MD Marcus J Kernt
email: marcus.kernt@med.uni-muenchen.de

Raffael G Liegl

Christoph Hirneiss

Aljoscha S Neubauer

Claudia S Alge

Armin Wolf

Michael W Ulbig

Anselm Kampik

Sorafenib Prevents Human Retinal Pigment Epithelium Cells from Light-Induced Overexpression of VEGF, PDGF, and PlGF

Keywords: AMD, bevacizumab, CNV, multikinase inhibitors, PDGF, PlGF, ranibizumab, sorafenib, VEGF

teaching and research institutions in France or abroad, or from public or private research centers.

Introduction

Exudative age-related macular degeneration (AMD) is a leading cause of visual deterioration and legal blindness in people over age 60 in developed countries [START_REF] Ehrlich | Age-related macular degeneration and the aging eye[END_REF] . Early stages of this disease are characterized by the formation of drusen and atrophic changes in the retinal pigment epithelium (RPE) [START_REF] Ehrlich | Age-related macular degeneration and the aging eye[END_REF] .

With progression of the disease, 10% of patients develop "wet" forms of AMD due to choroidal neovascularization (CNV) that often leads to a rapid loss of vision [START_REF] Ehrlich | Age-related macular degeneration and the aging eye[END_REF] . AMD is a multifactorial disease with several risk factors for development and progression, including ethnicity, gender, smoking, hypertension, genetics, diet, and sunlight exposure [START_REF] Ehrlich | Age-related macular degeneration and the aging eye[END_REF][START_REF] Cruickshanks | Sunlight and age-related macular degeneration. The Beaver Dam Eye Study[END_REF][START_REF] Cruickshanks | Sunlight and the 5year incidence of early age-related maculopathy: the beaver dam eye study[END_REF][START_REF] Tomany | Sunlight and the 10-year incidence of age-related maculopathy: the Beaver Dam Eye Study[END_REF] . CNV in the macular region often results in significant loss of central vision and high-resolution visual acuity and is the fundamental pathophysiologic process underlying this disease 5 6 . Without treatment, AMD can lead to irreversible loss of the ability to read, recognize faces, and drive 5 6 . Up-regulation of vascular endothelial growth factor (VEGF) is a major critical event in the development of CNV [START_REF] Aiello | Suppression of retinal neovascularization in vivo by inhibition of vascular endothelial growth factor (VEGF) using soluble VEGFreceptor chimeric proteins[END_REF] . Therefore, inhibition of VEGF is the main target of the currently used antiangiogenic agents in the treatment of AMD [START_REF] Aiello | Targeting intraocular neovascularization and edema--one drop at a time[END_REF] . The mechanism of action of these VEGF inhibitors (e.g., bevacizumab and ranibizumab) is blocking VEGF in the extracellular space and thereby preventing access to its receptor [START_REF] Van Wijngaarden | Inhibitors of ocular neovascularization: promises and potential problems[END_REF] . Studies have demonstrated that treatment of AMD with VEGF inhibitors is safe and effective [START_REF] Regillo | Randomized, double-masked, sham-controlled trial of ranibizumab for neovascular age-related macular degeneration: PIER Study year 1[END_REF][START_REF] Rosenfeld | Ranibizumab for neovascular age-related macular degeneration[END_REF][START_REF] Rosenfeld | Optical coherence tomography findings after an intravitreal injection of bevacizumab (avastin) for macular edema from central retinal vein occlusion[END_REF] . However, major prospective randomized trials revealed that despite an improvement in visual acuity, the neovascular tissue typically does not regress with VEGF inhibition alone and without continuous treatment often re-progression occurs 10 11 . The reason for this lack of sustained effect might be due to redundant pathways. Previous studies indicated that several angiogenic growth factors, including platelet-derived growth factor (PDGF) and placenta growth factor (PlGF), are overexpressed in the vitreous and retinas in proliferative retinal disease and play a crucial role in the development and progression of AMD [START_REF] Freyberger | Increased levels of platelet-derived growth factor in vitreous fluid of patients with proliferative diabetic retinopathy[END_REF][START_REF] Robbins | Platelet-derived growth factor ligands and receptors immunolocalized in proliferative retinal diseases[END_REF][START_REF] Schlingemann | Role of growth factors and the wound healing response in age-related macular degeneration[END_REF][START_REF] Witmer | Vascular endothelial growth factors and angiogenesis in eye disease[END_REF] . The reason for this could be that other molecular pathways remain active and binding VEGF in the extracellular space alone might have only limited effect on neovascular tissue. In addition, inhibition of a single molecule could induce a compensatory increase in stimulatory increase of alternative pathways. Sorafenib (Nexavar, BAY 43-9006) is an oral multikinase inhibitor, approved for the treatment of several forms of cancer [START_REF] Wilhelm | Preclinical overview of sorafenib, a multikinase inhibitor that targets both Raf and VEGF and PDGF receptor tyrosine kinase signaling[END_REF] . Previous case reports indicate that sorafenib, alone or in combination with other angiostatic drugs, might have a beneficial effect on exudative AMD 18 19 .

This study was designed to investigate the effect of sorafenib on lightinduced growth factor expression in the RPE, which plays a key role in the development and progression of AMD [START_REF] Ehrlich | Age-related macular degeneration and the aging eye[END_REF] . Therefore, we exposed primary human RPE cells to wide-band white light (spectral range 400-700 nm).

Cells were treated with sorafenib and the drug's effects on viability of the cells after light exposure were investigated. Expression of VEGF-A, PDGF-BB, and PlGF was determined.

Methods

Materials

Ethics

The methods of securing human tissue were humane, included proper consent and approval, complied with the Declaration of Helsinki, and were approved by the local ethics committee.

Human RPE Cell Culture

Primary RPE cells from four human donors (48, 52, 56, and 74 years old, obtained 3-10 h postmortem) without any history of eye disease were obtained from the Eye Bank of Ludwig Maximilian University and were prepared as previously described [START_REF] Kernt | Cytoprotective effects of a blue light-filtering intraocular lens on human retinal pigment epithelium by reducing phototoxic effects on vascular endothelial growth factor-alpha, Bax, and Bcl-2 expression[END_REF] . Dulbecco modified Eagle medium (DMEM; Biochrom, Berlin, Germany) supplemented with 10% fetal calf serum (FCS; Biochrom, Berlin, Germany) was used as the cell culture medium. An increased accumulation of lipofuscin is a common characteristic of ageing RPE cells in vivo and lipofuscin is known to act as a photosensitizer. It has been implicated to play a certain role in the development and progression of AMD [START_REF] Algvere | Age-related maculopathy and the impact of blue light hazard[END_REF][START_REF] Algvere | Age-related maculopathy: pathogenetic features and new treatment modalities[END_REF][START_REF] Holz | Pathogenesis of lesions in late age-related macular disease[END_REF] . To investigate the effects of white light on RPEs growth factor expression, we used primary RPE cells of passages 2 and 3 for our experiments. All investigated RPE cell cultures presented intracellular pigmented granules in phase-contrast microscopy. These granules contain, besides melanin and other pigments, a certain amount of lipofuscin. This characteristic disappears when RPE cells are cultured for long-term periods [START_REF] Barishak | In vitro behaviour of the pigmented cells of the retina and uvea of the adult human eye[END_REF][START_REF] Flood | Growth characteristics and ultrastructure of human retinal pigment epithelium in vitro[END_REF][START_REF] Nilsson | Aging of cultured retinal pigment epithelial cells: oxidative reactions, lipofuscin formation and blue light damage[END_REF] .

