C L Martin

M Duclos

S Aguerre

P Mormede

G Chaouloff2

Corticotropic and serotonergic responses to acute stress with/without prïor exercise training in différent rat strains

Keywords: ACTH, corticosterone, exercise training, immobilization, Lewis rats, serotonin, SHR

The ability to cope with exercise training dépends both on environmental and genetic background; however, whether the genetic status may affect (i) the hormonal status of trained subjects and, (ii) its responses to a heterotypic stressor is unknown. Herein, we hâve used Spontaneously Hypertensive Rats (SHR) and Lewis rats, that differ with regard to their psychoneuroendocrine profiles, to study the influences of an 8-week training programme and/or a 1-h immobilization stress on plasma adrenocorticotropin (ACTH) and corticosterone levels. In addition, brain serotonin metabolism was also measured as an index of neurochemical reactivity to stress. The amplitude of immobilizationelicited increases in ACTH levels which differed with the rat strain (Lewis > SHR), was amplified by prior training; besides, training decreased the strain différence in basai corticosterone (SHR > Lewis) and affected corticosterone response to immobilization in a strain-dependent manner. Thus, immobilization, which increased corticosterone levels in sedentary Lewis but not in SHRs, did not reveal interstrain différences in trained rats. Taken with the observation of a stimulatory effect of training on adrenal weights in SHRs, but not in Lewis, it is concluded that the effects of training on the corticotropic axis dépend on the genetic profile of the individual. Lastly, training amplified the response of midbrain (but not striatum or hippocampus) serotonin metabolism to immobilization in a strain-independent manner although the levels of serotonin precursor, namely tryptophan, varied with training and immobilization in a strain-dependent manner. This study shows that some neuroendo crine and neurochemical effects of training undergo interindividual variability.

1990), metabolic (Henriksson étal. 1985), and hor monal adaptations [START_REF] Watanabe | The effect of chronic exercise on the pituitary-adrenocortical response in conscious rats[END_REF][START_REF] Duclos | Trained versus untrained men: différent immédiate post-exercise responses of pituitary adrenal axis. A preliminary study[END_REF]) so that there is a minimal homeostatic disruption in the exercising human or animal. Actually, studies in humans and animais hâve demonstrated that endurance capacity has a heritable component [START_REF] Hagberg | VO2 max is associated with ACE génotype in postmenopausal women[END_REF], Koch et al. 1998). In rats, [START_REF] Koch | Heritability of treadmill running endurance in rats[END_REF] hâve reported that 39% of the variation in running endur ance performance berween low and high performing Sprague-Dawley rats were determined by heritable factors. Confirming this, a récent study using 11 inbred rats strains reported a genetic influence on running capacity on a treadmill [START_REF] Barbato | Spectrum of aérobic endurance running performance in eleven inbred strains of tats[END_REF].

The hypothalamo-pituitary-adrenal (HPA) axis is both stimulated by muscle exercise and subjected to adaptation widi endurance training [START_REF] Luger | Acute hypothalamic-pituitary-adrenal responses to the stress of treadmill exercise[END_REF].

Again, genetic différences in HPA axis activity hâve been demonstrated in humans [START_REF] Petrides | Marked différences in functioning of the hypothalamic-pituitaryadrenal axis between groups of men[END_REF]. In rodents, among différent inbred rat strains, Lewis rats exhibit impaired corticotropin-releasing hormone (CRH), ACTH and corticosterone (CORT) responses to physical and emotional stressors whereas Fisher 344 rats are characterized by their exquisitely sensitive and potent HPA axis hormonal responsiveness to thèse stressors [START_REF] Sternberg | ^(30 neuroendocrine responses to stress in Lewis and Fisher rats[END_REF]. As far as the influence of genetic factors on HPA axis activity is concerned, the question of the relevance of the genetic background further achieved by submitting rats to an 1-h immobi lization stress. Animais were then screened for (i) their body weight, (ii) the activity of their HPA axis (evaluated by measuring adrenal weight, plasma ACTH and CORT) and (iii) their 5-HT synthesis/metabolism rates in the midbrain, the striatum and the hippocampus.

MATERIALS AND METHODS

Animais

Experiments were conducted with 32 maie SHRs and 32 maie Lewis rats (IFFA CREDO, Les Oncins, France). The animais, 3 weeks old on arrivai at our laboratory, were housed by strain 4/cage (with food and water ad libitum, except during the running sessions) in an animal quarter under constant température and a 12 h/12 h light-dark cycle (lights on at 07.00 hours).

Rats were left undisturbed for 1 week before the beginning of the experiments. The animais were weighed once a week (initial weight: Lewis: 171 + 7 g and SHRs: 135 ± 10 g, P < 0.01). This study was conducted in conformity with the French publication on animal expérimentation.

Expérimental design

The animais were randomly assigned to either a trained motor [START_REF] Chaouloff | Effects of conditioned running on plasma, liver and brain tryptophan and on brain 5-hydroxytryptamine metabolism of the rat[END_REF]. Rats ran 5 days week"1, 1 h day~. In order to minimize stress, treadmill train ing began by familiarizing the rats to the apparatus for 1 week (five sessions, 5-20 min at a speed of 15-18 m min"1), electrical foot shocks being initially delivered when the rats stepped down from the tread mill. Throughout the study, each rat ran in the same compartment. After this first adaptation week, treadmill speed was gradually increased from 18 to 25 m min"1 (slope at 0°) at the end of training, electrical foot shocks not being delivered anymore. The animais exercised in the morning (08.00-12.00 hours). Meanwhile, animais belonging to the untrained group were removed from their respective cages and gently placed in a novel cage.

