Bart Staels
email: bart.staels@pasteur-lille.fr

Wahiba Berrabah

Pierrette Aumercier

Philippe Lefebvre

Control of nuclear receptor activities in metabolism by post-translational modifications

Keywords: NRs, metabolism, post-translational modifications

Nuclear receptors (NRs) are molecular transducers of endocrine and dietary signals allowing tissues to adapt their transcriptional responses to endogenous or exogenous cues. These signals act in many cases as specific ligands, converting of NRs into transcriptionally active molecules. This on-off mechanism needs, however, to be finely tuned with respect to the tissue environment and adjusted to the organism needs. These subtle adjustments of NR transcriptional activity are brought about by post-translational modifications (PTMs), which can be, in the case of orphan NRs, the sole regulatory mechanism. The role of PTMs, with a more specific focus on phosphorylation, affecting the functions of NR controlling metabolic events is described in this review.

Introduction

Nuclear receptors (NRs) regulate a wide range of biological processes such as proliferation, apoptosis, differentiation and energy homeostasis. These transcription factors are mostly known for their ability to adjust the transcriptional activity of cells in response to small hydrophobic ligands, which may emanate either from the endocrine system (steroids, vitamin D...) or from the metabolic transformation of dietary compounds (cholesterol, fatty acid derivatives...) [START_REF] Chawla | Nuclear receptors and lipid physiology: opening the X-files[END_REF]. However, these ligandregulated as well as orphan NRs, for which no ligand has been yet identified [START_REF] Saijo | Nuclear receptors, inflammation, and neurodegenerative diseases[END_REF], are proteins integrating a number of other cellular signals stemming from the activation of signalling cascades controlled by extracellular receptors. A wealth of data have enlightened the role of post-translational modifications (PTMs) in modulating the functions of NRs, among which phosphorylation seems to play a major role [START_REF] Lalevée | Phosphorylation control of nuclear receptors[END_REF]. In this respect, up to 30% of all human proteins may be modified by kinase-directed modifications [START_REF] Smith | Recent developments in mass spectrometry-based quantitative phosphoproteomics[END_REF]. However, the literature in the NR and other fields now clearly points to the existence of interrelationships between phosphorylation and other PTMs such as ubiquitination, SUMOylation, O-GlcNAcylation, and acetylation [START_REF] Hunter | The age of crosstalk: phosphorylation, ubiquitination, and beyond[END_REF]. In this review, we will restrict our discussion to mechanisms involving PTMs that regulate functions of NRs controlling metabolic events.

NRs are a superfamily of transcription factors (48 in the human genome) able to bind structurally diverse ligands such as steroid and thyroid hormones, retinoic acid, vitamin D receptors, cholesterol and fatty acid derivatives as well as xenobiotics. In most cases, endogenous ligands act as agonists, thereby increasing the transcriptional activity of the cognate NR, but it is likely that NRs displaying a constitutively high transcriptional activity such as Estrogen-Related Receptors (ERRs) and Constitutive Androstane receptor (CAR) might be regulated by endogenous inverse agonists.

NRs have an archetypical structure consisting of five or six functional regions called A, B, C, D, E and F (Figure 1). The amino terminus (A/B domain) of the receptor encompasses the ligand-independent transcriptional activation domain, called AF-1 (Activation Function-1). The DNA binding domain (DBD or domain C) is a zinc-stabilized structure highly conserved among the NRs, which contains two alpha-helices involved in DNA recognition and protein-protein interaction. The D domain is a hinge region between domains C and E involved in DNA recognition and allowing, owing to its structural flexibility [START_REF] Chandra | Structure of the intact PPAR-gamma-RXR-alpha nuclear receptor complex on DNA[END_REF], NR dimers to bind to geometrically diverse DNA response elements [Hormone Response Elements (HRE)], now known to occur most frequently in intronic and 3' UTR sequences [7; 8] . The C-terminal or E/F domain is the ligand-binding domain (LBD) composed of 10 to 12 alpha-helices [START_REF] Greschik | Structure-activity relationship of nuclear receptorligand interactions[END_REF].

In addition to the ligand-binding pocket and dimerization interfaces, the carboxy terminus of the LBD harbours the Activation Function (AF)-2 region, which is a structure critical for the acquisition of transcriptional activity by NRs. Ligand-binding induces conformational changes in this region, creating a hydrophobic groove accommodating a LXXLL peptidic structure flanked by charged aminoacids which is found on primary coactivators [START_REF] Mahajan | Nuclear hormone receptor coregulator: role in hormone action, metabolism, growth, and development[END_REF]. This initial event leads to the build-up of a multiprotein transcriptional complex whose main activity is to destabilize local chromatin structure and to propagate signals from the NR binding site to the promoter of NR-regulated promoters. The dimerization interface of NRs allows for, depending on the NR, either homodimerization or heterodimerization with Retinoid X Receptors (RXRs), which may be a pre-requisite for DNA binding of many NRs [11; 12]. This is however not an absolute rule since some NRs such as FXR [START_REF] Claudel | Bile acid-activated nuclear receptor FXR suppresses apolipoprotein A-I transcription via a negative FXR response element[END_REF] or NR4As [START_REF] Sacchetti | Requirements for heterodimerization between the orphan nuclear receptor nurr1 and retinoid X receptors[END_REF] can bind DNA as monomers.

It is therefore rather intuitive to postulate that PTMs will introduce structural constraints on NR functional domains and in turn alter their transcriptional properties. As mentioned above, in view of the large number of NRs and possible PTMs, we have chosen to focus only on NRs involved in metabolic regulation (PPAR; LXR, FXR, Rev-erb, ROR, Nurr7) and restrict our analysis to enzymes catalyzing PTMs in response to metabolic signals.

Protein kinases and metabolism

Protein kinases catalyze the phosphorylation of proteins by covalently adding phosphate groups to serine, threonine or tyrosine residues. There are [START_REF] Gallegos | Targeting protein kinase C activity reporter to discrete intracellular regions reveals spatiotemporal differences in agonistdependent signaling[END_REF]

Protein Kinase A

Protein kinase A (PKA) is a heterotetrameric cAMP-dependent protein kinase, composed of two catalytic and regulatory subunits. High levels of cAMP are sensed by regulatory subunits which release the catalytic subunit, and then interacts and modifies its substrates. Inactivation of the regulatory subunit II gene yield mice resistant to high fat diet [START_REF] Newhall | Deletion of the RIIbeta-subunit of protein kinase a decreases body weight and increases energy expenditure in the obese, leptin-deficient ob/ob mouse[END_REF], and PKA has been shown to serve several functions in cells, including the regulation of glycogen, glucose, and lipid metabolism. The physiological effects of glucagon are mediated by elevation of cellular cAMP levels and activation of cAMP-dependent PKA [START_REF] Minor | Preservation of livers from non-heart-beating donors: modulation of cAMP signal and organ viability by glucagon[END_REF], leading notably to the phosphorylation of the bifunctional enzyme PFK-2/F-2, 6-BiPhosphatase, hence favouring liver gluconeogenesis. In addition, exposure for 14 days to increased glucose concentrations caused an enhancement in cyclic AMP accumulation, PKA, and PKC activities in human dermal microvascular endothelial cell line (HMEC-1) [START_REF] Kamal | Antiproliferative effect of elevated glucose in human microvascular endothelial cells[END_REF]. Thus PKA is a kinase sensitive, among other stimuli, to metabolic cues.

Akt/PKB

Akt, also called Protein Kinase B (PKB), is a serine/threonine protein kinase playing a key role in multiple cellular processes (glucose metabolism, cell proliferation, apoptosis, transcription and cell migration). Akt/PKBs are encoded by three highly homologous genes with Akt1 being ubiquitously but most strongly expressed in brain, heart, testis and thymus, while Akt2 is mostly restricted to insulinsensitive tissues and Akt3 essentially found in brain and lungs [START_REF] Zdychová | Emerging role of Akt kinase/protein kinase B signaling in pathophysiology of diabetes and its complications[END_REF]. Activation of Akt/PKB proceeds from the PI3K-dependent conversion of phosphatidylinositol (4,5)-bisphosphate (PIP2) to PIP3, allowing the anchoring of cytosolic Akt to the plasma membrane and its phosphorylation by PDK-1 and the PDK2/mTOR complex 2 on Thr308 and Ser473 respectively [START_REF] Gonzalez | The Akt kinases: isoform specificity in metabolism and cancer[END_REF]. Activated Akt can then phosphorylate its numerous substrates including GSK3, AMPK and the lipid metabolism regulator, sterol-regulatory element-binding proteins (SREBPs) [START_REF] Krycer | The Akt-SREBP nexus: cell signaling meets lipid metabolism[END_REF]. Gene inactivation studies concur to demonstrate the central role of the Akt/PKB pathway as a critical regulator of glucose metabolism and insulin sensitivity in response to stress and nutrients, thus placing its downstream substrates under the control of these extracellular signals. In addition, pathological conditions such as type II diabetes are characterized by a reduced Akt signaling in human white adipose tissue [START_REF] Rondinone | Impaired glucose transport and protein kinase B activation by insulin, but not okadaic acid, in adipocytes from subjects with type II diabetes mellitus[END_REF] and in the skeletal muscle from diabetic patients and insulin-resistant Goto-Kakizaki rats [START_REF] Krook | Improved glucose tolerance restores insulin-stimulated Akt kinase activity and glucose transport in skeletal muscle from diabetic Goto-Kakizaki rats[END_REF]. Of note, Akt can itself be regulated by PTMs: Akt2 is O-GlcNacylated, leading to impaired phosphorylation and insulin resistance in rat primary adipocytes [START_REF] Park | O-Glcnac modification on IRS-1 and Akt2 by Pugnac inhibits their phosphorylation and induces insulin resistance in rat primary adipocytes[END_REF]. Thus Akt/PKBs are, by virtue of their central role in conveying adaptative cellular processes in response to extracellular signals (nutrients, hormones ...) and intracellular environment variations (oxidative stress), upstream signaling kinases which will alter the function(s) of their substrates in response to metabolic challenges. Interestingly, studies with a fluorescent reporter showed that PKB/Akt signaling propagates from the plasma membrane to the nucleus [START_REF] Kunkel | Spatio-temporal dynamics of protein kinase B/Akt signaling revealed by a genetically encoded fluorescent reporter[END_REF], emphasizing a potential role in controlling transcriptional events.

