Fanette Chassagne
email: fanette.chassagne@emse.fr

Jérôme Molimard

Reynald Convert

Pascal Giraux

Pierre Badel

Numerical model reduction for the prediction of interface pressure applied by compression bandages on the lower leg

Keywords: Finite element simulation, model reduction, compression bandages, interface pressure

Objective: To develop a new method for the prediction of interface pressure applied by medical compression bandages. Methods: A finite element simulation of bandage application was designed, based on patient-specific leg geometries. For personalized interface pressure prediction, a model reduction approach was proposed, which included the parametrization of the leg geometry. Pressure values computed with this reduced model were then confronted to experimental pressure values. Results: The most influencing parameters were found to be the bandage tension, the skin-to-bandage friction coefficient and the leg morphology. Thanks to the model reduction approach, it was possible to compute interface pressure as a linear combination of these parameters. The pressures computed with this reduced model were in agreement with experimental pressure values measured on 66 patients' legs. Conclusion: This methodology helps to predict patient-specific interface pressure applied by compression bandages within a few minutes whereas it would take a few days for the numerical simulation. The results of this method show less bias than Laplace's Law, which is for now the only other method for interface pressure computation.

I. INTRODUCTION

Compression bandages consist in stretched fabrics wrapped around the lower limb. This therapy, whose efficacy is admitted [START_REF] Amsler | In search of optimal compression therapy for venous leg ulcers: A meta-analysis of studies comparing divers bandages with specifically designed stockings[END_REF], is usually used in the treatment of venous or lymphatic pathologies. The stretched fabric applies a pressure onto the skin, called interface pressure, which is then transmitted to the vessels through soft tissues (mainly adipose and muscle tissues) [START_REF] Partsch | Calf compression pressure required to achieve venous closure from supine to standing positions[END_REF]. The target interface pressure, which is a key aspect of the treatment [START_REF] Partsch | Compression for the management of venous leg ulcers: which material do we have?[END_REF], may vary with the pathology to be treated. Indeed, the pressure required for severe pathologies such as venous leg ulcers may be over 40 mmHg [START_REF] Blair | Sustained compression and healing of chronic venous ulcers[END_REF] whereas other pathologies would require lower interface pressures [START_REF] Vicaretti | Compression therapy for venous disease[END_REF]. More than the success of the treatment, this target pressure can also impact the treatment observance [START_REF] Milic | The influence of different sub-bandage pressure values on venous leg ulcers healing when treated with compression therapy[END_REF], hence an important need to control it. Interface pressure generated by compression bandages results from complex phenomena [START_REF] Clark | Compression bandages : principles and definition[END_REF] [START_REF] Melhuish | The physics of sub-bandage pressure measurement[END_REF] which remain poorly understood [START_REF] Partsch | Evidence based compression therapy[END_REF]. On the one hand, this pressure is impacted by the fabric material: its mechanical properties (stiffness characterizing the tension needed to stretch the bandage), its stretch once applied on the leg, the application technique (spiral pattern, figure-ofeight, ...) and the interaction between the bandage layers (i.e. the frictional properties of the fabric) [START_REF] Ghosh | Pressure mapping and performance of the compression bandage/garment for venous leg ulcer treatment[END_REF]. On the other hand, the pressure varies with the lower leg morphology and its mechanical properties, both dependent on body position. Eventually, Also once applied on the leg, the bandage interacts with the skin through friction phenomena. Finally, interface pressure tends to vary over time because of the viscoelastic behavior of both bandage fabric materials [START_REF] Kumar | Effect of material and structure of compression bandage on interface pressure variation over time[END_REF] and leg soft tissues [START_REF] Gefen | Viscoelastic properties of ovine adipose tissue covering the gluteus muscles[END_REF]. Among the large diversity of commercially available bandages [START_REF] Partsch | Compression for the management of venous leg ulcers: which material do we have?[END_REF], practitioners have to select the one best suited to the patient's morphology and pathology. However, for now, the only method to compute interface pressure is Laplace's law, which states that interface pressure P is directly proportional to the bandage tension T [N/mm] and the number of layers n but inversely proportional to the local radius of curvature r C :

P = n T r C , T > 0 , r C > 0 (1)
Though it was adapted to compression bandage therapy [START_REF] Khaburi | Effect of bandage thickness on interface pressure applied by compression bandages[END_REF] [START_REF] Thomas | The use of the Laplace equation in the calculation of subbandage pressure[END_REF], the relevance of the use of this law was called into question [START_REF] Schuren | The efficacy of Laplace's equation in calculating bandage pressure in venous leg ulcers[END_REF]. First, the measure of interface pressure applied on 30 healthy subjects' legs by two bandages with similar fabric structure but different tension showed that pressure was not directly proportional to bandage tension T [START_REF] Chassagne | Experimental Investigation of Pressure Applied on the Lower Leg by Elastic Compression Bandage[END_REF]. Moreover, the use of this Law often considers a cylindrical approximation of the leg geometry (considering only the leg circumference) and an homogeneous bandage tension [START_REF] Williams | How compression therapy works[END_REF]. Eventually, this law does not take into account all parameters impacting interface pressure, like soft tissue deformation induced by bandage application for instance [START_REF] Chassagne | Numerical Approach for the Assessment of Pressure Generated by Elastic Compression Bandage[END_REF]. Another mean to predict interface pressure is finite element simulation. This method was shown to be efficient for the computation of pressure applied by compression stockings, with 2D [START_REF] Rohan | Prediction of the Biomechanical Effects of Compression Therapy on Deep Veins Using Finite Element Modelling[END_REF] or 3D models [START_REF] Dai | Numerical simulation and prediction of skin pressure distribution applied by graduated compression stockings[END_REF], but was rarely implemented to compute pressure applied by compression bandages [START_REF] Chassagne | Numerical Approach for the Assessment of Pressure Generated by Elastic Compression Bandage[END_REF]. Therefore, a new method for fast interface pressure computation, based on a finite element modelling, is proposed in this study. A 3D simulation of bandage application, based on a personalized leg geometry, was designed. Then a model reduction technique was developed, including a novel global geometrical description of the lower leg, to predict personalized pressure values, which were then confronted to experimental pressure values.

II. MATERIALS

A. Leg geometries

Two sets of leg geometries were required for this study: a first one for the geometrical parametrization of the leg and a second one for the validation of the reduced model. The first set of leg geometries was composed of the external geometries of the right leg of 35 subjects (20 women -15 men; mean age: 43 [25 -58]; mean BMI: 24.1 [18.3 -33.5]) which took part in two previous studies [START_REF] Chassagne | Experimental Investigation of Pressure Applied on the Lower Leg by Elastic Compression Bandage[END_REF] [START_REF] Chassagne | Numerical Approach for the Assessment of Pressure Generated by Elastic Compression Bandage[END_REF]. These geometries were acquired thanks to a 3D optical scanner (Artec tm MHT 3D scanner, Artec tm Group), in standing position. The acquisition method was described in previous articles [START_REF] Chassagne | Experimental Investigation of Pressure Applied on the Lower Leg by Elastic Compression Bandage[END_REF] [START_REF] Chassagne | Numerical Approach for the Assessment of Pressure Generated by Elastic Compression Bandage[END_REF]. These 35 geometries were then used for the parametrization of the leg geometry, detailed in the Methods section (III-A). The second set of geometries was obtained from a more recent study [START_REF] Chassagne | Superimposition of elastic and non-elastic compression bandages[END_REF], in which both legs of 25 patients (15 women -10 men; mean age: 48 [19 -72]; BMI: 25.6 [19.0 -37.8]) were scanned in sitting and standing position, following a similar protocol. Among these scans, 38 represented the complete lower leg and thus were suitable for the validation of the reduced model detailed in the Methods section (III-D).

B. Interface pressure measurements

In addition to leg shape measurements, interface pressures applied by different bandages were measured in the three previously cited studies [START_REF] Chassagne | Experimental Investigation of Pressure Applied on the Lower Leg by Elastic Compression Bandage[END_REF] [18] [START_REF] Chassagne | Superimposition of elastic and non-elastic compression bandages[END_REF]. First, two different elastic bandages (Biflex R 16 and Biflex R 17, Thuasne) were applied on the leg of the 35 subjects, whose leg geometries were used for the parametrization. For the most recent study [START_REF] Chassagne | Superimposition of elastic and non-elastic compression bandages[END_REF], only the pressure applied on the patients' leg by the Biflex R 16 (Thuasne) was considered for the validation of the reduced model. For both groups, pressure values were measured at measurement point B1 (where the Achille's tendon turns into the gastroscnemius muscles [START_REF] Partsch | Measurement of lower leg compression in vivo: recommendations for the performance of measurements of interface pressure and stiffness: consensus statement[END_REF]) thanks to pressure sensor Picopress R (Microlab, Padua, Italia). The measurement protocol was described in previous articles [START_REF] Chassagne | Experimental Investigation of Pressure Applied on the Lower Leg by Elastic Compression Bandage[END_REF] [18] [START_REF] Chassagne | Superimposition of elastic and non-elastic compression bandages[END_REF]. These measurements were then compared with the results given by the reduced model in the Results section (IV-B).

III. METHODS

A. Geometrical parametrization of the lower leg

To compute interface pressure with Laplace's law, the leg is geometrically described by its local radius of curvature. For subsequent model reduction, another parametrization of the global leg geometry was needed in the present study. This parametrization should require as few parameters as possible for the leg description within an acceptable reconstruction error. This objective was reached thanks to the Proper Orthogonal Decomposition (POD) of the 35 leg geometries previously described in the Materials section (II-A). These geometries were obtained from the 3D optical scans of the right leg (in standing position) of 35 subjects (20 women -15 men) from previous studies . They These geometries were all set in the same reference frame, then normalized to their lengths and divided into 100 sections (in the transverse plane). Each section was then approximated with Fourier polynomials:

r(θ, z) = r 0 + n m=1 a m * cos(mθ) + n m=1 b m * sin(mθ) (2)
with n = 5 the degree of the polynomials and r(θ, z) the radius for a given angle θ and a given height z (cylindrical coordinates system). For n = 5, each section was described with 11 Fourier polynomials coefficients and the coordinates of the centre (x 0 , y 0 ), so 13 parameters. Thereby, each leg geometry {U i } i=1..N , previously normalized to its length, was described with 1300 parameters (100 sections described by 13 parameters). The same methodology as described by Gogu et al. [START_REF] Gogu | Bayesian Identification of Elastic Constants in Multi-Directional Laminate from Moiré Interferometry Displacement Fields[END_REF] was followed to build the POD basis. All computations were implemented with Matlab R (Mathworks, Natick, MA, USA). The N = 35 leg geometries could then be approximated as a linear combination of the vectors of the orthogonal basis:

Ũ i = K k=1 α i,k φ k = K k=1 < U i , φ k > φ k , K ≤ N (3)
with Ũ i the approximated leg geometry, φ k the vectors of the orthogonal POD basis, K the size of the basis and N the number of leg geometries U i . For each section of the N = 35 leg geometries, an evaluation of the reconstruction error was given by the distance between a point on the approximated section and one on the actual section for a given angle θ (i.e. r(θ, z) -r(θ, z) with r(θ, z) the actual radius and r(θ, z) the approximated radius). The median reconstruction error ( U i -Ũ i ) with regards to the basis dimension K is presented in Figure 1. With the first 4 POD vectors, 95% of the reconstruction errors of all measuring points of the 35 legs were found to be smaller than 2 mm (Figure 1 -A).