Two days after the completion of thèse 8 weeks of training, each group (trained and untrained) was further divided into two groups. Animais were weighed, and then either underwent immobilization stress (first group), or remained in their home cage (second group: controls). This stress consisted in 1 h of immobilization in plastic restrainers [START_REF] Chaouloff | Effects of chlorisondamine and restraint on cortical [3H]ketaserm binding, 5-HT2A receptor-mediated head shakes, and behaviours in models of anxiety[END_REF]. Rats from the two groups were successively killed by décapitation in an adjacent room (09.00-12.00 hours). Trunk blood was collected in 10-mL polyethylene tubes containing Tryptophan (Trp), 5-HT and 5-hydroxyindoleacetic acid

(5-HIAA) analysis

Frozen midbrains, hippocampus and striati were homogenized by sonication in 0.4 N perchloric acid [START_REF] Chaouloff | Effects of conditioned running on plasma, liver and brain tryptophan and on brain 5-hydroxytryptamine metabolism of the rat[END_REF]. The resulting homogenate was centrifuged 10 min at 14000 X g. From the supernatant, 25 fxL were kept for the measurement of tissue Trp, 5-HT, and 5-HIAA concentrations by high perfor mance liquid chromatography (HPLC) coupled either to an electrochemical detector (650 mV: 5-HT and 5-HIAA) or to an ultraviolet detector (280 nm: Trp).

The mobile phase was a sodium phosphate buffer (50 nM, pH 3.3) containing 1-octanesulphonic acid (100 mgL"1) EDTA (150 mg L"1) and methanol (15%), as already described (Kulikov étal. 1997) When significant, analyses of variance were followed by post hoc individual comparisons (Newman-Keuls test). (/^60= 19.53, p< 0.001) (Table 1). However, post hoc analyses revealed that such a différence reached significance only in trained rats (P < 0.01). Beside, training per se resulted in a significant decrease of body weight in both strains {Fxfi0 = 13.74, P < 0.001).

RESULTS

Effects of training on body and adrenal weights

Absolute adrenal weights were heavier in SHRs than in Lewis rats (F159 = 17.78, P < 0.001) with this strain différence reaching significance only in trained rats (Table 1). When expressed as the ratio over body weights, the (relative) adrenal weight of SHRs was increased, compared with Lewis rats {F\,59 = 41.7, P < 0.001) both in untrained (P < 0.05) and trained conditions (P < 0.01). In addition, a strain X training interaction (Fl>59 = 4.18, P < 0.05) could be noted with a significant relative adrenal weight increase in 42 + 12 ng mL"1, P < 0.01). For trained control ani mais, the amplitude of the différence decreased, but remained significant (P < 0.05). In addition, immobili zation induced a significant increase in plasma CORT concentration (FU50 = 56.29, P < 0.001) (Fig. 2b).

However, post hoc analysis revealed no significant immobilization-induced plasma CORT increase in untrained SHRs compared with dieir trained counter parts, whereas in untrained Lewis rats, a marked immo bilization-induced CORT increase was noticed (+897%).

Lasdy, training was devoid of any effect per se.

The corticosterone/ACTH ratio is presented in With regard to 5-HT, the sole effect that was observed was a strain effect in the striatum (Ft 55 = 4.47, P < 0.05) where Lewis rats displayed slightly higher levels of the aminé than in SHRs (Table 2). Neither the strain nor the training affected central 5-HIAA levels; on the other hand, immobili zation was endowed with a stimulatory influence in midbrain (Fh55 -20.92, P < 0.01), hippocampus (Flj55 = 16.36,'P < 0.001) and striatum (Fli55 = 48.56, P < 0.001) (Table 2 and Fig. 3d). In midbrain, this stimulatory effect of immobilization was particularly évident in trained animais (Flj55 = 6.35, P < 0.05 for the training X immobilization interaction; Fig. 3d) whereas in the two other brain régions a strain Xtraining interaction could be noted (/*i ,55 = 6.40, P < 0.05; Fit55 -4.40, P < 0.05, in hippocampus and striatum, respectively). Thus, in the hippocampus of untrained rats, 5-HIAA levels tended to be higher in SHRs than in Lewis rats, an observation that did not extend to trained animais (Table 2). On the contrary, in striatum, 5-HIAA levels tended to be higher in untrained Lewis rats than in untrained SHRs whereas the converse was true for trained animais (Table 2). Results are expressed as mean + SE of eight rats. +P < 0.05 for the anova results. # P < 0.05 and ## P < 0.01 for the différences with SHRs;

*P < 0.05 and **P < 0.01 for the différences with the control rats.

