Clément Gaultier

Saurabh Kataria
email: saurabhk@iitk.ac.in

Antoine Deleforge

VAST : The Virtual Acoustic Space Traveler Dataset

Keywords: Sound Localization, Binaural Hearing, Room Simulation, Machine Learning

This paper introduces a new paradigm for sound source localization referred to as virtual acoustic space traveling (VAST) and presents a first dataset designed for this purpose. Existing sound source localization methods are either based on an approximate physical model (physics-driven) or on a specific-purpose calibration set (data-driven). With VAST, the idea is to learn a mapping from audio features to desired audio properties using a massive dataset of simulated room impulse responses. This virtual dataset is designed to be maximally representative of the potential audio scenes that the considered system may be evolving in, while remaining reasonably compact. We show that virtually-learned mappings on this dataset generalize to real data, overcoming some intrinsic limitations of traditional binaural sound localization methods based on time differences of arrival.

Introduction

Human listeners have the stunning ability to understand complex auditory scenes using only two ears, i.e., with binaural hearing. Advanced tasks such as sound source direction and distance estimation or speech deciphering in multi-source, noisy and reverberant environments are performed daily by humans, while they are still a challenge for artificial (two-microphone) binaural systems. The main line of research in machine binaural source localization along the past decades has been to estimate the time-difference of arrival (TDOA) of the signal of interest at the two microphones. An estimated TDOA can be approximately mapped to the azimuth angle of a frontal source if the distance between microphones is known, assuming free-field 1 and far-field 2 conditions. Two important limits of these assumptions can be identified. First, they are both violated in most practical scenarios. In the example of an indoor binaural hearing robot, users are typically likely to engage interaction in both far-and near-fields and nondirect sound paths exist due to reflection and diffusion on walls, ceiling, floor, other objects in the room and the robot itself. Second, the intrinsic symmetries of a free-field/far-field binaural system restrict any geometrical estimation to that of a frontal azimuth angle. Hence, 3D source position (azimuth, elevation, distance) is out of reach in this scope, let alone additional properties such as source orientation, receiver position or room shape.

To overcome intrinsic limitations of TDOA, richer binaural features have been investigated. These include frequency-dependent phase and level differences [START_REF] Viste | On the use of spatial cues to improve binaural source separation[END_REF][START_REF] Deleforge | Co-localization of audio sources in images using binaural features and locally-linear regression[END_REF], spectral notches [START_REF] Raykar | Extracting the frequencies of the pinna spectral notches in measured head related impulse responses[END_REF][START_REF] Hornstein | Sound localization for humanoid robots-building audio-motor maps based on the hrtf[END_REF] or the direct-to-reverberant ratio [START_REF] Lu | Binaural estimation of sound source distance via the directto-reverberant energy ratio for static and moving sources[END_REF]. To overcome the free-field/far-field assumptions, advanced mapping techniques from these features to audio scene properties have been considered. These mapping techniques divide in two categories. The first one is physics-driven, i.e., the mapping is inferred from an approximate sound propagation model such as the Woodworth's spherical head formula [START_REF] Viste | On the use of spatial cues to improve binaural source separation[END_REF] or the full wave-propagation equation [START_REF] Kitić | Hearing behind walls: localizing sources in the room next door with cosparsity[END_REF]. The second category of mapping is data-driven. This approach is sometimes referred to as supervised sound source localization [START_REF] Talmon | Supervised source localization using diffusion kernels[END_REF], or more generally acoustic space learning [START_REF] Deleforge | Acoustic space learning for sound-source separation and localization on binaural manifolds[END_REF]. These methods bypass the use of an explicit, approximate physical model by directly learning a mapping from audio features to audio properties using manually recorded training data [START_REF] Talmon | Supervised source localization using diffusion kernels[END_REF][START_REF] Deleforge | Co-localization of audio sources in images using binaural features and locally-linear regression[END_REF]. They generally yield excellent results, but because obtaining sufficient training data is very time consuming, they only work for a specific room and setup and are hard to generalize in practice. Unlike artificial systems, human listeners benefit from years of adaptive auditory learning in a multitude of acoustic environments. While machine learning recently showed tremendous success in the field of speech recognition using massive amounts of annotated data, equivalent training sets do not exist for audio scene geometry estimation, with only a few specialized manually annotated ones [START_REF] Deleforge | Acoustic space learning for sound-source separation and localization on binaural manifolds[END_REF][START_REF] Deleforge | Co-localization of audio sources in images using binaural features and locally-linear regression[END_REF]. Interestingly, a recent data-driven method [START_REF] Parada | A single-channel non-intrusive c50 estimator correlated with speech recognition performance[END_REF] used both real and simulated data to estimate room acoustic parameters and improve speech recognition performance, although it was not designed for sound localization.

We propose here a new paradigm that aims at making the best of physicsdriven and data-driven approaches, referred to as virtual acoustic space traveling. The idea is to use a physics-based room-acoustic simulator to generate arbitrary large datasets of room-impulse responses corresponding to various acoustic environments, adapted to the physical audio system considered. Such impulse responses can be easily convolved with natural sounds to generate a wide variety of audio scenes including cocktail-party like scenarios. The obtained corpus can be used to learn a mapping from audio features to various audio scene properties using, e.g., deep learning or other non-linear regression methods [START_REF] Deleforge | High-dimensional regression with gaussian mixtures and partially-latent response variables[END_REF]. The virtually-learned mapping can then be used to efficiently perform real-world auditory scene analysis tasks with the corresponding physical system. Inspired by the idea of an artificial system learning to hear by exploring virtual acoustic environments, we name this proposal the Virtual Acoustic Space Traveler (VAST) project. We initiate it by publicly releasing a dedicated project page : http://theVASTproject.inria.fr and a first example of VAST dataset. This paper details the guidelines and methodology that were used in the process of building this training set. It then demonstrates that virtually-learned mappings can generalize to real-world test sets, overcoming intrinsic limitations of TDOAbased sound source localization methods.

Dataset Design

General Principles

The space of all possible acoustic scenes is vast. Therefore, some trade-offs between the size and the representativity of the dataset must be made when building a training corpus for audio scene geometry estimation. During the process of designing the dataset, we imposed on ourselves the following guidelines:

• The dataset should consist of room impulse responses (RIR). This is a more generic representation than, e.g., specific audio features or audio scenes involving specific sounds. Each RIR should be annotated by all the source, receiver and room properties defining it. • Virtual acoustic space traveling aims at building a dataset for a specific audio system in a variety of environments. Following this idea, some intrinsic properties of the receiver such as its distance to the ground and its head-related transfer functions are kept fixed throughout the simulations. For this first dataset, called VAST KEMAR 0, we chose the emblematic KE-MAR acoustic dummy-head, whose measured HRTFs are publicly available.

It was placed at 1.70 from the ground, the average human's height. • We are interested in modeling acoustic environments which are typically encountered in an office building, a university, a hotel or a modern habitation. Acoustics of the type encountered in a cathedral, a massive hangar, a recording studio or outdoor are deliberately left aside here. Surface materials and diffusion profiles are chosen accordingly. • To make the dataset easily manipulable on a simple laptop, we aimed at keeping its total size under 10 GigaBytes. To handle datasets of larger order of magnitudes would require users to have access to specific hardware and software which is not desired here. VAST KEMAR 0 measures 6.4 GB.

Room Simulation and Data Generation

The efficient C++/MATLAB "shoebox" 3D acoustic room simulator ROOMSIM developed by Schimmel et al. is selected for simulations [START_REF] Schimmel | A fast and accurate "shoebox" room acoustics simulator[END_REF]. This software takes as input a room dimension (width, depth and height), a source and receiver position and orientation, a receiver's head-related-transfer function (HRTF) model, and frequency-dependent absorption and diffusion coefficients for each surface. It outputs a corresponding pair of room impulse responses (RIR) at each ear of the binaural receiver. Specular reflections are modeled using the image-source method [START_REF] Allen | Image method for efficiently simulating small-room acoustics[END_REF], while diffusion is modeled using the so-called rain-diffusion algorithm. In the latter, sound rays uniformly sampled on the sphere are sent from the emitter and bounced on the walls according to specular laws, taking into account surface absorption. At each impact, each ray is also randomly bounced towards the receiver with a specified probability (the frequency-dependent diffusion coefficient of the surface). The total received energy at each frequency is then aggregated using histograms. This model was notably showed to realistically account for sound scattering due to the presence of objects, by comparing simulated RIRs with measured ones in [START_REF] Wabnitz | Room acoustics simulation for multichannel microphone arrays[END_REF]. The study [START_REF] Kataria | Hearing in a shoe-box: Binaural source position and wall absorption estimation using virtually supervised learning[END_REF] suggests that such diffusion effects play an important role in sound source localization. VAST KEMAR 0 contains over 110, 000 RIR, which required about 700 CPU-hours of computation. This was done using a massively parallelized implementation on a large computer grid.

R 1 R 2 R 3 R 4 R 5 R 6 R 7 R 8 R 9 x y z Width = 3.5 m Depth = 5 m North Wall East Wall R 1 R 2 R 3 R 4 R 5 R 6 R 7 R 8 R 9

Room Properties: Size and Surfaces

An obvious choice to generate virtual rooms with maximal variability would be to draw a random room size and random frequency-dependent absorption and diffusion profiles of surfaces for each generated RIR. This approach however, has several drawbacks. First, it makes impossible the generation of realistic audio scenes containing several sources, for which the receiver position and the room must be fixed. Second, the space of possible rooms is so vast that reliably sampling it at random is unrealistic. Third, changing source, receiver and room parameters all at the same time prevents from getting insights on the individual influence of these parameters. On the other hand, sampling all combinations of parameters in an exhaustive way quickly leads to enormous data size. As a trade-off, we designed 16 realistic rooms representative of typical reverberation time (RT 60 ) and surface absorption profiles encountered in modern buildings. Two room sizes were considered: a small one corresponding to a typical office or bed room (Fig. 1(a)), and a larger one corresponding to a lecture or entrance hall (Fig. 1(b)). For each room, floor, ceiling and wall materials which are representative in terms of absorption profile and are commonly encountered in nowadays buildings were chosen from [START_REF] Vorländer | Auralization: fundamentals of acoustics, modeling, simulation, algorithms and acoustic virtual reality[END_REF]. The graph on Fig. 2 displays the absorption profiles of the selected materials, namely, 4 for the walls, 2 for the floor and 1 for the ceiling. The gypsum board material chosen for the ceiling was kept fixed throughout the dataset, as it represents well typical ceiling absorption profiles [START_REF] Vorländer | Auralization: fundamentals of acoustics, modeling, simulation, algorithms and acoustic virtual reality[END_REF]. "Walls hard surface average" is in fact an average profile over many surfaces such as brick or plaster [START_REF] Vorländer | Auralization: fundamentals of acoustics, modeling, simulation, algorithms and acoustic virtual reality[END_REF]. Combining all possible floors, walls and room sizes yielded the 16 rooms listed in Table 1.

Importantly, typical rooms also contain furniture and other objects responsible for random sound scattering effects, i.e., diffusion. Following the acoustic study in [START_REF] Faiz | Measurement of sound diffusion coefficients of scattering furnishing volumes present in workplaces[END_REF], a unique frequency-dependent diffusion profile was used for all surfaces. The chosen profile is the average of the 8 configurations measured in [START_REF] Faiz | Measurement of sound diffusion coefficients of scattering furnishing volumes present in workplaces[END_REF], corresponding to varying numbers of chairs, table, computers and people in a room. Both absorption and diffusion profiles are piecewise-linearly interpolated from 8 Octave bands from 125 Hz to 4 kHz.

