Bicontinuous Cubic Liquid Crystals as Potential Matrices for Non-Invasive Topical Sampling of Low-Molecular-Weight Biomarkers

Many skin disorders, including cancer, have inflammatory components. The non-invasive detection of related biomarkers could therefore be highly valuable for both diagnosis and follow up on the effect of treatment. This study targets the extraction of tryptophan (Trp) and its metabolite kynurenine (Kyn), two compounds associated with several inflammatory skin disorders. We furthermore hypothesize that lipid-based bicontinuous cubic liquid crystals could be efficient extraction matrices. They comprise a large interfacial area separating interconnected polar and apolar domains, allowing them to accommodate solutes with various properties. We concluded, using the extensively studied GMO-water system as test-platform, that the hydrophilic Kyn and Trp favored the cubic phase over water and revealed a preference for locating at the lipid–water interface. The interfacial area per unit volume of the matrix, as well as the incorporation of ionic molecules at the lipid–water interface, can be used to optimize the extraction of solutes with specific physicochemical characteristics. We also observed that the cubic phases formed at rather extreme water activities (>0.9) and that wearing them resulted in efficient hydration and increased permeability of the skin. Evidently, bicontinuous cubic liquid crystals constitute a promising and versatile platform for non-invasive extraction of biomarkers through skin, as well as for transdermal drug delivery.


Introduction
The detection of cancer at an early stage is highly important as it has a significant impact on patient survival. Currently, skin cancer diagnosis relies on visual evaluation of the suspected lesion, often followed by a tissue biopsy. The accuracy of the visual diagnosis varies significantly (49-81%) depending on, e.g., the clinician's experience and the characteristics of the lesion [1][2][3][4][5]. Benign nevus is one example of a very common but harmless lesion which may be mistaken for cutaneous melanoma, thus resulting in numerous unnecessarily excised benign lesions. Therefore, the development of alternative or complementary non-invasive methods for early stage skin cancer diagnosis based on, e.g., the extraction of endogenous biomarkers, is highly desirable. It has furthermore been shown that sustained inflammation sometimes acts as a precursor for cancer. For example, actinic keratoses and Bowen's disease are precursors for squamous-cell carcinoma [6]. Thus, the detection of inflammation biomarkers can also serve as an early warning for disease onset [7]. As a result, from recent progress in cancer research, there is an emerging number of endogenous substances associated with inflammation and cancer to choose between, e.g., NF-κB, IL-6, IFN-γ, TNF-α, enzyme indoleamine-2,3-dioxygenase Small-angle X-ray diffraction (SAXD) was performed on a Xeuss 3.0 SAXS/WAXS laboratory-based instrument (Xenocs, Grenoble, France) at Malmö University (Malmö, Sweden). The X-ray beam was generated by a Cu K α source (λ = 1.541 Å). All samples were kept in an ambient atmosphere during measurements at 25 • C using a temperature-controlled Peltier gel-holder stage. The gel-holder utilized an O-ring as a spacer between two Kapton films (DuPont TM Kapton ® , 0.013 mm thickness, Goodfellow, UK), sealed in between two metal plates with a 5 mm opening. The diffraction data were collected by a Pilatus3 R 300K hybrid photon counting detector at two different sample-to-detector distances (STDD) of 800 mm and 1700 mm. These two STDDs covered the q-range 0.0002 ≤ q (Å −1 ) ≤ 0.36, where q is the scattering vector and is defined as: where θ is the scattering angle. The q scale was calibrated using silver behenate. One-dimensional (1D) data were obtained by the azimuthal averaging of 2D-diffraction pattern recorded by the detector, and the data were corrected for background scattering and normalized to the direct beam using the Xenocs XSACT software (version 2.6). The exposure time was 30 min for each sample at each STDD.