B. Numerical Simulation

A finite element simulation of bandage application was designed with Abaqus R . This simulation was based on a 3D lower leg geometry on which a 10-cm wide stretched bandage was wrapped in a spiral pattern. The output of the simulation was the interface pressure measured over a 50 mm diameter disk located at measurement point B1 on the medial side of the leg (corresponding the Picopress R sensor area (Microlab, Padua, Italia), used in the experimental measurements [START_REF] Chassagne | Experimental Investigation of Pressure Applied on the Lower Leg by Elastic Compression Bandage[END_REF] [21]) (Figure 5 -A).

Leg geometry and mechanical properties

The external leg geometry was given thanks to reconstructed from the geometrical parametrization previously described and was then converted to a 3D volume. The geometry of bone holes (tibia and fibula) was obtained from anatomical slices of the 'Visible Human Server' (Computer Science Department, Peripheral Systems Lab., Ecole Polytechnique Fédérale de Lausanne), then scaled to the 3D leg geometry and implanted in the leg volume with the software Solidworks R . A preliminary study showed that considering one large hole surrounding the two bones (red dotted line in Figure 2 -B) had negligible impact on interface pressure. Thus, as a simplification, the envelope of the two bones geometries was considered for the modelused, whose. The edge of this envelop was pinned to mimic a non-deformable material. After a mesh convergence study, the leg volume was meshed in Abaqus R with 4-node linear tetrahedron hybrid elements (about 450,000 elements depending on the leg geometry). Leg soft tissues were modelled with one single homogeneous material whose behaviour was described by a Neo-Hookean constitutive law:

U = c 10 ( Ī1 -3) + κ 2 (J el -1) 2 (4)
with Ī1 the first invariant of the isochoric deformation, J el

Bandage geometry and mechanical properties

Compression bandage was modelled as a 10-cm wide shell geometry, whose length was adapted to the leg length (Figure 2 -C). It was meshed with 4-node shell elements with reduced integration (about 40,000 elements, depending on the leg geometry). Compression bandages material was described as an orthotropic linear elastic material. All material parameters were linked by the following equations:

     11 22 γ 12      =      1 K1 -ν12 K1 0 1 K2 -ν12 K2 0 0 0 1 G           N 11 N 22 N 12      (5)      M 11 M 22 M 12      =      F 1 0 0 0 F 2 0 0 0 τ 12           κ 11 κ 22 κ 12      (6)
with 11 and 22 the strains in the in-plane longitudinal and The material parameter of interest in the study was the elastic modulus in the longitudinal direction K 1 . The other parameters K 2 , ν 12 , G, F 1 , F 2 and τ 12 were set to the values measured in a previous study [START_REF] Chassagne | Numerical Approach for the Assessment of Pressure Generated by Elastic Compression Bandage[END_REF]. The elastic modulus in the longitudinal direction K 1 was given by the tension of the bandage T at a 1.3 stretch (circle in Figure 3) (secant modulus, ensuring the correct tension value at the prescribed 1.3 stretch).

Simulation strategy

The edge of the bones hole was pinned. The bandage was tied to the leg close to the ankle, then stretched to a 1.3 stretch (following manufacturer's recommendations) and wrapped on the leg in a 50% overlapping spiral-pattern application technique (Figure 4). The kinematics of bandage application (i.e. wrapping the bandage around the leg) was computed with an in-house Matlab R code for each leg geometry. The aim of these kinematic boundary conditions was to wrap the bandage, in a 2-layer spiral pattern, with a stretch equal to 1.3 at the midline of the bandage (Figure 2 -C), as the operator would do in the experiments. The contact between the leg and the bandage but also the contact between the different bandage layers allowed no penetration and were modeled with the Coulomb's friction law. Depending on the size of the leg, computation time varied from 1 to 3 days on 12 CPUs. Within the aim toat later compareing the values from the simulation with the experimental pressure values, the output of the simulation was the mean pressure over an area corresponding to the sensor Picopress R located at measurement point B1 (Figure 5 -A). This area of interest was determined from the curvature of the posterior part of the leg (in blue in Figure 5). Starting from the top of the zone of interest (the top of the leg was not taken into account), in green in Figure 5, the height of measurement point B1 was the first point with a curvature derivative lower than (very close to 0) (in red in Figure 5). This methodology was used to determine the location of measurement point B1 for all legs.

Output of the simulation

C. Numerical model reduction

From this numerical simulation, a model reduction approach was used to assess the impact of different parameters on interface pressure. This approach helps to model a complex phenomenon, in this case interface pressure at measurement point B1, depending on a large number of parameters, with a very few repetitions of the simulation [START_REF] Tinsson | Plans d'expérience: constructions et analyses statistiques[END_REF]. The parameters possibly impacting interface pressure were:

• the leg geometry,

• the leg soft tissue mechanical properties (c 10 -(Equation 4)) • the bandage tension (T ) • the skin-to-bandage friction coefficient (µ skin-bandage )

• the bandage-to-bandage friction coefficient (µ bandage-bandage ). First, a study was performed on a mean leg geometry in order to evaluate the impact of the four remaining parameters on interface pressure (soft tissue mechanical properties, bandage tension and the two friction coefficients). The mean leg geometry was obtained by setting all the geometrical parameters to their mean value ᾱk (obtained from the 35 geometries used for the parametrization):

U mean leg = 35 k=1 ᾱk φ k (7)
The impact of the variation of the four parameters was evaluated within the ranges given in Table I. A preliminary Table II: Ranges of variation for the skin-to-bandage friction coefficient (µ skin-bandage ), the bandage tension (T ), the leg length (L) and the four geometrical parameters (α 1..4 )

numerical study was performed to evaluate the variation of interface pressure induced by a variation of skin-to-bandage friction coefficient within the range found in the literature [START_REF] Gerhardt | Skin-textile friction and skin elasticity in young and aged persons[END_REF] [27]. The lowest value was obtained from the literature (0.10) and the maximum one corresponded to complete adhesion (0.3) (higher values would not lead to lower sliding). A similar methodology was followed for the range of variation of leg soft tissue mechanical properties, going from 2 to 8 kPa (higher values led to no difference in interface pressure). Minimum and maximum bandage tensions were chosen with regards to the tension of bandages Biflex R 16 and Biflex R 17 (Figure 3) and the experimental stretches measured in a previous study [START_REF] Chassagne | Experimental Investigation of Pressure Applied on the Lower Leg by Elastic Compression Bandage[END_REF]. The bandage-to-bandage friction coefficient range of variation was given by previous experimental measurements [START_REF] Chassagne | Characterization of fabric-to-fabric friction: application to medical compression bandages[END_REF].

The evaluation of the impact of these four parameters, in the ranges of variation summarized in Table I, showed that two parameters, skin-to-bandage friction coefficient and bandage tension, were responsible for more than 93% of interface pressure variation. Consequently, the bandage-to-bandage friction coefficient and the leg soft tissues material parameter were removed from the problem definition and set to their mean values: µ bandage-bandage = 0.6 and c 10 = 5 kP a.

The second step consisted in the evaluation of the impact of skin-to-bandage friction coefficient, bandage tension and leg geometry on interface pressure. The leg geometry was given with 4 geometrical parameters (Equation 3) and the leg length L. The ranges of variation of the morphological parameters, presented in Table II, were obtained from the 35 leg geometries. From the ranges of variation defined in Table II, the parameters were coded between -1 and 1:

X * = 2 * X -X min X max -X min -1 (8)
with X * the value of X in the coded space, X min and X max the minimum and maximum value of the parameter X.

A fractional factorial design was built [START_REF] Tinsson | Plans d'expérience: constructions et analyses statistiques[END_REF] to select the different combinations of the 7 parameters of interest. Each combination was used to run one simulation and eventually compute the response surface of the model. Here, 9 simulations were run for this model reduction.

From the output of these 9 simulations, i.e. the interface pressure at measurement point B1 on the medial side of the leg, it was possible to compute this interface pressure P at measurement point B1 as a linear combination of skin-tobandage friction coefficient µ * bandage-bandage , bandage tension T * , leg length L * and 4 geometrical parameters α * 1..4 :

P = P + β µ µ * bandage-bandage + β T T * + β L L * +β 1 α * 1 + β 2 α * 2 + β 3 α * 3 + β 4 α * 4 (9)
with all parameters coded between -1 and 1 (Equation 8). The coefficients β were obtained from the model reduction approach.

