Meral Gormen

Pascal Pigeon

Yong Wang

Anne Vessières

Siden Top
email: siden.top@upmc.fr

Franck Martial

Christina Gros

Michael J Mcglinchey

Gérard Jaouen

Gerard Jaouen
email: gerard.jaouen@chimie-paristech.fr

Side-chain effects on the 1-(bis-aryl-methylidene)-[3]ferrocenophane skeleton: antiproliferative activity against TNBC cancer cells and comparison with the acyclic ferrocifen series

Keywords: Ferrocene, tamoxifen, breast cancer, bioorganometallic chemistry, SERM

As part of our ongoing study of the toxicity of compounds derived from 1,1-di(4hydroxyphenyl)-2-ferrocenyl-but-1-ene, we recently showed that closely analogous [3]ferrocenophane complexes had an in vitro toxicity level substantially higher than that of their ferrocene counterparts, particularly in the case of mono-and diphenol complexes. In the current study we examined whether the presence of a dimethylamino chain, analogous to the chain in hydroxytamoxifen, was capable of producing in the ferrocenophane series the same antiestrogenic effect observed for OH-Tam and Fc-OH-Tam. To this end we synthesized and characterized new complexes bearing various side-chains, [O(CH2)3NMe2, O(CH2)3piperidine, O(CH2)3pyrrolidine, NHCO(CH2)2NMe2], and studied a number of biochemical properties in those complexes possessing appropriate solubility. The results revealed that the new complexes of [3]ferrocenophane have very strong antiproliferative effects; one of the compounds bearing an NHCO(CH2)2NMe2 chain has an IC50 value of 0.05 ± 0.02 M on MDA-MB-231 cells. All these complexes retain affinity for the estradiol receptor. At the low (nanomolar range) concentrations at which the estrogenic/antiestrogenic

effect is expressed in these molecules, the presence of an amino side-chain does not induce in the [3]ferrocenophane series the antiestrogenic effect observed with OH-Tam and Fc-OH-Tam. However, this effect is found for the complex with a slightly longer chain (O(CH2)4NMe2).

1-Introduction

Breast cancers remain the principal cause of cancer deaths in Europe causing almost 131,000 deaths in 2012. [START_REF]δ 2[END_REF] About two-thirds of primary tumours, those classed as hormone-dependent (ER+) express the estradiol receptor and are stimulated by estrogens. Adjuvant treatment for this type of cancer most commonly includes prescription of antiestrogens (or SERMs, selective estrogen receptor modulators), molecules that can inhibit the growth of these tumours. Hydroxytamoxifen (OH-Tam 1;

Figure 1), the reference antiestrogen, is administered in the form of tamoxifen citrate, the nonhydroxylated pro-drug. The mechanism of action of OH-Tam has been widely studied and extensively described. [2] Thanks to its phenol group, OH-Tam binds at the HBD (hormone binding site) of the estrogen receptor, but the presence of the long amino chain entails a significant modification at this level, namely the displacement of helix 12. This modified receptor binds as a dimer to the estrogen response element (ERE) of the DNA of ER+ cells, but does not permit recruitment of the co-factors necessary to activate DNA transcription. Thus low concentrations (10 nM) of OH-Tam produce a diminution in the proliferation of hormone-dependent breast cancer cells (MCF-7). However, since its effect is entirely linked to an interaction with the estrogen receptor, OH-Tam has no effect, at submicromolar concentration, on the growth of hormone-independent breast cancer cells, such as the triple negative breast cancer (TNBC) MDA-MB-231, which do not express the estrogen receptor. The two chief advantages of OH-Tam are thus its affinity for the estradiol receptor, and the presence of an amino chain that modifies the structure of the receptor such that cellular proliferation is significantly lowered. However, in the related acyclic ferrocifen series the presence of the "ferrocenyl-ene-phenol" unit triggers on cancer cells an additional cytotoxic effect that can be modulated by the basic amine chain. [3] We now describe this behavior in the ferrocenophane series. We have shown that Fc-OH-Tam, 2, in which the phenyl group in hydroxytamoxifen, 1, has been replaced by a ferrocenyl substituent, has an antiproliferative effect in vitro on both hormone-dependent (MCF-7) and hormone-independent (MDA-MB-231) breast cancer cells. [3][4][5][6][7] In hormone-dependent cells this effect is essentially mediated by interaction with the estradiol receptor, and reversed by addition of estradiol. In contrast, the antiproliferative effect observed on hormone-independent cells such as MDA-MB-231 cells is a cytotoxic one. [8] This cytotoxic effect is also observed with the diphenol compound Fc-diOH, 3. [9] We have found that the most effective compounds (IC50 values less than 1 µM) possess, like 2 and 3, a ferrocene-ene-paraphenol entity. [10,11] The ferrocene appears to act as a stimulus for a mild intramolecular oxidation involving the phenol group, leading to the facile production of quinone methides whose formation, structure and electrophilic behaviour we have established. [12][13][14][15] A Structure-Activity Relationship (SAR) study extended to include a number of ferrocene complexes has allowed us to identify another molecule, the cyclic diphenol 4 derived from [3]ferrocenophane, whose toxicity on MDA-MB-231 cells is noticeably greater than that of Fc-diOH (IC50 values of 0.09 M for 4 versus 0.6 µM for 3). [16] In addition, the toxicity of the two diphenols 3 and 4 has been tested on the panel of 60 cell lines of the National Cancer Institute (Bethesda, MD, USA). The results show that the [3]ferrocenophane 4 is more toxic overall than Fc-diOH, 3 (mean IC50 values are 0.18 and 0.52 µM, respectively). The activity profiles of these compounds also show that 3 and 4 probably do not share the same mechanism of action either with each other or with the 171 reference molecules in the database, and in particular that they do not act, like cisplatin, via an alkylation of DNA. [17] The diphenol 4 possesses, like 3, a moderate level of affinity for the estradiol receptor.

As a result, both show a proliferative effect at low concentrations (10 -8 M) on hormonedependent MCF-7 cells, that partially offsets the cytotoxic effect caused by the oxidation of the ferrocene. To better understand the effect of the side chain on the antiproliferative activity of ferrocene and [3]ferrocenophane derivatives, several new compounds containing an amino chain have been synthesized and studied for their cytotoxic and their estrogenic/antiestrogenic effects. The first such molecule was compound 7; subsequently, we prepared the analogous complexes of pyrrolidine, 10, of piperidine, 11, and also molecule 14 which contains an -O(CH2)4N(CH3)2 unit. Interestingly, it has recently been reported that the presence of an amide function on the basic chain of certain SERMs modified their properties by preventing their recognition by the estrogen receptor. [18] We therefore prepared complex 12, bearing the chain containing an NHCO(CH2)2NMe2 amide function. Since we also found that replacement of the OH groups in 4 by NH2 or H gave cytotoxic products (5 and 6), we also synthesized complexes 8, 9 and 13 that possessed alkoxyamino chains, but no hydroxyl units. Finally, to allow direct comparison between the ferrocene and ferrocenophane series, the ferrocene complexes 15 and 16 were synthesized. In total, ten new complexes, listed in Figure 2, were synthesized and studied.

2-1 Synthesis of the ferrocenophane and ferrocenyl complexes

2-1-1 Synthesis of the complexes with a dimethylaminopropyl chain 7 -9

Compounds 7, 8 and 9 were synthesized in a one-step reaction starting from 4, 17 and 18 by alkylation of the hydroxyl group (Scheme 1). Sodium hydride was used to generate the corresponding phenolate from each of these compounds which, when heated with 3dimethylamino-1-propyl hydrochloride in DMF at 80°C for 12 hours, furnished 7, 8 and 9 in 27%, 66% and 83% yields, respectively. All the products were obtained as mixtures of (E+Z) isomers in various proportions (see Experimental Section). Treatment of 20 with dimethylamine provides an alternative route to 7, but in this case the overall yield is quite low (13%). Similarly, reaction of the bromo precursor, 21, (obtained by alkylation of 4 with dibromobutane) with dimethylamine yielded 14 (26%), which contains an -O(CH2)4N(CH3)2 chain (Scheme 3). Scheme 3: Synthesis of the [3]ferrocenophane, 14, containing an -O(CH2)4N(CH3)2 chain.

2-1-3 Synthesis of the amidyl [3]ferrocenophane or ferrocene derivatives 12, 13, 15, and 16

Complexes 12, 13, 15, and 16, were prepared in two-step reactions starting from 17 [19] , 22 [20] , 23 [17] and 24 [21] (Scheme 4). The amino function was first transformed into a chloroamido chain by reaction of 3-chloropropionylchloride in the presence of pyridine as a base; in these cases, the acyl chloride reacts exclusively on the amino function. The [3]ferrocenophane chloro compounds 25 and 26 were obtained in high yields (88%, 98%), while the yields of the ferrocenyl chloro compounds 27 and 28 were only moderate (44% and 39%, respectively). Amination of the chloro compounds was carried out by heating a solution of each of the compounds in methanol containing dimethylamine at 60 °C. All compounds were obtained in high yields, 89-97%, as a mixture of E and Z isomers. Scheme 4. Synthesis of the amidyl [3]ferrocenophane and ferrocene derivatives 12, 13, 15 and 16

2-2 X-ray crystal structure of 26

To establish the identity of a typical example of one the new compounds unequivocally, the X-ray crystal structure of Z-1-[ (4-(3-chloropropionyl)aminophenylphenyl)-methylidene]- [3]ferrocenophane, 26, was determined. Crystallization from acetonitrile of the E+Z mixture gave a suitable sample of the Z isomer whose structure is shown in Figure 3. The geometry of the [3]ferrocenophane moiety in 26 closely resembles those reported previously. [19,22] The system crystallizes with two independent molecules in the unit cell. As expected, the three-carbon bridge between the two cyclopentadienyl rings is too short for them to maintain their coplanarity, and the dihedral angles between the ring planes in the independent molecules are 9.5° and 10°. The Fe-CCp distances range from 2.028(11) to 2.084 (14), and the bond lengths in the three-carbon bridge are C1-C11 = 1.509 (13), C11-C12

Biological Results

The biological effects of the newly synthesized complexes were studied and compared to those of two reference compounds, 2 and 4. Four types of experiments were carried out: (1) study of the antiproliferative effect on MDA-MB-231 cells, hormone-independent cells which allow the cytotoxicity of the molecules to be tested; (2) determination of Relative Binding Affinity (RBA) values for these compounds, to establish whether or not they possess an affinity for the estradiol receptor; (3) study of the proliferative/antiproliferative effect of these complexes on hormone-dependent MCF-7 cells at low concentrations (in the nanomolar range), to ascertain whether the addition of a long side chain reveals antiestrogenic effects, (4) measurement of the lipophilicity of the complexes.

