B Akinsanmi
email: tunde.akinsanmi@astro.up.pt

C Barros

N C Santos

P. F L Maxted A C M Correia

G Boué

J Laskar

S C C Barros

P F L Maxted

Detectability of shape deformation in short-period exoplanets

Keywords: methods, analyticaltechniques, photometricplanets and satellites, interiors * LSSTC Data Science Fellow

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Introduction

The existence of planets with short-period orbits around their stars came as a surprise at the inception of exoplanet discoveries especially because the first case was a gas giant (Mayor & Queloz 1995) bearing no resemblance to the planet configuration in our solar system. Several of these planets have now been found as they represent some of the most easily detected planets using both the transit and radial velocity methods. Planets reach their final shapes having attained hydrostatic equilibrium from balancing gravitational, pressure, and other external forces acting on them. Planet shapes are often assumed to be spherical for simplicity but they are triaxial in reality. For very-short-period planets (P < 1-2 days), the close proximity to their stars exposes them to strong tidal forces which deforms them and increases the triaxiality of their equilibrium shapes.

Contribution to deformation of a planet can also come from its rotation, making it oblate (Barnes & Fortney 2003).

Planet shape can have noticeable effects on the light curve obtained from transit observations [START_REF] Seager | [END_REF]Carter & Winn 2010a,b). Analysis of the transit light curve of a planet assuming planet sphericity allows for a spherical radius Rspr to be obtained. However, Leconte et al. (2011) showed that planet deformation due to tidal and rotational forces lowers the observed transit depth in comparison to a spherical planet. This causes an underestimation of the radius when sphericity is assumed in the transit light curve analysis of a deformed planet. Since the density of a planet is calculated from the assumed spherical radius, the obtained density will consequently be overestimated. Burton et al. (2014) therefore provided density corrections for some short-period planets expected to be tidally deformed based on the Roche approximation [START_REF] Chandrasekhar | Ellipsoidal figures of equilibrium[END_REF]. Tidal deformation is particularly significant for planets orbiting close to their stellar Roche limits and a number of planets have been discovered to orbit so close to this limit that they are bordering on tidal disruption (e.g., Gillon et al. 2014;Delrez et al. 2016). For some of these planets, theoretical calculations have been done using the Roche model by Budaj (2011) to estimate the planet shape and correct the derived spherical radii and densities for the expected planet deformation (e.g., Southworth et al. 2015;Delrez et al. 2016). Correia ( 2014) formulated an analytical model for computing the shape of a deformed planet based on the fluid second Love number and also showed the difference between light curves of deformed and spherical planets. Despite these efforts, there has been no observational detection of tidal deformation in short-period planets which would provide better estimates of their parameters. We therefore investigate the possibility of detecting deformation in the transit light curve of short-period planets with some current and near-future observational instruments. We modify the ellc transit tool by [START_REF] Maxted | [END_REF] 1 to incorporate the planet shape model by Correia (2014). The modified ellc is used to generate the light curve for a deformed planet based on its fluid second Love number. This allows us to obtain an estimate for the Love number of the planet that best matches the transit observations, which provides insights into the internal structure differentiation of the planet.

In Sect. 2, we summarize the model used to compute the shape of the planet and modification of the transit tool used to generate the light curves. In Sect. 3 we apply the modified tool to investigate the detectability of planet deformation in a case study of a known short-period planet. In Sect. 4, we discuss the results and some useful considerations for detecting planet deformation. We present our conclusions in the last section.

where G is the gravitational constant. The first term on the righthand-side is the deformation contribution from the centrifugal potential resulting from the planet's coplanar and synchronous rotation rate Ω about the Z-axis. The second term refers to the tidal contribution to the deformation along the X-axis by a star of mass M * .

Following [START_REF] Love | Some Problems of Geodynamics[END_REF], Correia (2014) describes this deformation using a Love number approach such that the fluid second Love number for radial displacement hf is related to the radial deformation of the planet ∆R. The equilibrium surface deformation is thus given by

∆R = -hf Vp/g, ( 2
)
where g is the average surface gravity of the planet, and hf is a dimensionless quantity that quantifies the response (in terms of deformation) of a planet to a perturbing potential 2 . The magnitude of hf depends on the mass distribution of the planet. More homogeneous planets have higher hf whereas planets that are more centrally condensed have lower hf (Kramm et al. 2011(Kramm et al. , 2012)). For an incompressible homogeneous planet, hf = 2.5 which is the theoretical maximum value (Leconte et al. 2011;Correia 2014). The physical values of hf range from 1 to 2.5 where hf = 1 would represent highly differentiated bodies with high core mass like FGK stars and hf = 2.5 is only possible for significantly homogeneous bodies like asteroids. In comparison, Jupiter has hf ≈ 1.5 and Earth has hf ≈ 2 [START_REF] Yoder | Global Earth Physics: A Handbook of Physical Constants[END_REF].

A first observational measurement of the Love number of Saturn was recently obtained by Lainey et al. (2017) leading to a value of hf = 1.39 (from k f = 0.39). Due to the synchronous rotation, the semi-principal axis a of the planet always points in the direction of the star leading to a tidal deformation along a. The shape of the planet is such that a > b > c and the deformation is kept constant along the circularized orbit. For the ellipsoid, we can define also the radius of a sphere that will enclose the same volume as the ellipsoid so that Rv = (abc) 1/3 . According to the formulation by Correia (2014), the semi-principal axes are related as a = b (1 + 3q) and c = b (1q). We can then write b as a function of Rv to first order in the parameter q as I 2 \

Modeling transit of deformed planets

2.1. Planet shape b � Rv so that 1 -3 q , (3)
Modeling the shape of a deformed planet follows the analytical formulation by Correia (2014) in which the planet is described by a triaxial ellipsoid centered at the origin of a Cartesian coordinate. As shown in Fig. 1, the semi-principal axes (a, b, c) of the ellipsoid are aligned with the X, Y, Z axes of the coordinate

a = b (1 + 3q) � Rv and I I 7 \ 1 + q 3 5 \ (4)
system, respectively. The equilibrium shape and mass distribu-c = b (1q) � Rv 1 -3 q , (5) tion of a planet depends on the forces acting on it, namely the planet's self gravity and other perturbing potentials. The planet 1 Available at https://pypi.org/project/ellc/ 2 hf = 1 + k f where k f is the fluid second Love number for potential (Correia et al. 2014). Calculation of the different Love numbers can be found in [START_REF] Sabadini | Global Dynamics of the Earth: Applications of Normal Mode Relaxation Theory to Solid-Earth Geophysics[END_REF] where q is an asymmetry parameter that relates to hf according to Table 1. System parameters for WASP-103b.

q = hf M * I Rv \ • (6) Quantity (Unit) Symbol Value 2 mp r0
The asymmetry parameter q quantifies the deformation of a planet, and is a measure of the difference between the semiprincipal axes of the ellipsoid. Maximum deformation (hence maximum q) is attained for a given planet when it orbits at the 1/3 Roche radius (R0) rR 3.7534

Roche radius (r0 = rR = 2.46 Rv[M * /mp] ). Therefore, for maximum hf = 2.5, we have qmax � 0.083. The equilibrium shape of a planet therefore depends on its radius, its fluid second Love number hf , the mass ratio between star and planet M * /mp, and also the distance from the planet to the star, r0.

Figure 2 shows how tidal deformation becomes negligible with semi-major axis (in units of its Roche radii) for a given body with hf = 2.5 and again with Jupiter's hf = 1.5. We see that far away from the star, irrespective of the value of hf , the planet does not deform (q � 0) and so its shape remains largely spherical (a � b � c from Eqs. (3)-( 5)). In general, Eq. ( 6) shows that tidal deformation is more relevant for large planets orbiting very close to their Roche radii. Planets with the highest absolute deformation (highest product q × Rv) provide the best chance to detect deformation.

Transit model

Planetary features that change the shape of a planet (oblateness or rings) have the effect of modifying the transit light curves (e.g., Barnes & Fortney 2003;Akinsanmi et al. 2018). In the same vein, tidal deformation of a planet can modify the observed transit light curve. To model the transit of a deformed planet, the above ellipsoidal shape model by Correia (2014) was incorporated as a subroutine into a new version of the ellc transit tool by [START_REF] Maxted | [END_REF]. The ellc light curve model allows the projection of the ellipsoid and generation of the corresponding transit light curve. The projected shape of the ellipsoid on the stellar disk is an ellipse whose dimensions depend on the phase of the planet due to rotation of the ellipsoid with phase (see Fig. A.1 in Correia 2014). The rotation of the ellipsoid causes the crosssection of the planet to vary during transit. It should be noted that the shape correction model by Budaj (2011) does not account for the varying ellipsoidal cross-section during transit, thereby making ellc a more complete model involving this observational effect. Detailed descriptions of the ellc tool and the input parameters can be found in [START_REF] Maxted | [END_REF].

