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Therapeutic Delivery

Flux through silicone and human skin fitted to a series/parallel model

Background: Recent reports of the good correlation between maximum flux through human skin in vitro from water, JMHAQ, and maximum flux through silicone from water, JMPAQ, demand that the mechanism of maximum flux across these two apparently quite different membranes be compared to understand the bases of the correlation. Results/discussion: A n = 70 log JMPAQ database and a matched n = 55 log JMHAQ database of molecules were found to fit well to a series/parallel model where three parallel solubility dependent pathways existed: a lipid pathway, an aqueous pathway, and a series pathway of alternating lipid and aqueous phases. Conclusion: The results of this analysis surprisingly suggest that the architecture of the two membranes present similar solubility based pathways through which drugs diffuse.

The topical delivery of drugs into (dermal) and through (transdermal) human skin to affect therapeutic benefits has been used as an alternative to oral delivery for centuries. The most obvious advantage of topical, compared with oral, delivery is that local therapeutic activity can be achieved while minimizing systemic delivery to off-target sites that could contribute to the side effects of the drug. The exact mechanism by which drugs permeate the assumed rate-limiting barrier to topical delivery in human skin, the stratum corneum (SC), has been the subject of much speculation and debate [1–3] . However, the resolution of the debate is important to the rational design of new prodrugs and the identification of new drug entities for which topical delivery is to be optimized. Equally controversial and important is the debate about which surrogate for in vivo human skin is most appropriate in experiments designed to measure topical delivery [45]. Although there are questions about the effect of nonphysiological hydration of in vitro human skin in diffusion cell experiments on absolute values of the amount of drug delivered in vitro versus in vivo conditions, in vitro human skin is probably the best surrogate for in vivo human skin. This is especially true if the use

10.4155/TDE.14.12 © 2014 Future Science Ltd

John Prybylski*,1 & Kenneth B Sloan1 1 University of Florida, Department of Medicinal Chemistry, Gainesville, FL 32611, USA *Author for correspondence: [email protected]

of various in vitro animal skins, as a surrogate for human skin, is precluded on ethical grounds. However, the use of in vitro human skin experiments is expensive and beset with problems of how to normalize intersubject variability [3] . In response to the debate about the exact mechanism by which drugs and prodrugs permeate and traverse the SC, substantial insight has been obtained from observations on trends in the effect of easily measured and understood physicochemical properties, such as molecular weight, lipid and aqueous solubilities, on the amount of drug or prodrug delivered per unit time and unit area: flux (J). For the maximum flux (JM) of several series of prodrugs through hairless mouse skin in vitro (JMM) from the lipid vehicle isopropyl myristate (IPM), JMMIPM, a balance of lipid and aqueous solubilities of the prodrug was observed to be essential if delivery of the parent drug by the prodrug or of the intact prodrug were to be optimized [6,7] . This observation precluded the possibility that the dependence of optimized flux on water solubility was due to a stagnant water layer at the interface between the donor phase and the membrane [8] . The donor phase was a lipid.

Therapeutic Delivery (2014) 5(4), 391–407

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Research Article  Prybylski & Sloan

Key Terms Fick’s Law: Differential equation describing diffusion of dissolved solutes through a solution. It can be used to describe passive diffusion across membranes. JMPAQ : Maximum flux of a permeant through silicone from a saturated solution of the permeant in water. JMHAQ : Maximum flux of a permeant through human skin in vitro from a saturated solution of the permeant in water. Series/parallel model: Modeling concept from electromagnetism wherein an overall property (e.g., total capacitance) of a circuit can be defined by the arrangement of individual similar properties (e.g., capacitors) on the circuit. Partition coefficient: Ratio of thermodynamic activities of a compound at equilibrium in a two solvent system. It is sometimes defined as a ratio of solubilities of a compound in two solvents since such saturated solutions are generally at maximum thermodynamic activity.

When molecular weight (MW) solubility in the lipid IPM ( SIPM) and in water (SAQ ) and JMMIPM data for seven series of prodrugs became available, the data was fit to an expansion of Fick’s Law, Equation 1, where JM and solubility in the first few layers of the membrane (SM1) were explicitly dependent on SIPM and SAQ. The result was the Roberts-Sloan (RS) Equation 2 [9] .

(Equation 1)



(Equation 2)

Where D is the diffusion coefficient, L is the thickness of the membrane, CM1 is the concentration of the drug or prodrug in the first few layers of the membrane, CMn is the concentration of the drug or prodrug permeant in the last few layers of the membrane and is assumed to approach zero at steady state, x is a constant, y and z are coefficients to the independent variables, SAQ, SIPM and MW, obtained by the regression analysis. The result of the fit was that the value of y for the JMMIPM database fit to RS Equation 2 was about 0.5, which meant that the water solubility of the permeant (1 – y = 0.5) was equally important in determining SM1 and the maximum flux of the permeants. Similar values for y and the dependence of optimized flux on SAQ have been obtained for the fit of larger, diverse databases to RS where the lipid solubility independent variable was solubility in octanol (SOCT ) or solubility in mineral oil (SMO) and the membranes were human skin in vitro (JMH) or silicone (JMP) [7] . The dependence of maximum flux on the water solubility does not derive from the use of an aqueous donor

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phase because the dependence obtains even if the donor phase is a lipid. The dependence of maximum flux on the water solubility of the permeant also does not derive from the inability of highly lipid soluble molecules to traverse the water rich regions of the viable epidermis and dermis. Prodrugs of moderately water soluble parent drugs that hydrolyze with short half-lives of 3–5 min provide evidence that this conclusion is valid [10] . For those types of prodrugs, the members of a series that exhibit greater lipid solubilities and lesser water solubilities than their parent drug, give lower maximum flux values than members of the same series that exhibit lesser lipid solubilities but greater water solubilities. During their diffusion across the membrane the more water soluble members and the more lipid soluble members of the series each hydrolyze to the same moderately water soluble parent drug. Thus, the viable epidermis and dermis do not present different water solubility-based resistances to the prodrug exhibiting greater initial lipid solubility than the one exhibiting initial greater water solubility in the same series. The different initial water and lipid solubilities of two members of the same series of prodrugs only matters when estimating differences in their initial solubilities in the first few layers of the membrane, SM1 (based on a balance of lipid and aqueous solubilities of the prodrugs), which dictate their JM values. The origin of the dependence of SM1 and JM on water solubility resides in the SC itself and the multiple alternating lipid and aqueous phases in the bilayers between corneocytes in the SC. In order to explain the origin in the SC of the dependence of JM on the SAQ, the JMMIPM database was also fit to Equation 3, which allows three parallel paths through the SC. In Equation 3, the relative contributions of flux through an aqueous phase (JD), which only depends on the SAQ of the permeant, in parallel with flux through a lipid phase (JC), which only depends on the SIPM of the permeant, in parallel with flux through a series of alternating aqueous and lipid phases (JA), which depends on a balance of SAQ and SIPM, can be assessed [11] . The result was that the path through the series of alternating aqueous and lipid phases exhibited the highest capacity to support flux of the members of a logJMMIPM database while the existence of a parallel path that only depended on SAQ of the permeant was not necessary to explain the data. The dependence of flux on SAQ (and SIPM) resides in the series/parallel path. To date only the JMMIPM data has been fitted to Equation 3 and the goodness of that fit is the same as the fit of JMMIPM data to Equation 2.



(Equation 3)

Recently it has been shown that JM through a silicone membrane from water (JMPAQ ) data could be fitted to

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Flux through silicone & human skin fitted to a series/parallel model 

Research Article

Table 1. The n = 75 database containing all the members of the n = 70 maximum flux through silicone from water (log JMPAQ ) database and matched n = 55 maximum flux through human skin from the water database (log JMHAQ). Compound no.

Compound

log KOCT:AQ 

log JMPAQ†

log JMHAQ†

Ref.

