Olivier Masson

Christine Prébois

Danielle Derocq

Aline Meulle

Cédric Dray

Danielle Daviaud

Didier Quilliot

Philippe Valet

Catherine Muller

Emmanuelle Liaudet-Coopman

Cathepsin-D, a key protease in breast cancer, is up-regulated in obese mouse and human adipose tissue, and controls adipogenesis

Keywords: cathepsin D, adipocyte, obesity, adipogenesis, differentiation, cancer

The aspartic protease cathepsin-D (cath-D) is overexpressed by human epithelial breast cancer cells and is closely correlated with poor prognosis in breast cancer. The adipocyte is one of the most prominent cell types in the tumor-microenvironment of breast cancer, and clinical studies have shown that obesity increases the incidence of breast cancer. Here, we provide the first evidence that cath-D expression is up-regulated in adipose tissue from obese human beings, as well as in adipocytes from the obese C57BI6/J mouse. Cath-D expression is also increased during human and mouse adipocyte differentiation. We show that cath-D silencing in 3T3-F442A murine preadipocytes leads to lipid-depleted cells after adipogenesis induction, and inhibits of the expression of PPAR, HSL and aP2 adipocyte differentiation markers.

Altogether, our findings demonstrate the key role of cath-D in the control of adipogenesis, and suggest that cath-D may be a novel target in obesity.

Introduction

The consumption of foods containing high levels of fat and carbohydrates is a major cause of obesity, resulting in the formation of excessive white adipose tissue. This increase in adipose tissue mass results from a combination of hypertrophy of existing adipocytes (hypertrophic adipocytes), and adipogenic differentiation of precursor cells (adipocyte hyperplasia). Recently, clinical studies have shown that obesity is a major risk factor for cancer [START_REF] Wright | Prospective study of adiposity and weight change in relation to prostate cancer incidence and mortality[END_REF][START_REF] Renehan | Body-mass index and incidence of cancer: a systematic review and meta-analysis of prospective observational studies[END_REF][START_REF] Van Kruijsdijk | Obesity and cancer: the role of dysfunctional adipose tissue[END_REF]. The presence of large amounts of adipose tissues has been associated with poor prognosis for breast cancer in obese postmenauposal women [START_REF] Calle | Overweight, obesity and cancer: epidemiological evidence and proposed mechanisms[END_REF].

Interestingly, proteases have also been recently shown to affect the biology of the adipocyte. The metalloproteinases [START_REF] Bouloumie | Adipocyte produces matrix metalloproteinases 2 and 9: involvement in adipose differentiation[END_REF][START_REF] Maquoi | Modulation of adipose tissue expression of murine matrix metalloproteinases and their tissue inhibitors with obesity[END_REF] and the cysteine cathepsins -K, -S and -L [START_REF] Xiao | Cathepsin K in adipocyte differentiation and its potential role in the pathogenesis of obesity[END_REF][START_REF] Taleb | Cathepsin s promotes human preadipocyte differentiation: possible involvement of fibronectin degradation[END_REF][START_REF] Yang | Cathepsin L activity controls adipogenesis and glucose tolerance[END_REF][START_REF] Naour | Cathepsins in human obesity: changes in energy balance predominantly affect cathepsin s in adipose tissue and in circulation[END_REF] stimulate adipogenesis, and are up-regulated in obesity. In contrast, stromelysin 3 inhibits adipogenesis and induces de-differentiation of adipocytes, generating a population of fibroblast-like cells that support the desmoplastic reaction [START_REF] Andarawewa | Stromelysin-3 is a potent negative regulator of adipogenesis participating to cancer cell-adipocyte interaction/crosstalk at the tumor invasive front[END_REF]. The aspartic protease cathepsin D (cath-D), a marker of poor prognosis in breast cancer [START_REF] Rochefort | Cathepsin D in breast cancer: a tissue marker associated with metastasis[END_REF][START_REF] Ferrandina | Relationship between cathepsin-D content and disease-free survival in node-negative breast cancer patients: a meta-analysis[END_REF][START_REF] Foekens | Cathepsin-D in primary breast cancer: prognostic evaluation involving 2810 patients[END_REF][START_REF] Westley | Prognostic value of cathepsin D in breast cancer[END_REF][START_REF] Rodriguez | Clinical significance of cathepsin D concentration in tumor cytosol of primary breast cancer[END_REF], is overexpressed and secreted at high levels by human epithelial breast cancer cells [START_REF] Westley | A secreted glycoprotein induced by estrogen in human breast cancer cell lines[END_REF][START_REF] Capony | Phosphorylation, glycosylation, and proteolytic activity of the 52-kD estrogen-induced protein secreted by MCF7 cells[END_REF][START_REF] Capony | Increased secretion, altered processing, and glycosylation of pro-cathepsin D in human mammary cancer cells[END_REF][START_REF] Rochefort | Cathepsin D in cancer metastasis: a protease and a ligand[END_REF][START_REF] Liaudet-Coopman | Cathepsin D: newly discovered functions of a long-standing aspartic protease in cancer and apoptosis[END_REF][START_REF] Vashishta | Pleiotropic effects of cathepsin D[END_REF][START_REF] Nicotra | The dilemma: does tissue expression of cathepsin D reflect tumor malignancy? The question: does the assay truly mirror cathepsin D mis-function in the tumor?[END_REF]. Cath-D stimulates cancer cell proliferation, fibroblast outgrowth, angiogenesis and metastasis [START_REF] Garcia | Overexpression of transfected cathepsin D in transformed cells increases their malignant phenotype and metastatic potency[END_REF][START_REF] Fusek | Mitogenic function of human procathepsin D: the role of the propeptide[END_REF][START_REF] Liaudet | Transfected cathepsin D stimulates high density cancer cell growth by inactivating secreted growth inhibitors[END_REF][START_REF] Liaudet | Cathepsin D maturation and its stimulatory effect on metastasis are prevented by addition of KDEL retention signal[END_REF][START_REF] Berchem | Cathepsin-D affects multiple tumor progression steps in vivo: proliferation, angiogenesis and apoptosis[END_REF][START_REF] Glondu | A mutated cathepsin-D devoid of its catalytic activity stimulates the growth of cancer cells[END_REF][START_REF] Glondu | Downregulation of cathepsin-D expression by antisense gene transfer inhibits tumor growth and experimental lung metastasis of human breast cancer cells[END_REF][START_REF] Laurent-Matha | Catalytically inactive human cathepsin D triggers fibroblast invasive growth[END_REF][START_REF] Vashishta | Ribozyme-targeting procathepsin D and its effect on invasion and growth of breast cancer cells: an implication in breast cancer therapy[END_REF][START_REF] Ohri | The propeptide of cathepsin D increases proliferation, invasion and metastasis of breast cancer cells[END_REF][START_REF] Hu | Thrombin up-regulates cathepsin D which enhances angiogenesis, growth, and metastasis[END_REF]. Interestingly, we recently published that the novel cath-D receptor, LRP1 (low-density lipoprotein receptor-related protein 1) [START_REF] Beaujouin | Procathepsin D interacts with the extracellular domain of the beta chain of LRP1 and promotes LRP1-dependent fibroblast outgrowth[END_REF], controls adipogenesis and is up-regulated in human and mouse obese adipose tissue [START_REF] Masson | LRP1 receptor controls adipogenesis and is up-regulated in human and mouse obese adipose tissue[END_REF].

Here, we investigated the expression of cath-D in adipocytes from obese subjects, and its role in the control of adipogenesis. We show, for the first time, that cath-D expression is upregulated in mouse and human obese adipose tissues, as well as during mouse and human adipogenesis. We also demonstrate that cath-D silencing inhibits the adipogenic process, indicating the crucial positive role of cath-D in adipogenesis.

Results

Cath-D expression is up-regulated in human and mouse obese adipose tissue

Because of the recently established relationship between obesity and cancer incidence [START_REF] Wright | Prospective study of adiposity and weight change in relation to prostate cancer incidence and mortality[END_REF][START_REF] Renehan | Body-mass index and incidence of cancer: a systematic review and meta-analysis of prospective observational studies[END_REF][START_REF] Van Kruijsdijk | Obesity and cancer: the role of dysfunctional adipose tissue[END_REF], and of the demonstrated role of cath-D in both cancer cells and stromal cells [START_REF] Liaudet-Coopman | Cathepsin D: newly discovered functions of a long-standing aspartic protease in cancer and apoptosis[END_REF], we investigated cath-D expression in human and mouse adipose tissues.

Cath-D mRNA expression was investigated in intra-abdominal visceral adipose tissue (VAT) from lean and obese human subjects (Figure 1A, panel a). Interestingly, cath-D mRNA was significantly increased in the obese human visceral adipose tissue (Figure 1A, panel a).

This differential expression of cath-D was also observed in subcutaneous adipose tissue (SAT) from lean and obese human subjects (Figure 1A, panel b).