Reverberation Time

A common acoustic descriptor for rooms is the reverberation time (RT 60 ). Figure 3(a) displays the estimated RT 60 distribution across the VAST Training Dataset. Fig. 3(b) shows the RT 60 for each room by octave band. RT 60 's were estimated from the room impulse responses following the recommendations in [START_REF] Schroeder | New method of measuring reverberation time[END_REF]. From these estimations, we decided to crop the room impulse responses provided in the datasets above the RT 60 , with a 30 ms margin. This technique allows to shrink the dataset while keeping data points of interest and discarding the rest. To further complies with memory limitations, we chose to encode the room impulse response samples with single floats (16 bit). As can be seen in Fig. 3 the 16 chosen rooms present a quite good variability in terms of reverberation times in the range 100ms-400ms. Larger RT 60 of the order of 1 second could be obtain by using highly reflective materials on all surfaces, creating an echo chamber. However, this rarely occurs in realistic buildings.

Source and Receiver Positions

A relatively poorly-studied though important effect in sound source localization is the influence of the receiver's position in the room, especially its distance to the nearest surface. In order to accurately capture this effect, 9 receiver positions are used for each of the 16 rooms, while the height of the receiver is fixed at 1.7 m. Figure 1 shows top views of the rooms with receiver positions. Positions from R 1 to R 8 are set 50 cm from the nearest wall(s) whereas R 9 is approximately placed in the middle of the room. Perfectly symmetrical configurations are avoided to make the dataset as generic as possible, without singularities. The receiver is always facing the north wall as a convention. For each of the 9 receiver positions, sources are placed on spherical grids centered on the receiver. Each sphere consists of regularly-spaced elevation lines each containing sources at regularly-spaced azimuths, with a spacing of 9 • . The equator elevation line and the first azimuth angle of each line are randomly offset by -4.5 • to +4.5 • in order to obtain a dense sphere sampling throughout the dataset. Six spherical grid radii are considered, yielding source distances of 1, 1.5, 2, 3, 4 and 6 meters. Sources falling outside of the room or less than 20cm from a surface are removed.

Test Sets

To test the generalizability of mappings learned on the VAST KEMAR 0 dataset, we built four simulated test sets differing from the training dataset on various levels. A first challenge is to test robustness to random positioning, since the training set is built with regular spherical source grids and fixed listener positions. Hence, the 4 testing sets contain completely random source and receiver positions in the room. Only the receiver's height is fixed to 1.7m, and both receiver and source are set within a 20 cm safety margin within the room boundaries. Test sets 2 and 4 feature random receiver orientation (yaw angle), as opposed to the receiver facing north in the training set. Test 1 and 2 contain 1,000 binaural RIRs (BRIRs) for each of the 16 rooms of Table 1. Finally, test sets 3 and 4 contain 10,000 BRIRs, each corresponding to a random room size (walls from 3m × 2m to 10m × 4m) and random absorption properties of walls and floor picked from Fig. 2. Different surfaces for all 4 walls are allowed.

In addition to these simulated test sets, three binaural RIR datasets recorded with the KEMAR dummy head in real rooms have been selected, as listed below:

• Auditorium 3 [START_REF] Ma | A machine-hearing system exploiting head movements for binaural sound localisation in reverberant conditions[END_REF] was recorded at TU Berlin in 2014 in a trapeziumshaped lecture room of dimensions 9.3m × 9m and RT 60 ≈ 0.7s. 3 individual sources placed 1.5m from the receiver at different azimuth and 0 • elevation were recorded. For each source, one pair of binaural RIR is recorded for each receivers' head yaw angle from -90 • to +90 • , with 1 • steps. • Spirit [START_REF] Ma | A machine-hearing system exploiting head movements for binaural sound localisation in reverberant conditions[END_REF] was recorded at TU Berlin in 2014 in a small rectangular office room of size 4.3m × 5m, RT 60 ≈ 0.5s, containing various objects, surfaces and furniture near the receiver. The protocol is the same as Auditorium 3 except sources are placed 2m from the receiver. • Classroom [START_REF] Shinn-Cunningham | Localizing nearby sound sources in a classroom: Binaural room impulse responses[END_REF] was recorded at Boston University in 2005 in a 5m × 9m × 3.5m carpeted classroom with 3 concrete walls and one sound-absorptive wall (RT 60 = 565ms). The receiver is placed in 4 locations of the room including 3 with at least one nearby wall.

Note that the KEMAR HRTF measurements used to simulate the VAST dataset was recorded by yet another team, in MIT's anechoic chamber in 1994, as described in [START_REF] Gardner | Hrtf measurements of a kemar[END_REF].

Virtually Supervised Sound Source Localization

For all experiments in this section, all training and test sets used are reduced to contain only frontal sources (azimuth in [-90 • , +90 • ]) with elevation in [-45 • , +45 • ] and distances between 1 and 3 meters. As mentioned in the introduction, sound source localization consists in two steps: calculating auditory features from binaural signals followed by mapping these features to a source position. Robustly estimating features can be difficult when dealing with additive noise, sources with sparse spectra such as speech or music, and source mixtures. We leave this problematic aside in this paper, and focus on mapping clean features to source positions. Hence, we use ideal features directly calculated from the clean room impulse responses in all experiments.

We first make an experiment to put forward some intrinsic limitations of TDOA-based azimuth estimation. Fig. 4 plots TDOAs against the source's azimuth angle for different subsets of VAST. TDOAs (in samples) were computed as the integer delay in [-15, +15] maximizing the correlation between the first 500 samples of the left and the right impulse responses. As can be seen in Fig. 4(a), a near-linear relationship between frontal azimuth and TDOA exists in the anechoic case, regardless of the elevation. This matches previously observed results in binaural sound localization [START_REF] Viste | On the use of spatial cues to improve binaural source separation[END_REF][START_REF] Sanchez-Riera | Online multimodal speaker detection for humanoid robots[END_REF][START_REF] Deleforge | Co-localization of audio sources in images using binaural features and locally-linear regression[END_REF]. When the receiver is placed in the middle of the 16 reverberant rooms, (Fig. 4(b)), some outliers appear due to reflections. This effect is dramatically increased when the receiver is placed 50 centimeters from a wall (Fig. 4 are present. This suggests that the TDOA, even when ideally estimated, is not adapted to binaural sound source localization in realistic indoor environments.

We then compare azimuth estimation errors obtained with the TDOA-based method described above, a learning-based method trained on anechoic HRTF measurements (Room 0), and a learning-based method trained on VAST, using the 4 simulated and 3 real test sets described in Section 2.6. TDOAs were mapped to azimuth values using the affine regression coefficients corresponding to the red line in Fig. 4(a). The chosen learning-based sound source localization method is the one described in [START_REF] Deleforge | Co-localization of audio sources in images using binaural features and locally-linear regression[END_REF]. It uses Gaussian Locally Linear Regression (GLLiM, [START_REF] Deleforge | High-dimensional regression with gaussian mixtures and partially-latent response variables[END_REF]) to map high-dimensional feature vectors containing frequency-dependent interaural level and phase differences from 0 to 8000 Hz to low-dimensional source positions. In our case, the GLLiM model with K locally-linear components was trained on N interaural feature vectors of dimension D = 1537 associated to 3-dimensional source positions in spherical coordinate (azimuth, elevation and 7.44 ± 4.3(30%) 0.52 ± 0.3(25%) Classroom [START_REF] Shinn-Cunningham | Localizing nearby sound sources in a classroom: Binaural room impulse responses[END_REF] 8.40 ± 4.1(45%) 0.41 ± 0.3(6.5%) distance). K = 8 components were used for the anechoic training set (N = 181) and K = 100 for the (reduced) VAST dataset (N ≈ 41, 000). All 3 methods showed comparably low testing computational times, in the order of 10ms for 1 second of input signal. Table 2 summarizes obtained azimuth estimation errors.

As can be seen, the learning method trained on VAST outperforms the two others on all datasets, with significantly less outliers and a globally reduced average error of inliers. This is encouraging considering the variety of testing data used. In addition, Table 3 shows that GLLiM trained on VAST is capable of approximately estimating the elevation and distance of the source, which is known to be particularly difficult from binaural data. While elevation estimation on real data remains a challenge, results obtained on simulated sets are promising.

Conclusion

We introduced the new concept of virtual acoustic space traveling and released a first dataset dedicated to it. A methodology to efficiently design such a dataset was provided, making extensions and improvements of the current version easily implementable in the future. Results show that a learning-based sound source localization method trained on this dataset yields better localization results than when trained on anechoic HRTF measurements, and performs better than a TDOA-based approach in azimuth estimation while being able to estimate source elevation and distance. To the best of the authors' knowledge, this is the first time a sound localization method trained on simulated data is successfully used on real data, validating the new concept of virtual acoustic space traveling. The learning approach could still be significantly improved by considering other auditory features, by better adapting the mapping technique to spherical coordinates and by annotating training data with further acoustic information. Other learning methods such as deep neural networks may also be investigated.

Fig. 1 .

 1 Fig. 1. Top views of training rooms with receiver positions and orientations.

Fig. 2 .

 2 Fig. 2. Absorption Profiles

Fig. 3 .

 3 Reverberation Time.

Fig. 4 .

 4 Fig. 4. TDOA as a function of source azimuth in various settings

Table 1 .

 1 Description of simulated training rooms in VAST

	Room Number	Floor	Ceiling	Walls	Width [m]	Depth [m]	Height [m]
	1	Thin Carpet Perforated 27 mm gypsum board Walls Hard Surfaces Average	9	6	3.5
	2	Thin Carpet Perforated 27 mm gypsum board Gypsum Board with Mineral Filling	9	6	3.5
	3	Thin Carpet Perforated 27 mm gypsum board Fabric-Covered Panel with Rockwool Core	9	6	3.5
	4	Thin Carpet Perforated 27 mm gypsum board Thin Plywood Paneling	9	6	3.5
	5	Linoleum	Perforated 27 mm gypsum board Walls Hard Surfaces Average	9	6	3.5
	6	Linoleum	Perforated 27 mm gypsum board Gypsum Board with Mineral Filling	9	6	3.5
	7	Linoleum	Perforated 27 mm gypsum board Fabric-Covered Panel with Rockwool Core	9	6	3.5
	8	Linoleum	Perforated 27 mm gypsum board Thin Plywood Paneling	9	6	3.5
	9	Thin Carpet Perforated 27 mm gypsum board Walls Hard Surfaces Average	3.5	5	2.5
	10	Thin Carpet Perforated 27 mm gypsum board Gypsum Board with Mineral Filling	3.5	5	2.5
	11	Thin Carpet Perforated 27 mm gypsum board Fabric-Covered Panel with Rockwool Core 3.5	5	2.5
	12	Thin Carpet Perforated 27 mm gypsum board Thin Plywood Paneling	3.5	5	2.5
	13	Linoleum	Perforated 27 mm gypsum board Walls Hard Surfaces Average	3.5	5	2.5
	14	Linoleum	Perforated 27 mm gypsum board Gypsum Board with Mineral Filling	3.5	5	2.5
	15	Linoleum	Perforated 27 mm gypsum board Fabric-Covered Panel with Rockwool Core 3.5	5	2.5
	16	Linoleum	Perforated 27 mm gypsum board Thin Plywood Paneling	3.5	5	2.5
	0	Anechoic room

Table 2 .

