Non-invasive skin sampling of tryptophan/kynurenine ratio in vitro towards a skin cancer biomarker

The tryptophan to kynurenine ratio (Trp/Kyn) has been proposed as a cancer biomarker. Non-invasive topical sampling of Trp/Kyn can therefore serve as a promising concept for skin cancer diagnostics. By performing in vitro pig skin permeability studies, we conclude that non-invasive topical sampling of Trp and Kyn is feasible. We explore the influence of different experimental conditions, which are relevant for the clinical in vivo setting, such as pH variations, sampling time, and microbial degradation of Trp and Kyn. The permeabilities of Trp and Kyn are overall similar. However, the permeated Trp/Kyn ratio is generally higher than unity due to endogenous Trp, which should be taken into account to obtain a non-biased Trp/Kyn ratio accurately reflecting systemic concentrations. Additionally, prolonged sampling time is associated with bacterial Trp and Kyn degradation and should be considered in a clinical setting. Finally, the experimental results are supported by the four permeation pathways model, predicting that the hydrophilic Trp and Kyn molecules mainly permeate through lipid defects (i.e., the porous pathway). However, the hydrophobic indole ring of Trp is suggested to result in a small but noticeable relative increase of Trp diffusion via pathways across the SC lipid lamellae, while the shunt pathway is proposed to slightly favor permeation of Kyn relative to Trp.

. Summary of tryptophan (Trp) and kynurenine (Kyn) quantities reported in the literature in human and mice blood, skin surface and the site of tumors.  Table S2. Comparison of tryptophan (Trp) and kynurenine (Kyn) concentrations in the lower Franz cell chamber, before and after the permeation experiment. The results are represented as a mean value ± standard error of the mean (Cbefore n=3 and Cafter n=6). Cbefore refers to the concentration of the aliquot taken before starting Franz cell experiment (kept in the fridge at +4 °C until the day of analysis (~60 h). Cafter is the concentration of the aliquot taken from the lower Franz cell chamber after 45 h of the permeation experiment (32 °C) and storing it in the fridge (+4 °C) overnight prior the analysis. Cbefore and Cafter were estimated the same day of analysis.

Calculation of tryptophan and kynurenine permeability constants based on the four permeation pathways theory
The theoretical flux of tryptophan (Trp) and kynurenine (Kyn) can be expressed according to the fourpathway model by the following equation: Eq. S1 where ! "# , ! $%&'(%$ , ! )*+,& , and ! !-(' are the permeability constants accounting for solute diffusion via free-volume diffusion through the lipid lamellar matrix, lateral diffusion along lipid multilamellar layers, diffusion through shunt pathways, and diffusion through aqueous pores (defects) of the lipid multilamellar matrix. 8 The concentration refers to the permeant (Trp or Kyn), which in this work was 1000 nmol cm -3 for all experiments. The equations describing the four permeability constants are presented below. 8 For the calculations of these constants, we used the physicochemical data summarized in the Table S4 for Trp and Kyn. The obtained results from the theoretical calculations are compiled in Table S7. where 0 represents the diffusion coefficient of the permeant in a lipid bilayer, 0 = -. 1.3 is the solute partition coefficient, * is the effective tortuosity factor, 56 is the thickness of SC (15×10 -4 cm), and #78,! is the van der Waals radius of the permeant. 8 The product of the parameters × 56 has previously been reported to be equal to 3.6 cm 9 and therefore used in this work, as well as in previous studies. 8,10 The parameter #78,! of Trp and Kyn was estimated from the molecular weight (see Table S1) based on the following relationship : ; 8 . Note that -/. is estimated to be equal to the distribution coefficient ( , see Table S1).

Lateral diffusion ( ! $%&'(%$ )
Lateral diffusion ( ! $%&'(%$ ) is mainly relevant for large hydrophobic solutes ( . > 500 Da) with similar molecular weights as the lipid species of the extracellular lipid lamellar matrix of SC. These molecules are likely to partition inside the lipid matrix, but unable to diffuse via free volume pockets as described above. Thus, this type of diffusion process is expected to be on the same order of magnitude as the lateral diffusion coefficient of the SC lipid species (3×10 -9 cm 2 /s) and can to a first approximation be calculated by the following equation. The aqueous pore pathway ( ! !-(' ) is suggested to represent a preferential pathway across SC for small hydrophilic molecules ( -/. < 1 and . < 500 Da). 11 The rationale for the existence of "pores" in the SC is based on highly dynamical imperfections in the multilamellar lipid matrix surrounding the corneocytes in the SC, which support water-filled pores. These imperfections may manifest themselves as, for example, separation of grain boundaries, vacancies in the lipid lattice leading to multimolecular voids, or defects created by steric constraints due to the highly curved geometry of the lipid matrix rounding the corneocytes. The overall effect of these defects is conceptualized as hydrophilic short-lived channels with a pore radius equal to where diffusion of water-soluble solutes across otherwise poorly permeable lipid regions can occur. 8,10 Diffusion via the pore pathway is based on several assumptions, which are discussed in detail elsewhere. 8,10-12 A general expression of the permeability coefficient ! !-(' is given by the following equation:

Eq. S5
In the equation above, is the SC porosity, ! is tortuosity of the SC, 56 is the SC thickness, and ! is the solute diffusion coefficient in the aqueous pore. 8,11 As shown, ! is a function of both the permeant and structural properties of the SC membrane, and can be represented as a product of the diffusion coefficient of the permeant at infinite dilution ! = and the hindrance factor ( ! ). Here, ! is the ratio of the hydrodynamic radius of the permeant *,! (see Table S1) and the effective pore radius of the SC (i.e., ! = *,! / ). For ! < 0.4, the diffusion hindrance factor, ( ! ), can be calculated as follows: 11,13 As proposed by Tang et al., 12 an equation similar to Eq. S5 can be written for the ions that carries the passive current during the impedance measurements. For clarity, this equation is presented below:

Eq. S7
In Eq. S7, >-, = *,>-, / where *,>-, is the hydrodynamic radius of the ion (a value equal to 2.2 Å was used for *,>-, ), while all other parameters have the same meaning as in Eq. S4, but for the ion instead of the permeant. By taking the ratio of Eq. S5 and Eq. S7 we can express the permeability of the hydrophilic permeant as a linear function of the passive ion permeability according to:

Eq. S8
The diffusion coefficient at infinite ion dilution, >-, = , is related to the absolute ion mobility %0) via the Einstein relation >-, = = %0) , which can be related to the conductivity of the electrolyte solution )-$ . 12 Further, by assuming that the cations and anions have the same mobilities, the following expression can be derived for >-, = : 12 Next, by defining the skin conductivity 56 on basis of the ion conductivity )-$ , in a similar manner as compared to the permeability coefficient of a permeant (e.g. see Eq. S5), the following equation can be derived: 12 Eq. S10 can be rewritten and inserted in Eq. S9, after which one obtains the following expression: 12 The expression of >-, = (Eq. S11) can now be inserted into Eq. S7 to obtain the following equation for >-, !-(' : 12 Eq. S12 where 56 can be defined in terms of the skin membrane resistance ?'? . The latter parameter can easily be determined experimentally and related to 56 according to: 12 Eq. S13 For clarity, we insert Eq. S13 into Eq. S12 and obtain the following expression: 12 Eq. S14 where @ is defined as:

Eq. S15
A unit analysis of the @ yields: Eq. S16 which is consistent with: Eq. S17 The expression of >-, !-(' (Eq. S14) can now be inserted in Eq. S8: Eq. S18 By defining A according to following: 12 Eq. S19 and inserting A into Eq. S18, we obtain: Eq. S20 By taking the logarithm of Eq. S20 one obtains:   Table S5. The permeability coefficients ( # ) were obtained from the cumulative amount permeated after 8h and the initial skin membrane resistance ( B)B ).   Fig. S3. Note that the slopes are theoretically expected to be −1, which is sometimes clearly not the case. Therefore, each data point in Fig. S3 was extrapolated using the ideal slope value of −1 to obtain individual values of D according to Eq. S21. The values of D were then averaged for each pH value and compiled in Table S6. This procedure follows from previous work. 12  Once the individual values of A (i.e., the intercepts) are obtained, it is possible to calculate the ratio

Condition
according Eq. S22: Note that 6 in Eq. S22 only contains parameters with known values and can be expressed according to: Eq. S23 In these calculations, the mean value of individual A values, from each pH level, was used to obtain the corresponding value of the ratio . In other words, the values of A obtained from the linear regression analysis was not used, which is in accordance to previous work. 12 Next, Eq. S22 was solved iteratively for a solution of the pore radius for each pH value (see Table S6). For clarity, Eq. S22 can be rewritten in the actual form that was iteratively evaluated by the software Wolfram Alpha for a solution of the pore radius : Eq. S24 As a control, ! = *,! / was calculated to confirm that ! < 0.4, which is the criterion for Eq. S6 to be valid. As shown in Table S6, when ! was determined based on values of A from each pH value, this criterion was not always fulfilled. This is likely due to the fact that the biological variation of the skin membranes become more pronounced in small data sets, while larger data sets tend to limit the influence of biological variation. Therefore, to resolve the problem when ! > 0.4 (or when could not be determined, which was the case at pH 12.0), it was decided to use a value of ! based on a wider data set, corresponding to the mean value of A obtained at pH values of 2.0, 5.5, 7.4, 8.8, and 12.0. This strategy was used in the three cases marked with * in Table S6. Finally, the permeability coefficient ! !-(' was calculated according to Eq. S20 by employing the initial values of ?'? from each skin membrane; the mean value of ! !-(' from each pH level is compiled in Table S7. For comparison, ! !-(' was also calculated according to Eq. S5. However, this equation always generated significantly higher values, most likely due to the great uncertainty of the estimated values of the input parameters. In addition, Eq. S5 only relies on the diffusion hindrance factor for the permeant ( ! ), while Eq. S20 uses the ratio of the hindrance factor for the permeant ( ! ) and the ion ( >-, ). For these reasons, we only consider the results obtained with Eq. S20 from now on.

Theoretical contribution of each of the four permeation pathways
Finally, the theoretical permeability constants ! "# , ! $%&'(%$ , ! )*+,& , and ! !-(' were calculated for each permeation pathway for Trp and Kyn at different pH values according to Eq. S2, S3, S4, and S20, respectively. All data are compiled in Table S7. Table S7. Contribution of each of the four permeability constants to the total permeability constant ( # ) for tryptophan (Trp) and kynurenine (Kyn) based on calculations following the four permeation pathways theory. Values marked with * indicate that # > 0.4 (or that could not be determined). In these cases, # #/*) was estimated from the mean value of D obtained at pH values of 2.0, 5.5, 7.4, 8.8, and 12.0 (see Table S6).