Protein kinases C

The PKC family can be divided into three groups: (i) conventional PKCs (α, βI, βII, and γ) requiring negatively charged phospholipids, diacylglycerol (DAG) and calcium for their activity; (ii) "novel" PKCs μ, ε, ζ, ε and δ which require negatively charged phospholipids, diacylglycerol but are calcium-independent; and (iii) atypical PKCs λ and ξ requiring only negatively charged phospholipids.

Each PKC differs in its primary structure, tissue distribution, subcellular localization, response to extracellular signals, and substrate specificity [START_REF] Steinberg | Structural basis of protein kinase C isoform function[END_REF]. Very schematically however, their mode of activation relies on the same process. G-protein linked membrane tyrosine kinases are activated by an extracellular signal, triggering phospholipase C action on PIP2 to generate inositol-1,4,5triphosphate (IP3) and diacylglycerol (DAG). IP3 induces calcium store release, whereas DAG activates membrane-bound PKC. Quite clearly however, this long portrayed and simple mechanism of activation by DAG is by far more complex and must take into account fatty acids, glycerolipids and sphingolipids as modulators of PKC activity [START_REF] Becker | Protein kinase C and phospholipase D: intimate interactions in intracellular signaling[END_REF]. Depending on the activating signal, PKCs can relocate to various subcellular compartments, including the Golgi apparatus and the nucleus [START_REF] Gallegos | Targeting protein kinase C activity reporter to discrete intracellular regions reveals spatiotemporal differences in agonistdependent signaling[END_REF].

Metabolic signals may regulate PKC activity in several ways. Oxidative stress can either activate or inhibit PKC activity, depending on its intensity [START_REF] Gopalakrishna | Protein kinase C signaling and oxidative stress[END_REF]. Bile acids, which play a critical role in cholesterol and glucose metabolism [START_REF] Lefebvre | Role of bile acids and bile acid receptors in metabolic regulation[END_REF], modulate the PKC pathway via different mechanisms. In the absence of DAG, bile acids increase PKC activity by promoting its association with phospholipids [START_REF] Rao | Activation of protein kinase C alpha and delta by bile acids: correlation with bile acid structure and diacylglycerol formation[END_REF].

Bile acids also stimulate phospholipase C activity, hence increasing DAG formation [START_REF] Nomoto | The effects of bile acids on phospholipase C activity in extracts of normal human colon mucosa and primary colon tumors[END_REF]. Glucose seems to be a major modulator of PKC activity. During hyperglycemia, increased DAG production correlates with an increased PKC β2 activity and high glucose concentrations activate PKCα and PKCβI/2 in macrophages [START_REF] Devaraj | Hyperglycemia induces monocytic release of interleukin-6 via induction of protein kinase C-{alpha} and -{beta}[END_REF]. In human dermal microvascular endothelial cell line (HMEC-1), glucose elevation cause an accumulation of cAMP, and an increase in PKA and PKC activities [START_REF] Kamal | Antiproliferative effect of elevated glucose in human microvascular endothelial cells[END_REF]. In contrast, glucose decreases PKC activity by altering DAG kinase subcellular localization in skeletal muscle [START_REF] Miele | Glucose regulates diacylglycerol intracellular levels and protein kinase C activity by modulating diacylglycerol kinase subcellular localization[END_REF]. As a result, chronic activation of PKC by hyperglycemia is believed to be a cause of cardiovascular complications in type 2 diabetic patients [34; 35].

Mitogen-Activated Protein Kinases

The mitogen-activated protein (MAP) kinase signalling cascade is organized in several modules, including the extracellular signal-regulated kinase (ERK), p38, and c-Jun NH 2 -terminal kinase (JNK). This vertical hierarchy is coupled to a layered structure, comprising at least 3 levels (MAPK kinase kinase, MAPK kinase and MAPK) which is biologically arranged as a multiprotein complex in which scaffolding proteins such as Kinase suppressor of Ras-1 or JNK-interacting proteins (JIPs) play crucial roles [START_REF] Kim | Pathological roles of MAPK signaling pathways in human diseases[END_REF]. As described for other kinases therein, MAPKs display pleiotropic activities which impact on multiple cellular processes. Whereas the ERK module is principally activated through the Ras/Raf pathway, the JNK and p38 modules are activated by deleterious signals such as pro-inflammatory signals or oxidative stress. While the role of these kinases has received considerable attention in the cancer field, it is now acknowledged that these signalling pathway play also important roles in metabolic control, and are targets for metabolic signals. Although the exact mechanisms are yet to be deciphered, it is clear that excessive activation of these signalling pathways participate to metabolic diseases [START_REF] Gehart | MAPK signalling in cellular metabolism: stress or wellness?[END_REF].

AMP-activated protein kinase

Belonging to the CAMK branch of the kinome, AMPK is a heterotrimeric complex composed of isoforms of the catalytic α subunit (α1 or α2), and the regulatory β (β1 or β2) and γ (γ1, γ2 or γ3) subunits. AMP-activated protein kinase (AMPK) is a master regulator of cellular energy homeostasis, behaving as a fuel sensor activated when the cellular ATP/AMP ratio decreases as a result, for example, of low glucose, hypoxia, ischemia, or heat shock [START_REF] Evans | Ion channel regulation by AMPK: the route of hypoxia-response coupling in the carotid body and pulmonary artery[END_REF][START_REF] Leclerc | AMP-activated protein kinase: a new beta-cell glucose sensor?: regulation by amino acids and calcium ions[END_REF][START_REF] Wang | The orphan nuclear receptor Rev-erb alpha regulates circadian expression of plasminogen activator inhibitor type 1[END_REF]. AMPK can be activated by two upstream pathways: a Ca² + -dependent pathway mediated by CaMKKβ and an AMP-dependent pathway mediated by LKB1 [START_REF] Hardie | Role of AMP-activated protein kinase in the metabolic syndrome and in heart disease[END_REF]. The latter process occurs through sensing of AMP levels by the γ subunit, which in turn renders the α cataytic subunit phosphorylatable by upstream activating kinases.

Several studies identified adipokines such as adiponectin and leptins as activators of AMPK [START_REF] Zhang | AMPK: an emerging drug target for diabetes and the metabolic syndrome[END_REF],

strengthening its role as a regulator of energy balance, which is also enlightened by its direct molecular interaction with a form of cellular energy storage, glycogen [START_REF] Hudson | A novel domain in AMP-activated protein kinase causes glycogen storage bodies similar to those seen in hereditary cardiac arrhythmias[END_REF], and its sensitivity to pathophysiological conditions. AMPK regulates glucose metabolism by promoting the translocation of the glucose transporter (GLUT)-4 to the plasma membrane and AMPK activation improves glucose homeostasis in animal model of insulin resistance [START_REF] Steinberg | AMPK in health and disease[END_REF]. Physiologically, exercise also activates AMPK and this activation is believed to constitute one of the key mechanisms for the beneficial effect of physical training on glucose homeostasis, which stems at least in part from transcriptional reprogramming of metabolic tissues [START_REF] Berglund | Glucagon and lipid interactions in the regulation of hepatic AMPK signaling and expression of PPARalpha and FGF21 transcripts in vivo[END_REF][START_REF] Mcgee | AMPK-mediated regulation of transcription in skeletal muscle[END_REF][START_REF] Richter | AMPK and the biochemistry of exercise: implications for human health and disease[END_REF].

GSK3

Unlike most of kinases, GSK3α and GSK3β are constitutively active proline-directed serine/threonine-specific kinases which phosphorylate at SXXXS sites and are inhibited by phosphorylation [START_REF] Ter Haar | Structure of GSK3beta reveals a primed phosphorylation mechanism[END_REF]. Since its description, GSK3 has been shown to play a role in multiple signalling pathways activated by the Wnt and Hedgehog pathways, growth factors and insulin. First described as glycogen synthase kinase [START_REF] Woodgett | Multisite phosphorylation of glycogen synthase. molecular basis for the substrate specificity of glycogen synthase kinase-3 and casein kinase-II (glycogen synthase kinase-5)[END_REF], a key enzyme in glycogen synthesis [50; 51], GSK3 is now known to phosphorylate dozens of substrates, including transcription factors regulating inflammatory processes, cell growth and differentiation [START_REF] Jope | The glamour and gloom of glycogen synthase kinase-3[END_REF]. GSK3 is inactivated by PKC, PKB/Akt and PKA [START_REF] Hardt | Glycogen synthase kinase-3beta: a novel regulator of cardiac hypertrophy and development[END_REF], exemplifying the complex interplay between kinase-regulated pathways [START_REF] Jope | The glamour and gloom of glycogen synthase kinase-3[END_REF]. Insulin is, via PKB/Akt activation, a GSK3 inactivating signal and GSK3 generally opposes the anabolic effect of insulin. In agreement with this, GSK3 inhibitors have been shown to have a positive effect on insulin sensitivity in preclinical models of type 2 diabetes [53; 54].