The modified transit model, in addition to the usual transit parameters, takes the value of hf and the ellipsoid's volumetric radius Rv as inputs. Therefore, by fitting the ellipsoidal model to the transit observation, all the parameters of the transit can be obtained, including the shape of the planet, and hf is estimated from the best fit of the model. Therefore, rather than obtaining the usual transit radius Rspr from spherical planet models, we obtain the best-match dimensions a, b, c of the ellipsoidal planet and calculate Rv.

The case of WASP-103b

To illustrate the output of ellc for an ellipsoidal planet, we take the case of WASP-103b, an ultra-short-period planet (P = 22.2 hr) reported to be bordering on tidal disruption (Gillon et al. 2014) making it an ideal candidate to detect deformation. Based on revised parameters by Southworth & Evans (2016), WASP-103b has an average radius of 1.596 RJup and mass of 1.47 MJup (Table 1). It orbits its star at a semi-major axis (r0) of 0.01979 AU and an inclination (inc) of 88.2 • . It is assumed to be on the edge of tidal disruption due to its semi-major axis of only 1.13 times its Roche radius. Taking the quoted radius as the volumetric radius of the ellipsoid, Fig. 3 compares the spherical planet light curve for WASP-103b to its ellipsoidal counterparts with different hf values. It is seen that the light-curve of the ellipsoidal model changes noticeably for different values of hf and also compared to the spherical case. This is because the ellipsoidal planet projects only a small cross-section of its shape during the transit thereby leading to a lower transit depth when compared to the spherical planet. The mid-transit phase has the smallest ellipsoidal cross-section of bc � R 2 (1 -7q/3) which is less bottom panel and represents the signature of deformation for the simulated planet. The parameters derived from the fitting process are systematically incorrect as they adjust to mimic the signature of deformation. This also shows that the assumption of sphericity for a planet affects not only the radius derived but also the other transit parameters, and models that adjust only this radius are than the cross-section R 2 if the planet were spherical. There-incomplete. We see in the residuals that the signature of deforfore, if a spherical model is used to make a fit to the observation of an ellipsoidal planet, the spherical radius Rspr derived will be smaller than the actual volumetric radius Rv = (abc) 1/3 of the ellipsoid (see Fig. 4). This is in agreement with the result from Leconte et al. (2011). Differences in transit depth as hf varies in Fig. 3 are due to the fact that higher hf for the same planet causes more deformation, which leads to even smaller projected crosssectional area. In our code, we allow for a case where hf = 0 (although not physical) to imply no deformation for the planet so that the ellipsoidal planet model is equivalent to that of a spherical planet and they produce the same light-curve with Rv = Rspr. This is important for the analysis we perform in the following section and allows us to use the same model to explain both a deformed and a spherical planet. [START_REF] Maxted | [END_REF] already showed that the spherical light curve of ellc is in agreement with other transit tools like BATMAN (Kreidberg 2015).

Signature of deformation in transit light curves

Figure 1 in Correia (2014) showed difference plots between ellipsoidal and spherical light curves assuming both planets cover the same stellar area at the start of transit (full ingress). This perfectly captures the flux variation induced by deformation as both planets transit but is not the signature one would obtain from real observations, since the transit parameters would initially be unknown and would be determined from a fitting process. The observable signature of planet deformation is the residual between the light curve of the deformed planet and the best-fit spherical model. In Fig. 4, we simulated the light curve of deformed WASP-103b using our ellipsoidal model with parameters given in Table 1 and performed least-squares fitting using a spherical planet model. The residual from the fit is shown in the mation manifests in two regions. The first is at ingress and egress phases owing to oblateness (b > c) of the planet as identified in previous studies (e.g., [START_REF] Seager | [END_REF]Barnes & Fortney 2003). A second prominent feature is seen as a bump centered on the mid-transit phase due to the varying star eclipsed area caused by ellipsoid rotation as it transits. This second feature is as a result of tidal deformation which was not accounted for in the previous studies mentioned but manisfests in our model due to full projection of the ellipsoidal shape as it rotates with phase (Correia 2014).

To compare the deformation signal obtained from the fitting process with the flux difference plot in Correia (2014), we perform spherical fits to the ellipsoidal simulation of other shortperiod giant planets WASP-19b, WASP-12b, WASP-4b, and WASP-121b that were presented in the study and were expected to be deformed. The residuals are shown in Fig. 5. We see from Figs. 4 and 5 that the amplitude of the deformation signature is just about 40 ppm for the most deformed planets (WASP-103b and WASP-121b) while the amplitudes from the difference curves in Correia (2014) are up to 100 ppm. We reiterate that the latter should not be taken to imply high signal detectability.

WASP-103b, WASP-121b, and WASP-12b have the highest residual amplitudes and therefore present the best possibility of detecting deformation. Other planets likely to be deformed are HATS-18b, WASP-76b, and WASP-33b, but they have lower residual amplitudes of 20, 14, and 12 ppm, respectively.

Detectability of planet deformation and measurement of planet Love number

The residuals of the spherical fit to the light curve of a deformed planet is informative in detecting deformation as it shows that the max_abs_res=44.62 spherical model does not fully explain the observation. However,

2.5

Detectability plot for WASP-103b some of the signature of the deformation is masked in the errors Simulated h f value of the parameters obtained. To correctly estimate the planet transit parameters, our ellipsoidal model can be used to fit the transit observation. In doing so, we also obtain a value for the Love number that best fits the observation if there is enough precision in the data. The benefit of this approach is that we can fit the ellipsoidal model to any transit observation and, by the value of hf recovered, ascertain if planet deformation is detectable or not. If we cannot detect the deformation, we get hf ≈ 0 which as shown in Fig. 3 is equivalent to the fit of a spherical planet model.

Therefore, detectability of tidal deformation using the ellipsoidal model relies on the ability to recover a nonzero value of hf with statistical significance from a fitting process. Despite being able to infer deformation with only detection of hf » 0, 2.0 1.5 1.0 0.5 99.7% Credible Interval Median of hf samples and 68% Credible Interval we will need to have hf ≥ 1 with some significance where the values give actual physical interpretation to astronomical bodies. To illustrate the detectability, we created simulated observations of deformed WASP-103b with one-minute cadence using its parameters as stated above with hf = 1.5. We used the Limb darkening toolkit (ldtk) by Parviainen & Aigrain (2015) to compute quadratic limb darkening coefficients of [0.5343, 0.1299] and their uncertainties [0.0012, 0.0027] in the CHEOPS bandpass for the star with stellar parameters given in Gillon et al. (2014). We added random Gaussian noise of different levels to the simulated data in each test run. We then investigated how well we can recover the value of hf and at what noise level it would be impossible to distinguish between the light curve of a spherical planet and that of a deformed planet. This is important to know the instrumental precision necessary to detect deformation in close-in planets.

We performed Markov Chain Monte Carlo (MCMC) analysis to estimate the transit parameters and their uncertainties using the emcee package (Foreman-Mackey et al. 2013) with uniform priors on hf in the range [0, 2.5]. As shown in Appendix A.1, when a noise level of 30 ppm is added to the simulated observation, hf is reliably recovered, with 99.7% of its samples (within � ±3σ) greater than 1. This proves that the result is statistically significant and implies that the planet is indeed deformed. Moreover, the residual from the fit does not show any structure related to the deformation signal. However, when a noise level of 100 ppm is added to the observation the median of the distribution suggests a deformed planet, but because its width encompasses hf = 0 (spherical model), planet deformation cannot be asserted (Appendix A.2). Figure 6 shows the detectability plot summarizing the results for the different noise levels added to the observation. We see that the significance of hf detection above 1 reduces as the noise level of the observation increases. For instance, at 50 ppm noise level, hf samples are well above zero, implying that the ellipsoidal model provides a better fit than the spherical model. However, the samples with hf < 1 do not represent physical values for a planet but the detection still gives ∼95% of the samples above 1. Beyond 50 ppm, fitting the observation with a spherical model becomes increasingly more probable. With noise levels as high as 100 ppm, the spherical and ellipsoidal models produce comparable fits.

Discussion

The results show that noise levels below 30 ppm offer the best chance at detecting deformation for our test case of WASP-103b since we retrieve hf with ≥3σ significance above 1. However, we could define a lower limit on our detection confirmation such that we require to have (hf -1σ) ≥ 1 which puts 84% of the recovered hf samples in physical values expected for planets. This is satisfied for noise levels of 50 ppm and below.