DISCUSSION

Baseline différences between untrained SHRs and Lewis rats

Absolute adrenal weights of SHRs tended to be higher than in Lewis rats; taken with the observation that the former strain weighs less than the latter one (thus confirming previous observations: [START_REF] Ramos | A multiple-test study of anxiety-related behaviours in six inbred rat strains[END_REF][START_REF] Berton | Differential effects of social stress on central serotonergic activity and emotional reactivity in Lewis and spontaneously hypertensive rats[END_REF], this tendency reached significance when relative adrenal weights were considered. In tum, it suggests that adrenal stimulation by ACTH is increased in SHRs compared with Lewis rats. However, compared with the values previously reported in undisturbed SHRs and Lewis rats [START_REF] Berton | Differential effects of social stress on central serotonergic activity and emotional reactivity in Lewis and spontaneously hypertensive rats[END_REF], SHR displayed a 12-fold and Lewis a 2-fold increase in plasma CORT. Basai values of plasma CORT in untrained control Lewis were within the values observed in a context of social stress in this strain but remained 5-fold above in SHRs [START_REF] Berton | Differential effects of social stress on central serotonergic activity and emotional reactivity in Lewis and spontaneously hypertensive rats[END_REF].

Thèse results suggest that under our expérimental conditions, untrained rats were significantly stressed.

This may be caused by the daily exposure to a novel environment as controls of each strain were gently handled and moved into a novel cage. Such a paradigm was used to obtain appropriate controls to the exercising rats, e.g. change in environment without exercise. Our study, using SHRs and Lewis rats, extends prior évidence for SHRs being more reactive than normotensive rats, e.g. Wistar-Kyoto and Sprague-Dawley rats, to a variety of stressful stimuli, including in their behavioural and HPA axis responses [START_REF] Mcmurtry | Corticosterone, brain mineralocorticoid receptors (MRs) and the activity of the hypothalamic-pituitaryadrenal (HPA) axis: the Lewis rat as an example of increased central MR capacity and hyporesponsive HPA axis[END_REF], Kràuchi étal. 1983[START_REF] Gentsch | Open field and elevated plus-maze: a behavioural comparison between spontaneously hypertensive (SHR) and Wistar-Kyoto (WKY) rats and the effects of chlordiazepoxide[END_REF][START_REF] Sôderpalm | The SHRexhibitless 'Anxiety' butincreased sensitivity to the anticonflict effect of donidine compared to normotensive controls[END_REF]. For example, our data in Lewis rats are in agreement with previous reports demonstrating a hyporesponsiveness of Lewis HPA axis to a wide range of acute (Glowa étal. 1992, Dhabhar étal. 1993, Chaouloff étal. 1995) and chronic stress situations [START_REF] Gomez | Glucocorticoid négative feedback on the HPA axis in five inbred rat strains[END_REF].

Previous reports hâve indicated that Trp levels were higher in the midbrain of SHRs, compared with those of Lewis rats [START_REF] Chaouloff | Effects of food deprivation on midbrain 5-HTja autoreceptors in Lewis and SHR rats[END_REF][START_REF] Berton | Differential effects of social stress on central serotonergic activity and emotional reactivity in Lewis and spontaneously hypertensive rats[END_REF]).

In the présent study, such a différence was confirmed and extended from midbrain serotonergic cell bodies to striatal and hippocampal serotonergic nerve terminais.

Interestingly, the genetic différence in brain Trp availability was associated with a strain-dependent différ ence in circulating Trp levels. Whether the latter différence underlies the former one is a possibility that merits considération. However, because brain Trp availability may dépend on other variables (e.g. bloodbrain barrier permeability, blood neutral amino acids, blood free Trp: see [START_REF] Chaouloff | Physiopharmacological interactions between stress hormones and central serotonergic Systems[END_REF]) it is prématuré to draw any conclusion as to the mechanisms underlying the strain-dependent différence in brain Trp levels.

Except for a strain effect on striatal 5-HT levels, neither 5-HT nor 5-HIAA were found to differ between SHRs and Lewis rats, a finding that fits with our observation of a lack of strain différences in midbrain and hippocampus 5-HT turnover, as assessed by the measurement of 5-hydroxytryptophan accumu lation in NSD-1015-pretreated rats [START_REF] Kulikov | Central serotonergic Systems in the SHR and LEW rat strains that differ in the elevated plusmaze test of anxiety[END_REF]. [START_REF] Walker | Abnormal glucocorticoid activity in subjects with risk factors for cardiovascular disease[END_REF]. Moreover, it has been demonstrated that adrenalectomy prevents the development of hypertension in SHRs [START_REF] Hashimoto | Abnormalities in the hypothalamo-pituitary-adrenal axis in spontaneously hypertensive rats during development of hypertension[END_REF]. Corticosterone replacement restored hyperten sion, which suggests that CORT is essential for the development of hypertension in SHRs. However, the former authors [START_REF] Hashimoto | Abnormalities in the hypothalamo-pituitary-adrenal axis in spontaneously hypertensive rats during development of hypertension[END_REF] ing the existence of ACTH-independent mechanisms [START_REF] Holzwarth | The rôle of adrenal nerves in the régulation of adrenocortical fonctions[END_REF].