 2 Azimuth absolute estimation errors in degrees with 3 different methods, showed in the form avg ± std(out%), where avg and std denote the mean and standard deviation of inlying absolute errors (< 30 • ) while out denotes the percentage of outliers.

	Test data ↓	TDOA	GLLiM (Anech. train.) GLLiM (VAST train.)
	VAST Testing Set 1 5.49 ± 4.6(5.6%)	8.63 ± 7.6(12%)	4.38 ± 4.9(1.8%)
	VAST Testing Set 2 5.37 ± 4.4(6.0%)	8.09 ± 7.5(12%)	4.32 ± 4.7(1.6%)
	VAST Testing Set 3 5.21 ± 4.5(4.6%)	8.46 ± 7.5(5.2%)	4.23 ± 4.4(1.8%)
	VAST Testing Set 4 5.14 ± 4.4(3.3%)	8.21 ± 7.2(4.8%)	4.25 ± 4.4(0.6%)
	Auditorium 3 [11] 7.02 ± 4.7(1.4%)	8.01 ± 7.0(5.9%)	5.03 ± 4.5(0.0%)
	Spirit [11]	5.19 ± 3.4(0.0%)	12.2 ± 8.3(15%)	4.50 ± 5.6(0.4%)
	Classroom [18]	5.71 ± 3.7(3.7%)	9.47 ± 7.3(5.2%)	6.50 ± 5.9(0.0%)

Table 3 .

 3 Elevation and distance absolute estimation errors obtained with GLLiM trained on VAST. Outliers correspond to errors larger than 15 • or 1m.

	Test data ↓	Elevation ( • )	Distance (m)
	VAST Testing Set 1 5.91 ± 4.1(23%) 0.43 ± 0.3(19%)
	VAST Testing Set 2 6.05 ± 4.2(27%) 0.44 ± 0.3(20%)
	VAST Testing Set 3 6.05 ± 4.1(27%) 0.43 ± 0.3(21%)
	VAST Testing Set 4 6.03 ± 4.2(26%) 0.44 ± 0.3(21%)
	Auditorium 3 [11] 7.92 ± 4.4(44%) 0.45 ± 0.3(23%)
	Spirit [11]

Free-field means that the sound propagates from the source to the microphones through a single direct path, without interfering objects or reverberations.

Far-field means that the source is placed far enough (e.g. > 1.8 meters[START_REF] Otani | Numerical study on source-distance dependency of head-related transfer functions[END_REF]) from the receiver so that the effect of distance on recorded audio features is negligible.


Houmam Belaidi

Salah Belaidi

Claudine Katan

Camille Latouche
email: camille.latouche@cnrs-imn.fr

Abdou Boucekkine
email: abdou.boucekkine@univ-rennes1.fr

Vibronic Coupling to Simulate the Phosphorescence Spectra of Ir(III) Based OLED Systems: TD-DFT Results Meet Experimental Data

Keywords: Iridium complexes, phosphorescence, TD-DFT, vibronic coupling, VMS software

In this paper we investigate theoretically the electronic and optical properties of six based Iridium imidazolylidene complexes (numbered 1a, 1b, 2, 2b, 3, 3b) serving as serious candidates for OLED systems. Computations using methods rooted into DFT and TD-DFT explain the observed optical properties. Observed absorption bands have been assigned and computations of the lowest triplet excited states have been performed. Whereas complexes 1a and 1b are non-emissive in solution, the simulated phosphorescence spectra of complexes 2, 2b 3, 3b taking into account the vibrational contributions to the electronic transitions fit nicely the observed ones. The use of vibronic coupling permitted to reproduce and explain the structured phosphorescence spectrum of complexes 2 and 2b, as well as the absence of such structure for complexes 3 and 3b.

Introduction

In the past decades, transition metal complexes have been extensively studied, especially thanks to their strong ability to luminesce. Furthermore, compounds demonstrating a high emission response to stimuli are of interest for the development of organic light-emitting diodes (OLED) systems or light-emitting cells (LEC). [START_REF] D'andrade | White Organic Light-Emitting Devices for Solid-State Lighting[END_REF][START_REF] Sun | High-efficiency white organic light emitting devices with three separate phosphorescent emission layers[END_REF][START_REF] Chen | A New Heteroleptic Ruthenium Sensitizer for Transparent Dye-Sensitized Solar Cells[END_REF] Among them, iridium complexes possess strong ability to emit light in a large energetic range. [START_REF] Schulze | Near-IR Phosphorescent Ruthenium(II) and Iridium(III) Perylene Bisimide Metal Complexes[END_REF][START_REF] Angelis F De | Spectroscopic properties of cyclometallated iridium complexes by TDDFT[END_REF][START_REF] Dragonetti | Functionalized styryl iridium (III) complexes as active second-order NLO chromophores and building blocks for SHG polymeric films[END_REF][START_REF] Broeckx | C-H activation of 2,4,6-triphenylphosphinine: synthesis and characterization of the first homoleptic phosphinine-iridium(III) complex fac-[Ir(C^P)3][END_REF][START_REF] Sun | Smart responsive phosphorescent materials for data recording and security protection[END_REF][START_REF] Vazart | Validation of a computational protocol to simulate near IR phosphorescence spectra for Ru(II) and Ir(III) metal complexes[END_REF][START_REF] Latouche | TD-DFT Benchmark on Inorganic Pt(II) and Ir(III) Complexes[END_REF] Furthermore, iridium, ruthenium or platinum complexes are among the most investigated compounds and numerous studies from both the experimental and computational sides have been reported due to their strong ability to be embedded in devices. [START_REF] Schulze | Near-IR Phosphorescent Ruthenium(II) and Iridium(III) Perylene Bisimide Metal Complexes[END_REF][START_REF] Angelis F De | Spectroscopic properties of cyclometallated iridium complexes by TDDFT[END_REF][START_REF] Sun | Smart responsive phosphorescent materials for data recording and security protection[END_REF][START_REF] Vazart | Validation of a computational protocol to simulate near IR phosphorescence spectra for Ru(II) and Ir(III) metal complexes[END_REF][START_REF] Latouche | TD-DFT Benchmark on Inorganic Pt(II) and Ir(III) Complexes[END_REF][START_REF] Heinze | Resonance Raman Studies of Bis(terpyridine)ruthenium(II) Amino Acid Esters and Diesters[END_REF][START_REF] Bhuiyan | Synthesis and Photophysical Properties of Zeolite-Entrapped Bisterpyridine Ruthenium(II). Dramatic Consequences of Ligand-Field-State Destabilization[END_REF][START_REF] Muhavini Wawire | Density-functional study of luminescence in polypyridine ruthenium complexes[END_REF][START_REF] Bergeron | Reductive Electron Transfer Quenching of MLCT Excited States Bound To Nanostructured Metal Oxide Thin Films[END_REF][START_REF] Johansson | Distance Dependent Electron Transfer at TiO2 Interfaces Sensitized with Phenylene Ethynylene Bridged RuII-Isothiocyanate Compounds[END_REF][START_REF] Lundqvist | Calculated Optoelectronic Properties of Ruthenium Tris-bipyridine Dyes Containing Oligophenyleneethynylene Rigid Rod Linkers in Different Chemical Environments[END_REF][START_REF] Schoonover | Application of Resonance Raman Spectroscopy to Electronic Structure in Metal Complex Excited States. Excited-State Ordering and Electron Delocalization in Dipyrido[3,2-a:2',3'-c]phenazine (dppz): Complexes of Re(I) and Ru(II)[END_REF] From an experimental point view, it remains challenging and difficult to fully characterize the electronic processes at work within the targeted compounds. As a matter of fact, chemists performing quantum chemical computations are now able to give crucial information on these electronic processes, namely those relevant to excitation and emission phenomena and the nature of the reached excited states, especially thanks to the very recent developments in this area. [START_REF] Latouche | Virtual Eyes Designed for Quantitative Spectroscopy of Inorganic Complexes: Vibronic Signatures in the Phosphorescence Spectra of Terpyridine Derivatives[END_REF][START_REF] Barone | Fully anharmonic IR and Raman spectra of medium-size molecular systems: accuracy and interpretation[END_REF][START_REF] Biczysko | Harmonic and Anharmonic Vibrational Frequency Calculations with the Double-Hybrid B2PLYP Method[END_REF][START_REF] Baiardi | Accurate simulation of Resonance-Raman spectra of flexible molecules: an internal coordinates approach[END_REF][START_REF] Vazart | Vibronic Coupling Investigation to Compute Phosphorescence Spectra of Pt(II) Complexes[END_REF][START_REF] Latouche | High-Accuracy Vibrational Computations for Transition Metal Complexes Including Anharmonic Corrections: Ferrocene, Ruthenocene and Osmocene as test cases[END_REF] Moreover, Density Functional Theory (DFT) and its time dependent extension (TD-DFT) are now routinely used to get both electronic and vibrational information from small organic to large-size organometallic and transition metal complexes systems. [START_REF] Latouche | TD-DFT Benchmark on Inorganic Pt(II) and Ir(III) Complexes[END_REF][START_REF] Green | Covalent Immobilization of Redox-Active Fe(κ2dppe)(η5-C5Me5)-Based π-Conjugated Wires on Oxide-Free Hydrogen-Terminated Silicon Surfaces[END_REF][START_REF] Sahnoune | A Metal-Capped Conjugated Polyyne Threaded through a Phenanthroline-Based Macrocycle. Probing beyond the Mechanical Bond to Interactions in Interlocked Molecular Architectures[END_REF][START_REF] Makhoul | Proton-Controlled Regioselective Synthesis of [Cp*(dppe)Fe-C≡C-1-(η 6 -C 10 H 7 )Ru(η 5 -Cp](PF 6 ) and Electron-Driven Haptotropic Rearrangement of the (η 5 -Cp)Ru + Arenophile[END_REF][START_REF] Green | Synthesis and Characterization of Redox-Active Mononuclear Fe(κ2-dppe)(η5-C5Me5)-Terminated π-Conjugated Wires[END_REF][START_REF] Latouche | Encapsulating Hydrides and Main-Group Anions in d10-Metal Clusters Stabilized by 1,1-Dichalcogeno Ligands[END_REF][START_REF] Liao | A twelvecoordinated iodide in a cuboctahedral silver(I) skeleton[END_REF][START_REF] Latouche | Au-Au chemical bonding induced by UV irradiation of dinuclear gold(I) complexes: a computational study with experimental evidence[END_REF] Indeed, DFT calculations are now accurate enough to predict or confirm the stability or existence of compounds, and they can also explain the luminescent and/or spectroscopic properties of complex systems. [START_REF] Boixel | Second-Order NLO Switches from Molecules to Polymer Films Based on Photochromic Cyclometalated Platinum(II) Complexes[END_REF][START_REF] Jacquemin | TD-DFT Performance for the Visible Absorption Spectra of Organic Dyes: Conventional versus Long-Range Hybrids[END_REF][START_REF] Steffen | Fluorescence in Rhoda-and Iridacyclopentadienes Neglecting the Spin-Orbit Coupling of the Heavy Atom: The Ligand Dominates[END_REF][START_REF] Jacquemin | Extensive TD-DFT investigation of the first electronic transition in substituted azobenzenes[END_REF][START_REF] Jacquemin | Thioindigo Dyes: Highly Accurate Visible Spectra with TD-DFT[END_REF][START_REF] Latouche | Computational Chemistry Meets Experiments for Explaining the Behavior of Bibenzyl: A Thermochemical and Spectroscopic (Infrared, Raman, and NMR) Investigation[END_REF][START_REF] Latouche | Shape Modulation of Octanuclear Cu (I) or Ag (I) Dichalcogeno Template Clusters with Respect to the Nature of their Encapsulated Anions: A Combined Theoretical and Experimental Investigation[END_REF][START_REF] Latouche | Anion Encapsulation and Geometric Changes in Hepta-and Hexanuclear Copper (I) Dichalcogeno Clusters: A Theoretical and Experimental Investigation[END_REF][START_REF] Latouche | Switching of excited states in cyclometalated platinum complexes incorporating pyridyl-acetylide ligands (Pt--C [triple bond, length as m-dash] C--py): a combined experimental and theoretical study[END_REF][START_REF] Barone | Gas-phase formation of the prebiotic molecule formamide: insights from new quantum computations[END_REF] In the field of spectroscopy calculations, Vlcek Jr. and Zális among other authors, have shown how DFT and TD-DFT are useful tools to study d 6 metal complexes. [START_REF] Vlček | Modeling of chargetransfer transitions and excited states in d6 transition metal complexes by DFT techniques[END_REF] The computation of the vibrational structure of electronic absorption or emission bands should permit to reproduce more accurately both the position and the band shape of the observed spectra. In this context, Barone and coworkers implemented recently the so called Virtual Multifrequency Spectrometer (VMS) [START_REF] Barone | Implementation and validation of a multi-purpose virtual spectrometer for large systems in complex environments[END_REF][START_REF] Licari | Implementation of a graphical user interface for the virtual multifrequency spectrometer: The VMS-Draw tool[END_REF] which is a powerful, mature and cheap tool to simulate accurately many types of spectra, even when one aims to investigate large systems or a large number of effects (solvent, anharmonicity and Duschinsky couplings). [START_REF] Baiardi | General Time Dependent Approach to Vibronic Spectroscopy Including Franck-Condon, Herzberg-Teller, and Duschinsky Effects[END_REF][START_REF] Muniz-Miranda | Benchmarking TD-DFT against Vibrationally Resolved Absorption Spectra at Room Temperature: 7-Aminocoumarins as Test Cases[END_REF][START_REF] Puzzarini | Accurate Harmonic/Anharmonic Vibrational Frequencies for Open-Shell Systems: Performances of the B3LYP/N07D Model for Semirigid Free Radicals Benchmarked by CCSD(T) Computations[END_REF][START_REF] Barone | Glycine conformers: a never-ending story?[END_REF][START_REF] Bloino | General Approach to Compute Vibrationally Resolved One-Photon Electronic Spectra[END_REF][START_REF] Barone | A fully automated implementation of VPT2 Infrared intensities[END_REF][START_REF] Biczysko | Harmonic and Anharmonic Vibrational Frequency Calculations with the Double-Hybrid B2PLYP Method: Analytic Second Derivatives and Benchmark Studies[END_REF][START_REF] Banerjee | Vibronic Effects on Rates of Excitation Energy Transfer and Their Temperature Dependence[END_REF][START_REF] Hodecker | Simulation of Vacuum UV Absorption and Electronic Circular Dichroism Spectra of Methyl Oxirane: The Role of Vibrational Effects[END_REF][59] Indeed, in the last years, the VMS approach has been used to simulate with high precision anharmonic and phosphorescence spectra of organometallics and transition metal complexes. [START_REF] Vazart | Validation of a computational protocol to simulate near IR phosphorescence spectra for Ru(II) and Ir(III) metal complexes[END_REF][START_REF] Latouche | Virtual Eyes Designed for Quantitative Spectroscopy of Inorganic Complexes: Vibronic Signatures in the Phosphorescence Spectra of Terpyridine Derivatives[END_REF][START_REF] Baiardi | Accurate simulation of Resonance-Raman spectra of flexible molecules: an internal coordinates approach[END_REF][START_REF] Vazart | Vibronic Coupling Investigation to Compute Phosphorescence Spectra of Pt(II) Complexes[END_REF][START_REF] Latouche | High-Accuracy Vibrational Computations for Transition Metal Complexes Including Anharmonic Corrections: Ferrocene, Ruthenocene and Osmocene as test cases[END_REF] New tridentate chelate Ir(III) complexes have been very recently synthesized and characterized by Chi and coworkers [personal communication]. These neutral complexes (Scheme 1) involving bis(imidazolylidene) benzene and 2-(5-trifluoromethyl-1H-pyrazol-3-yl)-6-(2,4-difluorophenyl) pyridine (pzpyF2p) or 2,6-bis(5trifluoromethylpyrazol-3-yl) pyridine (pz2py) ligands, exhibit phosphorescence at short wavelengths very suitable for OLED devices. Interestingly, it is observed that complex 1 does not phosphor in solution, contrarily to complexes 2 and 3, but all complexes emit when suitably processed as films. Moreover, whereas complexes 2 and 2b exhibit a structured emission band, it is not the case for complexes 3 and 3b that exhibit a structureless phosphorescence band. In this paper, we report a full quantum investigation based on DFT and TD-DFT methods of these Ir(III) complexes in order to explain the observed properties and to provide guidance for the design of complexes of technological interest. We first discuss the ground state (GS) characteristics, i.e. the geometric and electronic structures. In a second step we focus our attention on the optical properties. We propose an assignment of the observed absorption band using TD-DFT. Then, the lowest triplet excited state (ES) will be studied. The combinations of these computations together with the aforementioned powerful tools, namely taking into account vibronic couplings, allows us to rationalize the observed properties. Scheme 1. Investigated bis-tridentate Ir(III) complexes.