A photometric precision of 50 ppm min -1 is not yet attainable using current observational instruments. For our case system, WASP-103 is a twelfth-magnitude star and the photometric precision to be attained by the near-future instrument CHEOPS for this star is 855 ppm min -1 . Attaining a reduced photon noise level of 50 ppm min -1 for this star using CHEOPS requires ∼293 transit observations of WASP-103b. For the interesting candidate WASP-121b, which orbits its star of magnitude mV = 10 ( Delrez et al. 2016), our analysis also showed detectability of deformation with 50 ppm min -1 noise level. CHEOPS precision for a tenth-magnitude star is 319 ppm min -1 thereby requiring only 40 transit observations to detect deformation in this planet. Although information from the CHEOPS consortium indicates that WASP-121 might not be in the visibility region, new interesting planet candidates with short period orbits may appear from future surveys targeting bright stars, such as PLATO (Rauer et al. 2014) and TESS (Ricker et al. 2015). For these planets around stars brighter than mV = 9, we expect photon noise levels as low as 150 ppm min -1 with CHEOPS (Broeg et al. 2013) and <62 ppm min -1 with PLATO (Rauer et al. 2014) and thus require fewer transits to reach the 50 ppm limit needed to detect planet deformation as reported in Table 2. For these stars, TESS will have a relatively higher noise level of 464 ppm min -1 (Sullivan et al. 2015) which is not desirable for detecting deformation. Observations with the forthcoming JWST will also be immensely beneficial as it is expected to attain photon-noise floor ∼40 ppm (65 s) on its NIRCam instrument amongst others (Beichman et al. 2014). Attainment of this noise level implies that only one transit observation will be required in order to detect tidal deformation in a suitable shortperiod planet.

Unfortunately, interesting short-period planets expected to be significantly deformed were not found within the original Kepler survey field which would have allowed several transit observations of any found target. The WFC3 instrument on the Hubble Space Telescope (HST) achieved a noise level of 172 ppm (103 s) Notes. Noise levels of CHEOPS were obtained from CHEOPS science team (priv. comm.) and that for PLATO was converted to ppm min -1 from Rauer et al. 2014 (Table 2 and Fig. 14).

for two full-orbit observations of WASP-103 (Kreidberg et al. 2018). Therefore, with ∼40 transits of WASP-103b using HST, we can attain the required precision of 50 ppm min -1 . However, some factors can still affect the detectability of deformation, some of which are mentioned below.

Temporal resolution. We used one-minute cadence in our simulations to enable good resolution of the ingress and egress phases which have short durations especially for these shortperiod planets. A lower cadence than this reduces the precision with which hf and other parameters are recovered. At the 30 ppm noise level, changing the cadence from 1 min to 4 mins and 8 mins increases the error on hf from ±0.12 to ±0.23 and ±0.38, respectively.

Orbital inclination. The inclination of the orbit plays a role in the signature of deformation. Lower inclinations indicate a shorter transit duration so the effects referred to in residuals of Fig. 4 and Sect. 2.4 will be shorter in time, making them more difficult to temporally resolve, especially at the ingress and egress phases. In addition, a longer transit duration allows the projected ellipse area to vary more (longer phase rotation of ellipsoid) making the light-curve more markedly different from that of the spherical planet thereby leading to a higheramplitude bump around mid-transit (see also Fig. A.1 in Correia 2014). The effects of deformation in light curves is maximal at an inclination of 90 • where hf is recovered with the best precision.

Limb darkening coefficients (LDCs). As shown in Fig. 4, the signature of deformation is prominent at ingress and egress phases with a bump centered around the mid-transit phase. The stellar limb-darkening affects light curves similarly in these regions (see effects of LDC modeling in Neilson et al. 2017), so we tested the impact of inaccurate estimation of limb-darkening coefficients on the recovery of hf from the light curve. This was attempted on the 30 ppm noise level simulation in two ways and the results are summarized in Table 3. First we fixed the limb darkening coefficients to incorrect values that are slightly different from the true values used to generate the simulated observation. We found that for incorrectly fixed LDC values that are smaller than the true values, the signature of deformation gets damped as we recover lower hf values than those simulated. When the values are fixed at values up to 0.01 smaller than the true values, the entire hf distribution falls around zero and we infer a spherical planet (see left plot in Fig. A.3). On the other hand, hf values are amplified when LDCs are fixed at values higher than the true values. For LDC values fixed at 0.015 higher than the true values, the recovered hf distribution is pushed towards the maximum of 2.5. In the latter case, we can σ = [0.0012,0.0027] Notes. The plots are shown in Figs. A.3 and A.4. infer that the planet is deformed but cannot ascertain the extent of deformation due to inaccurate estimation of hf which is evident from the obtained marginalized distribution (see right plot in Fig. A.3). The other attempt was to fit the LDCs by including them in the hyperparameters. We use a Gaussian prior with the true LDC values as mean and σ = 0.01. The MCMC sampling produced a wide hf distribution centered close to the true value but with errors as large as ±0.4 (left plot in Fig. A.4) making it difficult to ascertain planet shape. However, when tighter priors (e.g., using errors obtained from deriving LDCs with ldtk) are imposed on the LDCs, hf is well-recovered with errors of just ±0.18 to infer deformation (right plot in Fig. A.4). It should be noted that the LDC error estimates from ldtk are very small and have often had to be inflated in the literature during fitting to account for systematic errors in the atmospheric models (e.g., Raynard et al. 2018;Maxted & Hutcheon 2018).

Alternatively, the power-2 limb darkening law has been recommended for the analysis of transit light curves as it has been shown to provide remarkable agreement between stellar atmospheric models and observations, particularly for cool stars (Morello et al. 2017;Maxted 2018). The transformation of the two parameters of the power-2 law in Maxted (2018) reduces the correlation between them during fitting and small errors of [0.011, 0.045] can be obtained on them. The fitting process can attempt different LDC laws so that the law with the best match to the observation and that produces the least errors on the derived parameters will be preferred.

Other noise sources. Our simulations considered the ideal situation where only photon (white) noise is present thereby allowing easy scaling of the noise with the number of observations/transits. However, in practice, other sources of noise (Pont et al. 2006) will impact the estimates given above and act to increase the number of transits required to detect deformation. These other noise sources can be from instrumental effects (e.g., satellite jitter and thermal instability) and also from astrophysical sources such as stellar activity (occulted or unocculted active regions; [START_REF] Oshagh | [END_REF], stellar oscillations and granulation [START_REF] Chiavassa | [END_REF]. These effects always have to be mitigated in transit analysis [START_REF] Oshagh | Asteroseismology and Exoplanets: Listening to the Stars and Searching for New Worlds[END_REF]Barros et al. 2014) but will still impact the detectability of shape deformation. Recent developments in Gaussian process analysis also provide a method for tackling astrophysical noise (e.g., Foreman-Mackey et al. 2017;Serrano et al. 2018).

Conclusion

Short-period planets, especially within two Roche radii from the host star, suffer from extreme tidal forces causing their shapes to depart from sphericity in a way that is difficult to detect in transit observations. With the increasing observational precision of near-future instruments, detecting deformation becomes more feasible as planet shape will have a higher impact on the observed transit light curves. We demonstrate detectability of deformation for WASP-103b and WASP-121b (which have the highest deformation signatures as seen in Sect. 2.4 and are regarded as some of the most deformed planets; Delrez et al. 2016) by employing a formulation from the literature in a way that allows an observational estimate of a planet's fluid Love number to be obtained. Because the Love number tells us how a planet deforms in response to perturbing potentials, we used it as a measure of deformation in the planet. Detecting and measuring planet deformation provides more accurate estimations of the radius and density of these planets as opposed to the estimates derived from spherical models or corrections calculated from only expectation of deformation. Additionally, measuring the Love number provides information about the interior structure of the planet. We showed that the instrumental precision needed to detect tidal deformation is ≤50 ppm which can be attained by CHEOPS with about 300 transits for WASP-103b and 40 transits for WASP-121b. The HST can also attain this precision for WASP-103b in approximately 40 transit observations. Fewer transit observations will be required if such short-period planets are found transiting very bright stars. Additionally, the precision expected from JWST will present the best opportunity to detect tidal deformation since only one transit of a suitable planet will be required. The chances of detecting deformation are increased for planets with inclinations of 90 • and also when the observations are taken with temporal resolution of ∼1 min. However detection can be severely hampered by improper modeling of the limb darkening which, in some cases, can cause the signature of deformation to be subdued, leading us to infer sphericity from the observations. Using the quadratic limb-darkening law, LDC errors smaller than 0.01 are required in order to confirm planet deformation. Proper treatment of noise sources will also be pertinent in order to identify the signature of shape deformation.

Fig. 1 .

 1 Fig. 1. Schematic of triaxial ellipsoid centered on the origin of the Cartesian coordinate system (X, Y, Z) with positive X-axis pointing towards the star.

Fig. 3 .

 3 Fig. 3. Comparison of ellipsoidal model light curves of different hf values with spherical model light curve for WASP-103b.

Fig. 4 .

 4 Fig. 4. Spherical fit to simulated deformed WASP-103b light curve. The bottom plot shows the residual representing the signature of deformation with amplitude quoted as the maximum absolute residual (max_abs_res). All length measurements are given in units of solar radii.

Fig. 5 .

 5 Fig. 5. Residuals from spherical fit to ellipsoidal simulations of different short-period planets in comparison to WASP-19b, 12b, and 4b from Correia (2014).

  ] Residual [ppm] Residual [ppm] ellipsoid simulated: Rv = (abc) 1/3 = 0. 1604, r0 = 4. 2555, inc = 88. 2, hf = 1. 5 Spherical fit: Rspr = 0. 1545, r0 = 4. 2214, inc = 87. 0180

Fig. 6 .