Effects of chronic exercise or acute stress in

It has been reported that treadmill endurance training may affect central 5-HT levels [START_REF] Brown | Chronic response of rat brain norepinephrine and serotonin levels to endurance training[END_REF]). In addition, a 7-week wheel running exercise was found to elicit region-dependent decreases in 5-HT turnover (Hoffmann étal. 1994). However, in our hands, 8 weeks of training on a treadmill were found to be ineffective on central Trp, 5-HT and 5-HIAA levels in Wistar rats [START_REF] Chaouloff | Brain serotonin response to exercise in the rat: the influence of training duration[END_REF]. The présent study confirms such a lack of effect of endurance training. On the other hand, central 5-HT synthesis and metabolism hâve been re ported to be stimulated by acute immobilization (for a review [START_REF] Chaouloff | Physiopharmacological interactions between stress hormones and central serotonergic Systems[END_REF]. This was also true herein as immobilization increased Trp and 5-HIAA in ail brain régions (albeit with différent intensities) of SHRs and Lewis rats, a change that was associated with a decrease in blood Trp levels. The latter observation, which is in line with past data, is noteworthy as stress-induced decreases in blood Trp levels may reflect sympathetic hyperactivity [START_REF] Chaouloff | Physiopharmacological interactions between stress hormones and central serotonergic Systems[END_REF]. Then, the observation that both strains displayed to similar extents such a stress-elicited decrease in blood Trp levels indicate that the aforementioned strain-dependent sensitivity of the HPA axis may be unique. Interestingly, immobilization-induced increases in brain Trp levels, and which are accounted for by an increase in blood-brain barrier permeability [START_REF] Chaouloff | Physiopharmacological interactions between stress hormones and central serotonergic Systems[END_REF] were greater in SHRs, compared with Lewis rats.

Whether such a genetic différence lies on différences in blood-brain permeability [START_REF] Werber | Hypertension and cérébral arteries: relationship to disruption of the blood-brain barrier[END_REF]) remains however, to be shown.

Effects of endurance training on the responses to acute stress in SHRs and Lewis rats

In Lewis rats, exercise training increased the effect of 1-h immobilization on plasma ACTH concentrations without further increasing plasma CORT levels.

Previous studies hâve emphasized the influence of an heterotypic stress in chronically stressed rats [START_REF] Watanabe | The effect of chronic exercise on the pituitary-adrenocortical response in conscious rats[END_REF][START_REF] Watanabe | Running training atténuâtes the ACTH responses in rats to swimming and cage-switch stress[END_REF], demonstrating that the sécrétion of CORT by adrenal cells could be augmented if the adrenal had been previously primed by ACTH (such as that elicited by prior chronic stress). The absence of any increase in CORT levels although ACTH stimulation increased lends further support to the above-mentioned hypothesis according to which Lewis rats display a decreased adrenocortical sensitivity to ACTH.

  Correspondance: C. Martin, Laboratoire de Physiologie de l'Exercice Musculaire et du Sport, Université Bordeaux II, Zone Nord, Bat 2A, RdC, in the capacity to produce adaptations with chronic physical training may arise. Using treadmill exercise 5 days a week for 6-12 weeks, protocols of endurance training hâve emerged in rats (Armstrong et al. 1983). Unfortunately, ail thèse endurance training programmes hâve been conducted with standard rat strains (Wistar, Sprague-Dawley). Another paradigm to define the factors that may modulate the physiological impact of exercise training is to take advantage of rat strains differing genetically in their pattern of neuroendocrine responses to différent stressors. Moreover, as it may appear difficult to ascertain if training-induced differentiation in neuroendocrine responses would hâve emerged on the basis of a standard endocrine screening, another approach is to examine the effect of exercise training on the HPA axis response elicited by a further acute heterotypic stress. Data on the putative influence of the genetic factors on neuroendocrine responses to acute stress following endurance training are however, presently lacking. In keeping with the aforementioned effect of the genetic background on endurance capacity and HPA axis responses to différent stressors, we hâve analysed the neuroendocrine responses to acute stress (immobilization) following 8 weeks of exercise training in two différent rat strains, namely the Spontaneously Hypertensive Rat (SHR) strain and the Lewis rat strain. The SHRs and Lewis rats were selected on the basis of their respective corticotropic responses to stressors that differ in intensity and type. Following a forced swimming stress (Armario étal. 1995), SHR and Lewis strains display, respectively, the highest stress-induced hyperglycaemia, and the lowest ACTH and CORT responses to this stress. Moreover, using chronic immobilization stress, Gomez et al. (1996) observed interstrain différences in ACTH and CORT levels, with a CORT hyporesponsiveness of Lewis rats to chronic immobilization. Finally, both endurance training and acute immobil ization affect différent Systems of central neurotransmitters. Among thèse neurotransmitters, serotonin (5-hydroxytryptamine, 5-HT) seems sensitive to both types of stress (Chaouloff 1993). Actually, stressinduced changes in 5-HT synthesis/metabolism relate to peripheral and central mechanisms (see below), thus indicating the usefulness of 5-HT synthesis/metabo lism assessments as indices of the individual's sensitivity to stress. The objective of the présent study was thus to détermine how the neuroendocrine effects of chronic exercise are affected by the genetic status of the ani mais. For this purpose, SHR and Lewis rats were submitted to an 8-week treadmill exercise protocol to induce an exercise training effect. At the end of this exercise training programme, an acute stress was

(

  Lewis: «=16, SHRs: «=16) or untrained (Lewis: n = 16, SHRs: « = 16) group. The trained group underwent 8 weeks of exercise training, which was performed on a horizontal treadmill, containing four running compartments, and driven by an electrical

  . For plasma Trp analysis, samples were mixed with 0.4 N perchloric acid, centrifuged, and 25 ^L of the super natant injected into the HPLC System. Trp was then measured as described above. Statistics Data are presented as mean ± SE. Body weight évolution was analysed by means of a two-way analysis of variance (anova) with repeated measures. Absolute body weights and adrenal weights were analysed by means of two-way ANOVAs with strain (two levels) and training (two levels) as between-subject factors. Ail other data were analysed by means of a three-way anova with strain (two levels), training (two levels) and immobilization (two levels) as between-subject factors.