Computational details

All calculations have been performed at the DFT level of theory employing the G09 suite of programs. [59] On the basis of several previous studies, [START_REF] Vazart | Validation of a computational protocol to simulate near IR phosphorescence spectra for Ru(II) and Ir(III) metal complexes[END_REF][START_REF] Latouche | TD-DFT Benchmark on Inorganic Pt(II) and Ir(III) Complexes[END_REF][START_REF] Vazart | Vibronic Coupling Investigation to Compute Phosphorescence Spectra of Pt(II) Complexes[END_REF] we have chosen the B3PW91 functional to perform the computations. [START_REF] Becke | Density-functional thermochemistry. III. The role of exact exchange[END_REF][61][START_REF] Perdew | Generalized gradient approximation for the exchange-correlation hole of a many-electron system[END_REF] The associated basis set is the socalled LANL2DZ one, including a pseudopotential for [69] Time-Dependent Density Functional Theory (TD-DFT) computations have been performed, using the optimized ground state geometries, to obtain excitations energies and spectra. Then, in order to plot the phosphorescence spectra, vibronic contributions to electronic emission have been considered using the Adiabatic Shift (AS) approach as implemented in the used version of the Gaussian Package. [START_REF] Barone | Implementation and validation of a multi-purpose virtual spectrometer for large systems in complex environments[END_REF][START_REF] Barone | Fully Integrated Approach to Compute Vibrationally Resolved Optical Spectra: From Small Molecules to Macrosystems[END_REF] The optimized geometries and vibration frequencies of the first triplet state have been obtained using unrestricted calculations. Spin-orbit coupling and Herzberg-Teller terms have not been taken into account in the calculations. Orbital visualization has been done using the GaussView [START_REF] Dennington | GaussView[END_REF] program and the orbital composition has been obtained using the AOmix package. [START_REF] Gorelsky | AOMix: Program for Molecular Orbital Analysis[END_REF] The simulated UV-visible and phosphorescence spectra have been respectively plotted using the Swizard [START_REF] Gorelsky | Swizard[END_REF] and the VMS programs. [START_REF] Licari | Implementation of a graphical user interface for the virtual multifrequency spectrometer: The VMS-Draw tool[END_REF]

Results and discussion

Ground state geometric structures

The optimized geometries are compared with the experimental data (Table 1 and ESI). In this section the discussion of the geometry will focuse on complex 1 but trends are similar for the other compounds.

Ground state electronic structures and electronic vertical excitations

We now focus our attention on the electronic structures. On the optimized GS geometries, TD-DFT vertical excitations computations have been performed. The charge transfers occurring during excitations for the six complexes are described thanks to their electronic structures. As the pimf and pimb ligands (scheme 1) differ only by replacing a CF3 by a t Bu group on the benzene ring, the properties of their related complexes (e.g. 1, 1b) are relatively similar; therefore the discussion will mainly focuse on complexes 1, 2 and 3. Furthermore, as we found that the frontier orbitals are similar for all complexes, only the molecular orbital (MO) diagram of 1 is discussed (Figure 1; MO diagrams for 1b, 2b and 3b are in ESI)). The highest occupied molecular orbitals (HOMO) are mainly localized on the metal atom (d orbitals) whereas the lowest unoccupied orbitals (LUMO) are π* types localized on the ligands.. One should mention that, as expected, the CF3 moieties are not involved in the frontier orbitals.

Using the GS optimized geometries, TD-DFT calculations have been performed to simulate the electronic absorption spectra based on the vertical excitations, and compared to the experimental ones (Figure 2). The experimental and simulated absorption spectra are in good agreement; both the computed transition energies and intensities fit nicely the experimental data. Furthermore, the observed absorption red shift between complexes 1 and 3 is also well reproduced in the simulations. It turns out that the modulation of the ligand also tunes the absorption bands. Indeed, a small red shift occurs when pimb ligand is used instead of pimf. This trend is also well portrayed in the simulations. In order to assign the transition bands, the MOs compositions are collected in Table S1. and the experimental and calculated electronic transitions are provided in Table 2 and Table 3. All complexes exhibit a very weak absorption band around 400 nm and an intense one between 315 and 345 nm. As it can be seen in scheme 1, complex 2 derives from complex 1 replacing one pyrazolyl ring by a difluorophenyl one, and complex 3 is obtained by substituting the remaining pyrazolyl ring of complex 2 by a second difluorophenyl one. The latter ring being more conjugated, one expects that its contribution to the frontier MOs will be higher than the pyrazolyl ring one, leading to smaller energy gaps between occupied and vacant MOs, thus likely to explain partly the observed red shifts. Indeed, for complex 2 the difluorophenyl contribution appears in HOMO, HOMO-3, LUMO and LUMO+2 whereas the pyrazolyl is involved mainly in LUMO+1 HOMO-2 and HOMO-3. For complex 3 that bears two difluorophenyl, this effect is more important, namely their contribution to the frontier MOs, thus explaining the higher red shift observed for this complex.

Absorance Wavelength (nm)

Ir-1

Ir-2

Ir-3

From Table 3, it is clear that for complexes 1 and 2 the lowest energy excitations correspond to HOMO → LUMO transitions. It corresponds to a Metal to Ligand Charge Transfer (MLCT). A similar trend is observed for other excitations despite that the HOMO-3, which is localized on the π orbitals of the pyridine ligand, becomes involved for transitions at higher energy. Indeed, it turns out that the highest energy excitations reported for complex 1 is mainly a HOMO-3 to LUMO+1 (82%) transition, whereas for complex 2 it is an admixture of two excitations with a weak involvement of this particular transition (27 %).

Luminescence properties

Experimentally, contrarily to complexes 2 and 3, complex 1 did not exhibit any luminescence signature in solution, but only when processed as a film [to be published].

