About the Influence of PEG Spacers on the Cytotoxicity of Titanate Nanotubes-Docetaxel Nanohybrids against a Prostate Cancer Cell Line

The association between chemotherapeutic drugs and metal oxide nanoparticles has sparked a rapidly growing interest in cancer nanomedicine. The elaboration of new engineered docetaxel (DTX)-nanocarriers based on titanate nanotubes (TiONts) was reported. The idea was to maintain the drug inside cancer cells and avoid multidrug resistance mechanisms, which often limit drug efficacy by decreasing their intracellular concentrations in tumor cells. HS-PEGn-COOH (PEG: polyethylene glycol, n = 3000, 5000, 10,000) was conjugated, in an organic medium by covalent linkages, on TiONts surface. This study aimed to investigate the influence of different PEG derivatives chain lengths on the TiONts colloidal stability, on the PEGn density and conformation, as well as on the DTX biological activity in a prostate cancer model (human PC-3 prostate adenocarcinoma cells). In vitro tests highlighted significant cytotoxicities of the drug after loading DTX on PEGn-modified TiONts (TiONts-PEGn-DTX). Higher grafting densities for shorter PEGylated chains were most favorable on DTX cytotoxicity by promoting both colloidal stability in biological media and cells internalization. This promising strategy involves a better understanding of nanohybrid engineering, particularly on the PEGylated chain length influence, and can thus become a potent tool in nanomedicine to fight against cancer.

To date, very few studies have investigated the functionalization of TiONts for drug delivery purposes. Multidrug resistance mechanisms often limit drug efficacy by decreasing intracellular concentrations of drugs in tumor cells [30]. Hence, the development of engineered nanocarriers to maintain the drug inside cancer cells and thus improve treatment efficacy seems highly relevant [27,31]. The most used type of stabilization is the steric hindrance which improves the long-term colloidal stability under biological conditions and thus increases the blood circulation time of NPs [19,20,32]. Indeed, this strategy with bulky molecules is much more efficient at higher salt concentrations than the one using electrostatic interactions [33]. Polyethylene glycol (PEG) grafting has become the most widely used approach to provide stealth properties to drug nanocarrier against the reticuloendothelial system. It avoids the adsorption of opsonin proteins due to the neutrality, lipophilicity at the same time as hydrophilicity, and capacity for hydration of the PEG moiety [34][35][36][37]. PEG are also biocompatible and biodegradable polymers used in a wide range of molecular weights (usually from 160 to 20,000 g·mol −1 for nanomedicine) and approved by the Food and Drug Administration (FDA) [32,36]. Besides, it has already been proven to promote the passive targeting of NPs by the enhanced permeability and retention (EPR) effect [38,39] and to improve the therapeutic efficacy [20,40]. PEGylated chain length of the polymer allows a screening effect to be observed [9], which enables the renal clearance of NPs as well as a reduced liver uptake [38]. Several studies reported the impact of grafting density and PEGylated chain length on the biological behavior of different NPs [19,20,35,36], such as liposomes [29,41,42], polymeric [43][44][45] and inorganic NPs (quantum dots, gold NPs, iron oxide NPs, silica NPs, etc.) [20,[46][47][48][49][50] as well as carbon nanotubes [51,52]. Nevertheless, no study, to the best of our knowledge, has been conducted on PEG-modified TiONts. It has been established that both higher PEG density and PEGylated chain length onto the nano-object surface allows improving the colloidal stability while reducing surface interaction with its environment (in particular nonspecific adsorption of proteins), hence minimizing its detection by the immune system, as well as their uptake by cells [47,53]. Adsorbed proteins may either facilitate cancer cell entry or mark inorganic NPs for macrophage detection followed by their clearance from the body [47]. For instance, higher grafting densities lead to less protein adsorption and lower NPs uptake by cell lines while shorter PEG chain lengths result in higher cellular uptake in cell lines at the cost of greater nonspecific protein adsorption. Thus, it is necessary to find a compromise between the PEG density and chain length used.
In the present study, the core strategy is based on the use of different PEG spacer (HS-PEG n -COOH; n = 3000, 5000, 10,000) between TiONts and one chemotherapeutic agent, herein docetaxel (DTX), to observe the influence of PEGylated length on nanotube properties and promote the interactions of DTX-functionalized TiONts with the tubulins present into microtubules [54,55]. DTX is a clinically well-established cytotoxic drug with inhibitory properties on mitosis [31]. It has been approved by FDA especially for the treatment of hormone-refractory prostate cancers [56,57]. In previous studies, TiONts have been synthesized by a hydrothermal process and functionalized with (3-aminopropyl)triethoxysilane (TiONts-APTES) to provide additional amine functions for PEG 3000 and DTX conjugation, making them promising drug carriers [9,14,15]. This report describes the functionalization of TiONts-APTES with different PEG n molecular weights in an organic medium to analyze the influence of PEGylated chain lengths on the colloidal stability and PEG n density as well as the cell survival after loading DTX molecules on PEG n -modified TiONts (TiONts-PEG n -DTX). In vitro efficacy of these latter is evaluated on a human PC-3 prostate adenocarcinoma cells using 3-(4,5-dimethylthiazol-2-yl)-5-(3-carboxymethoxyphenyl)-2-(4ulfophenyl)-2H-tetrazolium (MTS) assay. The analysis of each elaboration step of TiONts-PEG n -DTX is performed using several characterization techniques such as thermogravimetric analysis (TGA), transmission electron microscopy (TEM), ζ-potential measurement, X-ray photoelectron spectroscopy (XPS), Fourier-transformed infrared (FTIR), and UVvisible spectroscopies.