Humidity Scanning (HS) QCM-D
The hydration of the lipid films was investigated using humidity scanning QCM-D [38]. The technique, besides being a highly accurate for determination of a mass of materials adsorbed on piezoelectric quartz sensor based on Sauerbrey methodology [39], also provides information about the viscoelastic properties of the adsorbed material via the dissipation data [40]. It works by applying an oscillating potential on a quartz crystal and monitoring the frequency of the resulting oscillating shear motion, which generates an acoustic wave. The resonance condition occurs when the wavelength of the resulting acoustic wave is an odd integer of the quartz sensor's thickness. The information of the mass of the adsorbed material is obtained from the resonance frequency. The mass of the adsorbed material can be determined using the Sauerbrey equation (Equation (2)) [39] under the assumptions that the mass of the material is small compared to the mass of the crystal and that the material is rigidly adsorbed and homogenously distributed over the active area of the crystal.
The Sauerbrey equation describes the relationship between the negative frequency change ∆f, normalized per overtone n, and the product of the areal film m f (kg·m −2 ) and the fundamental resonance frequency f 0 of the quartz sensor (~5 MHz) normalized by the acoustic impedance of quartz Z q (8.8 × 10 6 kg·m −2 ·s −1 ). In addition to the areal masses of the films obtained from the QCM-D experiments, the films are also described by their estimated thicknesses. The thickness of a dry film, d, can be calculated from the areal mass of the dry film d = m f /ρ, where ρ is the density of the dry film. The density of a dry lipid film, constituting mostly of GMO in this work, was assumed to be 0.94 g·cm −3 . However, it is important to note that this was only an estimation of the film thickness. As mentioned earlier, the QCM-D technique also monitors the dissipation, D, which is related to the decay time of the oscillating resonator when the alternating potential is turned off. The viscoelastic properties of the film adsorbed on the quartz crystal have a strong impact on its dissipation energy, which is related to the decay time. Therefore, dissipation provides information about the rheological properties of the film as well as complementary data during the hydration process.
A q-sense QCM-D E4 with humidity module QHM 401 and AT-cut SiO 2 (QSX 303, 5 MHz) sensors from Biolin Scientific AB (Gothenburg, Sweden) were used in this work. The humidity module was equipped with a Gore membrane, which separated the flowing solution from the sensor, allowing only the water vapors from the solution to diffuse across the membrane and regulate the RH above the film coated on the surface. New sensors were gently washed with ethanol and Milli-Q water and dried by the flow of nitrogen, while used sensors were cleaned according to the cleaning protocol described in the q-sense guidelines manual (cleaning protocols B for QSX 303). No difference was observed in the measurements performed with new and reused sensors.
Lipids (GMO and DOTAP) were dissolved in ethanol in appropriate ratios so that the final concentration was 8 mM. The humidity scanning QCM-D experiment was initiated by measuring the uncoated sensor in a dry N 2 atmosphere at 25 • C. After that, sensors were coated with a lipid film by spin-coating, where 10-20 µL of lipid solution was applied once on the surface of the sensor. In a study by Björklund and Kocherbitov [41], it was found that film thickness was primarily dependent on the concentration and not on the number of solution applications. The coated sensors were then dried overnight in a vacuum and then placed back into the humidity module. The measurements were initiated by flowing dry N 2 gas until a stable baseline was observed (usually 30 min). After that, N 2 gas flow was stopped, and the hydration experiment was performed according to a procedure described in detail elsewhere [38]. In brief, the measurement relied on the continuous and controlled dilution of a saturated LiCl solution that was flowing through the humidity chamber. Since only water vapor could pass across the Gore membrane, the RH above the sensor was continuously regulated by adjusting the water activity, a w , of the LiCl solution (a w = RH/100%).

Swelling of Bicontinuous Liquid Crystalline Aqueous Phases
The swelling laws previously disclosed by Engblom and Hyde [42] for lyotropic liquid crystals were used together with X-ray data to verify structure determinations and more accurately identify the phase boarders and swelling limits. These equations further allowed for a more in-depth analysis of the internal geometries of individual phases, such as the lipid/water interfacial area per unit cell and how this relates to macroscopic volumes, water channel radii and lengths, etc.
According to Engblom and Hyde, the lattice parameter, a (see Section S1 in Supplementary Information for calculations of a from diffraction data [43,44]), can be derived for reverse bicontinuous cubic phases using Equation (3): where l is the average lipid monolayer thickness (here, 17 Å); χ is a topology index of the surface, known as Euler-Poincaré characteristics (-8 for Ia3d, -2 for Pn3m, and -4 for Im3m); and H is a dimensionless characteristic, the "homogeneity index," which combines the surface-to-volume ratio of a hyperbolic surface with its topology (0.7665 for Ia3d, 0.7498 for Pn3m, and 0.7163 for Im3m). ∆ is defined as, where Φ l = 1 − Φ w is the volume fraction of the lipid, and Φ w the water volume fraction. The water volume fraction can then be recalculated into weight fraction of water as: where ρ l is the density of the lipid (0.94 g·cm −3 ).

Partitioning of Trp and Kyn into Lipid Bilayer
The partition experiment of Trp and Kyn into the lipid bilayer of a cubic phase was performed in accordance with the method described by Engström et al. [45], where the authors investigated the lipid bilayer/water partition of model drug clomethiazole. Four concentrations of Trp and Kyn in the range from 0.125 mM to 1 mM, corresponding to the lipid:Trp(Kyn) ratio in the range 7200:1-900:1, were prepared in Milli-Q water in order to investigate the effect of concertation on the partitioning. The fully swollen cubic phases (~0.25 g) were prepared by mixing the appropriate amount of GMO with an excess of Milli-Q water (1:1 weight ratio) in 1.7 mL glass vials and left to equilibrate for 7 days. When the samples had equilibrated, excess water was removed and replaced with 500 µL of aqueous solution with different concentrations of Trp/Kyn (molar ratio 1:1). The first sampling was performed after one week of equilibration by withdrawing 50 µL of the aqueous phase. The second sampling was performed in an identical manner after 2 weeks of equilibration to investigate the time aspect on the partitioning. All samples collected during the partition study were diluted to a final volume 500 µL with Milli-Q water and filtered with 0.2 µm syringe filters (13 mm PTFE membrane, VWR International, Radnor, PA, USA) prior to the HPLC-UV analysis. All partition experiments were performed in triplicate.