4-aminobenzoic acid esters 1

C1‡

1.12

-0.61

-0.66

[8,17–18]

2

C2

[8,17–18]

1.64

-0.21

-0.92

3

C3

‡

2.18

-0.11

–

4

C4‡

2.69

-0.14

-1.26

5

C5‡

3.23

-0.50

–

[8,17]

6

C6

‡

3.76

-0.96

–

[8,17]

7

C7‡

4.29

-1.59

–

[8,17]

‡

[8,17] [8,17–18]

4-hydroxybenzoic acid esters 8

C1‡

1.45

-0.42

-1.60

[19–21]

9

C2

1.95

-0.44

-1.49

[19–21]

10

C3

‡

2.45

-0.49

-1.58

[19–21]

11

C4‡

2.95

-0.36

-1.62

[19–21]

12

C5

‡

3.45

-0.61

–

[20,21]

13

C6

‡

3.95

-1.07

-2.46

[19–21]

14

C7‡

4.45

-1.69

–

[20,21]

15

C8

4.95

-2.05

–

[20,21]

16

Aminopyrine

0.50

0.14

-0.60

[22,23]

17

Antipyrine

-1.55

-0.28

-0.53

[22,23]

18

Cyclobarbitol

0.87

-1.46

-1.98

[22,23]

19

5-fluorouracil

-0.86

–

-2.18

[22,23]

20

Flurbiprofen

3.86

-0.53

-1.27

[22,23]

21

Ibuprofen

3.94

0.41

-0.92

[22,23]

22

Indomethacin 3.19

-2.69

-2.79

[22,23]

23

Ketoprofen

3.11

-1.20

-1.36

[22,23]

24

Lidocaine

2.37

0.93

-0.54

[22,23]

25

Nicorandil

-1.02

-0.83

-1.47

[22,23]

26

Estradiol

3.86

-2.95

-4.74

[23–25]

27

Diclofenac sodium

-0.96

-1.57

-1.47

[22,23]

28

Phenol

1.49

2.11

0.84

[26,27]

1.17¶

–

‡

‡

Phenols with additional substituents 29

2,6-dichloro §

2.75

[26]

The information in the database were fit to series/parallel model in Equation 3. Only the compound names, octanol-water partition coefficients (log KOCT:AQ) and flux values are listed, as the solubility values (SAQ and SOCT) and molecular weights are provided elsewhere [12,13]. † Flux in µm cm−2 h-1. ‡ Refers to the number of carbons on the alkyl chain of the prodrug moiety. § Refers to the different substituent on the phenol apart from the OH. ¶ Calculated in [12] from permeability coefficient through silicone from water (log PPAQ) + log SAQ × log PAQ value was retrieved from the source reporting the log KOCT:AQ. # Calculated in [12] from log KOCT:AQ = log SOCT–log SAQ. †† Estimated in [12] from [41]. ‡‡ Interpolated by [12] from C1 and C4 log KOCT:AQ.

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Research Article  Prybylski & Sloan

Table 1. The n = 75 database containing all the members of the n = 70 maximum flux through silicone from water (log JMPAQ ) database and matched n = 55 maximum flux through human skin from the water database (log JMHAQ) (cont.). Compound no.

Compound

log KOCT:AQ 

log JMPAQ†

log JMHAQ†

Ref.

30

4-bromo §

2.59

1.47¶

0.50

[26,27]

31

2-nitro

§

1.79

–

32

3-nitro

§

33

4-nitro §

34

0.26

[26,28]

2.00

0.64

¶

-0.28

[26,27]

1.91

0.73 ¶

-0.25

[26,27]

Diazepam

2.82

-1.16

–

35

Lidocaine

2.33

1.10

-0.77

[25,26]

36

Nicotine

1.23 

3.04 ¶

2.11

[26,27]

37

Salicylic acid

2.26

0.03 ¶

-0.53

[4,27]

38

2-napthol

2.70

0.19

¶

-0.71

[4,27]

39

Thymol

3.34

0.69 ¶

-0.45

[4,27]

40

Captopril

0.63

-0.58

–

[29]

41

C1

¶

¶

[26]

Captopril esters 1.18

-0.72

–

[29]

42

‡

C2

1.66

-0.46

–

[29]

43

C3‡

2.14

-0.39

–

[29]

44

C4

‡

2.67

-0.13

–

[29]

45

C5

‡

3.21

-0.27

–

[29]

46

C6‡

3.67

-0.61

–

[29]

47

Caffeine

-0.61

-1.34

-1.83

[30]

48

Benzoic acid

1.78

0.34

0.69

[30,31]

49

Salicylic acid

1.89 #

-0.07

0.18

[30,31]

50

Ibuprofen

3.94

-0.04

-0.93

[32,33]

51

Piroxicam

0.69

-2.93

-3.47

 –

2.09

1.40

‡

#

#

#

††

††

Nicotinic acid esters 52

C1‡

0.85

53

C2

‡

1.39

1.80

0.30

[35,36]

54

C4‡

2.47

0.62

-0.46

[34–36]

55

C6‡

3.51

-0.22

-1.76

[34–36]

56

C8

4.71

-1.20

–

[34,35]

57

Benzyl

2.40

0.23

-1.21

[35–37]

‡

‡‡

[12,34–35]

Miscellaneous sunscreen structures and other compounds 58

Misc 1

5.75

-1.84

-2.72

[38,39]

59

Misc 2

6.51

–

-2.50

[38,39]

The information in the database were fit to series/parallel model in Equation 3. Only the compound names, octanol-water partition coefficients (log KOCT:AQ) and flux values are listed, as the solubility values (SAQ and SOCT) and molecular weights are provided elsewhere [12,13]. † Flux in µm cm−2 h-1. ‡ Refers to the number of carbons on the alkyl chain of the prodrug moiety. § Refers to the different substituent on the phenol apart from the OH. ¶ Calculated in [12] from permeability coefficient through silicone from water (log PPAQ) + log SAQ × log PAQ value was retrieved from the source reporting the log KOCT:AQ. # Calculated in [12] from log KOCT:AQ = log SOCT–log SAQ. †† Estimated in [12] from [41]. ‡‡ Interpolated by [12] from C1 and C4 log KOCT:AQ.

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Therapeutic Delivery (2014) 5(4)

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Flux through silicone & human skin fitted to a series/parallel model 

Research Article

Table 1. The n = 75 database containing all the members of the n = 70 maximum flux through silicone from water (log JMPAQ ) database and matched n = 55 maximum flux through human skin from the water database (log JMHAQ) (cont.). Compound no.

Compound

log KOCT:AQ 

log JMPAQ†

log JMHAQ†

Ref.

60

Misc 2’

4.43

-1.65

–

[12,39]

61

Misc 3

5.13

-1.94

-2.08

[38,39]

62

Misc 4

4.83

–

-1.79

[38]

63

Misc 5

3.82

-1.04

-1.72

[38,39]

64

Misc 6

4.64

-2.08

-2.44

[38,39]

65

Misc 7

4.39

-1.64

-1.87

[38,39]

66

Misc 8

3.42

-0.29

-0.78

[38,39]

67

Misc 9

4.53

-0.87

-1.25

[38,39]

68

Misc 10

3.07

–

-0.13

[38]

Recently added phenols with additional substituents 69

4-chloro-3methyl

3.10

1.01

0.29

[13–14,40]

70

4-chloro-3,5dimethyl

3.39

-0.03

-0.95

[13–14,40]

71

3,4-dimethyl

2.35

1.37

0.17

[13–14,40]

72

4-methyl

1.95

1.62

0.53

[13–14,40]

73

2,4-dichloro

3.08

1.16

0.27

[13–14,40]

74

2,4,6-trichloro 3.69

0.49

-0.57

[13–14,40]

75

3-methyl

1.61

0.54

[13–14,40]