D. Comparison between numerical pressure, pressure computed with Laplace's law and experimental pressure values

Experimental pressure measurements applied by two bandages (Biflex R 16 and Biflex R 17) were previously performed on the legs of 35 subjects, whose geometry was used for the geometrical parametrization [START_REF] Chassagne | Experimental Investigation of Pressure Applied on the Lower Leg by Elastic Compression Bandage[END_REF] [START_REF] Chassagne | Numerical Approach for the Assessment of Pressure Generated by Elastic Compression Bandage[END_REF]. Other pressure measurements applied by the Biflex R 16 were performed on both legs of 25 patients [START_REF] Chassagne | Superimposition of elastic and non-elastic compression bandages[END_REF],whose leg geometry was obtained with a 3D optical scanner (Artec tm MHT 3D scanner, Artec tm Group) in sitting and standing positions. As it was previously detailed in the Materials section (II), interface pressure measurements were performed on the legs of 35 healthy subjects and 25 patients. These measurements were coupled with leg shape measurements. Among the 3D scans of the 25 patients' legs in sitting and standing position, 38 represented the complete lower leg and thus were suitable for this study. Once normalized to their length, these 38 leg geometries were decomposed in the orthogonal basis {φ k } k=1..4 obtained from the geometrical parametrization. From the 38 sets of geometrical parameters seven were found to be out of the range of variation studied in the model reduction and were discarded. Eventually, 66 leg geometries and 101 experimental pressure values (two bandages for 35 healthy subjects' legs and one bandage for 31 patients' legs) were kept for the comparison. The pressure applied at measurement point B1 was computed thanks to the linear combination given by the reduced model (Equation 9). As no measurements were performed for the skin-to-bandage friction, this parameter was set to its mean value. In addition, interface pressure applied on the 66 leg 9)

geometries was computed thanks to Laplace's Law (Equation 1), following the same methodology described in a previous study [START_REF] Chassagne | Numerical Approach for the Assessment of Pressure Generated by Elastic Compression Bandage[END_REF]. For both computations, bandage tension was computed from the experimental stretch measurements:

T ension = (stretch -1) * bandage elastic modulus (K 1 ) (10) Interface pressure values computed with these two methods, reduced model and Laplace's Law, were confronted to experimental values. Note that a previous work showed that the presence of the pressure sensor induced little measurement error, which was previously evaluated thanks to a numerical approach providing a methodology to correct this error [START_REF] Chassagne | Numerical Approach for the Assessment of Pressure Generated by Elastic Compression Bandage[END_REF]. The same methodology was implemented here for the correction of experimental pressure values.

IV. RESULTS

A new simulation of bandage application was built, within the aim to wrap the bandage around the leg with a 1.3 stretch. The mean stretch measured at the midline of the bandage (Figure 2 -C) was equal to 1.282 ± 0.001, but this stretch was very variable over the bandage width: 1.411 ± 0.004 at the top edge of the bandage and 1.139 ± 0.002 at its bottom edge.

A. Model reduction

Thanks to the model reduction approach it was possible to compute interface pressure applied at measurement point B1 as a linear combination of seven parameters (Equation 8). The coefficients β of the linear combination are reported in Table III. The overall significance of the linear model obtained from the model reduction was tested with the Fischer test (p = 0.02). Moreover, in light of the very high coefficient of determination R 2 = 0.99, it can be considered that this seven parameter reduced model gave a relevant description of the variation of interface pressure. III) and Laplace's law (Equation 1), for 66 legs, as a function of the experimentally measured bandage stretch. For 35 of them, pressure values applied by two different bandages (Biflex R 16 and Biflex R 17) were measured at measurement point B1 [START_REF] Chassagne | Experimental Investigation of Pressure Applied on the Lower Leg by Elastic Compression Bandage[END_REF], whereas for the 31 remaining legs, only the pressure applied by the Biflex R 16 was measured [START_REF] Chassagne | Superimposition of elastic and non-elastic compression bandages[END_REF]. 101 pressure values, computed from the model reduction equation (Equation 9and Table III) and Laplace's law (Equation 1), are plotted as a function of the experimental pressure values in Figure 6.

Though the data from the model reduction were scattered, they were in agreement with the experimental data (slope = 1.04), with a mean error equal to 9.7 ± 5.0%. For Laplace's Law, the slope was further to 1 (slope = 0.87) and the mean error was equal to -11.6 ± 4.0%. Data from the model reduction were more scattered than the one given by Laplace's law because this model took into account more experimental parameters (seven) than Laplace's Law (two).

V. DISCUSSION

A new method, based on the reduction of a numerical simulation, was designed to compute interface pressure applied by compression bandages at measurement point B1. This method was based on a deformable 3D leg geometry described by 4 geometrical parameters and its length. Other influencing parameters were the bandage tension and the skin-to-bandage friction coefficient. The results obtained from this methodology were in agreement with previous experimental pressure measurements.

The simulation of bandage application was designed to apply the bandage in a spiral pattern with a 1.3 stretch. The stretch of the numerically applied bandage was found to be slightly lower (1.28). This could be explained by the little compression of the leg soft tissues induced by bandage application and the cross-section becoming rounder. Even though the stretch at the midline was close to the targeted value, it was found to be heterogeneous over the leg (Figure 4 and Figure 7). This stretch heterogeneity was the consequence of the "conical" shape of the leg (stretch is higher in the upper half of the bandage layer and lower in the lower half). Usually, leg geometry is locally described by its radius of curvature. This new global geometrical parametrization, based on 35 right leg geometries, resulted in very low reconstruction error with only 5 parameters (4 geometrical parameters and the leg length) and was suitable to geometrically describe other leg geometries (31 among the 38 available leg geometries). The model reduction approach showed that the last parameters α 4 had lower effect than the three other geometrical parameters α 1..3 (about 2% of the mean pressure) (Table III).

The impact of several parameters on interface pressure was evaluated thanks to this model reduction approach. First it was observed that the mechanical properties of soft tissues had not much influence on interface pressure, even though it was shown in a previous numerical study [START_REF] Chassagne | Numerical Approach for the Assessment of Pressure Generated by Elastic Compression Bandage[END_REF] that the deformability of the soft tissue was to be considered to understand pressure generation. Nonetheless, it was previously shown that soft tissue mechanical properties influence the transmission of interface pressure to the vessels [START_REF] Rohan | Prediction of the Biomechanical Effects of Compression Therapy on Deep Veins Using Finite Element Modelling[END_REF]. The second parameter with very low impact on interface pressure was bandage-to-bandage friction. The values of this friction coefficient, provided by experimental measurements [START_REF] Chassagne | Characterization of fabric-to-fabric friction: application to medical compression bandages[END_REF], was very high (from 0.5 to 0.7) and did not result in any sliding motion between the different layers, hence its very low impact on pressure. However, bandage layers are in interactions with each other, but also with the skin. Skin-to-bandage friction coefficient was found to be more influencing than bandage-to-bandage friction in the preliminary study on the mean leg geometry. The values were much lower than for the other frictional parameter. Thus, for the lowest value (0.10) the bandage tended to slide down over the leg (Figure 7), whereas for the highest value (0.3), the bandage did not. While sliding down, the stretch of the bandage decreased and so did interface pressure. Nonetheless, as expected considering Coulomb's friction law, it was observed that the impact of skin-to-bandage friction coefficient was influenced by the leg morphology and more especially by the slope of the leg shape. This is the reason why a friction coefficient equal to 0.1 did not lead to much sliding for some leg geometries and led to complete sliding of the bandage for others (Figure 7). This value was in the lowest range of skin-to-textile friction coefficient reported in the literature. The last parameter impacting interface pressure was, as expected, the tension, which in the study was a function of the bandage elastic modulus and the stretch (Equation 10). However, note that the reduced model is slightly more sensitive to the stretch than reality because the secant elastic modulus is higher than the tangent modulus (Figure 3).

In a second time, the pressure was computed for 66 legs and compared to experimental results. Though predicted pressure values were in agreement with experimental measured values, they sometimes showed large discrepancies. Four possible sources of error were identified. First, due to the non-cylindrical shape of the leg, wrapping the bandage in a spiral pattern resulted in high pressure areas (in red in Figure 4) induced by the overlapping of the bandage which is not perfectly equal to 2 layers all over the leg (being, sometimes, very locally one or three layers). Whether the sensor is located under such an overlapping zone or not will change the interface pressure. The source of variability was evaluated using the FE model, by moving the center of the area of interest on a 1 cm radius circle around its initial position and led to a mean absolute pressure variation of 1.27 ± 0.38 mmHg. The second source of error is the location of the sensor. In the simulation, it was determined from the curvature of the posterior part of the leg (Figure 5). However, experimentally, it is likely that this location slightly differs from the one numerically determined, which may lead to a small pressure variation, of the same order as that evaluated right above. Also, as it is not possible to patient-specifically characterize the skin-to-bandage friction coefficient, this parameter was set to its mean value. Thus all pressure values computed from the model reduction are given with a ± 2.70 mmHg uncertainty. The last source of error is body position. Indeed, the bandage is applied in supine position, but it was not possible to scan the leg in this position. So the leg geometries were either obtained in sitting or standing position. These geometries were neither the one on which the bandage was applied, nor the one corresponding to the measured stretch. Due to gravity, muscle groups fall down and bandage stretch may be increased and thus interface pressure may vary.

Limitations

This methodology was based on the lower leg geometrical parametrization. However, this parametrization was obtained from 35 legs of healthy subjects. Even though these subjects showed a wide range of morphologies, the parametrization should be enriched with more leg geometries, from patients with leg oedema for instance. For the numerical simulation, the kinematics of bandage application was based on the non-deformed shape of the leg and was not updated during the simulation (to take into account bandage sliding or leg deformation for example). An improvement of the simulation would be to update wrapping boundary conditions during the simulation, after each bandage turn for instance, as an operator does in reality. The leg geometry was obtained in different body position (sitting or standing) than the position in wich the bandage is applied on the leg (supine position). Therefore it seems crucial to be able to scan the leg geometry in supine position to eliminate the uncertainty about the leg geometry. Also, Modelling bandage material as an planar elastic material tended to increase the influence of stretch on interface pressure (secant elastic modulus considered (Figure 3)). Next step would be to consider the non-linear mechanical behaviour of fabric materials in the simulation but also to increase the complexity of the bandage fabric model (by replacing shell elements by solid elements for instance). Another important parameter was the skin-to-bandage friction coefficient. This study did not investigate the coupled effect of the leg geometry and this frictional parameter on interface pressure. Further mechanical studies would be needed for a better understanding of the effect of this frictional parameter. The output of the simulation was only the pressure value at measurement point B1. However, the complete pressure distribution was provided by the simulation and could be further investigated. Moreover, the experimental protocol may show some limitations. Bandage application is subject to large variabilities, either for the wrapping pattern (overlapping and angle) or the bandage stretch. Even though all bandages were applied by the same trained operator to prevent inter-operator variability, these sources of uncertainty may also explain the discrepancies between the experiments and the reduced model. Eventually, it seems crucial to be able to scan the leg geometry in the same position in which bandage is applied, to eliminate the uncertainty about the leg geometry. Finally, even if interface pressure was measured within a short time interval to prevent the effect of time, this study did not investigate the viscoelastic behaviour of both bandage materials and leg soft tissues and their impact on interface pressure..

VI. CONCLUSION

A new method to compute interface pressure applied by compression bandages at measurement point B1 was proposed. This methodology was based on the parametrization of the leg geometry and the numerical simulation of bandage application. In addition to the leg morphology, the bandage tension and the skin-to bandage friction coefficient impacted interface pressure. Thanks to this approach, it is possible to compute patient-specific pressure values in a few minutes when it would take a few days with numerical simulation. The pressure values computed for 66 legs were found to be in agreement experimental pressure values. This methodology could later be enriched to compute pressure applied by multi-layer bandages.