Study of the antiproliferative effect of the complexes on hormone-independent

MDA-MB-231 cells

The IC50 values of the new compounds 7-16 for the MDA-MB-231 cancer cells are collected in Table 1. We note that all the new compounds are characterized by antiproliferative activity that ranges from good to excellent. Replacement of the OH group by NH2, as in compounds 7 and 8, does not change the cytotoxic activity of these compounds. The IC50 values of compounds 7, 8, and 10 are between 0.17 and 0.19 M, that is two times less efficacious than the diphenol 4 (0.09 M), but they are still among the best compounds that we have obtained.

The lipophilicity of these four compounds does not appear to play an important role. Once again, it demonstrates that systems lacking an OH group, as in 9, 13 and 16, are less active than their analogues that do possess it. Substitution of the amino chain -O(CH2)3NMe2 by the amido chain -NHCO(CH2)2NMe2 produces different effects. Compounds 9 and 13 have almost the same IC50 value, but the amido compound 12 is three times more active than 7 (0.05 M versus 0.18 M). At present therefore, molecule 12 is one of the three most efficacious of all the ferrocenyl derivatives that we have prepared. [17] For comparison, we have also included the IC50 values for molecules 29 and 30 that were synthesized previously; [23] these latter compounds are less effective than compounds 12 et 13. The lengthening of the amido chain may be the cause of their diminished activity.

Globally, molecules in the ferrocenophane series are more active than their ferrocene counterparts; to be precise, compounds 4, 7, 12 and 13 are, respectively, 7, 3, 13 and 3 times better than compounds 3, 2, 15 and 16. We recently shown that enzymatic oxidation of 4, the most studied complex in the ferrocenophane series, leads to the formation of a transient shortlived species attributed to a quinone methide radical. [24] On the contrary, the enzymatic oxidation of the ferrocenyl complexes 2 or 3 leads to the formation of quinone methides. [25] Reactivity of a radical is expected to be higher than that of the quinone methide and could explain the higher cytotoxicity of the ferrocenophane complexes. Substitution of the amino chain of 4 by an amido chain gives access to 12, the most cytotoxic complex of the series. The precise role of this amido chain has not yet been elucidated and will be the subject of further study.

Relative binding affinity values for the alpha form of the estrogen receptor (ER) and LogPo/w of the compounds

The relative binding affinity values (RBA) of the compounds were measured for the alpha form of the estrogen receptor and are reported in Table 1. All the complexes showed a significant affinity for the estrogen receptor, even those lacking an OH substituent. There is no clear difference between the ferrocenophane and the ferrocenyl complexes. The RBA values found for the disubstituted complexes possessing an amino side chain plus another substituent (OH or NH2) are high (between 10-23%), the highest value being obtained for 15, the ferrocenyl derivatives with the NHCO(CH2)2NMe2 side-chain. Finally, values of around 4% were found for the three mono substituted complexes bearing only an amino chain.

The lipophilicity values obtained for the different complexes are shown in Table 1.

These values are very close for the three ferrocene complexes (4.3 -4.6) while varying significantly for the ferrocenophane complexes (2.4 -4.7). In addition, the logPo/w values of the ferrocene complexes are always higher than those of their ferrocenophane counterparts.

Finally, complexes 9 and 12 have lipophilicity values very close to those of estradiol (3.5) and OH-Tam (3.2 and 3.4). [3]

Estrogenic/antiestrogenic effect of the complexes in vitro on MCF-7 cells

The effect of the new complexes on the growth of MCF-7 hormone dependent cells was then studied and the results are shown in Figure 4. The characteristic proliferative effect of estradiol is observed, and it is clearly evident that the behavior of the complexes of the ferrocenophane family differs from that of the ferrocenyls. In the case of the ferrocene complexes 15 and 16 an antiproliferative effect is observed analogous to that observed earlier for Fc-OH-Tam, which is attributed to an antiestrogenic effect. This effect is not found in the ferrocenophane series. Instead a slight estrogenic effect is observed in the complexes of this series for 7, 8, 12 and 13, but not for 9 which shows no effect. This result appears to show that the constraint imposed by the presence of a carbon chain linking the two ferrocene rings prevents the expression of the antiestrogenic effect produced by the presence of the long dimethylamino chain in OH-Tam or Fc-OH-Tam. It is interesting to note that in the ferrocene series the antiestrogenic effect of the two complexes 15 and 16, both of which bear the NHCO(CH2)2NMe2 chain, is identical to that of Fc-OH-Tam 2 and does not depend on the presence of an OH substituent. In addition, it should be mentioned that the analogue of OH-Tam bearing a ferrocenic chain OCH2COFc instead of an amino chain expresses an estrogenic effect at 10 nM. [26] We then decided to take a closer look at the estrogenic/antiestrogenic effects of compounds 7 and 14 which differ only in the length of their aminated chain. Figure 5 shows the effect of these two complexes on MCF-7 at 3 concentrations (1, 10, 100 nM). At 1 nM compound 7 provokes an estrogenic effect; this effect diminishes at 10 nM and inverts at 100 nM, without doubt because of the appearance of the cytotoxic effect. By way of contrast, for compound 14 the antiestrogenic effect has already been evident from 1 nM. This result can perhaps be explained by the lengthening of the amino chain, from three to four methylenes, which allows the molecule to bind better with the antiestrogenic conformation of the receptor site, as verified by the modelling study below.

Molecular modeling

Molecular docking experiments using the crystal structure of the ligand binding domain (LBD) of human ER (hER) as described by Shiau and al. [27] were performed using the program Spartan 14. [START_REF] Wavefunctionco | 18401 Von Karman avenue[END_REF] Only the amino acids that constitute the wall of the cavity have been retained. The organic molecule was removed from the cavity and replaced successively with the organometallic bio-ligands. Only Z isomers were calculated since it had previously been shown that the Z form of ferrocifen 2 shows better recognition for the receptor. [3] Energy minimisation was then carried out using the Merck molecular force field (MMFF) with the heavy atoms (non-hydrogen) of the amino acids of the cavity wall immobilised, then the geometry was optimized using quantum mechanical semi-empirical PM3 methods. This allowed the ideal positions of the bio-ligands to be determined. Quantum mechanical semiempirical PM3 methods were then used to determine the affinity of the bio-ligands for the cavity. This requires calculation of the energies of bio-ligand cavity group, of the cavity itself, and of the ligand, the latter two in the conformations they had in the molecular assemblies to give the rH° enthalpy variations of the reactions: bio-ligand + cavity → molecular assembly (Table 2).

For the two compounds, binding to the ER is thermodynamically favoured, as evidenced by the negative enthalpy of formation for the ligand-receptor complex. The most negative value for 14 shows better affinity for the cavity than 7. Moreover, the calculations reveal a higher possibility for a hydrogen bond between the proton on the carboxylic moiety of the aspartic acid Asp 351 and the nitrogen atom of the bio-ligand for 14 than for 7. The These results could be explained by the fact that the cyclic character of the ferrocenophane engenders additional steric hindrance, as compared to the ferrocifen, that hampers the formation of the hydrogen bonds with the dimethylaminopropyl chain. The longer dimethylaminobutyl chain in 14 can compensate for this hindrance. This could be the reason for the loss of estrogenicity in 14, that appears for 7 at low concentrations (10 -8 , 10 -9 M). For clarity, the bioligands and three important amino acids are shown as ball and spoke while other amino acids appear as stick representations.

Conclusions

The synthesis of novel complexes in the ferrocene and ferrocenophane series with amino side-chains has produced molecules with very clear cytotoxic effects on MDA-MB-231 hormone-independent breast cancer cells. The mechanistic particularity of 4, the most studied complex in the ferrocenophane series, has recently been disclosed and is associated with an active radical intermediate. [24] All the complexes in the series retain an affinity for the estrogen receptor, but only those of the acyclic ferrocenyl series express an antiestrogenic effect analogous to that of OH-Tam on hormone-dependent MCF-7 cells. This effect is not found in their analogs in the ferrocenophane series except for 14. Actually it is possible to turn the estrogenic effect into an antiestrogenic one by lengthening the amino chain (as in the case of 7 and 14). However, it is noteworthy that compound 9 is neutral in this respect. At this time, where the issue of SERMs that act as endocrine disrupters is the focus of serious examination, these results illustrate the subtlety of the effects, and emphasise the care that one must bring to their analysis.

Experimental Section

General Remarks. THF was obtained by distillation from sodium/benzophenone. Thin layer chromatography was performed on silica gel 60GF254. The preparative HPLC separations were performed on a Shimadzu apparatus with a Nucleodur C18 column (length 25 cm, diameter 3.2 cm, and particle size 10 mm) using acetonitrile or acetonitrile/water as an eluent.

Column chromatography purifications were performed by using silica gel with appropriate eluent. The analytical HPLC controls were performed on a Shimadzu apparatus with a Nucleodur C18 column (length 15 cm, diameter 0.45 cm, and particle size 5 µm) using acetonitrile as an eluent. 1 H and 13 C NMR spectra were recorded on a 300 MHz Bruker spectrometer. Mass spectrometry was performed with a Nermag R 10-10C spectrometer. All compounds were isolated as a mixture of Z:E isomers. Identification of Z and E configurations was possible only for the compounds with a large excess of one isomer (9, 29,

30).