Complexes 2 and 3 exhibit interesting and different luminescence properties (Figure 2). Indeed complex 2 shows a structured emission band whereas complex 3 possesses a single band. Such difference is a good challenge for state-of-the-art simulations tools. For the reliability of the VMS on phosphorescence spectra, especially on transition metal complexes, has seldom been investigated. [START_REF] Vazart | Validation of a computational protocol to simulate near IR phosphorescence spectra for Ru(II) and Ir(III) metal complexes[END_REF][START_REF] Latouche | TD-DFT Benchmark on Inorganic Pt(II) and Ir(III) Complexes[END_REF][START_REF] Vazart | Vibronic Coupling Investigation to Compute Phosphorescence Spectra of Pt(II) Complexes[END_REF] First, we compute the excited state (ES) geometry. As one can see in Figure 3, the GS and ES geometries of complex 2 are almost identical. On the contrary, the ES and GS geometries of complex 3 show sizeable differences, but they remain similar enough to reasonably allow the vibronic treatment to be performed on these grounds. Experimental spectra shown Figure 2, reveal that complexes 3 and 3b have their absorption and emission maxima redshifted with respect to complexes 2 and 2b. Furthermore, complexes with pimb ligand (2b and 3b) also exhibit a redshift in comparison to complexes with pimf ligand (2 and 3). Figure 4 shows that these trends are nicely reproduced in our simulated spectra. The band maxima of experiment and simulations are also in a good agreement despite a small underestimation (less than 50 nm) of the maxima. Concerning the band shapes, the agreement is noteworthy. In fact, if one inspects the spectra of complexes 2 and 2b, three maxima, one shoulder and a long tail are observed. This band structure is perfectly reproduced in our simulations. It turns out that the relative intensities are also well described in the simulations but the absolute intensities remain underestimated, especially for the second maxima.

Finally, a small red shift is also observed between the absorption bands of complexes 1, 2, 3 and 1b, 2b, 3b, respectively, reminding that the difference between their structures is the substitution of the electron withdrawing CF3 group by the t Bu donating one. Whereas the CF3 group induces a lowering of the LUMO, the t Bu leads to an increase of the HOMO energies, so that their effects are in the same direction regarding the reduction of the HOMO-LUMO energy gap. However, replacing one group by the other one leads to cancel the lowering effect induced by the first one. Considering the observed red shifts, it can be concluded that the effect of the donating group is slightly more important to reduce this gap than the effect of the electron withdrawing group. Indeed, in our case, the HOMO-LUMO gap is reduced by 0.1-0.2 eV when replacing CF3 by t Bu.

Finally, complexes 3 and 3b exhibit a structureless emission band centred around 550 nm. This sharp band is also nicely reproduced in the simulation. The emission spectra of complexes 2 and 2b exhibit several bands contrarily to complexes 3 and 3b. Vibration modes of the pzpyF2p ligand, which is involved in the lowest virtual MOs, appear to participate to the vibronic structure of the emission spectrum of complex 2 computed using the adiabatic shift approach (see computational details); these facts are likely to explain the structured phosphorescence spectrum of this complex. On the contrary, such an influence of ligand on the emission spectrum is not observed for complex 3. One of the tools to characterize the principal vibrational progressions and the normal modes involved in the electronic transition in the AS method that we used, is called the shift vector (Figures S7 and S8 for complexes 2 and 3, respectively). The shift vector corresponds to the gradient of the final state projected on the normal modes of the initial state. [START_REF] Vazart | Vibronic Coupling Investigation to Compute Phosphorescence Spectra of Pt(II) Complexes[END_REF] The shift vectors of complexes 2 and 3 are rather different. Indeed, it appears that complex 2 possesses more normal modes with a strong shift vector (Figure S7) than complex 3 (Figure S8), leading to a larger vibrational contribution to the electronic transition. This fact could explain the differences in the phosphorescence spectra between both complexes.

Conclusion

In this article we have provided explanations of the optical (absorption and emission) properties of six new iridium complexes using quantum chemistry computations. As recently stated by some authors, the computational protocol that we used to perform excited state investigations on Ir(III) complexes seems to be efficient, e. g. B3PW91/LANL2DZ+pol. [START_REF] Vazart | Validation of a computational protocol to simulate near IR phosphorescence spectra for Ru(II) and Ir(III) metal complexes[END_REF][START_REF] Latouche | TD-DFT Benchmark on Inorganic Pt(II) and Ir(III) Complexes[END_REF] Complexes 2 and 3 have shown a strong phosphorescence signature, which have been nicely reproduced and rationalized in our simulations. Indeed, the simulated phosphorescence spectra using the VMS approach allowed a direct vis-à-vis between experiment and simulations.

  R=CF 3 ; [Ir(pimf)(pzpy)] (1b) R= t Bu; [Ir(pimb)(pzpy)] R=CF 3 ; [Ir(pimf)(pzpyF 2 p)] (2b) R= t Bu; [Ir(pimb)(pzpyF 2 p)] Ir and augmented with polarization functions on C(d; exponent 0.587), N(d; 0.736), F(d; 1.577) Ir(f; 0.938).[63-66] Solvent effects (CH2Cl2) have been taken into account by the Polarizable Continuum Model (PCM).[67, 68] All the GS geometries have been optimized and checked to be true minima on the Potential Energy Surface (PES), i.e. the computed frequencies of their normal modes of vibration are all real. Grimme's corrections for dispersion with Becke-Johnson damping (GD3BJ) have also been included in the computations.

Figure 1 .

 1 Figure 1. Frontier orbitals diagram of complex 1.

Figure 2 .

 2 Figure 2. Simulated absorption (top) and Observed Absorption and Luminescence Spectra (bottom).

2 3 Figure 3 .

 233 Superimposed GS and ES geometries of complexes 2 (left) and 3 (right).

Figure 4 .

 4 Figure 4. Simulated Phosphorescence Spectra of Complexes 2, 2b, 3 and 3b.

Table 1 .

 1 Selected experimental and computed structural data of complex 1. In average the computed M-L bond lengths fit nicely the observed ones, even if a slight underestimation in the simulation is observed. The angles around the metal are also well reproduced in our calculations with a deviation of less than 1° in comparison to the X-ray data. This trend also matches what some of us have reported before, i. e.

	Bond lengths (Å)	Ir-C	Ir-N
		1.965(5)	2.046(3)
	X-ray	2.078(5)	2.052(4)
		2.056(4)	2.038(4)
		1.969	2.028
	DFT	2.039	2.047
		2.040	2.031
	Angles (°)	C-Ir-C	N-Ir-N	C-Ir-N
	X-ray	154.9(18) 155.6(15) 178.7(18)
	DFT	155.7	156.9	179.5

Table 2 .

 2 Experimental and calculated vertical excitations maxima.

	Cplx	λExp /nm (ε) a	λCalc/nm (f) b	λmax/nm
	1	316 (21.9) 406 (0.8)	317 (0.204) 320 0.033) 390 (0.003)	317 390
	1b	318 (21.7) 409 (0.9)	397 (0.002) 309 (0.146) 322(0.204)	318
	2	323 (21.6) 407 (0.9)	318 (0.079) 328 (0.130) 393 (0.010)	324 393
	2b	325 (23.5) 418 (1.7)	324 (0.072) 334 (0.111) 401 (0,007)	329 400
	3	338 (23.3) 431 (0.9)	325 (0.070) 327 (0.183) 399 (0.008)	326 399
	3b	345 (20.4) 433 (0.7)	332 (0.309) 333 (0.156) 407(0.005)	333 407
	a 10 -3 M -1 cm -1
	b Oscillator strengths

Table 3 .

 3 Band assignments of complexes 1 and 2.

			1
	λCalc (nm)	f	Transitions
	390	0.003	HOMO ⟶ LUMO (98%)
	347	0.033	HOMO ⟶ LUMO+1 (89%)
	320	0.033	HOMO-3 ⟶ LUMO (52%) HOMO-2 ⟶ LUMO+1 (39%)
	317	0.204	HOMO-2 ⟶ LUMO (72%)
	302	0.209	HOMO-2 ⟶ LUMO+1 (54%) HOMO-3 ⟶ LUMO (42%)
	280	0.239 HOMO-3 ⟶ LUMO+1 (82%)
			2
	393	0.010	HOMO → LUMO (95%)
	351	0.031	HOMO → LUMO+1 (86%) HOMO-2 → LUMO (10%)
	328	0.130	HOMO-2 → LUMO (74%)
	318	0.079	HOMO-3 → LUMO (50%) HOMO-2 → LUMO+1 (31%)
	305	0.230	HOMO-2 → LUMO+1 (56%) HOMO-3 → LUMO (36%)
	285	0.217	HOMO-1 → LUMO+3 (44%) HOMO-3 → LUMO+1 (27%)

Acknowledgements

Prof. Yun Chi (National Tsing Hua University, Taiwan), who communicated his experimental results prior to publication, and Prof. Vincenzo Barone (SNS Pisa, Italy), who made available the VMS package developed in his laboratory, are gratefully acknowledged. We also acknowledge the HPC resources of CINES and of IDRIS under the allocations 2015-[x2015080649] and 2016-[x2016080649] made by GENCI (Grand Equipement National de Calcul Intensif).

Electronic Supplementary Information

Ground state optimized geometries of all complexes.

Orbital diagrams of complexes 1b, 2, 2b, 3, 3b. Simulated electronic absorption spectra of complexes 1b, 2b and 3b. Shift vectors/normal modes of complexes 2 and 3.

Energies and 5d metal orbital weights of frontier MOs of complexes 1a, 1b -3a, 3b.


Olivier Jc

In vitro biopharmaceutical evaluation of ciprofloxacin/metal cation complexes for pulmonary administration

Keywords: FQ-cation interaction, pulmonary delivery, controlled permeability, ciprofloxacin, Calu-3 cells. Chemical compounds studied

Pulmonary delivery of fluoroquinolones (FQs) is an interesting approach to treat lung infections as it may lead to high local concentrations while minimizing systemic exposure.

However, FQs have a rapid diffusion through the lung epithelium giving the pulmonary route no advantage compared to the oral route. Interactions between FQs and metal cations form complexes which limit the diffusion through the epithelial barrier and would reduce the absorption of FQs and maintain high concentrations in the lung. The effects of this complexation depend on the FQ and the metal cations and optimum partners should be selected through in vitro experiments prior to aerosol drug formulation. In this study, CIP was chosen as a representative FQ and 5 cations (Ca 2+ , Mg 2+ , Zn 2+ , Al 3+ , Cu 2+ ) were selected to study the complexation and its effects on permeability, antimicrobial efficacy and cell toxicity. The results showed that the apparent association constants between CIP and cations ranked with the descending order: Cu 2+ >Al 3+ >Zn 2+ >Mg 2+ >Ca 2+ . When a target of 80% complexation was reached with the adequate concentrations of cations, the CIP permeability through the Calu-3 lung epithelial cells was decreased of 50%. Toxicity of the CIP on the Calu-3 cells, with an EC50 evaluated at 7 µM, was not significantly affected by the presence of the cations. The minimum inhibitory concentration of CIP for Pseudomonas aeruginosa was not affected or slightly increased in the range of cation concentrations tested, except for Mg 2+ . In conclusion, permeability was the main parameter that was affected by the metal cation complexation while cell toxicity and antimicrobial activity were not or slightly modified. Cu 2+ , with the highest apparent constant of association and with no effect on cell toxicity and antimicrobial activity of the CIP, appeared as a promising cation for the development of a controlled-permeability formulation of CIP for lung treatment.