In order to find out whether this up-regulation of cath-D was a general characteristic of adipocytes from obese subjects, we next analysed cath-D mRNA levels in adipocytes isolated from C57BI6/J mice fed either a High Fat Diet (HFD) or a Normal Diet (ND) (Figure 1B). HFD-fed C57BI6/J mice exhibited significantly higher body mass (47.6 ± 1.4 g) than their control littermates (31.1 ± 1.2 g). Cath-D expression was significantly greater in adipocytes from HFD obese mice than in those from ND control mice (Figure 1B). Overall, our results indicate that cath-D expression is up-regulated in adipose tissues of obese human beings and mice.

Cath-D expression is increased in adipocytes during adipogenesis in mouse and human

Since we were not aware of any report establishing that cath-D protein is expressed in adipocyte cells, we analysed cath-D expression in well-established mouse adipocyte cell lines (3T3-F442A and 3T3-L1), and compared it to that in mouse fibroblasts (NIH-3T3). Cath-D is synthesized as a 52-kDa precursor that is rapidly converted in endosomes as an active 48-kDa single-chain intermediate, and then in the lysosomes into the fully active mature protease, composed of a 34 kDa heavy chain and a 14 kDa light chain. As Figure S1 shows, mouse cells mainly expressed the intermediate 48 kDa cath-D form, and only to a lesser extent the mature 34 +14 kDa cath-D double chain, as previously described [START_REF] Felbor | Neuronal loss and brain atrophy in mice lacking cathepsins B and L[END_REF]. Interestingly, cath-D expression was increased in mature adipocytes in both the 3T3-F442A and 3T3-L1 cell lines (Figure S1).

Obesity is characterized by the increased intracellular accumulation of lipids, a characteristic of adipocyte differentiation that is significantly correlated with adipocyte differentiation. Since cath-D expression was up-regulated in obese tissues, we next investigated whether cath-D plays any role in adipogenesis. We first investigated the regulation of cath-D expression during the course of differentiation of the 3T3-F442A preadipocyte cell line, a valuable model of adipogenesis [START_REF] Neese | Measurement in vivo of proliferation rates of slow turnover cells by 2H2O labeling of the deoxyribose moiety of DNA[END_REF] (Figure 2). Interestingly, cath-D mRNA (Figure 2A) and protein (Figure 2B) expression was progressively up-regulated during adipogenesis. Since the overexpression of cath-D leads to the hypersecretion of the 52 kDa pro-cath-D into the extracellular environment [START_REF] Capony | Increased secretion, altered processing, and glycosylation of pro-cathepsin D in human mammary cancer cells[END_REF], we then investigated whether adipocytes secrete 52 kDa pro-cath-D. Secreted 52 kDa pro-cath-D was only detected in fullydifferentiated adipocytes from day 10 of differentiation (Figure 2B). To validate our experimental conditions, we studied in parallel the expression of PPAR (Figure 2A), HSL (Figure 2B) and aP2 (Figure 2A) adipocyte markers of differentiation. As expected, the levels of these markers increased progressively during the acquisition of the adipocyte phenotype (Figure 2A-B). In addition, the amount of cytoskeletal -actin protein decreased during adipocyte differentiation, reflecting the change in cellular morphology (Figure 2B), as previously described [START_REF] Spiegelman | Decreases in tubulin and actin gene expression prior to morphological differentiation of 3T3 adipocytes[END_REF]. Interestingly, a similar up-regulation of cath-D protein expression was observed during 3T3-L1 adipocyte differentiation (Figure 3). It was previously shown that cath-D expression was stimulated by insulin in epithelial breast cancer cells [START_REF] Cavailles | Estrogens and growth factors induce the mRNA of the 52K-pro-cathepsin-D secreted by breast cancer cells[END_REF][START_REF] Cavailles | Regulation of cathepsin-D and pS2 gene expression by growth factors in MCF7 human breast cancer cells[END_REF]. To ensure that the insulin treatment was not involved in the effect observed, we used parental NIH-3T3 fibroblasts and fully-differentiated 3T3-F442A adipocytes and. As shown in Figure 4, the levels of cath-D protein remained unaffected in the adipogenic differentiation medium both in NIH-3T3 fibroblasts (Figure 4A) and in mature 3T3-F442A adipocytes (Figure 4B).

We also confirmed that cath-D protein expression was not altered in 3T3-F442A adipocytes by insulin in dose-response experiments at low serum concentrations (Figure 4C). Altogether, these results strongly suggest that cath-D up-regulation is induced by the differentiation process per se and not by insulin.

Although 3T3-F442A and 3T3-L1 cells are valuable experimental models, these preadipocytes have some distinct attributes compared with human cells in primary culture beyond the obvious species differences. We therefore next investigated the regulation of cath-D expression during adipogenesis in human preadipocytes purified from abdominal subcutaneous adipose tissue [START_REF] Bour | Adipogenesis-related increase of semicarbazide-sensitive amine oxidase and monoamine oxidase in human adipocytes[END_REF] (Figure 5). These primary human cells were differentiated in an efficient manner since about 75% of preadipocytes were converted into the adipocyte phenotype (Figure 5A). As observed for the mouse adipocyte, the expression of cath-D protein was also increased in the human differentiated adipocyte (Figure 5B). Taken together, these findings indicate that cath-D expression is up-regulated during the differentiation of both mouse and human preadipocytes.

Silencing of cath-D expression inhibits adipogenesis

Since cath-D was up-regulated in tissues from obese individuals, and as its expression increased during the adipocytic process, we went on to investigate whether preadipocytes require cath-D expression to differentiate into mature adipocytes. Cath-D expression was stably silenced in 3T3-F442A preadipocytes with cath-D shRNA1 and shRNA2 generating the D10 and A4 clones, respectively (Figure 6A). Control C34 and C37 clones were obtained using Luc shRNA stably transfected into 3T3-F442A preadipocytes (Figure 6A).

To evaluate the consequences of cath-D silencing on adipocyte differentiation, we analysed the cellular lipid levels in adipocytes which had or had not been silenced for cath-D at day 7 of differentiation (Figure 6). Indeed, the most obvious feature of adipocytes is the fact that they synthesise and store triglycerides in lipid droplets and therefore the gradual development of lipid droplets is characteristic of adipocyte precursor cells undergoing adipogenic differentiation. Quantification of cath-D mRNA at day 7 of differentiation revealed a significant inhibition of cath-D expression by 56+/-2.4% and 60+/-8.5% in A4 and D10 clones, respectively (Figure 6B

Discussion

Our results demonstrate, for the first time, that cath-D expression is up-regulated in abdominal visceral and subcutaneous tissues from obese human subjects. A previous study observed cath-D mRNA expression in abdominal subcutaneous adipose tissue [START_REF] Karlsson | Human adipose tissue expresses angiotensinogen and enzymes required for its conversion to angiotensin II[END_REF]. This upregulation of cath-D expression in the VAT and SAT of overweight/obese patients is consistent with our data from obese mice. Obesity is characterized by increased intracellular accumulation of lipids, which is significantly correlated with adipocyte differentiation.

Terminally differentiated adipocytes cannot divide, which means that any increase in the number of adipocytes in the body must result from the differentiation of preadipocytes, which act as a renewable source of adipocytes.

Our data show that cath-D expression increases gradually as 3T3-F442A and 3T3-L1 cells differentiate into mature adipocytes. Interestingly, our findings also reveal that fullydifferentiated 3T3-F442A adipocytes secrete pro-cath-D, suggesting a potential new function as an adipokine. A recent study analysing the secretome of adipocytes reported that cath-D is a secretory protein induced by insulin [START_REF] Zhou | Quantitative analysis of secretome from adipocytes regulated by insulin[END_REF]. Most functional studies of adipocyte differentiation and function have been performed using the murine adipogenic 3T3-L1 and 3T3-F442A cell lines or genetically-modified mice. However, there are fundamental differences in lipoprotein metabolism between mice and human beings [START_REF] Prawitt | Characterization of lipid metabolism in insulin-sensitive adipocytes differentiated from immortalized human mesenchymal stem cells[END_REF]. This is why it was important to investigate the regulation of cath-D expression in human adipocytes. We observed the up-regulation of cath-D during adipogenesis in a primary culture of preadipocytes isolated from human sub-cutaneous adipose tissue. Interestingly, cath-D expression has also been shown to be markedly increased during the differentiation process in primary cultures of brown adipocytes [START_REF] Moazed | Differentiation-dependent expression of cathepsin D and importance of lysosomal proteolysis in the degradation of UCP1 in brown adipocytes[END_REF].

Our report highlights that cath-D silencing by shRNAs in 3T3-F442A preadipocytes leads to lipid-depleted cells, and to a reduction of the expression of PPAR, HSL and aP2 adipocyte markers of differentiation, indicating the essential role of cath-D in the differentiation process of preadipocytes. Given that cath-D protein is required for adipocyte differentiation and as it is abundantly expressed in fully-differentiated adipocytes, we propose that cath-D may be involved in the onset of obesity. Moreover, murine cath-D deficiency led to the accumulation of cholesteryl esters in the brain, suggesting that cath-D may play a key role in lipid metabolism [START_REF] Mutka | Murine cathepsin D deficiency is associated with dysmyelination/myelin disruption and accumulation of cholesteryl esters in the brain[END_REF].