Cell Culture Treatment

For all cell culture experiments, RPE cells were seeded in 35-mm tissue culture dishes and cultured on confluence in darkness. RPE cells were kept for 24 h in serum-free conditions. After the cells were washed with phosphate-buffered saline (PBS), they were illuminated for 60 min.

Directly after illumination, PBS was replaced with serum-free cell culture medium and sorafenib was added with a final concentration of 1 µg/mL.

Illumination of Cells

A spot-light source (LC-8; Hamamatsu Photonics, Japan) from a mercuryxenon lamp equipped with an optic fiber as the light guide (spectral range: 400-700 nm) was used for illumination. The cell culture medium was replaced with PBS just before illumination. The plastic cover of the illuminated cell culture well was removed, and the cells were illuminated from above. They were illuminated (300 mW/cm 2 ) for 60 min. The illumination power and spectral range were measured with a spectrometer (C10083MD; Hamamatsu Photonics). Directly after illumination, PBS was replaced by serum-free cell culture medium, sorafenib was added with a final concentration of 1 µg/mL, and the cells were kept in darkness for another 24 h. Then, the methylthiotetrazole (MTT) assay, enzyme-linked immunosorbent assay (ELISA) for detection of growth factor concentrations in cell culture supernants, epifluorescence microscopy, phase-contrast microscopy, and RNA isolation were performed.

MTT Assay

The tetrazolium dye-reduction assay (MTT; 3-[4,5-dimethylthiazol-2-yl]-2,5-diphenyl tetrazolium bromide) was used to determine the cell survival rate. The MTT test, which is well-established for the assessment of cell viability, was performed as described by Mosmann, [START_REF] Mosmann | Rapid colorimetric assay for cellular growth and survival: application to proliferation and cytotoxicity assays[END_REF] with some modifications. The medium was removed; the cells were washed with PBS; and 1000 mL of MTT solution (1.5 mL MTT stock, 2 mg/mL in PBS, plus 28.5 mL MEM) was added to each well. RPE cells were incubated at 37°C for 1 h. The formazan crystals that formed were dissolved by the addition of 1000 mL DMSO per well. Absorption was measured by a scanning multiwell spectrophotometer at 550 nm (Molecular Probes). The results were expressed as the mean percentage of proliferation in the control.

To investigate the effects of different sorafenib concentrations on RPE cell viability, cells were brought to confluence, kept under serum-free conditions for 24 h, and then were treated with sorafenib concentrations of 0.5, 1, 1.25, 2.5, 5, 7.5, 10, 12.5, 15, 25, and 50 µg/mL for another 24 h. Then the MTT assay was performed. To investigate the effects of sorafenib on RPE cell viability after light exposure, cells were illuminated and treated as described above. At 24 h after illumination the MTT assay was performed. The experiments were performed in triplicate and repeated three times.

The control cells were RPE cells of the same passage; they were kept in darkness, without exposure to any radiation.

Detection of VEGF-A, PDGF-BB, and PlGF Secretion by RPE Cells

RPE cell cultures were grown to confluence and treated as described. Levels of VEGF-A, PDGF-BB, and PlGF in the culture supernatants were determined by ELISA. The supernatants were collected after 24 h, and the levels of VEGF-A, PDGF-BB, and PlGF were quantified using a VEGF-A, PDGF-BB, or PlGF Quantikine ELISA Assay Kit (R & D Systems) according to the manufacturer's instructions.

RNA Isolation and Real-Time PCR

Total RNA was isolated from 10-cm Petri dishes by the guanidium thiocyanate-phenol-chloroform extraction method (Stratagene, Heidelberg, Germany). The structural integrity of the RNA samples was confirmed by electrophoresis in 1% Tris-acetate-EDTA agarose gels. The yield and purity were determined photometrically (BioPhotometer; Eppendorf, Hamburg, Germany). Real-time polymerase chain reaction (PCR) enables quantitative detection of small amounts of mRNA. After the usual isolation of mRNA, this mRNA was transferred to complementary DNA (cDNA) through reverse transcriptase (RT). This cDNA was then used for the specific PCR. Quantification of VEGF-A, PDGF-BB, and PlGF mRNA was performed with specific primers with a LightCycler instrument (LightCycler System; Roche Diagnostics, Mannheim, Germany). Primers and probes were detected with ProbeFinder 2.04. All primers and probes were designed to cross intron/exon boundaries to avoid amplification of genomic DNA. All PCR products were sequenced to ensure product validity. Each 14-µL reaction volume contained 1× FastStart DNA Master Hybridization Probes Mix (Roche Diagnostics), 4 mM MgCl 2 , 0.5 mM of each primer, 0.2 mM TaqMan probe, and 2 µL cDNA. The amplification signals were detected in real time, which allowed accurate quantification of the amounts of the initial RNA template, because the system can select signals easily during the exponential amplification phase of PCR. The cDNA of RPE cells, either after incubation with sorafenib or untreated and then exposed to light, was amplified with specific primers for 40 cycles. Two oligonucleotides with different labeled fluorophores were hybridized to the amplified fragment during the annealing phase. When the two probes came in close proximity, fluorescence resonance energy transfer (FRET) developed between the two fluorophores. The emitted fluorescence was then measured by the LightCycler instrument. Hybridization probes were displaced during the extension step. Depending on the initial concentration of target genes, the signal intensity increased in different cycles, and these cycles were used as the crossing point. The standard curve was made with three different probes of untreated RPE cells. For normalization of differences in the amount of total RNA added to each reaction, 18S rRNA was simultaneously processed in the same sample as an internal control. The level of VEGF-A, PDGF-BB, and PlGF mRNA was determined as the relative ratio (RR), which was calculated by dividing the level of VEGF-A, PDGF-BB, and PlGF mRNA by the level of the 18S rRNA housekeeping gene in the same samples. The ratios are expressed as decimals. All experiments were performed at least in triplicate and repeated three times. Table 1 lists the primers used for RT-PCR.

Immunohistochemistry of RPE Cell Cultures

Cultured RPE cells were grown on microscope slides and treated as described above. After incubation, cells were fixed with 4% phosphonoformic acid (PFA) for 15 min and subsequently washed twice with PBS containing 0.1% Triton X-100. Primary incubation of all samples was performed with a mouse anti-human VEGF-A antibody (Santa Cruz Biotechnology, Santa Cruz, CA), a mouse anti-human PDGF-B antibody (Santa Cruz Biotechnology), and a goat anti-human PlGF antibody (Santa Cruz Biotechnology), diluted 1:200 in PBS for 4 h at room temperature. After washing three times, the culture dishes and sections were further processed with a Texas red-conjugated rabbit anti-mouse secondary antibody or a fluorescein-conjugated rabbit anti-goat secondary antibody (diluted 1:500 in PBS; Santa Cruz Biotechnology) for 1 h at room temperature, rinsed in PBS, and mounted with Kaiser's glycerine jelly (Merck, Darmstadt, Germany). Slides were investigated with a Zeiss Axio Imager fluorescence microscope (Carl Zeiss AG, Oberkochen, Germany). All experiments were performed at least nine times with RPE cells from three different cell cultures.

Statistical Evaluation

All data were analyzed with SPSS 13.0 for Windows (SPSS, Chicago, IL, USA). For all statistical tests, p < 0.05 was considered significant. Results of the MTT assay are presented as mean (SD) units of absorbance. Ten individual samples per group were measured in triplicate. The Mann-Whitney test was used. Results from VEGF-A, PDGF-BB, and PlGF ELISA are presented as mean (SD) ratios of each tested probe, which were normalized to the control. Results of the RT-PCR are presented as mean (SD) ratios of the investigated mRNA and 18S rRNA. Again, Mann-Whitney testing was applied; all experiments were performed at least in triplicate and repeated three times.