Protein Kinases and NRs Peroxisome proliferator-activated receptors

The three Peroxisome Proliferator-Activated Receptor (PPAR) isotypes (PPARα/NR1C1, β or δ/NR1C2, and γ/NR1C3) are encoded by distinct genes. First shown to be activated by substances that induce peroxisome proliferation in rodents [55; 56], PPARs are activated by endogenous fatty acid derivatives and synthetic normolipimiants (PPARα, fibrates) or insulin sensitizers (PPARγ, thiazolidinediones). PPARs are involved in the control of metabolic and energy homeostasis [START_REF] Lefebvre | Sorting out the roles of PPAR alpha in energy metabolism and vascular homeostasis[END_REF][START_REF] Seedorf | Emerging roles of PPAR delta in metabolism[END_REF][START_REF] Sharma | Review: peroxisome proliferator-activated receptor gamma and adipose tissue--understanding obesity-related changes in regulation of lipid and glucose metabolism[END_REF].

The expression of PPARα, β and γ varies widely from tissue to tissue, with PPARα being highly expressed in hepatocytes, cardiomyocytes, enterocytes, and the proximal tubule cells of the kidney and involved mostly in fatty acid oxidation. PPARβ/δ is expressed ubiquitously and often at higher levels than PPARα and PPARγ. PPARγ, expressed predominantly in adipose tissues and the immune system, exists as two distinct isoforms γ1 and γ2 which arise from differential transcription start sites and alternative splicing.

PPARα and PKC

The

PPARα and MAPKs

PPARα activity modulates heart functions by increasing fatty acid uptake and oxidation [START_REF] Duncan | Rescue of cardiomyopathy in peroxisome proliferatoractivated receptor-alpha transgenic mice by deletion of lipoprotein lipase identifies sources of cardiac lipids and peroxisome proliferator-activated receptor-alpha activators[END_REF].

The p38 MAPK pathway is activated by cardio-myocyte stressors such as ischemia, hypoxia and hypertrophic growth. p38 phosphorylates PPARα at its N terminus (S6, 12 and 21) and increases PPARα transcriptional activity, probably through increased coactivator recruitment [START_REF] Barger | p38 mitogen-activated protein kinase activates peroxisome proliferator-activated receptor alpha: a potential role in the cardiac metabolic stress response[END_REF]. This establishes a plausible link, although not formally tested in vivo, between PPARα, PTMs and cardiac function. In skeletal muscle, adiponectin activates PPARα in an AMPK/p38 manner, which may result in enhanced fatty acid oxidation hence improved peripheral insulin sensitivity [START_REF] Yoon | Adiponectin increases fatty acid oxidation in skeletal muscle cells by sequential activation of AMPactivated protein kinase, p38 mitogen-activated protein kinase, and peroxisome proliferatoractivated receptor alpha[END_REF]. In contrast, anisomycin, a p38 activator, induced a dose-dependent phosphorylation of PPARα and an inhibition of its transcriptional activity in COS-7 and in H4IIE hepatoma cells [START_REF] Diradourian | Involvement of ZIP/p62 in the regulation of PPARalpha transcriptional activity by p38-MAPK[END_REF]. Interestingly, the anabolic hormone insulin also promotes PPARα activation through ERK-catalyzed phosphorylation of the same residues (S12 and S21) in HepG2 hepatoma cells, but the physiological relevance of this PTM has not been addressed [START_REF] Juge-Aubry | Regulation of the transcriptional activity of the peroxisome proliferator-activated receptor alpha by phosphorylation of a ligand-independent transactivating domain[END_REF].

Finally, co-transfection of MAPK phosphatase 1 (MKP-1) together with PPARα affects negatively its transcriptional activity in a transient transfection assay [START_REF] Heuvel | Comprehensive analysis of gene expression in rat and human hepatoma cells exposed to the peroxisome proliferator WY14,643[END_REF]. Taken together, these studies strongly hint at a general activating roles of MAPK on PPARα activity, thereby placing this NR under the control of growth factors and various cellular stresses.

PPARα and AMPK

There is no evidence showing that AMPK directly phosphorylates PPARα. However, a number of studies reported the role of AMPK as a PPARα coactivator in a kinase-independent manner [START_REF] Bronner | Kinase-independent transcriptional coactivation of peroxisome proliferator-activated receptor alpha by AMP-activated protein kinase[END_REF], a property reminiscent of the kinase-independent action of PDK1 on PPARγ transcriptional activity [START_REF] Yin | 3phosphoinositide-dependent protein kinase-1 activates the peroxisome proliferator-activated receptor-gamma and promotes adipocyte differentiation[END_REF].

AMPK was also described as a modulator of PPARα expression in response to glucose levels or adiponectin [START_REF] Fujita | Adiponectin protects against angiotensin II-induced cardiac fibrosis through activation of PPAR-alpha[END_REF][START_REF] Joly | Glucose represses PPARα gene expression via AMP-activated protein kinase but not via p38 mitogen-activated protein kinase in the pancreatic β-cell[END_REF][START_REF] Ravnskjaer | Glucose-induced repression of PPARalpha gene expression in pancreatic beta-cells involves PP2a activation and AMPK inactivation[END_REF]. This suggests that cellular energy levels might regulate the PPARα-regulated signalling network in a ligand-independent manner.

PPARγ and MAPK

PPARγ2 is phosphorylated in the A/B domain at S112 by MAPK in response to several mitogenic growth factors that inhibit fat cell differentiation. This phosphorylation reduces the transcriptional activity of PPARγ in adipocytes [START_REF] Hu | Inhibition of adipogenesis through MAP kinase-mediated phosphorylation of PPARgamma[END_REF] and human omental fat [START_REF] Fuentes | The anti-adipogenic effect of angiotensin II on human preadipose cells involves ERK1,2 activation and PPARg phosphorylation[END_REF], which may result in part from the increased proteasomal degradation of PPARγ [START_REF] Floyd | Interferon-gamma-mediated activation and ubiquitin-proteasome-dependent degradation of PPARgamma in adipocytes[END_REF] and/or decreased ligand-binding affinity [START_REF] Shao | Interdomain communication regulating ligand binding by PPAR-gamma[END_REF]. Morever, ERK and JNK, which can be activated by TNFα and EGF [START_REF] Thoresen | Response to transforming growth factor alpha (TGFalpha) and epidermal growth factor (EGF) in hepatocytes: lower EGF receptor affinity of TGFalpha is associated with more sustained activation of p42/p44 mitogen-activated protein kinase and greater efficacy in stimulation of DNA synthesis[END_REF], phosphorylate S84 of the A/B domain of PPARγ1 in vitro and in turn inhibit both ligand-independent and ligand-dependent transactivation functions [START_REF] Adams | Transcriptional activation by peroxisome proliferator-activated receptor gamma is inhibited by phosphorylation at a consensus mitogen-activated protein kinase site[END_REF]. However, this view was challenged by a report showing that MEK1 can interact directly with the PPARγ AF2 domain and shuttle PPARγ to the cytosol in a phosphorylation-independent manner [START_REF] Burgermeister | Interaction with MEK causes nuclear export and downregulation of peroxisome proliferator-activated receptor gamma[END_REF], introducing a novel paradigm on how kinases may regulate transcription factor activity. ERK1/2 mediated phosphorylation of PPARγ was also shown to favor the transrepressive activity of PPARγ on NF-kappa-B [START_REF] Chen | Phosphorylation of PPARgamma via active ERK1/2 leads to its physical association with p65 and inhibition of NF-kappabeta[END_REF], further emphasizing the role of PTMs in specifying NR transcriptional activities. Finally, the neighboring S82 (S112 of mouse PPARγ2) aminoacid is a target for JNK, which decreases PPARγ1 transcriptional activity [START_REF] Camp | C-jun N-terminal kinase phosphorylates peroxisome proliferator-activated receptor-gamma1 and negatively regulates its transcriptional activity[END_REF].

PPARγ and PKA

In addition to the phosphorylation of PPARα and PPARβ/δ, Lazennec et al. documented that PPARγ transcriptional activity is increased upon PKA activation [START_REF] Lazennec | Activation of peroxisome proliferator-activated receptors (PPARs) by their ligands and protein kinase A activators[END_REF].

PPARγ and cdk5

Although widely acknowledged as a kinase involved in neuronal architecture and functions, as well as in cell cycle regulation, cdk5 has significant actions on the functions of pancreatic beta cells by regulating glucose-stimulated insulin secretion, and as a molecular relay for insulin-mediated glucose uptake in adipocytes [START_REF] Reha-Krantz | DNA polymerization in the absence of exonucleolytic proofreading: in vivo and in vitro studies[END_REF]. The activation of cdk5 in inflamed, obese white adipose tissues results in the cdk5-dependent phosphorylation of PPARγ at S273 and decreased PPARγ activity. Furthermore, this phosphorylation-dependent transcriptional extinction can be counteracted by specific PPARγ ligands, irrespective of their classification as full or partial agonists [START_REF] Choi | Anti-diabetic drugs inhibit obesity-linked phosphorylation of PPARgamma by CDK5[END_REF].

PPARγ and CK2

The activity of NRs is conditioned by mechanisms affecting their subcellular localization. CK-IIdependent PPARγ1 phosphorylation at Ser16 and Ser21 is necessary for CRM1/Ran/RanBP3mediated nucleocytoplasmic translocation of PPARγ, which may constitute a mechanism by which PPARγ regulates negatively inflammatory signalling pathways [START_REF] Von Knethen | Casein-kinase-IIdependent phosphorylation of PPARgamma provokes CRM1-mediated shuttling of PPARgamma from the nucleus to the cytosol[END_REF].