Titanate Nanotube (TiONts) Synthesis
Bare TiONts were synthesized by a hydrothermal process in a basic medium, according to ref [9,14]. Briefly, TiO 2 rutile as a precursor (1 g) was ultrasonicated in a NaOH aqueous solution (10 M, 250 mL) for 30 min at 375 W (Sonics Vibra-Cells, Newton, CT, USA). Then, the mixture was added into a Teflon reactor with mechanical stirring at 120 rpm and heating at 155 • C for 36 h. After cooling to room temperature, TiONts were washed and purified by centrifugation (24,000× g, 10 min), dialysis (Cellu·Sep tubular membranes of 12-14 kDa), and ultrafiltration (regenerated cellulose membranes with a molecular weight cut-off (MWCO) of 100 kDa) with ultrapure water.

Functionalization of TiONts-APTES by Polyethylene Glycol with Different Ethylene Oxide
Chain Lengths (PEG 3000/5000/10,000 ) The same method was used for the grafting of different heterobifunctional polymers (HS-PEG 3000 -COOH: PEG 3000 ; HS-PEG 5000 -COOH: PEG 5000 ; HS-PEG 10,000 -COOH: PEG 10,000 ) onto the TiONts-APTES surface. First, carboxyl groups of heterobifunctional polyethylene glycols have been activated with PyBOP (molar ratio was 1:1) in DMSO in the presence of DIEA (in 6 × excess) under nitrogen flow and magnetic stirring for 30 min. Then, TiONts-APTES were dispersed in DMSO before adding in the activation solution, for 24 h under magnetic agitation and nitrogen flow. Polymers were attached to the amine groups of APTES with a molar ratio of 1:1. Finally, the products (TiONts-PEG n : TiONts-PEG 3000 , TiONts-PEG 5000 , and TiONts-PEG 10,000 ) were washed by centrifugation (20,000× g, 20 min, mainly to remove DMSO less compatible with the ultrafiltration membrane), then purified by ultrafiltration (500 kDa) with ultrapure water.

Modification and Grafting of Docetaxel on TiONts-PEG n
The modification and grafting of the therapeutic agent (docetaxel, DTX) were described by Loiseau et al. [9,14] and occurred in the same conditions for each TiONts-PEG n . Briefly, DTX and the PMPI crosslinker were dissolved in DMSO (the molar ratio of DTX to PMPI was 1:4) and then added in borate buffered saline (0.1 M; pH 8.5) under magnetic agitation at 25 • C for 24 h. The resulting PMPI-activated DTX (DTX-PMPI) solution was then dialyzed (0.5-1 kDa) to remove unreacted PMPI and lyophilized to obtain a yellowish powder. TiONts-PEG n -DTX were synthesized from TiONts-PEG n and DTX-PMPI (large excess) using TCEP for cleavage of disulfides in PBS (0.1 M; pH 7.4). The mixture was homogenized beforehand in an ultrasonic bath and placed under magnetic stirring at 25 • C for 24 h. TiONts-PEG n -DTX were washed and purified by dialysis and ultrafiltration (500 kDa), and then, freeze-dried.

Surface Area Measurements
Specific surface area measurements were performed using a Micromeritics Tristar II apparatus (Micromeritics Instrument Corp., Norcross, GA, USA). Samples were outgassed in situ under 20 mTorr pressure for 16 h at 100 • C. The specific surface area value (S BET ) from N 2 gas adsorption was calculated from Brunauer-Emmett-Teller (BET) method.

Thermogravimetric Analysis (TGA)
TGA (TA instrument, Discovery TGA, Newcastle, UK) was used to determine the amount of the molecules on the surface of the TiONts after each grafting step. All powders were analyzed with a temperature ramp of 10 • C·min −1 from 50 to 800 • C under an airflow rate of 25 mL·min −1 . The experiments were reproduced from 2 to 10 times for each sample.

ζ-Potential Measurements
Zeta potentials of nanoparticle suspensions were measured with a Malvern Nano ZS instrument (Worcestershire, UK) supplied by DTS Nano V7.11 software (Worcestershire, UK). pH titrations from 3 to 11 were carried out using aqueous solutions of HCl (0.1 M), NaOH (0.1 M), or NaOH (0.01 M). Before each measurement, the powder was dispersed in an aqueous NaCl solution (10 −2 M) and sonicated for 10 min.

X-ray Photoelectron Spectroscopy (XPS)
A PHI 5000 Versaprobe apparatus (ULVAC-PHI, Osaka, Japan) from a monochromatic Al Kα1 X-ray source (EKα1 (Al) = 1486.7 eV with a 200 µm diameter spot size, an accelerating voltage of 12 kV, and a power of 200 W) was used to record XPS measurements. Powders were pressed on an indium sheet before analysis. Data analysis and curve fittings were realized with CasaXPS processing, and MultiPak software (ver. 9.0.1, Osaka, Japan) was employed for quantitative analysis. A Shirley background was subtracted and Gauss (70%)-Lorentz (30%) profiles were applied. The charge effects were minimized by a neutralization process and the Ti 2p peak at 458.7 eV was used as a reference to correct the charge effects. The resolution was 2.0 eV for global spectra and 1.3 eV for windows corresponding to selected lines.