Figure 1

 1 Figure 1 Body weight of untrained and trained Spontaneously Hypertensive Rats (SHR) and Lewis rats (LEW). Results are expressed as mean ± SE of 16 rats. *P < 0.05, **P < 0.01 for the différences between untrained and trained SHRs; #P < 0.05 for the différences between untrained and trained Lewis rats.

Figure 1

 1 Figure 1 shows tdme-dependent influence of training on the respective body weights of SHRs and Lewis rats. Compared with their untrained counterparts, trained Lewis rats did not show any body weight effect of training excepted during the last week of the experiment, when untrained Lewis weighed significantly more than their trained counterparts (P < 0.05). By contrast, trained SHRs had significantly lower body weights than untrained SHRs from the third week of training (P < 0.05). This différence grew up until the end of the experiment so that untrained SHRs were 11% heavier than trained SHRs whereas in Lewis rats that différence reached only 4%. At the end of the experiment (on the day of the sacrifice), untrained and trained Lewis displayed heavier mean body weights compared with their respective untrained and trained SHRs counterparts

  (/*i_51 = 5.02, P < 0.05) interactions could be noted.Thus, trained immobilized Lewis showed higher ACTH plasma concentration compared with their respective SHR counterparts whereas only trained immobilized Lewis showed higher ACTH concentration compared with their untrained counterparts (P < 0.01). With regard to the training X immobilization interaction, trained rats displayed a greater immobilization-induced increase in ACTH levels, compared with untrained rats.As Fig.2(b)shows, the anova revealed a strain effect (F1>50 = 11.30, P < 0.005) on basai CORT levels with untrained control SHRs showing higher plasma CORT values than their Lewis counterparts (300 + 40 vs.

Fig. 2 Figure 2 Figure 3

 223 Fig.2(c). The SHR strain displayed a significantly higher adrenal sensitivity to ACTH, compared with the Lewis strain (/*i,4g = 16.66, P < 0.001), with exercise training bearing no effect. When immobilized, both SHRs and Lewis rats showed decreased adrenal sensi tivity (Fli49 = 20.58, P < 0.001); however, post hoc analyses revealed a significant decrease between control and immobilized SHRs, whereas Lewis rats did not.

  the differential response between both strains of rats was the effect of chronic exercise on their weight évolution. As early as the third week of exercise training and thereon, SHRs displayed significantly less weight gain than their Lewis counterparts. Actually, the effect of exercise training on weight balance is controversial. Some studies hâve shown that exercise training such as treadmill running leads to hypophagia, and in turn weight loss[START_REF] Rivest | Hypothalamic paraventricular nucleus lésions do not prevent anorectic effect of exercise in maie rats[END_REF]. Others, however, hâve found no exercise effect on body mass using s^milar(Overton et al. 1991[START_REF] Watanabe | Running training atténuâtes the ACTH responses in rats to swimming and cage-switch stress[END_REF] or more intense exercise programmes (60 min at 30 m mkr1 for 6 consécutive weeks; White-Welkley étal. 1995). The observation of a precocious and important exercise-induced weight loss in SHRs strengthens the hypothesis that the two strains are differentially affected by exercise training. The precocious weight loss in SHRs may suggest that the exercise training was more intensive in SHRs compared with Lewis rats. We used a standard paradigm of exercise training that has been previously shown to elicit 50-60% of the Sprague-Dawley rat's T/b2max (Bedford et al. 1979). However, in that study which compared five inbred rats, Bedford et al. hâve demonstrated an interstrain Vo-i^^différ ence with a decreased Voïm!l^in SHRs, compared with Sprague-Dawley rats, thereby suggesting that in our study SHRs may hâve been overtrained compared with Lewis rats. Alternatively, SHRs hâve been shown to run long distances in another exercise paradigm, e.g. spontaneous wheel running (Hoffmann et al. 1990, Jonsdottir étal. 1998) indicating that SHRs display significant endurance capacities. Moreover, (i) using more intense exercise programmes than ours, White-Welkley et al. (1995) hâve not found any effect on body weight on female Sprague-Dawley rats and (ii) increases in basai CORT values hâve been reported in over trained subjects, e.g. an observation that differs from ours where a significant decrease in plasma CORT values after 8 weeks of exercise training was observed in SHRs compared with Lewis rats (see below). With regard to Lewis rats, the possibility that this strain resists to some physiological conséquences of training (e.g. corticotropic ones: see below) must be advanced. It is noteworthy that Lewis rats underwent a training protocol that did not differ from that of SHRs, thereby excluding différences in the distances covered during the training programme as a source of the aforementioned interstrain variability. However, to explore the intrinsic effects of training in Lewis rats, compared with SHRs, experiments devoted to the analysis of muscular oxidative enzyme activities in sedentary and trained SHRs and Lewis rats are already in progress in our laboratory.The activity of the HPA axis was also differentially affected by exercise training. Forty-eight hours after the end of the exercise training program, a 40% decrease in basai plasma CORT was noticed in the SHR strain compared with untrained rats (albeit without statistical significance), whereas a significant basai plasma CORT increase was observed in the Lewis strain. This discrepancy concerning the effects of chronic exercise on HPA activity (i) between both strains and (ii) within the same strain compared with the effect of environmental

