator σ = -k 0 σ + µsat(s/µ) (4)
in which µ is the boundary layer, k 0 is a positive parameter,

K 1 ∈ R n×n is chosen such a way that K 1 + sI n is Hurwitz.
The saturation function is determined as:

sat(s/µ) = s/ s if s ≥ µ s/µ if s < µ (5)
We denote O µ as the region neighborhood of (e 1 , e 2 ) = (0, 0) with a radius R µ for s < µ

O µ = {e = (e 1 , e 2 ) ∈ R n × R n | e ≤ R µ } (6)
We state the following assumptions on the forcing terms f (e 1 , e 2 ) and g(e 1 , e 2 ) to design the control algorithm. optionally, ( 10) can be written as

g(e 1 , e 2 )g -1 (0) -I n f (0) ≤ υ(e 1 , e 2 ) ( 11
)
in which, υ(e 1 , e 2 ) is a suitable function satisfying

υ(e 1 , e 2 ) = υ 1 e 1 + υ 2 e 2 ≤ K υ ( 12
)
where υ 1 , υ 2 and K υ are suitable positive parameters. Following these conditions, the controller u defined below in ( 13) can be applied to (2) to stabilize the system. u = -Π(e 1 , e 2 )sat(s/µ) [START_REF] Sarigul-Klijn | Selection of a carrier aircraft and a launch method for air launching space vehicles[END_REF] in which,

Π(•) = Π 0 + (γ(•) + k 0 µ + F 0 )/λ (14)
Π 0 , k 0 are positive, µ is the boundary layer as defined above.

When designing this controller, it is important to pay attention that inside the boundary layer, i.e. s ≤ µ, Π(•) must satisfy the condition:

Π(•) -Π(0, 0) ≤ χ(•) = λχ 1 e 1 + λχ 2 e 2 (15)
where χ 1 , χ 2 are suitable positive constants and λ was defined earlier in [START_REF] Nguyen | Simulator study of fighter airplane with relaxed longitudinal static stability[END_REF]. The stability of the control law (13) for system (2) can be demonstrated following the results of [START_REF] Damm | Mimo conditional integrator control for a class of nonlinear systems[END_REF].

B. Longitudinal control design

In the longitudinal control design, we assume that all lateral state variables are null or constant, only longitudinal states are time varying. Moreover it is assumed that the airspeed's response is much slower than other states, and that the control surface deflection has no effects on the aerodynamic force components (lift and drag) but only on moments.

Aerodynamic forces F x , F z and moment M can be calculated by its aerodynamic coefficients (see more in [START_REF] Lee | Nonlinear adaptive flight control using backstepping and neural networks controller[END_REF]).

F x = (C x (α) + cC xq (α)q/(2V ))qS, F z = (C z (α, β) + cC zq (α)q/(2V ))qS, M = (C m (α) + C mq (α)qc/(2V ) +
C m δe (α)δ e )qSc . By replacing F x , F z , moment M and β = 0, φ = 0, p = 0, r = 0 in (1). The model for longitudinal dynamic can be written as: [START_REF] Seshagiri | Robust output regulation of minimum phase nonlinear systems using conditional servocompensators[END_REF] in which S is wing area, q air pressure, c equivalent width,

           α= 1 mV [-sin α(T + C x (α)qS) + cos αC z (α)qS] +q + ρS 4m (-sin αC xq (α)c + cos αC zq (α)c)q + g V cos (θ 0 -α) q =I 7 qS(C m (α)c + C mq (α)cq + C m δe (α)cδ e ) θ =q
I 7 = 1/I yy , C x (α), C xq (α), C z (α), C zq (α), C m (α), C mq (α) C m δe (α)
are aerodynamic coefficients taken from [START_REF] Morelli | Global nonlinear parametric modeling with application to f-16 aerodynamics[END_REF].

Equation ( 16) can be rearranged as:

we skip the proof, that is straightforward and based on a Lyapunov function. It can be shown to go to a residual set that can be attenuated by higher gain. The conclusions we can have are that all errors will be ultimately bounded, where the remaining signals stands for the disturbance on the aircraft speed. It is interesting to remark that variable θ was left free, in order to allow situations as a looping, where θ is continuously varying. Its derivative on the other hand is bounded, and also goes to a residual set (by equation 20).

Since the airspeed control is only a secondary objective, we design a simple PI controller for the thrust to regulate airspeed. Its form is:

T = -k P (V -V ref ) -k I ( V -Vref )
where V ref is the airspeed reference, k P = 1242 and k I = 955.

C. Lateral control design

As in the case of longitudinal control design, in the lateral case it is considered that only lateral state variables are time varying.