Bilayer Partition Coefficient
The cubic liquid-crystalline phase consists of two domains: a lipid bilayer domain and a water domain. The calculation of the lipid bilayer/water partition coefficient, K bl/w , was described by Engström et al. [45]. Briefly, their work states that the partition coefficient is defined as: where [X] is the concentration of an analyte of interest (e.g., Trp and Kyn) in the bilayer (bl) and in water (w). Whereas the concentration of a substance in the aqueous phase can easily be determined by a suitable analytical procedure (e.g., HPLC, LC-MS etc.), the determination of the concertation in the bilayer requires two assumptions. The first assumption is based on the fact that the GMO has very low solubility in water, around 10 −6 M [46] with an overall HLB of 3.8 [47], implying that there is no free GMO existing in the aqueous phase (i.e., all GMO makes up the lipid bilayer). The second assumption is that the concentration of an analyte in the water channels of the cubic phase is the same as in the water bulk phase, which is based on the equilibrium between chemical potentials of analytes in water channels and in the bulk phase. Thus, the partition coefficient can be calculated by rewriting Equation (7) as follows: where V w is the volume of a water solution containing analyte X added to the cubic phase, [X] 0w is the initial concentration of an analyte, [X] w is the concentration of analyte in the water phase after equilibration, V bl is the volume of GMO, and V w , cube is the volume of water that was added to GMO to form a cubic phase. The cubic phase/water partition coefficient, K Q/w , can then be obtained from the expression disclosed as Equation (8):

HPLC-UV Analysis
The quantification of Trp and Kyn was performed by the HPLC-UV system (Agilent 1100 Series, Waldbronn, Germany). The chromatographic separation of Trp and Kyn was carried out on a 250 mm × 4.6 mm Kromasil C18 column with particle size of 5 µm (AkzoNobel, Bellefonte, PA, USA). Analytes were separated by gradient elution using mobile-phase A consisting of 10 mM NaH 2 PO 4 (pH 2.8) and mobile-phase B consisting of 100% MeOH at 0.9 mL/min flow rate and 40 • C column temperature. The gradient profile was adopted from previous work [48] and modified as follows: mobile-phase B was kept at 25% for 7 min; then, phase B was gradually increased to 95% over 4 min and kept at 95% for 4 min, after which phase B was decreased to 25% over 0.1 min and kept at 25% for the final 1.9 min, resulting in a total run time of 17 min. The injection volume was set to 20 µL. The detection of Trp and Kyn was performed at their UV absorbance maxima, at 280 nm and 360 nm, respectively. Stock solutions of 10 mM of Trp and Kyn for calibration curve were prepared in Milli-Q water and kept in the freezer (−20 • C) for no longer than one day after preparation. Calibration standards for the calibration curve were analyzed in the range from 0.78 µM to 100 µM (R 2 > 0.999) the same day as the experimental samples. The quantity of analytes was determined by manual integration of the corresponding peaks using OpenLAB software (Lab Advisor Basic Software, Agilent, Germany). The concentrations of Trp and Kyn in the unknown samples were determined using the calibration curve obtained from standards solutions. The LOQ for Trp and Kyn were determined to 0.43 µM and 0.69 µM, respectively (see Section S2 in Supplementary Information for further information regarding the LOD, LOQ, accuracy, and precision of the HPLC-UV method, Tables S1-S3).

The Matrix
Due to their specific physicochemical properties, bicontinuous cubic lipid-based liquid crystals have a high potential to be used as matrices for the non-invasive topical sampling of low-molecular-weight biomarkers. In this work, we adopted the extensively studied GMOwater system as our model and introduced a structurally related cationic lipid (DOTAP) with the dual purpose to increase water swelling and to obtain a charged lipid-water interface. GMO alone forms a reversed micellar (L 2 ) phase at 25 • C and low water content, which, on further hydration, first transitions into a lamellar liquid crystal (L α ), and then to two subsequent reversed types of bicontinuous cubic phases-first a Gyroid cubic phase (C G , space group Ia3d) and then a Double Diamond cubic phase (C D , space group Pn3m), which has a limited swelling of about 40% (w/w) and co-exists with excess water [49][50][51]. DOTAP, on the other hand, only forms a lamellar phase (L α ), which swells up to about 95% (w/w) water, corresponding to a lattice parameter a, of 708 Å (see Figure S1). The further addition of water most probably results in the formation of fully hydrated unilamellar vesicles dispersed in excess water, which has previously been observed for other charged lipids [52]. Figure 1 shows a part of the phase diagram for the ternary system GMO/DOTAP/H 2 O, outlined based on visual inspection of the samples between crossed polarized windows, polarized light optical microscopy (PLOM), and small-angle X-ray diffraction (SAXD) (see Figure S2). Phase boarders and swelling limits were further determined by comparing the lattice parameters obtained by SAXD with the expected dimensions estimated from the appropriate swelling laws previously disclosed by Engblom and Hyde. These laws are also briefly outlined in the Materials and Methods section above, and the results are depicted in Figure 2 (also see Figure S3) [31,42]. SAXD data and corresponding calculated dimensions are summarized in Table 1 (see also Supplementary Information Tables S4-S8).