  An overview of midbrain, striatum and hippocam pus Trp levels suggests that the amplitude of immobilization-elicited increases in Trp levels was decreased by training in SHRs but increased by training in Lewis rats, this being especially true in the midbrain and the hip pocampus. Thus, with regard to brain Trp availability, training amplified (Lewis rats) or diminished (SHRs) the stimulatory effect of immobilization stress. This could not be accounted for by changes in blood Trp levels as in Lewis rats, immobilization-elicited réduction in blood Trp was slightly diminished in trained rats, compared with untrained rats. Clearly, some additional factors, e.g. other than blood Trp, played a key rôle in the aforementioned genetic variability in brain Trp availability during immobilization. With regard to the effects of training on immobilization-elicited increases in tissue 5-HIAA levels (which arise from parallel changes in tissue Trp levels, and possibly Trp hydroxylase hyperactivity: Chaouloff 1993), the picture was far from being clear. In midbrain, training amplified the stimulatory effect of immobilization in both strains, Trp hydroxylase activity) took place so that the genetic différences in Trp availability were masked. In the hippocampus, besides the overall stim ulatory effect of immobilization in 5-HIAA levels, it could be observed that training amplified (Lewis) or diminished (SHRs) the amplitude of the latter stimula tion; in the striatum, however, such a strain-dependent profile was not observed. Whether thèse régional différences reflect spécifie effects of immobilization and training with regard to the dorsal raphe nucleus (where striatal serotonergic nerves corne from) as opposed to the médian raphe nucleus (where a majority of hippocampal serotonergic nerves corne from) is unknown. REFERENCES Armario, A., Gavalda, A. & Marri, J. 1995. Comparison of the behavioural and endocrine response to forcéd swimming stress in five inbred strains of rats. Psychoneuroendocrinology 20, 879-890. Armstrong, R.B., Laughlin, M.H., Rome, L. & Taylor, C.R. 1983. Metabolism of rats running up and down an incline. / Appl Physiol 55, 518-521.

Table 2

 2 Effects of an 8-week treadmill training and/or 1 h of immobilization stress (Imm) on the concentrations (nmol g ) of tryptophan 5-hydroxytryptamine (5-HT) and 5-hydroxyindoleacetic acid (5-HIAA) in the hippocampus and striatum of SHRs and Lewis rats

		Hippocampus			Striatum
	Group	Trp	5-HT	5-HIAA	Trp	5-HT	5-HIAA
	SHR untrained control	17.98 ± 0.41	1.39 ± 0.07	1.40 ± 0.10	20.10 ± 0.66	1.77 ± 0.08	1.44 ± 0.05
	LEW untrained control	14.68 ± 0.75	1.46 ± 0.12	1.22 ± 0.05	17.29 ± 0.57	2.17 ± 0.08	1.52 ± 0.06
	SHR trained control. LEW trained control SHR untrained Imm LEW untrained Imm SHR trained Imm LEW trained Imm	18.94 ± 0.87 14.17 ± 0.53## 21.60 ± 0.89* 16.43 ± 0.53## 21.82 ± 1.17 18.46 ± 0.71**	1.45 ± 0.09 1.35 ± 0.09 1.51 ± 0.07 1.55 ± 0.14 1.47 ± 0.16 1.57 ± 0.13	1.23 ± 0.05 1.21 ± 0.04 1.51 ± 0.07 1.40 + 0.07 1.36 ± 0.06 1.56 ± 0.07*	20.04 + 0.69 16.65 ± 0.25# 23.18 ± 0.70* 19.65 ± 0.45## 23.97 ± 1.25** 20.40 ± 0.48" "	2.00 ±0.11 2.04 ± 0.10 2.03 ± 0.04 1.97 ± 0.10 1.91 ± 0.10 2.05 ± 0.08	1.48 ± 0.08 1.39 ± 0.04 1.71 ± 0.04 1.87 ± 0.10* 1.82 ± 0.10* 1.76 ± 0.03*'
	1 -Strain effect
	2 -Training effect
	3 -Immobilization effect
	Interaction effect			x2		1x2x3	1 x 2

rue Léo Saignât, 33076 Bordeaux Cedex, France. © 2000 ScandinavianPhysiological Society

© 2000 Scandinavian Physiological Society

© 2000 Scandinavian Physiological SocietyActa Physiol Scand 2000, 168, 421-430

immobilization. Endocrinology 108, 1730-1736. © 2000 Scandinavian Physiological Society


Idir Hamaz
email: ihamaz@laas.fr

Laurent Houssin
email: lhoussin@laas.fr

Sonia Cafieri
email: sonia.cafieri@enac.fr

The Cyclic Job Shop Problem with uncertain processing times

Keywords: Cyclic scheduling, budgeted uncertainty set, robust optimization

Introduction

Most models for scheduling problems assume deterministic parameters. In contrast, real world scheduling problems are often subject to many sources of uncertainty, for example activities duration can decrease or increase, machines can break down, new activities can be incorporated, etc. In this paper, we focus on scheduling problems that are cyclic and where activity durations are affected by uncertainty. Indeed, the best solution for a deterministic problem can quickly become the worst one in the presence of uncertainties.