General Procedure 1: Alkylation of phenol groups

In each case, the appropriate compound was dissolved in DMF and sodium hydride was added. The mixture was stirred for 10 min, 3-dimethylamino-1-propyl chloride hydrochloride was added and the mixture heated at 90°C overnight. Additional 3-dimethylamino-1-propyl chloride hydrochloride was then added, and heating was continued for 4 hours. The mixture was cooled and concentrated under reduced pressure, the residue was dissolved in dichloromethane and was washed twice with a diluted aqueous solution of sodium hydroxide, followed with water. After drying over magnesium sulphate, the solution was concentrated under reduced pressure and the residue was chromatographed on silica gel with a 4/1 solution of chloroform/triethylamine as eluent. The residue was recrystallized from appropriate solution to yield the product. prepared previously by using another synthetic procedure and tested for its antiplasmodial activity. [START_REF] Bellotti De Souza | [END_REF] General procedure 2: Preparation of compounds 7 (second method), 10, 11. Titanium chloride (4.66 g, 2.7 mL, 24.6 mmol) was added dropwise to a suspension of zinc powder (2.41 g, 36.8 mmol) in 100 mL of dry THF at 10-20°C and the mixture was heated at reflux for 2 h. A second solution was prepared by dissolving [3]ferrocenophan-1-one (1.47 g, 6.14 mmol) and bromo compound 19 (2.06 g, 6.14 mmol) in 25 mL of dry THF. This latter solution was added dropwise to the first solution and then the reflux was continued overnight.

1-[(4-(3-dimethylaminopropoxy)phenyl-4-hydroxyphenyl)methylidene]-[

After cooling to room temperature, the mixture was stirred with water and dichloromethane.

The mixture was acidified with diluted hydrochloric acid until the dark color disappeared and was decanted. The aqueous layer was extracted with dichloromethane and the combination of organic layers was dried on magnesium sulphate. After concentration under reduced pressure, the crude product was chromatographed on silica gel column with dichloromethane as an eluent to recover the second of the most colored bands (MS (CI, NH3) m/z: 543 [M+H] + ) that contained the compound 20 contaminated by inseparable dehydrohalogenated compound.

This crude compound was used without further purification in the second step. It was transferred into a pressure tube and a solution of amine in methanol (60 mmol of amine) was added. The pressure tube was heated at 60°C for 24 hours, then cooled to room temperature.

The work-up was done depending on the amine.

1-[(4-(3-Dimethylaminopropoxy)phenyl-4-hydroxyphenyl)methylidene]-[3]ferrocenophane, 7 (second method).

Dimethylamine in methanol (2 M, 30 mL, 60 mmol) was commercially available. The mixture was concentrated under reduced pressure and the residue was chromatographed on a silica gel column with acetone, then acetone/triethylamine 10/1 as the eluents. After concentration under reduced pressure, the residue was recrystallized from acetone to obtain yellow crystals of 7 (yield 21%). 13

1-[(4-(3-(N-piperidinyl)propoxy)phenyl-4-hydroxyphenyl)methylidene]-

[3]ferrocenophane, 11. The solution of piperidine was made up with 5.22 g of piperidine in 15 mL of methanol. The compound 11 precipitated and was simply filtered off to recover 1.23 g (yield : 37%) as a mixture of Z and E isomers (90/10). [START_REF]δ 2[END_REF] H NMR (DMSO-d6, 300 MHz): δ.

General Procedure 3: Acylation of aniline groups

In a Schlenk flask, the appropriate ferrocenyl amino compound was dissolved in 30 mL of anhydrous THF. Appropriate acetyl chloride derivatives and pyridine were added and the reaction mixture was left to stir at room temperature for 3 hours. The mixture was poured into water and extracted with dichloromethane. The organic layer was washed with water, dried over magnesium sulphate, filtered, and concentrated under reduced pressure. The crude mixture was filtered over silica gel using petroleum ether and CH2Cl2, concentrated under reduced pressure, and purified by HPLC (acetonitrile/H2O). Then, recrystallization from appropriate solvent systems formed desired products as crystals consisting of a mixture of Z and E isomers. Analogously, 2-Ferrocenyl-1-(4-aminophenyl)-

1-[(4-(3-chloropropionyl)aminophenyl)-(4-hydroxyphenyl)methylidene]-

General Procedure 4: Dimethylamination

In a pressure tube, the appropriate 3-chloropropionylamino compound was dissolved in 2.0 M dimethylamine solution in methanol. The reaction mixture was heated to 60° C with stirring for 1 day. The mixture was concentrated under reduced pressure, a saturated solution of NaHCO3 and dichloromethane were added and, after decantation, the organic layer was washed with water, dried on magnesium sulfate and concentrated under reduced pressure. The crude mixture was purified by flash column chromatography (Acetone/Et3N: 10 / 1); some were recrystallized from appropriate solvent system to yield a mixture of Z and E isomers.

Table of contents

Figure 1 :

 1 Figure 1 : OH-Tamoxifen and several ferrocenyl and [3]ferrocenophane derivatives

Figure 2 :

 2 Figure 2 : Newly synthesized complexes

Scheme 1 :Scheme 2 .

 12 Scheme 1: Synthesis of the[3]ferrocenophane derivatives with an alkyl dimethylamino chain

Figure 3 .

 3 Figure 3. Molecular structure of Z-1-[(4-(3-chloropropionyl)aminophenyl-phenyl)-

Figure 4 .

 4 Figure 4. Study of the estrogenic / antiestrogenic effect of the complexes on MCF-7 cells after 5 days of culture in the presence of 1 nM of E2, 7, 8, 12 and 10 nM of 2, 4, 9, 13, 15, 16, in a medium without phenol red. The grey bars represent the ferrocenophane complexes and the hatched bars the ferrocenyl complexes. Representative data of one experiment performed twice or three times with similar results.

Figure 5 .

 5 Figure 5. Study of the estrogenic / antiestrogenic effect of 7 and 14 on MCF-7 cells after 4 days of culture in the presence of 1, 10, 100 nM in a medium without phenol red. Representative data of one experiment performed twice with similar results.

Figure 6 .

 6 Figure 6. The bio-ligands, the aspartic acid Asp 351 and two other important amino acids for

Figure 6 .

 6 Figure 6. Docking of Z isomers of 7 (left) and 14 (right) in the antagonist binding site of the  form of the human estrogen receptor (h-ER). For clarity, the bioligands and three important amino acids are shown as ball and spoke while other amino acids appear as stick representations.

HRMS measurements were performed

  on a Thermo Fischer LTQ-Orbitrap XL apparatus equipped with an electrospray source by the Institut Parisien de Chimie Moléculaire (UMR 7201), Université Pierre et Marie Curie, Paris. Elemental analyses were performed by the microanalysis service of ICSN (Gif sur Yvette, France). Cytotoxicity measurements on MCF-7 breast cancer cells, and some of MDA-MB-231 breast cancer cells in vitro, were performed by Institut Parisien de Chimie Moléculaire (UMR 8232), Université Pierre et Marie Curie, Paris and by ImaGIF Ciblothèque Cellulaire (Institut de Chimie des Substances Naturelles).

10 .

 10 The solution of pyrrolidine was made up from 4.36 g of pyrrolidine in 15 mL of methanol. The compound 10 precipitated and was just filtered off to recover 0.88 g (yield : 27%) as a mixture of Z and E isomers (79/21

0 (

 0 C NMR (DMSO-d6, 75.4 MHz): δ 22.7 (CH2 + 2CH2 pyrrolidine), 25.5 (CH2, cycle), 27.9 (CH2, cycle), 51.3 (CH2N), 52.9 (2CH2, pyrrolidine), 64.8 (CH2O), 68.0 (2CH, C5H4), 68.4 (2CH, C5H4), 69.6 (2CH, C5H4), 70.0 (2CH, C5H4), 83.6 (C, C5H4), 86.4 (C, C5H4), 113.1 and 114.2CH, C6H4), 114.1 and 114.9 (2CH, C6H4), 130.0 (2CH, C6H4), 131.1 (2CH, C6H4), 132.3 (C), 133.8 (C), 136.0 (C), 139.7 (C), 155.4 (C), 156.9 (C). MS (CI, NH3) m/z: 534 [M+H] + , 453 [M-(CH2)3N(CH2)4+H] + . HRMS (ESI, C33H36FeNO2: [M+H] + ) calcd: 534.2095, found: 534.2111.

  [3]ferrocenophane, 25. 1-[(4-Aminophenyl-4-hydroxyphenyl)methylidene]-[3]ferrocenophane, 17 (0.3 g,

[ 3 H 4 . 4 . 3 . 4

 34434 ]-E2. The RBA value of E2 is by definition equal to 100%.Measurement of octanol/water partition coefficient (logPo/w) of the compounds. The logPo/w values of the compounds were determined by reverse-phase HPLC on a C-8 column (Nucleosil C8, from Macherey Nagel, France) according to the method previously described in reference Culture Conditions. Cells were maintained in monolayer culture in DMEM with phenol red/Glutamax I, supplemented with 9% of decomplemented fetal calf serum and 0.9% kanamycine, at 37°C in a 5% CO2 air humidified incubator. For proliferation assays, cells were plated in 24-well sterile plates at a density of 1.1.10 4 cells for MDA-MB-231 and of 3.10 4 cells for MCF-7 in 1 mL of DMEM without phenol red, supplemented with 9% of fetal calf serum desteroided on dextran charcoal, 0.9% Glutamax I and 0.9% kanamycine, and were incubated for 24 h. The following day (D0), 1 mL of the same medium containing the compounds to be tested diluted in DMSO, was added to the plates (final volumes of DMSO: 0.1% ; 4 wells for each conditions). After three days (D3), the incubation medium was removed and 2 mL of fresh medium containing the compounds was added. At different days (D4, D5), the protein content of each well was quantified by methylene blue staining as follows. Cell monolayers were fixed and stained for 1h in methanol with methylene blue (2.5 mg/mL), and then washed thoroughly with water. Two milliliters of HCl (0.1 M) was then added, and the plate was incubated for 1h at 37°C. Then the absorbance of each well was measured at 655 nm with a Biorad spectrophotometer (microplate reader). The results are expressed as the percentage of proteins versus the control. Experiments were performed at least in duplicate. Some cytotoxicity measurements on MDA-MB-231 breast cancer cells were performed by ImaGIF Ciblothèque Cellulaire (Institut de Chimie des Substances Naturelles).