Results

Viability of Cells

Testing concentrations of sorafenib in primary RPE cells No gross abnormalities, such as abnormal shape and appearance, cellular lysis, cellular death, or other abnormalities, were detected with phasecontrast microscopy up to a concentration of 12.5 µg/mL sorafenib in primary RPE cells after 24 h treatment. The number of cells counted in phase-contrast microscopy correlated well with the quantitative results of the MTT test. MTT assay Sorafenib showed no significant toxic effects in the investigated RPE cell cultures (24-h exposure) at concentrations between 0.5 and 12.5 µg/mL.

No significant decrease (Wilcoxon with α correction for multiple testing) in cellular viability was detected with RPE cells compared with the control. Concentrations of sorafenib between 15 and 25 µg/mL showed an increasing reduction of cell viability, but still >60% of the cells revealed activity. At a sorafenib concentration of 50 µg/mL a more rapid, dosedependent and significant reduction of viability was seen (Fig. 1).

Testing the effects of sorafenib on viability of RPE cells after light exposure When cells were illuminated with unfiltered white light (300 mW/cm 2 ) for 60 min, a significant reduction of RPE cell viability was detected (Fig. 2).

In contrast, cells treated with sorafenib, 1 µg/mL, immediately after illumination showed a significantly smaller less decrease in viability compared to cells that were not treated with sorafenib (Fig. 2).

Expression of VEGF-A, PDGF-B, and PlGF mRNA

VEGF-A, PDGF-BB, and PlGF mRNA expression was detected in every sample. All detected mRNA levels of VEGF-A, PDGF-BB, and PlGF were normalized to those of 18S rRNA; the values are expressed as the RR of VEGF-A/18S, PDGF-BB/18S, or PlGF/18S. Illumination with white light for 60 min led to a significant increase in VEGF-A, PDGF-B, and PlGF mRNA expression in RPE cells (Fig. 3). Treatment of RPE cells with sorafenib, 1 µg/mL, directly after light exposure significantly reduced this light-induced increase in VEGF-A, PDGF-BB, and PlGF mRNA after 24 h (Fig. 3).

Immunohistochemical Detection of VEGF-A, PDGF-B, and PlGF Expression in RPE Cells

For verification that the light-induced increase of VEGF-A, PDGF-B, and PlGF mRNA transcription translates into increased protein synthesis, immunohistochemistry was performed 24 h after illumination. In both untreated and non-illuminated control cells and cells that were treated with sorafenib, 1 µg/mL, and had no illumination, only a faint staining for VEGF-A, PDGF-B, and PlGF was observed (Fig. 4). After 60 min of light exposure, the expression of VEGF-A, PDGF-B, and PlGF was markedly increased.

In contrast, for RPE cells that were illuminated for 60 min and had sorafenib at a dose of 1 µg/mL added directly after illumination, staining showed only a weak expression of VEGF-A, PDGF-B, and PlGF, which was comparable to those cells that served as non-illuminated controls (Fig. 4).

Detection of VEGF-A, PDGF-B, and PlGF Secretion of Human RPE Cells

To investigate the effect of sorafenib on VEGF-A, PDGF-BB, and PlGF secretion after light exposure, a quantitative detection of VEGF-A, PDGF-BB, and PlGF in cell culture supernants was conducted using the ELISA method 24 h after illumination. In our experimental set-up, light exposure led to a significant increase of VEGF-A, PDGF-BB, and PlGF in cultured RPE cells after 60 min of light exposure. In contrast, when cells were treated with sorafenib, 1 µg/mL, directly after light exposure, sorafenib treatment decreased the amount of VEGF-A, PDGF-BB, and PlGF significantly compared to those cells that were not treated with sorafenib after illumination (Fig. 5).

Discussion

RPE forms the outer blood-retina barrier to facilitate selective transport between the choroidal blood vessels and the outer retina. As a phagocytic system it is essential for the renewal of photoreceptors and plays a major role in rod and cone photoreceptor integrity [START_REF] Ehrlich | Age-related macular degeneration and the aging eye[END_REF] . AMD is a disease of the elderly population [START_REF] Ehrlich | Age-related macular degeneration and the aging eye[END_REF] . Loss and degeneration of RPE cells, particularly in the macular center, is pathognomonic for this disease 1 21 . With advancing age, RPE cells undergo an increase in pleomorphism and accumulate metabolic debris from remnants of incomplete degradation of phagocytized rod and cone membranes 1 21 . The incomplete degradation of phagocytized photoreceptor membranes results in a continuous increase in intracellular lipofuscin in the RPE cells over time. This lipofuscin accumulation seems to be associated with deterioration in cellular function potentially resulting in a higher sensitivity to radiation damage 22 28-30 .

Furthermore, the formation of drusen in Bruch's membrane might compromise RPE cell function by impeding fluid transport and inducing inflammatory responses, which have been implicated in the development of AMD and CNV [START_REF] Hageman | An integrated hypothesis that considers drusen as biomarkers of immune-mediated processes at the RPE-Bruch's membrane interface in aging and age-related macular degeneration[END_REF][START_REF] Starita | Localization of the site of major resistance to fluid transport in Bruch's membrane[END_REF][START_REF] Moshfeghi | Role of genetic factors and inflammation in age-related macular degeneration[END_REF] . Once damaged, RPE cells secrete inadequate amounts of growth factors, such as VEGF, PDGF, PlGF, and others [START_REF] Freyberger | Increased levels of platelet-derived growth factor in vitreous fluid of patients with proliferative diabetic retinopathy[END_REF][START_REF] Robbins | Platelet-derived growth factor ligands and receptors immunolocalized in proliferative retinal diseases[END_REF][START_REF] Schlingemann | Role of growth factors and the wound healing response in age-related macular degeneration[END_REF][START_REF] Witmer | Vascular endothelial growth factors and angiogenesis in eye disease[END_REF] . An imbalance between these growth factors in the eye potentially leads to aberrant angiogenesis resulting in the formation of dysfunctional blood vessels and CNV [START_REF] Bhutto | Pigment epithelium-derived factor (PEDF) and vascular endothelial growth factor (VEGF) in aged human choroid and eyes with agerelated macular degeneration[END_REF] . Cumulative light exposure is thought to induce proangiogenic factors in RPE cells and to promote the development of exudative AMD 16 35 . Previous studies have demonstrated that light exposure can lead to an increased production of VEGF-A in RPE cells 20 36 37 . The reason for this could be that continuous light exposure induces sublethal cellular stress, which results in an up-regulation of proangiogenic VEGF-A secretion [START_REF] Yanagi | Effects of yellow intraocular lenses on light-induced upregulation of vascular endothelial growth factor[END_REF] . In accordance with these findings, our results clearly indicate that light exposure not only leads to an up-regulation of VEGF-A but also to an increased expression and secretion of PDGF-BB and PlGF in primary human RPE cells. VEGF-A, a member of the VEGF family, is a dimeric 36-46-kDa glycosylated protein with a predominant role in the development of pathologic angiogenesis in AMD 1 7 . A secondary important role of VEGF-A is the induction of increased vascular permeability 1 6 7 15 16 . In RPE cells out of the macular region of patients with AMD VEGF-A is significantly increased, and vitreous VEGF-A levels are significantly higher in patients with AMD and CNV, compared to healthy control subjects 38 39 . Therefore, VEGF-A has become the main target of the currently used antiangiogenic agents in the treatment of AMD 8 . However, endothelial cells and pericytes that form the structure of neovascular tissue seem not to respond to VEGF-A inhibition alone and currently used anti-VEGF agents seem to have little effect on existing capillaries 15 16 . In addition, not all attributes of CNV are related to vessels, but many of the structural abnormalities associated with CNV are related to fibroblasts, damage of the RPE, and the remodeling of the nascent extracellular matrix 15 16 . PlGF, a member of the VEGF family, induces increased vascular permeability, proliferation, chemotaxis, and angiogenesis and may act synergistically with VEGF-A in the development of CNV 15 16 . Both VEGF-A and PlGF have a recruiting effect on pericytes during angiogenesis, either in the maturation process of endothelial tubes, but as well in the early phase of angiogenesis, where both growth factors act as an integral part of sprouting capillaries 16 40 41 . PDGF-BB, another growth factor expressed by the RPE, acts as a survival factor for retinal pericytes. PDGF-BB is the key regulator of the pericyte endothelial bond and known to recruit pericytes in the development of CNV 15 41-43 . Pericytes are an important component of the choroidal neovascular complex, providing stabilization of vessels and are thought to limit the penetration of anti-VEGF agents 15 41-43 . In addition, PDGF is thought to have an important role in fibroplasia as a wound healing response in CNV 15 43 44 .