Introduction

Pulmonary delivery of antibiotics is an interesting approach to treat lung infections as it may lead to high local concentrations with expected high efficiency while minimizing systemic exposure to reduce side effects. This is especially true for drugs that slowly diffuse through the lung epithelium such as colistin or tobramycin (Gontijo et al., 2014b;[START_REF] Marchand | Biopharmaceutical Characterization of Nebulized Antimicrobial Agents in Rats: 3. Tobramycin[END_REF]. As a matter of facts, the most common antibiotics used in nebulized therapy have also a low lung epithelial permeability, such as tobramycin, colistimethate or aztreonam [START_REF] Marchand | Aerosol therapy with colistin methanesulfonate: a biopharmaceutical issue illustrated in rats[END_REF][START_REF] Marchand | Biopharmaceutical Characterization of Nebulized Antimicrobial Agents in Rats: 3. Tobramycin[END_REF][START_REF] Marchand | Biopharmaceutical Characterization of Nebulized Antimicrobial Agents in Rats[END_REF]. On the contrary, fluoroquinolones (FQs) such as ciprofloxacin (CIP) have a rapid diffusion through the lung epithelium [START_REF] Brillault | Relative contributions of active mediated transport and passive diffusion of fluoroquinolones with various lipophilicities in a Calu-3 lung epithelial cell model[END_REF] and following nebulization FQ lung concentrations quickly equilibrate with the plasma concentrations, giving the pulmonary route of administration no advantages compared to the oral route (Gontijo et al., 2014a). However FQs, which are commonly used in patients to treat lung infections by oral administration [START_REF] Hurley | Fluoroquinolones in the treatment of bronchopulmonary disease in cystic fibrosis[END_REF], could benefit from an aerosolized form that would reduce their diffusion through the lung epithelium. Several formulations have been developed to achieve this goal, such as dry powder of CIP but results showed a rapid pulmonary absorption of CIP into the plasma [START_REF] Stass | Tolerability and pharmacokinetic properties of ciprofloxacin dry powder for inhalation in patients with cystic fibrosis: a phase I, randomized, dose-escalation study[END_REF]. Interactions between FQs and metal cations are well-known to decrease the oral absorption and bioavailability [START_REF] Marchbanks | Drug-drug interactions with fluoroquinolones[END_REF]. FQs form complexes of various stoichiometries with various metal cations [START_REF] Uivarosi | Metal complexes of quinolone antibiotics and their applications: an update[END_REF]. These complexes have a higher molecular weight with an often ionized molecular structure which limits the diffusion through the intestinal barrier. While this interaction is a disadvantage for the oral route, it may be of great interest for the pulmonary route since it would reduce the absorption of FQs and maintain high concentrations of FQs in the lung. Previous work has shown the feasibility of an inhalable calcium-based microparticle formulation of CIP for pulmonary administration [START_REF] Tewes | Ciprofloxacin-loaded inorganic-organic composite microparticles to treat bacterial lung infection[END_REF]. In this study calcium (Ca 2+ ) at a high Ca 2+ /CIP mass ratio of 200 decreased the permeability of CIP to 80% in an in vitro model of the pulmonary epithelium.

However, other metal cations and FQs could be used for an optimized controlledpermeability formulation. The optimum partners of FQs and metal cations should be selected through in vitro experiments prior to microparticle formulation, in order to maximize the decrease in FQ permeability, concomitant with a lowest toxicity (i.e. lowest amount of cations and FQ that would be administered to the lung) and high efficiency.

Considering the numerous available FQs (about 30 compounds) and also the various metal cations that can bind to FQs (Ca 2+ , Mn 2+ , Mg 2+ , Zn 2+ , Fe 2+ , Fe 3+ , Al 3+ , Cu 2+ , Ag + , Co 2+ , Ni 2+ , Bi 3+ , etc.), several hundreds of possibilities may be considered. It is then necessary to develop first in vitro assays to screen these combinations and predict their interest for the development of new formulations. In this goal, the first point to consider was the ability of FQs and ions to interact together and how it influences the FQ diffusion through the lung.

The second point was to verify if the presence of metal cations and their association with the FQ modified the antimicrobial efficacy and cell toxicity of the antibiotic.

In this study, CIP was chosen as a representative FQ and the 5 five following cations were used to study the complexation with CIP: Ca 2+ , Mg 2+ , Zn 2+ , Al 3+ and Cu 2+ . Assays were carried out in medium and conditions that mimic the biological characteristics of the lung: Interaction between FQs and cations was assayed in a physiological saline buffer, the permeability of CIP in the presence of cations was assayed using the Calu-3 cell line and the antimicrobial efficacy of CIP in the presence of cations was evaluated against Pseudomonas aeruginosa, a frequent opportunistic infectious agent in the lung. The main purpose of this study was to better understand the interaction between CIP and metal cations in the lung and to help defining the assays needed for a systematic screening of FQ/metal cation complexes for pulmonary delivery. MOPS, TRIS and HEPES were obtained from Sigma-Aldrich. HPLC-grade acetonitrile was purchased from VWR International (Fontenay sous Bois, France). Mueller Hinton II agar and Mueller Hinton II Broth (cation adjusted) were from Becton Dickinson (Le Pont-de-Claix, France). All other reagents were of analytical grade.

Materials & Methods

Chemicals

Apparent constant of association (K)

To study the interaction between FQs and metal cations in medium having ion composition and pH close to biological samples such as the epithelial lining fluid (ELF) of the lung alveoli, CIP was incubated in saline solution (NaCl and KCl) at pH = 7.4. To assess the possible interaction between CIP and buffers, HEPES, MOPS or TRIS buffer was added to a 30 µM CIP solution in water at different concentrations (0, 1, 2.5, 7.5 and 10 mM) and pH was adjusted to 7.4 with 1 M sodium hydroxide. One ml of each solution was placed in 24 well plates and fluorescence intensity emission spectrum of CIP was recorded at room temperature with a plate reader (λexc = 274 nm and λem ranging from 360 to 500 nm; VarioskanFlash, Thermo Scientific, Villebon sur Yvette, France). MOPS and Tris buffers shifted and lowered the spectrum respectively, HEPES buffer did not affect the CIP fluorescence from 360 to 500 nm with a concentration up to 10 mM (data not shown). Moreover, HEPES is generally considered a non-complexing buffer and is suitable for use in solutions with metal ions [START_REF] Ferreira | Un)suitability of the use of pH buffers in biological, biochemical and environmental studies and their interaction with metal ions -a review[END_REF]. This buffer was then chosen for all the following experiments.

Fluorescence emission spectrum of CIP in the presence of increasing concentrations of the different cations did not show a shift of the maximum emission wavelength. The set of 274 and 408 nm for the excitation and emission wavelengths was chosen for all the titration experiments. Fluorescence titration profiles were obtained by adding cation solutions with concentrations ranging from 500 to 10 5 µM for calcium and magnesium ions, from 15 to 500 µM for zinc ions and from 15 to 150 µM for copper and aluminum ions to a 3 µM CIP solution. Solutions contained 5.3 mM KCl and were maintained at constant pH 7.4 with 10 mM HEPES and adjusted with NaCl to a constant ionic strength (155 mM for Mg 2+ , Zn 2+ , Al 3+ , Cu 2+ and 1205 mM for Ca 2+ ). The final volume of each sample was 1 ml and fluorescence was recorded using the VarioskanFlash plate reader. Binding isotherm equations for 1:1 and 2:1 complexes were built to describe the data according to Hargove et al. [START_REF] Hargrove | Algorithms for the determination of binding constants and enantiomeric excess in complex host : guest equilibria using optical measurements[END_REF].

Equations and mathematical development can be found in the Appendix A. The experimental data were fitted with the two models (1:1 and 2:1) and the comparison was evaluated with the Akaike's information criteria (AIC).

Apparent permeability (Papp) of CIP in the presence of metal cations

Calu-3 cell culture

Calu-3 cells were purchased from the American Type Culture Collection (Manassas, VA, USA).

The cells were cultured in DMEM/Ham's F12 (1/1) supplemented with L-glutamine (2 mM) and 10% foetal calf serum (PAN-Biotech GmbH, Aidenbach, Germany) and incubated at 37°C under 90-95% of relative humidity and 5% v/v of CO 2 in air. The Calu-3 cells at passages 50-60 were seeded at a density of 15 x 10 4 cells/cm 2 onto 12-well plate Transwell inserts (Corning Transwell Clear PET membrane 0.4µm, Thermofischer Scientific). The cells were cultured under air-interface conditions for 15 days. The growth medium in the basolateral compartment (1.5 ml) was replaced by fresh medium every other day.

Transport experiments

Transport experiments were conducted in apical-to-basolateral directions as described elsewhere [START_REF] Brillault | Relative contributions of active mediated transport and passive diffusion of fluoroquinolones with various lipophilicities in a Calu-3 lung epithelial cell model[END_REF]. Briefly, on study day the Calu-3 monolayers were quickly rinsed with the transport medium (TM: NaCl 134 mM, KCl 5.3 mM, glucose 5.5 mM, CaCl 2 1.3 mM, MgCl 2 1 mM, buffered with 10 mM HEPES and adjusted to pH 7.4) and then incubated for 30 min in TM. This transport medium is a modified formula of the classical HBSS medium without bicarbonate or phosphate known to form complexes with the metal ions. Following the equilibration period, the TM in the donor compartment (apical side) was replaced by fresh TM containing 50 µM of CIP with 0, 5, 10, 50 or 100 mM Mg 2+ . After 60 min of incubation at 37°C, sample aliquots were taken from the acceptor compartment (basolateral side). Apparent permeability (Papp) was calculated using eqn (1) where Q is the amount of CIP in the acceptor compartment after a time Δt, S is the insert membrane surface (1.12 cm²), [CIPo] is the initial CIP concentration in the donor compartment.

(1) Papp versus Mg 2+ concentration data were analysed with the following equation (eqn 2).

(2)

Where Papp Min is the low plateau of Papp, [X] the Mg 2+ concentration, EC50 the Mg 2+ concentration necessary to get 50% of the maximum effect (100-Papp Min) and nH the Hill number. In a second experiment, Papp were determined after cells were incubated in TM with 50 µM of CIP and 40 mM of Ca 2+ , 5.5 mM of Mg 2+ , 1.5 mM of Zn 2+ , 0.1 mM of Al 3+ or 0.04 mM of Cu 2+ for a 60 min incubation period before sampling in the acceptor compartment.

Following the transport studies, routine controls of the monolayer integrity were performed using sodium fluorescein. Briefly, the monolayers were rinsed with TM, fresh TM was added in the basolateral side and a solution of sodium fluorescein in TM (10 µg/ml) was poured in the apical side. The inserts were incubated and samples were taken after 60 min from the acceptor compartment. A threshold P app value of 0.7 x 10 -6 cm.s -1 for fluorescein was retained for the tight junction integrity rejection parameter for all experiments. This corresponds to the transfer of less than 0.5% of the initial amount in the apical compartment [START_REF] Brillault | Relative contributions of active mediated transport and passive diffusion of fluoroquinolones with various lipophilicities in a Calu-3 lung epithelial cell model[END_REF].

CIP and sodium fluorescein assay

CIP was assayed using a HPLC method with fluorometric detection (λexc =280 nm; λem =460 nm) using a Jasco FP-920 fluorescence detector (Jasco France, Lisses, France). The stationary phase was an XTerra MS C18 column, 5 µm, 100 × 2.1 mm (Waters, Milford, MA). The mobile phase (flow rate: 0.25 ml/min using a Hitachi L-2130 pump, Hitachi High technologies Co., Berkshire, UK) consisted of a 20:80 (v:v) mixture of acetonitrile and water containing 0.1% formic acid and 0.2% heptane sulfonic acid. Samples, standards (7 levels with concentrations ranging from 1.56 to 50 ng/ml) and quality controls (3.12, 12.5 and 37.5 ng/ml) prepared in the same solvent were injected (75 µl using a Hitachi L-2200 autosampler) and eluted over a run time of 6.5 min. The precision and accuracy were less than 15% for the 3 quality control concentrations. Controls with various concentrations of CIP and cations were assayed to ensure that the presence of cations did not interfere with the analysis of CIP.