[ 3 ]CaptionsScheme 1 : 2 . 3 :Scheme 4 . 16 Figure 1 :

 31234161 Scheme 1: Synthesis of the [3]ferrocenophane derivatives with an alkyl dimethylamino chain Scheme 2. Synthesis of the [3]ferrocenophane derivatives with a pyrrolidine or piperidine, side-chain Scheme 3: Synthesis of the [3]ferrocenophane 14 , containing an -O(CH2)4N(CH3)2 chain Scheme 4. Synthesis of the amidyl [3]ferrocenophane and ferrocene derivatives 12, 13, 15 and 16

Figure 2 :Figure 3 .

 23 Figure 2 : Newly synthesized complexes Figure 3. Molecular structure of Z-1-[(4-(3-chloropropionyl)aminophenyl-phenyl)-

Figure 4 .

 4 Figure 4. Study of the estrogenic/antiestrogenic effect of the complexes on MCF-7 cells after 5 days of culture in the presence of 1 nM of E2, 7, 8 and 12 and of 10 nM of 2, 4, 9,

Figure 5 .Figure 6 .

 56 Figure 5. Study of the estrogenic/antiestrogenic effect of 7 and 14 on MCF-7 cells after 4 days of culture at 10 -7 , 10 -8 and 10 -9 M Figure 6. Docking of Z isomers 7 (left) and 14 (right) in the antagonist binding site of the  form of the human estrogen receptor (h-ER). For clarity, the bioligands and three important amino acids are shown as ball and spoke while other amino acids appear as stick representations..

Table 1

 1 IC50 values of the ferrocenophane (A series) and ferrocenyl (B series) complexes on hormone-independent breast cancer cell line (MDA-MB-231), Relative Binding Affinity (RBA) on the alpha form of the estrogen receptor, and lipophilicity (LogPo/w)

Table 1

 1

		IC50 values of the ferrocenophane (Series A) and ferrocenyl (Series B) complexes on
	the hormone-independent breast cancer cell line (MDA-MB-231), Relative Binding Affinity
	(RBA) on the alpha form of the estrogen receptor, and lipophilicity (LogPo/w)
	Compound R1	R2	Z, E % a	MDA-MB-231 IC50 (M) on	on ER RBA(%)	LogPo/w
	Series A
	4	OH	OH	-	0.09 ± 0.01 c	7.2 c	4.6
	7	O(CH2)3NMe2	OH	72/28	0.18 ± 0.04	17.2	2.4 ; 2.7 e
	8	O(CH2)3NMe2	NH2	52/48	0.17 ± 0.02	14.4	4.4 ; 4.7 e
	9	O(CH2)3NMe2	H	94/6 b	0.37 ± 0.11	4.8	3.5
	10	O(CH2)3Npyr	OH	79/21	0.19 ± 0.05	-	-
	11	O(CH2)3Npip	OH	90/10	1.10 ± 0.11	-	-
	12	NHCO(CH2)2NMe2	OH	59/41	0.05 ± 0.02	10.3	3.3
	13	NHCO(CH2)2NMe2	H	83/17	0.39 ± 0.03	4.4	4.4
	14	O(CH2)4NMe2	OH	60/40	0.12 ± 0.06	-	3.0, 3.1 e
	29	NHCO(CH2)6NH2	H	94/6 b,f	0.84 ± 0.28 f	-	-
	30	NHCO(CH2)6NHOH	H	89/11 b,f	0.94 ± 0.08 f	-	-
	Series B
	3	OH	OH	-	0.64 ± 0.06	9.6 d	5.0 g
	Fc-OHTam 2 O(CH2)3NMe2	OH	50/50 h	0.50	11.5 d	4.3 ; 4.5 e
	15	NHCO(CH2)2NMe2	OH	53/47	0.67 ± 0.00	23	4.5 ; 4.6 e
	16	NHCO(CH2)2NMe2	H	67/33	1.13 ± 0.03	4	4.6

a) all the compounds are mixtures of (E+Z) isomers; b) Z configuration attributed to the major isomer (see experimental section); c) values from ref. 16; d) values from ref. 3; e) values for each isomer; f) values from ref. 23; g) values from ref. 9. h) value from ref 4.

Table 2

 2 Enthalpy variation values for the Z bio-ligands docked into ER, and H-N distances Compounds rH°/kJ mol -1 O-H…N distance (Å)

	7	-97	2.81
	14	-106	1.91

  Hz, 4H, and 135.9 (C), 140.5 and 140.6 (C), 143.4 and 143.8 (C), 157.1 and 157.7 (C). MS (EI, 70 eV) m/z: 491 [M] + , 405 [M-NMe2CH2CH2] + , 86 [NMe2CH2CH2] + , 58 [NMe2CH2] + . HRMS (ESI, C31H34FeNO: [M+H] + ) calcd: 492.1990, found: 492.1998. This compound has been

	chromatography with acetone/NEt3 10/1 eluent system and then recrystallization from
	acetone, 7 (162 mg, 27%) was obtained as a bright yellow product as a mixture of E and Z
	isomers (72/28). 1 H NMR (DMSO-d6, 300 MHz): δ 1.69-1.91 (m, 2H, CH2), 2.10 and 2.15 (s,
	6H, NMe2), 2.22-2.41 (m, 4H, CH2N+CH2 cycle), 2.57-2.69 (m, 2H, CH2 cycle), 3.86 and
	3.99 (t, J = 6.4 Hz, 2H, CH2O), 3.93 (t, J = 1.8 Hz, 2H, C5H4), 3.96 (t, J = 1.8 Hz, 2H,
	C5H4), 3.98 (t, J = 1.8 Hz, 2H, C5H4), 4.27 (t, J = 1.8 Hz, 2H, C5H4), 6.45 and 6.61 (d, J =
	8.7 Hz, 2H, C6H4), 6.73 and 6.90 (d, J = 8.7 Hz, 2H, C6H4), 6.74 and 6.83 (d, J = 8.7 Hz, 2H,
	C6H4), 6.97 and 7.08 (d, J = 8.7 Hz, 2H, C6H4), 9.23 and 9.43 (s, 1H, OH). 13 C NMR (DMSO-
	d6, 75.4 MHz): δ 26.8 (CH2), 27.9 (CH2), 40.4 (CH2), 45.1 (2CH3, NMe2), 55.6 (CH2), 65.4
	(CH2O), 68.0 (2CH, C5H4), 68.4 (2CH, C5H4), 69.6 (2CH, C5H4), 70.0 (2CH, C5H4), 83.6
	(Cip), 86.6 (Cip), 113.0 (2CH, C6H4), 114.9 (2CH, C6H4), 130.0 (2CH, C6H4), 131.2 (2CH,
	sodium hydride (23 mg, 0.9 mmol), 3-dimethylamino-1-propyl chloride hydrochloride (42
	mg, 0.3 mmol) were treated as described above. After purification by column chromatography
	with acetone / NEt3 (10/1) eluent system and then recrystallization from diethylether +
	pentane solvent system, 8 (79 mg, 66%) was obtained as a bright yellow product as a mixture
	3]ferroceno-of E and Z isomers (52/48). 1 H NMR (300 MHz, acetone-d6): δ 1.84-1.92 (m, 2H, CH2), 2.14
	phane, 7. Compound 4 (500 mg, 1.18 mmol), prepared as indicated in ref. 16, sodium hydride and 2.19 (s, 6H, CH3), 2.30-2.56 (m, 4H, CH2), 2.65-2.69 and 2.72-2.78 (m, 2H, CH2), 3.90-
	(94 mg, 2.36 mmol), 3-dimethylamino-1-propyl chloride hydrochloride (150 mg, 0.95 mmol),
	40 mL of DMF were treated as described above. After purification by column

C6H4), 133.9 (C), 135.6 (C), 139.8 (C), 145.4 (C), 156.0 (C), 156.6 (C). MS (EI, 70 eV) m/z: 508 [M] +. , 86 [NMe2CH2CH2] + , 58 [NMe2CH2] + . HRMS (ESI, C31H34FeNO2: [M+H] + ) calcd: 508.1939, found: 508.1943. 1-[(4-(3-Dimethylaminopropoxy)phenyl-4-aminophenyl)methylidene]-[3]ferrocenophane, 8. Analogously, 17 (100 mg, 0.24 mmol) prepared as indicated in ref. 19, 4.07 (m, 8H, CH2O+C5H4), 4.24 (s, 2H, C5H4), 4.49-4.66 (s broad, 2H, NH2), major isomer [6.36, 6.72, 7.14] (d, J = 8.7 Hz, 6H, C6H4), minor isomer [6.61 and 6.66] (d, J = 8.7

  1-phenyl-but-1-ene, 24 (0.46 g, 1.13 mmol)

	prepared as indicated in ref. 21, 3-chloropropionyl chloride (0.16 g, 1.2 mmol) and pyridine
	(0.098 g, 1.2 mmol) were treated as described above. After purification by HPLC
	(acetonitrile/water 90/10), recrystallization from dichloromethane/hexane yielded 28 as
	orange crystals (0.22 g, 39% yield) consisting of a mixture of Z and E isomers. 1 H NMR (300
	MHz, CDCl3): δ 0.89-1.00 (m, 3H, CH3), 2.43-2.55 (m, 2H, CH2), 2.61-2.75 (m, 2H, CH2),
	3.73-3.89 (m, 4H, CH2 + C5H4), 3.98-4.06 (m, 7H, C5H4 + C5H5), 6.90-7.51 (m, 9H, C6H5 +
	C6H4). 13 C NMR (75.4 MHz, CDCl3): δ 15.6 (CH3), 28.0 and 28.1 (CH2), 40.0 (CH2), 40.6
	(CH2), 68.5 (2CH, C5H4), 69.5 (7CH, C5H5+C5H4), 87.0 (Cip), 119.9 and 120.1 (2CH, C6H4),
	126.3 (CH, C6H5), 128.4 (2CHarom), 129.5 and 130.0 (2CHarom), 130.1 and 130.7 (2CHarom),
	135.7 (C), 137.4 (C), 137.8 (C), 141.2 (C), 144.4 and 144.7 (C), 167.7 (CO). MS (CI, CH4)
	m/z : 498 [M+H] + . HRMS (ESI, C29H28ClFeNO: [M] +. ) calcd: 497.1210, found:
	497.1234. Anal. Calcd for C29H28ClFeNO.(H2O)0.25: C 69.33, H 5.71, N 2.78; found: C 69.48,
	H 5.63, N 2.71.