Transmission Electron Microscopy (TEM)
Nanotube morphology and agglomeration state characterization were performed using a JEOL JEM-2100F (Tokyo, Japan), with an accelerating voltage of 200 kV and fitted with an ultra-high pole-piece achieving a point-to-point resolution of 0.19 nm. Samples were prepared by evaporating a diluted suspension of nanoparticles onto the carbon-coated copper grids.

Fourier Transformed Infrared (FTIR) Spectroscopy
A Bruker Vertex 70v (Billerica, MA, USA) supplied by OPUS version 3.1 software (Billerica, MA, USA) was used to record FTIR spectra using the KBr method. The pellets were made by mixing 2 mg of the sample within 198 mg of dried KBr.

Inductively Coupled Plasma (ICP) Spectroscopy
Determination of titanium content in nanohybrids in contact with cells was performed by ICP coupled to mass spectrometry (ICP-MS) analysis (ThermoScientific iCAP 6000 series ICP Spectrometer (Waltham, MA, USA)). A dried sample of centrifuged cells in contact with nanohybrids (TiONts-PEG 3000 -DTX or TiONts-PEG 10,000 -DTX) were dissolved in 1 mL aqua regia during 72 h in a PTFE reactor submitted to microwaves. The resulting solutions were diluted to a total volume of 5 mL with 2% HNO 3 before analysis at the Ti wavelength (336.121 nm). The measured concentration (in ppt) allowed the calculation of the Ti concentration (in µg·L −1 ) and deducing the mass of nanohybrids per cell (knowing the number of cells per sample).

Results and Discussion
The titanate-based nanohybrid has been elaborated step-by-step following the strategy described in Figure 1 to create a very attractive nanocarrier for chemotherapy.
Transmission electron microscopy (TEM) is used to highlight the formation of TiONts with a coiled spiral-shaped structure and an internal cavity, as presented in Figure 2 and described in previous work [12,14,59]. They are 10 ± 1 nm in outer diameter, 4 ± 1 nm in inner diameter, as well as 170 ± 50 nm in length and they, present a high specific surface area due to their specific morphology (S BET = 174 ± 1 m 2 ·g −1 ). Reference source not found. and described in previous work [12,14,59]. They are 10 ± 1 nm in outer diameter, 4 ± 1 nm in inner diameter, as well as 170 ± 50 nm in length and they, present a high specific surface area due to their specific morphology (SBET = 174 ± 1 m 2 •g −1 ).

Figure 1. Illustration of (A) TiONts (a) and step-by-step pre-functionalization with APTES (b) and
α-acid-ω-thiol-polyethylene glycol (c) using one of the three different carbon chain lengths (PEGn; n = 3000, 5000, or 10,000); (B) in the second step, DTX (e) and PMPI (f) were combined to form PMPI-modified DTX (g) to create the final nanohybrid TiONts-PEGn-DTX (d). TGA results have first demonstrated the effective synthesis of the TiONts-PEGn nanohybrids (Error! Reference source not found.; Error! Reference source not found.). TGA analysis shows a more consequent mass loss after PEGn grafting due to the additional organic matter on TiONts as is the case at each successive step of grafting (details on the calculation are given in Figure S1). Moreover, as expected, the greater the molecular weight (MW) of polymer, the more important the mass losses in TGA but, on the contrary, the lower the grafting yields (0.09 PEG3000•nm −2 ; 0.05 PEG5000•nm −2 ; 0.03 PEG10,000•nm −2 ). The Figure 1. Illustration of (A) TiONts (a) and step-by-step pre-functionalization with APTES (b) and α-acid-ω-thiolpolyethylene glycol (c) using one of the three different carbon chain lengths (PEG n ; n = 3000, 5000, or 10,000); (B) in the second step, DTX (e) and PMPI (f) were combined to form PMPI-modified DTX (g) to create the final nanohybrid TiONts-PEG n -DTX (d). Reference source not found. and described in previous work [12,14,59]. They are 10 ± 1 nm in outer diameter, 4 ± 1 nm in inner diameter, as well as 170 ± 50 nm in length and they, present a high specific surface area due to their specific morphology (SBET = 174 ± 1 m 2 •g −1 ).