Fluorescein concentrations in TM were measured using the VarioskanFlash plate reader with the excitation and emission wavelengths set at 490 nm and 530 nm, respectively.

Cytotoxicity assay

Calu-3 cells were seeded in 96 well plates at the density of 5000 cells/well. Incubation medium (100 µl) was Gibco MEM (Thermo Fisher Scientific) supplemented with 5% (v/v) foetal calf serum. CIP and ions solutions were prepared at concentrations necessary to achieve 80 % of complex. Namely, 150 µM of CIP were mixed with 40.1 mM of Ca 2+ , 5.6 mM of Mg 2+ , 1.6 mM of Zn 2+ , 0.17 mM of Al 3+ or 0.125 mM of Cu 2+ . The cells were then incubated with a serial dilution of these solutions or the CIP alone with concentrations ranging from 0.3 to 150 µM and the plates were returned to the incubator. Control cells were incubated with ions alone with serial dilution from 100 to 0.05 mM for Ca 2+ and Mg 2+ and from 5 to 0.0025 mM for Zn 2+ , Al 3+ and Cu 2+ . Following a 24 h incubation time, the incubation medium was removed and replaced with HBSS medium and cell viability was evaluated with a MTS assay kit (CellTiter 96® AQueous One Solution Cell Proliferation Assay from Promega, Charbonnières-les-Bains, France) according to the manufacturer protocol. The linearity of the response was verified thanks to preliminary experiments. Data were analysed with the following equation (eqn 3).

(3) where [X] is the concentration of CIP or ions, Top and Bottom are plateaus in the units of the Y axis, EC50 is the concentration that gives half of the total effect (Top-Bottom) and nH is the Hill number.

MIC assay

The effect of cation (Mg 2+ , Ca 2+ , Al 3+ , Zn 2+ , Cu 2+ ) concentrations on the CIP antibacterial activity was assessed by measuring the apparent CIP minimum inhibitory concentration (MIC) against Pseudomonas aeruginosa PAO1 (CIP 104116, Institut Pasteur, Paris, France).

Bacteria were stored at -80°C. One day before the experiment, they were grown on Mueller-Hinton II agar for 24 h at 37°C. Prior to MIC test, the strains were grown to logarithmic phase in fresh Mueller-Hinton broth II (MHB) for 2-3 hours and then adjusted to 0.5 McFarland standards. The MIC test was performed using the broth microdilution method: The adjusted cultures were diluted 100-times in MHB containing cations, CIP or both and 100 µl of these bacterial suspensions were seeded in 96 well plates. CIP concentrations were 8, 4, 2, 1, 0.5, 0.25, 0.125, 0.063, 0.031, 0 µg/ml. Mg 2+ concentrations were 20, 10, 5, 2, 1, 0.5, 0 mM. Ca 2+ concentrations were 100, 50, 20, 10, 5, 2, 1, 0.5, 0 mM. Zn 2+ concentrations were 1, 0.5, 0.1, 0.05, 0.02, 0.01, 0 mM. Al 3+ and Cu 2+ concentrations were 0.1, 0.05, 0.02, 0.01, 0.005, 0 mM. The growth of bacterial cultures at 37°C was determined after 18 hours by monitoring the optical density of the culture at 600 nm using the VarioskanFlash plate reader. Controls without bacteria were made to check the absence of contamination of MHB and to evaluate the effect of the cations on the absorbance reading at 600 nm. Controls without CIP were made to assess the effect of the cations on bacterial growth.

Statististical analysis

Data analysis and modeling were performed using GraphPad Prism version 5.02 for Windows (GraphPad Software, San Diego California USA, www.graphpad.com).

Results

Apparent constants of association

Titration curves of CIP with Mg 2+ , Ca 2+ , Zn 2+ , Al 3+ and Cu 2+ ions were made in HEPES buffered saline solutions (Figure 1). Increasing the concentration of Ca 2+ , Mg 2+ and Zn 2+ resulted in an increase in the total fluorescence, while with Al 3+ and Cu 2+ the total fluorescence was quenched. The equation corresponding to a 1:1 complex model fitted the data well for all the ions with a satisfactory accuracy for the estimated apparent constant of association (Table 1). On the other hand, the equation from the 2:1 complex model resulted in a very broad estimation of the parameters and higher AIC values (data not shown). This suggested a 1:1 (CIP:metal cation) complex stoichiometry. The estimated apparent association constants ranked with the descending order: Cu 2+ >Al 3+ >Zn 2+ >Mg 2+ >Ca 2+ , with almost a 9000 fold ratio between the minimum and maximum values (Table 1).

Influence of complexation on Calu-3 cell layer permeability

In a preliminary experiment, Mg 2+ was chosen to test the influence of the ion concentration on the apical to basolateral permeability of CIP through the Calu-3 cell model. In the control conditions where no magnesium was added to the transport medium, the Papp was 0.34 ± 0.02 x 10 -6 cm/s. The results on figure 2A showed a decrease in the CIP Papp dependent on the concentration of Mg 2+ . As estimated by the modeling, 6.7 mM of added magnesium reduced the Papp to 50% of the control and a plateau was reached at 11.5 % of the control Papp (0.04 x 10 -6 cm/s). According to the mass balance equations from 1:1 model (Appendix A) and to the apparent constant of association determined in table 1, the percentage of complexation of CIP by Mg 2+ was calculated and plotted against the Papp (Figure 2B). These data were modeled with eqn 2 and showed that it is necessary to form 86% of complexation to reduce the Papp of 50%. Since the complexation apparently correlated with the decrease in permeability, the transport of CIP was assayed at concentrations of metal cations necessary to reach the same level of complexation. As seen with the Mg 2+ , a high level of complexation is needed to induce a significant decrease in permeability, but high concentrations of ions, as for Ca 2+ would lead to hypertonic and deleterious conditions for the cells. For these reasons, a target of 80% complexation was chosen for the next experiment and theoretical ion concentrations were calculated for Ca 2+ , Mg 2+ , Zn 2+ , Cu 2+ and Al 3+ . Thus the cells were incubated in the presence of 50 µM of CIP and 40 mM of Ca 2+ , 5.5 mM of Mg 2+ , 1.5 mM of Zn 2+ , 0.1 mM of Al 3+ or 0.04 mM of Cu 2+ . Results confirmed that such cation concentrations leaded to a decrease in CIP permeability close to 50% (Figure 3).

Cytotoxicity assay

As shown in figure 4A and table 2, ions may be classified into two groups according to their cytotoxicity: the first group (low toxicity) includes Mg 2+ and Ca 2+ with an estimated EC50 at 36 x10 3 and 131 x10 3 µM, respectively; the second group (higher toxicity) includes Zn 2+ , Al 3+ and Cu 2+ with EC50 close to 1 x10 3 µM. Cytotoxicity of the CIP was evaluated in the presence of cations. The highest CIP concentration was 150 µM and ion concentrations were chosen to reach 80 % complexation. For Cu 2+ , Mg 2+ , Al 3+ and Ca 2+ , the concentrations were several times lower than their respective EC50 and for Zn 2+ equal to its EC50 (Table 2). Thus, the presence of ions at concentrations forming 80% complexes with CIP should not increase the cell toxicity of the CIP. As shown in figure 4B and table 2, the EC50 of the CIP over the Calu-3, which was evaluated to be 7 µM, was not apparently affected by the presence of these ions.

MIC assay

The influence of the cations was also tested on the antibacterial effect of CIP against P. aeruginosa. In the presence of the ions alone at all concentrations tested, the bacterial growth was similar to the control (data not shown). The MIC of CIP was 0.25 µg/ml. In the presence of Ca 2+ or Mg 2+ the MIC of CIP was increased from an ion concentration of 5 mM (33% of complexation) and 2 mM (50% of complexation) onwards, respectively (Figure 5A).

In the presence of Zn 2+ , the MIC was unchanged up to a concentration of 500 µM (50% of complexation) where it decreased of one level. The MIC remained unchanged for Al 3+ and Cu 2+ , except at 50 µM for copper (98% of complexation) (Figure 5B).

Discussion

Interactions between FQs and metal cations have been widely studied and it has been shown that the presence of metal cations affects both solubility and membrane permeability of FQs [START_REF] Stojkovic | Biopharmaceutical characterisation of ciprofloxacin-metallic ion interactions: comparative study into the effect of aluminium, calcium, zinc and iron on drug solubility and dissolution[END_REF][START_REF] Zakelj | Influence of metal cations on the solubility of fluoroquinolones[END_REF]. The consequence for the oral route is a decrease in their bioavailability. However for the pulmonary route, low permeability with high solubility could be of great advantage for antibacterial lung treatment since it would increase the drug residence time in the lung and lower the systemic side effects.

Antimicrobial efficacy is also sometimes affected in a positive or negative way [START_REF] Uivarosi | Metal complexes of quinolone antibiotics and their applications: an update[END_REF]. The mechanisms underlying these effects are not clearly understood and may involve FQs electric charge, molecular weight, lipophilicity, membrane permeability and/or binding with their bacterial enzymatic target. These modifications of the bioavailability or efficacy are not predictable and needs to be evaluated. In this work in vitro assays have been developed to study the interaction between CIP and Mg 2+ , Ca 2+ , Zn 2+ , Al 3+ , Cu 2+ .