Recent studies demonstrated that combined inhibition of VEGF and PDGF enforces vessel regression by interfering with pericyte-mediated endothelial cell survival and produced inhibition and regression of corneal neovascularization and CNV compared to anti-VEGF treatment alone 42 43 . Therefore, a combined approach of targeting several key molecules or pathways in a complex disease state as AMD might lead to significant improvements in outcome and seems to be worthwhile [START_REF] Spaide | Rationale for combination therapy in age-related macular degeneration[END_REF] . The multikinase inhibitor sorafenib was initially identified as an RAF kinase inhibitor, but it also inhibits several receptor tyrosine kinases involved in angiogenesis. Sorafenib's antiproliferative and antiangiogenic efficacy seems to be derived from its blocking capability of the RAF/mitogenactivated protein (MAP)/extracellular signal-regulated kinase (ERK) kinase (MEK)/ERK (RAF/MEK/ERK) cascade and its effect on receptor tyrosine kinases, including VEGF receptor 2 (VEGFR2), VEGFR3, PDGF receptor, FLT3, Ret, and c-Kit 17 46-49 . Furthermore, sorafenib interacts with hypoxiainducible factors 1 and 2 and seems to have an influence on expression of growth factors, such as VEGF and PDGF 17 46-48 . In this study, sorafenib at a concentration of 1 µg/mL led to a significant reduction of the light-induced increase in expression and secretion of VEGF, PlGF, and PDGF in primary human RPE cells. Moreover, this attenuation of light-induced growth factor overexpression was accompanied by a significant improvement of light-induced decrease in RPE cell viability. One potential reason for this might be that sorafenib does not only interact with growth factor regulation, but also interferes with certain proteins within the intrinsic apoptotic cascade. The exact mechanisms are not completely understood, however, it has been demonstrated that sorafenib inhibits for example the phosphorylation of the initiation factor eIF4E which is known to regulate the translation of a large number of mRNAs, including member so the Bcl-2 family 17 48 .

Further research is warranted. Sorafenib appears to be comparable to systemic anti-VEGF medications in its safety profile 11 50 . The most common side effects after oral administration in patients treated for renal cell carcinoma (RCC) were dermatologic symptoms such as rash or hand-foot skin reactions, diarrhea, and low-grade hypertension. Severe adverse events have been described but are rare 50 51 . In addition, in our experimental set-up, sorafenib did not have a significant influence on RPE cell viability after a 24-h exposure up to a concentration of 12.5 µg/mL. This is more than 10fold higher than the sorafenib concentration of 1 µg/mL effective in our experiments. The standard dosage of sorafenib as oral treatment for RCC is 800mg per day. From several clinical trials we know that after a daily dose of 800mg sorafenib, plasma levels are within the range of 10µg/mL, after 200mg per day around 4.5µg/mL can be reached [START_REF] Abou-Alfa | Phase II study of sorafenib in patients with advanced hepatocellular carcinoma[END_REF][START_REF] Houben | MAPK-independent impairment of T-cell responses by the multikinase inhibitor sorafenib[END_REF][START_REF] Kupsch | Results of a phase I trial of sorafenib (BAY 43-9006) in combination with oxaliplatin in patients with refractory solid tumors, including colorectal cancer[END_REF] . To date, there is no data regarding the penetration of sorafenib into ocular tissue, neither after systemic, nor after topic application, available and this issue needs further investigation. However, the sorafenib concentration of 1 µg/mL effective in our experiments, might be achievable even with a low dose treatment.

Our data provide the first evidence that sorafenib effectively interacts in human RPE cells with three important targets of AMD treatment: VEGF, PlGF, and PDGF. Due to its activity against multiple targets and pathways in angiogenesis, sorafenib seems to be promising as a potential treatment for AMD [START_REF] Peyman | Combination angiostatic therapies: current status[END_REF] . Another substantial difference between sorafenib to the currently used extracellular VEGF inhibitors might be that the substance potentially acts upstream and downstream in the angiogenic cascade and therefore potentially prevents transcription and protein production of growth factors in the tissue from where they are derived 17 55 . Recent reports have demonstrated beneficial effects of sorafenib in AMD treatment. Kernt et al reported about a patient with occult CNV who experienced visual improvement and resolution of macular edema under oral sorafenib treatment due to advanced RCC, where intravitreal bevacizumab treatment failed [START_REF] Kernt | Resolution of macular oedema in occult choroidal neovascularization under oral Sorafenib treatment[END_REF] . Other reports describe improvement in visual acuity under low-dose sorafenib treatment alone or in combination with intravitreal ranibizumab [START_REF] Diago | Ranibizumab combined with low-dose sorafenib for exudative agerelated macular degeneration[END_REF] . In this in vitro study sorafenib had a significant impact on growth-factor expression in the human RPE. The RPE is only one component interacting in retinal neovascular disease and not all aspects of mechanisms of action of sorafenib regarding growth factor expression and signaling are completely understood. Its additional effects on receptor tyrosine kinases and other cell types involved in the development of AMD need further investigation. However, the data presented in this in vitro study indicate that sorafenib provides properties to reduce light-induced growth factor 20 overexpression in human RPE and, therefore, might prevent development and progression of CNV in vivo. Further experimental and clinical studies will have to substantiate our in vitro findings. Nevertheless, sorafenib seems to be a promising adjunctive treatment for patients with AMD. and cells that were treated with sorafenib, 1 µg/mL, and had no illumination presented only a faint staining for VEGF-A, PDGF-B, and PlGF. After 60 min of light exposure, the expression of VEGF-A, PDGF-B, and PlGF was markedly increased. In contrast, RPE cells that were illuminated and had sorafenib added directly after illumination showed only a weak staining of VEGF-A, PDGF-B, and PlGF, which was comparable to those cells that served as non-illuminated controls. Sorafenib concentrations of up to 12.5 mg/mL showed no significant reduction in viability (Wilcoxon with α correction for multiple testing) compared to controls. Immunohistochemical staining of VEGF-A, PDGF-B, and PlGF expression in RPE cells. Both untreated and non-illuminated control cells and cells that were treated with sorafenib, 1 µg/mL, and had no illumination presented only a faint staining for VEGF-A, PDGF-B, and PlGF. After 60 min of light exposure, the expression of VEGF-A, PDGF-B, and PlGF was markedly increased. In contrast, RPE cells that were illuminated and had sorafenib added directly after illumination showed only a weak staining of VEGF-A, PDGF-B, and PlGF, which was comparable to those cells that served as non-illuminated controls.

