TABLE 1.

Available QSAR models for predicting various parameters in the MPML MechDermA (default methods in bold)

Parameter	QSAR name and equation	Reference	Description
Drug partition parameters
Stratum corneum lipid to water partition coefficient (K SClip:w)	Equation 42 ‐ Nitsche 2006 $K_{\text{SClip}:\mathrm{w}}=0.43\cdot {\left(K_{\mathrm{o}:\mathrm{w}}\right)}^{0.81}$ Equation 43 ‐ Raykar 1988 $K_{\text{SClip}:\mathrm{w}}=0.15\cdot {\left(K_{\mathrm{\text{o}}:\mathrm{\text{w}}}\right)}^{0.91}$ Equation 44 ‐ Hansen 2013 ${\mathbf{K}}_{\mathbf{\text{SClip}}\mathbf{:}\mathbf{w}}\mathbf{=}\mathbf{1.32}\mathbf{\cdot }{\left({\mathbf{K}}_{\mathbf{o}\mathbf{:}\mathbf{w}}\right)}^{\mathbf{0.67}}$	108, 109, 110	K SClip:w describes the relative affinities of water and the stratum corneum lipid phase
Sebum: water partition coefficient (K sb:w)	Equation 45 ‐ Valiveti 2008 $\left.K_{\mathrm{sb}:\mathrm{w}},=\right){10}^{\left(\left(0.6044\cdot \mathrm{Log}{P}_{\mathrm{o}:\mathrm{w}}\right)+1.33\right)}$ Equation 46 ‐ Yang 2018 where: f ni – fraction of the drug which is in non‐ionized form for current pH f CAT – fraction of the drug which is cation form for the current pH	111	K sb:w describes the relative affinities of water and sebum
Stratum corneum to viable epidermis partition coefficient (K SC:VE)	Equation 47 ‐ Shatkin and Brown 1991 ${\mathbf{K}}_{\mathbf{\text{SClip}}:\mathbf{VE}}=\frac{\left(\mathbf{1}\mathbf{-}{\mathbf{f}}_{\mathbf{fat},\mathbf{SC}}\right)+\left({\mathbf{f}}_{\mathbf{fat},\mathbf{SC}}·{\mathit{K}}_{\mathit{O}:\mathit{W}}\right)}{\left(\mathbf{1}\mathbf{-}{\mathbf{f}}_{\mathbf{fat},\mathbf{VE}}\right)+\left({\mathbf{f}}_{\mathbf{fat},\mathbf{VE}}·{\mathit{K}}_{\mathit{O}:\mathit{W}}\right)}$ $\text{where}{\mathrm{f}}_{\mathrm{fat},\mathrm{SC}}\text{is lipid fraction in}\mathrm{SC}\left(5\%\right);$ ${\mathrm{f}}_{\mathrm{fat},\mathrm{VE}}\text{is lipid fraction}\mathrm{on}\mathrm{VE}\left(2\%\right)$ Equation 48 ‐ Modified Chen 2015 $K_{\text{SClip}:\mathrm{VE}}=\frac{K_{\mathrm{sc},\mathrm{lip}:w}}{0.7\cdot \left(0.68+\frac{0.32}{f_{u,\text{plasma}}}+\left(0.025\cdot f_{\mathrm{ni},\mathrm{VE}}·K_{\mathrm{sc},\mathrm{lip}:w}\right)\right)}$ $\begin{array}{c}\text{where}{\mathrm{f}}_{\mathrm{u},\text{plasma}}\text{is the plasma protein binding};{\mathrm{f}}_{\mathrm{ni},\mathrm{VE}}\hfill \\ \text{is the}\text{non}-\text{ionised fraction in}\mathrm{VE}\mathrm{at}\mathrm{pH}7\hfill \end{array}$	20, 50	K SClip:VE describes the relative affinities of viable epidermis and stratum corneum The Modified Chen is an option here even though this actually describes dermis. Therefore, using this option assumes that viable epidermis is very aqueous like the dermis–if using this option then K D:VE should be set to 1 Shatkin and Brown is the default model because it describes VE more mechanistically–This should be used in combination with the calculation of K D:VE below
Dermis to viable epidermis partition coefficient (K D:VE)	Equation 49	20, 50	Calculated based on estimated affinities from Chen and Shatkin and Brown methods