  After a 10 min period of incubation at 4°C, the precipitates were recovered by filtration on 25 mm circle glass microfibre filters GF/C filters using a Millipore 12 well filtration ramp. The filters were rinsed twice with cold phosphate buffer and then transferred

	13 C NMR (75.4 MHz, CDCl3): δ 28.8 (CH2), 33.5 (CH2), 41.1 (CH2), 44.5 (2CH3), 55.2 1 H NMR (300 MHz, CDCl3): 1.04 (t, J = 5.4 Hz, 3H, CH3), 2.35 and 2.37 (s, 6H, CH3), 2.50
	(CH2), 68.4 (2CH, C5H4), 68.9 (2CH, C5H4), 70.4 (4CH, C5H4), 83.7 (Cip), 86.8 (Cip), 118.8 (t, J = 5.4 Hz, 2H, CH2), 2.58-2.68 (m, 2H, CH2), 2.73-2.83(m, 2H, CH2), 3.88 and 3.95 (t, J
	and 119.7 (2CH, C6H4), 126.1 and 126.7 (CH, C6H5), 127.4 and 128.2 (2CHarom), 129.4 and = 1.8 Hz, 2H, C5H4), 4.08 (t, J = 1.8 Hz, 2H, C5H4), 4.11 (s, 5H, C5H5), 7.01 and 7.06 (d, J =
	130.0 (2CHarom), 130.7 and 131.2 (2CHarom), 134.4 and 134.0 (C), 136.7 (C), 138.6 and 139.1 8.6 Hz, 2H, C6H4), 7.31 and 7.15 (m, 5H, C6H5), 7.38 and 7.48 (d, J = 8.6 Hz, 2H, C6H4). 13 C in 20 mL plastic vials. After addition of 5 mL of scintillation liquid (BCS Amersham) the
	(C), 140.7 (C), 143.7 (C), 170.6 and 170.7 (CO). MS (CI, NH3) m/z : 505 [M+H] + . HRMS NMR (75.4 MHz, CDCl3): 15.6 (CH3), 28.1 (CH2), 33.5 (CH2), 44.5 (2CH3), 55.2 (CH2), 68.3 radioactivity of each fraction was counted in a Packard tri-carb 2100TR liquid scintillation
	(ESI, C31H32FeN2NaO: [M+Na] + ) calcd: 527.17578, found: 527.17403. (2CH, C5H4), 69.3 (5CH, C5H5), 69.5 (2CH, C5H4), 86.8 (Cip), 119.7 and 119.9 (2CH, C6H4), analyzer. The concentration of unlabeled steroid required to displace 50% of the bound [ 3 H]-
	2-Ferrocenyl-1-[4-(3-dimethylaminopropionyl)aminophenyl]-(4-hydroxyphenyl)-but-1-126.2 (CH, C6H5), 128.2 and 128.3 (2CHarom), 129.5 (2CHarom), 130.0 and 130.5 (2CHarom), E2 was calculated for 17-E2 and for each complex by plotting the logit values of Y (logit Y
	ene, 15. Analogously, 27 (0.12 g, 0.24 mmol) and 2.0 M dimethylamine solution in methanol 136.9 (C), 137.4 (C), 137.6 (C), 140.3 (C), 144.7 (C), 170.6 (CO). MS (CI, CH4) m/z : 507 = ln(Y/100-Y) versus the mass of the competing complex. The RBA (relative binding
	(1.22 mL, 2.4 mmol), were treated as described above, purified by flash column chromatography (acetone/Et3N: 10/1) to give 15 as an orange compound (0.11 g, 89%) consisting of a mixture of Z and E isomers (53/47). 1 H NMR (300 MHz, acetone-d6): 1.02 (t, J = 7.5 Hz, 3H, CH3), 2.28 and 2.30 (s, 6H, CH3), 2.43-2.48 (m, 2H, CH2), 2.58-2.68 (m, 4H, CH2), 3.91-3.93 (m, 2H, C5H4), 4.06-4.08 (m, 2H, C5H4), 4.12 (s, 5H, C5H5), 6.71 and 6.82 (d, J = 8.7 Hz, 2H, C6H4), 6.88 and 7.06 (d, J = 8.7 Hz, 2H, C6H4), 6.96 and 7.15 (d, J = 8.7 Hz, 2H, C6H4), 7.48 and 7.58 (d, J = 8.7 Hz, 2H, C6H4). 13 C NMR (75.4 MHz, acetone-d6): 15.9 (CH3), 28.4 (CH2), 35.2 (CH2), 45.0 (2CH3), 56.0 (CH2), 68.7 (2CH, C5H4), 69.9 (5CH, C5H5), 70.0 (2CH, C5H4), 87.7 (Cip), 115.8 and 115.9 (2CH, C6H4), 119.7 and 119.8 (2CH, C6H4), 130.4 and 130.9 (2CH, C6H4), 131.2 and 131.7 (2CH, C6H4), 137.0 (C), 137.3 (C), affinity) was calculated as follows: RBA of a compound = concentration of E2 required to [M+H] containing 21, was collected, but despite being contaminated with inseparable displace 50% of [ 3 H]-E2 x 100 / concentration of the compound required to displace 50% of
	137.5 (C), 138.5 (C), 140.8 (C), 156.7 (C), 170.8 (CO). MS (CI, NH3) m/z : 523 [M+H] + . dehydrohalogenation compounds, was used in the next step without further purification. The
	HRMS (ESI, C31H35FeN2O2: [M+H] + ) calcd: 523.20429, found: 523.20405. residue was transferred into a pressure tube and General Procedure 4 was followed, giving,
	2-Ferrocenyl-1-[4-(3-dimethylaminopropionyl)aminophenyl]-1-phenyl-but-1-ene, after crystallization from acetone, compound 14 (1.35 g, 26% overall yield) as a mixture of Z 16.
	Analogously, 2-ferrocenyl-1-(4-(3-chloropropionyl)aminophenyl)-1-phenyl-but-1-ene, 28 (0.1 and E isomers (60/40). 1 H NMR (DMSO-d6) :  1.44-1.84 (m, 4H, CH2-CH2), 2.16 and 2.19
	g, 0.19 mmol) and 2.0 M dimethylamine solution in methanol (0.97 mL, 1.9 mmol) were (s, 6H, NMe2), 2.23-2.39 (m, 4H, CH2N+CH2 cycle), 2.60-2.74 (m, 2H, CH2 cycle), 3.88 and

treated as described above. Recrystallization from dichloromethane/hexane gave 16 as an orange colored compound (0.095 g, 97%) consisting of a mixture of Z and E isomers (67/33).

+

. HRMS (ESI, C31H34FeN2NaO: [M+Na] + ) calcd: 529.191272, found: 529.19006.

1-[(4-(4-dimethylaminobutoxy)phenyl-4-hydroxyphenyl)methylidene]-[3]ferroceno-

phane, 14. Compound 4 (4.22 g, 10 mmoles), was dissolved in dry DMF (50 mL) then sodium hydride (60% in oil, 0.060 g, 15 mmoles) was slowly added. The mixture was heated at 80°C, then after 10 min, 1,4-dibromobutane (6.5 g, 30 mmoles) was added. The heating was continued for 4 hours, then the mixture was cooled, water was added dropwise, and the mixture was poured into water. After extraction by diethyl ether twice, the organic layer was concentrated under reduced pressure. The residue was chromatographed on silica gel with a 1/1 dichloromethane/petroleum ether solution as the eluent. The second yellow fraction, 4.00 (t, J = 5.9 Hz, 2H, CH2O), 3.97 (s, 2H, C5H4), 4.01 (s, 2H, C5H4), 4.02 (s, 2H, C5H4), 4.31 (s, 2H, C5H4), 6.49 and 6.65 (d, J = 8.2 Hz, 2H, C6H4), 6.77 and 6.88 (d, J = 8.2 Hz, 2H, water).

Table 2

 2 Enthalpy variation values for the bio-ligands docked into ER, and H-N distances

Acknowledgements

We thank the Agence Nationale de la Recherche for financial support (ANR 2010 BLAN 7061 blanc "Mecaferrol") and the Ministère des Affaires Etrangères for a doctoral fellowship (M.G.). We thank Marie-Aude Plamont and Renette Saint-Fort for technical assistance, Barbara McGlinchey for translating the manuscript, Michel Huché for helping in modeling, and P. Herson for the crystal structure determination.

C6H4), 6.78 and 6.94 (d, J = 8.2 Hz, 2H, C6H4), 7.01 and 7.11 (d, J = 8.2 Hz, 2H, C6H4), 9.27 and 9.47 (s, 1H, OH). 13 C NMR (DMSO-d6) :  24.3 and 24.4 (CH2), 27.4 and 27.5 (CH2), 28.9 (CH2), 41.1 and 41.2 (CH2), 45.9 and 46.0 (2CH3 NMe2), 59.5 (CH2), 66. 0 Compounds 29 and 30 were prepared as described in ref 23

X-ray crystal structure determination for 26

Crystal data were collected at 200K on a Kappa-CCD Enraf-Nonius diffractometer with graphite monochromated MoK radiation ( = 0.71073 Å). Orientation matrix and lattice parameters were obtained by least-squares refinement of the diffraction data of 105 reflections within the range 3º    19º. The structure was solved by direct methods and refined with full-matrix least-squares technique on F 2 using the CRYSTALS programs. [30] All nonhydrogen atoms were refined anisotropically. All hydrogen atoms were set in calculated positions and isotropically refined. The values of the discrepancy indices R1 (Rw2) were 0.079 (0.262). The final Flack [31]

Biological methods

Materials. Stock solutions (1 x 10 -3 M) of the ferrocenyl complexes to be tested were prepared in DMSO and were kept at 4°C in the dark; under these conditions they are stable for at least two months. Serial dilutions in DMSO were prepared just prior to use. A stock solution (1 x 10 -3 M) of 17-E2 was prepared in ethanol. (Dulbecco's modified eagle medium (DMEM) was purchased from Gibco BRL, fetal calf serum from Dutscher, Brumath, France, glutamine, E2 and protamine sulfate were from Sigma.) MCF-7 and MDA-MB-231 cells were from the Human Tumor Cell Bank. Sheep uteri weighing approximately 7g were obtained from the slaughterhouse at Mantes-la-Jolie, France. They were immediately frozen and kept in liquid nitrogen prior to use.