Figure 1. Illustration of (A) TiONts (a) and step-by-step pre-functionalization with APTES (b) and
α-acid-ω-thiol-polyethylene glycol (c) using one of the three different carbon chain lengths (PEGn; n = 3000, 5000, or 10,000); (B) in the second step, DTX (e) and PMPI (f) were combined to form PMPI-modified DTX (g) to create the final nanohybrid TiONts-PEGn-DTX (d). TGA results have first demonstrated the effective synthesis of the TiONts-PEGn nanohybrids (Error! Reference source not found.; Error! Reference source not found.). TGA analysis shows a more consequent mass loss after PEGn grafting due to the additional organic matter on TiONts as is the case at each successive step of grafting (details on the calculation are given in Figure S1). Moreover, as expected, the greater the molecular weight (MW) of polymer, the more important the mass losses in TGA but, on the contrary, the lower the grafting yields (0.09 PEG3000•nm −2 ; 0.05 PEG5000•nm −2 ; 0.03 PEG10,000•nm −2 ). The TGA results have first demonstrated the effective synthesis of the TiONts-PEG n nanohybrids ( Figure 3; Table 1). TGA analysis shows a more consequent mass loss after PEG n grafting due to the additional organic matter on TiONts as is the case at each successive step of grafting (details on the calculation are given in Figure S1). Moreover, as expected, the greater the molecular weight (MW) of polymer, the more important the mass losses in TGA but, on the contrary, the lower the grafting yields (0.09 PEG 3000 ·nm −2 ; 0.05 PEG 5000 ·nm −2 ; 0.03 PEG 10,000 ·nm −2 ). The PEG density of each polymer grafted onto the TiONts surface seems to be related to the polymer chain length (the longer the chains, the lower the PEG density), in particular for reasons of steric hindrance: the anchoring group might be embedded into the organic layer limiting thus the ease of access for grafting. PEGylation density is commonly related to the Flory radius (RF) of the grafted PEG, the distance between grafted PEG (D = 4S PEG n /π), or the length/thickness of the grafted PEG layer. There are two main conformations that PEG chains can acquire based on these parameters: "mushroom" (RF < D) or "brush" (RF > D) conformation [36,[60][61][62][63]. The determined coverage rates (S PEG n ) obtained by the DMSO/PyBOP pathway correspond to areas of 11, 20, and 33 nm 2 relative to PEG 3000 , PEG 5000 , and PEG 10,000 , respectively. These values are approximately 5 to 8-fold lower than the theoretical projected surface areas (πRF 2 ) for polymer chains of 3, 5, and 10 kg·mol −1 , for which the values reported in the literature of RF are about 4.4, 6.0, and 9.1 nm [63,64], respectively, which corresponds to a covering surface of 61, 113 and 260 nm 2 . Moreover, the calculated distances (D) between grafted PEG n are 3.7, 5.0, and 6.5 nm relative to PEG 3000 , PEG 5000 , and PEG 10,000 . These results then indicate a PEG n brush conformation (RF > D), relatively sparse, less for the PEG 10,000 chains grafted which seem more stretched than those of PEG 3000 and PEG 5000 (RF/D = 1.2, 1.2 and 1.4 for PEG 3000 , PEG 5000 , and PEG 10,000 , respectively). Considering these ratios close to 1, the conformation of the PEG coatings would be more likely between little stretched chains and loose mushrooms. PEG density of each polymer grafted onto the TiONts surface seems to be related to the polymer chain length (the longer the chains, the lower the PEG density), in particular for reasons of steric hindrance: the anchoring group might be embedded into the organic layer limiting thus the ease of access for grafting. PEGylation density is commonly related to the Flory radius (RF) of the grafted PEG, the distance between grafted PEG (D = 4S PEG n / ), or the length/thickness of the grafted PEG layer. There are two main conformations that PEG chains can acquire based on these parameters: "mushroom" (RF < D) or "brush" (RF > D) conformation [36,[60][61][62][63]. The determined coverage rates (S PEG n ) obtained by the DMSO/PyBOP pathway correspond to areas of 11, 20, and 33 nm 2 relative to PEG3000, PEG5000, and PEG10,000, respectively. These values are approximately 5 to 8-fold lower than the theoretical projected surface areas (πRF 2 ) for polymer chains of 3, 5, and 10 kg•mol −1 , for which the values reported in the literature of RF are about 4.4, 6.0, and 9.1 nm [63,64], respectively, which corresponds to a covering surface of 61, 113 and 260 nm 2 . Moreover, the calculated distances (D) between grafted PEGn are 3.7, 5.0, and 6.5 nm relative to PEG3000, PEG5000, and PEG10,000. These results then indicate a PEGn brush conformation (RF > D), relatively sparse, less for the PEG10,000 chains grafted which seem more stretched than those of PEG3000 and PEG5000 (RF/D = 1.2, 1.2 and 1.4 for PEG3000, PEG5000, and PEG10,000, respectively). Considering these ratios close to 1, the conformation of the PEG coatings would be more likely between little stretched chains and loose mushrooms.  As shown in Error! Reference source not found.a, ζ-potential measurements highlight the presence of PEGn on the surface of APTES-modified TiONts with the observation of a significant charge shielding for the different PEGylated chain lengths. This effect is  As shown in Figure 4a, ζ-potential measurements highlight the presence of PEG n on the surface of APTES-modified TiONts with the observation of a significant charge shielding for the different PEGylated chain lengths. This effect is clearly pronounced when the PEGylated chain length increases and even more in this synthesis pathway leading to higher PEG grafting yields when compared to the water pathway published earlier [14]. These measurements confirm TGA results by proving a PEG brush conformation as the carbon chain length tends to hide the charges present on the TiONts surface. ζ-potential is then close to 0 mV over the entire studied pH range. Thus, ζ-potential for TiONts-PEG n indicates an isoelectric point (IEP) at pH 3.5 and varies between 0 mV and −5 mV at physiological pH (pH 7.4) by suggesting that the steric effect mainly governed the colloidal stability at this pH value. synthesis pathway leading to higher PEG grafting yields when compared to the water pathway published earlier [14]. These measurements confirm TGA results by proving a PEG brush conformation as the carbon chain length tends to hide the charges present