Dermis to blood partition coefficient (K D:b )	Equation 50 ‐ Shatkin and Brown ${\mathbf{K}}_{\mathbf{D}:\mathbf{B}}=\frac{\left(\mathbf{1}-{\mathbf{f}}_{\mathbf{fat},\mathbf{D}}\right)+\left({\mathbf{f}}_{\mathbf{fat},\mathbf{D}}·\mathbf{P}\right)}{\left(\mathbf{1}\mathbf{-}{\mathbf{f}}_{\mathbf{fat},\mathbf{\text{blood}}}\right)+\left({\mathbf{f}}_{\mathbf{fat},\mathbf{\text{blood}}}·\mathbf{P}\right)}$ $\text{where}{\mathrm{f}}_{\mathrm{fat},D}\text{is lipid fraction in dermis}\left(2·\right);$ ${\mathrm{f}}_{\mathrm{fat},\text{blood}}\text{is lipid fraction in blood}\left(0.7·\right);\mathrm{P}={10}^{{\text{LogP}}_{\mathrm{o}:\mathrm{w}}}$	50
Dermis to Sebum partition coefficient (K D:sb)	Equation 51 ${\mathit{K}}_{\mathit{D}:\mathbf{sb}}=\frac{\mathbf{0.7}\mathbf{·}\left(\mathbf{0.68}\mathbf{+}\frac{\mathbf{0.32}}{{\mathit{f}}_{\mathit{u}}}\mathbf{+}\left(\mathbf{0.025}\mathbf{·}{\mathit{f}}_{\mathbf{ni}\mathbf{,}\mathbf{\text{dermis}}}·{\mathit{K}}_{\mathbf{lip}:\mathit{w}}\right)\right)}{{\mathit{K}}_{\mathbf{s}\mathit{b}:\mathit{w}}}$
Subcutis to dermis; muscle to subcutis; blood to subcutis; blood to muscle partition coefficients	User defined (No QSARs available) Default value = 1		These subdermal tissue partition coefficients should be obtained from experimental methods or other theoretical calculations or QSARs. These tissues can be modified to mimic other deep tissues such as synovial fluid
Drug Diffusion Parameters
Diffusion coefficient for SC and sebum lipid (D sc,lip/D sb) (cm2/h)	Equation 52 ‐ Johnson Method $D_{\mathrm{SC},\mathrm{lip}}\text{OR}{D}_{\mathrm{sb}}$ A = 0.000145 B = 1.32 K bolt = 1.38E‐16 J/K T [°K] = Skin[°C] + 273.15 ${\eta }_{\mathrm{lip}}\text{is the viscosity of}\mathrm{SC}\text{lipids}\left(1\mathrm{P}\right)\text{or sebum}\left(0.75\mathrm{P}\right)$ $\eta \text{is the viscosity of water}\left(0.01\mathrm{P}\right)$ $\mathrm{MW}\text{is the molecular weight of compound}$ $h\text{is the height of bilayer}=5.5{\mathrm{e}}^{-7}$ ${\mathrm{r}}_{\mathrm{c}}\text{is the molecular radius in}\mathrm{cm}\left(\text{calculated from}\mathrm{MW}\right)$ ${\gamma }_e\text{is}{\text{the Euler}}^{’}\mathrm{s}\text{constant}=0.5772$ Equation 53 ‐ Mitragotri Method Where ${\mathbf{r}}_{\mathbf{c}}\mathbf{\text{is the molecular radius in Angstroms}}$ Equation 54 ‐ Wang 2006 $D_{\mathrm{SC},\mathrm{Lip}}=3600\cdot \left[\left(8.98·{10}^{-3}\cdot {\mathrm{MW}}^{-2.43}\right)+\left(2.34\cdot {10}^{-9}\right)\right]$	112	Johnson model is an adaptation of Stokes‐Einstein equation for diffusivity of the molecule where the parameters A, B, and gammas were estimated using the dermal diffusion data through lipid bilayer systems. The MPML MechDermA model allows modification of viscosity of SC over depth as well as that of sebum Mitragotri derived a relationship with molecular weight based on first principles and parameterization from experimental data Wang equation is similar to Mitragotri where the coefficients were estimated with a different set of experimental data