The Matrix
Due to their specific physicochemical properties, bicontinuous cubic lipid-based liquid crystals have a high potential to be used as matrices for the non-invasive topical sampling of low-molecular-weight biomarkers. In this work, we adopted the extensively studied GMO-water system as our model and introduced a structurally related cationic lipid (DOTAP) with the dual purpose to increase water swelling and to obtain a charged lipidwater interface. GMO alone forms a reversed micellar (L2) phase at 25 °C and low water content, which, on further hydration, first transitions into a lamellar liquid crystal (Lα), and then to two subsequent reversed types of bicontinuous cubic phases-first a Gyroid cubic phase (CG, space group Ia3d) and then a Double Diamond cubic phase (CD, space group Pn3m), which has a limited swelling of about 40% (w/w) and co-exists with excess water [49][50][51]. DOTAP, on the other hand, only forms a lamellar phase (Lα), which swells up to about 95% (w/w) water, corresponding to a lattice parameter a, of 708 Å (see Figure  S1). The further addition of water most probably results in the formation of fully hydrated unilamellar vesicles dispersed in excess water, which has previously been observed for other charged lipids [52]. Figure 1 shows a part of the phase diagram for the ternary system GMO/DOTAP/H2O, outlined based on visual inspection of the samples between crossed polarized windows, polarized light optical microscopy (PLOM), and small-angle X-ray diffraction (SAXD) (see Figure S2). Phase boarders and swelling limits were further determined by comparing the lattice parameters obtained by SAXD with the expected dimensions estimated from the appropriate swelling laws previously disclosed by Engblom and Hyde. These laws are also briefly outlined in the Materials and Methods section above, and the results are depicted in Figure 2 (also see Figure S3) [31,42]. SAXD data and corresponding calculated dimensions are summarized in Table 1 (see also Supplementary  Information Tables S4-S8).  At low water content (up to about 30% (w/w)), there was no significant effect on the phase behavior from adding the positively charged DOTAP (within the range from GMO/DOTAP 100/0 to 80/20 (w/w)) (see Figure S4). The transition from L α to cubic C G occurred at approximately the same water content, independently of the amount of DOTAP added, while the C G swelled extensively from 30% (w/w) water (a = 126.8 Å) in the pure system to 45% (w/w), with the highest amount of DOTAP (a = 184.3 Å), before transforming to the second cubic phase, C D . Based on the analysis shown in Figure 2 (left), we conclude that the C G phase, without exception, closely resembled the predicted swelling of a gyroid IPMS with an Ia3d space group symmetry and genus 5. It is further noteworthy that the C D phase also swelled significantly upon DOTAP addition, from covering only a narrow band (from a maximum swelling of about 38% (w/w) water corresponding to a = 93.5 Å) and coexisting with excess water in the pure system, to spanning from 45 to about 70% (w/w) water (114.3 Å < a < 214.4 Å) with a GMO/DOTAP ratio of 80/20 (w/w) before transforming into the third cubic phase, the primitive C P (Im3m). A small amount of DOTAP (i.e., GMO/DOTAP 97.5/2.5) had already generated a phase transition from C D to C P and caused the C D phase to swell from a maximum 38% (w/w) water in the pure system up to 45% (w/w). Referring to the analysis provided in Figure 2 (left), it is evident that experimental data on swelling of the C D phase overlapped well with the predicted curve for a diamond IPMS with a Pn3m space group symmetry and genus 2. On a few occasions, the experimentally determined lattice parameter deviated from the predicted curve, which was indicative of the limited swelling of the C D phase and could be used to estimate the phase boundaries. The C P phase first appeared at about 45% (w/w) water and then only as a very narrow band with a limited swelling in equilibrium with excess water at a GMO/DOTAP ratio of 97.5/2.5. When increasing the amount of DOTAP (to GMO/DOTAP 95/5), the C P phase swelled further to about 50 wt% water; at GMO/DOTAP 90/10, it comprised from approximately 45 to about 80% (w/w) water; and at GMO/DOTAP 80/20, it appeared to take close to 90% (w/w) water before transitioning into a lamellar (L α ) phase ( Figure S4). The presence of vesicles at 95% (w/w) water content was confirmed by PLOM. At low water content (up to about 30% (w/w)), there was no significant effect on the phase behavior from adding the positively charged DOTAP (within the range from GMO/DOTAP 100/0 to 80/20 (w/w)) (see Figure S4). The transition from Lα to cubic CG occurred at approximately the same water content, independently of the amount of DOTAP added, while the CG swelled extensively from 30% (w/w) water (a = 126.8 Å) in the pure system to 45% (w/w), with the highest amount of DOTAP (a = 184.3 Å), before transforming to the second cubic phase, CD. Based on the analysis shown in Figure 2 (left), we conclude that the CG phase, without exception, closely resembled the predicted swelling of a gyroid IPMS with an Ia3d space group symmetry and genus 5. It is further noteworthy that the CD phase also swelled significantly upon DOTAP addition, from covering only a narrow band (from a maximum swelling of about 38% (w/w) water corresponding to a = 93.5 Å) and coexisting with excess water in the pure system, to spanning from 45 to about 70% (w/w) water (114.3 Å < a < 214.4 Å) with a GMO/DOTAP ratio of 80/20 (w/w) before transforming into the third cubic phase, the primitive CP (Im3m). A small amount of DOTAP (i.e., GMO/DOTAP 97.5/2.5) had already generated a phase transition from CD to CP and caused the CD phase to swell from a maximum 38% (w/w) water in the pure Some further interesting features can be extracted from the analyses provided in Figure 2 (left). First, we observed the co-existence of C D and C P at GMO/DOTAP 97.5/2.5 and different sample water contents (45% (w/w) and 60% (w/w)), while there was no sign of the C D at higher water contents, indicating a narrow three-phase region (C D +C P +water) close to the base line of our phase diagram. Evidently, small variations in GMO/DOTAPratios, originating from sample preparations, could determine if the sample were in this three-phase region or in the neighboring two-phase region comprising slightly more DOTAP. Second, the small dip in the C P lattice parameter seen at high water content (>90% (w/w)) for these samples, which was more pronounced for GMO/DOTAP 95/5 at the same hydration levels, could indicate that the tie lines in this two-phase region (C P +water) were not pointing toward the water corner but were rather more horizontal and parallel to the base line. Another explanation of this observation becomes plausible if we analyze the swelling of C P comprising the higher amounts of DOTAP (Figure 2 (left)). When experimental data on the swelling of the C P phase are expected to coincide with the predicted curve for a primitive IPMS with an Im3m space group symmetry and genus 3, the swelling laws we used here assume that the lipid monolayer thickness, l, is constant and equal to that adopted for GMO alone, 17 Å [42]. If appending DOTAP to the system, especially at high water contents, an increase in the average lipid headgroup area would occur due to the excessive hydration of the charged DOTAP headgroup; then, the lipid monolayer thickness would shrink, and the a/l used for our calculations would become too small. Indeed, for GMO/DOTAP 80/20, in particular, we see that experimental data were located below the calculated swelling curve. If this is the explanation to our observations, then it would also induce some uncertainty to the swelling limits determined at higher water contents.