1.96

The information in the database were fit to series/parallel model in Equation 3. Only the compound names, octanol-water partition coefficients (log KOCT:AQ) and flux values are listed, as the solubility values (SAQ and SOCT) and molecular weights are provided elsewhere [12,13]. † Flux in µm cm−2 h-1. ‡ Refers to the number of carbons on the alkyl chain of the prodrug moiety. § Refers to the different substituent on the phenol apart from the OH. ¶ Calculated in [12] from permeability coefficient through silicone from water (log PPAQ) + log SAQ × log PAQ value was retrieved from the source reporting the log KOCT:AQ. # Calculated in [12] from log KOCT:AQ = log SOCT–log SAQ. †† Estimated in [12] from [41]. ‡‡ Interpolated by [12] from C1 and C4 log KOCT:AQ.

the RS equation and that there was a good correlation between JMPAQ and JM through human skin in vitro from water, JMHAQ [12,13] . This suggests that JMPAQ may be a good surrogate for predicting JMHAQ. Here, we explore whether an equally good fit can be obtained when JMPAQ and JMHAQ data are fitted to the series/parallel Equation 3, and whether any similarities in the capacity of each path in Equation 3 to support flux through the two different membranes also supports the conclusion arrived at by their fit to Equation 2 that demonstrates JMPAQ is a good surrogate for predicting JMHAQ. Experimental In order to ensure a valid comparison between the fit of log JMPAQ and log JMHAQ values to the series/parallel model, Equation 3, and their fit to RS Equation 2, a recently extended n = 70 log JMPAQ database and n =

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55 log JMHAQ database (containing in vitro:in vivo data, 45:10), of which 52 members were common to both databases, were used (Table 1, the n = 75 database contained all the members of the n = 70 and n = 55 databases). These databases have demonstrated good fits to the RS equation (Equation 2) [12,13] . Because a larger n = 185 log JMHAQ database (containing only in vitro data) [14–16] is available, which has demonstrated a good fit to Equation 2, this database was also fitted to Equation 3, but only to investigate how the log JMHAQ fit changes when the database size and range increases. For all databases used, the independent variables were water solubility (SAQ ), octanol solubility (SOCT, as a substitute for SLIPID or SIPM) and MW, and the dependent variable was the maximum flux through silicone from water (log JMPAQ ) or the maximum flux through human skin in vitro from water (log JMHAQ ). All independent and dependent vari-

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395

Research Article  Prybylski & Sloan ables were calculated or obtained from literature sources by those who assembled the databases [12,13] . Regressions were performed using IBM SPSS v. 20. The regressions were given as starting points, a = 1, b = 1, c = 0, d = 0 and ϕ = 0 and the non-ϕ coefficients were constrained from dropping below zero; these precautions were taken to prevent irrational output from failed regressions, and should not have grossly affected the outcome. In the original paper wherein the series/parallel model was constructed from in vitro JMMIPM data, the ratios of maximum flux through the series pathway (JA) and flux through the lipid-only pathway (JC) were found to have a negative, nonlinear correlation with the IPM–water partition coefficient (log K IPM:AQ ) with a threshold for switch from JA to JC as the predominant pathway of logK IPM:AQ = 1. This correlation demonstrated the threshold of log KIPM:AQ values below which the series pathway is the dominant pathway for diffusion through hairless mouse skin in vitro from IPM. This threshold is of interest because it indicates which solubility value (aqueous or lipid) for a given compound has the greatest influence on that compound’s maximum flux based upon the compound’s log K IPM:AQ. Following this reasoning, similar ratio trends were investigated from the n = 70 log JMPAQ and n = 55 log JMHAQ databases fitted to Equation 3. The correlations of the ratios of JA/JC, JA/JD, JA/JC+ JD and JA1/JA2 with the octanol–water partition coefficients (log KOCT:AQ ) were determined from Equation 3 for the purpose of defining the dominant pathway thresholds quantitatively, rather than the graphical approach used previously. The correlation equations were determined by the pathway flux terms defined in the original paper [11] with the addition of JA1 and JA2 for fluxes through the lipid and aqueous phases in the series pathway.



(Equation 4)



(Equation 5)

octanol and water (SOCT/SAQ ), exact expressions for ratios of interest in terms of KOCT:AQ and MW can be determined (see Supplementary data for the expressions). These expressions are useful because they determine the dominant flux term – either describing the dominant pathway or the limiting domain of the series pathway – relative to measurable properties of a compound. Thus, if the compounds in both the n = 55 log JMHAQ and n = 70 log JMPAQ databases are found to diffuse through the same type of pathway in both silicone and SC as determined by JA /JC, JA /JD, JA /JC + JD and JA1/ JA2, then that will be evidence that it is a comparable architecture of these two membranes under the conditions of the diffusion experiments that allows their measured maximum flux values through them to correlate well. This is especially indicated if all the respective pathways in silicone and human skin are similarly comparable to one another. For these dominant pathways to be ‘similarly comparable’, the equations describing their maximum flux in terms of measurable physicochemical properties should transform similarly (i.e., the coefficients a, b, c and d in Equations 4–8 found for the log JMPAQ database should each have the same ratio to the respective coefficients found for the log JMHAQ database); this similar comparability is necessary for a good correlation between log JMPAQ and log JMHAQ in their fit to Equation 3 across a broad range of KOCT:AQ values, which has been demonstrated for these databases in their fit to Equation 2 [13] . The KOCT:AQ value for the switch from the series pathway to the lipid-only pathway should also be similar for both JMPAQ and JMHAQ. Finally, to determine whether or not all parallel pathways in the series/parallel model are necessary to explain the maximum flux data in the n = 70 log JMPAQ and the n = 55 log JMHAQ databases, the adjusted r2 for the databases fitted to Equation 3, where c, d or a and b are set to 0, were compared. The adjusted r2 was used to normalize the quality of fit indicated by r2 to the number of regression coefficients, so the calculation of adjusted r2 took the usual form of 1-(1-r2)(n-1)/(n-p-1), where n is the database size and p is the number of regression coefficients. Results & discussion



(Equation 6)



(Equation 7)



(Equation 8)

From these definitions, and the assumption that KOCT:AQ is equivalent to the solubility ratio between

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Therapeutic Delivery (2014) 5(4)

Fit of flux through silicone from water to the series/parallel equation

When the n = 70 log JMPAQ database was fit to the series/ parallel model, Equation 3, the r2 was 0.907, the average absolute residual log JMPAQ (Δlog JMPAQ ) was 0.293, and the coefficient values were a = 0.0114, b = 6.45, c = 0.000957, d = 0.00380 and ϕ = -0.00562. This is comparable to the fit of this database to the RS equation (Equation 2) , which also gives an r2 of 0.907 and gives a similar Δlog JMPAQ of 0.300. Figure 1 displays how the log JMPAQ values calculated by Equation 3 correlate

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Flux through silicone & human skin fitted to a series/parallel model 

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Figure 1. The fit of the series/parallel model (Equation 3) to the n = 70 maximum flux through silicone from water database. The solid line indicates when the experimental log JMPAQ is equivalent to the log JMPAQ calculated by the series/parallel model. The dashed lines indicate the boundaries where the absolute residual log JMPAQ is greater than 1.0. Calc: Calculated; Exp: Experimental; Log JMPAQ : Maximum flux through a silicone membrane from water.

with the experimental log JMPAQ values in the n = 70 log JMPAQ database. Based only upon the adjusted r2 analysis, each parallel monophasic (lipid or aqueous) pathway seems to contribute to the good fit of the n = 70 log JMPAQ database to Equation 3 : when c was set to 0, the adjusted r2 was 0.883; when d was set to 0, the adjusted r2 was 0.887; when both c and d were set to 0, the adjusted r2 was 0.859. However, removing the series term from Equation 3 gives an equation that resembles RS, Equation 2, but with a different MW transformation and a logarithm of sums of solubility terms rather than a sum of logarithms of solubility terms; the estimates for the coefficients when the series term is removed are c = 0.0164, d = 0.00932, ϕ = -0.00842 and the adjusted r2 was 0.836. All of the adjusted r2 values were lower than the adjusted r2 of the complete model, which is 0.900, and the unadjusted r2 of the complete model, which is 0.907. Table 2 lists the calculated flux through these pathways, along with key flux ratios. From this data, it is apparent that the aque-