on the TiONts surface. ζ-potential is then close to 0 mV over the entire studied pH range. Thus, ζ-potential for TiONts-PEGn indicates an isoelectric point (IEP) at pH 3.5 and varies between 0 mV and −5 mV at physiological pH (pH 7.4) by suggesting that the steric effect mainly governed the colloidal stability at this pH value. Error! Reference source not found. shows the dispersion of TiONts-PEGn in the same suspension concentration. The PEGn grafting on the nanotube surface greatly enhances nanohybrid individualization, regardless of the molecular weight used, as compared with TiONts and TiONts-APTES ( Figure S2). Despite the different grafting densities of PEGn on TiONts, the PEGylated chain length offsets the number of grafted molecules and leads to a similar dispersion state of the nanohybrids. Namely, a decrease in the PEG density does not lead to a greater agglomeration of nanotubes. Thus, this excellent dispersion state highlights the effectiveness of the peptidic coupling with PyBOP on the grafting yields and the colloidal stability of nanotubes functionalized by PEG chains in a brush conformation. XPS analyses have been carried out to evaluate the chemical composition on the surface of the different nanohybrids (Error! Reference source not found.). The XPS quantitative analysis reveals the presence of PEGn on nanotubes, with a significant increase in carbon and oxygen rates compared to TiONts-APTES and as the PEG MW is greater. In addition, XPS shows that sulfur (originally at the end of PEG chains and involved in the C-  Figure 5 shows the dispersion of TiONts-PEG n in the same suspension concentration. The PEG n grafting on the nanotube surface greatly enhances nanohybrid individualization, regardless of the molecular weight used, as compared with TiONts and TiONts-APTES ( Figure S2). Despite the different grafting densities of PEG n on TiONts, the PEGylated chain length offsets the number of grafted molecules and leads to a similar dispersion state of the nanohybrids. Namely, a decrease in the PEG density does not lead to a greater agglomeration of nanotubes. Thus, this excellent dispersion state highlights the effectiveness of the peptidic coupling with PyBOP on the grafting yields and the colloidal stability of nanotubes functionalized by PEG chains in a brush conformation.
XPS analyses have been carried out to evaluate the chemical composition on the surface of the different nanohybrids ( Table 2). The XPS quantitative analysis reveals the presence of PEG n on nanotubes, with a significant increase in carbon and oxygen rates compared to TiONts-APTES and as the PEG MW is greater. In addition, XPS shows that sulfur (originally at the end of PEG chains and involved in the C-S coupling between PEG and DTX-PMPI) is only observed for both TiONts-PEG 3000 (0.3%) and TiONts-PEG 5000 (0.2%) samples. This could be explained by a thinner layer of lower MW PEG (3000 and 5000) on the TiONts' surface even if their grafting density is higher compared to greater PEG MW in TiONts-PEG 10,000 samples grafted in smaller amounts (Table 1). This is correlated by a significant decrease in the Na KLL component as the corresponding chemical element, belonging to the chemical composition of TiONts, becomes more hidden when using a polymer with increasing molecular weight, until complete disappearance ( Table 2). This is probably related to either the depth of XPS analysis (a few nanometers) as the grafting of PEG n partially hides the titanate core or the repeated washings (ultrafiltration after each grafting step) which decrease the Na content below the detection limit. By comparison with the literature, it is interesting to note that the grafting of PEG 3000 on TiONts using a PyBOP crosslinker rather than EDC/NHS carbodiimide coupling [14] leads to higher concentrations of carbon and oxygen in the resulting TiONts-PEG 3000 nanohybrid: C/Ti = 1.5 and O/Ti = 3.5 for PyBOP versus C/Ti = 1.0 and O/Ti = 2.5 for EDC/NHS. Besides, from the TGA study, the grafting ratio of PEG 3000 on TiONts-APTES is almost doubled with the use of PyBOP versus carbodiimide coupling (0.09 PEG 3000 ·nm −2 , as shown in Table 1, versus 0.05 PEG 3000 ·nm −2 , respectively) and the improved grafting yield confirms that the PEG n grafting is more efficient in the organic medium than in water. The decomposition of the C 1s and O 1s threshold of the TiONts-PEG n samples also highlights the formation of the characteristic bonds of the PEG n grafting on TiONts ( Figure 6). This contribution of the latter corresponds to (C=O)-OH, (C=O)-NH-C, and C-O PEG , proving once again the presence of polymers as well as the formation of the covalent amide bonds. The proportions of components for the C 1s and O 1s thresholds vary according to the carbon chain length of PEG n (from n = 3000 to 10,000). Indeed, a decrease is observed for the components located at 530.3 eV (O 2− , from 67.6% to 64.7%) and 533.2 eV ((C=O)-OH, from 10% to 7%) on the O 1s threshold and at 288.2 eV ((C=O)-OH; (C=O)-NH-C) for the C 1s peak (4.5%, 3.1%, and 1.9%, respectively, for n = 3000 to 10,000). This observation demonstrates not only a shielding effect when the size of the PEG carbon chain increase by hiding in-depth bonds but also a decrease of the grafted PEG amount due to a higher steric hindrance ((C=O)-OH; (C=O)-NH-C).
Elements (TiONts-PEG10,000)/Ti 1.8 3.8 - The decomposition of the C1s and O1s threshold of the TiONts-PEGn samples also highlights the formation of the characteristic bonds of the PEGn grafting on TiONts (Error! Reference source not found.). The C1s peak of the different TiONts-PEGn shows one component located at 286.4 eV (C-OPEG, C-OH and (C=O)-NH-C) and the appearance of a new component at 288.2 eV ((C=O)-OH and (C=O)-NH-C) attributed to the formation of secondary amide bonds characterizing the PEGn grafting on TiONts-APTES and the polymers proper bonds. The appearance of a new component in the O1s peak attributed to the carboxyl function of polymers ((C=O)-OH; 533.2 eV) and the slight shift of the component located at 532.2 eV, in comparison with TiONts-APTES, show the presence of new characteristic grafting bonds. This contribution of the latter corresponds to (C=O)-OH, (C=O)-NH-C, and C-OPEG, proving once again the presence of polymers as well as the formation of the covalent amide bonds. The proportions of components for the C1s and O1s thresholds vary according to the carbon chain length of PEGn (from n = 3000 to 10,000). Indeed, a decrease is observed for the components located at 530.3 eV (O 2− , from 67.6% to 64.7%) and 533.2 eV ((C=O)-OH, from 10% to 7%) on the O1s threshold and at 288.2 eV ((C=O)-OH; (C=O)-NH-C) for the C1s peak (4.5%, 3.1%, and 1.9%, respectively, for n = 3000 to 10,000). This observation demonstrates not only a shielding effect when the size of the PEG carbon chain increase by hiding in-depth bonds but also a decrease of the grafted PEG amount due to a higher steric hindrance ((C=O)-OH; (C=O)-NH-C).  