Taken together, our findings reveal that cath-D is up-regulated in tissues from obese humans and mice, and that it is a novel key regulator of adipogenesis. We propose that targeting cath-D in obesity could reduce the number of hypertrophic adipocytes and decrease adipocyte hyperplasia. In the future, we intend to investigate the mechanism(s) by which cath-D controls adipogenesis. Since experimental studies have demonstrated that adipocytes play a supportive role in breast growth [START_REF] Iyengar | Adipocyte-derived collagen VI affects early mammary tumor progression in vivo, demonstrating a critical interaction in the tumor/stroma microenvironment[END_REF][START_REF] Iyengar | Adiponectin/Acrp30, an adipocyte-specific secretory factor: physiological relevance during development[END_REF][START_REF] Manabe | Mature adipocytes, but not preadipocytes, promote the growth of breast carcinoma cells in collagen gel matrix culture through cancer-stromal cell interactions[END_REF], and as clinical studies have shown that obesity increases the incidence of breast cancer [1,2,3], we will analyse the role of cath-D upregulation in obese adipocytes with regard to cancer.

Materials and Methods

Ethics Statement. All subjects gave their informed written consent to participate to the study.

Our protocol is using adipose tissues from plastic surgery considered as "waste", and we thus do not need a specific agreement. However the study was performed accordingly to the declaration of Helsinki as revised in 2000 (http://www.wma.net/e/policy/b3.htm) and approved by the Ethical commitee of the Rangueil hospital (Toulouse, France) with permit number 07/858/03/07. Mice were handled in accordance with National Institute of Medical Research (INSERM) principles and guidelines. C57Bl6/J female mice were obtained from Charles River laboratory (l'Arbresle, France). Philippe Valet, with the license number # 31-147 given by the French government, performed the experiments on the animals. This study was approved by the ethics committee of Midi-Pyrénées (France) with the permit number MP/01/01/01/2010.

Cells and cell culture

Cell lines were cultured in DMEM (Invitrogen) supplemented with 10% fetal calf serum (FCS). Differentiation was induced by incubating confluent 3T3-F442A cells in differentiation medium (DMEM supplemented with 10% FCS and 50 nM insulin) as described [START_REF] Prawitt | Characterization of lipid metabolism in insulin-sensitive adipocytes differentiated from immortalized human mesenchymal stem cells[END_REF]. Differentiation was induced by incubating 3T3-L1 confluent cells in differentiation medium (DMEM supplemented with 10% FCS and 10 µg/ml insulin, 250 µM isobutylmethylxanthine, 1 µM rosiglitazone, 1 µM dexamethasone).

RNA extraction and analysis

Total RNA was extracted using the Reasy minikit (QIAGEN Sciences, Maryland) according to the manufacturer's instructions. Reverse transcription of total RNA was performed at 37°C using Moloney murine leukemia virus reverse transcriptase enzyme (Invitrogen, Carlsbad, CA) and random hexanucleotide primers (Promega, Madison, WI). Quantitative PCR was carried out by real-time PCR using a LightCycler and the DNA double-strand-specific SYBR green I dye for detection (Roche, Basel, Switzerland). Results for mouse RNA were normalized to RS9 levels. For human RNA, analysis of the 18 S ribosomal RNA was performed in parallel using the ribosomal RNA control Taqman Assay Kit (Applied Biosystem) to normalize gene expression.

The sequences of the primers were: All subjects were drug-free, and were not suffering from any disorder other than obesity. Tissue samples were immediately frozen in liquid nitrogen, and stored at -80°C. Total RNAs were extracted from isolated adipocytes, and their cath-D expression analysed by RT-PCR.

For in vitro differentiation, human preadipocytes were isolated from human subcutaneous adipose tissue obtained from patients undergoing abdominal lipectomy in the plastic surgery department of Rangueil Hospital (Toulouse, France) with the approval of the locals Ethic Committee. All subjects gave their informed written consent to participate in the study.

Adipose tissue fragments were immediately used for collagenase digestion, as previously described [START_REF] Bour | Adipogenesis-related increase of semicarbazide-sensitive amine oxidase and monoamine oxidase in human adipocytes[END_REF]. The digestate was centrifuged to separate the adipocytes from the stromavascular fraction, which contained preadipocytes (pellet). Cells isolated from the SVF fraction were induced to differentiate into adipocytes as previously described [START_REF] Gesta | Culture of human adipose tissue explants leads to profound alteration of adipocyte gene expression[END_REF]. Briefly, confluent cells (day 0) were induced to differentiate in DMEM/Ham's F12 (1:1) medium containing 0.01 mg/ml transferrin, 100 nM cortisol, 0.2 nM triiodothyronine, and 20 nM insulin. To trigger differentiation, 25 nM dexamethasone, 500 mM IBMX and 2 mM rosiglitazone were included from day 0 to day 4. Intracellular accumulation of lipid droplets became clearly evident at day 10 [START_REF] Bour | Adipogenesis-related increase of semicarbazide-sensitive amine oxidase and monoamine oxidase in human adipocytes[END_REF].

Mice

Mice were handled in accordance with National Institute of Medical Research (INSERM) principles and guidelines. C57Bl6/J female mice were obtained from Charles River laboratory (l'Arbresle, France). Mice were housed conventionally in an animal room at constant temperature (20-22°C) and humidity (50-60%), and with a 12 h light-dark cycle. All the mice had free access to food and water throughout the experiment. The C57Bl6/J mice were assigned to a normal diet (ND) or high-fat diet (HFD) (SAFE, France). The energy contents of the diets were as follows: 20% protein, 70% carbohydrate, and 10% fat for the ND; and 20% protein, 35% carbohydrate, and 45% fat for the HFD. The main source of fat in the HFD was lard (20 g/100g of food). C57Bl6/J mice (initially 10 weeks old) were fed an ND or HFD for 20 weeks. A 20 weeks period of HFD is used to mimic the slow development of obesity in humans associated with the settlement of insulin resistance and low grade inflammation. All the mice were sacrificed at 30 weeks of age.

Isolation of adipocytes from mouse adipose tissue

Mouse intra-abdominal adipose tissues were dissected immediately after sacrifice, minced in 5 ml of Dulbecco's modified Eagle's medium (DMEM; Life Technologies, Inc., Invitrogen, Paisley, UK) supplemented with 1 mg/ml collagenase (SIGMA) and 1% BSA for 30 min at 37°C while shaking. Digestion was followed by filtration through a 150 µm screen, and the floating adipocytes were separated from the medium containing the stroma-vascular fraction

(C) Effect of increasing doses of insulin on cath-D expression in adipocytes. 3T3-F442A

adipocytes differentiated for 10 days were treated with increasing doses of insulin (6.25 nM to 50 nM) in 0.5% or 1% FCS for 24h. Cath-D protein expression was analysed by immunoblotting. ERK2 served as loading control.

Figure 5. Expression of cath-D during adipogenesis in human

  , panel a). As illustrated in Figure 6B (panel b), detection of neutral lipid by oil red O staining after 7 days of differentiation revealed that C34 and C37 clones accumulated numerous large lipid droplets and adopted the non-adherent, round morphology characteristic of mature 3T3-F442A adipocytes. In contrast, in A4 and D10 clones silenced for cath-D, the lipid droplets were markedly smaller and fewer in number (Figure 6B, panel b). A4 and D10 clones retained the morphology of adherent fibroblastic cells, suggesting that the preadipocyte differentiation process did not occur in the absence of cath-D (Figure 6B, panel b). Quantification of lipids demonstrated that silencing cath-D in A4 and D10 clones resulted in significantly lower lipid content at day 7 of differentiation than in the C34 and C37 control clones (Figure 6B, panel c). We finally analysed the expression of PPAR, HSL and aP2 adipocyte differentiation markers in Luc and cath-D shRNA-transfected 3T3-F442A clones at day 7 of differentiation (Figure 6B, panel d). Cath-D silencing was associated with inhibition of PPAR, HSL and aP2 mRNA levels (Figure 6B, panel d). Taken together, these findings indicate that cath-D silencing in preadipocytes inhibits adipogenesis, leading to lipid-depleted cells.

  cath-D (5'TTGCTGTTTTGTTCTGTGGTTTTC', reverse 5'CAGACAGGCAGGCAGCATT3'). Stable transfection of shRNAs in 3T3-F442A cells 3T3-F442A cells were transfected with 1 µg of shLuc, anti-cath-D shRNA1 or shRNA2 expression vectors (Invivogen) using Nucleofector Technology (Amaxa biosystems) according to the manufacturer's instructions and 40 clones resistant to Blasticidin (4 µg/ml) were isolated. Clone D10 transfected with anti-cath-D shRNA1 and clone A4 transfected with anti-cath-D shRNA2 were the best clones selected for cath-D silencing. Adipocytes were washed with phosphate-buffered saline (pH 7.4) and then fixed with Antigenfix (Diapath, Italy). Cells were stained with Oil Red O dye (saturated Oil Red O dye in six parts of isopropanol and four parts of water), an indicator of cell lipid content, and then exhaustively rinsed with water. Spectrophotometric quantification of the stain was performed by dissolving the stained oil droplets in the cell in isopropanol and measuring their absorbance at 540 nm. Human samples Human adipose tissue was collected according to the guidelines of the Ethical Committee of Toulouse-Rangueil and Nancy J. d'Arc Hospitals and with the full ethical approval of the Ethical Committee of Toulouse-Rangueil and Nancy J. d'Arc Hospitals. All subjects gave their informed written consent to participate in the study. Human abdominal visceral (VAT) adipose tissue and human subcutaneous adipose tissue (SAT) samples were obtained from 9 healthy volunteer patients (42.7 +/-4.5 yr old, BMI: 23.1 +/-3.3 kg/m 2 ) undergoing cosmetic abdominal lipectomy. No clinical data from these patients were available. Human VAT adipose tissue samples were obtained from 27 morbidly (grade-III) obese subjects (44.5+/-1.8 yr old, BMI: 47.6 +/-1.3 kg/m 2 ) before they underwent bariatric surgery.