Matrix Interactions with Skin
It is a well-accepted fact that skin permeability can be facilitated by occlusion, leading to increased hydration, and the relation between the degree of skin hydration and its permeability to various polar and non-polar compounds has been studied in quite some detail, both at our lab and elsewhere [20,53]. Therefore, it is also recommended that a matrix intended for optimal non-invasive topical extraction of biomarkers comprises a relatively high amount of water and possesses a high inherent water activity to prevent dehydration of the tissue. Based on the obtained phase diagram (Figure 1), we decided to proceed with investigating two candidate matrices, a fully hydrated GMO-water C D -phase with 38% (w/w) water and a GMO/DOTAP/H 2 O C P -phase, comprising a GMO/DOTAP ratio of 90/10 and 60% (w/w) water.
Water sorption isotherms of pure GMO and DOTAP, as well as of GMO/DOTAP 90/10 (w/w), were obtained at 25 • C with humidity scanning (HS) QCM-D to further characterize their lyotropic phase behavior, as shown in Figure 3. The water uptake by GMO alone revealed the expected phase transitions from L 2 to L α around a w 0.60-0.70 (i.e., 3-4% (w/w) water), and then from L α to bicontinuous cubic phases (first C G ) at a w 0.96-0.98 (i.e., 15-16% (w/w) water), which is in good agreement with similar data previously reported by Björklund and Kocherbitov [41]. The water sorption of GMO/DOTAP 90/10 (w/w) was evidently very similar to that of pure GMO with respect to a w values where phase transitions occurred. Further, the phase transitions from C G to C D and C P , which should occur very close to a w equal to 1, were not observed by the measurements performed in this work as they were terminated before reaching a w ≈ 1. Instead, complimentary determinations of the a w at 25 • C of the specific lipid-water compositions were made using a water activity meter. Pure GMO with 15% (w/w) water (L α ) showed an a w of 0.900, while GMO/DOTAP 90/10 (w/w) with 30 (C G ), 45 (C D +C P ), and 60 (C P ) %(w/w) water had an a w corresponding to 0.962, 0.991, and 0.999, respectively. characterize their lyotropic phase behavior, as shown in Figure 3. The water uptake by GMO alone revealed the expected phase transitions from L2 to Lα around aw 0.60-0.70 (i.e., 3-4% (w/w) water), and then from Lα to bicontinuous cubic phases (first CG) at aw 0.96-0.98 (i.e., 15-16% (w/w) water), which is in good agreement with similar data previously reported by Björklund and Kocherbitov [41]. The water sorption of GMO/DOTAP 90/10 (w/w) was evidently very similar to that of pure GMO with respect to aw values where phase transitions occurred. Further, the phase transitions from CG to CD and CP, which should occur very close to aw equal to 1, were not observed by the measurements performed in this work as they were terminated before reaching aw ≈ 1. Instead, complimentary determinations of the aw at 25 °C of the specific lipid-water compositions were made using a water activity meter. Pure GMO with 15% (w/w) water (Lα) showed an aw of 0.900, while GMO/DOTAP 90/10 (w/w) with 30 (CG), 45 (CD+CP), and 60 (CP) %(w/w) water had an aw corresponding to 0.962, 0.991, and 0.999, respectively. To take this one step further and investigate the effect of topical application of such matrix, we performed a two-hour experiment during a parallel in vivo study on 35 healthy test subjects, which was approved by the Swedish Ethical Review Agency (Dnr 2020-04943). For a more detailed description of the in vivo study, refer to reference [54]. In this in vivo study, we compared the capacity of four alternative matrices with different colloidal properties for the non-invasive sampling of low-molecular-weight biomarkers. To validate the stability of the chosen lipid-based matrices, SAXD measurements were performed after the two-hour application, the results of which are shown in Figure 4. The fully swollen GMO (Pn3m phase), which contained approximately 38 wt% water, and GMO/DOTAP 90/10 (w/w), containing 60% (w/w) water (Im3m phase), showed only a minor decrease of the lattice parameter in the case of the GMO/DOTAP matrix (the lattice parameter, a, decreased by 8 Å, from 186.6 to 178.7 Å). However, a more pronounced change was observed with the GMO matrix, where the application on skin caused a phase transition from Pn3m (a = 94.3 Å) to Ia3d (a = 133.6 Å). These effects were most likely caused by the absorption of water from the matrices by the skin. Again, relying on the swelling laws used in Figure 2 above, we calculated the corresponding amounts of water to 2.1 and 7.0 mg·cm -2 , respectively. This correlates well with the expected water uptake by the skin to reach full hydration at from normal ambient conditions of about 30-40% RH [55,56] and has only a marginal effect on the intended application of these matrices, which is further discussed below. To take this one step further and investigate the effect of topical application of such matrix, we performed a two-hour experiment during a parallel in vivo study on 35 healthy test subjects, which was approved by the Swedish Ethical Review Agency (Dnr 2020-04943). For a more detailed description of the in vivo study, refer to reference [54]. In this in vivo study, we compared the capacity of four alternative matrices with different colloidal properties for the non-invasive sampling of low-molecular-weight biomarkers. To validate the stability of the chosen lipid-based matrices, SAXD measurements were performed after the two-hour application, the results of which are shown in Figure 4. The fully swollen GMO (Pn3m phase), which contained approximately 38 wt% water, and GMO/DOTAP 90/10 (w/w), containing 60% (w/w) water (Im3m phase), showed only a minor decrease of the lattice parameter in the case of the GMO/DOTAP matrix (the lattice parameter, a, decreased by 8 Å, from 186.6 to 178.7 Å). However, a more pronounced change was observed with the GMO matrix, where the application on skin caused a phase transition from Pn3m (a = 94.3 Å) to Ia3d (a = 133.6 Å). These effects were most likely caused by the absorption of water from the matrices by the skin. Again, relying on the swelling laws used in Figure 2 above, we calculated the corresponding amounts of water to 2.1 and 7.0 mg·cm −2 , respectively. This correlates well with the expected water uptake by the skin to reach full hydration at from normal ambient conditions of about 30-40% RH [55,56] and has only a marginal effect on the intended application of these matrices, which is further discussed below.