  ]the]orhogonal]basis](K) Median]error]with]95.]IC][mm] A B Size]of]the]orthogonal]basis](K) Median]error]with]95.]CI][mm]

Figure 1 :

 1 Figure 1: Median absolute error between the initial and the approximated leg geometry, as a function of the dimension of the orthogonal POD basis K (A) and illustration of the reconstruction error with regards to the size of the basis K (B)

Figure 2 :

 2 Figure 2: Design of the 3D model: first the leg external geometry is given by the geometrical parametrization (A) and converted to a 3D volume in which bones are implanted (B); eventually, a flat bandage is added to the model (C)

Figure 3 :

 3 Figure 3: Illustration of two secant elastic moduli from two tension-stretch curves

Figure 4 :

 4 Figure 4: Illustration of the simulation -bandage application on the leg and resulting interface pressure distribution (top: first turn, bottom: end of simulation)

3 Figure 5 :

 35 Figure 5: Location of the output of the simulation on the mean leg geometry, i.e. a 50-cm diameter area around measurement point B1 (A); Determination of the height of measurement point B1 from the curvature of the posterior part of the leg (B)

  Ranges of variation for the skin-to-bandage friction coefficient (µ skin-bandage ), the bandage-to-bandage friction coefficient (µ bandage-bandage ), the bandage tension (T ) and the soft tissue material parameter (c 10 )

Figure 6 :

 6 Figure 6: Pressure computed from the model reduction and Laplace's law as a function of the experimental pressure values

Figure 7 :

 7 Figure 7: Illustration of the influence of the skin-to-bandage friction coefficient on a very conical leg geometry

Table III :

 III Coefficients of the linear model β obtained from the model reduction approach (Equation

	Parameter (coded between -1	Coefficient	Value
	and 1)
	Mean pressure	P	32.73
	Skin-to-bandage friction	βµ	2.70
	coefficient µ * bandage-bandage
	Bandage tension T *	β T	11.54
	Lower leg length L *	β L	2.85
	1 st geometrical parameter α * 1	β 1	4.54
	2 nd geometrical parameter α * 2	β 2	3.92
	3 rd geometrical parameter α * 3	β 3	-1.74
	4 th geometrical parameter α * 4	β 4	-0.51


Ph.D David Monchaud
email: david.monchaud@cnrs.fr

QUADRUPLEX DETECTION IN HUMAN CELLS

I. Introduction.

"You will never be able to hit a target that you cannot see". [START_REF] Sharma | The Monk Who Sold His Ferrari: A Fable About Fulfilling Your Dreams & Reaching Your Destiny[END_REF] This wise advice suits perfectly the exploration of the world of the infinitely small, notably the word of nucleic acids. Nearly half a century of research was required to unveil the complicated processes the canonical DNA duplex is involved in. These heroic decades, which saw the rise of cross-cutting scientific disciplines (from molecular biology to chemical biology and epigenetics), have afforded invaluable insights into the many cellular processes in which the duplex participates. [START_REF] Klug | The discovery of the DNA double helix[END_REF][START_REF] Crick | On protein synthesis[END_REF] They have provided critical clues about the cellular mechanisms underlying the very notion of life, and-because targets were made visible-as many novel therapeutic opportunities.

However, scarcely had the duplex revealed (not all) its secrets when alternative nucleic acid structures appeared. They differ from the duplex in many ways, the most distinguishing feature being their strandness (from two to four strands), which leads to the folding of higherorder architectures such as triplexes, DNA junctions and quadruplexes. [START_REF] Mirkin | Discovery of alternative DNA structures: a heroic decade (1979-1989)[END_REF][START_REF] Bacolla | DNA structure matters[END_REF][START_REF] Bochman | DNA secondary structures: stability and function of G-quadruplex structures[END_REF] Understanding the dynamics of these new players was a novel, rather daunting challenge for the community of nucleic acids: how, where and when these structures fold in cells (if any)? From which sequences? With which stability? Etc. A new burst of questions that required a new portfolio of molecular tools aimed at characterizing furtive, certainly low-abundance structures in an environment (the nucleus) that was already difficult to characterize.

Efforts were thus invested to combine and use knowledge and know-how acquired during the study of duplex-DNA to assemble an array of molecular tools poised to address new and challenging issues. Among them, the detection of quadruplex in cells: do these four-stranded DNA structures exist in cells? Can they represent a novel class of therapeutically relevant targets? Etc. "You will never be able to hit a target that you cannot see". This advice primarily emphasizes the need for tools able to cast light on quadruplexes in cells. In the following sections will be demonstrated how the creativity of scientists has been instrumental in the design of exquisite molecular flashlights that have been developed and are currently used for understanding how, where and when quadruplexes fold and unfold in cells.

II. Four-stranded DNA structures and quadruplex ligands, a bit of history.

The structure of the double DNA helix was unraveled in 1953 by Watson, Crick, Wilkins and Franklin. [START_REF] Watson | Molecular structure of nucleic acids[END_REF][START_REF] Wilkins | Molecular structure of deoxypentose nucleic acids[END_REF][START_REF] Franklin | Molecular configuration in sodium thymonucleate[END_REF] The events that swirl around the elucidation of its molecular structure are among the most fascinating stories of modern science. [START_REF] Watson | The double helix[END_REF][START_REF] Maddox | Rosalind Franklin: The dark lady of DNA[END_REF] This discovery, which marked the start of modern genetics, drew on hard-won results acquired since the initial attempts by Miecher in 1871 to characterize the substance found in the nucleus, initially referred to as "nuclein" and now known as nucleic acids. [START_REF] Dahm | Friedrich Miescher and the discovery of DNA[END_REF] A part of these efforts was dedicated to the characterization of a given subclass of nucleic acid, the guanylic acid, initially isolated from bovine pancreas by Hammarsten in 1894. Levene (1909) 13,[START_REF] Levene | On guanylic acid[END_REF] and Bang (1910) [START_REF] Bang | Examination of the guanylic acid[END_REF] noticed the tendency of concentrated guanylic acid solutions to form hydrogels; the exact nature of the structural unit responsible for the gelation process, the self-assembly of four guanines in a G-quartet, [START_REF] Stefan | Applications of guanine quartets in nanotechnology and chemical biology[END_REF] was unveiled by Davies in 1962 by X-ray crystallography. [START_REF] Gellert | Helix formation by guanylic acid[END_REF] Inferred as early as in 1982, [START_REF] Lipps | Higher order DNA structure in macronuclear chromatin of the hypotrichous ciliate Oxytricha nova[END_REF] the formation of G-quartets in biologically relevant guanine (G)-rich sequences (immunoglobulin switch regions, telomeres) was demonstrated in vitro by Gilbert (1988) [START_REF] Sen | Formation of parallel four-stranded complexes by guanine-rich motifs in DNA and its implications for meiosis[END_REF] and Klug (1989) [START_REF] Sundquist | Telomeric DNA dimerizes by formation of guanine tetrads between hairpin loops[END_REF] via the study of sequences in which continuous guanine tracts assemble into G-quartets that selfstack to form higher-order G-quadruplex structures. Further structural support to this theory were soon provided in vitro by the first nuclear magnetic resonance (NMR, Feigon, [START_REF] Smith | Quadruplex structure of Oxytricha telomeric DNA oligonucleotides[END_REF] Patel [START_REF] Wang | Guanine residues in d(T2AG3) and d(T2G4) form parallel-stranded potassium cation stabilized G-quadruplexes with anti glycosidic torsion angles in solution[END_REF] and Lilley, 1992) [START_REF] Aboulela | NMR study of parallel-stranded tetraplex formation by the hexanucleotide d(TG4T)[END_REF] and X-ray crystallography investigations (Rich, 1992 [START_REF] Kang | Crystal structure of four-stranded Oxytricha telomeric DNA[END_REF] and Lilley, 1994). [START_REF] Laughlan | The high-resolution crystal structure of a parallel-stranded guanine tetraplex[END_REF] As discussed in the following sections, the demonstration of the formation of quadruplexes in a cellular context has proved markedly more challenging.

Despite the lack of firm evidences of the existence of quadruplexes in vivo, chemical programs were soon launched to identify chemicals capable of interacting with quadruplexes, also referred to as G-quadruplex ligands. Neidle & Hurley reported in 1997 on the first prototype of a small molecule specially dedicated to interact with quadruplexes for therapeutic dividends, [START_REF] Sun | Inhibition of human telomerase by a G-quadruplex-interactive compound[END_REF] giving dramatic impetus to the field of quadruplex ligands. This momentum has never slackened since then, with dozens of new ligands reported every year, displaying ever better quadruplex-interacting properties (affinity, selectivity). [START_REF] Monchaud | A hitchhiker's guide to G-quadruplex ligands[END_REF][START_REF] Neidle | Quadruplex Nucleic Acids as Novel Therapeutic Targets[END_REF] Rapidly, the idea of using ligands endowed with specific spectroscopic properties (fluorescence) emerged as a way to detect quadruplexes in cells. The use of small-molecules is indeed a pledge of cellpermeability, the possible toxicity issue being easily tackled by antiproliferative investigations implemented prior to optical cellular imaging. First attempts were reported as soon as in 1999

with the use of metallic porphyrins on metaphase spreads from human cancer cells. [START_REF] Izbicka | Effects of cationic porphyrins as G-quadruplex interactive agents in human tumor cells[END_REF] These first images raised more questions than answers, delineating the limits of this new research field to come: are these dyes quadruplex-specific enough (not to say specific for nucleic acids over other cellular components such as proteins)? Do their spectroscopic properties suited to detect low-abundance targets (mostly the amplitude of the fluorescence modulation upon interaction with quadruplexes only)? Etc. These first images were not convincing enough to build a consensus across scientific fields (chemistry, biophysics, biology, genetics) on the existence of quadruplexes in cells, and beyond this, on their relevance as antiproliferative targets. This skepticism compelled scientist to fine-tune their strategy and sharpened their molecular tools to provide undisputable proofs of the existence of quadruplexes in human cells. This two-decade quest, further described below, has led to the design of highly sophisticated molecular tools now able to deliver reliable evidences of the biological relevance of quadruplexes: antibodies on one side, a guarantee of high-affinity and specificity for quadruplexes, and fluorescent ligands on the other side, which offer bioavailability and tunable spectroscopic properties. The respective advantages and drawbacks of these two approaches (e.g., poor bioavailability and technical access for the former, low quantum yields and off-target labeling for the latter) make them complementary techniques that are often implemented in concert.