The FTIR spectra correlate with the TGA and XPS results by confirming the PEG n presence on TiONts surface, notably with a new C-O PEG specific band to the ethylene glycol repeat units (Figure 7). Indeed, the most intense vibration bands, attributed to C-O PEG at 1100 cm −1 (red highlight on FTIR spectra) and aliphatic carbons (CH/CH 2 /CH 3 ) between 3000-2800 cm −1 and 1550-1250 cm −1 (dark gray highlight on FTIR spectra), can be assigned to the characteristic bonds of PEG. Once more the PEG n grafting thanks to DMSO/PyBOP showed more intense vibration bands by comparison with the EDC/NHS coupling in our previous study [14].
DTX pristine molecule is not readily reactive to be attached as is to TiONt nanohybrids. To activate the coupling of DTX, p-maleimidophenyl isocyanate (PMPI) crosslinkers have been reacted thanks to their isocyanate groups on one of the hydroxyl groups of DTX. In a second step, the maleimide groups of PMPI crosslinkers have been used to form new carbon-sulfur bonds with the end thiols of PEGs to eventually form TiONts-PEG n preferentially at pH 7.4 in PBS. Whereas the reaction is possible with both thiol and amine functions above pH 7.5, the specificity of maleimide for thiols is preserved when the reaction is carried out between pH 6.5 and 7.5 [65] (Figure S3). presence on TiONts surface, notably with a new C-OPEG specific band to the ethylene glycol repeat units (Error! Reference source not found.). Indeed, the most intense vibration bands, attributed to C-OPEG at 1100 cm −1 (red highlight on FTIR spectra) and aliphatic carbons (CH/CH2/CH3) between 3000-2800 cm −1 and 1550-1250 cm −1 (dark gray highlight on FTIR spectra), can be assigned to the characteristic bonds of PEG. Once more the PEGn grafting thanks to DMSO/PyBOP showed more intense vibration bands by comparison with the EDC/NHS coupling in our previous study [14]. DTX pristine molecule is not readily reactive to be attached as is to TiONt nanohybrids. To activate the coupling of DTX, p-maleimidophenyl isocyanate (PMPI) crosslinkers have been reacted thanks to their isocyanate groups on one of the hydroxyl groups of DTX. In a second step, the maleimide groups of PMPI crosslinkers have been used to form new carbon-sulfur bonds with the end thiols of PEGs to eventually form TiONts-PEGn preferentially at pH 7.4 in PBS. Whereas the reaction is possible with both thiol and amine functions above pH 7.5, the specificity of maleimide for thiols is preserved when the reaction is carried out between pH 6.5 and 7.5 [65] ( Figure S3).
The grafting yields of DTX-PMPI on the surface of TiONts-PEGn were determined by TGA and are presented in Error! Reference source not found.Error! Reference source not found. and Error! Reference source not found.a. The amount of grafted therapeutic molecules, in the case of TiONts-PEG3000 prepared thanks to DMSO/PyBOP, is higher than the one obtained, in a previous study, by EDC/NHS coupling in water [14]: 0.32 DTX-PMPI•nm −2 versus 0.24 DTX-PMPI•nm -2 , respectively. Indeed, the number of grafted polymers on the TiONts surface is also higher, promoted by our new strategy of TiONts-DTX nanohybrid elaboration. Thus, the smaller the PEGylated chain size, the greater the DTX-PMPI amount. Furthermore, the number of DTX on TiONts-PEG3000 and TiONts-PEG5000 have been found greater than that of sulfur groups initially present at the nanotube surface: 0.32 DTX-PMPI•nm −2 versus 0.09 PEG3000•nm −2 for TiONts-PEG3000-DTX and 0.24 DTX-PMPI•nm −2 versus 0.05 PEG5000•nm −2 for TiONts-PEG5000-DTX. To some extent, DTX-PMPI seems to have another strong interaction with the surface (in addition to the one with PEGn thiols). Additional experiments are then carried out and confirm the presence of modified-DTX on simple contact with the use of an inactive polymer grafted The grafting yields of DTX-PMPI on the surface of TiONts-PEG n were determined by TGA and are presented in Table 1 and Figure 8a. The amount of grafted therapeutic molecules, in the case of TiONts-PEG 3000 prepared thanks to DMSO/PyBOP, is higher than the one obtained, in a previous study, by EDC/NHS coupling in water [14]: 0.32 DTX-PMPI·nm −2 versus 0.24 DTX-PMPI·nm -2 , respectively. Indeed, the number of grafted polymers on the TiONts surface is also higher, promoted by our new strategy of TiONts-DTX nanohybrid elaboration. Thus, the smaller the PEGylated chain size, the greater the DTX-PMPI amount. Furthermore, the number of DTX on TiONts-PEG 3000 and TiONts-PEG 5000 have been found greater than that of sulfur groups initially present at the nanotube surface: 0.32 DTX-PMPI·nm −2 versus 0.09 PEG 3000 ·nm −2 for TiONts-PEG 3000 -DTX and 0.24 DTX-PMPI·nm −2 versus 0.05 PEG 5000 ·nm −2 for TiONts-PEG 5000 -DTX. To some extent, DTX-PMPI seems to have another strong interaction with the surface (in addition to the one with PEG n thiols). Additional experiments are then carried out and confirm the presence of modified-DTX on simple contact with the use of an inactive polymer grafted onto TiONts-APTES, preventing any chemical reaction with PMPI-DTX ( Figure S4). As its grafting ratio does not vary despite repeated purifications, these DTX-PMPI molecules being thus less likely embedded within PEG chains. DTX-PMPI molecules could presumably interact with the remaining amine groups of APTES (not already functionalized by PEG n ), or could also be trapped inside the cavity of nanotubes. Indeed for DTX-PMPI grafting, the reaction carried out at pH 7.4 used to promote the formation of covalent bonds with the thiol groups of PEG n , might have undergone a pH drift to higher values resulting in unexpected coupling with the amine function of APTES [65], as described above. It should be noted that the grafting ratio of DTX-PMPI on TiONts-PEG 10,000 