Sampling for Analysis
Furthermore, the extensive swelling induced by appending a charged lipid to the GMO-water system offers an interesting opportunity, as aiming for a matrix to be used for non-invasive topical extraction of endogenous biomarker molecules also means that what is absorbed by the matrix must be quantified in some way, preferably by analyzing the absorbed solutes in a liquid phase. Thus, we decided to investigate the effect on the phase behavior of the GMO/DOTAP system from adding an electrolyte. In this experiment, 150 mM NaCl aqueous solution was added instead of pure water to the dry lipid mixture.
The result is summarized in the partial phase diagram provided in Figure 5 (also see Figure S5) based on the collected data in Figure 2 (right). Evidently, the addition of 150 mM NaCl resulted in a significantly decreased swelling of the system due to a more or less complete screening of interfacial charges. No Im3m phase was formed, and an excess of water in equilibrium with a Pn3m phase was present in all samples, exceeding a water content of 45% (w/w). Thus, dispersing the Im3m cubic phase in an aqueous 150 mM NaCl solution would result in a phase transition to a less swollen Pn3m phase, expelling water that comprises a significant fraction of the absorbed biomarker molecules. This may provide a simple way to extract the absorbed biomarkers from the lipid matrix for further analysis by a suitable analytical method (e.g., HPLC-UV or LC-MS).

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11 of 16 Figure 4. The effect of two-hour in vivo skin application. Diffraction patterns of GMO/DOTAP (90/10 (w/w)) with 60% (w/w) water cubic phase (Im3m) measured before (dark violet) and after (dark red), and fully swollen GMO measured before (dark green) and after (light green).

Sampling for Analysis
Furthermore, the extensive swelling induced by appending a charged lipid to the GMO-water system offers an interesting opportunity, as aiming for a matrix to be used for non-invasive topical extraction of endogenous biomarker molecules also means that what is absorbed by the matrix must be quantified in some way, preferably by analyzing the absorbed solutes in a liquid phase. Thus, we decided to investigate the effect on the phase behavior of the GMO/DOTAP system from adding an electrolyte. In this experiment, 150 mM NaCl aqueous solution was added instead of pure water to the dry lipid mixture. The result is summarized in the partial phase diagram provided in Figure 5 (also see Figure S5) based on the collected data in Figure 2 (right). Evidently, the addition of 150 mM NaCl resulted in a significantly decreased swelling of the system due to a more or less complete screening of interfacial charges. No Im3m phase was formed, and an excess of water in equilibrium with a Pn3m phase was present in all samples, exceeding a water content of 45% (w/w). Thus, dispersing the Im3m cubic phase in an aqueous 150 mM NaCl solution would result in a phase transition to a less swollen Pn3m phase, expelling water that comprises a significant fraction of the absorbed biomarker molecules. This may provide a simple way to extract the absorbed biomarkers from the lipid matrix for further analysis by a suitable analytical method (e.g., HPLC-UV or LC-MS). . The effect of two-hour in vivo skin application. Diffraction patterns of GMO/DOTAP (90/10 (w/w)) with 60% (w/w) water cubic phase (Im3m) measured before (dark violet) and after (dark red), and fully swollen GMO measured before (dark green) and after (light green). Figure 4. The effect of two-hour in vivo skin application. Diffraction patterns of GMO/DOTAP (90/10 (w/w)) with 60% (w/w) water cubic phase (Im3m) measured before (dark violet) and after (dark red), and fully swollen GMO measured before (dark green) and after (light green).