III. Immunodetection of quadruplexes in cells.

Immunodetection is an invaluable technique for tagging cellular targets, [START_REF] Giepmans | The fluorescent toolbox for assessing protein location and function[END_REF] usually via a twostep protocol comprising the target labeling per se with a primary antibody followed by a signal amplification with a secondary antibody conjugated to a fluorescent reporter. This approach was successfully implemented for the detection of quadruplexes in cells; however, due to their intracellular location, quadruplexes were stained in fixed and permeabilized cells only, which might raise questions regarding their existence in functional, living cells.

The very first antibody reported to react with quadruplexes was me n IIB4, described in 1998 by Hardin. [START_REF] Brown | Isolation and Characterization of a Monoclonal Anti-Quadruplex DNA Antibody from Autoimmune "Viable Motheaten[END_REF] This antibody was not used for the immunofluorescent detection of quadruplexes in cells but was assessed in vitro for its ability to discriminate quadruplexes from other DNA structures including duplexes and triplexes. It was also shown to have a high affinity for the quadruplex sequences found in the ciliated protozoan Stylonychia lemnae telomeres d(TG 4 )

and d(T 2 G 4 ).

Soon after, Plückthun reported on Sty3 and Sty49, [START_REF] Schaffitzel | In vitro generated antibodies specific for telomeric guaninequadruplex DNA react with Stylonychia lemnae macronuclei[END_REF] also raised against the Stylonychia lemnae telomeric sequences d(TG 4 T). Sty3 displayed better affinity for parallel versus antiparallel quadruplexes, while Sty49 was found to interact with both topologies. Only Sty49 was found efficient to label quadruplexes in isolated Stylonychia macronuclei, after a two-step protocol using fluorescein isothiocyanate (FITC)-labeled secondary antibody. Collected images provided the first visual confirmation of the existence of quadruplexes in nuclei but indicated also that quadruplexes do form in vegetative nuclei only, i.e., in absence of replication. This points towards a possible protective roles of quadruplexes at telomeric levels (capping), regulated by telomere end-binding proteins (TEBPs) that control quadruplex formation, as it was confirmed afterwards. [START_REF] Paeschke | Telomere end-binding proteins control the formation of G-quadruplex DNA structures in vivo[END_REF] Balasubramanian reported on the hf2 antibody that was, similarly to me n IIB4, described for its ability to interact with quadruplexes in vitro. 34 hf2 was found to strongly discriminate between various quadruplex topologies (with a preference for c-kit quadruplex) and was subsequently used to pull-down quadruplex from genomic DNA, providing an unbiased, sequencing (seq)-based demonstration of the existence of quadruplexes in the doublestranded genomic DNA of the human breast cancer MCF-7 cells. [START_REF] Lam | G-quadruplex structures are stable and detectable in human genomic DNA[END_REF] Regarding quadruplex immunodetection, the same group developed BG4, an antibody used to visualize both DNA and RNA quadruplexes in human cells (Figure 1a). The three-step protocol implemented to amplify the fluorescence detection (BG4 incubation per se, then secondary and tertiary labeled antibodies) allowed for visualizing quadruplexes not only in the nuclei of MCF-7 and osteosarcoma U2OS cells [START_REF] Biffi | Quantitative visualization of DNA G-quadruplex structures in human cells[END_REF] and both the nuclei and cytoplasm of SV40-transformed human MRC5 fibroblasts, [START_REF] Biffi | Visualization and selective chemical targeting of RNA G-quadruplex structures in the cytoplasm of human cells[END_REF] but also in metaphase chromosome spreads (from human cervical cancer HeLa cells), suggesting that quadruplex formation occur during chromosome segregation.

Interestingly, the pretreatment of cells with DNA quadruplex-specific (pyridostatin, PDS) [START_REF] Rodriguez | A Novel Small Molecule That Alters Shelterin Integrity and Triggers a DNA-Damage Response at Telomeres[END_REF] and RNA quadruplex-specific ligands (carboxyPDS, cPDS) [START_REF] Antonio | Selective RNA Versus DNA G-Quadruplex Targeting by In Situ Click Chemistry[END_REF] prior to cell fixation and BG4

immunostaining increased the number of quadruplex foci (as compared to untreated cells), lending credence to both the existence of quadruplexes in human cells and their druggability with cell-permeable small-molecules. BG4 was also used for tracking quadruplexes in human tissues: [START_REF] Biffi | Elevated Levels of G-Quadruplex Formation in Human Stomach and Liver Cancer Tissues[END_REF] the immunohistochemical labelling of stomach and liver cancer tissues revealed a higher density of quadruplex landscapes compared to non-cancerous tissues, supporting again the strategic relevance of quadruplex-directed anticancer strategy. Beyond quadruplex detection in cells and tissues, BG4 was also instrumental for the development of G4 ChIP-Seq, a method that combines chromatin immunoprecipitation (ChIP) of quadruplexes and sequencing. [START_REF] Hänsel-Hertsch | G-quadruplex structures mark human regulatory chromatin[END_REF] This protocol was implemented to map the genome-wide location of quadruplexes in epidermal keratinocyte HaCaT cells. G4 ChIP-seq confirmed the prevalence of the quadruplex landscape in a chromatin context (with approximately 10,000 quadruplex sites), proving beyond doubts their biological relevance.

Lansdorp reported on a series of immunofluorescence studies performed with the antibody 1H6 (Figure 1b). This antibody was found efficient to label both nuclei and metaphase chromosome spreads from HeLa cells, [START_REF] Henderson | Detection of G-quadruplex DNA in mammalian cells[END_REF] and the macronuclei of Stylonychia lemnae. [START_REF] Hoffmann | Guanine quadruplex structures localize to heterochromatin[END_REF] Similarly to BG4, the pretreatment of cells with quadruplex ligands, TMPyP4 [START_REF] Siddiqui-Jain | Direct evidence for a Gquadruplex in a promoter region and its targeting with a small molecule to repress c-MYC transcription[END_REF] and telomestatin, [START_REF] Shin-Ya | Telomestatin, a novel telomerase inhibitor from Streptomyces anulatus[END_REF] increased the number of quadruplex foci, further supporting the capability of 1H6 to detect quadruplexes in cells. However, it was subsequently reported that 1H6 crossreacts with non-quadruplex targets, primarily single-stranded thymidines, highlighting the need to exercise caution when interpreting 1H6 sub-cellular binding patterns. [START_REF] Kazemier | Guanine quadruplex monoclonal antibody 1H6 cross-reacts with restrained thymidine-rich single stranded DNA[END_REF] Finally, D1 antibody was also reported to be effective in immunostaining quadruplexes in human cervical cancer SiHa cells (Figure 1c), [START_REF] Liu | Conformation Selective Antibody Enables Genome Profiling and Leads to Discovery of Parallel G-Quadruplex in Human Telomeres[END_REF] and assessing the modulation of quadruplex landscapes upon ligand treatments, including N-methyl mesoporphyrin IX (NMM). 48 Altogether, these investigations have established that antibodies are exquisite molecular tools to visualize quadruplexes in cells by optical imaging. The only sour note of immunostaining is that investigations have to be performed with fixed and permeabilized cells, that is, with cells whose morphology is chemically altered, thus giving rise to doubts as to the biological relevance of observed staining patterns. This issue was alleviated thanks to the versatility of antibodies, which could be used in ChIP-seq protocols to gain reliable insights into the prevalence of the quadruplex landscapes in the human genome. The combination of these two approaches thus allowed the initial, bona fide doubts about the existence of quadruplexes in cells to be reliably dispelled. As further discussed below, a similar strategy was devised with small-molecules, combining chemical labelling and chemical affinity capture and sequencing (chem-seq) [START_REF] Rodriguez | Unravelling the genomic targets of small molecules using high-throughput sequencing[END_REF] to obtain complementary clues on the relevance of quadruplexes in functional, living cells.

IV. Quadruplex-selective fluorescent dyes.

Quadruplex ligands are usually small-molecules (molecular weight < 2000 g.mol -1 ) that display water-solubility and cell permeability properties suited to be used in living cells. The diversity of scaffolds that can be designed and synthesized through organic synthesis has offered access to a broad portfolio of molecular tools endowed with ever more accurate properties in a fully controllable manner. This explains the wide range of ligands now reported, [START_REF] Monchaud | A hitchhiker's guide to G-quadruplex ligands[END_REF][START_REF] Neidle | Quadruplex Nucleic Acids as Novel Therapeutic Targets[END_REF][START_REF] Neidle | Quadruplex nucleic acids as targets for anticancer therapeutics[END_REF][START_REF] O'hagan | Binding and beyond: what else can Gquadruplex ligands do?[END_REF] and made available for cell-based investigations. When displaying fluorescence properties, ligands become quadruplex-specific probes, [52][START_REF] Ma | Recent development of Gquadruplex probes for cellular imaging[END_REF][START_REF] Suseela | Far-red fluorescent probes for canonical and non-canonical nucleic acid structures: current progress and future implications[END_REF] prone to be used in both fixed and living cells, the later allowing to track and detect quadruplexes in a functional context. These dyes could be divided in several categories as a function of their chemical nature (organometallic complexes versus organic molecules), cell-permeability (fixed cells versus live-cell imaging) and selectivity (DNA versus RNA quadruplexes, or both).

It is no coincidence that, historically, the first small-molecules described as quadruplexinteracting compounds, i.e., a cyanine (DODC) [START_REF] Chen | Spectroscopic recognition of guanine dimeric hairpin quadruplexes by a carbocyanine dye[END_REF] and a porphyrin (NMM) [START_REF] Li | Recognition of anionic porphyrins by DNA aptamers[END_REF] in 1996, an anthraquinone in 1997, [START_REF] Sun | Inhibition of human telomerase by a G-quadruplex-interactive compound[END_REF] a perylenetetracarboxylic diimide (PIPER) [START_REF] Fedoroff | NMR-based model of a telomerase-inhibiting compound bound to G-quadruplex DNA[END_REF] in 1998 and a series of metal complexes of tetra(N-methyl-4-pyridyl) and tetra(N-methyl-3-quinolyl) porphines (TMPyP4 and QP3, respectively) [START_REF] Izbicka | Effects of cationic porphyrins as G-quadruplex interactive agents in human tumor cells[END_REF] in 1999, were also endowed with spectroscopic properties that make them suited to be used as quadruplex probes. These laid the foundation for a new area of research focused on the use of condensed polyaromatic molecules and metal complexes to track quadruplexes in cells. Several strategies were implemented over the past years, from the fine-tuning of the chemical structure of known quadruplex ligands (to make them fluorescent) to that of known dyes (to make them quadruplex-specific).