corresponds to the same as that of PEG 10,000 (0.03 DTX-PMPI·nm −2 and 0.03 PEG 10,000 ·nm −2 for TiONts-PEG 10,000 -DTX). This observation seems to be a direct consequence of the total shielding of APTES by the PEG 10,000 layer. Thus, DTX-PMPI tends to attach mainly to the thiol groups provided by the PEG 10,000 , contrary to PEG 3000 and PEG 5000 , which would also have another way of adhesion, improving the DTX grafting yields and probably, the therapeutic effect of nanohybrids on tumor cells. from dietary choline that is further converted into trimethylamine oxide (TMAO) in the liver. The levels of TMAO have been associated strongly with hyperglycemia, cardiovascular diseases [5] and colorectal cancer [10]. To summarize, the metabolites produced by the GM can have both positive and adverse effects on the host. Figure 1 shows examples of the GM-produced metabolites, and how they affect the bodily functions of the host. Figure 1. Examples of the metabolites produced by the gut microbiota (GM), and some effects of these metabolites on the bodily functions of the host. Diet and exercise are known to modulate the composition, species richness and diversity of the GM, which further leads to alterations in the production of the microbial metabolites. For example, the GM affect the metabolism of tyrosine and tryptophan that are precursors of dopamine and serotonin, respectively. Within the gut, for instance, dopamine affects the innate immune system and serotonin plays a critical role in regulating gut peristalsis. However, these gut-derived classical neurotransmitters can also have direct effects on the brain. The possible pathways include direct signaling via enteric nervous system (ENS), autonomic nervous system (ANS) and the vagus nerve, or via aryl hydrocarbon receptor-mediated pathway, or via still unknown pathways. Additionally, the GM can alter the production of several other neurotransmitters and neuropeptides. In the brain, these regulate, e.g., satiety, reward, and cognition. The GM produce short-chain fatty acids (SCFA) from the dietary fiber, for instance. These metabolites can regulate various functions in the gastrointestinal tract and affect the ENS. The SCFA TiONts-PEG n -DTX (mean ± SD) (the horizontal dotted lines allow for an estimate of the different nanohybrids' IC 50 ). The studied range was from 0.5 to 500 nM in DTX concentration, which corresponded to a concentration range of 4.5 × 10 −3 to 4.5 µg·mL −1 , 5.75 × 10 −3 to 5.75 µg·mL −1 , and 5 × 10 −2 to 50 µg·mL −1 for TiONts-PEG 3000 -DTX, TiONts-PEG 5000 -DTX and TiONts-PEG 10,000 -DTX, respectively.
Additionally, ICP-MS measurements have been realized on cells incubated with TiONts-PEG n -DTX, the results of which are presented in Table 3. First, a dose-effect can be noticed with an increase in the mass of nanohybrids per cell when the DTX concentration is doubled (10 to 20 nM). However, this effect is more pronounced when the PEG chain is shorter: when DTX concentration varies from 10 to 20 nM, the TiONts-PEG 3000 -DTX mass is increased 5-fold compared to the 2.5-fold increase in the case of TiONts-PEG 10,000 -DTX nanohybrids. This may be due to the steric hindrance of the polymer shell, bigger in the case of MW = 10,000 g·mol −1 . The thinner shell could thus improve interaction with cells. MTS assays on a PC-3 human prostate cancer cell lines evaluate the cytotoxicity of DTX (modified or not) and associated nanohybrids (Figure 8b). The first results reveal that TiONts-PEG n -DTX nanohybrids have a cytotoxic activity according to their half-maximum inhibitory concentration (IC 50 ). DTX-nanohybrids cytotoxicity are lower than that of DTX (IC 50 : 20 nM; black curve) and DTX-PMPI (IC 50 : 35 nM; pink curve), as described in a previous report [9,14,15]. Note that PMPI-activated DTX molecules have a slightly lower cytotoxic activity compared with free DTX, most probably because of the covalent bond formed between PMPI and DTX. Nevertheless, the survival curves show also a "plateau effect" at high doses around the IC 50 for each TiONts-PEG n -DTX nanohybrid and suggest a phenomenon called mitotic catastrophe, which is a type of cell death, as already observed in the literature [66][67][68]. Indeed, DTX binding can inhibit mitotic cell division by blocking the microtubule repolymerization and prevent further cell proliferation, but some cells could continue to replicate their DNA without dividing [69]. This leads to a higher survival rate for high doses in DTX due to hypermetabolic cells before inducing the apoptosis or necrosis shortly after mitosis dysfunction. Even with this phenomenon, the cytotoxic activity of TiONts-PEG 3000 -DTX (green curve) is more than three times greater than that observed for the same nanohybrids elaborated in water (IC 50 : 100 nM versus 360 nM in ref [14], respectively) and is close to that of a previous study by using the same organic way (IC 50 : 82 nM) [9]. PEG brush conformation may affect the biological performance of these nanohybrids, as already demonstrated with PEG-modified carbon nanotubes [70], being most favorable on DTX cytotoxicity while promoting both colloidal stability in biological media and the interaction of the therapeutic agent with microtubules. In addition, the IC 50 of TiONts-PEG 10,000 -DTX (IC 50 : 360 nM; yellow curve) is greater than the IC 50 of TiONts-PEG 3000 -DTX and TiONts-PEG 5000 -DTX (IC 50 : 100 nM; green and blue curves, respectively). Therefore, the PEGylated chain length plays an important role in the DTX interactions with the PC-3 prostate cancer cells and, as corroborated by the ICP-MS results, these results show that DTX has a better efficiency when attached on shorter-chains (PEG 3000/5000 versus PEG 10,000 ) which tends indeed to promote the interaction between DTX and microtubules. Despite a similar surface charge and dispersion state for all TiONts-PEG n -DTX nanohybrids, a lower internalization rate for TiONts-PEG 10,000 -DTX can occur in comparison with TiONts-PEG 3000/5000 -DTX. Thus, about the PEGylated chain, the higher the grafting densities, the shorter the lengths, the greater the cytotoxicity. These achievements are then very promising to understand the influence of the PEGylated chain length in nanomedicine to improve tumor cell internalization and might ensure better access of DTX to microtubules to fight prostate cancer.