In this paper, we consider the Cyclic Job Shop Problem (CJSP) where processing times are affected by uncertainty. Several studies were conducted on the deterministic CJSP. The CJSP with identical parts is studied in [START_REF] Roundy | Cyclic schedules for job shops with identical jobs[END_REF]. The author shows that the problem is NP-hard and designs a branch and bound algorithm to solve the problem. [START_REF] Hanen | Study of a NP-hard cyclic scheduling problem: The recurrent job-shop[END_REF] investigates the general CJSP and presents a branch and bound procedure to tackle the problem. A general framework for modeling and solving cyclic scheduling problems is presented in [START_REF] Brucker | A general model for cyclic machine scheduling problems[END_REF]. The authors present different models for cyclic versions of the job shop problem. However, a few works consider cyclic scheduling problems under uncertainty. [START_REF] Che | Robust optimization for the cyclic hoist scheduling problem[END_REF] investigate the cyclic hoist scheduling problem with processing time window constraints where the hoist transportation times are uncertain. The authors define a robustness measure for cyclic hoist schedule and a bi-objective mixed integer linear program to optimize the cycle time and the robustness.

In order to deal with uncertainty, we use a robust optimization approach. We model the uncertain parameters by using the idea of uncertainty set proposed by [START_REF] Bertsimas | The price of robustness[END_REF]. Each task duration belongs to an interval, and the number of parameters that can deviate from their nominal values is bounded by a positive number called budget of uncertainty. This parameter allows us to control the degree of conservatism of the resulting schedule. Finally, we propose a branch and bound procedure that computes the minimum cycle time for the robust CJSP such that, for each scenario in the uncertainty set, there exists a feasible cyclic schedule.

Problems description

Basic Cyclic Scheduling Problem (BCSP)

We are given a set of n generic operations T = {1, ..., n}. Each operation i ∈ T is characterized by a non-negative processing time p i and has to be performed infinitely often without preemption. We denote < i, k > the k th occurrence of the generic operation i and t(i, k) the starting time of k th occurrence of the operation i.

The operations are subjected to a set of precedence constraints (uniform constraints). The constraints between the occurrences < i, k > and < j, k + H ij > are given by

t(i, k) + p i t(j, k + H ij ), ∀ i ∈ T , ∀ k ≥ 1 (1)
where H ij is an integer that represents the depth of the occurrence shift, usually referred to as height. The H ij parameter is an occurrence shift between the operations i and j.

For instance, for each execution of the occurrence < i, k >, the next execution of j is the occurrence < j, k + H ij >.

A schedule S is an assignment of starting time t(i, k) for each occurrence < i, k > of task i ∈ T . Such schedule is called periodic with cycle time α if it satisfies

t(i, k) = t(i, 0) + αk, ∀ i ∈ T , ∀ k ≥ 1 (2)
where α is the cycle time and represents the difference between the stating times of two successive occurrences of the same task. Therefore, a schedule S can be entirely defined by the staring times t i = t(i, 0) of the first occurrences and the cycle time.

In this study, the objective is to minimize the cycle time α while satisfying the precedence constraints between operations. Notice that different objective functions exist for cyclic scheduling problems, such as work in progress minimization or both cycle time and work in progress minimization.

A bi-valued directed graph G = (T , U ) can be associated with any instance of BCSP. In this graph, a node (resp. an arc) of G corresponds to a generic operation (resp. constraints) in the BCSP. Each arc (i, j) of G has two valuations, the length L ij = p i and the height H ij . These arcs are called uniform arcs and are built by considering the precedence constraints. For instance, a precedence constraint between task i and task j leads to an arc (i, j) of G labeled with L ij = p i and H ij . We denote H(c) (resp. L(c)) the height (resp. length) of a circuit c in graph G the sum of heights (resp. lengths) of the arcs composing the circuit c.

The minimum cycle time is given by the maximum circuit ratio of the graph which is defined by α = max c∈C (i,j)∈c L ij (i,j)∈c H ij where C is the set of all circuits in G.

We call critical circuit the circuit c realizing the maximum circuit ratio. Several algorithms have been proposed for the computation of critical circuits. An experimental study about maximum circuit ratio algorithms was published in [START_REF] Dasdan | Experimental analysis of the fastest optimum cycle ratio and mean algorithms[END_REF]). The author remarks that, among the several tested algorithms, the most efficient one is the Howard's algorithm. Although the algorithm has a pseudo-polynomial complexity, it shows noteworthy practical results.

Once the cycle time is determined, the starting times (t i ) i∈T can be determined by computing the longest path in the graph G where each arc (i, j) ∈ U is valued with p i -αH ij .