Aerodynamic force F y and moments L, N are calculated by their aerodynamic coefficients (see more in [START_REF] Lee | Nonlinear adaptive flight control using backstepping and neural networks controller[END_REF]).

F y = (C y (β) + (C yp (α)p + +C yr (α)r) b/(2V ))qS, L = (C l (β) + C lp (α, β)p b/(2V ) + C lr (α, β)r b/(2V ) + C l δa (α)δ a + C l δr (α)δ r )qS b, N = (C n (β) + C np (α, β)p b/(2V ) + C nr (α, β)r b/(2V ) + C n δa (α)δ a + C n δr (α)δ r )qS b.
By replacing F y , moments L, N and α = α 0 , θ = θ 0 in [START_REF] Burlacu | An analysis of the nanosatellites launches between 2004 and[END_REF]. The lateral nonlinear dynamic model used for the control design procedure is consequently reduced as below:

                                                 β= 1
mV (-cos(α 0 ) sin(β)(T + C x (α 0 )qS) + cos(β)C y (β)qS -sin(α 0 ) sin(β)C z (α 0 , β)qS) + sin(α 0 )p -cos(α 0 )r + ρS 4m (cos(β)C yp (α 0 ) bp + cos(β)C yr (α 0 ) br) + g V (cos(α 0 ) sin(β) sin(θ 0 ) + cos(β) cos(θ 0 ) sin(φ) -sin(α 0 ) sin(β) cos(φ)) φ=p + cos(φ) tan(θ 0 )r

ṗ =I 3 C l (α 0 , β)qS b + I 4 C n (α 0 , β)qS b + ρV S b 4 [(I 3 C lp (α 0 ) +I 4 C np (α 0 ))p + (I 3 C lr (α 0 ) + I 4 C nr (α 0 ))r] +qS[(I 3 C l δa (α 0 ) + I 4 C n δa (α 0 ))δ a + (I 3 C l δr (α 0 ) +I 4 C n δr (α 0 ))δ r ] ṙ =I 4 C l (α 0 , β)qS b + I 9 C n (α 0 , β)qS b + ρV S b 4 [(I 4 C lp (α 0 ) +I 9 C np (α 0 ))p + (I 4 C lr (α 0 ) + I 9 C nr (α 0 ))r] +qS[(I 4 C l δa (α 0 ) + I 9 C n δa (α 0 ))δ a + (I 4 C l δr (α 0 ) +I 9 C n δr (α 0 ))δ r ] (23) In which b is equivalent length, I 3 = Izz (IxxIzz-I 2 xz ) , I 4 = Ixz (IxxIzz-I 2 xz ) , I 9 = Ixx (IxxIzz-I 2 xz ) . C y (α, δ e ), C yp (α 0 ), C yr (α 0 ), C l (α 0 , β), C n (α 0 , β), C lp (α 0 ), C np (α 0 ), C lr (α 0 ), C nr (α 0 ), C l δa (α 0 ), C n δa (α 0 ), C l δr (α 0 ), C n δr (α 0
) are lateral aerodynamic coefficients taken from [START_REF] Morelli | Global nonlinear parametric modeling with application to f-16 aerodynamics[END_REF].

Equation ( 23) can be rearranged as: The second model is disturbed on its aerodynamic force and moments during an interval T int as in Section II.

       β φ =f β 11 (β, φ) + f β 12 (β, φ) p r ṗ ṙ =f β 21 (β, φ) + f β 22 (β, φ) p r + g β 2 (β, φ) δ a δ r (24)
We simulate three sets of time lengths. T int = 0.2s (corresponding to solid lines in Fig. 6 to Fig. 8) produces damped oscilations. In the case with T int = 0.227s, it was shown in Section II that the uncontrolled system become completely unstable. In this case the Conditional Integrator is able to stabilize the system as can be seen in the dashed lines in Fig. 6 to Fig. 8. When T int = 0.3s (corresponding to dash dotted lines in Fig. 6 to Fig. 8) one can see that the controller is still able to stabilize the system. Fig. 6 illustrates the convergence of the system output to the operating point of the aircraft at the end of 5s without static steady error for the three cases of T int = (0.2s, 0.227s, 0.3s). All system outputs are still under their physical limitation. In Fig. 7, it can be seen that the control variables are saturated by their physical limitations due to a high perturbation on aerodynamic forces and moments.

Finally we show in Fig. 9 and Fig. 10 that the system will be unstable even with the robust conditional integrator controller for an interval T int = 0.4s.