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ous-only pathway is dominant for only a small number of compounds in the n = 70 database (compounds 17, 27 and 47), so there is not enough statistical strength to conclude that the aqueous-only pathway is necessary to explain flux of most molecules through silicone at this time. As the fit of the database to Equation 3 is somewhat improved by including the aqueous-only pathway, the analysis will continue to include the aqueous-only pathway, however, it should be emphasized that any results presented including this pathway, at present, lack statistical power. Fit of flux through human skin in vitro from water to the series/parallel equation

When the n = 55 log JMHAQ database was fit to Equation 3, the r2 was 0.872, the Δlog JMHAQ was 0.301, and the coefficient values were a = 0.000734, b = 0.334, c = 0.0000563, d = 0.00138 and ϕ = -0.00244. This is somewhat worse than the fit of the n = 55 log JMHAQ database to the RS equation (Equation 2), which gave an

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Table 2. The pathway flux values and octanol–water partition coefficients for the n = 70 maximum flux through silicone from water database. Compound log KOCT:AQ  JM†

JA†

JA1†

JA2†

J C†

J D†

JA /(JC+ JD) ‡ JA1/JA2‡

1

1.12

0.245

0.513

0.534

13.177

0.045

0.008

9.759

0.041

2

1.64

0.617

0.538

0.601

5.135

0.050

0.003

10.063

0.117

3

2.18

0.776

0.587

0.794

2.254

0.067

0.001

8.638

0.352

4

2.69

0.724

0.401

0.796

0.806

0.067

0.000

5.952

0.988

5

3.23

0.316

0.150

0.592

0.200

0.050

0.000

3.003

2.958

6

3.76

0.110

0.042

0.401

0.046

0.034

0.000

1.235

8.641

7

4.29

0.026

0.010

0.266

0.011

0.022

0.000

0.455

25.185

8

1.45

0.380

0.655

0.711

8.287

0.060

0.005

10.143

0.086

9

1.95

0.363

0.526

0.650

2.750

0.055

0.002

9.359

0.236

10

2.45

0.324

0.386

0.637

0.981

0.053

0.001

7.146

0.649

11

2.95

0.437

0.364

1.013

0.569

0.085

0.000

4.271

1.779

12

3.45

0.245

0.141

0.826

0.170

0.069

0.000

2.031

4.858

13

3.95

0.085

0.042

0.600

0.045

0.050

0.000

0.836

13.241

14

4.45

0.020

0.011

0.407

0.011

0.034

0.000

0.322

36.012

15

4.95

0.009

0.002

0.209

0.002

0.018

0.000

0.121

97.757

16

0.50

1.380

0.432

0.434

101.742

0.036

0.060

4.482

0.004

17

-1.55

0.525

0.123

0.123

2052.244

0.010

1.210

0.101

0.000

18

0.87

0.035

0.051

0.051

5.406

0.004

0.003

6.778

0.009

20

3.86

0.295

0.042

0.402

0.046

0.034

0.000

1.230

8.684

21

3.94

2.570

0.088

1.439

0.094

0.121

0.000

0.729

15.334

22

3.19

0.002

0.004

0.005

0.011

0.000

0.000

7.804

0.508

23

3.11

0.063

0.168

0.396

0.293

0.033

0.000

5.038

1.353

24

2.37

8.511

1.272

1.662

5.429

0.139

0.003

8.918

0.306

25

-1.02

0.148

0.013

0.013

82.635

0.001

0.049

0.264

0.000

26

3.86

0.001

0.001

0.011

0.002

0.001

0.000

1.644

6.235

27

-0.96

0.027

0.003

0.003

40.148

0.000

0.024

0.121

0.000

28

1.49

128.825

90.089

104.209

664.881

8.746

0.392

9.859

0.157

29

2.75

14.791

4.961

12.585

8.189

1.056

0.005

4.675

1.537

30

2.59

29.512

19.536

38.336

39.837

3.217

0.023

6.028

0.962

32

2.00

4.365

13.687

18.400

53.432

1.544

0.032

8.686

0.344

33

1.91

5.370

21.759

27.850

99.495

2.337

0.059

9.081

0.280

34

2.82

0.069

0.019

0.028

0.056

0.002

0.000

7.877

0.492

35

2.33

12.589

3.661

4.683

16.776

0.393

0.010

9.086

0.279

36

1.23

1096.478 139.823 146.377

3122.844

12.285

1.841

9.898

0.047

37

2.26

1.072

8.306

0.441

0.005

7.218

0.633

3.218

5.254

The pathway flux values for the JA, JA1, JA2, JC and the JD are not in logarithm form, and are calculated using Equation 4–8. The value for JM is the experimental value (Exp log JMPAQ) not in logarithm form. The compound numbers correspond to the numbering scheme in Table 1. † Units are μm cm−2 h-1. ‡ The series pathway is dominant when JA is greater than both JC and JD. The lipid domain of the series pathway is limiting when JA1 is less than JA2. See Supplementary data for more discussion on these ratios. J: Pathway flux; JA: Lipid–aqueous series pathway; JA1: The lipid domain of the series pathway; JA2:The aqueous domain of the series pathway; JC: The lipid-only pathway; J D: The aqueous-only pathway; Log KOCT:AQ: Octanol–water partition coefficients, log JMPAQ: Maximum flux through silicone from water.

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Table 2. The pathway flux values and octanol–water partition coefficients for the n = 70 maximum flux through silicone from water database (cont.). Compound log KOCT:AQ  JM†