Diffusion Coefficient in VE and Dermis (D D or D VE) (cm2/h)	Equation 55 ‐ Modified Chen 2015 ${\mathbf{D}}_{\mathbf{D}}=\frac{\mathbf{3600}\cdot {\mathbf{D}}_{\mathbf{D},\mathbf{\text{free}}}}{\left(\mathbf{0.68}\mathbf{+}\frac{\mathbf{0.32}}{{\mathbf{f}}_{\mathbf{u}}}\mathbf{+}\left(\mathbf{0.025}\cdot {\mathbf{f}}_{\mathbf{ni},\mathbf{D}}\cdot {\mathbf{K}}_{\mathbf{sc},\mathbf{lip}:\mathbf{w}}\right)\right)}$ $\begin{array}{c}\mathbf{\text{where}}{\mathbf{D}}_{\mathbf{D},\mathbf{\text{free}}}\left(\frac{{\mathbf{cm}}^2}{\mathit{sec}}\right)={\mathbf{10}}^{-\mathbf{4.38}\mathbf{-}\left(\mathbf{0.207}\mathbf{·}{\mathbf{MW}}^{\frac{\mathbf{1}}{\mathbf{3}}}\right)}\hfill \end{array}$ Where: fu–unbound fraction of the drug; f ni,D–fraction of the drug which is in non‐ionized form for current pH; D D,free–free (unbound) drug diffusion in the dermis	20, 68	This is an adaptation of original Kretsos 2008 model by Chen et al. 2015 by using lipid fraction of 2.5% and using K sc,lip:w rather than LogP
Diffusion coefficients in muscle and subcutis compartments	User defined (No QSARs available) Default = 1 · 10−5	‐	These subdermal tissue partition coefficients should be obtained from experimental methods or other theoretical calculations or QSARs
Binding in various tissues and Corneocyte permeability
Cornecoyte permeability (P cell) (cm/h)	User defined (No QSARs available). Default = 1 · 10−5	‐	The default value of this parameter is 10−5. However, this likely varies by compound. Currently no methods are available to predict this parameter
Steady state binding in SC (f u,sc)	Equation 56 ‐ Polak et al. 2018 (requires HBA, and LogP) f u,sc  = 1 – (EXP(logK Nernst )/(1 + EXP(logK Nernst )) where: logK Nernst  = (ln[HBA + 4.824]) (ln(abs[LogP])) Equation 57 ‐ Nitsche 2006 f u,sc = 1 / (1 + PCpro) where PCpro = 5.4·(K o:w 0.27) $\text{where}{K}_{\mathrm{o}:\mathrm{w}}={10}^{{\text{LogP}}_{\mathrm{o}:\mathrm{w}}}$ PCpro is the SC protein to water partition coefficient	108, 113	This model assumes the keratin binding is non‐saturable and equilibrium is established instantaneously. Binding is reversible
Dynamic Binding in SC (K on/K off model)	Equation 58 ‐ Seif et al. 2012 $\mathrm{Log}{\mathrm{K}}_{\mathrm{b}}=1.26+\left(0.34\cdot \mathrm{Log}{\mathrm{D}}_{\mathrm{pH}}\right)$ $K_{\mathrm{off}}\left({\mathrm{h}}^{-1}\right)=\frac{60}{25.75+\left(8.35\cdot \left(D_{\mathrm{pH}}^{0.34}\right)\right)}\text{where}{D}_{\mathrm{pH}}={10}^{\mathrm{Log}{\mathrm{D}}_{\mathrm{pH}}}$ $K_{\mathrm{on}}\left({\mathrm{h}}^{-1}\right)=K_{\mathrm{off}}*K_b\text{where}{K}_b={10}^{\mathrm{Log}{\mathrm{K}}_{\mathrm{b}}}$	114	This model accounts for difference in “on and off” rate for drug adsorption onto skin protein accounting for time‐dependent nonlinearity in binding. Binding/adsorption is reversible
Binding in muscle (f u,muscle)	Equation 59 $\begin{array}{c}{\mathrm{fu}}_{\text{muscle}}=-\left(0.0723\cdot \text{LogP}\right)+\left(0.4328\cdot {\mathrm{fu}}_{\text{plasma}}\right)\hfill \\ +0.3158\hfill \end{array}$ Minimum predicted value truncated to 0.001	In‐house empirical model
Binding in dermis and VE	Equation 60 ${\mathrm{Cu}}_t=\frac{{\mathrm{C}}_t}{\left(0.68+\frac{0.32}{f_u}+\left(0.025\cdot f_{\mathrm{ni},t}\cdot K_{\mathrm{sc},\mathrm{lip}:w}\right)\right)}$ where: f u –unbound fraction of the drug; f ni,t –fraction of the drug which is in non‐ionized form for current pH; Cut is the unbound concentration in tissue (dermis or VE)	20, 68

Abbreviations: MPML MechDermA, multiphase, multilayer mechanistic dermal absorption; QSAR, quantitative structure activity relationship; SC, stratum corneum; VE, viable epidermis.