Most of the early examples of quadruplex ligands displayed spectroscopic (fluorescence) properties potentially suited to being used for tracking quadruplexes in cells.

However, their polyaromatic nature along with that of their binding sites within the quadruplex structure (external G-quartets) makes them sensitive to the presence of their nucleic acid targets, which usually results in a "turn-off" (or "light-off")-type interactions, mostly via photoinduced electron transfer mechanisms. [START_REF] Seidel | Nucleobase-specific quenching of fluorescent dyes. 1. Nucleobase one-electron redox potentials and their correlation with static and dynamic quenching efficiencies[END_REF] While "turn-off" probes turned out to be useful for in vitro investigations, 52 they have only poor applicability for the detection of quadruplex in human cells. Astute strategies have been devised to counteract fluorescence quenching. 52,[START_REF] Suseela | Far-red fluorescent probes for canonical and non-canonical nucleic acid structures: current progress and future implications[END_REF][START_REF] Ma | Recent developments in G-quadruplex probes[END_REF][START_REF] Umar | G-Quadruplex-Based Fluorescent Turn-On Ligands and Aptamers: From Development to Applications[END_REF] The fluorescence of properly designed aromatic molecules can be "turnedon" upon interaction with quadruplexes through a panel of possible mechanisms that include i-the restriction of internal rotation (RIR), which occurs with cyanine (e.g., DODC, [START_REF] Chen | Spectroscopic recognition of guanine dimeric hairpin quadruplexes by a carbocyanine dye[END_REF] thiazole orange (TO) [START_REF] Allain | FRET templated by G-quadruplex DNA: A specific ternary interaction using an original pair of donor/acceptor partners[END_REF] and Thioflavin T (ThT)), [START_REF] Gabelica | Multiple and Cooperative Binding of Fluorescence Light-up Probe Thioflavin T with Human Telomere DNA G-Quadruplex[END_REF] carbazole (e.g., BMVC) [START_REF] Chang | Verification of antiparallel G-quadruplex structure in human telomeres by using two-photon excitation fluorescence lifetime imaging microscopy of the 3, 6-Bis (1-methyl-4-vinylpyridinium) carbazole diiodide molecule[END_REF] or triphenylmethane dyes (e.g., malachite green (MG), [START_REF] Bhasikuttan | Interaction of malachite green with guaninerich single-stranded DNA: preferential binding to a G-quadruplex[END_REF] crystal violet (CV)); [START_REF] Kong | Discrimination of G-quadruplexes from duplex and single-stranded DNAs with fluorescence and energy-transfer fluorescence spectra of crystal violet[END_REF] ii-the protection provided by the DNA matrix against solvent-mediated non-radiative deexcitation (e.g., porphyrins (e.g., NMM) [START_REF] Nicoludis | Interaction of human telomeric DNA with N-methyl mesoporphyrin IX[END_REF] and metal complexes); [START_REF] Cao | G-quadruplex DNA targeted metal complexes acting as potential anticancer drugs[END_REF] iii-the quadruplex-mediated disaggregation of non-emitting aggregates (e.g., NDI) [START_REF] Pirota | Naphthalene Diimides as Multimodal G-Quadruplex-Selective Ligands[END_REF] or conversely, iv-the aggregation-induced emission (AIE, e.g., the tetraphenylethene TTAPE); [START_REF] Hong | Label-free fluorescent probing of G-quadruplex formation and real-time monitoring of DNA folding by a quaternized tetraphenylethene salt with aggregationinduced emission characteristics[END_REF] v-the quadruplex-mediated molecular rearrangement of smart probes; [START_REF] Laguerre | A Twice-As-Smart Synthetic G-Quartet: PyroTASQ Is Both a Smart Quadruplex Ligand and a Smart Fluorescent Probe[END_REF] Etc. While hundreds of quadruplex-specific probes have been studied and reported, we will focus in the next sections on quadruplex-specific probes whose spectroscopic properties have been used to assess the existence of quadruplex landscapes in cells. The first immediate strategy to track quadruplexes within cells is to exploit the fluorescence properties of established quadruplex ligands, even if these properties are non-optimized. As stated above, the first reported example reported (in 1999) relied on the live-incubation of MCF7 cells with a sub-toxic dose (40 µM, 3 days) the metal complex QP3.In prior to the preparation of metaphase spreads (Figure 2a). [START_REF] Izbicka | Effects of cationic porphyrins as G-quadruplex interactive agents in human tumor cells[END_REF] The collected images were rather ill-defined and allowed for demonstrating the accumulation of the complex in the nuclei of cancer cells only. Soon after, Stevens reported on the synthesis and studies of a series of acridinium salts, [START_REF] Heald | Antitumor polycyclic acridines. 8. Synthesis and telomerase-inhibitory activity of methylated pentacyclic acridinium salts[END_REF][START_REF] Stanslas | Antitumor polycyclic acridines. 7. Synthesis and biological properties of DNA affinic tetra-and pentacyclic acridines[END_REF] including RHPS4 whose complex with a quadruplex was the very first to be elucidated by NMR. [START_REF] Gavathiotis | Recognition and stabilization of quadruplex DNA by a potent new telomerase inhibitor: NMR studies of the 2 : 1 complex of a pentacyclic methylacridinium cation with d(TTAGGGT)(4)[END_REF] They also exploited the intrinsic fluorescence properties of RHPS4 to gain insights into the drug localization after short live-cell incubations (30 µM, 15 min) in both MCF7 and human lung carcinoma A459 cells by confocal microscopy (Figure 2b). Again, the low-resolution images did not allow for identifying precisely the quadruplex sites but they enlighten an accumulation in the nucleoli of A459 cells. Of note, higher-resolution images were collected recently in mouse embryonic fibroblast (MEF) cells using a high-speed confocal microscope, and showed an accumulation of RHPS4 in mitochondria. [START_REF] Falabella | G-quadruplex dynamics contribute to regulation of mitochondrial gene expression[END_REF] Later on, the fluorescence of the fluoroquinolone CX-3543 (or quarfloxin) was exploited for a more accurate analysis of the biodistribution of quadruplex ligands (5 µM, 1 h), confirming a privileged accumulation of quadruplex ligands in the nucleoli of A459 cells after live-cell incubation (Figure 2c). [START_REF] Drygin | Anticancer Activity of CX-3543: A Direct Inhibitor of rRNA Biogenesis[END_REF] This observation opened the way towards a redefinition of the in-cell targets of quadruplex ligands, which challenge the ribosomal biogenesis efficiently. However, these images failed in provided irrefutable arguments about the existence of quadruplexes in cells, and highlight the need of designing specially dedicated molecular tools to this end.

IVb. From fluorescent dyes to quadruplex-specific probes

Another approach was thus devised with the aim of providing undebatable evidence about the relevance of quadruplexes in cellular contexts. This strategy was based on the use of-and then, the design of new systems from-commercially available nucleic acid stains. This approach was yet thoroughly followed but, as further detailed below, did not address all the aforementioned pitfalls.

IVb.1. Fluorescent dyes with non-optimized quadruplex-interacting properties.

The illustrative example of a firmly established dye that found numerous applications as DNA staining agent is thiazole orange (TO). Its ability to interact with (owing to its positive charge)

and label nucleic acids in a "turn-on" manner (RIR mechanism) whatever its secondary structure was thoroughly exploited, notably for the development of fluorescent intercalator displacement (FID) assays used to assess and quantify the apparent affinity of small molecules to duplexes [START_REF] Tse | A fluorescent intercalator displacement assay for establishing DNA binding selectivity and affinity[END_REF] and/or quadruplexes. [START_REF] Monchaud | Ligands playing musical chairs with G-quadruplex DNA: A rapid and simple displacement assay for identifying selective G-quadruplex binders[END_REF] However, TO does not discriminate between nucleic acid structures, making it of poor interest for the detection of quadruplexes in cells. Thioflavin T (ThT) is a closely related dye with better quadruplex-versus-duplex discriminating ability. [START_REF] Mohanty | Thioflavin T as an efficient inducer and selective fluorescent sensor for the human telomeric G-quadruplex DNA[END_REF] It was used for visualizing quadruplexes in polyacrylamide gels [START_REF] De La Faverie | Thioflavin T as a fluorescence light-up probe for G4 formation[END_REF] and also found to be suited for cellular imaging (Figure 3a). [START_REF] Zhang | Direct visualization of nucleolar G-quadruplexes in live cells by using a fluorescent light-up probe[END_REF]