JA†

JA1†

JA2†

J C†

J D†

JA /(JC+ JD) ‡ JA1/JA2‡

38

2.70

1.549

1.754

4.642

2.819

0.390

0.002

4.483

1.647

39

3.34

4.898

3.031

23.603

3.477

1.981

0.002

1.529

6.787

40

0.63

0.263

0.192

0.193

28.912

0.016

0.017

5.771

0.007

41

1.18

0.191

0.330

0.337

16.501

0.028

0.010

8.687

0.020

42

1.66

0.347

0.735

0.774

14.613

0.065

0.009

9.991

0.053

43

2.14

0.407

0.879

1.000

7.289

0.084

0.004

9.967

0.137

44

2.67

0.741

1.988

2.762

7.099

0.232

0.004

8.426

0.389

45

3.21

0.537

1.636

3.568

3.023

0.299

0.002

5.432

1.181

46

3.67

0.245

0.633

2.476

0.851

0.208

0.001

3.041

2.909

47

-0.61

0.046

0.023

0.023

47.359

0.002

0.028

0.776

0.000

48

1.78

2.188

2.378

2.954

12.193

0.248

0.007

9.321

0.242

49

1.89

0.851

2.026

2.573

9.536

0.216

0.006

9.145

0.270

50

3.94

0.912

0.184

3.006

0.196

0.252

0.000

0.729

15.334

0.000

51

0.69

0.001

0.000

0.182

0.000

0.000

2.807

0.002

52

0.85

123.027

108.497 111.192

4476.592

9.332

2.640

9.063

0.025

53

1.39

63.096

10.133

144.484

0.915

0.085

10.135

0.075

10.898

54

2.47

4.169

2.647

4.465

6.500

0.375

0.004

6.991

0.687

55

3.51

0.603

0.257

1.708

0.303

0.143

0.000

1.793

5.637

56

4.71

0.063

0.018

1.188

0.018

0.100

0.000

0.177

66.244

57

2.40

1.698

0.307

0.418

1.157

0.035

0.001

8.586

0.361

58

5.75

0.014

0.000

0.107

0.000

0.009

0.000

0.026

458.519

60

4.43

0.022

0.003

0.117

0.003

0.010

0.000

0.297

39.135

61

5.13

0.011

0.001

0.199

0.001

0.017

0.000

0.084

141.683

63

3.82

0.091

0.017

0.172

0.019

0.014

0.000

1.167

9.204

64

4.64

0.008

0.003

0.166

0.003

0.014

0.000

0.210

55.769

65

4.39

0.023

0.011

0.220

0.011

0.018

0.000

0.574

19.761

66

3.42

0.513

0.418

2.637

0.497

0.221

0.000

1.888

5.304

67

4.53

0.135

0.032

0.797

0.033

0.067

0.000

0.474

24.120

69

4.53

10.233

15.431

79.860

19.127

6.702

0.011

2.298

4.175

70

3.10

0.933

0.860

6.976

0.980

0.585

0.001

1.467

7.116

71

3.39

23.442

11.263

21.401

23.775

1.796

0.014

6.222

0.900

72

2.35

41.687

34.813

48.884

120.947

4.103

0.071

8.341

0.404

73

1.95

14.454

11.963

51.268

15.603

4.303

0.009

2.774

3.286

74

3.08

3.090

1.899

19.890

2.099

1.669

0.001

1.137

9.475

75

3.69

40.738

41.576

58.772

142.101

4.932

0.084

8.288

0.414

The pathway flux values for the JA, JA1, JA2, JC and the JD are not in logarithm form, and are calculated using Equation 4–8. The value for JM is the experimental value (Exp log JMPAQ) not in logarithm form. The compound numbers correspond to the numbering scheme in Table 1. † Units are μm cm−2 h-1. ‡ The series pathway is dominant when JA is greater than both JC and JD. The lipid domain of the series pathway is limiting when JA1 is less than JA2. See Supplementary data for more discussion on these ratios. J: Pathway flux; JA: Lipid–aqueous series pathway; JA1: The lipid domain of the series pathway; JA2:The aqueous domain of the series pathway; JC: The lipid-only pathway; J D: The aqueous-only pathway; Log KOCT:AQ: Octanol–water partition coefficients, log JMPAQ: Maximum flux through silicone from water.

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Figure 2. The fit of the series/parallel model Equation 3 to the n = 55 log JMHAQ database. The solid line indicates when the experimental log JMHAQ is equivalent to the log JMHAQ calculated by the series/parallel model. The dashed lines indicate the boundaries where the absolute residual log JMHAQ is greater than 1.0. Calc: Calculated; Exp: Experimental; Log JMHAQ : Maximum flux through human skin from water.

r2 of 0.883 and a Δlog JMHAQ of 0.282. The fit of the n = 55 log JMHAQ database to Equation 3 is comparable to the fit of the n = 185 log JMHAQ database to Equation 3, which gave an r2 of 0.820, a ΔlogJMHAQ was 0.502, and the coefficient values were a = 0.00270, b = 0.263, c = 0.0000564, d = 0.00119 and ϕ = -0.00634. It is interesting to note that both the a and ϕ coefficients increased in magnitude when the database size and range increased, but all other coefficients remained essentially the same. This suggests a greater influence of octanol solubility and molecular weight on log JMHAQ than is indicated by the relatively small n = 55 database, but the consistency in the other coefficients indicates that the good fit of the n = 55 log JMHAQ database is not just an artifact of the chosen n = 55 compounds. Figure 2 displays how the log JMHAQ values calculated by Equation 3 correlate with the experimental log JMHAQ values in the n = 55 log JMHAQ database. The adjusted r2 analysis for the n = 55 log JMHAQ database resulted in findings similar to the n = 70 log JMPAQ database with each pathway contributing to the

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good fit to Equation 3 : when c was set to 0, the adjusted r2 was 0.820; when d was set to 0, the adjusted r2 was 0.842; when both c and d were set to 0, the adjusted r2 was 0.718; when the series term was removed, the coefficients were c = 0.000946, d = 0.00328 and ϕ = -0.00639, and the adjusted r2 was 0.789. All of these adjusted r2 values were lower than the adjusted r2 of the complete model which is 0.859. Table 3 lists the calculated flux through these pathways, along with key flux ratios. Similar to the n = 70 database in Table 2, the data for the n = 55 database indicate that the aqueous-only pathway cannot be claimed as statistically significant, and any further results about this pathway can only be confirmed if more compounds are added to the database for which the aqueous-only pathway is dominant. Comparison of coefficients for fit of JMPAQ & JMHAQ data to the series/parallel equation

In comparing the coefficients of fit for the n = 70 log JMPAQ and the n = 55 log JMHAQ databases with

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Table 3. The pathway flux values and octanol–water partition coefficients for the n = 55 maximum flux through human skin from water database. Compound