 6 Fig. 6. Detectability of deformation in WASP-103b considering different noise levels. The black dashed line is the simulated hf value. The points are the median of the hf samples at each noise level. The red error bars show the 68% credible interval (� ±1σ) while the blue error bars show the 99.7% credible interval (� ±3σ).

  .

		0.08					hf = 1.5 hf = 2.5	1.000
		0.06
								0.995
	q	0.04
								0.990
		0.02
		0.00	1	2	3 Semi-major axis [Roche radii] 4	5	6	0.985	0.05	0.00 Orbital Phase	0.05
	Fig. 2. Quantification of tidal deformation as a function of distance to
	the star for two different hf values.

Table 2 .

 2 Number of transits required to reach 50 ppm min -1 noise level with CHEOPS and PLATO for different stellar magnitudes.

		CHEOPS			PLATO
	mV	Noise/min	# transits	mV	Noise/min	# transits

Table 3 .

 3 Results of LDC tests and hf values recovered.

	LDC tests	Values	hf recovered
	Fixed at 0.01 below Fixed at 0.015 higher [0.5493,0.1449] [0.5243,0.1199] Gaussian priors Mean [0.5343,0.1299], σ = [0.01, 0.01] Gaussian priors Mean = [0.5343,0.1299],	0.12 +0.11 -2.44 +0.04 -0.06 1.56 +0.31 -0.53 1.59 +0.18 -

Acknowledgements. This work was supported by Fundação para a Ciência e a Tecnologia (FCT, Portugal) through national funds and by FEDER through COMPETE2020 by these grants UID/FIS/04434/2013 & UID/MAT/04106/2013 and POCI-01-0145-FEDER-007672 & PTDC/FIS-AST/1526/2014 & POCI-01-0145-FEDER-016886 & POCI-01-0145-FEDER-022217 & POCI-01-0145-FEDER-029932 & POCI-01-0145-FEDER-028953 &l POCI-01-0145-FEDER-032113. We also acknowledge support from FCT (Portugal) and POPH/FSE (EC) through fellowship PD/BD/128119/2016. NCS and SCCB also acknowledge support from FCT through Investigador FCT contracts IF/00169/2012/CP0150/CT0002 and IF/01312/2014/CP1215/CT0004 respectively. BA acknowledges support from FCT through the FCT PhD programme PD/BD/135226/2017. BA also thanks the LSSTC Data Science Fellowship Programme; his time as a fellow has benefited this work.


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Differentiation Capacity of Monocyte-Derived Multipotential Cells on Nanocomposite Poly(e-caprolactone)-Based Thin Films

Keywords: multipotential cells, Poly(e-caprolactone), Silica nanotubes, Strontium hydroxyapatite nanorods

BACKGROUND: Lonocyte-derived multipotential cells (MOMCs) include progenitors capable of differentiation into multiple cell lineages and thus represent an ideal autologous transplantable cell source for regenerative medicine. In this study, we cultured MOMCs, generated from mononuclear cells of peripheral blood, on the surface of nanocomposite thin films. METHODS: For this purpose, nanocomposite Poly(e-caprolactone) (PCL)-based thin films containing either 2.5 wt% silica nanotubes (SiO 2 ntbs) or strontium hydroxyapatite nanorods (SrHAnrds), were prepared using the spin-coating method. The induced differentiation capacity of MOMCs, towards bone and endothelium, was estimated using flow cytometry, real-time polymerase chain reaction, scanning electron microscopy and fluorescence microscopy after cells' genetic modification using the Sleeping Beauty Transposon System aiming their observation onto the scaffolds. Moreover, Wharton's Jelly Mesenchymal Stromal Cells were cultivated as a control cell line, while Human Umbilical Vein Endothelial Cells were used to strengthen and accelerate the differentiation procedure in semi-permeable culture systems. Finally, the cytotoxicity of the studied materials was checked with MTT assay. RESULTS: The highest differentiation capacity of MOMCs was observed on PCL/SiO 2 ntbs 2.5 wt% nanocomposite film, as they progressively lost their native markers and gained endothelial lineage, in both protein and transcriptional level. In addition, the presence of SrHAnrds in the PCL matrix triggered processes related to osteoblast bone formation. CONCLUSION: To conclude, the differentiation of MOMCs was selectively guided by incorporating SiO 2 ntbs or SrHAnrds into a polymeric matrix, for the first time.

Introduction

As our population ages and life expectancy increases there is a great need for research in the field of regenerative medicine. Stem cell and biomaterial based therapies are being actively investigated [START_REF] Dawson | Biomaterials for stem cell differentiation[END_REF][START_REF] Keane | Biomaterials for tissue engineering applications[END_REF][START_REF] O'brien | Biomaterials & scaffolds for tissue engineering[END_REF]. The key is to find the best combination of biomaterials and cell lines in order to regenerate specific tissues [START_REF] Vacanti | Tissue engineering and regenerative medicine: from first principles to state of the art[END_REF][START_REF] Howard | Tissue engineering: strategies, stem cells and scaffolds[END_REF]. Both Human Bone Marrow Mesenchymal Stromal Cells (hBMSCs) and Human Wharton's Jelly Mesenchymal Stromal Cells (WJSCs) have the potential of regeneration [START_REF] Chen | Mesenchymal stem cells: a promising candidate in regenerative medicine[END_REF][START_REF] Bianco | Mesenchymal'' stem cells[END_REF]. BMSCs' and WJSCs' collection has no ethical concerns, unlike embryonic stem cells (ESCs), share few embryonic features, have high cell proliferation rate and wide differentiation potential while they are hypo-immunogenic and non-tumorigenic [START_REF] Shamsi | In vitro proliferation and differentiation of human bone marrow mesenchymal stem cells into osteoblasts on nanocomposite scaffolds based on bioactive glass (64SiO 2 -31CaO-5P 2 O 5 )-poly-L-lactic acid nanofibers fabricated by electrospinning method[END_REF][START_REF] Kim | Wharton's jelly-derived mesenchymal stem cells: phenotypic characterization and optimizing their therapeutic potential for clinical applications[END_REF].

Nevertheless, both hBMSCs and WJSCs present the disadvantage of harvest. Harvest of hBMSCs involves an invasive procedure, while WJSCs need to be harvested during birth [START_REF] Abdallah | Human mesenchymal stem cells: from basic biology to clinical applications[END_REF]. During the last years a new cell line, isolated by Seta and Kuwana called Lonocyte-derived Multipotential Cells (MOMCs) has shown potential to differentiate into multiple cell lineages in a specific permissive environment and thus represent an autologous transplantable cell source for regenerative medicine [START_REF] Seta | Human circulating monocytes as multipotential progenitors[END_REF][START_REF] Seta | Derivation of multipotent progenitors from human circulating CD14? monocytes[END_REF][START_REF] Kuwana | Human circulating CD14? monocytes as a source of progenitors that exhibit mesenchymal cell differentiation lineages[END_REF][START_REF] Kuwana | Endothelial differentiation potential of human monocytederived multipotential cells[END_REF]. MOMCs are a human-derived cell population with a fibroblast-like morphology characterized by a unique immunophenotype positive for CD14, CD45, CD34 and type I collagen. MOMCs have the capacity to differentiate into a variety of mesenchymal cell types including endothelial and osteogenic cells and can be easily harvested from circulating blood [START_REF] Seta | Plateletderived stromal cell-derived factor-1 is required for the transformation of circulating monocytes into multipotential cells[END_REF][START_REF] Seta | Fibronectin binding is required for acquisition of mesenchymal/ endothelial differentiation potential in human circulating monocytes[END_REF].

In the present study, we investigated the differentiation capacity of MOMCs on the surface of nanocomposite thin films based on poly(e-caprolactone) (PCL), reinforced either with 2.5 wt% silica nanotubes (SiO 2 ntbs) or strontium hydroxyapatite nanorods (SrHAnrds). PCL is a biodegradable aliphatic polyester with many biomedical applications because of its biocompatibility and its modifiable properties. PCL also plays an increasingly important role in tissue engineering because it can be fashioned into porous scaffolds or carriers of cells, extracellular matrix components and bioactive agents. Since all living systems are governed by molecular behavior at nanoscale, the introduction of a nanoscopic reinforcing phase to PCL matrix offers great possibilities of obtaining improved biological properties. As a result, nanometer structural components could be considered promising biomaterials [START_REF] Chrissopoulou | Effects of nanoscopic-confinement on polymer dynamics[END_REF][START_REF] Peters | Nanoscopic medicine: the next frontier[END_REF][START_REF] Grigoriadou | Evaluation of silica-nanotubes and strontium hydroxyapatite nanorods as appropriate nanoadditives for poly(butylene succinate) biodegradable polyester for biomedical applications[END_REF][START_REF] Abedalwafa | Biodegradable polyepsilon-caprolactone (PCL) for tissue engineering applications: a review[END_REF][START_REF] Nerantzaki | Novel poly(butylene succinate) nanocomposites containing strontium hydroxyapatite nanorods with enhanced osteoconductivity for tissue engineering applications[END_REF].