Figure 1 .

 1 Figure 1. Cath-D expression is up-regulated in adipose tissues from obese human beings

Figure 2 .

 2 Figure 2. Cath-D expression increases during 3T3-F442A adipogenesis

Figure 3 .

 3 Figure 3. Cath-D expression increases during 3T3-L1 adipogenesis

Figure 4 .

 4 Figure 4. Effect of insulin on cath-D expression in NIH-3T3 fibroblasts and 3T3-F442A

(SVF). Adipocytes were washed twice in DMEM, and then processed for RNA extraction using the RNeasy mini kit (Qiagen, Germany).

Immunoblots

Cells were lysed in lysis buffer (50 mM HEPES pH 7.5, 150 mM NaCl, 10% glycerol, 1% Triton X100, 1.5 mM MgCl 2 , 1 mM EGTA, 100 mM NaF, 10 mM NaPPI, 500 µm Na-Vanadate, 1 mM PMSF, 10 µM Aprotinine, and a protease inhibitor cocktail). After shaking gently for 20 min at 4°C, cell extracts were obtained by centrifugation in a microfuge at 13,000 rpm for 15 min at 4°C. Equal amounts of protein (100 μg) from cell extracts, quantitated by the Bradford assay, were separated on a 7% gel by SDS-PAGE. Proteins were electro-transferred to a PVDF membrane, and then incubated with 1 µg/ml anti-mouse cath-D (Santa Cruz Biotechnology), 1 µg/ml anti-human cath-D (BD Biosciences), 1 μg/ml anti-α tubulin (Lab Vision Corporation), 1 µg/ml anti-actin (Sigma), 1 µg/ml ERK2 (Santa Cruz Biotechnology), or 0.4 µg/ml anti-HSL (Santa Cruz Biotechnology). Proteins were visualized with horseradish peroxidase-conjugated sheep anti-mouse immunoglobulin (ECL Amersham) or horseradish peroxidase-conjugated rabbit anti-goat immunoglobulin (ECL Amersham) followed by the Renaissance chemiluminescence system (Perkin Life Sciences).

Statistical analysis.

Results are expressed as means ± SEM. Statistical differences between two groups were evaluated using Student's t tests. The level of significance was set at P < 0.05.

(A) Micrographs of human adipocytes. Human preadipocytes isolated from subcutaneous adipose tissue digested with collagenase and separated from the stromal vascular fraction were grown for 0, 3, 7 and 14 days in the presence of the adipogenic medium as illustrated in the micrographs. A representative experiment is shown.

(B) Cath-D expression during adipogenesis. Protein expression of cath-D and HSL was analysed by immunoblotting after the indicated time following induction of the differentiation process (panel a). Ku70 was used as loading control, as previously described [START_REF] Meulle | Positive regulation of DNA double strand break repair activity during differentiation of long life span cells: the example of adipogenesis[END_REF]. One representative experiment out of 2 is shown.


Guo Hong

Veronique Letort

Hong Lingxia

Fourcaud Thierry

Cournede Paul-Henry

Lu Yuanchang

De Reffye Philippe

Adaptation of the GreenLab model for analyzing sink-source relationships in Chinese Pine saplings

Since the 1990s, a new generation of models has emerged to simulate tree growth with consideration of both tree structure and functional processes. However, calibration of these functional-structural models (FSMs) often remains an open problem due to the topological complexity of trees and to the heavy measurements required. In this paper, we explore a possible way for dealing with the fitting problem, based on the GreenLab model approach.

Detailed organ-level data including topological and geometrical measurements were collected on eight Chinese Pine saplings (Pinus tabulaeformis carr.) grown near Beijing. Adaptation of GreenLab to introduce a flexible modeling for biomass allocation to ring growth is presented. The main assumptions, such as allometry rules and sink relationships, were investigated. The problem of calibration of a complex branching structure was solved by defining an average tree. The results were interpreted with particular focus on the ones concerning the hidden mechanisms of secondary growth.

Introduction

Pinus tabulaeformis Carr., also called Chinese pine, is the most widespread temperate coniferous species [START_REF] Luo | Productivity distribution patterns and modeling of Pinus tabulaeformis forest in china[END_REF] and grows in over 10 provinces in China. As it is one of the most important ornamental conifers used for reafforestation, many studies have been carried out on this species, including forest management, ecology and genetics aspects. Mathematical simulation of individual growth was developed with structure information [START_REF] Han | Mathematical simulation of individual tree growth of Pinus tabulaeformis[END_REF]. In most studies, the biomass of an individual tree, the biomass of stands and its net primary productivity were considered on the basis of statistical analysis of measurement data [START_REF] Dong | Studies on productivity of Pinus tabulaeformis stands in Taiyue mountain, Shanxi province[END_REF][START_REF] Ma | A Study on the Biomass of Chinese Pine Forests[END_REF]. However, considering both structure and biomass points of view can help to understand the growth process and biomass allocation of this species. For example, to simulate key processes such as light interception [START_REF] Soler | An efficient instantiation algorithm for simulating radiant energy transfer in plant models[END_REF] [START_REF] Sinoquet | Foliage randomness and light interception in 3-D digitized trees : an analysis from multiscale discretization of the canopy[END_REF] or competition for resources (light, water, nutriments) inter and intra trees, it is crucial to take into account the tree branching architecture. This is why functional-structural models have recently emerged [START_REF] Sievänen | Components of functionalstructural tree models[END_REF]. They aim at combining organogenesis and photosynthesis, organs playing their true roles as sources and sinks for biomass during the development process. However, validation and calibration of these models remains an open problem and often relies on qualitative observations or on global scale variables such has crown diameter or total biomass. Moreover, the large stochastic variability of branching patterns of a same species in given environmental conditions is a major obstacle to fit the precise architecture of a tree. For example, the LIGNUM model [START_REF] Perttunen | Application of the functional-structural tree model LIGNUM to sugar maple saplings (Acer saccharum Marsh) growing in forest gaps[END_REF] was parameterized on young Scott Pines and Jack Pine using parameter values from bibliography or estimated by fitting global scale variables and the validation was done only on height and trunk diameter. The EMILION model [START_REF] Bosc | EMILION, a tree functional-structural model: presentation and first application to the analysis of branch carbon balance[END_REF] simulates very precisely physiological processes such as maintenance and growth respiration or biomass fluxes at the organ level for maritime pines but the parameterization of the corresponding equations are taken from the literature and are not necessarily available for other species. Although this kind of approach provides powerful methods to analyze the inside processes such as the causes of axes death, it is not suitable for integration in support decision systems for forest management, since data concerning micro-climate and geometrical shape at organ level are almost impossible to get for a large number of individuals.

In this paper, a simplified approach of tree simulation is presented and illustrated on eight young Chinese pines. This approach relies on the GreenLab model [START_REF] De Reffye | The dynamic equations of the tree morphogenesis: GreenLab Model[END_REF] that was developed in LIAMA (Laboratory of Computer Sciences, Automation and Applied Mathematics, Beijing, China) and that is oriented to be a functional-structural model for agronomy and forestry applications [START_REF] Hu | GreenLab: A new Methodology towards Plant Functional-structure Model-Structural Aspect[END_REF]. Its main characteristic is to extract some relevant assumptions to simplify the tree growth simulation and calibration, thus opening the way to deal with tree complexity [START_REF] Cournède | Structural factorization of Plants to Compute their Functional and Architectural Growth[END_REF]. In agronomy, it has been calibrated on many crops such as maize [START_REF] Guo | Parameter optimization and field validation of the functional-structural model GREENLAB for maize[END_REF], sunflower [START_REF] Guo | Modeling of biomass acquisition and partitioning in the architecture of sunflower[END_REF] or tomato [START_REF] Dong | Tomato Growth Modeling Based on Interaction of its Structure-Function[END_REF]. These examples illustrate the generic property of the model but they all deal with plants with simple architecture. However, thanks to its automaton-based organogenesis process [START_REF] Zhao | Interactive simulation of plant architecture based on dualscale automaton model[END_REF], GreenLab can simulate complex architectures as well and the use of a substructure factorization algorithm [START_REF] Cournède | Structural factorization of Plants to Compute their Functional and Architectural Growth[END_REF] speeds up dramatically the simulation, which is a key point for any fitting process at whole tree level. In recent developments of the model, influence of photosynthesis on organogenesis has been introduced [START_REF] Rostand-Mathieu | A dynamical model of plant growth with full retroaction between organogenesis and photosynthesis[END_REF][START_REF] Rostand-Mathieu | Essai sur la modélisation des interactions entre la croissance et le développement d'une plante : cas du modèle GreenLab[END_REF], allowing realistic simulations of tree growth depending on a global environmental factor. In our preliminary study, only the deterministic version of the model was used to fit the source-sink balance of the Chinese pine saplings, that is to say neither stochastic nor environment-driven variations were included.