log KOCT:AQ 

JM† 

JA† 

JA1†

JA2†

J C†

J D†

JA /(JC+ JD) ‡

JA1/JA2‡

1

1.12

0.219

0.090

0.104

0.683

0.008

0.003

8.399

0.153

2

1.64

0.120

0.087

0.130

0.266

0.010

0.001

7.930

0.488

4

2.69

0.055

0.035

0.212

0.042

0.016

0.000

2.139

5.062

8

1.45

0.025

0.105

0.140

0.430

0.011

0.002

8.482

0.325

9

1.95

0.032

0.071

0.142

0.143

0.011

0.001

6.234

0.994

10

2.45

0.026

0.038

0.154

0.051

0.012

0.000

3.198

3.026

11

2.95

0.024

0.027

0.271

0.030

0.021

0.000

1.279

9.184

13

3.95

0.003

0.002

0.197

0.002

0.015

0.000

0.154

83.969

16

0.50

0.251

0.148

0.152

5.274

0.012

0.022

4.440

0.029

17

-1.55

0.295

0.031

0.031

106.386

0.002

0.438

0.071

0.000

18

0.87

0.010

0.017

0.019

0.280

0.001

0.001

6.785

0.067

19

-0.86

0.007

0.006

0.006

3.864

0.000

0.016

0.392

0.002

20

3.86

0.054

0.002

0.155

0.002

0.012

0.000

0.199

64.721

21

3.94

0.120

0.005

0.421

0.005

0.032

0.000

0.150

86.467

22

3.19

0.002

0.000

0.005

0.001

0.000

0.000

1.346

8.678

23

3.11

0.044

0.014

0.165

0.015

0.013

0.000

1.101

10.849

24

2.37

0.288

0.191

0.597

0.281

0.046

0.001

4.097

2.120

25

-1.02

0.034

0.004

0.004

4.284

0.000

0.018

0.222

0.001

27

-0.96

0.034

0.002

0.002

2.081

0.000

0.009

0.188

0.001

28

1.49

6.918

9.642

13.388

34.467

1.021

0.142

8.288

0.388

30

2.59

3.162

1.672

8.796

2.065

0.671

0.009

2.461

4.259

31

1.79

1.820

0.218

0.378

0.516

0.029

0.002

7.047

0.732

32

2.00

0.525

1.504

3.289

2.770

0.251

0.011

5.731

1.188

33

1.91

0.562

2.533

4.978

5.158

0.380

0.021

6.316

0.965

35

2.33

0.170

0.573

1.681

0.870

0.128

0.004

4.347

1.933

36

1.23

128.825 26.003

30.979

161.885

2.364

0.667

8.580

0.191

37

2.26

0.295

0.295

0.932

0.431

0.071

0.002

4.040

2.165

38

2.70

0.195

0.125

0.861

0.146

0.066

0.001

1.885

5.890

39

3.34

0.355

0.173

4.574

0.180

0.349

0.001

0.496

25.373

47

-0.61

0.015

0.006

0.006

2.455

0.000

0.010

0.585

0.003

49

1.89

1.514

0.237

0.457

0.494

0.035

0.002

6.437

0.924

50

3.94

0.117

0.010

0.879

0.010

0.067

0.000

0.150

86.467

51

0.69

0.000

0.000

0.000

0.009

0.000

0.000

4.597

0.031

52

0.85

25.119

18.062

19.587

232.062

1.494

0.956

7.371

0.084

The pathway flux values for JA, JA1, JA2, JC and JD are not in logarithm form, and are calculated using Equations 4–8. The value for JM is (experimental log JMHAQ) not in logarithm form. The compound numbers correspond to the numbering scheme in Table 1. † Units are μm cm -2 h-1. ‡ The series pathway is dominant when JA is greater than both JC and JD, indicating that JA should be a good approximation of JM. The lipid domain of the series pathway is limiting when JA1 is less than JA2, indicating that JA1 will be a good approximation of JM if the series pathway is dominant. See Supplementary data for more discussion on these ratios. J: Pathway flux; JA: Lipid–aqueous series pathway; JA1: Lipid domain of the series pathway; JA2: Aqueous domain of the series pathway; JC: Aqueous-only pathway; J D: Aqueous-only pathway; JM : Experimental value; log KOCT:AQ: Octanol–water partition coefficients.

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Table 3. The pathway flux values and octanol–water partition coefficients for the n = 55 maximum flux through human skin from water database (cont.). Compound

log KOCT:AQ 

JM† 

JA† 

JA1†

JA2†

J C†

J D†

JA /(JC+ JD) ‡

JA1/JA2‡

53

1.39

1.995

1.657

2.127

7.490

0.162

0.031

8.577

0.284

54

2.47

0.347

0.256

1.071

0.337

0.082

0.001

3.085

3.178

55

3.51

0.017

0.015

0.503

0.016

0.038

0.000

0.396

32.023

57

2.40

0.062

0.042

0.140

0.060

0.011

0.000

3.833

2.343

58

5.75

0.002

0.000

0.053

0.000

0.004

0.000

0.003

4347.1

59

6.51

0.003

0.000

0.353

0.000

0.027

0.000

0.001

26073.4

61

5.13

0.008

0.000

0.083

0.000

0.006

0.000

0.012

1136.071

62

4.83

0.016

0.000

0.148

0.000

0.011

0.000

0.022

581.88

63

3.82

0.019

0.001

0.059

0.001

0.004

0.000

0.211

60.995

64

4.64

0.004

0.000

0.060

0.000

0.005

0.000

0.033

392.0

65

4.39

0.013

0.001

0.109

0.001

0.008

0.000

0.069

189.037

66

3.42

0.166

0.025

0.701

0.026

0.053

0.000

0.464

27.187

67

4.53

0.056

0.002

0.428

0.002

0.033

0.000

0.052

250.137

68

3.07

0.741

0.088

1.235

0.095

0.094

0.000

0.935

12.967

69

3.10

1.950

0.929

14.701

0.992

1.122

0.004

0.825

14.827

70

3.39

0.112

0.049

1.423

0.051

0.109

0.000

0.451

28.005

71

2.35

1.479

0.903

3.377

1.232

0.258

0.005

3.437

2.740

72

1.95

3.388

3.298

6.960

6.270

0.531

0.026

5.923

1.110

73

3.08

1.862

0.753

10.930

0.809

0.834

0.003

0.900

13.513

74

3.69

0.269

0.107

5.443

0.109

0.415

0.000

0.257

50.012

75

1.96

3.467

3.918

8.368

7.366

0.638

0.030

5.858

1.136

The pathway flux values for JA, JA1, JA2, JC and JD are not in logarithm form, and are calculated using Equations 4–8. The value for JM is (experimental log JMHAQ) not in logarithm form. The compound numbers correspond to the numbering scheme in Table 1. † Units are μm cm -2 h-1. ‡ The series pathway is dominant when JA is greater than both JC and JD, indicating that JA should be a good approximation of JM. The lipid domain of the series pathway is limiting when JA1 is less than JA2, indicating that JA1 will be a good approximation of JM if the series pathway is dominant. See Supplementary data for more discussion on these ratios. J: Pathway flux; JA: Lipid–aqueous series pathway; JA1: Lipid domain of the series pathway; JA2: Aqueous domain of the series pathway; JC: Aqueous-only pathway; J D: Aqueous-only pathway; JM : Experimental value; log KOCT:AQ: Octanol–water partition coefficients.

Equation 3,

it can be seen that the flux through each pathway should be greater in silicone relative to the flux of each respective pathway in human skin: the ratios of the coefficients were a P/aH = 15.5, bP/bH = 19.3, cP/cH = 17.1 and dP/dH = 1.23 (a subscript denotes whether the coefficient is an estimate for the log JMPAQ database [P] or the log JMHAQ database [H]). This relative similarity among the ratios indicates that if matched compounds in the two databases generally have the same dominant pathway and/or limiting domain (lipid or aqueous phase) in each membrane, then the correlation between log JMPAQ and log JMHAQ is consistent for all compounds in the database. The low ratio for the d coefficients may indicate a lower capacity for flux through the silicone aqueous-only pathway compared with the human skin aqueous-only pathway, but more research should be performed on compounds,

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Therapeutic Delivery (2014) 5(4)

which diffuse primarily through these aqueous-only pathways before any conclusions can be drawn. Log KOCT:AQ thresholds for switch between predominant pathways

Finally, Table 4 lists the log KOCT:AQ values, which indicate the thresholds at which the dominant pathway or limiting domain changes. Despite the thresholds being significantly different (p < 0.05, indicated by the 95% confidence intervals) between the n = 55 log JMHAQ and n = 70 log JMPAQ database, it can be observed that the thresholds are similar to a practical extent. These thresholds can be seen in Figures 3 & 4, which plot the ratios JA /JC + JD and JA1/JA2 against logKOCT:AQ for the n = 70 logJMPAQ and n = 55 logJMdatabases, respectively. The significant difference HAQ between the thresholds for the n = 55 and n = 185

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Figure 3. The plot of two informative ratios of pathway flux values against log KOCT:AQ for the n = 70 maximum flux through silicone from water database. The ratios indicated are composed of pathway flux values for the JA , JA1, JA2 JC and the JD pathway, which are calculated using Equations 4–8. J: Pathway flux; JA : Lipid–aqueous series pathway; JA1: Lipid domain of the series pathway; JA2: Aqueous domain of the series pathway; JC: Aqueous-only pathway; JD : Aqueous-only pathway; Log KOCT:AQ : Octanol–water partition coefficients.

log JMHAQ databases can be explained by the significantly higher average MW of the compounds in the n = 185 log JMHAQ database, which suggests an index for determining dominant flux which considers MW may also be more useful for comparing databases. Notably, the log KOCT:AQ range for the lipid domain of the series pathway being limiting (the range indicated by JA1/JA2 and JA /JD) is larger in the n = 70 log JMPAQ database than in the n = 55 log JMHAQ database, suggesting that the key architectural difference between the two membranes is the abundance of lipid components in the silicone membrane capable of interacting with water in such a way as to create a series pathway. Overall, these differences suggest an explanation for the lack of a perfect correlation between log JMPAQ and log JMHAQ, which is beyond random or systematic error in diffusion experiments. The fact that it requires log KOCT:AQ values greater than 3, for the predominant pathway, for flux to switch from the series, JA, to the lipid pathway, JC,

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suggests that even for fairly lipid soluble molecules, as judged by their log KOCT:AQ values, the series pathway is more important for logJMPAQ and logJMHAQ. This suggests that flux is limited for molecules exhibiting log KOCT:AQ values greater than 3 because the series pathway is not available to them. The use of log KOCT:AQ values, or the ratio of solubility in the lipid octanol to the solubility in water, of a permeant to predict a switch in the predominant pathway for flux does not suggest that it is useful in the design of new molecules or prodrugs where flux is optimized. In those examples, the absolute lipid and aqueous solubilities (in addition to molecular weight) are the only important design criteria using the Roberts-Sloan equation or the series/parallel equation. Conclusion This investigation has primarily demonstrated that the series/parallel model applies well to both human skin and silicone. This suggests that silicone acts as a