Collision Avoidance

Airlaunch problem does not only require stability of system's states, but also to avoid the possibility of collision between the aircraft and the rocket after the drop phase. Fig. 11 shows the altitude of the aircraft from 0 to 1s in the three previous cases of study T int = (0.2s, 0.227s, 0.3s). They are compared with the trajectory of the rocket that drop freely with the initial airspeed of the aircraft (the solid plot). It is important to remark that there is a small distance from the initial height of the rocket and the aircraft, representing the distance between the aircraft and the rocket. In the three cases (dotted plot, dashed plot and dash dotted plot), the altitude of the aircraft satisfies the specification that requires there is no collision between the aircraft and the rocket in the airlaunch phase.

V. CONCLUSION

We have introduced the modeling and simulation of an airlaunch system at the stage separation from the reusable airlaunch vehicle from the down stage. This work has studied the effects of the staging phase in the stability of the airlaunch system. Because our airlaunch system have a down stage mass close to the launch vehicle's one, the separation phase produces large changes in aerodynamic force and moment, as demonstrated in section II, which may turn the system unstable. These changes may, specially in the case of a non perfect separation phase, produce large impulses on forces and moments, making the system unstable. These impulses are considered to last a time interval, that is then evaluated in simulations.

To stabilize the airlaunch system after this stage separation phase, a conditional integrator control is considered. This controller is designed using an F-16 model representing the aircraft just after dropping the second stage, but disturbed by large impulses.

For a perturbation on aerodynamic forces and moments during an interval T int , the stability of the system after the drop stage may be assured for small time intervals. When T int becomes large, the system becomes unstable even with the proposed controller.

In future works other disturbances will be considered, as well as other control strategies for this particularly interesting and difficult problem. The objective being to perform flight tests in a near future.

Fig. 1 .

 1 Fig. 1. Airlauch system: EOLE in PERSEUS project

Fig. 2 .

 2 Fig. 2. Frames: Body fixed axes OX B Y B Z B , Stability axes OX S Y S Z S , Aerodynamic axes OX W Y W Z W

  , 45 • ] and sideslip of [-30 • , 30 • ] • flag deflection is ignored • physical constraints for aileron (|δ a | ≤ 21.5 • ), rudders (|δ e | ≤ 25 • ) and elevator (|δ r | ≤ 30 • )

Fig. 3 .

 3 Fig. 3. Angle of attack α, Sideslip β and Airspeed VWe will stabilize the second model following the launch phase to its equilibrium point (V, h) = (154m/s, 6500m), that means angle of attack α 0 to 2.7 • , sideslip β to 0 • , and roll angle φ to 0 • . At first, we take an interval of perturbation T int = 0.2s, a simulation of this model with fixed control signals can be seen in Fig.3. There one can see that the angle of attack and the sideslip are stabilized after the impulsional disturbances on the aerodynamic force and moments. However, Fig.4shows that roll angle and pitch angle even if remaining bounded, are not asymptotic stable to their equilibrium at the origin.

Fig. 4 .

 4 Fig. 4. Outputs stability: Angular Rates and Euler's Angles

Fig. 5 .

 5 Fig. 5. instability of Angle of attack, Sideslip and Airspeed

Assumption 3 . 1 : 9 )

 319 f (e 1 , e 2 ) is bounded by a function γ(e 1 , e 2 ) of class K function and a positive constant F 0 f (e 1 , e 2 ) ≤ γ(e 1 , e 2 ) + F 0 (7) for (e 1 , e 2 ) ∈ R n × R n and while the sliding surface does not enter the boundary layer, i.e. s ≥ µ. Inside the boundary layer, the function f (e 1 , e 2 ) is required to be Lipschitz for (e 1 , e 2 ) ∈ O µ , as a consequence f (e 1 , e 2 ) -f (0, 0) ≤ L 1 e 1 + L 2 e 2 (8) where L 1 and L 2 ∈ R + . Assumption 3.2: g(e 1 , e 2 ) satisfies two hypothesis: Hypothesis 1: for (e 1 , e 2 ) ∈ R n × R n g(e 1 , e 2 ) + g T (e 1 , e 2 ) ≥ 2λI n with λ > 0 (Hypothesis 2: for (e 1 , e 2 ) ∈ O µ , function g(e 1 , e 2 ) is Lipschitz and as a consequence g(e 1 , e 2 ) -g(0, 0) ≤ g(0, 0) υ(e 1 , e 2 ) (10)

Fig. 7 .