Cyclic Job Shop Problem (CJSP)

In the present work, we focus on the cyclic job shop problem (CJSP). The difference with the problem defined above is that for CJSP the number of machines is lower than the number of tasks to perform. As a result, the same resource must be shared between different operations. A CJSP can be considered as a BCSP equipped with resource constraints. Each occurrence of an operation i ∈ T has to be executed, without preemption, on the machine M (i) ∈ M = {1, ..., m}. Operations are grouped on a set of jobs J , where a job j represents a sequence of elementary operations that must be executed in order. To avoid overlapping between the tasks executed on the same machine, for each pair of operations i and j where M (i) = M (j) , the following disjunctive constraint holds

∀ i, j s.t. M (i) = M (j) , ∀k, l ∈ N : t(i, k) ≤ t(j, l) ⇒ t(i, k) + p i ≤ t(j, l) (3)
In summary, a cyclic job shop problem is defined by

• a set T of elementary tasks,

• a set M of machines,

• for each task i ∈ T , a processing time p i and a machine M (i) ∈ M on which the task has to be performed, • a set P of precedence constraints, • a set D of disjunctive constraints that occur when two tasks are mapped on the same machine, • a set J of jobs corresponding to a production sequence of generic operations. More precisely, a job J 1 defines a sequence J 1 = t 1,1 . . . t 1,k to be executed in that order.

The CJSP can be represented by directed graph G = (V, P ∪ D), called disjunctive graph. The sequence of operations that belongs to the same job are linked by uniform arcs in P where the heights are equal to 0. Additionally, for each pair of generic operations i and j executed on the same machine, a disjunctive pair of arcs (i, j) and (j, i) occurs. These arcs are labeled respectively with L ij = p i and H ij = K ij , and L ji = p j and H ji = K ji where K ij is an occurrence shift variable that satisfies K ij + K ji = 1 [START_REF] Hanen | Study of a NP-hard cyclic scheduling problem: The recurrent job-shop[END_REF].

The following bounds on occurrence shift variables K ij have been proposed in [START_REF] Hanen | Study of a NP-hard cyclic scheduling problem: The recurrent job-shop[END_REF]:

K - ij ≤ K ij ≤ 1 -K - ij . (4)
with

K - ij = 1 -min{H(µ) | µ from j to i in G}. (5)
A schedule is an assignment of all the occurrence shifts, i.e., determine precedence relations on the operation occurrences mapped to the same machine. Note that once the occurrence shifts are determined the problem is equivalent to the BCSP, therefore, the minimum cycle time can be obtained by the cited algorithms.

Previous studies have shown that the problem is NP-Hard [START_REF] Hanen | Study of a NP-hard cyclic scheduling problem: The recurrent job-shop[END_REF] for cycle time minimization.

Robust Cyclic Job Shop Problem (RCJSP)

In this paper, we investigate the robust version of the CJSP. More precisely, we are interested in the CJSP where processing times are affected by uncertainty and belong to a finite uncertainty set U. Based on the budget of uncertainty concept introduced in [START_REF] Bertsimas | The price of robustness[END_REF], the processing time deviations can be modeled trough the following uncertainty set:

U Γ = (p i ) i∈T ∈ R n : p i = pi + pi ξ i , ∀ i ∈ T ; ξ i ∈ {0, 1}; i∈T ξ i ≤ Γ
where pi represents the nominal processing time of operation i and pi its deviation. The parameter Γ is a positive integer and represents an upper bound on the number of processing times deviating from their nominal value.

The objective of the problem is to find, for a given budget of uncertainty Γ , the minimum cycle time such that, for each p ∈ U Γ , there exists a vector (t(p) i ) i∈T satisfying both the precedence and disjunctive constraints.

3 Branch and bound procedure for the RCJSP Recently, an Howard's algorithm adaptation taking into account the uncertainty set U Γ has been presented in [START_REF] Hamaz | Robust Basic Cyclic Scheduling Problem[END_REF]. The computational experiments on the algorithm show small execution times for robust BCSP instances.

To take into account the uncertainty on the processing times for the RCJSP, we develop a branch and bound procedure that uses the robust version of the Howard's algorithm. The procedure starts by initializing the upper bound on the cycle time to i∈T p i + p f where p f is the sum of the first Γ greatest deviations and the lower bound to the optimal cycle time of G = (T , U ) computed by the Howard's algorithm adaptation.

We use the same branching scheme as in [START_REF] Fink | A new procedure for the cyclic job shop problem[END_REF]. The search tree is initialized with a node (the root) where the graph G = (T , U ) contains only the uniform arcs U and no fixed disjunctions. Then, the branching is performed on unfixed disjunctions K ij . For this purpose, a successor node is created for each value on the interval

The value of the node is then computed by running the robust version of the Howard's algorithm with G = (T , U ∪ {(i, j), (j, i)}), where U contains the uniform arcs and a precedent fixed disjunctive arcs. When all the occurrence shifts are fixed, a feasible schedule is obtained, then the upper bound can be updated.

Preliminary numerical results show that the branch and bound procedure (implemented in C++ and executed on an Intel Xeon E5-2695 processor running at 2.30GHz CPU) delivers promising results. Besides, the algorithm is insensitive regarding the value of the budget of uncertainty.

Once the optimal cycle time computed by the branch and bound procedure, a periodic schedule S Γ = (α, ((t(p) i ) i∈T ) can be determined for each p ∈ U Γ .

Conclusion

The RCJSP with budgeted uncertainty set is addressed in this paper. We present a branch and bound procedure that uses a Howard's algorithm adaptation. Further investigation will address dominance rules to speed up the branch and bound procedure.