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Research Article  Prybylski & Sloan

Figure 4. The plot of two informative ratios of pathway flux values against octanol–water partition coefficients (log KOCT:AQ) for the n = 55 maximum flux through human skin from water (log JMHAQ) database. The ratios indicated are composed of pathway flux values for the JA, JA1, JA2, JC and the JD pathway, which are calculated using Equations 4 – 8. JA: Lipid–aqueous series pathway; JA1: Lipid domain of the series pathway; JA2: Aqueous domain of the series pathway; JC: Aqueous-only pathway; JD: Aqueous-only pathway; JM : Experimental value; Log KOCT:AQ: Octanol–water partition coefficients; Log JMHAQ: Maximum flux through human skin from water.

good surrogate for human skin because of the similar architecture of the lipid and aqueous components of the pathways within the membranes during diffusion experiment conditions, rather than both simply being lipoidal in nature. A larger matched maximum flux through silicone and maximum flux through human skin database with different vehicles and a greater range of log KOCT:AQ values would allow further testing and confirmation of the results presented here. Future perspective As the number of approved topical medications continues to increase, and the use of animal models continues to be deterred by increased regulations, simple surrogates of human skin for diffusion-cell experiments will become more essential. In silico models will continue to improve, but will still be unlikely to observe unpredictable processes which would only occur in in vitro or in vivo testing. More options will be available for Parallel Artificial Membrane Permeability Assays in

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vitro, but the effort and expense required to develop or purchase a membrane designed to mimic the architecture of human skin may not be necessary if other currently available polymeric membranes are assessed for comparability. Supplementary data To view the supplementary data that accompany this paper please visit the journal website at: www.future-science.com/ doi/full/10.4155/TDE.14.12

Financial & competing interests disclosure The authors have no relevant affiliations or financial involvement with any organization or entity with a financial interest in or financial conflict with the subject matter or materials discussed in the manuscript. This includes employment, consultancies, honoraria, stock ownership or options, expert t-estimony, grants or patents received or pending, or royalties. No writing assistance was utilized in the production of this manuscript.

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Flux through silicone & human skin fitted to a series/parallel model 

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Table 4. The average and 95% CI of the octanol–water partition coefficients (log KOCT:AQ ) where the flux through the designated pathways are equivalent. n = 70 log JMPAQ database

n = 55 log JMHAQ database

n = 185 log JMHAQ database

–

Average

95% CI

–

Average

95% CI

–

MW (Da)

206

13.2

MW (Da)

195

15.3

MW (Da) 273

Flux ratio

log KOCT:AQ where ratio = 1

Flux ratio log KOCT:AQ where ratio = 1

Flux ratio log KOCT:AQ where ratio = 1

JA /JC†,‡

3.79

0.06

JA /JC‡,§

3.07

0.02

JA /JC‡,¶

4.17

0.09

JA /JD

Average

95% CI 16.8

-0.47

0.06

JA /JD

-0.39

0.02

JA /JD

0.16

0.09

JA1/JA2†,‡

2.75

0.06

JA1/JA2‡,§

1.99

0.02

JA1/JA2‡,¶

2.50

0.09

JA /(JC + JD)†,‡

3.79

0.06

JA /(JC + JD) ‡,§

3.07

0.02

JA /(JC + JD) ‡,¶

4.17

0.09

JA /(JC + JD)†,‡

-0.44

0.06

 

-0.36

0.02

JA /(JC + JD) ‡,¶

0.17

0.09

†,‡

‡,§

†

Using coefficients a = 0.0114, b = 6.45, c = 9.57E-4, d = 0.00380 and ϕ = -0.00562.

‡

See Supplementary data for calculation details.

‡,¶

§

Using coefficients a = 7.34E-4, b = 0.334, c = 5.63E-5, d = 0.00138 and ϕ = -0.00244. Using coefficients a = 2.70E-3, b = 0.263, c = 5.64E-5, d = 0.00119 and ϕ = -0.00634. JA1: Flux through the lipid domain of the series pathway = aS OCT10 ϕMW; JA2: Flux through the aqueous domain of the series pathway = bS AQ /MW1/2; JA : Total flux through the series pathway = 1/(1/JA1+1/JA2); J C: Flux through the lipid-only pathway = cS OCT10 ϕMW; J D : Flux through the aqueous-only pathway = dS AQ /MW1/2. ¶

Executive summary Fit of flux through silicone from water to the series/parallel equation • When a n = 70 log J MPAQ database was fit to a lipid-aqueous series/parallel model, the r2 was 0.907 and the average absolute residual log J MPAQ (Δlog J MPAQ ) was 0.293, and the coefficient values were a = 0.0114, b = 6.45, c = 0.000957, d = 0.00380 and ϕ = -0.00562.

Fit of flux through human skin in vitro from water to the series/parallel equation • When a n = 55 log J MHAQ database was fit to a lipid-aqueous series/parallel model, the r2 was 0.872, the Δlog J MHAQ was 0.301, and the coefficient values were a = 0.000734, b = 0.334, c = 0.0000563, d = 0.00138 and ϕ = -0.00244. • When a n = 185 log J MHAQ database was fit to a lipid-aqueous series/parallel model, the r2 was 0.820, a ΔlogJ MHAQ was 0.502, and the coefficient values were a = 0.00270, b = 0.263, c = 0.0000564, d = 0.00119 and ϕ = -0.00634.

Fit of flux through silicone from water to the series/parallel equation & fit of flux through human skin in vitro from water to the series/parallel equation • All databases fit to the lipid-aqueous series/parallel model exhibited an r2 > 0.8, and comparable coefficients. • For both the n = 70 log J MPAQ and n = 55 log J MHAQ databases, too few compounds permeate the aqueousonly pathway to conclude that the pathway is necessary to describe maximum flux through silicone or human skin.

Comparison of coefficients for fit of JMPAQ & JMHAQ data to the series/parallel equation

• It was found that each coefficient for the silicone membrane pathways was estimated to a value about 17-times that of the value for human skin pathways. The exception was the aqueous-only pathway coefficient, which was approximately the same for both membranes.

Log KOCT:AQ thresholds for switch between predominant pathways

• Although there are significant differences found when comparing the log KOCT:AQ values where the predominant pathways change for compounds permeating silicone or human skin, the values are generally similar. • The results of this analysis surprisingly suggests that the architecture of the two membranes present similar solubility based pathways through which drugs diffuse.

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Research Article  Prybylski & Sloan References Papers of special note have been highlighted as: • ••

of interest of considerable interest

1

Higuchi T. Physical chemical analysis of percutaneous absorption process from creams and ointments. J. Soc. Cosmet. Chem. 11, 85–97 (1960).

2

Anderson BD, Higuchi WI, Raykar PV. Heterogeneity effects on permeability-partition coefficient relationships in human stratum corneum. Pharm. Res. 5, 566–573 (1988).  

•

Presents a thermodynamic analysis of diffusion through the human skin lipid pathway, in consideration of the lipid-aqueous series pathway.

3

Mitragotri S. Modeling skin permeability to hydrophilic and hydrophobic solutes based on four permeation pathways. J. Control. Release. 86, 69–92 (2003).  

•

A model similar to the series/parallel model was developed in this article, with an output of permeability coefficient.

4

Ottaviani G, Martel S, Carrupt PA. Parallel artificial membrane assay: a new membrane for the fast prediction of passive human skin permeability. J. Med. Chem. 49, 3948–3954 (2006).

5

6

Sloan KB. Prodrugs for Dermal Delivery. Ad. Drug Deliv. Rev. 3, 67–101 (1989).