The nuclear bile acid receptor BAR/FXR

FXR is highly expressed in liver, intestine, kidney and adrenal glands and weakly in adipose tissue [START_REF] Lefebvre | Role of bile acids and bile acid receptors in metabolic regulation[END_REF]. Initially identified as a receptor for farnesol [START_REF] Forman | Identification of a nuclear receptor that is activated by farnesol metabolites[END_REF], bile acids (BA) were later identified as natural ligands of FXR [89; 90]. In addition to its natural ligands such as cholic acid and chenodeoxycholic acid, FXR can be activated by more specific synthetic ligands such as GW4064 and fexaramine [START_REF] Downes | A chemical, genetic, and structural analysis of the nuclear bile acid receptor FXR[END_REF]. There are two FXR genes, FXRα (NR1H4) encoding four major isoforms, and FXRβ (NR1H5) which is a pseudogene in humans but which encodes a receptor for lanosterol in other primates and rodents [START_REF] Otte | Identification of farnesoid X receptor beta as a novel mammalian nuclear receptor sensing lanosterol[END_REF]. In addition to its hepato-protective action against the cytotoxic effects of excessive bile acid concentrations, FXR plays a crucial role in the enterohepatic recycling of bile acids, in glucose and lipid metabolism [START_REF] Lefebvre | Role of bile acids and bile acid receptors in metabolic regulation[END_REF].

FXR and PKC

Gineste et al. [START_REF] Gineste | Phosphorylation of farnesoid X receptor by protein kinase C promotes its transcriptional activity[END_REF] showed that PKCα phosphorylates FXR in the DBD at S135 and S154. This phosphorylation increases the transcriptional activity of FXR by promoting recruitment of coactivators, such as PGC-1α [START_REF] Gineste | Phosphorylation of farnesoid X receptor by protein kinase C promotes its transcriptional activity[END_REF]. Moreover, PKC activity is necessary for a maximal ligand-dependent induction of FXR transcriptional activity, in analogy with PPARα. Quite intriguingly, ATPase class I type 8B member 1 (FIC1) expression favors PKCzeta-mediated phosphorylation of FXR at S448 and controls FXR nucleocytoplasmic repartition, thereby exerting a positive control on FXR transcriptional activity [START_REF] Frankenberg | The membrane protein ATPase class I type 8b member 1 signals through protein kinase C zeta to activate the farnesoid X receptor[END_REF]. Interestingly, PKC can be modulated by bile acid [30; 31]. We hypothesize that endogenous FXR ligands, such as bile acids, may sensitize FXR to their own ligand effect, by inducing PKCα-mediated FXR phosphorylation, suggesting the existence of a double, converging FXR activation pathway by bile acids.

Liver X Receptors

Liver X Receptors (LXRα/NR1H3 and LXRβ/NR1H2) function as nutritional sensors for cholesterol and derivatives. LXRα is primarily expressed in liver, macrophages, adipose tissue and the intestinal epithelium, while LXRβ is ubiquitously expressed [START_REF] Calkin | Liver X receptor signaling pathways and atherosclerosis[END_REF]. Oxysterols, which are oxidized derivatives of cholesterol, are the major ligands for LXR [START_REF] Pavan | Lipids from oxidized low-density lipoprotein modulate human trophoblast invasion: involvement of nuclear liver X receptors[END_REF]. Glucose and glucose-6-phosphate have also been reported as direct LXR agonists [START_REF] Mitro | The nuclear receptor LXR is a glucose sensor[END_REF]. But this observation has not been confirmed [START_REF] Denechaud | CHREBP, but not LXRs, is required for the induction of glucose-regulated genes in mouse liver[END_REF]. In addition, unsaturated fatty acids, such as arachidonic acid, may act as LXR antagonists. LXRs play important roles in lipid metabolism, glucose homeostasis and inflammation [START_REF] Oosterveer | The liver X receptor: control of cellular lipid homeostasis and beyond implications for drug design[END_REF].

LXR and PKC

LXRα is phosphorylated by PKCα in vitro and pharmacological activation of PKC by phorbol esters altered the transactivation of LXRα, without altering the DNA binding activity [START_REF] Delvecchio | Protein kinase C alpha modulates liver X receptor alpha transactivation[END_REF].

LXR and PKA

Yamamoto et al. [START_REF] Yamamoto | Protein kinase A suppresses sterol regulatory element-binding protein-1c expression via phosphorylation of liver X receptor in the liver[END_REF] showed that LXRα is phosphorylated by PKA. Two consensus PKA target sites were identified in the ligand binding/heterodimerization domain of LXRα (S195/196 and S290/291). PKA-mediated phosphorylation at these sites inhibits ligand-mediated activation of LXR by a combined decrease in LXR/RXR heterodimerisation, decreased coactivator and increased corepressor recruitment [START_REF] Yamamoto | Protein kinase A suppresses sterol regulatory element-binding protein-1c expression via phosphorylation of liver X receptor in the liver[END_REF].

LXR and CK2

Although initially thought to be the major LXRα phosphorylation site in the hinge domain, S198 mutation had no reported impact on LXR transactivation when assayed in HEK and RAW cells on three LXR target genes (FAS, ABCA1 and ABCG1) [START_REF] Chen | Phosphorylation of the liver X receptors[END_REF]. In line with this, Pineda Torra et al. [START_REF] Torra | Phosphorylation of liver X receptor alpha selectively regulates target gene expression in macrophages[END_REF] showed that S198 in LXRα is a CK2 phosphorylation site, which affects LXR-mediated transactivation on a limited subset of LXR target genes, including CCL24, AIM and LPL, but not ABCA1, ABCG1, SREBP1c or PLTP [START_REF] Torra | Phosphorylation of liver X receptor alpha selectively regulates target gene expression in macrophages[END_REF].

Nur77

Nur77 belongs to the NR4A orphan receptor subclass which also includes Nor1 and Nurr1.

Nurr77, Nor1 and Nurr1 bind to and activate transcription through "Nur77 Binding Response

Elements" (NBRE) that display variable geometry [START_REF] Sacchetti | Requirements for heterodimerization between the orphan nuclear receptor nurr1 and retinoid X receptors[END_REF]. Nur77, Nor1, and Nurr1 can form homodimers, heterodimer or monomers on NBREs to regulate yet poorly characterized direct target genes which have been mostly identified in the central nervous system [START_REF] Zhao | NR4A orphan nuclear receptors in cardiovascular biology[END_REF]. They display inflammatory regulatory properties in the vascular wall [START_REF] Vantiel | NR4 All in the vessel wall[END_REF]. More recently, a metabolic role for these receptors has emerged, with a specific emphasis on Nur77. This immediate early gene (also called NGFI-B or TR3) was initially described as a regulator of T cell antigen receptor-mediated cell death [START_REF] Lee | Unimpaired thymic and peripheral T cell death in mice lacking the nuclear receptor NGFI-b (nur77)[END_REF], but is now known to regulate hepatic glucose [START_REF] Pei | NR4A orphan nuclear receptors are transcriptional regulators of hepatic glucose metabolism[END_REF] and lipid homeostasis [START_REF] Pols | Nur77 modulates hepatic lipid metabolism through suppression of SREBP1c activity[END_REF]. The lack of known ligand for Nur77 has sparkled intense investigation of PTMs, as they appeared as major events regulating Nur77 activity [START_REF] Davis | Functional domains and phosphorylation of the orphan receptor Nur77[END_REF][START_REF] Hazel | Nur77 is differentially modified in PC12 cells upon membrane depolarization and growth factor treatment[END_REF][START_REF] Katagiri | Differential regulation of the transcriptional activity of the orphan nuclear receptor NGFI-b by membrane depolarization and nerve growth factor[END_REF].

Nur77 and Akt

In fibroblast cell lines, Nur77 is phosphorylated at S350 in its DBD by Akt/PKB, which interacts physically with Nur77. This PI3K-dependent phosphorylation of Nur77 by Akt impinges negatively on the transcriptional activity of Nur77 [112; 113], which may result from an increased nuclear export and tethering to 14.3.3 proteins [112; 114]. A contradictory report, however, noted that Nur77 was not phosphorylated by Akt, but by ribosomal S6 kinase (RSK) or by mitogen and stress-activated kinase (RSK) in vitro [START_REF] Wingate | Nur77 is phosphorylated in cells by RSK in response to mitogenic stimulation[END_REF]. Intriguingly, membrane depolarization of PC-12 pheochromocytoma cells also leads to S350 phosphorylation and Nur77 transcriptional deactivation [START_REF] Katagiri | Differential regulation of the transcriptional activity of the orphan nuclear receptor NGFI-b by membrane depolarization and nerve growth factor[END_REF].

Nur77 and PKA

Corticotrophin releasing hormone (CRH) is a central regulator of the pituitary Nur77 target gene proopiomelanocortin (POMC). CRH promotes PKA activation and subsequent DNA binding of Nur77 dimers, favoring NBRE-dependent transactivation of the POMC gene through an increased tethering of coactivators to the N terminal AF-1 [START_REF] Maira | Dimer-specific potentiation of NGFI-b (Nur77) transcriptional activity by the protein kinase A pathway and AF-1-dependent coactivator recruitment[END_REF]. This CRH-mediated activation of Nur77 was however traced back to MAPK activation and MAPK-mediated Nur77 phosphorylation in an analogous system [START_REF] Kovalovsky | Activation and induction of Nur77/Nurr1 in corticotrophs by CRH/cAMP: involvement of calcium, protein kinase A, and MAPK pathways[END_REF].

Hepatocyte Nuclear Factor-4

Hepatocyte Nuclear Factor-4 (HNF-4) is expressed in the liver, gut, kidney and pancreatic beta cells. HNF-4 is critical for liver development and mutations in the HNF4 gene form a monogenic cause of maturity-onset diabetes of the young [START_REF] Shih | Molecular etiologies of MODY and other early-onset forms of diabetes[END_REF]. In humans, there are two isotypes of HNF-4, alpha and gamma encoded by two separate genes HNF4A and HNF4G, respectively. Linoleic acid (LA) has recently been identified as the endogenous ligand of native HNF4 expressed in mouse liver [START_REF] Yuan | Identification of an endogenous ligand bound to a native orphan nuclear receptor[END_REF]. From a molecular perspective, HNF-4 is viewed as a critical regulator of liver differentiation and of hepatic genes involved in lipid and glucose metabolism [START_REF] Stegmann | Metabolome, transcriptome, and bioinformatic cis-element analyses point to HNF-4 as a central regulator of gene expression during enterocyte differentiation[END_REF].