In the way to extend the application area of the GreenLab model to forestry field, particular attention was given to secondary growth modelling, which is the kernel of any model aiming at simulating tree growth. A pioneer work was realized by Mitchell et al. [START_REF] Mitchell | Dynamics and simulated yield of Douglas-fir[END_REF] on Douglas-fir: they took into account crown competition through their projected surface and stipulated that radial growth increment is proportional to the number of leaves above the ring position in the tree. Then Houllier et al. [START_REF] Houllier | Linking growth modelling to timber quality assessment for Norway spruce[END_REF] adapted that model to spruce (CEP). The LIGNUM model incorporates the pipe theory [START_REF] Shinozaki | A quantitative analysis of plant form -the pipe model theory I. Basic Analysis[END_REF] to relate the thickness increment in the main stem to the above living foliage. Recently, some attempts have been made to bridge the gap between process-based models and structural models that output global relationships between radial growth and crown size [START_REF] Ottorini | Relationships between crown dimensions and stem development in Fraxinus excelsior[END_REF][START_REF] Pouderoux | Analysis of crown efficiency in a Common Beech thinning trial using a process-based model[END_REF]. Deleuze and Houllier [START_REF] Deleuze | A flexible radial increment taper equation derived from a process-based carbon partitioning model[END_REF] used a reactiondiffusion model for radial growth but it was not related to the crown structure and to the assimilate allocation to the whole tree. In this paper, by referring to those concepts, a new way to simulate secondary growth is introduced: first, biomass is allocated to a global pool for rings, depending on the current vigor state of the tree, and then this biomass is distributed all over the tree with respect to its architecture through an extension of the Pressler law. This method allows overcoming the often-stated limitations of the widely used Pressler law [START_REF] Deleuze | A flexible radial increment taper equation derived from a process-based carbon partitioning model[END_REF].

This paper presents an adaptation of GreenLab to explore the possibilities of tree source-sink calibration. We tested and partially validated some of the basis hypotheses of the model such as allometric relationships and constant sinks on the Chinese pine saplings.

Model and main hypotheses 2.1. Organogenesis based on botanical rules

Studies on tree architecture were initiated in 1978 by the botanists Francis Hallé et al. [START_REF] Hallé | Tropical trees and forests[END_REF] who defined 23 architectural models that represent tree development. Plants can be considered as a set of basic botanical units, called metamers, made of one internode and axillary buds that give birth to leaves, fruits and axes. Pine tree growth is rhythmic with a period of one year, called growth cycle (GC), which is the time step of the model: all growth variables are integrated at this time scale. The number of growth cycles since the appearance of an organ or an axis is called its chronological age (CA). The succession of metamers appearing during one growth cycle is called a growth unit (GU). Axes are sorted into categories according to their physiological age (PA), which are defined based on the differentiation states of their apical meristem. Each class is defined by the structure of its GU (acrotony, fruit presence...), as presented in Barthélémy and Caraglio [START_REF] Barthelemy | Plant architecture: a dynamic, multilevel and comprehensive approach to plant form, structure and ontogeny[END_REF]. All axes of same PA have the same set of parameters, driving allometry and functioning rules.

In the analysis of Chinese pine, for sake of simplicity, a GU was regarded as a single virtual metamer and the needles in one GU were considered as a single virtual leaf. The axis PA was defined according to its branching order: axis of PA 1 (the main stem) bear axes of PA 2, axes of PA 2 bear axes of PA 3 and so on.

Biomass production and allocation

Biomass production and allocation are calculated at each GC based on sink-source relationships between the organs in the plant. The sources include biomass from the seed (available at the first cycles only) and the production of biomass by the leaves through photosynthesis. This production is set up based on the transpiration law of plant and an empiric relationship adapted from Beer-Lambert law to simulate the effects of self-shading in an isolated plant [START_REF] Howell | Relationship of dry matter production of field crops to water consumption[END_REF]. The amount of biomass Q(i) generated by the green needle surface S(i) at GC i can be expressed by Eqn (1):

                ⋅ - - ⋅ = p p S i S k r S i E i Q ) ( exp 1 ) ( ) ( (1).
r is defined as the hydraulic resistance of the plant to transpiration [START_REF] Guo | Parameter optimization and field validation of the functional-structural model GREENLAB for maize[END_REF], E(i) is the average potential environmental factor during GC i. Sp is the total ground projection area available for the plant, as defined in [START_REF] Wilson | Analysis of light interception by single plants[END_REF], and k is a parameter taking into account leaf inclination.. GreenLab assumes that this biomass is gathered in a common pool and then allocated to the living organs (internodes, needles, rings, and fruits) that compete according to their sink strength to get it, regardless to their position on the tree. The total demand of the plant consists of two parts: demand for buds and demand for ring compartment Drg(i). For an organ o of PA k, with sink strength Po, the biomass acquisition ) , ( i k q o ∆ at GC i can be described as:

{ } ∑ ∈ + - ⋅ = ∆ e a o rg o o o o i D i k N k P i Q k P i k q , ) ( ) , ( ) ( ) 1 ( ) ( ) , ( (2)
whith Q(i-1) the total biomass production at GC i-1, Drg(i) the demand of rings at GC i and where o represents indices for organ types (needles: a; internodes: e). No(k, i) is the number of organs belonging to category o at GC i and PA k. For trees, a major assumption of the model is that the organ expansion can be considered as immediate since it lasts less than one GC and is of short duration compared to the GC duration (one year). Thus this sink strength can be regarded as constant, which implies that the ratio between newly created needles and internodes should be constant.

Secondary growth

In standard conditions, it has been observed that tree primary growth in height take precedence over their secondary growth [START_REF] Lanner | On the insensivity of height growth to spacing[END_REF]. To simulate this behaviour, it is assumed that the ring compartment can play a buffer role: its demand Drg depends on available supply and demand of biomass at GC i :

) ( ) 1 ( ) ( 1 i D i Q P P i D O rg - ⋅ + = (3)
where P0 is the constant sink (dimensionless) of the rings compartment and P1 is the corresponding slope per mass unit (g -1 ). D(i) is the total demand of the plant at GC i.

Biomass allocated to the ring pool Qrg is proportional to its demand and to the ratio Q/D. From this pool, biomass is partitioned to the ring of each internode individually, through two possible modes: the common pool mode and the Pressler [START_REF] Assmann | Vorläufige Fichten-Ertragstafel für Bayern[END_REF] mode.

In the common pool mode, biomass for all the rings in the whole tree at GC i goes to a common pool and then reallocation to each new ring is done according to its PA k and to its length l(k,i). It is represented as:

∑ = ⋅ ⋅ = m PA k rg i pool i k l k p i k N i D 1 ) , ( ) ( ) , ( ) ( (4)
where PAm is the maximal PA in the tree, l(k,i) is the length of the Ni(k,i) internodes of PA k on plant of CA i and prg (k) is the linear density of sink of rings for internodes of PA k. In the Pressler mode, the biomass going to each ring is proportional to the number of leaves above it in the branching structure [START_REF] White | Relationships between foliar number and the cross-sectional areas of sapwood and annual rings in red oak (Quercus rubra) crowns[END_REF]. It means that each leaf gives its biomass production to a "pipe" [START_REF] Shinozaki | A quantitative analysis of plant form -the pipe model theory I. Basic Analysis[END_REF] running until the bottom of the tree and the demand of this pipe is proportional to its length. With the same notations, it can be expressed as in Eqn ( 5):

∑ ∑ = ∈ ⋅ ⋅ = m k PA k rg P p a pressler i k l k p p i k N i D 1 ) , ( ) ( ) , , ( ) ( (5)
where Na (k,i,p) is the number of leaves at GC i above the considered internode at PA k and whose position in the tree architecture is represented by p. Pk is the set of possible positions p of metamers of PA k in the whole plant of age i. It has been reported in some cases [START_REF] Deleuze | A flexible radial increment taper equation derived from a process-based carbon partitioning model[END_REF][32] that the Pressler rule is affected by environmental changes or throughout the tree growth and that it does not represent buttress formation. So a parameter λ (0 ≤ λ ≤ 1) allows mixing the two modes together, assuming that they can have combined effects with different degrees in different species during biomass partitioning to each new ring. Thus the biomass qrg given to the new ring of an internode of PA k and position p at GC i is: [START_REF] Sinoquet | Foliage randomness and light interception in 3-D digitized trees : an analysis from multiscale discretization of the canopy[END_REF] where the parameter definitions are the same than in Eqn (3)-Eqn(5).