Conclusions
TiONts were successfully functionalized to develop docetaxel-grafted nanohybrids using a step-by-step process. Each grafting step was characterized by different techniques to prove their success. The grafting of PEG n has been achieved via a peptide coupling with Py-BOP in DMSO on the surface of TiONts-APTES and the resulting TiONts-PEG n nanohybrids have significantly improved the colloidal stability of suspensions under physiological conditions consistent with the targeted biomedical applications. The high number of polymers on the nanotube surface (0.09 PEG 3000 ·nm −2 ; 0.05 PEG 5000 ·nm −2 ; 0.03 PEG 10,000 ·nm −2 ) allowed to significantly improve the amount of therapeutic agent (DTX) modified by PMPI on nanohybrids, especially with the use of smaller PEGylated chain lengths (PEG 3000 : 0.32 DTX·nm −2 ; PEG 5000 : 0.24 DTX·nm −2 ; PEG 10,000 : 0.03 DTX·nm −2 ). Indeed, the steric hindrance generated by PEG on nanotubes was progressively improved with increasing molecular weight. In vitro (MTS) tests highlighted satisfactory cytotoxicities of DTX for each TiONts-PEG n -DTX nanohybrids on human PC-3 prostate adenocarcinoma cells. Finally, this study demonstrated that the PEG grafting with high molecular weights on TiONts (in our case: PEG 10,000 ) decreased the cytotoxic activity of DTX and reduce the internalization in cells. Thus, higher grafting densities of shorter PEG chain lengths have been found more favorable to greater cytotoxicities. Understanding the influence of PEGylated chain lengths allows one to move towards an approach to fight tumor cells and in this context, titanate nanotubes appear as new theranostic tools to improve the efficacy of cancer treatment.
Supplementary Materials: The following are available online at https://www.mdpi.com/article/10 .3390/nano11102733/s1, Figure S1: (a) TGA curves of bare TiONts under air atmosphere and theoretical calculation of the hydroxyl rates. (b) Theoretical calculation for the graft ratios of functionalized-TiONts; Figure S2: TEM images show the evolution of the dispersion (a) before and (b) after APTES grafting on TiONts surface; Figure S3: (a) Maleimide reacts specifically with a thiol function at pH < 7.5 and (b) lose its specificity to react either with a thiol function or with amine function at pH > 7.5; Figure S4: (a) Polymer (Boc-NH-PEG 3000 -COOH; M = 3173 g·mol −1 ) having an inactive function (Boc) and carboxyl function to react with an amine group via peptide coupling and (b) TGA curves showing the adsorption of DTX-PMPI upon contact between TiONts-PEG 3000 -Boc and DTX-PMPI (TiONts-DTX were washed by dialysis and ultrafiltration (100 kDa)). (c) Results of relative mass loss and graft ratio of bare TiONts, TiONts-APTES, TiONts-PEG 3000 -Boc and after mixing DTX-PMPI with TiONts-PEG 3000 -Boc. Funding: This research was funded by the Cancéropôle Est through the call "Emergence 2015" (Région Bourgogne Franche Comté) and by the European Union through the PO FEDER-FSE Bourgogne 2014/2020 programs. This work has been also supported by the EIPHI Graduate School (contract "ANR-17-EURE-0002").

Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.

Data Availability Statement:
The data presented in this study are available on request from the authors.