HNF-4 and PKA

HNF-4 is phosphorylated in vitro by PKA [START_REF] Viollet | Protein kinase A-dependent phosphorylation modulates DNA-binding activity of hepatocyte nuclear factor 4[END_REF], and PKA activation leads to a decreased activation of HNF-4-regulated reporter genes by HNF-4 [START_REF] You | Transcriptional control of the human aldehyde dehydrogenase 2 promoter by hepatocyte nuclear factor 4: inhibition by cyclic AMP and COUP transcription factors[END_REF]. Although this possibility has not been investigated, it is interesting to note that physiological effects of glucagon are mediated by an elevation of cellular cAMP levels and ensuing activation of cAMP-dependent PKA [START_REF] Minor | Preservation of livers from non-heart-beating donors: modulation of cAMP signal and organ viability by glucagon[END_REF] and that this would place HNF-4 under the control of pancreatic hormones. However, HNF4 activity is also blunted by insulin through a FoxO1-dependent mechanism [START_REF] Hirota | Hepatocyte nuclear factor-4 is a novel downstream target of insulin via FKHR as a signal-regulated transcriptional inhibitor[END_REF], excluding the possibility of simple, opposite effects of insulin and glucagon on HNF-4 activity.

Retinoid acid receptor-related orphan receptors (RORs)

The retinoid acid receptor-related orphan receptors (RORs) α, β and γ, initially referred to as RZRs, constitute a subfamily of nuclear orphan receptors which regulate the expression of genes involved in cellular differentiation by binding to ROR response elements (ROREs) in the promoter regions of various genes [START_REF] Jetten | The ROR nuclear orphan receptor subfamily: critical regulators of multiple biological processes[END_REF]. RORα plays a role in development of cerebellar Purkinje cells, smooth muscle cell differentiation and bone formation. It regulates inflammatory responses, participates in the maintenance of circadian rhythmicity [START_REF] Teboul | How nuclear receptors tell time[END_REF], protects against atherosclerosis by and regulates lipoprotein metabolism activating apolipoprotein A-I and C-III gene transcription [START_REF] Laitinen | Potential roles of ROR-alpha in cardiovascular endocrinology[END_REF]. RevErbα competes with RORα for binding to the same target sequences and thus represents a constitutive repressor antagonizing RORα functionality [START_REF] Lechtken | Extracellular signal-regulated kinase-2 phosphorylates RORalpha4 in vitro[END_REF]. RORβ plays a role in retina maturation, whereas RORγ participates in the development of secondary lymphoid tissues [START_REF] Jetten | Retinoid-related orphan receptors (RORs): critical roles in development, immunity, circadian rhythm, and cellular metabolism[END_REF] ROR and PKC RORα1 is highly expressed in Purkinje cells and conventional PKC phosphorylates RORα and inhibits RORα transcriptional activity, but a causal link between these two phenomena has not yet been demonstrated [START_REF] Duplus | Phosphorylation and transcriptional activity regulation of retinoid-related orphan receptor alpha 1 by protein kinases C[END_REF].

ROR and ERK2

RORα4 is phosphorylated by ERK2 in vitro in its hinge domain at T128. U0126, an inhibitor of ERK1&2, completely suppressed phosphorylation of RORα4 which was found to be inhibitory of ROR transcriptional activity [START_REF] Lechtken | Extracellular signal-regulated kinase-2 phosphorylates RORalpha4 in vitro[END_REF]. Interestingly, the MAPK cascade is involved in the resetting of circadian gene expression [START_REF] Akashi | Involvement of the MAP kinase cascade in resetting of the mammalian circadian clock[END_REF], adding a potential new layer of control on this complex regulatory network.

Rev-Erbα

Rev-erbα (NR1D1) and its paralog Rev-erbβ (NR1D2) are encoded by two distinct genes.

Unlike other members of the NR superfamily, Rev-erbs are devoid of a ligand-dependent transactivation activation domain-2 [START_REF] Akashi | Involvement of the MAP kinase cascade in resetting of the mammalian circadian clock[END_REF], and therefore behave as constitutive transcriptional repressors by binding corepressors. More recently, heme has been identified as a natural Rev-erb ligand. They are expressed in most tissues and are particularly abundant in liver, muscle, adipose tissue and the cerebellum. Their expression follows a robust circadian rhythm, since Rev-erb and RORα, regulate clock genes such as BMAL. Rev-Erbs are involved in various biological processes such as adipocyte and muscle differentiation, and regulation of lipid metabolism [START_REF] Burris | Nuclear Hormone for Heme: REV-ERB{alpha} and REV-ERB{beta} are ligand-regulated components of the mammalian clock[END_REF].

Rev-Erbα and GSK3

Rev-erbα is phosphorylated at S55 and S59 by GSK3β and this can be blocked by lithium, a treatment used in bipolar disorders. This phosphorylation protects Rev-erbα from proteosomal degradation [START_REF] Yin | Nuclear receptor Rev-erbalpha is a critical lithium-sensitive component of the circadian clock[END_REF]. GSK3-mediated phosphorylation of Rev-erbα may thus constitute a potential molecular link between NR PTMs and cyclical pathologies.

Phosphorylation and other PTMs Phosphorylation and SUMOylation

Small Ubiquitin-like Modification (SUMOylation) is an important PTM which modulates positively or negatively the activity, the stability and the localization of intracellular proteins.

SUMOylation consists in the covalent modification by SUMO proteins of the ε amino-group of lysine residues, and impinges on essential cellular processes such as transcription factor activity and genome stability [133; 134]. The human genome encodes four Small Ubiquitin-like Modifier isoforms called SUMO-1/2/3/4. The SUMO 2/3 proteins share 97% sequence identity, but only 50% sequence identity with SUMO-1. In mammals, SUMO-1/2/3 proteins are ubiquitously expressed, whereas SUMO-4 is only expressed in kidney, lymph nodes and spleen. In eukaryotic cells, about 10% of intracellular proteins are SUMOylated. Protein SUMOylation is performed by a cascade of three enzymes. First, the SUMO E1 enzyme SEA1/2 activates mature SUMO proteins. Second, the activated mature SUMO-protein is conjugated to the only SUMO E2 enzyme called Ubc9. The last step is the formation of a covalent link between SUMO and lysine residue(s) of target proteins by one of the various E3 ligases (PIAS family, HDAC4) [135; 136]. Through this enzymatic cascade, intracellular proteins can be tagged by monomeric SUMO-1, multiple momoneric SUMO-2/3 or by polySUMO-2/3 chains. The SUMOylation reaction is reversible through the activity of sentrin-specific proteases (SENPs) [START_REF] Mukhopadhyay | Modification in reverse: the SUMO proteases[END_REF]. In most cases, SUMOylation occurs at Ψ-K-x-E/D consensus sequences, Ψ being an hydrophobic aminoacid and x any aminoacid.

SUMOylation has been initially shown to be dependent on phosphorylation of the heat shock factor HSF-1. A phosphorylation-dependent SUMOylation motif (PDSM) ΨKxExxSP has been identified and found in 78 proteins, including the NR Estrogen Related Receptors (ERRs), PPARγ, thyroid hormone receptor TRβ, and the NR coactivator NCoA2 [START_REF] Hietakangas | Pdsm, a motif for phosphorylation-dependent SUMO modification[END_REF]. The notion of PDSM has been extended to show that phosphorylation of aminoacids downstream of the SUMO consensus sequence facilitates SUMOylation [START_REF] Yang | An extended consensus motif enhances the specificity of substrate modification by SUMO[END_REF].

Phosphorylation-dependent SUMOylation of nuclear receptors

NRs are generally SUMOylated at a regular consensus sequence. The overall concept emerging from these studies is that, like for many other transcriptional regulators [START_REF] Geiss-Friedlander | Concepts in SUMOylation: a decade on[END_REF], SUMOylation inhibits NR-mediated transactivation. In one case (RORα), SUMOylation was shown to increase transcriptional activation [START_REF] Hwang | SUMOylation of RORalpha potentiates transcriptional activation function[END_REF]. Quite surprinsingly, SUMOylation is correlated to the acquisition by NR of a more pronounced transrepressive activity, which correlates, broadly speaking, to an increased anti-inflammatory activity of the SUMOylated NRs. Initially dissected for PPARγ [START_REF] Pascual | A SUMOylation-dependent pathway mediates transrepression of inflammatory response genes by PPAR-gamma[END_REF], this concept has been extended to many other NRs including LXRs, FXR and ERRs [START_REF] Treuter | Transcriptional control of metabolic and inflammatory pathways by nuclear receptor SUMOylation[END_REF].

A phospho-dependent SUMOylation has been described for several NRs. A PDSM occurs in the orphan receptor TR2/NR2C2. TR2 is phosphorylated at T210 by ERK2, and this stimulates K238

SUMOylation. This strengthens the interaction of TR2 with the corepressor RIP140 and leads to the repression of TR2 target genes [START_REF] Gupta | Retinoic acid-stimulated sequential phosphorylation, PML recruitment, and SUMOylation of nuclear receptor TR2 to suppress OCT4 expression[END_REF].

The AF-1 domain of PPARγ2 is composed of an activation and a repression domain. PPARγ2 is SUMO1-ylated in vivo, on K107 in the repression domain [START_REF] Floyd | Control of peroxisome proliferator-activated receptor gamma2 stability and activity by SUMOylation[END_REF]. A PPARγ2 sumoylation-defective K107R mutant displays increased transactivation properties and promotes adipocyte differentiation more efficiently. Phosphorylation of PPARγ2 at S112 promotes K107 SUMOylation, which then exerts more potent transrepressive effects [145; 146] by targeting PPARγ to the promoter of Toll-Like

Receptor-regulated target genes and preventing corepressor clearance from these promoters [START_REF] Pascual | A SUMOylation-dependent pathway mediates transrepression of inflammatory response genes by PPAR-gamma[END_REF].