) ( ) , ( ) ( ) ) ( ) , , ( ) ( 1 ( ) , , ( i Q i k l k p i D p i k N i D p i k q rg rg pressler a pool rg ⋅ ⋅ ⋅ + - = λ λ

Allometries for organ shape

Since, the model variables are biomass increments, the organ shape is derived from its current mass using simple allometric rules. The fresh matter of an internode consists of two parts: the pith (primary growth) and the rings (secondary growth). The pith is regarded as a perfect cylinder and the relationship giving the length l(k, i) from the pith mass at GC i and PA k is estimated as in Guo et al. [START_REF] Guo | Parameter optimization and field validation of the functional-structural model GREENLAB for maize[END_REF]. [START_REF] Sievänen | Components of functionalstructural tree models[END_REF] where qe(k,i) is the fresh matter available at GC i for the internode of PA k and be and β are shape coefficients which are fitted from measurements of the GU lengths and fresh masses, assuming here that pith wood density is constant (Figure 1). For secondary growth, the thickness of the new ring of a GU depends on the allocated quantity of biomass to build it: a new layer is added on the initial cylinder.

β + ⋅ = i k q k b i k l e e
Concerning needle active surface area, the functioning of the needles of one GU is considered to be the same as the one of a single virtual leaf whose thickness ε is constant. The leaf surface area is related to leaf mass qa.according to Yang and Yang [START_REF] Yang | Studies on biomass and productivity of Pinus tabulaeformis plantation in the Wufengshang of Wudu, Gansu Province[END_REF]:

a a q S ⋅ = 4176 . 12 (8)

Data Analysis

Tree materials

The eight Chinese pine sapling's data included two trees of one-year-old, two-year-old, three-year-old trees and five-year-old respectively. They were taken from the nursery garden which is open area in Shisanling forest farm, Beijing (39°50′N,116°25′E) in the spring of 2006.

In these experiments, the generative organs were not considered. For each metamer, GU length and GU diameter, needle fresh mass and internode fresh mass were measured. The needles functioning time [START_REF] Guo | Parameter optimization and field validation of the functional-structural model GREENLAB for maize[END_REF] was set to 3 GC since no needles were found on GU older than 3 years.

Parameters estimated from data

Concerning our Chinese pine saplings, several types of input parameters can be calculated directly from the measurements.

Internode Allometry.

From the measurement of fresh mass and length of internodes located at tips of axes of each PA (when secondary growth can be considered as negligible), the parameters be and β needed in Eqn.7 can be estimated for each PA (Figure 1). The detailed results can be seen in Table 1 (logarithmic scale). The R 2 coefficient ranges from 0.76 to 0.94, confirming the choice for the relationship between internode mass and internode length for Chinese Pine saplings. Figure1. Internode Allometry

Internode and needle sinks.

As explained in the first part, assuming that needles and internodes on the newly created tips of axes expand immediately implies that their sink ratios can be measured directly. It means that there should be a simple proportionality between internode and needle mass on the newly created GU (Eqn. 2), the proportionality ratio being the sink value. Thus the sink of an organ o of PA k is estimated as in Eqn (11):

) , 1 ( ) , ( ) ( i q i k q k P a o o = (11)
where o q (k,i) is the average mass of organ o of PA k that appeared at last GC i (the tip axes one) and where a q (1,i) is the average needles fresh mass on the tip of the main stem. The sink of the needles on the main stem (PA 1) is the reference and is arbitrarily set to 1 so sinks for all the other organs with different PA are relative values. The sink values are gathered in Table 1. To test the assumption of constant sink ratios, the needle mass is drawn with regard to internode mass of the same GU (Figure 2). It reveals that there is a good linear relationship between needle mass and internode mass of GU of axis tips for each PA (R 2 coefficient ranges from 0.7 to 0.93). It implies that the assumption of constant sink ratios is reasonable.

Table1. Sinks and Allometric coefficients

Figure 2. Internodes and needles mass ratio

Moreover, from the slope coefficients of figure 2, it can be observed that the average ratio of needle mass over internode mass increases with PA of the GU. It means that for Chinese pine saplings, the allocation to internodes decreases with branching order to the benefit of needles.

Hidden parameters: fitting methods and results

Tree topology

For each tree, an average topology (axes numbers per whorl, GU numbers per axis) was defined according to the substructure factorization algorithm implemented in GreenLab to speed up simulation. The algorithm consists of a multi-scale factorization of the parts that replicate several times in the branching system. It is based on the botanical observations given in part 2.1and [START_REF] Barthelemy | Plant architecture: a dynamic, multilevel and comprehensive approach to plant form, structure and ontogeny[END_REF]. It reduces drastically the simulation time -since each structure having given physiological and chronological ages is computed only once -but still allows realistic outputs.

Concerning the functional data, metamer fresh weights (needles and internodes) were averaged for each axis type and length and diameter were kept from the measured axis that was the closest from the average one. Thus a target file could be built in the same way as described in Guo et al. [START_REF] Guo | Parameter optimization and field validation of the functional-structural model GREENLAB for maize[END_REF]. The axes were identified by their PA and CA. They were described GU by GU with internode weight, length and diameter and needle weight. The target files included the eight trees. They were gathered in categories based on their axes numbers on the main stem so that it could be assumed that trees with the same topology were in fact repetitions of the same tree at different ages. Thus it can be considered that the target file includes data from only three trees at different growth stages.

Hidden parameters: calibration of the model

The hidden parameters of GreenLab are more difficult to calibrate since they are all linked through the dynamical mechanisms of the model and each of them can have a complex influence on all the outputs. So, even if the data concerns different types of organs and are of different ranges of orders, all of them have to be considered together in the fitting procedure. For the eight young trees, the target files included about 60 items of GU data. A same set of parameters should fit dynamically the three growth trajectories, since the trees were assumed to share the same species-specific parameters and to differ only on their topological structure and biomass seeds. To solve this inverse problem [START_REF] Zhan | Fitting a structuralfunctional model with plant architectural data[END_REF], the nonlinear generalized least square method was implemented in the Digiplante software [START_REF] Cournède | Structural factorization of Plants to Compute their Functional and Architectural Growth[END_REF].

For Chinese pine saplings, only five parameters remained to be fitted: the coefficient for needle resistance r, the sink strength of rings and the corresponding slope, P0 and P1, the parameter λ driving the biomass repartition from the ring biomass pool and the linear density of sink of rings for internodes of PA 2. This sink linear density is found negligible for internodes of PA 3 and PA 4. Since there was very few axes overlapping on the measured young trees, Sp had too little influence on estimating the Q(i) in Eqn 1and could be set to one. Calibration results are gathered in Table 2. Figure 3 shows the comparison between calibrated and measured data for some of the outputs, the axis scale being logarithmic whenever required by the large order range of the data. The fitting graphs represent cumulated internode (3a) and needle mass (3b) of the tree at each GC (from year 1 to year 5), internode mass (3c) and diameter (3d) GU by GU on the main stem, internode (3e) and needle (3f) mass on each GU of the branches for each PA. On figures 3e and 3f, each x-abscissa represents one branch of the tree and each point of this abscissa corresponds to one simulated (filled symbols) or measured (empty symbols) GU of the branch. On several PA 3 branches, data are missing, especially for needle mass, and are yet simulated.

The fitting of the compartment data had priority on the organ-by-organ one since it was used to set the initial values of the parameters that have a global effect (the resistance and the parameters defining the ring demand). Thus the total biomass evolution of the trees was reasonably well fitted, even if it can be noticed that the first stages were under-estimated. Although the fitting on branches is not perfect, in particular due to the large variability of data, the global trend of organ mass variation according to their age and position in the tree is correctly reproduced. The same set of parameters allows reproducing the growth trajectory of the three trees and more particularly of two quite different five-year old trees, the cumulated internode mass of the strongest one being more than four times higher than the second one. The only difference between these two simulated trees is their seed biomass (ranging from 0.4 to 1.4g) and their axis numbers for each PA. This is sufficient to get strong differences in the evolution of their Q/D ratio and thus to their radial growth. The parameters have high coefficient of variation values because the main sources of error are the topological structure and the sinks. Indeed, concerning rings, only data of five-year-old trees can help to discriminate the parameters. But our objective was to present a generic model so the parameters concerning biomass allocation to rings were kept. The fitting of the model allows estimating at the same time the biomass quantity allocated to secondary growth and the proportion of assimilate going up in the tree architecture, the rest of it being only authorized to be allocated in the part below the considered source. The small value of λ (=0.14) found for the pine saplings shows that there is almost uniform reallocation of rings biomass, i.e. the localization of biomass sources does not influence a lot the allocation. One purpose of the simulations with GreenLab model was to produce realistic Chinese pine saplings based on observation and measurement data. The calibrated parameters were used to simulate and visualize 3D representation of pine trees using the Digiplante software (Figure 4).