  Sorafenib (Nexavar, BAY 43-9006 [N-(3-trifluoromethyl-4-chlorophenyl)-N-(4-(2-methylcarbamoyl pyridin-4-yl)oxyphenyl)urea]) was dissolved in 100% dimethyl sulfoxide (DMSO; Sigma, St. Louis, MO) and diluted with DMSO and the cell culture medium to the desired concentration with a final DMSO concentration of 0.1% for in vitro studies. DMSO was added to cultures at 0.1% (v/v) as a solvent control.

Fig. 1 .

 1 Fig. 1. Viability of primary human RPE cells after treatment with the various concentrations of sorafenib, measured by a colorimetric test (MTT). Untreated RPE cells of the same passage served as controls. The results shown are the mean percentage of control cell survival from three experiments, each performed in triplicate with error bars indicating SEM. Sorafenib concentrations of up to 12.5 mg/mL showed no significant reduction in viability (Wilcoxon with α correction for multiple testing) compared to controls.

Fig. 2 .

 2 Fig.2. Viability of primary human RPE cells after illumination with plain white light (black column) and after incubation with sorafenib at a concentration of 1 µg/mL (light gray column), as measured by a colorimetric test (MTT). The decrease in cellular viability was significantly reduced when cells were additionally incubated with sorafenib after 60 min of illumination. Error bars: SD.

Fig. 3 .

 3 Fig. 3. VEGF-A, PDGF-BB, and PlGF mRNA expression of primary RPE cells after illumination with plain white light (black columns) and after incubation with sorafenib at 1 µg/mL (light gray columns), as investigated by quantitative RT-PCR. X-axis: relative ratio (RR) of VEGF-A, PDGF-BB, or PlGF mRNA normalized to 18s rRNA, expressed in decimal format. Yaxis: time of illumination.

Fig. 4 .

 4 Fig. 4. Immunohistochemical staining of VEGF-A, PDGF-B, and PlGF expression in RPE cells. Both untreated and non-illuminated control cells

Fig. 5 .

 5 Fig. 5. Inhibitory effect of sorafenib on light-induced secretion of VEGF-A, PDGF-BB, and PlGF, as investigated by ELISA: untreated RPE cells after illumination with plain white light (black columns) and after additional treatment with sorafenib (light gray columns). Each value was normalized to a standard curve of VEGF-A, PDGF-BB, or PlGF and expressed as concentration in nanograms per milliliter. Data values are means ± SD.

Fig. 1 :

 1 Fig. 1: Viability of primary human RPE cells after treatment with the various concentrations of sorafenib, measured by a colorimetric test (MTT). Untreated RPE cells of the same passage served as controls. The results shown are the mean percentage of control cell survival from three experiments, each performed in triplicate with error bars indicating SEM.

Fig. 2

 2 Fig. 2.: Viability of primary human RPE cells after illumination with plain white light (black column) and after incubation with sorafenib at a concentration of 1 µg/mL (light gray column), as measured by a colorimetric test (MTT). The decrease in cellular viability was significantly reduced when cells were additionally incubated with sorafenib after 60 min of illumination. Error bars: SD.

Fig. 3 :

 3 Fig. 3: VEGF-A, PDGF-BB, and PlGF mRNA expression of primary RPE cells after illumination with plain white light (black columns) and after incubation with sorafenib at 1 µg/mL (light gray columns), as investigated by quantitative RT-PCR. X-axis: relative ratio (RR) of VEGF-A, PDGF-BB, or PlGF mRNA normalized to 18s rRNA, expressed in decimal format. Y-axis: time of illumination.

Fig. 4 :

 4 Fig. 4:

Fig. 5 :

 5 Fig. 5: Inhibitory effect of sorafenib on light-induced secretion of VEGF-A, PDGF-BB, and PlGF, as investigated by an ELISA method: untreated RPE cells after illumination with plain white light (black columns) and after additional treatment with sorafenib (light gray columns). Each value was normalized to a standard curve of VEGF-A, PDGF-BB, or PlGF and expressed as concentration in nanograms per milliliter. Data values are means ± SD.

Acknowledgments

The authors thank Katja Obholzer for excellent technical assistance.


Guimarães Glenio

Euzebio Santos

Robélio Leandro Medrado Da Silva

Pedro Marchão

Ary Marques Da Silveira

Francois Bruand

Thierry James

Becquer

Santos

Euzebio Medrado Da Silva

Robélio Leandro Marchão

Pedro Marques Da Silveira

Ary Bruand

Francois James

Thierry Becquer

Analysis of physical quality of soil using the water retention curve: Validity of the S-index Analyse de la qualité physique du sol à partir de la courbe de rétention de l'eau : validité de l'indice S

Keywords: soil compaction, bulk density, van Genuchten model, S-index Résumé compaction du sol, densité apparente, modèle de van Genuchten, indice S

teaching and research institutions in France or abroad, or from public or private research centers.

Parmi les différents indicateurs qui ont été proposés pour rendre compte des propriétés physiques du sol, l'indice S, qui correspond à la pente de la courbe de rétention en eau du sol à son point d'inflexion, a été largement utilisé. Dans cet article, nous discutons de la valeur de la pente au point d'inflexion de la courbe de rétention en eau du sol en fonction de la variable indépendante qui est utilisé pour le déterminer. Nous montrons que la représentation de la teneur en eau en fonction de l'expression arithmétique de la succion au lieu de son expression logarithme, comme pour l'indice S, conduit à un résultat différent pour le sol sélectionné. Plus généralement, nos résultats montrent qu'une discussion des propriétés physiques du sol en utilisant une représentation de la courbe de rétention d'eau en fonction de

Introduction

Water movement in soils as described using hydrogeophysics [START_REF] Cousin | From spatial-continuous electrical resistivity measurements to the soil hydraulic functioning at the field scale[END_REF][START_REF] Frangi | New in-situ techniques for the estimation of the dielectric properties and moisture content of soils[END_REF] is related to their hydraulic properties which in turn are closely dependent on soil structure. Its high lateral and vertical variability in soils has led soil physicists to seek out physical indicators enabling the discussion of its characteristics, and more generally of the quality of physical properties [START_REF] Dexter | Soil physical quality: Part I, Theory, effects of soil texture, density, and organic matter, and effects on root growth[END_REF][START_REF] Dexter | Soil physical quality: Part II, Friability, tillage, tilth and hard-setting[END_REF][START_REF] Dexter | Soil physical quality: Part III, Unsaturated hydraulic conductivity and general conclusions about S-theory[END_REF][START_REF] Dexter | Methods for predicting the optimum and the range of soil water contents for tillage based on the water retention curve[END_REF][START_REF] Dexter | Applications of S-theory in the study of soil physical degradation and its consequences[END_REF][START_REF] Reynolds | Indicators of good soil physical quality: density and storage parameters[END_REF]. Among these indicators, the index proposed by Dexter and Bird [START_REF] Dexter | Methods for predicting the optimum and the range of soil water contents for tillage based on the water retention curve[END_REF] and Dexter [START_REF] Dexter | Soil physical quality: Part I, Theory, effects of soil texture, density, and organic matter, and effects on root growth[END_REF] enables the physical quality of soil (workability, permeability, structure stability, etc) to be investigated and should be particularly effective for providing information on the soil hydric functioning. This index is the slope (S) of the soil-water retention curve (SWRC) at its inflection point.