Apparent constants of stability between metal cations and CIP have been evaluated in biological conditions. Since the ionic composition of the ELF is not known, a simple saline buffer (pH 7.4) containing extra-cellular concentrations of sodium, potassium and chloride was chosen. In this medium the apparent association constants K ranked as Cu 2+ >Al 3+ >Zn 2+ >Mg 2+ >Ca 2+ (Table 1). These results are in accordance with previous works with an equivalent ranking where the highest interactions were obtained with Al 3+ and Cu 2+ [START_REF] Ma | Mechanistic investigation of the reduction in antimicrobial activity of ciprofloxacin by metal cations[END_REF][START_REF] Seedher | Effect of metal ions on some pharmacologically relevant interactions involving fluoroquinolone antibiotics[END_REF]. Interestingly, for Ca 2+ , Mg 2+ and Zn 2+ the interactions increased the fluorescence intensity of the solutions while for Cu 2+ and Al 3+ the interactions resulted in a strong decrease of the fluorescence. Similar results had been obtained previously, where Cu 2+ strongly decreased the CIP fluorescence while Mg 2+ increased it [START_REF] Drevensek | Influence of copper(II) and magnesium(II) ions on the ciprofloxacin binding to DNA[END_REF]. This may be due to different sites of interaction on the CIP molecule, which has two main sites of metal chelate formation: one on the carbonyl and carboxyl groups and the second on the piperazin group [START_REF] Uivarosi | Metal complexes of quinolone antibiotics and their applications: an update[END_REF]. Quinolone-metal cation chelates may be synthetized as 1:1, 2:1 or 3:1 (FQ:metal cation) complexes depending on the cation, pH and the synthesis process. Here, the titration of CIP in biological conditions showed a spontaneous interaction with metal cations as 1:1 complexes as shown by the modeling of the data (Figure 1). To evaluate if these interactions could affect CIP permeability across the epithelial cells of the lung, CIP apparent permeability was assessed with the Calu-3 cell model in the presence of the different cations (Figure 2 and3). It should be noted that Mg 2+ and Ca 2+ concentrations of about 1 mM are needed for the cell layer integrity since the intercellular junctions that seals the cells together need these two cations to be effective. Thus the transport experiments were made in conditions where Ca 2+ and Mg 2+ were already present and would be responsible for 11% and 41% complexation of CIP, respectively. Since the concentration of Mg 2+ in plasma is close to 1 mM, this also would suggest that in biological fluids CIP is in part present as a Mg 2+ complex (Jahnen-Dechent and Ketteler, 2012). This might be also the case in the ELF of the alveolar space. For the same reason, in the bacteria cytoplasm where the concentration of free Mg 2+ is about 1-2 mM [START_REF] Alatossava | Manipulation of intracellular magnesium content in polymyxin B nonapeptide-sensitized Escherichia coli by ionophore A23187[END_REF], CIP is expected to be present inside the cell mostly as a CIP:Mg 2+ complex. Nevertheless the results showed a strong correlation between metal cation concentration and decrease in CIP apparent permeability through the cells. With Mg 2+ , a maximum decrease in permeability of about 90% was observed in conditions were the CIP is almost completely complexed. It is not known whether the 10% remaining apparent flux of CIP is due to the diffusion of the CIP:Mg 2+ complex or of the free CIP. The permeability experiments with the other cations showed that the apparent association constant is useful to predict the effect of the interaction over the cell permeability. The complexation of 80 % of the CIP affected the apparent CIP permeability with the same extent, whatever the nature of the metal cations. This result suggests that only the electric charges brought by the metal cations are responsible for the decrease in permeability. Indeed, in the case of a 1:1 CIP:metal cation interaction, a bicationic complex CIP + -M + appears, while CIP is an overall uncharged zwitterionic molecule at pH 7. It is also unlikely that the extra molecular weight brought by the cations would influence the CIP diffusion since they represent only 7 to 19% of the CIP MW. The apparent association constants varied from 100 to 900000 M -1 for Ca 2+ and Cu 2+ respectively (Table 1). This difference has huge consequences on the amount of cations necessary for the complexation of the CIP. For instance, if a pharmaceutical pulmonary drug formulation is designed to deliver in the ELF 1 µg/ml (3 µM) of CIP, which is in the range of MIC for the majority of P. aeruginosa from environmental sites and patients [START_REF] Macdonald | Early Pseudomonas aeruginosa infection in individuals with cystic fibrosis: is susceptibility testing justified?[END_REF], the ion concentration in the ELF needed to reach 80% of complexation would be 1600 µg/ml for Ca 2+ and only 0.4 µg/ml for Cu 2+ . Metal cations are known to be potentially toxic to the cells mainly through reactive oxygen species generation and then increased intra-cellular oxidative stress [START_REF] Stohs | Oxidative mechanisms in the toxicity of metal ions[END_REF]. Cytotoxicity studies showed that for cations with the highest association constant with CIP (Cu 2+ , Al 3+ and Zn 2+ ), the relative cell toxicity was about 100 times higher than for Mg 2+ and Ca 2+ (Figure 4 and Table 2). However, in the hypothesis of a pulmonary drug formulation that could deliver in the lining fluid of the alveoli a CIP concentration 50 times higher than the MIC for P. Aeruginosa (i.e. 150 µM), the corresponding concentration of cations necessary to achieve complexation of most of the CIP is several times lower than the EC50 of the cations for the cell toxicity. Thus, the higher toxicity of Cu 2+ , Al 3+ or Zn 2+ may be counterbalanced by the lower concentration needed for complexation compared to that of Ca 2+ and Mg 2+ . Several articles have reported that FQ:metal cation complexes had a limited or no effect on the antibacterial activity. For instance, complexes of CIP with Zn 2+ or Cu 2+ have been shown to have no influence on the MIC against S. aureus, P. aeruginosa or K. pneumoniae (López-Gresa et al., 2002) while complexes of levofloxacin with Mg 2+ slightly decreased the antibacterial activity with the same strains [START_REF] Drevenšek | X-Ray crystallographic, NMR and antimicrobial activity studies of magnesium complexes of fluoroquinolones -racemic ofloxacin and its S-form, levofloxacin[END_REF]. Here MIC assays have been done to evaluate this influence over P. aeruginosa (Figure 5). The growth medium for the bacteria already contains limited amounts of Ca 2+ and Mg 2+ (0.5 and 0.4 mM, respectively). However, due to the low concentrations and the weak constants of association of these two ions, their influence can be considered negligible. None or slight increase in MIC have been shown in the range of cation concentration tested, except for Mg 2+ at 10 mM where its presence greatly decreased the antimicrobial activity of CIP. This is in agreement with a previous study with sparfloxacin, ciprofloxacin, norfloxacin and pefloxacin where Mg 2+ was shown to decrease the antibacterial activity of the FQs in correlation with a lower uptake into the bacteria. These results suggested that Mg 2+ impaired the CIP uptake into the bacteria [START_REF] Lecomte | Effect of magnesium complexation by fluoroquinolones on their antibacterial properties[END_REF].

In conclusion, this work showed the influence of metal cations on permeability and antimicrobial activity of the CIP in the goal of pulmonary administration. Permeability was the main parameter that was affected by the metal cation complexation while cell toxicity or antimicrobial activity were not or slightly modified, as shown by the in vitro experiments.

While Al 3+ is suspected of brain toxicity, Cu 2+ seems to be an interesting cation for the development of a controlled-permeability formulation of CIP for lung treatment and further studies will evaluate the pharmacokinetics of CIP after lung administration of CIP:Cu 2+ loaded microparticles. More generally, in the goal of selecting the best FQ:metal cation couple for lung delivery formulation, the association constant between FQ and metal cation should be estimated first since this parameter is of great influence on permeability. Lipophilicity of the FQ was not addressed in this study but it should also be taken into account because the effect of complexation over permeability could have a major effect for the most lipophilic drugs such as moxifloxacin, grepafloxacin or pefloxacin. Toxicity and antimicrobial activity should be then investigated with the most interesting couples. Further studies will focus on the effects of metal cation interactions with FQs of different lipophilicities and on in vivo pharmacokinetic evaluations of novel FQ-metal cation formulations. 2. Cell toxicity EC50 of cations alone or CIP:cations mix in 80% complexation conditions over a 24 h incubation period. Values are given with their 95% confidence interval. was evaluated in the presence of increasing concentrations of Mg 2+ (A). Permeability was also plotted against the % of complexation calculated with the constant of association between CIP and Mg 2+ (B).

Results were expressed as a the percentage of the CIP Papp (0.34 ± 0.02 x 10 -6 cm/s ) determined with no Mg 2+ added to the transport medium (means ± S.E.M., n=3). (8) For 2:1 complex (CIP2:I) between ciprofloxacin (CIP) and a metal ion (I), the equilibriums, binding constants K1 and K2 and mass balance equations are expressed in eqn ( 9)-( 14). For eqn ( 14), the assumption that the initial concentration of ions ([I]t) is much higher than the initial concentration of CIP ([CIP]t) leads to a simplified equation. Experimentally, ion concentrations were always at least 5 times higher than CIP. Rearranging eqn ( 11) and ( 12) with eqn ( 13) and ( 14) yields to the quadratic equation ( 15) from which the eqn ( 16) is a solution. gives the final 2:1 binding isotherm (eqn 18) together with eqn ( 16).

(18)

Figure 1 .

 1 Figure 1. Titration curve of the total fluorescence against the molar concentration of ions. 3µM of CIP were mixed with increasing concentrations of Mg 2+ , Ca 2+ , Zn 2+ (A), Al 3+ or Cu 2+ (B). Total fluorescence (Ft) has been recorded at λexc = 274 nm and λem = 408 nm. Data are expressed as means ± range (n=2-3) and were fitted with the 1:1 complex model.

Figure 2 .

 2 Figure 2. Influence of added Mg2+ concentration and Mg-complexation on the apparent permeability for CIP. The apical-to-basolateral permeability of the Calu-3 cell layer for CIP (50 µM) was evaluated in the presence of increasing concentrations of Mg 2+ (A). Permeability was also plotted against the % of complexation calculated with the constant of association between CIP and Mg 2+ (B). Results were expressed as a the percentage of the CIP Papp (0.34 ± 0.02 x 10 -6 cm/s ) determined with no Mg 2+ added to the transport medium (means ± S.E.M., n=3).

Figure 4 .

 4 Figure 4. Toxicity of CIP, ions or CIP:ions complexes on Calu-3 cells. Cells were incubated for 24 h with different concentrations of cations (A) and different concentrations of CIP in the presence of cations (B). Cytotoxicity was evaluated with MTS test kit. 100% correspond to the control condition where cells were cultured for 24 h without CIP and/or cations. Data are expressed as mean ± S.E.M. (n=3).

  Figure 5. CIP apparent MIC against P. aeruginosa in Mueller-Hinton broth II in the presence of increasing concentrations of Ca 2+ , Mg 2+ (A), Zn 2+ , Al 3+ or Cu 2+ (B). MICs represent non-continuous data and are accurate to only plus or minus one two-fold dilution.

CIP

  (Ft) is the sum of the CIP, CIP:I and CIP2:I complex fluorescences (FCIP, FCIP:I and FCIP2:I), considering that the ions are not fluorescent:(17) where δCIP, δCIP:I and δCIP2:I are the proportionality coefficients between concentration and fluorescence for the CIP and the complexes. Rearranging eqn (17) with eqn (11) and (12)

  Sodium fluorescein, CIP, CaCl 2 , 2H 2 O; MgCl 2 , 4.5H 2 O; ZnSO 4 , 7H 2 O; CuSO 4 , 5H 2 O; Al(OH) 3 ;

Table 1 .

 1 Apparent association constant between CIP and ions (with the 95% confidence interval) in saline solution at pH 7.4.

	Apparent association constant K (M -1 )
	Ca 2+	1 x 10 2	[13-188]
	Mg 2+	7.2 x 10 2 [176-1272]
	Zn 2+	27 x 10 2 [1792-3614]
	Al 3+	880 x 10 2 [56540-119406]
	Cu 2+	9069 x 10 2 [849417-964359]
			Calu-3 cell toxicity EC50 (µM)
				CIP	7 [5-11]
	Ca 2+	36 x 10 3 [22-61 x 10 3 ]	CIP:Ca 2+	5 [4-6]
	Mg 2+	131 x 10 3 [111-152 x 10 3 ]	CIP:Mg 2+	11 [8-14]
	Zn 2+	0.9 x 10 3 [0.7-1.1 x 10 3 ]	CIP:Zn 2+	3 [3-4]
	Al 3+	1.0 x 10 3 [0.7-1.4 x 10 3 ]	CIP:Al 3+	7 [5-9]
	Cu 2+	1.1 x 10 3 [0.7-1.5 x 10 3 ]	CIP:Cu 2+	14 [12-16]
	Table

Appendix A.

For 1:1 complex (CIP:I) between ciprofloxacin (CIP) and a metal ion (I), the equilibrium, apparent binding constant K and mass balance equations are expressed in eqn ( 1 3) and ( 4) yields to the quadratic equation ( 5) from which the eqn ( 6) is a solution.

(

The observed fluorescence (Ft) is the sum of the CIP and CIP:I complex fluorescences (FCIP and FCIP:I), considering the ions are not fluorescent:

where δCIP and δCIP:I are the proportionality coefficients between concentration and fluorescence for the CIP and the complex respectively. Rearranging eqn (7) with eqn (3) and into eqn (6) gives the final 1:1 binding isotherm (eqn 8).