ERRα1 and ERRγ2 have both PDSM sites located at the N-terminus. Phosphorylation of S19 of ERRα1 increases SUMOylation at K14, whose mutation to alanine increases ERRα activity [START_REF] Vu | Phosphorylation-dependent SUMOylation of estrogen-related receptor alpha1[END_REF].

Similarly, inactivation of the N-terminal ERRγ2 PDSM yields a superactive receptor and conversely, mutations of neighboring, phosphorylatable serine residues blunted ERRγ2 activity [START_REF] Hentschke | Transcriptional ERRgamma2mediated activation is regulated by sentrin-specific proteases[END_REF].

Phosphorylation and ubiquitination

The ubiquitin-proteasome system (UPS) was discovered by Irvin Rose, Avram Hershko and Aaron Ciechanover in 1970 [START_REF] Santner | The ubiquitin-proteasome system regulates plant hormone signaling[END_REF]. By allowing the highly controlled funnelling of proteins to either proteasomal degradation or other subcellular compartments, the UPS is not surprisingly involved in all aspects of cellular processes. The UPS is composed of about a thousand proteins (ubiquitin ligases, de-ubiquitinases, peptidases, ...) that regulate finely ubiquitination and degradation of proteins by the 26S proteasome. Ubiquitin is a highly conserved peptide structure present in all eukaryotic cells which is covalently linked to target proteins through an enzymatic cascade very similar in its principle to the SUMO cascade. First, ubiquitin is activated through the formation of a thioester bond between ubiquitin and E1 activating enzyme. The activated ubiquitin is then transferred to ubiquitin conjugating enzymes (E2 or UBE) [START_REF] Hauser | Degradation of the peroxisome proliferator-activated receptor gamma is linked to liganddependent activation[END_REF]. Ubiquitin ligases (E3) are then required to bind ubiquitin to the targeted protein. A more recently described enzyme (E4) facilitates the elongation of the poly-ubiquitin chain.

Ubiquitin Specific Peptidases (USP) catalyzes the de-ubiquitination proteins and the recycling of ubiquitin monomers [START_REF] Daviet | Targeting ubiquitin specific proteases for drug discovery[END_REF].

The relationship between phosphorylation and ubiquitinylation has been documented for several systems. One of them has received particular intention due to its importance in inflammation, the NF-kappa-B system. Quite schematically, cytosolic inhibitor molecules (I-kappa-B) sequester active NF-kappa-B subunits in the cytoplasm. Activation of this network by extracellular signals leads to the rapid phosphorylation of I-kappa-B and its proteasomal degradation [START_REF] Scheidereit | IkappaB kinase complexes: gateways to NF-kappaB activation and transcription[END_REF]. Although not mandatory, phosphorylation is thus very often preceding ubiquitin conjugation in cytosolic and nuclear compartments [START_REF] Haglund | Ubiquitylation and cell signaling[END_REF].

Phosphorylation-dependent NR ubiquitinylation

Agonist binding triggers PPARγ proteasomal degradation [START_REF] Hauser | Degradation of the peroxisome proliferator-activated receptor gamma is linked to liganddependent activation[END_REF]. Likewise, IFNγ promotes PPARγ proteasomal degradation, a process which is ERK-dependent and requires PPARγ S112 phosphorylation [START_REF] Floyd | Interferon-gamma-mediated activation and ubiquitin-proteasome-dependent degradation of PPARgamma in adipocytes[END_REF]. Rev-erbα can be phosphorylated at S55 and S59 by GSK3β, a PTM protecting rev-erbα from proteasomal degradation [START_REF] Yin | Nuclear receptor Rev-erbalpha is a critical lithium-sensitive component of the circadian clock[END_REF].

Phosphorylation and O-GlcNAcylation

O-GlcNAcylation consists in the attachment of a single N-acetylglucosamine moiety via an Oβ-glycosidic linkage to serine and threonine residues. Glucosamine-6-phosphate, the precursor of UDP-N-acetylglucosamine is synthesized by the Hexosamine Biosynthetic Pathway, which converts 3-5% of intracellular glucose. The amount of O-GlcNAcylated proteins is therefore proportional to the intracellular glucose content. O-GlcNAcylation is catalyzed by a highly conserved and unique enzyme, uridine diphospho-N-acetylglucosamine: polypeptide β-N-acetylglucosaminyltransferase (O-GlcNAc transferase, OGT). O-GlcNAcylation is reversible through the action of β-N-acetylglucosaminidase (O-GlcNAcase, OGA) [START_REF] Love | The hexosamine signaling pathway: deciphering the "O-GlcNAc code[END_REF]. Proteins can be O-GlcNAcylated in response to stress, hormones or nutrients, and this follows in many cases a competitive phosphorylation reaction at the same or neighboring sites of proteins such as c-Myc and SP1 [START_REF] Zeidan | The intersections between O-GlcNAcylation and phosphorylation: implications for multiple signaling pathways[END_REF]. Moreover, a correlation between O-GlcNAcylation, ubiquitination and phosphorylation has been described for p53 [START_REF] Guinez | Protein ubiquitination is modulated by O-GlcNAc glycosylation[END_REF], suggesting a complex interplay between PTMs.

NR, phosphorylation and O-GlcNAcylation

There is little or no evidence for a competitive O-GlcNAcylation/phosphorylation of "metabolic"

NRs. The estrogen receptor beta displays such an alternative, dynamic labelling at S16 located in a PEST region, suggesting that these PTMs could regulate ERβ stability [157; 158]. LXRα is O-GlcNAcylated and the AF-1 and DBD regions are targeted by this PTM [START_REF] Anthonisen | Nuclear receptor liver X receptor is O-GlcNAc-modified in response to glucose[END_REF]. Since LXRα is phosphorylated by PKA, PKC and CK2 (see above) in these domains, one can speculate that O-GlcNAcylation of LXRα may be affected by its phosphorylation. Similarly, a bioinformatics search (PM and WB, unpublished data) shows that S73 of PPARα is a potential O-GlcNAcylation site which is phosphorylated by GSK3 [START_REF] Burns | Modulation of PPAR activity via phosphorylation[END_REF], again raising the possibility of a dynamic PTM at this site.

Conclusions

NRs regulate, in many organisms, several biological functions (growth, development, reproduction, metabolism ...). Protein kinases, by phosphorylating NRs, play a key role in modulating NR activity in pathophysiological contexts. The activity of protein kinases is itself modified by the cellular metabolic status and environment, therefore integrating NRs into a very complex regulatory network (figure 2). This complexity is even increased when taking into account the role of NRs as a physical assembly platform for corepressor or coactivator complexes, which are also targets for PTMs.

This point has been addressed in recent reviews [161; 162] and will not be detailed here, but it is worth noting that these comodulator complexes have enzymatic activities (acetylases, methylases) which may affect NR themselves.

In addition, phosphorylation may not be the sole PTM acting at a given site, but it may compete or act in synergy with other modifications such as sumoylation and ubiquitinylation which will tag NRs for a distinct fate (figure 3). Beside proteasomal degradation, these PTMs can target NRs to different subcellular localizations, introduce steric hindrance in recognition surfaces that will prevent essential functions of NRs such as dimerization, or convert the receptor into a transrepressor. A full understanding of these very complex patterns of regulation will require a complete characterization of the NR interactome and of its dynamic interactions with modifying enzymes. This is undoubtedly one of the biggest challenges that the NR community is facing today, and this will be made possible by the most recent and future technological developments in protein identification by mass spectrometry, as well as high throughput technologies in the cell biology field.

  families of protein kinases which constitutes one of the largest and most important protein superfamilies, totaling approximately 2000 protein kinases. The human kinome is divided into 9 groups: AGC kinases (PKA, PKC and PKG); CaM kinases (calcium/calmodulin-dependent protein kinases and CAMK-like kinases); CK1 (casein kinase 1 group); CMGC (CDK, MAPK, GSK3 and CLK kinases), STE (homologs of yeast Sterile 7, Sterile 11, and Sterile 20 kinases), TK (tyrosine kinases), TKL (tyrosine-kinase like group of kinases), atypical kinases (PDHK and PIKK) and other unrelated kinases (such as IKK and CK2). In this review, we focus below on protein kinases which can be modulated by altered metabolic states [cAMP-dependent kinase (PKA), Protein Kinases C (PKCs); Protein Kinase B or Akt (Akt/PKB); Mitogen-Activated Kinases (MAPKs), Glycogen Synthase Kinase-3 (GSK3), AMP-activated Protein Kinase (AMPK)].

  identification of potential PKC phosphorylation sites in the PPARα sequence prompted the investigation of the effect of this kinase on PPARα transcriptional activity. The synthetic PKC activator and DAG analog phorbol myristol acetate (PMA) increased the level of phosphorylated PPARα. Inhibitors of PKC decreased agonist-induced PPARα transactivation [60; 61]. Overexpression of different PKC isoforms (PKCα, -β, -δ, and -δ) affected both basal and agonist-induced PPARα activity[START_REF] Gray | Regulation of peroxisome proliferator-activated receptor alpha by protein kinase C[END_REF]. Blanquart et al.[START_REF] Blanquart | The protein kinase C signaling pathway regulates a molecular switch between transactivation and transrepression activity of the peroxisome proliferator-activated receptor alpha[END_REF] and Gray et al.[START_REF] Gray | Regulation of peroxisome proliferator-activated receptor alpha by protein kinase C[END_REF] identified three PKC phosphorylation sites (T129, S179 and S230) required for ligand-induced PPARα transcriptional activity. Interestingly, the loss in transactivating potential observed upon alanine substitution of phosphorylated aminoacids, which may relate to a blunted ability to heterodimerize with RXRα[START_REF] Gray | Regulation of peroxisome proliferator-activated receptor alpha by protein kinase C[END_REF], correlated to an increased transrepressive potential[START_REF] Blanquart | The protein kinase C signaling pathway regulates a molecular switch between transactivation and transrepression activity of the peroxisome proliferator-activated receptor alpha[END_REF]. Intriguingly, the cholesterol synthesis inhibitor simvastatin requires PPARα expression to exert its anti-inflammatory effects in vivo. Simvastatin inhibited PPARα phosphorylation by lipopolysaccharide-activated PKCα, resulting in enhanced PPARα ability to transrepress the proinflammatory transcription factor NF-kappa-B[START_REF] Paumelle | Acute anti-inflammatory properties of statins involve peroxisome proliferator-activated receptor-alpha via inhibition of the protein kinase C signaling pathway[END_REF], underlining the role of PKC in shifting PPARα towards transactivating instead of transrepressing activities.PPARα and PKACholera toxin and other PKA activators enhanced mouse PPARα transcriptional activity in the absence and the presence of exogenous ligands in transient transfection experiments. The main site of phosphorylation is located in the DBD and the N-terminus of PPARα is dispensable for PKAmediated transcriptional activation[START_REF] Lazennec | Activation of peroxisome proliferator-activated receptors (PPARs) by their ligands and protein kinase A activators[END_REF]. Thus PPARα activity is potentially modulated by physiological cAMP modulators such as fasting, stress or exercise.