It is determined for the SWRC when the gravimetric water content (W), a function of soil-water suction (h) and expressed using the van Genuchten equation [START_REF] Richard | Effect of compaction on the porosity of a silty soil: Consequences on unsaturated hydraulic properties[END_REF], is plotted with the natural logarithm of h. In this study we use W to denote the gravimetric water content, rather than , as in Dexter and Bird [START_REF] Dexter | Methods for predicting the optimum and the range of soil water contents for tillage based on the water retention curve[END_REF], to be more consistent with the literature since  usually represents the volumetric water content. As for the van Genuchten equation [START_REF] Van Genuchten | A closed-form equation for predicting the hydraulic conductivity of unsaturated soils[END_REF] which was written for , it remains valid for W.

Dexter [START_REF] Dexter | Soil physical quality: Part I, Theory, effects of soil texture, density, and organic matter, and effects on root growth[END_REF] derived the expression of the slope of the SWRC analytically to calculate the value of S, thus leading to the following expression:

  ) 1 ( 1 1 m r s m W W n S             (1)
with m and n the fitted dimensionless shape parameters of the van Genuchten equation [START_REF] Van Genuchten | A closed-form equation for predicting the hydraulic conductivity of unsaturated soils[END_REF], and W s and W r , in g of water per g of oven-dried soil, and the saturated and residual gravimetric water contents of the van Genuchten equation, respectively. This characteristic of the SWRC was considered by Dexter [START_REF] Dexter | Soil physical quality: Part I, Theory, effects of soil texture, density, and organic matter, and effects on root growth[END_REF] as a physical parameter (Sindex) of the physical quality of soil. Dexter [START_REF] Dexter | Soil physical quality: Part I, Theory, effects of soil texture, density, and organic matter, and effects on root growth[END_REF] showed that it was related to the texture, bulk density, organic matter content and root growth of soil. Since its early developments, the S-index has been used by many authors [9, 11-14, 17, 26].

Dexter and Bird [START_REF] Dexter | Methods for predicting the optimum and the range of soil water contents for tillage based on the water retention curve[END_REF], however, noted that there were two possible inflection points depending on whether W is plotted against log(h) or against h. They reported that the two inflection points are in close proximity for soils with a narrow pore-size distribution. This explains why they used the inflection point of curves of W vs. log(h), believing this was an estimate of air entry into granular materials which were considered in their study [START_REF] Dexter | Methods for predicting the optimum and the range of soil water contents for tillage based on the water retention curve[END_REF]. Another point not raised by Dexter and Bird [START_REF] Dexter | Methods for predicting the optimum and the range of soil water contents for tillage based on the water retention curve[END_REF] concerned their choice for computing the slope in a graph W vs. ln(h) of the W curve as a function of h according to the van Genuchten equation [START_REF] Dexter | Applications of S-theory in the study of soil physical degradation and its consequences[END_REF] instead of the slope of the W curve vs. ln(h) which would have been mathematically more consistent.

In this study we discuss the choice of Dexter and Bird [START_REF] Dexter | Methods for predicting the optimum and the range of soil water contents for tillage based on the water retention curve[END_REF] and compare the Sindex with the slope of the SWRC at its inflection point when it is expressed as a function of the independent variable h, ln(h) or log(h). The equations developed are applied to a non-compacted and compacted soil and the resulting values of the slope are compared to the S-index.

Theory

Expression of W according to h, ln(h) and log(h)

On the basis of the van Genuchten equation [START_REF] Van Genuchten | A closed-form equation for predicting the hydraulic conductivity of unsaturated soils[END_REF], W can be expressed as:

      r r s 1 ˆW h W W W m n       (2)
with W the gravimetric soil water content (g g -1 ); s W the measured gravimetric saturated soil water content (g g -1 ); r Ŵ the fitted residual gravimetric soil water content (g g -1 );  ˆthe fitted scaling parameter (kPa -1 ); and n ˆ and

n m / 1 1 ˆ  [19]
dimensionless fitted shape parameters. In order to facilitate presentation, it can be admitted that Eq. 2 can be represented as:

  m n W W h g W , , , , r s   (3)
with g being W as a function of h, given that parameters

) g (g 1 s  W , ) g (g ˆ1 r  W , n ˆ (dimensionless), ) hPa ( ˆ1  α
, and m ˆ (dimensionless) are known. The circumflex on a letter is used to identify a fitted parameter value ( m ˆcan also be fitted but in this study it was forced to 1-1/n).

Similarly, W vs. ln(h), can be represented by f using Eq. 2 as:

  1 1 1 r1 s ) ln( m , α , n , W , W h f W  (4)
with the fitted parameters ), g (g

ˆ1 r1  W 1 n (dimensionless), ), hPa ( ˆ1 1  α
and 1 m (dimensionless) and W vs. log(h), can be represented by k using Eq. 2 as:

  1 2 1 1 r s , , , , ) ( log m n W W h k W   (5)
with 2  the only new fitted parameter such as

10 α α ln ˆ1 2 
, the other fitted parameters being identical to those determined for f.

Derivation of the SWRC to obtain the inflection point

Taking Eqs. ( 3), (4), and ( 5) as general representations of the WRC and using

Eq. 4, we can write the following derivatives:

        1 1 r s ˆ1 ) ( ˆ        n m n n h h α W W α n m dh dW g  (6) with g  the first derivative of W in relation to h,         1 1 1 1 r s 1 1 1 1 1 1 1 ) ln( ) ln( 1 ) ( )) (ln(         n m n n h h α W W α n m h d dW f  (7)
with f  the first derivative of W in relation to ln (h), and:

        1 1 2 1 r s 2 1 1 1 1 1 1 ) log( ) log( 1 ) ( )) (log(         n m n n h h α W W α n m h d dW k  ( 8
)
with k  the first derivative of W in relation to log (h).

It is important to state that

  ) ln(h d dW f  
cannot be computed by simply applying the chain rule from Eq. ( 3) because the parameters determined by fitting either g (Eq. 3) or f (Eq. 4), subjected to Eq. 2, are not necessarily the same. This can be also said for functions g (Eq. 3) and k (Eq. 5), except that here the only difference between f  and k  is the magnitude of the scaling parameters 1 α and 2 α .

It is known that any continuous and differentiable mathematical function has its inflection points located where the second derivative is null throughout its real domain. Thus, at the inflection points for function g, we can set:

                  0 1 1 1 ) ( ˆ1 2 ˆ2 2 2 r s 2 2                  m n n n m n n n h α h n h h α α n n m W W α n m dh W d g  (9)
with g  , the second derivative of W in relation to h. After simplifying Eq. ( 9), we obtain:

                0 1 1 1 ˆ1 2 2 2 2 ˆ             m n n n m n n h α h n h h α α n n m ( 10
)
Eq. 10 can be solved for h to obtain the precise location of its inflection point

  i h as follows:    n i m h 1 1   (11)
Similarly, we can compute the second derivative of Eqs. ( 7) and ( 8) to obtain:

    1 1 1 1 1 ) ln( n i m α h  (12) with   i h) ln(
, the inflection point of W vs. ln(h), and:

    1 1 1 2 1 ) log( n i m α h  (13) with   i h) log(
, the inflection point of W vs. log(h).