Determination of the Relative Binding Affinity (RBA) of the compounds for ER

RBA values were measured on ER from lamb uterine cytosol. Sheep uterine cytosol prepared in buffer A (0.05 M Tris-HCL, 0.25 M sucrose, 0.1% -mercaptoethanol, pH 7.4 at 25°C) as described previously (ref 3) was used as a source of ER. Aliquots (200 ml) of ER in glass tubes were incubated for 3 h at 0°C with [6,7-3 H]-E2 (2 x 10 -9 M, specific activity 1.62 TBq/mmol, NEN Life Science, Boston MA) in the presence of nine concentrations of the ferrocenyl complexes to be tested (between 6x10 -7 M and 6x10 -9 M for the complexes with RBA values higher than 5% and between 6x10 -6 M and 6x10 -8 M for the compounds with RBA values lower than 5%) or of 17-E2 (between 8x10 -8 M and 7.5x10 -10 M). At the end of the incubation period, the fractions of [ 3 H]-E2 bound to the estrogen receptors (Y values) were precipitated by addition of a 200 ml of a cold solution of protamine sulfate (1 mg/mL in Supporting Information Available CCDC 913875 contains the supplementary crystallographic data for this paper. These data can be obtained free of charge from The Cambridge Crystallographic Data Centre via www.ccdc.cam.ac.uk/data_request/cif.


Xuan Son Nguyen
email: xuan-son.nguyen@inria.fr

Thanh Phuong Nguyen
email: thanh-phuong.nguyen@univ-tln.fr

Franc ¸ois Charpillet
email: francois.charpillet@inria.fr

Effective Surface Normals Based Action Recognition in Depth Images

In this paper, we propose a new local descriptor for action recognition in depth images. The proposed descriptor relies on surface normals in 4D space of depth, time, spatial coordinates and higher-order partial derivatives of depth values along spatial coordinates. In order to classify actions, we follow the traditional Bag-of-words (BoW) approach, and propose two encoding methods termed Multi-Scale Fisher Vector (MSFV) and Temporal Sparse Coding based Fisher Vector Coding (TSCFVC) to form global representations of depth sequences. The highdimensional action descriptors resulted from the two encoding methods are fed to a linear SVM for efficient action classification. Our proposed methods are evaluated on two public benchmark datasets, MSRAction3D and MSRGesture3D. The experimental result shows the effectiveness of the proposed methods on both the datasets.

I. INTRODUCTION

Approaches for human action recognition in depth images have received a large attention in recent years thanks to the rich information provided by depth sensors. These approaches usually exploit depth information to build highly discriminative low-level descriptors, or use skeletal data which can be more easily obtained using depth images to build high-level descriptors. Although many approaches have achieved impressive results, they still face a number of challenges, e.g. rate variations, temporal misalignment, composite actions, noise, human-object interaction. Moreover, most of them require high computation time to extract features and recognize actions.

In this paper, we propose a new local descriptor that relies on surface normals in 4D space of depth, time and spatial coordinates which have been shown to carry important shape and motion cues for action recognition [START_REF] Oreifej | HON4D: Histogram of Oriented 4D Normals for Activity Recognition from Depth Sequences[END_REF], [START_REF] Yang | Super Normal Vector for Activity Recognition Using Depth Sequences[END_REF]. In our proposed descriptor, the shape cue is enhanced by augmenting surface normals with higher-order partial derivatives of depth values along spatial coordinates, while the motion cue is characterized by combining a set of local descriptors extracted at consecutive 3D points along the temporal dimension. In order to effectively encode local descriptors into a global representation of depth sequences, we propose two encoding methods MSFV and TSCFVC, which are based on Fisher Vector (FV) [START_REF] Sanchez | Image Classification with the Fisher Vector: Theory and Practice[END_REF] and Sparse Coding based Fisher Vector Coding (SCFVC) [START_REF] Liu | Encoding High Dimensional Local Features by Sparse Coding Based Fisher Vectors[END_REF].

This paper is organized as follows. Section 2 introduces the related work on action recognition in depth images. Section 3 explains our proposed local descriptor, MSFV and TSCFVC for feature encoding. Section 4 presents the experimental evaluation of the proposed methods. Finally, Section 5 offers some conclusions and ideas for future work.

II. RELATED WORK

Existing approaches for action recognition in depth images can be broadly grouped into three main categories: skeletonbased, depth map-based and hybrid approaches. Xia et al. [START_REF] Xia | View Invariant Human Action Recognition Using Histograms of 3D Joints[END_REF] partitioned the 3D space using a spherical coordinate defined at the hip joint position. Each 3D joint casted a vote into a bin to generate a histogram of 3D joint. These histograms were then used to construct visual words whose temporal evolutions were modeled using discrete Hidden Markov Models [START_REF] Rabiner | A Tutorial on Hidden Markov Models and Selected Applications in Speech Recognition[END_REF]. Yang and Tian [START_REF] Yang | EigenJoints-based Action Recognition Using Naive-Bayes-Nearest-Neighbor[END_REF] learned EigenJoints from differences of joint positions and used Naïve-Bayes-Nearest-Neighbor [START_REF] Boiman | In Defense of Nearest-Neighbor Based Image Classification[END_REF] for action classification. Zanfir et al. [START_REF] Zanfir | The Moving Pose: An Efficient 3D Kinematics Descriptor for Low-Latency Action Recognition and Detection[END_REF] relied on the configuration, speed, and acceleration of joints to construct the action descriptor. A modified kNN classifier was then used for action classification. Vemulapalli et al. [START_REF] Vemulapalli | Human Action Recognition by Representing 3D Skeletons as Points in a Lie Group[END_REF] used rotations and translations to represent 3D geometric relationships of body parts in a Lie group [START_REF] Murray | A Mathematical Introduction to Robotic Manipulation[END_REF], and then employed Dynamic Time Warping [START_REF] Müller | Information Retrieval for Music and Motion[END_REF] and Fourier Temporal Pyramid [START_REF] Wang | Mining Actionlet Ensemble for Action Recognition with Depth Cameras[END_REF] to model the temporal dynamics. Eweiwi et al. [START_REF] Eweiwi | Efficient Pose-Based Action Recognition[END_REF] learned a compact representation of depth sequences from joint locations, joint velocities and joint movement normals. Evangelidis et al. [START_REF] Evangelidis | Skeletal Quads: Human Action Recognition Using Joint Quadruples[END_REF] proposed skeletal quad to describe the positions of nearby joints in the human skeleton and used FV for feature encoding.

Depth map-based approaches usually rely on low-level features from the space-time volume of depth sequences to compute action descriptors. Li et al. [START_REF] Li | Action Recognition Based on A Bag of 3D Points[END_REF] proposed a bag of 3D points to capture the shape of the human body and used an action graph [START_REF]Expandable Data-Driven Graphical Modeling of Human Actions Based on Salient Postures[END_REF] to model the dynamics of actions. Representative 3D points used to describe a posture were sampled from a very small set of points in depth maps. Kurakin et al. [START_REF] Kurakin | A Read-Time System for Dynamic Hand Gesture Recognition with A Depth Sensor[END_REF] proposed cell occupancy-based and silhouette-based features which were then used with action graphs for gesture recognition. Wang et al. [START_REF] Wang | Robust 3D Action Recognition with Random Occupancy Patterns[END_REF] introduced random occupancy patterns which were computed from subvolumes of the spacetime volume of depth sequences with different sizes and at different locations. Since the number of subvolumes can be extremely large, a weighted random sampling scheme was proposed to effectively explore the space-time volume. Yang et al. [START_REF] Yang | Recognizing Actions Using Depth Motion Maps-based Histograms of Oriented Gradients[END_REF] projected depth maps onto three orthogonal Cartesian planes to obtain Depth Motion Maps (DMMs) which were used to extract HOG descriptors [START_REF] Mikolajczyk | A Performance Evaluation of Local Descriptors[END_REF] for action recognition. Xia and Aggarwal [START_REF] Xia | Spatio-temporal Depth Cuboid Similarity Feature for Activity Recognition Using Depth Camera[END_REF] proposed a filtering method to extract local spatio-temporal interest points of depth sequences. The histograms of depth pixels in 3D cuboids centered around the extracted interest points were calculated and used in a BoW approach for action recognition. Wang et al. [START_REF] Wang | An Approach to Pose-Based Action Recognition[END_REF] represented actions by histograms of spatial-part-sets and temporal-partsets, where spatial-part-sets are sets of frequently co-occurring spatial configurations of body parts in a single frame, and temporal-part-sets are co-occurring sequences of evolving body parts. Oreifej and Liu [START_REF] Oreifej | HON4D: Histogram of Oriented 4D Normals for Activity Recognition from Depth Sequences[END_REF] and Yang and Tian [START_REF] Yang | Super Normal Vector for Activity Recognition Using Depth Sequences[END_REF] relied on surface normals in 4D space of depth, time, and spatial coordinates to capture the shape and motion cues in depth sequences. However, they used different methods to construct action descriptors. The method of [START_REF] Oreifej | HON4D: Histogram of Oriented 4D Normals for Activity Recognition from Depth Sequences[END_REF] used polychorons to quantize possible directions of 4D normals, while the method of [START_REF] Yang | Super Normal Vector for Activity Recognition Using Depth Sequences[END_REF] used SC to compute visual words and spatial average pooling and temporal max pooling to aggregate local descriptors into a global representation of depth sequences.