Simulation and Visualization

Discussion

Functional-structural model GreenLab has been previously tested on crops and other herbaceous but, even if tree simulation was already performing [START_REF] Cournède | Structural factorization of Plants to Compute their Functional and Architectural Growth[END_REF], it was the first attempt to calibrate it on tree functioning. The results on allometric rules revealed to be correct in view of the data on internodes (Figure 1). The assumption of immediate expansion, which implies a constant mass ratio between needles and internodes of a newly created GU, was in accordance with the data analysis (Figure 2). This hypothesis allows strong simplifications and is one of the bases of GreenLab. However, it needs to be tested on adult trees and to study whether shading and competitions have an effect on the sink ratios, which is highly probable [START_REF] Niinemets | Site fertility and the morphological and photosynthetic acclimatation of Pinus sylvestris needles to light[END_REF]. Further study is required to detect possible evolution of sink values or relationship between sink strength of an organ and its position within the tree.

Concerning secondary growth, we presented a model for biomass allocation to a ring compartment that depends on the current trophic state of the tree (through the Q/D ratio). Thus the resulting system is self-adaptive to environmental changes. The process of biomass partitioning in the tree structure is considered as an independent step. The introduction of parameter λ to mix the Pressler mode and Pipe mode brings more flexibility to the model of biomass partitioning for rings but there is always an affine relationship between ring increment surface and number of leaves above its position, as soon as the parameter λ is strictly positive. By calibrating the value of λ, the fitting procedure acts as a tool to analyze the allocation processes inside the trees. The value found was λ=0.14 for the Chinese saplings, which means there is almost uniform allocation of rings biomass. This results seems reasonable since the trees are still very young, but the fitting has few interest and cannot be considered as a validation of the model for the ring part, biomass allocation to ring being influent only in five year-old trees.

For saplings, the substructure factorization algorithm can seem unnecessary, but it allows simulating adult trees in a low computational time [START_REF] Rostand-Mathieu | A dynamical model of plant growth with full retroaction between organogenesis and photosynthesis[END_REF], which is a key condition to open access to any fitting procedure at organ level. However, the measurement protocol will need to be adapted to the structural complexity of older trees.

Further work still need to be done to complete this study and to deal with different environmental conditions and tree ages. However, this first work indicates that the basic hypotheses are relevant for Chinese pine trees. So this functional-structural model, based on botanical principles, has a good potential to describe tree growth and development.

Figure 3 .

 3 Figure 3. Multi-fitting results.

Figure 4 .

 4 Figure 4. 3D visualization of the one-year-old, three-year-old and five-year-old trees based on the fitted parameters.

Table 2 . Hidden parameter value

 2

	Name	Meaning	Value	CV(% )
	r	Needles resistance	0.64	3.5
	P0	Sink for ring pool	2.64 g	47.5
	P1	Slope for ring sink variation	0.77	41.6
	λ	Ring biomass allocation parameter	0.14	74.8
	prg(2)	Linear density of PA 2 ring sink	0.11	39.7

Acknowledgements

The authors thank the students and the colleagues from CAF involved in collecting the measurement data. This study was funded by National Natural Science Foundation of China (Grant No. 60073007 ; 30230290 ;60473110) and supported by Sino-French Laboratory for Computer Sciences, Automation and Applied Mathematics (LIAMA) in Beijing.


Véronique Letort
email: letort@mas.ecp.fr

Paul-Henry Cournede

Jérémie Lecoeur

Irène Hummel

Philippe De Reffye

Angélique Christophe

Effect of topological and phenological changes on biomass partitioning in Arabidopsis thaliana inflorescence: a preliminary model-based study

Although the existence of phenological impact on biomass partitioning in the plant is known for many species, it is difficult to quantify this effect and to unravel it from the complex functional processes that interact during plant growth. This work explores the variations of biomass allocated to fruits according to simple changes in the topological and phenological development of Arabidopsis thaliana plants. Four plants of the same genotype (ecotype Columbia) were grown in controlled conditions in growth chamber. Their topological differences were studied using the functional-structural model GreenLab. It showed that when fitting the four plants with a single set of parameters, but each plant being given its own topological structure, half of the biomass variability can be reproduced.

Introduction

The existence of a link between plant phenology and biomass allocation, and more particularly reproductive allocation is a well-known phenomenum for many plant species [1] [START_REF] Baker | Flowering phenology and sexual allocation in single-mutation lineages of Arabidopsis thaliana[END_REF] [START_REF] Routhier | Impact of tree leaf phenology on growth rates and reproduction in the spring flowering species Trillium erectum (Liliaceae)[END_REF]. For example, using single-mutation lineages of Arabidopsis thaliana, Baker et al. [START_REF] Baker | Flowering phenology and sexual allocation in single-mutation lineages of Arabidopsis thaliana[END_REF] found a pleiotropic covariation between flowering time and sexual allocation. However, this kind of relationship is often difficult to quantify. Moreover, it is crucial to unravel the complex influences of all the interacting processes: genetic or environmental, phenological or functional… This is where modelling can play a role. It provides a simplified framework to analyze plant growth and to test hypotheses.

In order to take into consideration topological variations between plants, models should be able to account for both architectural and functional developments [START_REF] Sievänen | Components of functional-structural tree models[END_REF]. GreenLab [START_REF] Yan | A dynamic, architectural plant model simulating resourcedependent growth[END_REF][6] [START_REF] Guo | Parameter optimization and field validation of the functional-structural model GREENLAB for maize[END_REF] is such a functional-structural model. It is a dynamic mathematical model that combines a description of plant architecture at the level of organs and computes biomass production and repartition among organs according to a source-sink approach.

This paper explores the variations of biomass allocation in the inflorescence of Arabidopsis thaliana (L.) Heynh. plants (ecotype Columbia) in relationship with topological variations. Although it is not a plant of agronomic interest, Arabidopsis is a perfect modelplant for this kind of study where the environmental and genetic backgrounds need to be carefully controlled. Moreover, its development is similar to other herbaceous ones (e.g. chrysanthemum, canola) so the procedures and the results can be generalized. We first present briefly the model specificities for Arabidopsis, integrating branching patterns. It was calibrated on average target data that were measured on four plants grown in controlled conditions, without environmental stress. The model was then used to investigate the influence of the topological structure of inflorescences on biomass partitioning. Indeed, the compartment demands depend on the number of organs that may appear or expand at each cycle. A sensitivity analysis can reveal which proportion of the biomass variability can be explained by this simple mechanism. In application, the ability of the model to fit the experimental data obtained on four plants with a single set of parameters is tested, plants differing only by their topological structures and elongation delays for the lateral axes of the inflorescences.

Materials and Methods

Experimental data

Four plants of Arabidopsis thaliana (L.) Heynh. plants, ecotype Columbia (Col-0), were grown in a growth chamber. Seeds were sown with a pipetman in plastic pots (9 cm high, 4.5 cm diameter) filled with a mixture (1:1, v:v) of a loamy soil and organic compost. The water content of the substrate was maintained at a constant level of 0.40 g.g -1 of dry soil. The photoperiod was 12h and light in the growth chamber was provided by a bank of a cool-white fluorescent tubes and sodium lamps. Mean daily cumulative photosynthetic photon flux density in the growth chamber was approx. 8 mol m -2 d -1 . Mean air temperature was 19.3 °C and air humidity was maintained at approximately 75%. Mean leaf-air vapour pressure deficit (VPD leaf-air) was calculated continuously during the experiment and maintained below 0.8 kPa.

From leaf emergence to the end of vegetative growth, the seedlings were photographed every 2-3 days to follow the rosette development. The projected leaf area was measured using image analysis software (Bioscan-Optimas V 4.10, Edmonds, WA). The rate of phytomer appearance, expansion duration and specific weight of each leaf were recorded from experiments in the same growth conditions (see [START_REF] Chenu | Integrated responses of rosette organogenesis, morphogenesis and architecture to reduced incident light in Arabidopsis thaliana results in higher efficiency of light interception[END_REF] and [START_REF] Granier | Individual leaf development in Arabidopsis thaliana : a stable thermal-time-based programme[END_REF]). The four plants were harvested when they had reached the stage 6.90, according to the specifications of Boyes et al. [START_REF] Boyes | Growth stage-based phenotypic analysis of Arabidopsis: a model for high throughput functional genomics in plants[END_REF]. Their topologies were recorded by counting and positioning the internodes, leaves and fruits on a schematic drawing. Note that the part situated above the lowest silica for each axis was considered as a single organ, called fruit hereafter. Their organs, including roots, were oven-dried at 80 °C for 4d and then weighted.

GreenLab model for Arabidopsis thaliana

The model.