Calculation of the slope at the inflection point of the SWRC

The slope, S h , from function g (Eq. 3) at its inflection point (Eq. 11) is obtained by substituting Eq. ( 11) into Eq. ( 6), which yields:

       1 r s 1 1 ˆ       m m h m m W W n α S ( 14
)
Similarly, the slope, S ln(h) , from function f (Eq. 4) at its inflection point (Eq. 12), is obtained by substituting Eq. ( 12) into Eq. ( 7):

       1 1 1 1 r s 1 1 ) ln( 1 1 1 1 ˆ       m m h m m W W n α S ( 15
)
The slope, S log(h) , from function k (Eq. 5) at its inflection point (Eq. 13) is obtained by introducing Eq. ( 13) into Eq. ( 8):

       1 1 1 1 r s 1 2 ) log( 1 1 1 1 ˆ       m m h m m W W n α S ( 16
)
3. Application to a case study

The soil and methods used

The equations developed in this study were applied to samples from a cultivated soil where compacted layers were identified [START_REF] Balbino | Changes in porosity and microagregation in clayey Ferralsols of the Brazilian Cerrado on clearing for pasture[END_REF]. The soil studied was a clayey Oxisol (Typic Acrustox) [START_REF]Soil Survey Staff, Keys to Soil Taxonomy[END_REF], a Latossolo Vermelho according to the Brazilian Soil Classification [START_REF] Santos | Sistema brasileiro de classificação de solos, 2nd ed, Embrapa Solos[END_REF] and a Ferralsol according to the IUSS-WRB [START_REF]World reference base for soil resources 2006: a framework for international classification, correlation and communication[END_REF] (diameter = 5.1 cm, height = 5.0 cm) in the compacted 0-5 cm and non-compacted 70-75 cm layers (Table 1). The higher bulk density found in the 0-5 cm layer is accounted for soil compaction since under native vegetation, this type of soil exhibits a uniform bulk density profile according to depth, with bulk density close to 1.0 g cm - 3 [START_REF] Balbino | Changes in porosity and microagregation in clayey Ferralsols of the Brazilian Cerrado on clearing for pasture[END_REF][START_REF] Volland-Tuduri | A relationship between mass proportion of microaggregates and bulk density in a Brazilian Clayey Oxisol[END_REF].

Gravimetric water contents (W in g g -1 ) at -10, -30, -60, -100, -330, -800, -4000, -10000, and -15000 hPa were determined in triplicate for the two layers studied (Table 2) using the centrifuge method [START_REF] Reatto | Validity of the centrifuge method for determining the water retention properties of tropical soils[END_REF][START_REF] Silva | Valores de tensão na determinação da curva de retenção de água de solos do Cerrado[END_REF]. An SWRC was fitted using the van Genuchten equation [START_REF] Van Genuchten | A closed-form equation for predicting the hydraulic conductivity of unsaturated soils[END_REF] (see Eq. 2) to the different water contents measured for the compacted and non-compacted layers, using h, ln(h) or log(h) as independent variable. The Solver routine embedded in Microsoft Excel was used to obtain the fitting parameters r W ˆ, ˆ, n ˆ, and m ˆ (Table 3). During the fitting process, W s was taken as the mean value of the three saturated water contents measured [START_REF] Reatto | Validity of the centrifuge method for determining the water retention properties of tropical soils[END_REF]: 0.367 g g -1 and 0.544 g g -1 for the compacted and non-compacted layer, respectively, and therefore was not adjusted. can be considered as the "breakthrough" matrix potential at which air penetrates throughout the soil as discussed by White et al. [START_REF] White | Boundary effects in desaturation of porous media[END_REF] and Dullien [START_REF] Dullien | Porous media: fluid transport and pore structure, 2nd Edition[END_REF]. The slopes at the inflection point of the SWRC using Eq. 14 (using h as independent variable) were 0.0020 and 0.0046 for the compacted and non-compacted soil. These values are 41 and 72 times smaller than the corresponding S-index values (Table 3). Suction at the corresponding inflection point using Eq. 11 was 6 and 22 hPa for the compacted and non-compacted soil, while according to Dexter [START_REF] Dexter | Soil physical quality: Part I, Theory, effects of soil texture, density, and organic matter, and effects on root growth[END_REF] it was 52 and 43 hPa (Table 3).

Using Jurin's law [START_REF] Bruand | Effect of water content on the fabric of a soil material: an experimental approach[END_REF], we computed the equivalent pore diameter corresponding to the suction at the inflection point of the SWRC (Table 3). The results showed a close equivalent pore diameter for compacted and non-compacted soil at the inflection point when the SWRC was plotted with ln(h) or log(h) as independent variable (60 and 74 µm) and according to Dexter [START_REF] Dexter | Soil physical quality: Part I, Theory, effects of soil texture, density, and organic matter, and effects on root growth[END_REF] (58 and 70 µm). On the other hand, the equivalent pore diameter at the inflection point of the SWRC was about four times higher for compacted soil (510 µm) than for the non-compacted soil (134 µm) when the SWRC was plotted with h as independent variable (Table 3).

In contrast to what is indicated by the S-index, however, air would penetrate throughout the soil at a smaller suction, and consequently for a larger equivalent pore diameter for compacted than for non-compacted soil. This result may appear surprising since compaction leads to smaller porosity with a shift of the inflection point on the SWRC to larger suction [START_REF] Bruand | Variation of textural porosity of a clay-loam soil during compaction[END_REF][START_REF] Cui | Soil compaction by wheeling: changes in soil suction caused by compression[END_REF][START_REF] Richard | Effect of compaction on the porosity of a silty soil: Consequences on unsaturated hydraulic properties[END_REF]. The effects of compaction on pore geometry are difficult to understand since they depend on the structure and related pore types prior to compaction, on soil composition and water content, and on the intensity of compaction.

Beneath native vegetation, the soil studied had a weak macrostructure and a pronounced granular structure at the micrometer scale [START_REF] Balbino | Changes in porosity and microagregation in clayey Ferralsols of the Brazilian Cerrado on clearing for pasture[END_REF][START_REF] Volland-Tuduri | A relationship between mass proportion of microaggregates and bulk density in a Brazilian Clayey Oxisol[END_REF]. Since the structure of non-compacted soil is considered as similar to the structure under native vegetation, its theoretical SWRC would be a bimodal curve with two inflection points: (i) the first inflection point would correspond to pore draining resulting from the assemblage of the micro-aggregates and occurring for a very low suction of several hPa such as for coarse sandy soils, and (ii) the second corresponding to pore draining resulting from the assemblage of elementary particles in micro-aggregates and occurring for values of several hundred hPa. Because of the difficulty to correctly measure water retention of the soils studied at several hPa, the second inflection point is the only one that is usually measured [START_REF] Balbino | Changes in porosity and microagregation in clayey Ferralsols of the Brazilian Cerrado on clearing for pasture[END_REF].

When soil is compacted, the pores resulting from the assemblage of microaggregates are transformed into smaller pores [START_REF] Richard | Effect of compaction on the porosity of a silty soil: Consequences on unsaturated hydraulic properties[END_REF][START_REF] Bruand | Variation of textural porosity of a clay-loam soil during compaction[END_REF]. The resulting SWRC contains one inflection point which is related to a continuous distribution of equivalent pore diameters from the smaller pores which were distorted by compaction into those resulting from the assemblage of the elementary particles in micro-aggregates. Fig. 1, based on the results of several studies on similar soils [START_REF] Balbino | Comportement de la phase argileuse lors de la dessiccation dans des Ferralsols microagrégés du Brésil : rôle de la microstructure et de la matière organique[END_REF][START_REF] Vollannd-Tuduri | Direct analysis of microaggregates shrinkage for drying: Application to microaggregates from a Brasilian clayey Ferralsol[END_REF][START_REF] Volland-Tuduri | A relationship between mass proportion of microaggregates and bulk density in a Brazilian Clayey Oxisol[END_REF] illustrates how using such a transformation of porosity makes it possible to pass from a SWRC with a given inflection point and its related equivalent pore diameter for a non-compacted soil, to another SWRC with an inflection corresponding to a larger equivalent pore diameter for compacted soil.

Finally, our results question the value of S as a possible index to determine the physical quality of soil. The values of h at the inflection point determined for compacted and non-compacted soil are low, thus corresponding to a water content close to saturation which should not be optimal for soil tillage.