Hybrid approaches combine skeletal data and depth maps to create action descriptors. Wang et al. [START_REF] Wang | Mining Actionlet Ensemble for Action Recognition with Depth Cameras[END_REF] introduced local occupancy patterns computed in spatio-temporal cells around 3D joints which were treated as the depth appearance of these joints. They proposed Actionlet Ensemble Model where each actionlet is a particular conjunction of the features for a subset of 3D joints. An action was then represented as a linear combination of a set of discriminative actionlets which were learned using data mining. Du et al. [START_REF] Du | Hierarchical Recurrent Neural Network for Skeleton Based Action Recognition[END_REF] divided the human skeleton into five parts, and fed them to five subnets of a recurrent neural network [START_REF] Schmidhuber | Deep Learning in Neural Networks: An Overview[END_REF]. As the number of layers increases, the representations extracted by the subnets are hierarchically fused to be the inputs of higher layers. Once the final representations of the skeleton sequences have been obtained, actions are classified using a fully connected layer and a softmax layer.

III. OUR METHOD

We follow the traditional BoW approach. For feature extraction, we rely on surface normals in 4D space of depth, time, and spatial coordinates and higher-order partial derivatives of depth values along spatial coordinates. In order to encode local descriptors into a global representations of depth sequences, we propose two encoding methods termed MSFV and TSCFVC. Action recognition is performed using a linear SVM classifier. In what follows we explain in more detail the different steps of our method.

A. Local Feature Extraction

Our local descriptor is extracted using surface normals in 4D space (SN4D) of depth, time, and spatial coordinates, which are the extensions of surface normals in 3D space of depth and spatial coordinates [START_REF] Tang | Histogram of Oriented Normal Vectors for Object Recognition with a Depth Sensor[END_REF]. The depth sequence can be considered as a function R 3 ! R 1

: z = f (x, y, t), which constitutes a surface in the 4D space represented as the set of points (x, y, z, t) satisfying S(x, y, t, z) = f (x, y, t) z = 0. The normal to the surface S is computed as:

n = rS = [ @z @x ; @z @y ; @z @t ; 1].
The first three components of n are the partial derivatives of depth values along the spatial and temporal dimensions, which have been shown [START_REF] Oreifej | HON4D: Histogram of Oriented 4D Normals for Activity Recognition from Depth Sequences[END_REF], [START_REF] Yang | Super Normal Vector for Activity Recognition Using Depth Sequences[END_REF] to carry important shape and motion cues. For each pixel p t = (x, y, z) at frame t of the depth sequence, we combine the first three components of n with the third-order partial derivatives of depth values along x and y axes to form a 5-dimensional feature descriptor l(p t ) as follows:

l(p t ) = [ @z @x ; @z @y ; @z @t ; @ 3 z @x 3 ; @ 3 z @y 3 ].
To better characterize the local motion, we concatenate l for a set of n neighboring pixels {p

t n 1 2 , p t n 1 2 +1 , . . . , p t+ n 1 2 } of p t in the temporal dimension. The final feature descriptor v extracted at pixel p t is thus given as: v = [l(p t n 1 2
); l(p

t n 1 2 +1 ); . . . l(p t+ n 1 2 )].
In our approach, the shape and motion cues are effectively encoded into a compact representation, where the shape cue is described by the first and third order partial derivatives of depth values along the spatial coordinates, and the motion cue is characterized by the first-order partial derivatives of depth values along the temporal dimension and by combining a set of local descriptors computed at consecutive 3D points along the temporal dimension.

B. Feature Encoding

Given a depth sequence which can be written as a set of whitened vectors X = {v t , t = 1, . . . , T }, where v t 2 R M , M is the dimension of a local descriptor, T is the number of local descriptors extracted in the sequence, we propose two encoding methods to construct a global representation of the sequence. In the following, we explain MSFV and TSCFVC for this purpose.

1) MSFV: FV was first introduced in [START_REF] Perronnin | Fisher Kernels on Visual Vocabularies for Image Categorization[END_REF] which assumes that the generation process of local descriptors v t can be modeled by a probability density function p(.; ✓) with parameters ✓. In order to describe the contribution of individual parameters to the generative process, one can compute the gradient of the log-likelihood of the data on the model:

G X ✓ = 1 T r ✓ log p(X; ✓).
The probability density function is usually modeled by Gaussian Mixture Model (GMM), and covariance matrix of Gaussian k. In our work, we use the following formulas [START_REF] Perronnin | Improving the Fisher Kernel for Large-scale Image Classification[END_REF] to calculate the FV components:

✓ = {w 1 , µ µ µ 1 , 1 , . . . , w K , µ µ µ K , K }
G X µ µ µ k = 1 T p w k T X t=1 t (k) v t µ µ µ k k ! , G X k = 1 T p 2w k T X t=1 t (k) (v t µ µ µ k ) 2 2 k 1 ! , where t (k) is the soft assignment of v t to Gaussian k. The FV representation of the sequence is the concatenation of G X µ µ µ k and G X k . Since G X µ µ µ k and G X k are M -dimensional vectors, our FVs are 2MK-dimensional vectors.
Following [START_REF] Yang | Super Normal Vector for Activity Recognition Using Depth Sequences[END_REF], we partition the space-time volume of the depth sequence into the spatio-temporal grids illustrated in Fig. 1, where the largest spatio-temporal grid corresponds to the bounding box of the action, and adaptive temporal pyramid is used to take into account the variations in motion speed and frequency when different people perform the same action. We calculate the FV for each grid, and apply two normalization steps: l 2 -normalization and power normalization [START_REF] Sanchez | Image Classification with the Fisher Vector: Theory and Practice[END_REF]. We then concatenate the FVs of all the grids to form the final representation of the depth sequence.

In order to improve the recognition accuracy, we rely on multiple scales of the depth sequence. The diagram of our proposed method is described in Fig. 2, where three different scales of the sequence are used. First, local descriptors are extracted at different scales of the depth sequence. Then, a fixed proportion of local descriptors is randomly selected from each scale and the selected local descriptors are combined to train a GMM. In the testing phase, the FV of each scaled sequence is computed using the trained GMM and the local descriptors of that scale (for each scaled sequence we use the spatio-temporal grids given in Fig. 1). These FVs are then concatenated to form the final FV of the sequence.

2) TSCFVC: FV relies on the assumption that p(.; ✓) is a Gaussian mixture with a fixed number of components K. As the dimensionality of the feature space increases, K must also increase to model the feature space accurately. This results in the explosion of the FV representation dimensionality. In order to deal with this problem, Liu et al. [START_REF] Liu | Encoding High Dimensional Local Features by Sparse Coding Based Fisher Vectors[END_REF] proposed SCFVC which assumes that local descriptors are drawn from a Gaussian distribution N (Bu, I), where B = [b 1 , . . . , b K ] is a matrix of bases (visual words) and u is a latent coding vector randomly generated from a zero mean Laplacian distribution. This corresponds to modeling p(.; ✓) using a Gaussian mixture with an infinite number of components. The generative model can be written as:

p(v, u|B) = p(v|u, B)p(u). Thus: p(v) = Z u p(v, u|B)du = Z u p(v|u, B)p(u)du.

Denote u ⇤

= arg max u p(v|u, B)p(u), then p(v) can be approximated by:

p(v) ⇡ p(v|u ⇤ , B)p(u ⇤
). Taking the logarithm of p(v), one obtains:

log(p(v|B)) = min u 1 2 kv Buk 2 2 + kuk 1 . (1)
Eq. 1 reveals the relationship between the generative model and a sparse coding model. Liu et al. [START_REF] Liu | Encoding High Dimensional Local Features by Sparse Coding Based Fisher Vectors[END_REF] showed that the FV representation of X is given by:

Q = [q 1 ; . . . ; q K ], q k = T X t=1 u ⇤ t (k)(v t Bu ⇤ t ), (2)
where u ⇤ t is the solution of the sparse coding problem, u ⇤ t (k) is the k th dimension of u ⇤ t . In order to take into account the temporal order of local descriptors in X, we follow the approach of [START_REF] Yang | Super Normal Vector for Activity Recognition Using Depth Sequences[END_REF]. For the k th visual word, we compute the FV of the set of local descriptors extracted at the same frame of the depth sequence: Method Accuracy Li et al., 2010 [START_REF] Li | Action Recognition Based on A Bag of 3D Points[END_REF] 74.70 Xia et al., 2012 [START_REF] Xia | View Invariant Human Action Recognition Using Histograms of 3D Joints[END_REF] 79.00 Yang and Tian, 2012 [START_REF] Yang | EigenJoints-based Action Recognition Using Naive-Bayes-Nearest-Neighbor[END_REF] 82. 30 Wang et al., 2012 [19] 86.50 Wang et al., 2012 [START_REF] Wang | Mining Actionlet Ensemble for Action Recognition with Depth Cameras[END_REF] 88. 20 Yang et al., 2012 [20] 88.73 Oreifej and Liu, 2013 [START_REF] Oreifej | HON4D: Histogram of Oriented 4D Normals for Activity Recognition from Depth Sequences[END_REF] 88.89 Xia and Aggarwal, 2013 [START_REF] Xia | Spatio-temporal Depth Cuboid Similarity Feature for Activity Recognition Using Depth Camera[END_REF] 89.30 Wang et al., 2013 [23] 90.00 Zanfir et al., 2013 [START_REF] Zanfir | The Moving Pose: An Efficient 3D Kinematics Descriptor for Low-Latency Action Recognition and Detection[END_REF] 91.70 Vemulapalli et al., 2014 [START_REF] Vemulapalli | Human Action Recognition by Representing 3D Skeletons as Points in a Lie Group[END_REF] 92.46 Yang and Tian, 2014 [START_REF] Yang | Super Normal Vector for Activity Recognition Using Depth Sequences[END_REF] 93.09 SN4D-MSFV 93.27 SN4D-TSCFVC 95.42

q k (f ) = 1 |N f | X i2N f u ⇤ i (k)(v i Bu ⇤ i ), (3)
where N f is the set of 3D points at frame f of the depth sequence. The FV is normalized to avoid the dependence on the image resolution.

If q k (f ) = [q 1 k (f ); . . . ; q M k (f )], then the j th dimension q j k of q k is computed as:

q j k = max f =1,...,F q j k (f ), for j = 1, . . . , M, (4)
where the frame indices of the depth sequence are supposed to be 1, . . . , F . Now, q k is calculated using Eqs. 3 and 4 instead of Eq. 2. As for MSFV, we use the spatio-temporal grids described in Fig. 1 to capture the spatial geometry and temporal order of the depth sequence. The final representation of the depth sequence is the concatenation of the FVs from all the grids.