 7 Fig. 7. Control surface: Aileron, Elevator and Rudder Its initial condition is the final state of the first model (α = 12.5 • , β = 0 • and φ = 0 • ) as in Section II. Moreover, we add on its initial condition a small disturbance on system output. That means the initial condition of second model is (α 0 = 17.5 • , β 0 = 4 • and φ 0 = 10 • ) for all numerical simulations.The second model is disturbed on its aerodynamic force and moments during an interval T int as in Section II.We simulate three sets of time lengths. T int = 0.2s (corresponding to solid lines in Fig.6to Fig.8) produces damped oscilations. In the case with T int = 0.227s, it was shown in Section II that the uncontrolled system become completely unstable. In this case the Conditional Integrator is able to stabilize the system as can be seen in the dashed lines in Fig.6to Fig.8. When T int = 0.3s (corresponding to dash dotted lines in Fig.6to Fig.8) one can see that the controller is still able to stabilize the system. Fig.6illustrates the convergence of the system output to the operating point of the aircraft at the end of 5s without static steady error for the three cases of T int = (0.2s, 0.227s, 0.3s). All system outputs are still under their physical limitation.

Fig. 8 .

 8 Fig. 8. State variables: Angular rates of system

Fig. 9 .Fig. 10 .

 910 Fig. 9. Angle of attack, Sideslip Angle and Roll angle unstable

Fig. 11 .

 11 Fig. 11. Altitude of the aircraft

where f α 11 (α), f α 12 (α), f α 13 (α, θ), f α 21 (α), f α 22 (α) and g α 2 (α) represent the terms of ( 16) respectively.

Let us define x α 1 = α, x α 2 = ẋα 1 = α and u α = δ e , which allow us to rewrite [START_REF] Sonneveldt | Nonlinear F-16 Model Description[END_REF] into:

where

We define now the reference for the angle of attack α ref considered as constant in this study, and the error vector of angle of attack e α 1 = x α 1 -x α 1ref = α -α ref and the variable e α 2 = ėα 1 . Equation (18b) can be transformed into (20):

Here we remark that G α (x α 1 , x α 2 ) is invertible, and that

are Lipschitz for the entire domain of actuation of the system.

Applying the control algorithm presented in (13) for system (20) (in this case a nonlinear single input single output system) gives the controller:

where

1 and k α 0 are positive constants. The controller can be shown to assure the stability of angle of attack and its derivative. For the sake of brevity where

, and g β 2 (•) represent the terms of (23) respectively. Equation ( 24) is mainly used for controller design and stability analysis.

Let us define

T and u β = (δ a , δ r ) T , that allow us to rewrite equation (24) to:

where [START_REF] Sarigul-Klijn | Selection of a carrier aircraft and a launch method for air launching space vehicles[END_REF] for system (27) leads to the controller:

where λ β = min( G β (•) ) for β ∈ (-30 • , 30 • ), φ ∈ (-90 • , 90 • ). Π β 0 is a constant large enough, k β 0 is a positive parameter, µ β is the boundary layer and K β 1 is a positive definite matrix chosen such a way that K 1 + sI 2 is Hurwitz.

IV. SIMULATION RESULTS

In section III, the design methodology of the conditional integrator controller to stabilize the angle of attack, sideslip and roll angle is proposed when full knowledge of the aerodynamic characteristics is available. This section presents numerical simulation results for the controller to demonstrate the performance of the proposed conditional integrator control laws in the drop phase.

As mentioned in section II, we have considered the launch phase as disturbances on aerodynamic force and moments during a time interval T int , and that the model following the launch phase is that of an F-16. This model is used since it has already been applied for (manned) airlaunch, and because its nonlinear model, wind tunnel informations and data are widely known and used for control design. It is important to remark that the model used in the following simulations is even more complete than that used in the control design, for example it includes actuator dynamics and their limitations. As a consequence, simulations also illustrate some properties of robustness to unmodeled dynamics.

In the following simulations, we have simultaneously applied the SISO longitudinal controller for angle of attack, and the MIMO lateral one for the sideslip and roll angles in the full nonlinear F-16 aircraft model. We may note that the control inputs are limited by their physical limitations introduced in section II.

The control law in [START_REF] Seshagiri | Robust output feedback regulation of minimum-phase nonlinear systems using conditional integrators[END_REF] whose Π(•) can be written more simply as:

, γ 1 and γ 2 are positive constant.

Application of this control law to two motion modes presented in subsections (III-B) and (III-C) is done by determining the set of parameters Π i 0 , γ i 1 , γ i 2 , µ i , K i 1 and k i 0 with i = α, β corresponding to longitudinal mode and lateral mode respectively. We use the design parameters in the Table I for the longitudinal controller, and the design parameters in Table II for the lateral controller. In Table II, Π β 0 and k β 0 are defined in matrix form because of the difference in the dynamic property of two state variables sideslip and roll angle. This definition does not have any consequence on the stability of the system. We will stabilize the second model following the launch phase to its equilibrium point (V, h) = (154m/s, 6500m) corresponding to (angle of attack α r to 2.7 • , sideslip β r to 0 • , and roll angle φ r to 0 • ).