IVb.2. Fine-tuning the quadruplex-interacting properties of fluorescent probes

The two chemical motifs found in the TO scaffold, i.e., the N-methylquinolinium and Nmethylbenzothiazolium moieties (the latter being also found in the ThT scaffold), were truly inspirational and subsequently thoroughly exploited with the hope of obtaining quadruplexspecific probes with an alternative cellular activity. For instance, the p-surface of the TO was extended with a benzofuran to obtain the benzothiazole-fused benzofuroquinolinium dye 1, [START_REF] Lu | Benzothiazole-substituted benzofuroquinolinium dye: a selective switchon fluorescent probe for G-quadruplex[END_REF] which proved useful for labelling living MCF7 cells (2 µM, 15 min), highlighting nuclei and nucleoli only (Figure 4a). Higher-resolution images were collected with a styryl-substituted TO referred to as 4a, [START_REF] Lu | Molecular engineering of thiazole orange dye: Change of fluorescent signaling from universal to specific upon binding with nucleic acids in bioassay[END_REF] which was useful for labelling both live and fixed human prostate cancer PC3 cells (5 µM, 15 min), the latter providing a clear visualization of a nucleolar accumulation of the dye (Figure 4b). The p-conjugation was further expanded introducing 3-vinylindole arms but the images of live PC3 cells incubated with compound 3c (5 µM, 5 min) demonstrated, again, that the localization of foci remained globally centered on the nucleoli (Figure 4c), [START_REF] Lu | Selective visualization of DNA G-quadruplex structures in live cells with 1methylquinolinium-based molecular probes: The importance of indolyl moiety position towards specificity[END_REF] without providing deeper insights into the localization of quadruplexes in cells. For instance, the cyanine CyT was found to be particularly sensitive to RNA quadruplexes and suited to the detection of RNA quadruplexes in living A459 cells (1.25 µM, 24 h), the foci being exclusively localized in the cytoplasm of the cells (Figure 5a). [START_REF] Xu | Directly lighting up RNA G-quadruplexes from test tubes to living human cells[END_REF] Another benzofuroquinolinium dye named CYTO was implemented with both live and fixed PC3 cells (1 µM, 30 min) and leads to an interesting nuclear pattern from which nucleoli were found as the privileged labelling sites along with some-unfortunately unexploited-minor nuclear foci (Figure 5b). [START_REF] Lu | Benzothiazole-substituted benzofuroquinolinium dyes as new fluorescent probes for G-quadruplex DNA[END_REF] The squaraine-based cyanine CSTS was found live cell-compatible (2 µM, 30 min) and accumulated in the lysosomes of MCF7 cells. [START_REF] Zhang | Development of squaraine based G-quadruplex ligands using click chemistry[END_REF] Similarly, another cyanine named DMOTY was found to accumulate in lysosomes of living HeLa and MCF7 cells (10 µM, 4 h) and be fluorescently responsive to the presence of quadruplexes (Figure 5c), making it a promising autophagy probes. 90 (Figure 6b). A very complete study was recently reported using the coumarine-based QUMA-1 for labelling quadruplexes in both fixed and living HeLa cells. [START_REF] Chen | Tracking the dynamic folding and unfolding of RNA G-quadruplexes in live cells[END_REF] The fixed conditions (1 µM, 15 min) were useful not only to show the very high selectivity of QUMA-1 for RNA quadruplexes (cytoplasmic foci along with some isolated nucleolar sites, Figure 6c) but also to perform competitive experiments with RNA quadruplex-interacting ligands such as cPDS, [START_REF] Antonio | Selective RNA Versus DNA G-Quadruplex Targeting by In Situ Click Chemistry[END_REF] which results in the loss of QUMA-1 foci. Live-cell conditions (0.5 µM, 3 h) uniquely provided insights into the dynamics of RNA folding and unfolding, notably upon addition of the helicase DHX36, which unfolds efficiently RNA quadruplexes resulting in the complete disappearance of the cytoplasmic foci. However-and again-, additional manipulations (enzymatic digestions, co-incubation with ligands, helicases or specific antibodies, etc.) were still required to demonstrate the relevance of these approaches, and some pitfalls still exist, notably the influence of local microenvironments (pH, viscosity, etc.) that might trigger the fluorescence of the dyes in a quadruplex-independent manner. Smarter-and even more sophisticated-molecular systems were thus required to provide ever more convincing evidence about the existence of quadruplexes in cells.

IVc. From quadruplex ligands to quadruplex-specific probes.

Another strategy was thus implemented in the hope of providing molecular tools with first, a high affinity and selectivity for quadruplexes and then, the capacity of delivering readily detectable outputs once in interaction with their targets. This strategy was mostly based on the modifications of the chemical structure of well-established quadruplex ligands.

IVc.1. Optimizing the scaffold of know quadruplex ligands

As indicated above, fusing known quadruplex-interacting and TO scaffolds was soon envisioned as a way to design quadruplex probes suited to cellular investigations. This was pioneered fusing the TO scaffold with the pyridodicarboxamide (PDC) core of 360A to provide PDC-M-TO, [START_REF] Yang | Engineering Bisquinolinium/Thiazole Orange Conjugates for Fluorescent Sensing of G-Quadruplex DNA[END_REF] with the acridine core of BRACO-19 to provide a dual, pH sensitive and quadruplex-specific probe, [START_REF] Percivalle | Two-in-one: a pH-sensitive, acridine-based, fluorescent probe binds G-quadruplexes in oncogene promoters[END_REF] and with an isaindigotone core to provide ISCH-1 (vide supra), [START_REF] Yan | Development of a new colorimetric and red-emitting fluorescent dual probe for G-quadruplex nucleic acids[END_REF] which was the only dye from that series that was attempted in cells. Some well-known nucleic acid stacking motifs were also revisited with successes, such as the quinacridone motif, notably with QAB that was made water soluble and bioavailable via the addition of solubilizing amine appendages, [START_REF] Liu | DNA interaction, cellular localization and cytotoxicity of quinacridone derivatives[END_REF] the anthracene motif, notably with 9CI that was used for labelling exogenous quadruplexes, [START_REF] Zhai | Selective recognition of c-MYC Pu22 G-quadruplex by a fluorescent probe[END_REF] or the carbazole motif, whose quadruplex labelling properties have been thoroughly studied, spurred on by the compelling results obtained with BMVC [START_REF] Chang | Verification of antiparallel G-quadruplex structure in human telomeres by using two-photon excitation fluorescence lifetime imaging microscopy of the 3, 6-Bis (1-methyl-4-vinylpyridinium) carbazole diiodide molecule[END_REF] and its closely related analog o-BMVC. These two carbazoles were the first probes used for the detection of quadruplex in living human lung cancer CL1-0 cells (5 µM, 2 h), being suited to fluorescence lifetime imaging microscopy (FLIM) that enhanced the resolution of the collected images (Figure 7a). [START_REF] Tseng | Fluorescent probe for visualizing guanine-quadruplex DNA by fluorescence lifetime imaging microscopy[END_REF] They localized differently, BMVC being located in the nucleus with o-BMVC in the cytoplasm, likely in mitochondria. The carbazoles that belong to the BMVC family found numerous applications: they have been used to track exogeneous quadruplexes in CL1-0 cells (BMVC), [START_REF] Tseng | In-cell optical imaging of exogenous G-quadruplex DNA by fluorogenic ligands[END_REF] to illuminate mitochondrial DNA quadruplexes in living HeLa cells (BMVC-12C-P, 5 µM, 24 h; o-BMVC-12C-P, 5 µM, 4 h), 100 to implement a biosensing assay for the detection of cancer versus healthy cells (o-BMVC, 5 µM, 10 min, including fixed cancerous MCF-7 and CL1-0 cells versus non-cancerous fibroblast MRC5 and BJ cells, applicable in tissue biopsies as well), 101 and to assess the modifications of the quadruplex landscapes in HeLa and MRC-5 cells live-treated with the quadruplex ligands BRACO-19 and TMPyP4 (10 µM, 16 h) after fixation (o-BMVC, 5 µM, 10 min). 102 Many other derivatives have been synthesized and studied for live-cell imaging, such BPBC and BTC, found to localize in the cytoplasm and nucleoli of MCF7 cells (BPBC, 10 µM, 2 h), 103 and in the nucleoli of human liver cancer HepG2 cells (BTC, 5 µM, 4 h, Figure 7b). 104 Finally, another well-known nucleic acid stacking motif that was implemented for optical imaging purposes was the naphthalene diimide (NDI) unit. This motif was thoroughly exploited for the recognition of quadruplexes in vitro, [START_REF] Pirota | Naphthalene Diimides as Multimodal G-Quadruplex-Selective Ligands[END_REF] and examples were also reported for tracking them in cells. The spectroscopic properties of NDI, notably of core-extended NDI (c-exNDI), are based on a quadruplex-mediated disaggregation of nonemitting aggregates. Live incubation of human embryonic kidney HEK293T cells with c-exNDI

(1 µM, 30 min) allowed for an accumulation of foci within the nuclei (Figure 7c), which partially overlapped with 1H6 immunostaining, and more precisely in the nucleoli, as demonstrated by nucleolin displacement investigations. 105

IVc.2. Adding tags to known quadruplex ligands

Attempts have been also made to covalently link a fluorescent tag directly to a quadruplex ligand scaffold. For instance, a BODIPY has been linked to a macrocyclic heptaoxazole (L1BOD-7OTD), 106 a TO and a BODIPY to the PDC core (PDC-L-TO [START_REF] Yang | Engineering Bisquinolinium/Thiazole Orange Conjugates for Fluorescent Sensing of G-Quadruplex DNA[END_REF] and PDC-BODIPY, 107 respectively), a Cy5 to a PDS derivative (PDP-Cy5) 108 and a fluorescein to a triarylimidazole (IZFL-2). 109 This approach turned out to be highly valuable for in vitro quadruplex detection: L1BOD-7OTD and

IVc.4. Using metallic probes to track quadruplexes in cells

After the initial impetus given by QP3.In, many metal complexes have been investigated as quadruplex-specific reporter probes. The quadruplex field was indeed a fertile playground for organic and inorganic chemists, owing to the manipulation of metal chelating moieties (sometimes referred to as ligands, avoided here for disambiguation) with broad aromatic surfaces (e.g., phen, dppn, dppz, dpq, etc.), 119,120 prone to interact efficiently with the accessible quartet of quadruplexes. While dozens of metal complexes have been studied in vitro, [START_REF] Cao | G-quadruplex DNA targeted metal complexes acting as potential anticancer drugs[END_REF] far less complexes have been used for cellular imaging, which can originate in the globally lower resolution of the obtained images as compared to those obtained with organic probes. The dinuclear ruthenium complex [(phen) 2 Ru(tpphz)Ru(phen) 2 ] was for instance used to label the genomic DNA of both human MCF7 cells (500 µM, 1 h) and mouse lymphoma L5178Y-R cells (characterized by longer telomere than MCF7 cells; 200 µM, 30 min), but allowed for identifying quadruplexes via lambda stacking experiments (Figure 10a), given that its emissive maxima were dependent on the topology of the nucleic acid targets (630-640 nm for quadruplexes versus 670-700 nm for duplex). 121 The tetrakis-(diisopropylguanidinio)zinc phthalocyanine Zn-DIGP was used to label quadruplexes in living melanoma SK-Mel-28 cells (3 µM, 2 h) 122 or mouse embryo fibroblast NIH 3T3 cells (2 µM, 24 h, Figure 10b), 123 revealing foci localized in perinuclear regions, while the metal-free counterpart labelled nuclei only.

Interestingly, the intrinsic chirality of the metal complexes was found to play an important role in the biodistribution of the probes. For instance, the two enantiomers of the ruthenium complex [Ru(bpy) 2 (p-BEPIP)], referred to as RM0627 were found to enter rapidly living breast cancer MDA-MB-231 cells (5 µM, 2 h) and accumulate either in perinuclear regions (the dextrorotary D-RM0627) or in the nuclei exclusively (the levorotary L-RM0627). 125 More recently, the platinum complex Pt-SCC (for supramolecular coordination complex) was used in fixed MCF7 cells (50 µM, 30 min, Figure 10c) and lead to an intense nuclear labelling and the interaction with quadruplexes was confirmed via competition with quadruplex ligands (e.g., PDS, TMPyP4) and co-localization with quadruplex-specific antibody (BG4). 125 Interestingly, Pt-SCC was found to provide a dual labeling, fluorescently staining the genomic DNA on one hand and increasing the contrast of nucleoli in direct transmission mode (DIC, for differential interference contrast) on the other hand, thus providing another modality (so called 'dark staining', relying on the absorption of light by the Pt-SCC/quadruplex complex) for the observation of quadruplex in cells.