C. Action Recognition

The FV has been shown [START_REF] Perronnin | Improving the Fisher Kernel for Large-scale Image Classification[END_REF], [START_REF] Evangelidis | Skeletal Quads: Human Action Recognition Using Joint Quadruples[END_REF] to give good performance on image classification and action recognition when it is combined with linear classifiers. Thus for both the encoding methods, we rely on linear SVMs trained in an one-versus-all fashion to build a multi-class classifier for action recognition. A significant benefit of linear classifiers is that they are efficient to train and test. In our experiments, we use the LIBLINEAR library [START_REF] Fan | LIBLINEAR: A Library for Large Linear Classification[END_REF] that provides the implementation of linear SVMs.

IV. EXPERIMENTS

In this section, we evaluate the proposed methods on two benchmark datasets: MSRAction3D [START_REF] Li | Action Recognition Based on A Bag of 3D Points[END_REF] and MSRGes-ture3D [START_REF] Wang | Robust 3D Action Recognition with Random Occupancy Patterns[END_REF]. The two encoding methods presented in Section III-B result in two algorithms termed SN4D-MSFV and SN4D-TSCFVC, which use MSFV (see Section III-B1) and TSCFVC (see Section III-B2) for feature encoding, respectively. These two methods are compared against several stateof-the-art methods. We use the recognition accuracy reported in the original papers for comparison. The number of neighboring pixels n was set to n = 5, which has been experimentally found to give good results. For SN4D-TSCFVC, the number of visual words was set to K = 100. Since each local descriptor has 25 dimensions, the vector representation of a spatiotemporal grid has 2500 dimensions. The final representation of a depth sequence is the concatenation of 3 ⇥ 4 ⇥ 7 2500dimensional vectors, which is a 210000-dimensional vector. For SN4D-MSFV, the number of GMM components K was set to K = 50. The vector representation of a sequence for each scale is the concatenation of 3 ⇥ 4 ⇥ 7 FVs which is 210000dimensional. We used 3 spatial scales spaced by a factor of 1/ p 2, which has been experimentally found satisfactory. The image width and height at the first scale are those of the original depth images. The final representation of a sequence is the concatenation of its vector representations in 3 scales and is thus a 630000-dimensional vector.

A. MSRAction3D Dataset

The MSRAction3D is an action dataset captured using a depth sensor similar to Kinect. It contains 20 actions performed by 10 different subjects. Each subject performs every action two or three times.

For a fair comparison, we used the experimental setting described in [START_REF] Li | Action Recognition Based on A Bag of 3D Points[END_REF]. We divided the 20 actions into three subsets AS1, AS2 and AS3, each having 8 actions. The AS1 and AS2 were intended to group actions with similar movement, while AS3 was intended to group complex actions together. Action recognition was performed on each subset separately. We followed the cross-subject test setting, in which subjects 1,3,5,7,9 were used for training and subjects 2,4,6,8,10 were used for testing. Tab. I shows the accuracy of the proposed methods and different state-of-the-art methods. SN4D-TSCFVC achieves an accuracy of 95.42% which is the best method among the competing ones. Note that SN4D-TSCFVC outperforms the methods in [START_REF] Oreifej | HON4D: Histogram of Oriented 4D Normals for Activity Recognition from Depth Sequences[END_REF], [START_REF] Yang | Super Normal Vector for Activity Recognition Using Depth Sequences[END_REF] which also rely on surface normals in 4D space of depth, time, and spatial coordinates to calculate local descriptors. SN4D-MSFV has lower accuracy than SN4D-TSCFVC but it still outperforms the majority of the methods. In Tab. II, we compare SN4D-TSCFVC and SN4D-MSFV against other state-of-the-art methods that reported the results on AS1, AS2 and AS3 separately. As can be observed, SN4D-TSCFVC achieves the highest accuracy for AS2 and the highest average accuracy. The confusion matrices are shown in Fig. 3. The most confusions occur between the actions hammer

B. MSRGesture3D Dataset

The MSRGesture3D dataset contains 12 dynamic hand gestures defined by the American sign language. Each gesture is performed two or three times by 10 subjects.

For a fair comparison, we used the leave-one-subject-out cross validation scheme proposed by [START_REF] Wang | Robust 3D Action Recognition with Random Occupancy Patterns[END_REF]. The accuracy of the proposed methods and different state-of-the-art methods are given in Tab. III. For this dataset, SN4D-MSFV and SN4D-TSCFVC perform comparably with an accuracy of 95.39% and 95.27%, and are the best methods among the competing ones. The confusion matrices are shown in Fig. 4. Most of the confusions are between the actions store and green (SN4D-MSFV), finish and bathroom (SN4D-TSCFVC).

C. Effect of Higher-Order Partial Derivatives in The Local Descriptor

In this section, we compare the performance of different local descriptors obtained by combining the first three components of a surface normal with different higher-order partial derivatives of z along x and y axes. Three descriptors are considered: d 1 = [ @z @x ; @z @y ; @z @t ], d 2 = [ @z @x ; @z @y ; @z @t ; @ 2 z @x 2 ; @ 2 z @y 2 ], and d 3 = [ @z @x ; @z @y ; @z @t ; @ 2 z @x 2 ; @ 2 z @y 2 ; @ 3 z @x 3 ; @ 3 z @y 3 ]. We do not consider

Method Accuracy

Kurakin et al., 2012 [START_REF] Kurakin | A Read-Time System for Dynamic Hand Gesture Recognition with A Depth Sensor[END_REF] 87.70 Wang et al., 2012 [START_REF] Wang | Robust 3D Action Recognition with Random Occupancy Patterns[END_REF] 88.50 Yang et al., 2012 [20] 89.20 Oreifej and Liu, 2013 [START_REF] Oreifej | HON4D: Histogram of Oriented 4D Normals for Activity Recognition from Depth Sequences[END_REF] 92.45 Yang and Tian, 2014 [START_REF] Yang | Super Normal Vector for Activity Recognition Using Depth Sequences[END_REF] 94.74 SN4D-MSFV 95.39 SN4D-TSCFVC 95.27 other higher-order partial derivatives of z along x and y axes as well as higher-order partial derivatives of z along t since in our experiments, we did not observe any improvement in recognition accuracy. Using MSFV and TSCFVC for feature encoding, we obtain 6 methods for comparison. Tab. IV shows the accuracy of these methods. For both the datasets, our descriptor outperforms the other descriptors if the same encoding method is used for all the descriptors.

D. Comparison of MSFV against FV

We compare SN4D-MSFV against two methods: SN4D-FV in which FV is used instead of MSFV in the encoding step, and SN4D-MSFV2 in which one GMM is trained for each scale and the final FV representation of a depth sequence is the concatenation of three FVs from three scales. Hence, the difference between SN4D-MSFV and SN4D-MSFV2 is

MSRAction3D MSRGesture3D

Ave. that only one GMM is trained in SN4D-MSFV while three different GMMs are trained in SN4D-MSFV2. Tab. V shows the accuracy of these methods. As can be observed, SN4D-MSFV outperforms both SN4D-MSFV2 and SN4D-FV. The accuracy of the proposed multi-scale encoding method is 1.73% better than that of FV on MSRAction3D, and is 1.19% better than that of FV on MSRGesture3D.

E. Comparison of TSCFVC against SCFVC

We compare SN4D-TSCFVC against its two variants: SN4D-SCFVC in which TSCFVC is replaced by SCFVC, and SNV-SC in which TSCFVC is replaced by the encoding method of [START_REF] Yang | Super Normal Vector for Activity Recognition Using Depth Sequences[END_REF]. Tab. VI shows the accuracy of these methods. SN4D-TSCFVC outperforms SNV-SC by 1.35% on MSRAc-tion3D and by 0.98% on MSRGesture3D. SN4D-TSCFVC outperforms SN4D-SCFVC by 0.55% on MSRAction3D and by 1.25% on MSRGesture3D.

V. CONCLUSIONS AND FUTURE WORK

We have proposed a new descriptor for human action recognition in depth images. Our proposed descriptor is based on surface normals in 4D space of depth, time, spatial coordinates and higher-order partial derivatives of depth values along spatial coordinates. We have proposed MSFV and TSCFVC to effectively encode local descriptors into a global representation of depth sequences. Action recognition can then be simply performed using a linear SVM. We have presented the experimental evaluation on two benchmark datasets showing the effectiveness of the proposed methods.

For future research, we study the fusion of the proposed descriptor with other descriptors. We also consider improving it by using the joint trajectories as methods which compute local descriptors along the trajectories of feature points have achieved state-of-the-art performance for human action recognition in color images.

  are the model parameters of the K-component GMM, where w k , µ µ µ k and k are respectively the mixture weight, mean vector, and diagonal

Fig. 1 .

 1 Fig. 1. The spatio-temporal grids used in our experiments. From left to right: the first, second and third temporal pyramids.

Fig. 2 .

 2 Fig. 2. The diagram of MSFV.

Fig. 3 .

 3 Fig. 3. (Best viewed in color) The confusion matrices of our methods on MSRAction3D (top: SN4D-MSFV, bottom: SN4D-TSCFVC, left: AS1, middle: AS2, right: AS3).

Fig. 4 .

 4 Fig. 4. (Best viewed in color) The confusion matrices of our methods on MSRGesture3D (left: SN4D-MSFV, right: SN4D-TSCFVC).

TABLE III RECOGNITION

 III ACCURACY COMPARISON OF OUR METHODS AND PREVIOUS APPROACHES ON MSRGESTURE3D.

TABLE V COMPARISON

 V OF SN4D-MSFV AGAINST SN4D-MSFV2 AND SN4D-FV.

		SNV-SC	SN4D-SCFVC SN4D-TSCFVC
	MSRAction3D	94.07	94.87	95.42
	MSRGesture3D	94.29	94.02	95.27

TABLE VI COMPARISON

 VI OF SN4D-TSCFVC AGAINST ITS VARIANTS.