Silica-based nanoparticles (NPs) have been widely used in the field of biomaterials science since 1970s, when several studies revealed the requirement of silicon in bone development [START_REF] Nerantzaki | Design of a multifunctional nanoengineered PLLA surface by maximizing the synergies between biochemical and surface design bactericidal effects[END_REF][START_REF] Elzein | FTIR study of polycaprolactone chain organization at interfaces[END_REF]. As silica plays an important role in skeletal tissue formation, bioactive silica has been used in order to produce bioactive glasses. When implanted into the body, bioactive glass bonds with the surrounding tissue without promoting inflammation or forming fibrous tissue [START_REF] Chen | One-step synthesis of functional chiral porous silica nanorods using an achiral surfactant[END_REF]. The biological role of strontium has been well documented including its effects on bone cells (up-regulation of osteoblasts and down-regulation of osteoclasts). Oral administration of strontium has also been shown to increase bone density and reduce fracture risk in osteoporotic patients. Recent studies have published on other delivery methods of strontium in the form of bioactive glasses, Sr-HA and Sr-containing cements [START_REF] Xue | Hydrothermal synthesis and biocompatibility study of highly crystalline carbonated hydroxyapatite nanorods[END_REF][START_REF] Koliakos | Mesenchymal cells isolation from Wharton's jelly, in perspective to clinical applications[END_REF]. The advantages of biomaterial incorporation of strontium include the local and controlled release of the Sr-ion [START_REF] Nerantzaki | Novel poly(butylene succinate) nanocomposites containing strontium hydroxyapatite nanorods with enhanced osteoconductivity for tissue engineering applications[END_REF]. The use of microfabrication technique in silicon and Pyrex to generate hepatic tissue and vascular tissue may be able to be combined to form thick, three-dimensional vascularized tissues. Using standard photolithography techniques, trench patterns reminiscent of branched architecture of vascular and capillary networks were etched onto silicon and Pyrex surfaces to serve as templates. With the use of microfabrication technology in tissue engineering, it now seems feasible to consider lifting endothelial cells as branched vascular networks from two-dimensional templates that may ultimately be combined with layers of parenchymal tissue, such as hepatocytes, to form three dimensional conformations of living vascularized tissue for implantation [START_REF] Kaihara | Silicon micromachining to tissue engineer branched vascular channels for liver fabrication[END_REF]. In brief, the released ionic dissolution products are capable of enhancing proliferation and differentiation of bone cells and inducing angiogenesis.

Thus, in the present study by incorporating SiO 2 ntbs or SrHAnrds in the PCL matrix by applying the spin-coating method, we expect to improve the ability of PCL to selectively guide the differentiation capacity of MOMCs. WJSCs are used as a control cell line in order to compare the differentiation potential of MOMCs with WJSCs respectively. We also use Human Umbilical Vein Endothelial Cell line (HUVEC) [START_REF] Skaat | Magnetic scaffolds enriched with bioactive nanoparticles for tissue engineering[END_REF] to strengthen and accelerate MOMCs differentiation to endothelium given that, in contrast to WJSCs, MOMCs are unable to be maintained in cell culture for a long time [START_REF] Seta | Plateletderived stromal cell-derived factor-1 is required for the transformation of circulating monocytes into multipotential cells[END_REF][START_REF] Tuan | Adult mesenchymal stem cells and cell-based tissue engineering[END_REF]. The presence of HUVEC in a new semi-permeable co-culture system with MOMCs, ensures that in a limited time this easily collected category of stem cells could be exploited for autologous transplantation of a scaffold for endothelium regeneration [START_REF] Meng | Stem cells in a threedimensional scaffold environment[END_REF][START_REF] Patrı ´cio | Characterisation of PCL and PCL/PLA scaffolds for tissue engineering[END_REF].

To our knowledge this is the first study on the effect of nanophase reinforcement such as SiO 2 ntbs and SrHAnrds, on the capacity of MOMCs to differentiate on nanocomposite materials based on PCL. Therefore, this paper will provide practical guidance for rationally designing nanocomposite PCL films for multiple applications in regenerative medicine.

Materials and methods

Materials

PCL with average Mn * 65,000 g/mol and glass slides (plain, size 25 mm 9 75 mm), were purchased from Sigma-Aldrich (St.Louis, MO, USA). Chloroform (CHCl 3 ) (99.5%), was supplied from Chem-Lab NV (Zedelgem, Belgium). Sulfuric acid (H 2 SO 4 ) (95-98%) and hydrogen peroxide (H 2 O 2 ) (solution 110 vol, 30%w/w) were supplied from Scharlab S.L. (Barcelona, Spain). Phosphate Buffer Saline (PBS) was used as purchased from Sigma Aldrich (St. Louis, MO, USA). DMEM high glucose w/Lglutamine w/sodium pyruvate, penicillin-streptomycin solution 100X, fetal bovine serum (FBS) and trypsin-EDTA 1x in PBS were purchased from BIOSERA (Kansas city, MO, USA), Osteogenesis medium from GIBCO-BRL (Grand Island, NY, USA) while the (3-(4,5-dimethylthiazol-2-yl)-2,5-diphenyltetrazolium bromide) powder-MTT, hydrogen peroxide, uric acid, 3,3 0 ,5,5 0 -tetramethylbenzidine (TMB) tablets, Histopaque and DMSO from Sigma Aldrich (St. Louis, MO, USA).

Cell lines

The collection of biological samples from different sources for this study approved by the Ethics Committee of Aristotle University of Thessaloniki, School of Medicine (390-9/1.7.2017) and University Hospital AXEPA of Thessaloniki (3868/24.1.2018) as described below in ethical statement section.

Optimized harvest, culture and characterization of MOMCs

The blood sampling of the healthy volunteer donors was performed after their endorsed consent. More precisely, 10 ml of peripheral blood were collected in anti-coagulant CPD and upon dilution in 20 ml of PBS were loaded in the half volume of Ficoll Paque. She mononuclear cell layer (Peripheral blood mononuclear cells-PBMCs) was collected upon centrifugation at 700 g for 20 min, with no brakes added. 1.5 9 10 6 PBMCs in DMEM complete media supplemented with 50 ng/ml SDF-1a (Millipore, MA, USA) were plated in a 6-well plate pre-coated overnight with either fibronectin or poly-L-lysine in gelatin. The cells were incubated for 12-14 days in 37 °C with 5% CO 2 with SDF-1a enriched media changes every 2 days. Aiming the characterization of the harvested cells, flow cytometry was performed for the detection of typical surface marker expression. Briefly, upon detachment of cells with Trypsin-EDTA 1x in PBS and mild centrifugation, staining with monoclonal antibodies (mAbs) CD45, CD14, CD34, Collagen type I and CD184 (BD Biosciences, San Jose, CA USA) was performed for 15 min in the absence of light and finally analysis in BD FACS Calibur (BD Biosciences, San Jose, CA USA).

Harvest, culture and characterization of WJSCs

35 cm of umbilical cord were collected after the parents endorsed consent in a sterilized box. Following a normal saline wash and a mild cut up with a lancet, an overnight lysis with 4 mg/ml collagenase and 2 mg/ml dispase contained in PBS in a stirring incubator was performed. The next day, the mixture was filtered through a 70 lm Filter Unit and was subsequently centrifuged in 850 g for 10 min in RT. The pellet was re-suspended in DMEM media supplemented with 10% FBS ? 1% penicillin/streptomycin (DMEM full medium) and was then plated in culture flasks for 72 h until the full cell adherence in a 37 °C incubator with 5% CO 2 . Following media changes every 2-3 days and after 2-3 passages, the cells were characterized via flow cytometry for the expression of the CD90-CD105 markers and the absence of the CD45-CD34 markers.

Genetic modification of the WJSCs with venus plasmid via the Sleeping Beauty Transposon system

By applying genetic modification to WJSCs we enable the observation of our cells on scaffolds via fluorescence microscopy. The generation of a cell line capable of stable expression of green fluorescence, allow us to check the gradual differentiation of our cells throughout the culture. Between the 4-5 passage a Pt2-Venus-neo mediated nucleofection was performed. Lore precisely, 4 9 10 5 cells were mixed with 7.5 lg of plasmid DNA SB100X transposase and pT2-Venus-neo transposon expression plasmids (1:10 ratio) and were electroporated according to the manufacturer's instructions (Lonza, Basel, Switzerland). The cells were then plated in one well of a 6-well plate in the presence of DMEM full medium until reaching a 90% confluency, whereas 100 mg/ml G418 (InvivoGen, San Diego, CA, USA) was added for the selection of the genetically modified WJSCs. The cells were incubated in 37 °C with 5% CO 2 and were subjected to media changes every 2-3 days.