Sampling for Analysis
Furthermore, the extensive swelling induced by appending a charged lipid to the GMO-water system offers an interesting opportunity, as aiming for a matrix to be used for non-invasive topical extraction of endogenous biomarker molecules also means that what is absorbed by the matrix must be quantified in some way, preferably by analyzing the absorbed solutes in a liquid phase. Thus, we decided to investigate the effect on the phase behavior of the GMO/DOTAP system from adding an electrolyte. In this experiment, 150 mM NaCl aqueous solution was added instead of pure water to the dry lipid mixture. The result is summarized in the partial phase diagram provided in Figure 5 (also see Figure S5) based on the collected data in Figure 2 (right). Evidently, the addition of 150 mM NaCl resulted in a significantly decreased swelling of the system due to a more or less complete screening of interfacial charges. No Im3m phase was formed, and an excess of water in equilibrium with a Pn3m phase was present in all samples, exceeding a water content of 45% (w/w). Thus, dispersing the Im3m cubic phase in an aqueous 150 mM NaCl solution would result in a phase transition to a less swollen Pn3m phase, expelling water that comprises a significant fraction of the absorbed biomarker molecules. This may provide a simple way to extract the absorbed biomarkers from the lipid matrix for further analysis by a suitable analytical method (e.g., HPLC-UV or LC-MS).

Matrix Optimization
Non-invasive topical extraction of endogenous substances from the skin is inevitably linked to the partitioning of the targeted solutes between the skin and the matrix. Octanolwater partitioning coefficients are furthermore known and tabulated for a vast number of substances, where octanol could perhaps be accepted as a rough substitute for skin, and the water part could be represented by a hydrogel matrix applied on the skin. A hydrogel should thus also work well for the extraction of hydrophilic compounds through skin. Both Kyn and Trp have several pKa values, but none close to the physiological pH. The standard octanol/water partitioning further identified both Kyn and Trp as rather hydrophilic substances (logD o/w (pH7.4): -1.9 and -1.1 (D o/w (pH7.4): 0.0 and 0.1, respectively). From looking at their chemical structures, shown in Figure 6, it is evident that they also could be somewhat surface active and prefer to localize at a lipid-water interface. Indeed, the partitioning of Kyn and Trp between a fully swollen Pn3m cubic phase (GMO/water) and water is in favor of the cubic phase (i.e., K Q/w : 1.3 and 2.2, respectively), and the more universal entity derived by Engström and coworkers [45], referred to as the bilayer/water partitioning coefficient, was calculated to K bl/w : 1.5 and 3.0 for Kyn and Trp, respectively ( Figure 6). The large interfacial area between the interconnected polar and apolar domains of the bicontinuous cubic phases is obviously an asset that can be further explored to optimize the extraction of solutes with specific physicochemical properties. Figure 7 (left) illustrates how this interfacial area varied with water content in the GMO/DOTAP system from less than 50,000 Å 2 to more than 500,000 Å 2 per unit cell, easily corresponding up to 500 m 2 ·cm −3 . This figure further shows how the K Q/w depended on K bl/w , as well as its superiority over a hydrogel-based extraction matrix for very hydrophilic solutes (Figure 7 right).
could be somewhat surface active and prefer to localize at a lipid-water interface. Indeed, the partitioning of Kyn and Trp between a fully swollen Pn3m cubic phase (GMO/water) and water is in favor of the cubic phase (i.e., KQ/w: 1.3 and 2.2, respectively), and the more universal entity derived by Engström and coworkers [45], referred to as the bilayer/water partitioning coefficient, was calculated to Kbl/w: 1.5 and 3.0 for Kyn and Trp, respectively ( Figure 6). The large interfacial area between the interconnected polar and apolar domains of the bicontinuous cubic phases is obviously an asset that can be further explored to optimize the extraction of solutes with specific physicochemical properties. Figure 7 (left) illustrates how this interfacial area varied with water content in the GMO/DOTAP system from less than 50,000 Å 2 to more than 500,000 Å 2 per unit cell, easily corresponding up to 500 m 2 ·cm-3 . This figure further shows how the KQ/w depended on Kbl/w, as well as its superiority over a hydrogel-based extraction matrix for very hydrophilic solutes (Figure 7  right).
These findings were also confirmed in the parallel in vivo study, which included 35 healthy test persons, wherein the capacity of four alternative matrices with different colloidal properties was studied. Four matrices, a chitosan-based hydrogel, an agarose-based hydrogel, and the two lipid-based matrices from the current study, were compared for the non-invasive sampling of low-molecular-weight biomarkers (i.e., tryptophan, kynurenine, tyrosine, and phenylalanine) [54]. The lipid-based matrices were twice as effective as the corresponding hydrogels, and the benefit from electrostatic attraction between matrix and solute was also evident as it appeared to compensate for the smaller interfacial area per unit volume at higher water contents.