GreenLab is a generic model of dynamic plant growth whose parameter values are species-dependent. It considers organogenesis, biomass production and allocation at organ scale. A detailed description can be found in [START_REF] Yan | A dynamic, architectural plant model simulating resourcedependent growth[END_REF], [START_REF] Mathieu | A dynamical model of plant growth with full retroaction between organogenesis and photosynthesis[END_REF] and [START_REF] Guo | Parameter optimization and field validation of the functional-structural model GREENLAB for maize[END_REF]. Some specific features were chosen for Arabidopsis modelling: (i) as the model is used as a tool to analyze the growth processes, observable parameters are input directly from the measurements (in particular for leaf projected area) and (ii) as Arabidopsis inflorescence has a branching architecture with top-down delays, this new topological feature is introduced.

The elementary units for the modelling of organogenesis are phytomers. They can be gathered into categories according to their physiological ages. The physiological age (PA) of a phytomer characterizes the state of differentiation of its apical bud [START_REF] Barthélémy | Plant architecture: a dynamic, multilevel and comprehensive approach to plant form, structure and ontogeny[END_REF]. Each category has its own set of physiological and topological parameters. Concerning Arabidopsis, the basal rosette has been chosen as PA 1 (short internode, one leaf and one lateral bud) and the inflorescence phytomers as PA 2 (long internode, one leaf, one lateral bud and potentially one fruit); see Figure 1.

The model time step is defined according to the thermal time between the appearances of two successive phytomers. Biomass production is computed at each cycle. It is set to be proportional to the projected leaf area, which was input directly from the measurements to avoid biases due to its calculation. The conversion coefficient (R) between absorbed light and produced biomass is a parameter of the model. At each time step, the topological structure of the plant is updated according to the chosen branching rules. The total demand of the plant can be computed as the sum of the individual sink strengths of all existing organs. The biomass increment of an organ is proportional to its sink strength and to the ratio of available biomass over the total demand.

We detail below So, the sink strength of an organ of type o, o in {b, i, f, r}, respective indices for blade, internode, fruit and root and of physiological age k. It depends on its chronological age i and on the axis it belongs to. An axis is characterized by its physiological age k and the growth cycle j it appeared at. The sink strength is thus written as:

) , , ( ) ( ) ( ) , , ( j i k d i f k P j i k S o o o o ⋅ ⋅ =
(1) where Po(k) is the sink reference value for organ o of PA k and fo(i) is an empiric function defining the evolution of the sink value according to its chronological age i. It is defined through three parameters that were estimated from the observations for each leaf rank: ao and bo defining the curve shape and Te which is the expansion duration. In Arabidopsis inflorescences, axes expand bottom-up, following the principle of apical dominance, as defined by Cline [START_REF] Cline | Concept and terminology of apical dominance[END_REF]. To model this feature, each axis of PA k appearing at cycle j is given a delay do(k,j) which is a parameter driving the sink emergence of organs belonging to this axis [START_REF] Kang | Building Virtual Chrysanthemum Based on Sink-Source Relationships: Preliminary Results[END_REF], as in Eq(2):

   ≤ = . 1 ) , ( 0 ) , , ( else
j k d i if j i k d o o (2)
Geometrical shape of organs is only needed for visualization purpose and have no effect in the model. It is set following simple allometric rules. A detailed study of organ growth rates in length can be found in [START_REF] Mündermann | Quantitative Modeling of Arabidopsis Development[END_REF] and geometrical modelling and 3D-visualization in [START_REF] Visser | 3D digitization and modeling of flower mutants of Arabidopsis thaliana[END_REF].

Identification procedure.

The software Digiplante, developed in the lab of applied mathematics at Ecole Centrale Paris [START_REF] Cournède | Structural factorization of plants to compute their functional and architectural growth[END_REF] was used to estimate the numerical values of GreenLab parameters from experimental data. A non-linear generalized least square algorithm was run; details can be found in [START_REF] Guo | Parameter optimization and field validation of the functional-structural model GREENLAB for maize[END_REF]. The types of observations are represented in figure 1, on a plant simulated with Digiplante software. They consist in individual organ weights for each phytomer of the main axis and cumulated data by compartment for the lateral axes. The average topology of inflorescences was simply defined as the average number of organs on each lateral axis. The number of phytomers in the basal rosette was assumed to be constant and the remaining leaves were set to belong to lateral shoots that did not reach their full expansion (only leaves were visible). As biomass weights were measured at compartment level for lateral axes, the average target can easily be defined. Figure 2 shows the fitting results for the fruit masses according to their positions in the inflorescence (the last one is that of the main shoot).

Results

Fitting on average target

Influence of phenological and topological changes on biomass allocation

As shown in Figure 2, there is a high variability in the measurements of fruit masses (up to 100% variation). Although the sources of variations are difficult to detect (the plants were of the same genotype and grown in the same controlled environmental conditions), it is interesting to explore which proportion of biomass variability can be explained by phenological and topological variability in the model. The sensitivity of the model outputs to changes in the inflorescence topology can be illustrated through the simulated results of Table 1. When several organs are concerned (e.g. for internodes on the main stem), the average value is given.

Table 1. Simulated biomass variation according to topological changes on lateral axes. Using the set of calibrated parameters, two simulations were run with respectively one more phytomer (case "+1") and one less phytomer (case "-1") on each lateral axis. The simulated allocation to the main biomass compartment was compared with the reference plant. As the fruit is borne by the last phytomer of each axis, the topological change induces a change in phenology: the lateral fruits appear at a different time (one cycle later than for the reference plant for case +1). The total biomass production is very slightly affected by topological changes in the inflorescence as it is mainly performed in earlier stages. Root and rosette compartments are not affected

PA 1

Lateral axes: By compartments : -total internode mass -total blade mass -fruit mass

Main axis:

For each phytomer : -blade mass -internode mass -fruit mass

PA 2

Target data either since they have almost finished their expansions when the changes occur. Although the variation of organ weights on the main axis is small, the trend is easily interpretable: increasing the appearance time of lateral fruits reduces the trophic competition that organs of the main axis have to face. The most important variations are to be seen on the lateral biomass compartments. A decrease of one phytomer induces an average increase of the fruit weight of 34%. This is the result of the combination of (i) a decrease in the global demand due to the lacking phytomers and (ii) a highest duration of expansion for the lateral fruits.

It is interesting to take advantage of this high variability of biomass to fit the four plants taking into account their own topological structures. The inflorescence topology was defined for each plant according to the records of the numbers of organs on lateral axes. Then delays were estimated for each axis independently by model inversion. All other parameters of the model were common to the four plants. Their values were found similar to the fitting results on average target (relative difference varies from 0.4% (for R) to 35% for fruit sink). Figure 3 presents the fitting results concerning fruit mass on lateral and main axes (logarithmic scale). In Figure 3A, there is only one simulated plant to be compared with four observed plants (dotted lines). In Figure 3B, there are four simulated plants sharing the same set of parameters except for their inflorescence topology. The linear regression results show that part of the fruit biomass variability among the plants can be reproduced with variability on organ numbers and appearance delays only. The average variance of measured fruit masses is 1.74 (10 -5 g 2 ) and the simulated one is 0.95: simulations with estimated parameter values and variations on topology and phenology of the lateral axes produce a variance of fruit biomass which is 52% of the observed one.

Discussion and conclusion

The model parameters were estimated using average target data and average topology. Then, the estimated parameters were used to simulate plants with topological differences in their inflorescence architectures. It revealed that a spatial and temporal difference of one phytomer in the lateral axes could induce a variation in mass of 34%. Then a new estimation was done on four plants sharing the same set of parameters and only differing by their topological structures. These topological differences explained 52% of the variance of observed data.

However, this study raises several problems. The first one is to determine the causes of the topological variations among plants that are from the same inbred line and growing in the same controlled conditions. It can be hypothesized that micro-climate fluctuations (hydric, light, temperature), or small differences in seed weight [START_REF] Houssard | The effects of seed weight on growth and competitive ability of Rumex acetosella from two successional old-fields[END_REF], seed dormancy or sowing depth [START_REF] Zheng | Effects of burial in sand and water supply regime on seedling emergence of six species[END_REF] could be the major factors.

Another problem is the determination of the exact axis delays: as they were not measured, they were estimated without constraints and thus their variability could be over-estimated compared to the real one. Instead of considering delays as input parameters of the model, a further step would be to link them to the functional state of the plant. As suggested in Mathieu et al. [START_REF] Mathieu | A dynamical model of plant growth with full retroaction between organogenesis and photosynthesis[END_REF], a possible way would be to link the delay determination to the ratio of biomass supply over demand. This global key variable of the model reflects the trophic competition during plant growth and may thus be chosen as the main variable driving plant plasticity.

[1] F. Roos, J. Quinn. "Phenology and reproductive allocation in Andropogon scoparius (Gramineae) popuations

Figure 1 .

 1 Figure 1. Plant architecture (with PAs) and target measurements to fit the model.

Figure 2 .

 2 Figure 2. Comparison between average target data (black symbols) and fitted values (white symbols) for fruit weights.

  main axis, averaged var. (%): +0.35 -0.45 Internode mass, lateral axes, averaged var.

Figure 3 .

 3 Figure 3. Identification results on fruit dry masses (g) for the average plant (A) and the four plants with their own topology and delays (B).

in communities of different successional stades". American Journal of Botany. 64(5): 535-540, June 1977.