Isolation, characterization and culture of HUVEC

20-25 cm of umbilical cord near the placenta height, were collected after the parents endorsed consent in a sterilized box. Following a double saline wash, the umbilical cord was placed in a plastic surface with its both ends cut transversely with a lancet, in order for the umbilical vein to be visible from both sides. After a mild restrain with the use of a pincher, a wash with PBS was performed 3 times from every side of the umbilical cord in the internal side of the vein using a 5 ml syringe and 18G needle. Subsequently, the one side of the vein was wide shut and in the one a PBS solution supplemented with 25 mg collagenase was added, preheated in 37 °C for 30 min, until the complete filling of the vein cavity. After the closure of the open side, the umbilical cord was cautiously transferred in a preheated saline solution in 37 °C for 15 min. Upon the complete incubation and the opening of the one side, the content of the vein was collected following mild massages while 3 washes with PBS were performed from every side and the content was also collected. After a centrifugation at 700 g for 15 min in RT, the pellet was resuspended in Endothelial Cell Growth Medium (Lonza, Basel, Switzerland) and was subsequently plated in a T-25 culture flask and incubated in 37 °C with 5% CO 2 with media changes every 2-3 days. The cells were then characterized via flow cytometry for the expression of the CD144 surface marker.

Preparation and characterization of PCL nanocomposite thin films by spin-coating

Evaluation of the cytotoxicity levels SiO 2 ntbs and SrHAnrds

In order to assess the cytotoxicity levels of SiO 2 ntbs and SrHAnrds which were synthesized by the sol-gel method and a hydrothermal treatment, according to a process that has been described by us in detail previously [START_REF] Nerantzaki | Design of a multifunctional nanoengineered PLLA surface by maximizing the synergies between biochemical and surface design bactericidal effects[END_REF]. Prior to cell plating, WJSCs cells were exposed to both type of NPs and the MTT assay was carried out for 24 and 72 h. As day 0 was defined as the NP's addition in the culture supernatants at three different concentrations: 10, 100 and 200 lg/ml in DMEM. For the sterilization of the solutions, 0.22 lm filter units were used. Non-NP treated cells were used as a control group in the same number as the other groups. Briefly, after the medium removal from the wells, MTT reactant was introduced in a ratio of 1:10 in DMEM culture medium and was followed by a 4 h incubation in 37 °C with 5% CO 2 . Upon the removal of the MTT, 1 ml/ well of DMSO was introduced for one additional hour of incubation in the same conditions. The optical density of MTT formazan deposits was quantified by a spectrophotometer at 570 nm and 630 nm wave length (PerkinElmer, Waltham, MA, USA).

Preparation of PCL nanocomposite thin films by spin-coating

Nanocomposites based on PCL matrix (PCL/SiO 2 ntbs 2.5 wt% and PCL/SrHAnrds 2.5 wt%) were prepared according to the following procedure. Firstly, PCL was dissolved in CHCl 3 to form a 10 wt% solution using magnetic stirring for 2 h at room temperature. At the same time, SrHAnrds and SiO 2 ntbs, were weighted to achieve the desired final concentration (2.5 wt% based on the weight of the composite material) and dispersed separately using magnetic stirring for 2 h and ultrasonication for 20 min. In the second step, both the polymer solution and the suspensions of NPs were mixed, stirred and sonicated (15 min) to form nanocomposites with 2.5% weight fraction. The produced nanocomposite PCL films were spincoated on glass substrates (slides), cut into 2 cm 9 2 cm square-pieces. Several coating speeds were tested to achieve the desired thickness which was dependent on the used featured height. Prior to spin coating piranha solution (3:1 mixture of H 2 SO 4 H 2 O 2 30%.) was used to clean organic residues off substrates and to enhance the polymer adherence. For comparison purposes pure PLC films were also prepared using a similar process.

Chemical characterization by Fourier transform infrared spectroscopy (FTIR)

To evaluate the chemical composition of the nanocomposite samples obtained by the spin-coating process, the PCL/SiO 2 ntbs 2.5 wt% and PCL/SrHAnrds 2.5 wt% nanocomposite films and their pure components: PCL (as spin-coated polymer thin film), SiO 2 ntbs and SrHAnrds (in powdered form) were examined using Fourier transform infrared spectroscopy (FTIR). FTIR spectra were obtained using a Perkin-Elmer FTIR spectrometer, model Spectrum One, in absorbance mode, in the spectral region of 400-4000 cm -1 , using a resolution of 4 cm -1 and 64 coadded scans.

Differentiation towards bone and endothelium

Cell culture plating

Neat PCL films and the nanocomposites incorporating SiO 2 ntbs or SrHAnrds, cut into pieces (10 mm 9 10 mm squares) were sterilized in gradually reduced ethanol concentrations (100%-70%-50%) and after being washed three times with ddH 2 O were let to air dry for 4 h under sterile conditions. Fibrin glue was prepared after the blood sampling of a healthy volunteer donor. 15 ll of fibrin glue per film were placed in the bottom of a 24-well plate and the materials were seeded using a sterile pincher from above by applying minimal manual pressure and were let to air dry overnight under sterile conditions.

WJSCs were detached using Trypsin-EDTA 1x in PBS and were counted in a Neubauer cell counting chamber. 3 9 10 5 cells were re-suspended in DMEM full medium and were subsequently placed above the films of each condition. Upon air drying for 4 h in the incubator 1 ml DMEM full medium was added per well for the culture initiation. For the adherence of the MOMCs in the upper PCL surface 3 days before the completion of the culture (day 8-9), a mild detachment using Trypsin-EDTA 1x in PBS was performed and transfer without centrifugation in pre-coated with 0.1% poly-L-lysine in gelatin PCL films. 4 9 10 5 cells dissolved in DMEM full medium enriched with SDF-1a were plated per PCL film and were let to air dry as described above for the WJSCs. After 48 h the medium was changed for the final time towards the culture completion.

2.6.2 Induction of differentiation 2.6.2.1 Induction of differentiation towards endothelium Aiming the cell differentiation towards endothelial ones, endothelial cell growth medium was added in the WJSCs that covered the PCL film surfaces in a confluency of approximately 80% for 32 days with medium changes every 2-3 days and incubation in 37 °C with 5% CO 2 . As for the attached MOMCs respectively, the induction was introduced 2 days before the completion of their 12 days generation culture and lasted 14 days with differentiation medium changes every 2-3 days in the same conditions as the WJSCs. Solely plated cells in plastic surfaces were used as a control group in the same number as the rest of the groups.

Aiming the amplification of the inducted MOMC differentiation towards endothelium, 2 9 10 5 HUVEC cells were counted and plated per well in the upper department of semi-permeable transwell membrane systems. 0.2 ll of endothelial cell growth medium were introduced in the start of the differentiation and remain until the first change of medium.

Induction of differentiation towards bone

The induction of differentiation towards bone cells was accomplished by introducing osteogenesis medium in the culture additionally to the endothelial growth medium in both WJSCs and MOMCs for 28 days. Cells plated in plastic surfaces were used as a control group, in the same number as the rest of the other groups.

Evaluation of differentiation

Fluorescent microscopy

The observation of the cells above the materials was performed in a fluorescence microscope 0, 14 and 30 days upon their attachment upon the films until the completion of the inducted differentiation for every cell line. HBO 50 mercury lamp as well as reflectors with fluorescence filter (excitation 488 nm, emission 509 nm) were used while the program for the download and editing of the photos was the Fluorescence Lite software module of AxioVision LE (Carl Zeiss, Oberkochen, German).

Scanning electron microscope (SEM)

All the included materials were fixed in 4% Paraformaldehyde for 20 min in RT and were subsequently let to air dry overnight. All materials and controls were covered with carbon black and observed with JEOL type SEM (JMS-840, Peabody, MA, USA), in 20 kV acceleration, electric current 45 nA and counting time 60.

Monitoring of the immunophenotypical differentiation potential with flow cytometry

The differentiation capacity of both WJSCs and MOMCs towards endothelial cells was estimated in the 0, 3, 14 and 31 days and 0, 3 and 14 days respectively via flow cytometry for the co-expression of the CD45/CD144 surface markers as described above.

Evaluation of the differentiation capacity in transcriptional level with real-time PCR

Aiming the comparison of the expression levels of genes related with self-renewal (CD34) and differentiation towards endothelial cells (CD144, VEGF) in all the includes types of films for both WJSCs and MOMCs, realtime polymerase chain reaction (PCR) with the use KAPA SYBR Ò FAST one step qPCR Master Mix (2X) Kit was performed. More precisely, 0, 14 and 30 days upon differentiation, the cells were detached by using 0.05% Trypsin-EDTA followed by RNA extraction procedure according to the manufacturer's instructions (Macherey-Nagel, Du ¨ren, Germany) and a subsequent RNA quantification in a NanoDrop ND-1000 UV-Vis Spectrophotometer. After a cautious primer design as well as HPLC Purification (Lab Supplies, Athens, Greece), Q-PCR for 10 ng of RNA template was performed, the results of which were analyzed by using ddCt algorithm for the analysis of the relative changes in gene expression.