Conclusion

Our results show that the expression of the SWRC according to ln(h) or log(h) instead of h as independent variable leads to different values of the S-index.

Computing the S-index when the SWRC is expressed with h as independent variable is both mathematically and physically consistent. We also show that independently of the consistency of the approach, the discussion the physical properties of the soil can thus be limited according to the independent variable used. For the soil selected, our results in fact show that calculation of the S-index when it is expressed with h as independent variable significantly increases the relevance of the analysis compared to the range of the S-indices when it is expressed as proposed by Dexter [START_REF] Bruand | Variation of textural porosity of a clay-loam soil during compaction[END_REF]. Further work will aim at determining in which proportion the S-index is affected for a large range of soils and verifying if the use of h as independent variable effectively increases sensitivity of the analysis.

Figure and table legends

Table 1

Principal physicochemical characteristics of the 0-5 cm compacted and 70-75 cm noncompacted layers selected in the studied soil.

Tableau 1

Principales caractéristiques physico-chimiques de l'horizon 0-5 cm compacté et de l'horizon 70-75 cm non-compacté, sélectionnés dans le sol étudié.

Table 2

Gravimetric soil water content (W g g -1 ) of the cores originating from the 0-5 cm compacted (C) and 70-75 cm non-compacted (NC) layers according to the suction (hPa).

Tableau 2

Teneur en eau gravimétrique du sol (W g g -1 ) des cylindres de sol provenant de l'horizon 0-5 cm compacté (C) et de l'horizon 70-75 cm non-compacté (NC), en fonction de la succion (hPa).

Table 3

Fitted parameter values for W vs. h, ln(h), or log(h), and corresponding inflection points and S-values for the 0-5 cm compacted (C) and 70-75 cm non-compacted (NC) layers.

Tableau 3

Valeurs estimées des parameters pour W en fonction de h, ln(h), ou log(h), et valeurs correspondantes des points d'inflexions et des valeurs S pour l'horizon 0-5 cm compacté (C) et de l'horizon 70-75 cm non-compacté (NC).

Table 1

Particle size distribution (1)

Soil

Clay Silt Sand Organic carbon (1) Bulk density (2) Compacted 485 71 444 0.70 1.27 Non-compacted 549 72 380 0.16 1.03 (1) g kg -1

(2) g cm -3 Water content at the inflection point (6) 0.300 0.394 0.266 0.373 0.266 0.365 0.266 0.365 RMSE (7) 0.0065 0.0114 0.0065 0.0106 0.0065 0.0106 0.0065 0.0114 R 2 0.987 0.991 0.988 0.992 0.988 0.992 0.987 0.988 (1) Dimensionless. (2) Units in hPa -1 for h; ln hPa -1 for ln h; and log hPa -1 for log h. (3) Units in hPa for h; ln hPa for ln h; and log hPa for log h. (4) Units for S h (g g -1 hPa -1 ); S ln h (g g -1 ln hPa -1 ); or S log h (g g -1 log hPa -1 ). (5) Unit in µm. (6) Unit in g g -1 .

(7)

      N i i i W W N RMSE 1 2
1 in g g -1 . (8) The standard errors for W s were calculated directly from the measured values. Those for W r , n, α, and m originated from the analysis of variance of errors due to regression when fitting these parameters.

Fig. 1 .

 1 Fig. 1.

Fig. 1 .

 1 Fig. 1.

Fig. 1 .

 1 Fig. 1.

  soil classification. It was located on a private farm (latitude 16.493246 S, longitude 49.310337 W, and altitude 776 m), near the Embrapa Arroz e Feijão Agricultural Research Center, at Santo Antônio de Goiás, GO, Brazil. The native vegetation was a typical Cerrado until 1985. After clearing the land, the soil was occupied by annual crops with conventional tillage for two years and then by a pasture of Brachiaria decumbens cv. Basilisk stapf. The soil was managed according to intensive animal grazing without any addition of fertilizer. This management led to a compaction of the topsoil. In 2006, soil cores were collected with stainless steel 100 cm 3 cylinders

Table 2

 2

	Suction	W -Compacted layer		W -Non-compacted layer
	(hPa)	Replicate 1	Replicate 2	Replicate 3	Replicate 1 Replicate 2	Replicate 3
	0	0.366	0.356	0.380	0.558	0.549	0.523
	10	0.356	0.346	0.355	0.540	0.542	0.516
	30	0.332	0.324	0.306	0.456	0.455	0.432
	60	0.297	0.290	0.281	0.337	0.360	0.333
	100	0.277	0.287	0.271	0.287	0.278	0.277
	330	0.237	0.242	0.237	0.240	0.231	0.227
	800	0.222	0.230	0.226	0.218	0.213	0.214
	4000	0.199	0.206	0.204	0.201	0.195	0.195
	10000	0.185	0.190	0.190	0.193	0.184	0.187
	15000	0.178	0.180	0.181	0.182	0.176	0.175

Acknowledgments

This research is part of the project Embrapa Cerrados-IRD, No. 0203205 (Mapping of the Biome Cerrado Landscape and Functioning of Representative Soils).

Comparison of the different S-index values obtained

At this point, it should be remembered that Dexter and Bird [START_REF] Dexter | Methods for predicting the optimum and the range of soil water contents for tillage based on the water retention curve[END_REF] and Dexter [START_REF] Dexter | Soil physical quality: Part I, Theory, effects of soil texture, density, and organic matter, and effects on root growth[END_REF] derived the S-index formulation from the slope of SWRC plotted in an ln scale, and the result was transformed to a log scale by multiplying it by ln 10; this log scale was then used afterwards. In order to compare and discuss the location of the inflection point according to the independent variable used, we applied the equations developed here and those of Dexter and Bird [START_REF] Dexter | Methods for predicting the optimum and the range of soil water contents for tillage based on the water retention curve[END_REF] and Dexter [START_REF] Dexter | Soil physical quality: Part I, Theory, effects of soil texture, density, and organic matter, and effects on root growth[END_REF] to water retention properties found for compacted and non-compacted soils (Table 2).

The S-index computed using Eq. 1 and multiplied by ln 10 according to Dexter [START_REF] Dexter | Soil physical quality: Part I, Theory, effects of soil texture, density, and organic matter, and effects on root growth[END_REF] was 0.082 and 0.329 for the compacted and non-compacted soils. Using Eq. 16, the slope at the inflection point of the SWRC expressed according to log(h) as independent variable was 0.081 and 0.326 for the compacted and non-compacted soils. These values are very close to the S-index computed as described by Dexter [START_REF] Dexter | Soil physical quality: Part I, Theory, effects of soil texture, density, and organic matter, and effects on root growth[END_REF].

Thus, using an equation of W fitted with h as independent variable and plotted with log(h) as abscissa, or an equation of W fitted with log(h) as independent variable and plotted according to log(h), the slopes of the two curves at the inflection point are very similar. This could be expected since the experimental points remain at the same place in the W -log(h) graph regardless of the independent variable used for the equation to describe the SWRC. Consequently, the slope at the inflection point of the SWRC computed according to Dexter [START_REF] Dexter | Soil physical quality: Part I, Theory, effects of soil texture, density, and organic matter, and effects on root growth[END_REF] to lead to the S-index and used by many authors would have been similar using Eq. 16 instead of Eq. 1.

On the other hand, the location of the inflection point of the curve of W vs. h, and the slope of the curve at this point, have more physical meaning than the corresponding values computed by Dexter [START_REF] Dexter | Soil physical quality: Part I, Theory, effects of soil texture, density, and organic matter, and effects on root growth[END_REF]. The value of h at the inflection point