Conclusions
We concluded that there was extensive swelling of the GMO-water system and the formation of a third cubic phase (Im3m) in the presence of DOTAP. We also observed that the cubic phases in this system all formed at rather extreme water activities (>0.9). Physiological salt concentrations counteracted the electrostatic effect of swelling and prevented the formation of the Im3m phase, while wearing the matrix on skin in vivo for several hours only induced a marginal decrease in lattice parameters-most probably an effect of water uptake by the skin tissue. Still, the presence of DOTAP at high salt concentrations resulted in the increased swelling of both the Ia3d and the subsequent Pn3m cubic phases.
The standard octanol/water partitioning identified both Kyn and Trp as rather hydrophilic substances (logDo/w (pH 7.4): -1.9 and -1.1 (Do/w (pH 7.4): 0.0 and 0.1 for Kyn and Trp, respectively), while the partitioning between a fully swollen Pn3m cubic phase (GMO/water) and water was more in favor of the cubic phase (KQ/w: 1.3 and 2.2 for Kyn and Trp, respectively). This could be attributed to the large interfacial area between the interconnected polar and apolar domains of almost 500 m 2 ·cm -3 where the bilayer/water partitioning was calculated for Kbl/w (1.5 and 3.0 for Kyn and Trp, respectively). In a parallel in vivo study [54], we showed that the addition of DOTAP had a positive effect on the extraction capabilities for Trp and Kyn (as well as other related amino acids), despite the fact that the significant swelling of the Im3m cubic phase and the related increase in interfacial area per unit cell led to a reduction of the interfacial area per unit volume to about 250 m 2 ·cm -3 . This is a strong argument for the fact that electrostatic attraction also plays a vital role in the extraction process. Evidently, bicontinuous cubic liquid crystals constitute a promising and versatile platform for both transdermal drug delivery and noninvasive extraction of endogenous low-molecular-weight biomarkers through the skin, where the interfacial area per unit volume in a matrix, as well as the incorporation of cationic or anionic molecules at the interface, can be used to optimize the delivery or extraction of particular solutes by the matrix.
Supplementary Materials: The following supporting information can be downloaded at: www.mdpi.com/xxx/s1, Figure S1: Diffraction patterns of DOTAP 5 wt %, 2.5 wt % and 1.25 wt % in H2O; Figure S2: Electrostatic swelling of GMO in water caused by addition of different amounts of cationic lipid DOTAP at 25 °C; Figure S3: Swelling curves showing the ratio between the lattice parameter, a, and the lipid monolayer thickness, l, plotted as a function of the lipid weight fraction. Interfacial area per unit cell (triangles, ×10 3 Å 2 ) and per unit volume (circles, m 2 ·cm −3 ). The relationship between K Q/w and interfacial area with respect to K bl/w (10 (squares); 3 (triangles); 1.5 (diamonds); 0.1 (crosses) and 0.01 (circles)).
These findings were also confirmed in the parallel in vivo study, which included 35 healthy test persons, wherein the capacity of four alternative matrices with different colloidal properties was studied. Four matrices, a chitosan-based hydrogel, an agarose-based hydrogel, and the two lipid-based matrices from the current study, were compared for the non-invasive sampling of low-molecular-weight biomarkers (i.e., tryptophan, kynurenine, tyrosine, and phenylalanine) [54]. The lipid-based matrices were twice as effective as the corresponding hydrogels, and the benefit from electrostatic attraction between matrix and solute was also evident as it appeared to compensate for the smaller interfacial area per unit volume at higher water contents.

Conclusions
We concluded that there was extensive swelling of the GMO-water system and the formation of a third cubic phase (Im3m) in the presence of DOTAP. We also observed that the cubic phases in this system all formed at rather extreme water activities (>0.9). Physiological salt concentrations counteracted the electrostatic effect of swelling and prevented the formation of the Im3m phase, while wearing the matrix on skin in vivo for several hours only induced a marginal decrease in lattice parameters-most probably an effect of water uptake by the skin tissue. Still, the presence of DOTAP at high salt concentrations resulted in the increased swelling of both the Ia3d and the subsequent Pn3m cubic phases.
The standard octanol/water partitioning identified both Kyn and Trp as rather hydrophilic substances (logD o/w (pH 7.4): -1.9 and -1.1 (D o/w (pH 7.4): 0.0 and 0.1 for Kyn and Trp, respectively), while the partitioning between a fully swollen Pn3m cubic phase (GMO/water) and water was more in favor of the cubic phase (K Q/w : 1.3 and 2.2 for Kyn and Trp, respectively). This could be attributed to the large interfacial area between the interconnected polar and apolar domains of almost 500 m 2 ·cm −3 where the bilayer/water partitioning was calculated for K bl/w (1.5 and 3.0 for Kyn and Trp, respectively). In a parallel in vivo study [54], we showed that the addition of DOTAP had a positive effect on the extraction capabilities for Trp and Kyn (as well as other related amino acids), despite the fact that the significant swelling of the Im3m cubic phase and the related increase in interfacial area per unit cell led to a reduction of the interfacial area per unit volume to about 250 m 2 ·cm −3 . This is a strong argument for the fact that electrostatic attraction also plays a vital role in the extraction process. Evidently, bicontinuous cubic liquid crystals constitute a promising and versatile platform for both transdermal drug delivery and non-invasive extraction of endogenous low-molecular-weight biomarkers through the skin, where the interfacial area per unit volume in a matrix, as well as the incorporation of cationic or anionic molecules at the interface, can be used to optimize the delivery or extraction of particular solutes by the matrix.
Supplementary Materials: The following supporting information can be downloaded at: https:// www.mdpi.com/article/10.3390/pharmaceutics15082031/s1, Figure S1: Diffraction patterns of DOTAP 5 wt %, 2.5 wt % and 1.25 wt % in H 2 O; Figure S2: Electrostatic swelling of GMO in water caused by addition of different amounts of cationic lipid DOTAP at 25 • C; Figure S3: Swelling curves showing the ratio between the lattice parameter, a, and the lipid monolayer thickness, l, plotted as a function of the lipid weight fraction. Figure S4: The change in the lattice parameter as function of DOTAP composition ranging from 2.5 wt % to 20 wt % of the total lipid content at various water contents; Figure S5: The effect of NaCl (150 mM) on the electrostatic swelling of GMO with various amounts of DOTAP; Tables S1-S3: LOD and LOQ for tryptophan and kynurenine, the precision and the accuracy of the HPLC-UV method, respectively; Tables S4-S8