Figure 1

 1 Figure 1 Schematic representation of different functional domains of a NR. DBD: DNA Binding Domain; LBD: Ligand Binding Domain, AF-1: Activation Function -1, AF-2: Activation Function -2, A/B: activation domain of ligand-independent transcription, C: DNA binding domain, D: hinge region, E: ligand binding domain.

  Figure 2. Effect of metabolic signals on kinases and NR activities.

Figure 3

 3 Figure 3 Cross-talk between phosphorylation and other PTMs.


Onanong Hlaoittinun
email: onanong.hlaoittinun@ens2m.fr

Eric Bonjour
email: eric.bonjour@ens2m.fr

Maryvonne Dulmet
email: maryvonne.dulmet@ens2m.fr

Managing the Competencies of Team Members in Design Projects Through Multi-period Task Assignment

Keywords: Project management, Design project, Task assignment, Multi-skilled Resource allocation, Competency modeling

Product design projects involve multiple team members with various knowledge and competencies that have to evolve with time, due to rapid organizational, technological and marketing changes. Project managers require management methods to optimize the assignment of tasks to human resources according to their competency levels and the need for competency evolution. In this paper, we tackle this optimization problem in the context of multiple design projects and multiple periods. The model we propose seeks to minimize two function objectives: (i) minimize the supplementary salary cost due to the extended task duration when using under-competent employees and (ii) minimize the financial penalties when the competency goals have not been reached. This problem has been solved by means of a simulated annealing -based optimization algorithm.

Introduction

In product development projects, project managers face highly complex situations in which they have to deal with a great number of components with their interactions, a multiplicity of design tasks with their interdependencies, and a great number of team members with their evolution in competencies. They have to make difficult decisions concerning the allocation of numerous team members to design tasks.

The rapid evolution of technology in product design and business process reengineering often results in a change in the definition of design tasks. Consequently, R&D departments can suffer from a lack of competencies and may be unable to design future innovative products. In this paper, we are interested in tackling the problem of managing the team members' competencies and their evolution during the execution of design projects. This issue becomes one of the greatest concerns of project managers.

It has been commonly accepted that an appropriate task assignment can either maintain or improve the competency level of the team member assigned to the corresponding task. So project managers need methods to help them to optimize task assignments and to ensure that the evolution of team members' competencies is relevant to the objectives of future projects.

Research works concerning task assignment problem can be classified according to two criteria: "single-period" or "multi-period" task assignment and "static" or "dynamic" competency modeling. "Single-period" task assignment refers to the situation in which all tasks are considered as a single group, in other words, when time constraints between tasks have not been taken into account. "Multi-period" task assignment concerns the situation in which precedence constraints have been considered. "Static" competency modeling represents the situation in which the levels of competency for each actor are unchanged during the execution of tasks. "Dynamic" competency modeling aims at representing and simulating the evolution of the competency level for each actor during the execution of tasks.

These criteria, when combined, help us to divide related works into four categories.

The first category concerns "mono-period" task assignment with "static" modeling of competency. This is the easiest case because there is a single group of tasks to be assigned and competency levels are unvaried during the task execution.

The second category concerns "mono-period" task assignment with "dynamic" competency modeling [START_REF] Sayin | Assigning cross-trained workers to departments: A two-stage optimization model to maximize utility and skill improvement[END_REF]. This category concerns the evolution of competency levels but these competency levels are measured and followed during only one period (at the beginning and at the end). So, this task assignment model is not aimed to plan competency levels of actors in the long term. However, it needs incorporating learning and forgetting curves in the decision model.

The third category deals with "multi-period" task assignment with "static" competency modeling [START_REF] Bellenguez | Lower Bounds for the Multi-Skill Project Scheduling Problem with Hierarchical Levels of Skill. Practice and Theory of Automated Timetabling V[END_REF][START_REF] Corominas | Rotational allocation of tasks to multifunctional workers in a service industry[END_REF]. In project scheduling problems, this problem is called MSPSP which stands for Multi-skill Project Scheduling Problem. For instance, Bellenguez-Morineau [START_REF] Bellenguez | Lower Bounds for the Multi-Skill Project Scheduling Problem with Hierarchical Levels of Skill. Practice and Theory of Automated Timetabling V[END_REF] proposes a method that solves the MSPSP problem and ensures that the assigned actors are competent enough to carry out project tasks. This method seeks to minimize the total completion time of the project (Cmax).

The fourth category concerns "multi-period" task assignment with "dynamic" competency modeling [START_REF] Gutjahr | Competence-driven project portfolio selection, scheduling and staff assignment[END_REF][START_REF] Fowler | Heuristics for workforce planning with worker differences[END_REF]. The authors propose a model that optimizes the long term resource allocation. The evolution of competency (learning effect and knowledge depreciation) is also considered. The authors assume that the competency level of the assigned person will increase in accordance to the number of periods he/she activates this competency and his/her learning rate. Similarly, the competency level of a particular actor will decline in accordance to a knowledge depreciation rate if this actor has not been assigned to tasks corresponding to this competency. However, the authors have not modeled design project environments [START_REF] Gutjahr | Competence-driven project portfolio selection, scheduling and staff assignment[END_REF] or they have not focused on competency-based objectives [START_REF] Fowler | Heuristics for workforce planning with worker differences[END_REF].

Because of the increasing importance of competency evolution in the field of project management and due to a lack of research works concerning this issue, we are interested, in this paper, in dealing with the latter type of problem described above.

In competency modeling, Harzallah et al. suggests the CRAI model (Competency, Resource, Aspect, Individual), associated with axioms based on set theory [START_REF] Harzallah | Analysis and modeling of individual competencies: toward better management of human resources[END_REF]. Competencies are characterized by sets of knowledge, know-how and behavior associated to a context and linked to individual actors. Based on a classical evaluation of the "knowledge", "know-how" and "behavior" characteristics, a mathematical aggregation is suggested to provide a quantitative evaluation of competencies. Boucher et al. [START_REF] Boucher | Formalisation and use of competencies for industrial performance optimisation: a survey[END_REF] propose a literature review of competency management from a performance point of view. They underline that the characterization of competency is a first step for modeling the development of competency and improving goals of competency management.

Different attributes of competency have been used in the field of team formation to model competency, such as qualification (0 or 1) [START_REF] Caron | The assignment problem with seniority and job priority constraints[END_REF], technical knowledge, skills and know-how [START_REF] Tseng | Novel approach to multi-functional project team formation[END_REF][START_REF] Hadj-Hamou | Cooperative design-A framework for a competency-based approach[END_REF], psycho-sociological capacities or personal traits [START_REF] Fitzpatrick | Forming effective worker teams with multi-functional skill requirements[END_REF]. In the rest of this paper, to simplify the terminology, the concept of knowledge will cover all these attributes.

The organization of this paper is as follows: Section 2 presents the main steps of the task assignment modeling we propose. Section 3 outlines the mathematical formulation and the optimization approach for the considered problem. To illustrate the interests of this approach, simulation results are presented and shortly discussed in section 4. Section 5 sums up the paper and opens new directions of research.

Proposition for Modeling Multi-period Task Assignment

The method we propose is decomposed into four main stages of modeling that will be shortly outlined in this part.

Identifying Relevant Knowledge to Characterize Tasks and Actors

We define a generic set of tasks, indexed by i (i=1,…,M), a set of projects, indexed by l (l = 1, ..., P), a set of periods, indexed by k, (k = 1, ..., K), a set of actors, indexed by j (j = 1, ..., N) and a set of knowledge, indexed by c, (c = 1, ..., C).

We can classify two types of tasks used in multi-period task planning: generic and specific tasks. Each generic task

k l i T . We assume that , , 1 1 , , k l k l i c i c i r r rq = ×
, where 1 ,

i c
r is the performance level in knowledge c required by the generic task i. Actor characterization. The variable 2 , k c j r represents the performance level in knowledge c that is acquired by actor j in period k. We assume that the performance levels in knowledge c evolve during the task execution and depend on period k.

Calculating the "A priori" Compatibility Level and the Work Efficiency

The compatibility level aims at estimating the similarity between specific task , k l i T and actor j before the assignment of tasks in period k. This similarity is computed for each actor j by penalizing his/her insufficient performance level for each type of knowledge according to the performance level required by , k l i T (Equation 1). This indicator has been presented in detail in [START_REF] Suman | A survey of simulated annealing as a tool for single and multiobjective optimization[END_REF]. The value of this indicator is included between 0 and 1.