Control of the osteogenesis induction with alizarin red staining

The successful induction of differentiation towards bone cells was verified with Alizarin Red staining. The quantification of the procedure was carried out with 10% cetylpyridinium chloride (CPC) in 10 nM sodium phosphate, pH 7.0 for 15 min in RT. She extracts were 10 times dissolved in 10% CPC and the optical density was counted in 562 nm wave length in a Perkin Elmer spectometer.

Statistical analysis

Data are presented as the mean ± SD and the Student's t test (unpaired, two-tailed) was used for the two-group comparisons. Differences were considered statistically significant at a value of p B 0.05.

Results

Cell lines

WJSCs and HUVEC characterization

Upon the completion of the cultures, the WJSCs displayed a typical fibroblast like-morphology before and after the genetic modification (Fig. 1A) and were additionally characterized by the co-expression of the CD90/CD105 markers as well as the absence of hematopoietic markers (CD45-/CD34-) as expected (Fig. 1B). The HUVEC cell line, respectively, displayed an endothelial cell like-morphology (Fig. 1A) while, approximately in total, expressed the endothelial marker CD144 following its successful adherence upon the plastic surface (Fig. 1B).

Optimization of MOMCs culture

The cultivation of MOMCs in plastic surfaces coated with poly-L-lysine in gelatin leads to the isolation of a morphologically more purified cell population in contrast to the cultures of MOMCs on fibronectin layer, where except of the MOMCs isolation, cells with different morphology such as macrophages, are also observed. The adherence of a specific cell population allow as to perform differentiation tests to specific cell subpopulations (Fig. 2A). The Poly-L-lysine/gelatin cultivated MOMCs were characterized by high expression of the CD45/CD14/CD34/CD184/ Col I markers (Fig. 2B). The efficient and successful MOMCs growth in the improved and novel coating medium, combined with the addition of the SDF-1a chemotactic factor, augmented the adherence capacity of the MOMCs, aiming their subsequent adherence upon the biomaterials.

In vitro cytotoxicity assay by MTT and chemical characterization by FTIR

MTT assay of SiO 2 ntbs and SrHAnrds incubated with WJSCs

SiO 2 ntbs and SrHAnrds displayed no significant toxicity upon their addition, even in high concentrations, in WJSCs cultures after 24 h (Fig. 3A). Even 72 h after SrHAnrds initiation in the culture and also in the maximum concentration of 200 lg/ml, NPs-mediated cytotoxicity was not observed (Fig. 3A). This rather non-cytotoxic activity of the tested NPs had therefore led us to the next step of their incorporation upon PCL films.

Study of chemical composition by FTIR

In this study, FTIR was used to examine the incorporation of SiO 2 ntbs and SrHAnrds into the PCL biopolymer matrix by the spin-coating technique. Figure 3B shows the FTIR absorption spectra of PCL/SiO 2 ntbs 2.5 wt% and PCL/ SrHAnrds 2.5 wt% nanocomposite films. The FTIR spectra of pure SiO 2 ntbs, SrHAnrds and PCL are also presented in Fig. 3B, for comparison purposes. In the spectrum of PCL/ SiO 2 ntbs 2.5 wt% the band broadening at 2942 and 2862 cm -1 (assigned to asymmetric and symmetric stretching of CH 2 groups of PCL) and at 1723 cm -1 (due to the carbonyl stretching vibration of PCL) can be seen as an is evidence of chemical interactions between the components (Fig. 3B) [START_REF] Elzein | FTIR study of polycaprolactone chain organization at interfaces[END_REF]. Additionally, while the characteristic band of the silica network (symmetric and asymmetric -Si-O-Si-stretching at 1100 cm -1 and 473 cm -1 , respectively) can't be observed in the spectrum of PCL/ SiO 2 ntbs 2.5 wt% sample, because PCL has multiple bands in the same spectral region, some new bands which could be attributed to O-H stretching for the silicate, arise at 3633 and 3385 cm -1 [START_REF] Chen | One-step synthesis of functional chiral porous silica nanorods using an achiral surfactant[END_REF]. In Fig. 3B, the spectrum of PCL/SrHAnrds 2.5 wt% the broadening of the characteristic bands of PCL at 3000-2850 cm -1 and at 1723 cm -1 (due to asymmetricsymmetric stretching of CH 2 groups and stretching vibration of C=O group, respectively) is critical for the presumed intramolecular interaction between the nanofiller and the polymer matrix. As before, multiple overlapped peaks were detected and the characteristic absorption bands of the apatite (at 1082, 1017, 598 and 561 cm -1 , due to the asymmetric stretching and bending vibrations of O-P-O in PO 4

3-groups) can't be seen in the spectrum of the nanocomposite PCL/SrHAnrds 2.5 wt% sample [START_REF] Xue | Hydrothermal synthesis and biocompatibility study of highly crystalline carbonated hydroxyapatite nanorods[END_REF]. Nevertheless, the successful incorporation of SrHAnrds in the polymer matrix can be confirmed by the typical OH stretching, which is present as a distinctively large band above 3300 cm -1 .

Evaluation of MOMCs and WJSCs differentiation

3.3.1 Differentiation towards endothelium 3.3.1.1 Morphological differentiation She differentiation of MOMCs upon the PCL films was completed 14 days after the culture initiation, due to the LOLCs distinct properties, which don't permit their time consuming culture. On the contrary, the control group WJSCs differentiated after 30 days. Aiming to accelerate the induction of differentiation, the MOMCs cultures were also boosted, apart from the differentiation medium, by the presence of HUVEC cells into semi-permeable culture systems. The morphology of the cells was characterized by gradually observed differences in their size and shape suggesting a possible differentiation towards endothelial that was finally confirmed both in transcriptional and protein level with real time PCR and flow cytometry respectively (Fig. 4). The seeding of WJSCs and MOMCs on PCL scaffolds is totally different before the induction of differentiation. This can be explained by the morphology, shape, size and cell interaction during the initial seeding. According to this observation, the following changes to the cellular membranes as a result of induced differentiation towards endothelial cells, also lead to different final image, despite the fact that the final cell populations are characterized by similar endothelial markers. Moreover, the origin of MOMCs comparing to the WJSCs pluripotency capacity, limit us to apply different time duration for the differentiation process, something that could also affect the final cellular morphology upon the end of endothelial induction. We present for the first time MOMCs cultures upon PCL films, before and after their induced differentiation towards endothelial cells, with SEM. Differences that depicted in cells' morphology and adherence on PCL nanocomposites with SEM, suggesting a possible differentiation that was finally confirmed with appropriate methods for the accurate quantification of endothelial induction.

Evaluation of differentiation in both transcriptional and protein level

The immunophenotypic characterization with flow cytometry (Fig. 5A) showed an unambiguous differentiation towards endothelial cells with a gradual increase of the respective endothelial marker CD144 expression during the culture (Fig. 5B). In both MOMCs as well as the WJSCs cultures, the final percentages of the CD144 expression were high, while the PCL/SiO 2 ntbs sample displayed a statistically significant difference, proving the induced angiogenetic activity of silica. In just 14 days of triple mediated induction of differentiation, MOMCs express the endothelial marker in percentages far greater that the WJSCs ones even 30 days upon the differentiation.

In the transcriptional level, as proved by the Q-PCR upon the completion of the differentiation cultures, the CD144 expression manifests a similar path compared with the flow cytometry, while the PCL-Si films maintain the highest expression levels in both MOMCs and WJSCs (Fig. 6). The expression of the angiogenetic factor VEGFR is also high in both cell categories (Fig. 6), while the MOMCs differentiation was additionally confirmed by the gradual loss of the CD34 expression, initially characterizing the MOMCs (Fig. 6).

Differentiation towards bone

Morphological differentiation

The morphology of the cells was characterized by gradually observed differences suggesting a possible differentiation towards bone cells for both MOMCs and WJSCs after the completion of the induced differentiation as depicted with SEM (Fig. 7).

Quantification of differentiation

Following the completion of the induced differentiation towards bone cells, the evaluation was performed with the CPC method.

A distinct differentiation towards bone cells was observed in both MOMCs and WJ-SCs upon the PCL/SrHAnrds 2.5 wt% films, with the MOMCs being characterized by a potential greater induction although being cultivated for just 14 days in the presence of a differentiation medium without an exogenous cellular stimulus this time (Fig. 8). It seems that for the PCL/SiO 2 ntbs 2.5 wt% films the induction follows a similar differentiation capacity with the control group, presenting the beneficial role of silica in osteogenesis (Fig. 8).

Discussion

During the endothelial differentiation, MOMCs are progressively losing their native markers and gain endothelial lineage features in both protein as well as transcriptional level, with a statistically significant difference over the differentiated cells onto PCL/SiO 2 ntbs 2.5 wt% nanocomposite films versus pristine PCL ones (*p = 0.008). Moreover, the nanocomposite materials, during the culture, remain non-cytotoxic, allow the growth and cell differentiation, while the impact on cell morphology confirms the successful differentiation in the presence of the appropriate stimulations.