7

Sloan KB, Wasdo SC, Rautio J. Design for optimized topical delivery: prodrugs and paradigm change. Pharm. Res. 23, 2729–2747 (2006).

8

Flynn GL, Yalkowsky SH. Correlation and prediction of mass transport across membranes I: influence of alky chain length on flux-determining properties of barrier and diffusant. J. Pharm. Sci. 61, 838–852 (1972).

9

Roberts WJ, Sloan KB. Correlation of aqueous and lipid solubilities with flux for prodrugs of 5-fluorouracil, theophylline, and 6-mercaptopurine: a Potts-Guy approach. J. Pharm. Sci. 88, 515–522 (1999).

10

Beall HD, Sloan KB. Transdermal delivery of 5-fluorouracil (5-FU) by 1-alkylcarbonyl-5-FU prodrugs. Int. J. Pharm. 129, 203–210(1996).

11

Roberts WJ, Sloan KB. Prediction of transdermal flux of prodrugs of 5-fluorouracil, theophylline, and 6-mercaptopurine with a series/parallel model. J. Pharm. Sci. 89, 1415–1431 (2000).  

•

The paper wherein the series/parallel model was developed. Maximum flux from isopropyl myristate through mouse skin was found to fit well to the model.

12

Sloan KB, Synovec J, Ketha H. A surrogate for topical delivery in human skin: silicone membranes. Ther. Deliv. 4, 203–224 (2013).  

•

406

Sinko B, Garrigues TM, Balogh GT et al. Skin-PAMPA: a new method for fast prediction of skin permeation. Eur. J. Pharm. Sci. 45, 698–707 (2012).

Assembled and analyzed a majority of the database. Silicone flux data were found to demonstrate a good correlation with human skin flux data for the large database.

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13

Prybylski J, Sloan KB. The Flux of phenolic compounds through silicone Membranes. Pharmaceutics 5, 434–444 (2013).

14

Majumdar S, Thomas J, Wasdo S, Sloan KB. The effect of water solubility of solutes on their flux through human skin in vitro. Int. J. Pharm. 329, 25–36 (2007).

15

Thomas J, Majumdar S, Wasdo S et al. The effect of water solubility of solutes on their flux through human skin in vitro: an extended Flynn database fitted to the RobertsSloan equation. Int. J. Pharm. 339, 157–167 (2007).

16

Juntunen J, Majumdar S, Sloan KB. The effect of water solubility of solutes on their flux through human skin in vitro: a prodrug database integrated into the extended Flynn database. Int. J. Pharm. 351, 92–103 (2008).  

•

Demonstrated that aqueous solubility has a positive and significant influence on maximum flux through human skin from water for a large database of compounds.

17

Yalkowsky SH, Valvani SC. Solubility and partitioning I: solubility of nonelectrolytes in water. J. Pharm. Sci. 69, 912–922 (1980).

18

Roy SD, Fujiki J, Fleitman JS. Permeability of alkyl p-aminobenzoates through living skin equivalents and cadaver skin. J. Pharm. Sci. 82, 1266–1268 (1993).

19

Dal Pozzo A, Pastori N. Percutaneous absorption of parabens from cosmetic formulations. Int. J. Cosmet. Sci. 18, 57–66 (1996).

20

Hansch C, Lien EJ. Structure activity relationship in antifungal agents: a survey. J. Med. Chem. 14, 653–670 (1971).

21

Wasdo S, Juntunen J, Davarajan H et al. Modeling of flux through silicone membrane from water. Eur. J. Pharm. Sci. 34, 321–332 (2008).

22

Morimoto Y, Hatanaka T, Sugibayashi K et al. Prediction of skin permeability of drugs: comparison of human and hairless rat skin. J. Pharm. Parmacol. 44, 634–639 (1992).

23

Hatanaka T, Inuma M, Sugibayashi K et al. Prediction of skin permeability of drugs. I. Comparison with artificial membrane. Chem. Pharm. Bull. 38, 3452–3459 (1990).

24

Kasting GB, Smith RL, Cooper ER. Effect of lipid solubility and molecular size on percutaneous absorption. In: Pharmacology and the Skin. Volume 1. Shroot B, Schaefer H. (Eds). Karger, Basel, Switzerland, 138–153 (1987).

25

Johnson ME, Blankschtein D, Langer R. Evaluation of solute permeation through the stratum corneum: lateral bilayer diffusion as the primary transport mechanism. J. Pharm. Sci. 86, 1162–1172 (1997).  

•

Discussed and analyzed the characteristics and physical properties of the lipid pathway of the human skin.

26

Geinoz S, Rey S, Boss G et al. Quantitative structurepermeation relationships for solute transport across silicone membranes. Pharm. Res. 19, 1622–1629 (2002).

27

Magnusson BM, Anissimov YG, Cross SE et al. Molecular size as the main determinant of solute maximum flux across the skin. J. Invest. Dermatol. 122, 993–999 (2004).

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Flux through silicone & human skin fitted to a series/parallel model 

28

Potts RO, Guy RH. Predictive algorithm for skin permeability: the effect of molecular size and hydrogen bond activity. Pharm. Res. 12, 1628–1633 (1995).

29

Moss GP, Gullick DR, Cox PA et al. Design, synthesis and characterization of captopril prodrugs for enhanced percutaneous absorption. J. Pharm. Pharmacol. 58, 167–177 (2006).

30

Dias M, Hadgraft J, Lane ME. Influence of membrane-solventsolute interactions on solute penetration in model membrane. Int. J. Pharm. 336, 108–114 (2007).

Research Article

through silicone membrane. Drug Dev. Ind. Pharm. 39, 1494–1497 (2013). 36

Dal Pozzo A, Donzelli G, Liggeri E et al. Percutaneous absorption of nicotinic acid derivates in vitro. J. Pharm. Sci. 80, 54–57 (1991).

37

Guy RH, Carlstrom EM, Bucks DAW et al. Percutaneous penetration of nicotinates: in vivo and in vitro measurements. J. Pharm. Sci. 75, 968–972 (1986).

38

Hagedorn-Lewke U, Lippold BC. Absorption of sunscreens and other compounds through human skin in vivo: derivation of a method to predict maximum fluxes. Pharm. Res. 12, 1354–1360 (1995).

39

Sloan KB, Devarajan-Ketha H. Synovec J et al. Fit of fluxes of sunscreens and other compounds from propylene glycol: water (30:70) through human skin and silicone membrane to the Roberts-Sloan equation: the effect of polar vehicle (or water) solubilities. J. Soc. Cosmet. Chem. 64, 181–192 (2013).

31

Dias M, Hadgraft J, Lane ME. Influence of membrane solventsolute interactions on solute permeation in skin. Int. J. Pharm. 340, 65–70 (2007).

32

Watkinson RM, Herkenne C, Guy RH et al. Influence of ethanol on the solubility, ionization and permeation characteristics of ibuprofen in silicone and human skin. Skin Pharmacol. Physiol. 22, 15–21 (2009).

33

Hatanake T, Inuma M, Sugibayashi K et al. Prediction of skin permeability of drugs II. Development of composite membrane as a skin alternative. Int. J. Pharm. 79, 21–28 (1992).

40

Le VH, Lippold BC. Influence of Physicochemical properties of homologous esters of nicotinic acid on skin permeability and maximum flux. Int. J. Pharm. 124, 285–292 (1995).

Roberts MS, Anderson RA, Swarbrick J. Permeability of human epidermis to phenolic compounds. J. Pharm. Pharmacol. 29, 677–683 (1977).

41

Pellett MA, Castellano S, Hadgraft J et al. The penetration of supersaturated solutions of piroxicam across silicone membrane and human skin in vitro. J. Control. Release 46, 205–214 (1997).Tab

34

35

Synovec J, Wasdo SC, Sloan KB. The effect of lipid and aqueous solubilities on flux of nicotinic acid esters from water

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