,

1 1 2 , , , , 1 , 1 , , , , 1 1 , , max(0, ) 1 , 0 1.
O k l k i c c j k l k l k k l c 3 1 2 3 i j i j i j O c k l i c r r v r r v r - - = • • = = = - ≤ ≤ - ∑ ∑ (1)
The compatibility level helps to select the appropriate actor for the th k assignment by turning it into the coefficient of work efficiency. We suppose that the time spent on a task has to be adjusted according to the "a priori" compatibility level , , k l 3 i j v . Therefore, there will be additional costs due to the assignment of specific task , k l i T to under-competent actor j.

We introduce the coefficient of work efficiency , ,

k l i j γ (Equation 2 -note that , , k l i j γ =1 if , , k l 3 i j v =1
, that is, if the actor is competent). Then this coefficient is used to compute the actual execution time of specific task , k l i T for actor j: , , ,

k l k l i j i L γ ×
, where the theoretical time , k l i L is given. This indicator is explained in detail in [START_REF] Hlaoittinun | Contribution à la constitution d'équipes de conception couplant la structuration du projet et le pilotage des compétences[END_REF].

, , , , 2 .
k l k l 3 i j i j v γ = - (2)

Propagating the Evolution of Competency after Each Period of Task Assignment

We assume that if actor j A is allocated to task x = 0), his/her performance level in knowledge c will decrease. To shorten this paper, we have not presented in detail how we have modeled the competency evolution.

, k l i T (that is, , , k l i j x >0),

Calculating the "A posteriori" Compatibility Level (Competency Level)

The variable 3 , k i j r estimates the competency level of actor j for generic task i T (that is, the compatibility between actor j and generic task i T ). This variable is calculated at the end of period k when actor j has carried out the tasks he/she has been responsible for.

1 2 , , 1 , , , , 1 1 , max(0, ) 1 , 0 1.
O k i c c j k k k c 3 1 2 3 i j i j i j O c i c r r r r r r r = • • = = = - ≤ ≤ - ∑ ∑ . ( 3
)

Mathematical Formulation for the Task Assignment Problem

The proposed model is based on the following assumptions:

• An under-competent actor could be assigned to a task but he/she will be accompanied by a trainer (or teaching tutor), which will generate additional costs to the project.

• Each assigned task is supposed to be carried out with success.

• There is no load constraint for tutors • The actor's capacity can be estimated in any time unit (day, month, etc). This capacity is supposed to exclude all the absence time due to the unavailability of employees (planned/unplanned absence, legal and social constraints, etc.) The overall objective function, the cost functions and the constraints that are used in the proposed task assignment model are described as follows:

, , , , , , , , 1 1 1 1 1 Min ( ) ( 1) ( )
K P M N M k l k l k l k l k l i j i j i j i i j i i i k l i j i L S L ST x O R γ γ ϕ = = = = =         × × + -× × + -             ∑∑∑∑ ∑ . (4) , , 1 1 , 1,... , 1,..., , 1,..., N k l i j j x i M l P k K = = ∀ = ∀ = ∀ = ∑ (5) , , , , , , 1 1
, 1,... , 1,...

M P k l k l k l i j i i j j k i l L x LM j N k K γ = = ≤ ∀ = ∀ = ∑∑ (6) , , , , 0 1,
, , , ;

k l k l i j i j x i j k l x R + ≤ ≤ ∀ ∈ (7)
The optimization of the assignment problem aims at minimizing the total project costs by determining the best assignment of tasks to actors. The overall objective function is split up into three criteria (or kinds of cost): the actors' salary, the tutors' salary and the financial penalties due to a lack of competent actors at the end of the horizon.

Criterion related to actors' salary [ , , , ( )

k l k l i j i j L S γ × × ]
k l k l i j i L ST γ -× × ] ( 1)
This criterion is derived from the case when tutors have to help the under-competent actor to accomplish the assigned tasks. This cost is based on the tutoring duration (calculated from the coefficient of work efficiency) and the salary rate of tutors.

Criterion related to financial penalties

These penalties are explained as lost incomes that companies could have if their competency objectives have not been reached. Competency objectives i O (i = 1,..., M) are used to describe the number of expected competent actors, required by generic tasks. To determine whether a person is competent, we define required performance thresholds, called thres i (i = 1,..., M). Actor j is judged competent for task i if 3 , ≥ k i j i r thres . At the end of the horizon of task assignment (k= K), we have obtained the number of competent actors i R for each task i (i= 1, ..., M):

3 , 1 max(0; [ 1]) = = - + ∑ N K i i j i j R E r thres
. The penalty rate for each missing competent actor is defined by constant i ϕ .

( )

M i i i i O R ϕ = -

∑

Two types of constraints are used in this model. Workload constraint (Equation 4) This constraint aims at ensuring that each task is completely assigned.

Resource load constraint (Equation 5) This constraint aims at ensuring that the total assigned load concerning an actor does not exceed his/her capacity.

To solve this problem, we have to face two difficulties: the non-linearity in competency evolution and the objectives in competency development at the end of the horizon of task assignment. To deal with these difficulties, this N-P hard problem can not be solved by the known exact optimization methods. Therefore, we develop a meta-heuristic approach to solve the problem. Simulated annealing (SA) is a generic probabilistic meta-algorithm for the overall optimization problem, namely locating a good approximation to the minimum of a given function in a large search space [START_REF] Kirkpatrick | Optimization by simulated annealing[END_REF][START_REF] Suman | A survey of simulated annealing as a tool for single and multiobjective optimization[END_REF].

The choice of using the simulated annealing is justified by the fact that we are able to find an initial solution to the global problem and to generate neighbors. The initial solution of this task assignment problem is found by considering k sub-problem separately (for each period k). The optimal solution of each sub-problem is found by using the linear programming successively for each period k and by propagating the evolution of competency (the algorithm starts from k=1,…, K). The parameter setting of SA (such as neighbor function, acceptance probabilities, annealing schedule) is described in detail in [START_REF] Hlaoittinun | Contribution à la constitution d'équipes de conception couplant la structuration du projet et le pilotage des compétences[END_REF]. When the SA algorithm reaches the stop condition, it returns the final assignment solution.

Computational Results

The case study concerned two projects that have been planned over three periods. The lists of 15 generic tasks, 20 actors and 23 types of knowledge have been generated. The performance levels in knowledge have been defined for each task and each actor. The project managers are in charge of defining these data for their projects. To shorten this paper, we sum up the results according to two viewpoints: competency-based aspect and financial aspect. For more information, please see [START_REF] Hlaoittinun | Contribution à la constitution d'équipes de conception couplant la structuration du projet et le pilotage des compétences[END_REF]. shows the variation of competency levels (concerning generic tasks) acquired by actor N°1 after each period. These results confirm that knowledge and competencies that have been activated to carry out tasks have been developed. The performance levels in knowledge that have not been mobilized in order to carry out tasks have declined.

Financial Viewpoint

By using the simulated annealing based algorithm, the total cost obtained by the partial optimization of the k sub-problems has been decreased about 3%. The variation of the total cost is presented by the first graph in Figure 2, and the variation of three sub-costs is presented by the other graphs. Concerning the financial penalty, we found that, before task assignment (k=0), 9 competent actors were missing. At the end of the horizon, the number of competent actors was increased and only 5 competent actors were still missing.

Conclusion

In this article, we have proposed a model of the multi-period task assignment problem with the modeling of the evolution of competencies. The short literature review that we have presented reveals that this problem has been rarely studied. This NP-hard problem has been solved by a simulated annealing -based optimization algorithm. The main assumption of this model is justified by psychological studies: an actor develops his/her knowledge when he/she has to carry out the task that activates this knowledge. Two types of tasks have been defined: generic tasks for modeling competencies and specific tasks for modeling their occurrences. Tasks have been characterized according to two levels: performance level in knowledge and competency level. A compatibility indicator between tasks and actors has also been proposed in order to calculate the coefficient of work efficiency that is used to penalize under-competent actors in the assignment problem.

The obtained results confirm that this method is convincing from the financial and competency-based viewpoints. Globally, we decreased the project costs, even if this decrease seems to be rather low. On the one hand, this can be explained by the fact that this decrease depends on how we fix the penalty rate. On the other hand, the initial solution (obtained by linear programming) is a good solution. From the competency-based viewpoint, the increase in the number of competent actors after the horizon of task assignment has proved that the proposed algorithm tried to reach the objectives of competency development.

Further work will concern the sensitivity analysis of the proposed algorithm. Project managers' estimations concerning the performance level in knowledge and the competency level that is required by a specific task may be imprecise. Due to the way of computing the compatibility level (Equation 1), we have good reasons to assume that the proposed method is few sensitive. Other experimentations will be led to prove this point.

iT

  corresponds to one competency and covers a class of specific tasks , k l i T sharing the same knowledge but with different performance levels, depending on period k and project l. Task characterization. Performance levels concerning a task can be characterized by two types of expertise levels: competency level and knowledge level. The variable , k l i rq represents the competency level required by specific task , performance level in knowledge c required by specific task ,

  This criterion relates to the competency level of employees concerning the assigned tasks. It is calculated from their salary rates and their estimated work duration (based on the coefficient of work efficiency). The product of the coefficient of work efficiency and the theoretical work duration ( estimated work duration for specific task , k l i T of actor j.This duration is longer than the theoretical work duration ( , for specific tasks.Criterion related to tutors' salary [ , , ,

4. 1 .

 1 Competency-Based Viewpoint.

Figure 1 :Figure 1 -( 1 )

 111 Figure 1: Evolutions of the performance levels in knowledge and in competency (2) (1) Knowledge index Competency index

Figure 2 :

 2 Figure 2 : Financial viewpoint

  this actor either maintains his/her performance level in knowledge c if

		r	, k l 1 , i c	≥ 2 , k c j r	or develops this
	performance level in knowledge c if , 1 , k l i c r < 2 , k c j r . If actor j is not allocated to task , k l i T (that
	is,	, k l , i j