Absorption and Drug Development

NOMENCLATURE

A area of the PAMPA filter (cm2) C0 aqueous concentration of the uncharged species (mol·cm−3) Cm(x) solute concentration inside of a membrane, at position x (mol·cm−3) solute concentration inside a membrane, at position x (mol cm−3) CR, CD                                receiver and donor aqueous solute concentration, respectively (mol·cm−3) D Lipid–water distribution pH-dependent function (also called the apparent partition coefficient) Daq (Dm) diffusivity of a solute in aqueous (membrane) solution (cm2·s−1) diff difference between the partition coefficient of the uncharged and the charged species DMEM diffusivity of a solute inside a membrane (cm2·s−1) DMEM/W pH-dependent membrane–water apparent partition coefficient (dimensionless) Double-Sink two sink conditions present: ionization and binding E(Δφ) function due to potential drop across the cell junction (dimensionless) f(0), f(+), f(−) molecule concentration fraction in the uncharged, positively charged and negatively charged forms, respectively F(rHYD/R) Renkin molecular sieving function, dimensionless fraction in the range of 0 to 1 Fpf cerebrovascular flow velocity of perfusion fluid (mL·g−1·s−1 brain tissue) h membrane thickness (cm) hABL, , thickness of the ABL (cm), at the receiver (R), donor (D) side, respectively total thickness of the ABL, equals hit a molecule with (a) confirmed activity from a primary assay, (b) a good profile in secondary assays, and (c) a confirmed structure hm membrane thickness (cm) , , excess lipid layer thicknesses (receiver/donor sides), and filter thickness total thickness of the lipid layers: in combo methodology where a measured property (e.g., PAMPA permeability coefficient) is additively “combined” with a calculated (in silico) descriptor (e.g., H-bond potential) J flux across a membrane (mol·cm−2·s−1) jH low-pH junction potential parameter in the Avdeef–Bucher four-parameter electrode standardization equation jOH high-pH junction potential parameter in the Avdeef–Bucher four-parameter electrode standardization equation ka absorption rate constant (min−1) Ke extraction constant Kin unidirectional transfer constant (mL·g−1·s−1): Kin = (Qbr/Cpf)/T, where Qbr = test compound parenchymal brain concentration (nmol·g−1 brain tissue) (corrected for the vascular volume), Cpf = perfusion fluid concentration (nmol·mL−1), T = perfusion time (s). kS slope factor in the Avdeef–Bucher four-parameter electrode standardization equation Ksp solubility product, e.g., [Na+][A−] or [BH+][Cl−] nH total number of dissociable protons contributed to the solution by the sample substance (in the form it is introduced to solution) Bjerrum function: average number of bound protons on a molecule at a particular pH P lipid–water pH-independent partition coefficient; also designated POCT, PX/W, where X = ALK, DD, HXD, LIPO, MEM, OCT, O, etc. P0 intrinsic permeability (chargeless form of drug) (cm·s−1), pH-independent Pa apparent artificial-membrane permeability (cm·s−1)—like Pe, but with some limiting assumption PABL ABL permeability coefficient (cm·s−1): PABL = Daq/hABL, in vitro or PAMPA model Papp apparent in vitro transcellular permeability coefficient (cm·s−1) PC in vitro transendothelial (cellular) permeability (cm·s−1); derived from Papp corrected for hydrodynamic effects (ABL, paracellular, filter); depends on pH for ionizable permeants pcH pH scale based on hydrogen ion concentration BBB luminal permeability coefficient (cm·s−1) from in situ brain perfusion technique: ; corrected-for-flow permeability coefficient; depends on pH for ionizable permeants Pe effective permeability coefficient (cm·s−1)—the experimentally determined value effective luminal permeability coefficient (cm·s−1), not corrected for flow: Pe = Kin/S; depends on pH for ionizable permeants pH operational pH scale pcH concentration-based pH scale pH-CRE pH-dependent Crone–Renkin equation (CRE) flow correction method Pi (or ) permeability coefficient (cm·s−1) of the ionized form of permeant pKa ionization constant (negative log form), based on the concentration scale apparent pKa in the presence of precipitation in the DTT method the apparent pKa derived from the log Pe–pH profile, the pH at which the resistance to transport is 50% due to the artificial membrane barrier and 50% due to the ABL pH at which both the chargeless and salt forms of a substance coprecipitate membrane pKa (limiting apparent pKa in high membrane lipid–water volume ratio titrations) octanol pKa (limiting apparent pKa in high octanol–water volume ratio titrations) Pm PAMPA transmembrane permeability (cm·s−1)—Pe corrected for ABL and aqueous pore diffusion effects; pH dependence follows Henderson–Hasselbalch equation. refers to the intrinsic permeability of the bilayer membrane to the uncharged form of an ionizable molecule POCT octanol–water partition coefficient for an uncharged species BBB intrinsic luminal permeability coefficient of the uncharged form of permeant; for ionizable compounds, , “+” for acids, “−” for bases PAMPA–BBB intrinsic permeability coefficient of the uncharged form of permeant; for ionizable compounds, , where “+” is for acids, “−” is for bases Ppara PAMPA paramembrane permeability coefficient (cm·s−1)—diffusion of permeant via aqueous pores formed in the thin PAMPA–BBB membrane: Ppara = (ε/δ)2 Daq paracellular permeability coefficient (cm·s−1), indicating aqueous diffusion of permeant through the tight junctions formed by the blood–brain...