24 h exposure of WJSCs to both SiO 2 ntbs and SrHAnrds indicated no cytotoxicity. In all three concentrations, 10 lg/ml, 100 lg/ml and 200 lg/ml no significant change was observed versus the control group. In addition, after 72 h, the presence of SiO 2 ntbs and SrHAnrds has no significant impact on the cell viability even in the highest given concentrations. Furthermore, MTT shows cell proliferation from day 1 to day 4.

These results indicate that both NPs present no adverse effect to WJSCs for exposure for at least 3 days. It is also worth noting that in the presence of NPs in the culture, even 3 days after the initiation, the cell proliferation rate remains in high levels and in a parallel stability in comparison with the control group. This long time period, for which the addition of NPs does not consist with toxic response, grants an extension provided either to their in vivo time of action or the in vitro induced differentiation towards the regeneration of damaged areas of the body. Several researchers have reported that using nanomaterials as 2D cell culture substrate could effectively promote the differentiation of stem cells into specific lineages, and the stiffness, surface chemistry, alignment and several other parameters of the cell culture substrate (matrix) may work together to influence the fate of stem cells [START_REF] Wei | Nanomaterials modulate stem cell differentiation: biological interaction and underlying mechanisms[END_REF]. Our findings provide strong evidence that the resulting nanocomposite PCL thin films not only passively interact with cells, but also serve as mechanical stimuli that trigger a series of biological alterations and modulate cell behaviors. As for the biological interaction and underlying mechanisms, further studies are needed to better understand how PCL matrix and the reinforcing components (SiO 2 ntbs or SrHAnrds) mediate the molecular processes that are essential for regulating cell functions.

The intense regenerative potential of WJSCs renders them ideal candidates for various regenerative medicine applications [START_REF] Kim | Wharton's jelly-derived mesenchymal stem cells: phenotypic characterization and optimizing their therapeutic potential for clinical applications[END_REF][START_REF] Koliakos | Mesenchymal cells isolation from Wharton's jelly, in perspective to clinical applications[END_REF]. Their respective durability, even in the presence of high concentrations, increase the perspectives of using the two NPs for local injections in areas suffering bone damages or the accumulation of solid scaffolds enriched with either SiO 2 ntbs or SrnHAnrds aiming the construction of new tissues upon a pre-constructed matrix [START_REF] Skaat | Magnetic scaffolds enriched with bioactive nanoparticles for tissue engineering[END_REF].

Successful generation of MOMCs has been already confirmed in the presence of specific factors. MOMCs binding to the RGD domain of fibronectin via cell-surface a5b1 integrin [START_REF] Seta | Fibronectin binding is required for acquisition of mesenchymal/ endothelial differentiation potential in human circulating monocytes[END_REF] in combination with the interaction of soluble SDF-1 factor with CXCR4 surface marker [START_REF] Seta | Plateletderived stromal cell-derived factor-1 is required for the transformation of circulating monocytes into multipotential cells[END_REF] is essential for the transformation of circulating monocytes into MOMCs, as we have proven here. This interaction throughout the culture maybe affects other cell types generation during this procedure, like macrophages, explaining larger number of observed cells compared to culture in the presence of poly-L-lysine in gelatin. For the first time, we present the successful development of MOMCs on PCL scaffolds for application to a variety of regenerative medicine applications. This study confirms the ability of MOMCs to maintain their ability to differentiate towards the desired tissues on PCL films. This element is particularly important as it makes the easily accessible MOMCs an ideal source for tissue engineering applications after their attachment to stable substrates.

Nowadays, the most promising strategy for the restore of damaged areas of the body is the stem cell therapy [START_REF] Tuan | Adult mesenchymal stem cells and cell-based tissue engineering[END_REF]. However, cell proliferation and differentiation resulting in tissue regeneration is difficult while cell organization to form complex tissue structure is limited without using a scaffold [START_REF] O'brien | Biomaterials & scaffolds for tissue engineering[END_REF]. A three-dimensional matrix is necessary to guide and stimulate cellular activities [START_REF] Meng | Stem cells in a threedimensional scaffold environment[END_REF]. It works as an anchor for cells that decreases the possibility of cell migration from the place of destination and allows tissue Enhancement of endothelial differentiation in the presence of HUVEC in semi-permeable culture systems contributes to the fastest differentiation of MOMCs in just 14 days compared to the WJSCs control group. Due to their previous cultivation in SDF-1a chemotactic factor for several days, MOMCs are exhausted before the initialization of differentiation procedure which requires at least 20 days without other stimulus except of the endothelial induction differentiation medium (Data not shown). By applying the co-culture HUVEC-mediated system we facilitate and accelerate the differentiation process, especially taking into consideration that all this procedure must be performed on PCL surfaces. The HUVEC-mediated differentiation is not recommended as a way to prepare nanocomposite PCL films for endothelium regeneration. It is only an evidence that under strong stimulus MOMCs have the ability to rapidly differentiated towards the desirable tissue, as a commonly used technique to promote stem cells differentiation on a scaffold [START_REF] Nguyen | Collagen hydrogel scaffold promotes mesenchymal stem cell and endothelial cell coculture for bone tissue engineering[END_REF]. The combination of application of SiO 2 ntbs and endothelial cell line in the cell culture environment accelerates the differentiation of MOMCs by ensuring the limited exhaustion of the cells in the culture. By applying the upper induction-mediated differentiation conditions we propose a novel system for fast and successful in vitro generation of endothelium from easily accessible MOMCs on PCL-based scaffolds.

In our work we managed to successfully isolate MOMCs from the peripheral blood of healthy volunteer donors which characterized by intense plasticity and differentiation ability towards multilineage directions. Both their successive isolation from adult tissues and their differentiation capacities make these cells ideal candidates for various forms of cellular therapies. However, cell proliferation and differentiation resulting in tissue regeneration for some diseases, is difficult without using a scaffold. Recent studies show that isolated cells are hardly able to organize themselves spontaneously to form complex tissue structures in the absence of a three dimensional matrix that guide and stimulate their activities. For this reason, we decided to use the PLC for the study of endothelial and osteogenic differentiation because it has excellent mechanical properties and slow degradation; thus it might be an optimal candidate to be used in vivo for tissue transplantation [START_REF] Ikada | Challenges in tissue engineering[END_REF]. By incorporating SiO 2 ntbs or SrHAnrds to PCL we suggest a novel way to stimulate, accelerate and facilitate the differentiation procedure during the tissue reconstruction, providing stimuli for targeted differentiation. The aim of this study was to demonstrate that nanocomposite PCL is a promising material to use as a support scaffold for the autologous reconstruction of new tissue starting from easily accessible MOMCs.

Here, we propose MOMCs as an alternative and easily accessible cell source for tissue repair applications. The developed nanocomposite PCL-based films, reinforced with SiO 2 ntbs or SrHAnrds, support MOMCs attachment on their surface and promote their in vitro differentiation towards endothelium and bone, respectively. However, further studies should be performed to identify the underlying mechanisms of MOMCs differentiation on the surface of nanocomposite PCL-based films, in order to optimize the upper protocols, make the procedure less time-consuming and be able to propose these materials for commercial clinical use in combination with blood derivatives of patients, for applications in regenerative medicine.

Fig. 1 A

 1 Fig. 1 A Morphology of genetically modified normal WJSCs (a, b) and HUVEC (c, d) in cell culture. B Immunophenotypic characterization of WJSCs (a, b) and HUVEC (c) via flow cytometry

Fig. 2 AFig. 3 AFig. 4

 234 Fig. 2 A Comparative MOMCs culture in the presence of poly-L-lysine (upper) and fibronectin (below). B Immunophenotypic characterization of MOMCs after culture in the presence of poly-L-lysine and medium supplemented with SDF-1a

Fig. 5 A

 5 Fig. 5 A Immunophenotypic evaluation of the WJSCs (left) and MOMCs (right) differentiation towards endothelial cells. B Flow cytometry images of the CD45/CD144 marker expression before and

Fig. 6

 6 Fig. 6 Real-time PCR for the evaluation of MOMCs and WJSCs differentiation in transcriptional level

Fig. 7 A

 7 Fig. 7 A, B SEM depiction of the WJSCs and MOMCs before and after their differentiation upon PCL films

Acknowledgements The authors thank Biohellenika SA Biotechnology Company for providing the facilities and consumables that enabled the completion of this study. EG and GK conceived the study; MN and DB fabricated and characterized the materials; IK and EG designed and performed the experiments (equal contribution to this work); IK, EG, EP, MK and DB analysed the data; IK, EG and MN wrote the manuscript. All authors reviewed the manuscript.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical statement This study was approved by the Ethics Committee of Aristotle University of Thessaloniki, School of Medicine (390-9/ 1.7.2017) and University Hospital AXEPA of Thessaloniki (3868/ 24.1.2018). This research involves Human Participants after their informed consent. Peripheral blood samples were collected from healthy volunteer donors while mesenchymal stromal cells and HUVEC were isolated from Wharton's jelly after parents approval during stem cell banking in Biohellenika SA Biotechnology Company.