Globally speaking, the optical images collected so far with metal complexes did not reach an exquisite level of resolution, which can be attributed to the fact that their structures, for most of them, relied on planar metal chelating moieties that failed in creating discriminating interactions with quadruplexes, as simple organic intercalators did. However, the chemical and structural diversity that uniquely offers this field of research, along with the various modalities of images that can be implemented with metal complexes, are the best promises for future advances and successes.

V. Conclusion.

The detection of quadruplex in human cells was and remains a challenging task. In spite of the massive efforts that have been invested for almost 20 years now, no turnkey solutions have been delivered and the examples discussed above highlighted that only multipronged approaches (co-localization of small molecule probes and antibodies; competition between established ligands and probes; etc.) can provide solid evidence about their existence in cells.

The visualization of quadruplexes involves probes (antibodies, chemicals) suited to optical imaging but the very notion of detection of quadruplexes is boarder: it also encompasses the sequencing-based techniques that have been developed recently to gain insights into the relevance and prevalence of the quadruplex landscapes. [126][127][128] Once again, the role of quadruplex-specific antibodies and chemicals was instrumental in these investigations: for instance, the antibody BG4 was the central molecular tool for the development of G4 ChIPseq (vide supra), [START_REF] Hänsel-Hertsch | G-quadruplex structures mark human regulatory chromatin[END_REF] which assessed the formation of DNA quadruplexes in the human genome; the small molecule PDS was used in both G4-seq 129 and rG4-seq 130 to promote and/or stabilize DNA and RNA quadruplexes, respectively, to make them detectable during the sequencing analysis steps; and biotinylated PDS 131 and TASQ-based BioTASQ 132 was useful to purify (pulldown) and identify quadruplexes (i.e., G4RP-seq). 133 These examples demonstrate again that (bio)molecular tools created to detect quadruplexes have to be versatile to be used in complementary fields, since only cross-disciplinary investigations can provide reliable insights into the cellular relevance and functions of quadruplexes. These examples have also casted a bright light on antibodies and small molecules but scientists have other strings in their bow, such as fluorescently labelled proteins (e.g., the helicase GFP-hPif1, vide supra) or short oligonucleotides (e.g., the oligonucleotide-templated reactions (OTR) 134 or G-quadruplextriggered fluorogenic hybridization (GTFH) 135 approaches). This highlights the need for the quadruplex community to both keep growing and pull together to develop transdisciplinary research programs aimed at providing ever more convincing evidence to support therapeutic strategies based on the quadruplex targeting with ad hoc drugs.

"You will never be able to hit a target that you cannot see". We are now able to hit this target. The examples presented above showed that scientists have now a panel of molecular lights to enlighten quadruplexes in our genome and transcriptome, a target that can no longer hide-and will be hit-even in the remotest parts of the human cells.

IVb. 1 14 IVc. 1 14 IVc. 2 15 IVc. 3 17 IVc. 4

 1141142153174 -stranded DNA structures and quadruplex ligands, a bit of history Page 02 III. Immunodetection of quadruplexes in cells Page 04 IV. Quadruplex-selective fluorescent dyes Page 06 IVa. Quadruplex-specific ligands with non-optimized spectroscopic properties Page 08 IVb. From fluorescent dyes to quadruplex-specific probes Page 09 Fluorescent dyes with non-optimized quadruplex-interacting properties Page 09 IVb.2 Fine-tuning the quadruplex-interacting properties of fluorescent probes Page 11 IVc. From quadruplex ligands to quadruplex-specific probes Page Optimizing the scaffold of known quadruplex ligands Page Adding tags to known quadruplex ligands Page Specially dedicated small molecule probes Page Using metallic probes to track quadruplexes in cells Page 18 V. Conclusion Page 20

Figure 1 .

 1 Figure 1. Immunodetection of DNA quadruplexes by (a) BG4 in U2OS cells (red foci, the nuclei being counterstained with DAPI, in blue), 36 (b) 1H6 in HeLa cells, 42 and (c) D1 in SiHa cells (green foci, co-incubated with an antibody raised against TRF2 (red foci), the nuclei being counterstained with DAPI, in blue).

47

 47

Figure 2 .

 2 Figure 2. Images of (a) metaphase spreads of MCF7 cells live-treated by QP3.In, 29 and A459 cells live-treated with RHPS4 (b) 71 and CX-3543 (c).72

  Collected images indicated a privileged accumulation of quadruplex-specific probes in the nucleoli of cancer cells (MCF7), both for post-fixation labelling (5 µM, 15 min) or via live-cell incubation protocols (5 µM, 24 h). These results indicated that ThT might interact with either ribosomal DNA (rDNA) or ribosomal RNA (rRNA), or both. The RNA-interacting properties of both ThT and the closely related analog ThT-NE were further investigated using the two probes for enlightening viral RNA (vRNA) in human hepatoma cells that express the full-length RNA genome of the hepatitis C virus (HCV).[START_REF] Luo | Lighting up the Native Viral RNA Genome with a Fluorogenic Probe for the Live-Cell Visualization of Virus Infection[END_REF] Obtained images (Figure3b) demonstrated a clear accumulation of the fluorescent foci within the cytoplasm of living cells (1 µM, 10 min), making this vRNA "turn-on" system a promising strategy for viral infection diagnosis. Another ThT analog, N-Isopropyl-2-(4-N,Ndimethylanilino)-6-methylbenzothiazole or IMT, was used for labelling quadruplexes in both fixed and living human cervical adenocarcinoma (HeLa) cells (Figure3c).[START_REF] Zhang | Real-time monitoring of DNA G-quadruplexes in living cells with a smallmolecule fluorescent probe[END_REF] IMT turned out to be particularly suited for live-cell investigations, allowing for monitoring the modifications of the DNA quadruplex landscapes real-time (4 µM, 0 -90 min), notably upon treatment with the quadruplex ligands PDS, RHPS4 and TMPyP4.[START_REF] Zhang | Evaluation of the selectivity of G-quadruplex ligands in living cells with a small molecule fluorescent probe[END_REF]

Figure 3 .

 3 Figure 3. Images of (a) living MCF7 cells treated by ThT (yellow foci, the nuclei being counterstained with SYTO59, in red), 80 (b) living hepatoma cells infected by the hepatitis C virus treated by ThT-NE (green foci, the nuclei being counterstained with DAPI, in blue), 81 and (c) living HeLa cells treated by IMT (red foci, the nuclei being counterstained with DAPI, in blue).82

Figure 4 .

 4 Figure 4. Nuclear labelling of (a) living MCF7 cells treated by the benzofuroquinolinium dye 1, 84 and of living PC3 cells treated by the styryl-substituted thiazole orange 4a (b) 85 and the vinylindole-substitued Nmethylquinolinium 3c (c).

86 A

 86 higher level of precision was reached with N-methylbenzothiazolium-based probes.

Figure 5 .

 5 Figure 5. Labelling of (a) RNA quadruplexes by CyT in living A459 cells (red foci, the nuclei being counterstained with Hoechst 33258, in blue), 87 (b) the nucleoli of PC3 cells by CYTO (red foci, the nuclei being counterstained with DAPI, in blue), 88 and (c) the lysosomes of living HeLa cells by DMOTY (green foci, co-incubated with LysoTracker, in red).

90 N

 90 -methylquinolinium-based probes were also further developed and studied. Two redemitting dyes (with emission wavelength (l em ) > 650 nm) were notably developed: ISCH-1, whose structure results in merged isaindigotone and coumarine scaffolds, was used with both fixed and living A459 and HeLa cells (5 µM, 30 min) and lead to an accumulation of foci in nucleoli (Figure6a), presumably targeting rDNA quadruplexes as further demonstrated by ChIP assay; 91 NCT, whose structure results in conjugated TO and coumarine scaffolds, was used with living HeLa cells (1 µM, 15 min) and found to accumulate exclusively in mitochondrial DNA quadruplexes,[START_REF] Li | Mitochondrial G-quadruplex targeting probe with near-infrared fluorescence emission[END_REF] as demonstrated by co-localization with MitoTracker TM

Figure 6 .

 6 Figure 6. Confocal images of fixed HeLa cells treated by (a) ISCH-1, 91 (b) NCT (red foci, co-incubated with MitoTracker, in red, resulting in yellow foci), 92 and (c) QUMA-1 (red foci, the nuclei being counterstained with DAPI, in blue).93

Figure 7 .

 7 Figure 7. (a) Time-gated FLIM images of fixed HeLa cells treated with o-BMVC (red foci for decay times ≥2.4 ns, corresponding to quadruplexes, green foci for decay times <2.4 ns); 102 (b) nucleoli labelling of HepG2 cells by BTC; 104 (c) nuclear labelling of HEK293T cells by c-exNDI.105

PDP-

  Figure 8a).108

Figure 8 .IVc. 3 .

 83 Figure 8. Detection of (a) exogenously added fluorescein-labelled quadruplex RNA in HeLa cells by PDP-Cy5 (red foci, fluroscein in green, resulting in yellow foci, the nuclei being counterstained with DAPI, in blue), 108 (b) DNA quadruplexes in fixed U2OS cells thanks to PDS-a after CuAAC with AF-594 (red foci, co-localization with GFP-hPif1 in green, the nucleus being delineated by a dotted white line), 110 and (c) DNA quadruplexes in fixed HT29, after live-treatment with PhenDC-az and SPAAC with Cy5-DBCO.111

Figure 9 .

 9 Figure 9. (a) Autoradiograph of metaphase spreads of T98G cells live-treated with 3 H-360A (black arrows indicate chromosome ends, red arrows intrachromosomal sites); 114 (b) detection of RNA quadruplexes in the cytoplasm of MCF7 cells live-treated with N-TASQ; 116 (c) general staining obtained with U2OS cells treated with DAOTA-M2.118

  124

Figure 10 .

 10 Figure 10. (a) Mutliple-emission images of L5178Y-R cells treated with [(phen)2Ru(tpphz)Ru(phen)2] (L = phen), highlighting the genomic DNA in red (emission: 670-700 nm) and the quadruplex foci (emission 630-640 nm) in yellow; confocal images of (b) NIN 3T3 cells treated with Zn-DIGP, 123 and (c) fixed MCF7 cells stained by Pt-SCC.