Historical milestones in the elucidation of bilayer structure.

Cross sections of spherical or discoid phospholipid aggregates: (A) liposomes, (B) supported bilayers on microspheres, (C) monolayers on alkylated microspheres, (D) nanodisks, (E) immobilized artificial membranes, and (F) bicelles. The schematic structures are not drawn to proportion. More details are given in the text.

Fractions of the chemicals in the core region, as predicted from the C₁₆/DAcPC partitioning, versus the difference between C₁₆/W and C₁₆/O partition coefficients. The compounds with experimentally determined locale are shown as full points. The sigmoidal curve connects the compounds with known locales in the headgroups or the core and corresponds to eq 2.(552)

Compartmentalization of the bilayer for the description of passive transport of chemicals as dependent on lipophilicity and amphiphilicity of chemicals. The headgroups and the core are represented by the low-density bilayer subregions 1 and 4, respectively. The core/headgroups interface is depicted as a volume, where amphiphilic chemicals accumulate and includes (portions of) the high-density subregions 2 and 3. The headgroups/water interface is not shown, because of insufficient information about the accumulation of chemicals there. The schematic phospholipid structures in the bottom right corner indicate these correspondences. The overall transfer time is the time needed for a complete equilibration of a chemical across a liquid-ordered bilayer, based on the experimental data referenced in the text. The transfer rate parameters are listed in the order of individual steps, from the donor aqueous phase (left) to the acceptor aqueous phase (right). For the backward processes, the order of individual steps is in the right-to-left direction.

Structure of the bacterial ABC transporter Sav1866^1171,1172 (PDB(1173) file 2ONJ) is shown in the ribbon mode (gray). The bound molecules of the ATP analog adenosine-5′-(β,γ-imido)triphosphate are shown in blue.(1291) The approximate position of the bilayer is indicated by horizontal lines.

The X-ray structure of human serum albumin (HSA) with ligands bound in the drug sites I (right) and II (left). Structures of the ligands (tubes shown in colors) are summarized in Chart 4 (number, the Protein Databank (PDB) file): 3-carboxy-4-methyl-5-propyl-2-furanopropionic acid, CMPF (46, 2BXA);(1290) propofol (47, 1E7A); halothane (48, 1E7B);(1287) diflunisal (49, 2BXE); diazepam (50, 2BXF); ibuprofen (51, 2BXG); indoxyl sulfate (52, 2BXH); azapropazone (53, 2BX8); oxyphenbutazone (54, 2BXB); phenylbutazone (55, 2BXC); warfarin (56, 2BXD); 3,5-diiodosalicylic acid, DIS (57, 2BXL);(1290) and 2,3,5-trioiodobenzoic acid, TIB (58, 1BKE).(1285) The PDB(1173) files were superimposed with respect to C-α carbon atoms. The cyan spheres(1290) represent potential binding cavities identified using the Sybyl module SiteID.(1291) Many of the cavities serve as binding sites for fatty acids and thyroxine and as secondary sites for some of the shown drugs. Individual domains are marked.

Milestones in the history of classical pharmacokinetics. More details and references are given in the text.

Schematic outline of the distribution of the chemicals, which do not interact with the headgroups, in a morphologically compartmentalized system consisting of alternating aqueous phases and membranes (represented by the cores). The chemicals can be present as free non-ionized molecules (C_i), free molecules ionized to the jth degree (C_ij), or ion pairs with the kth counterion (CZ_ijk); each species can be bound to proteins (P) or enzymes (E), and eliminated by spontaneous and/or enzymatic reactions. The subscripts i, j, and k are typically used throughout the paper, in the meanings that are shown here. Two-sided arrows represent fast processes, whereas one-sided arrows represent time-dependent processes.

Transport kinetics in the sixth, core compartment of a 10-compartment system, relative to lipophilicty.(2089) The system consists of alternating aqueous (5) and core (5) phases. The concentrations of chemicals do not exceed the equilibrium concentrations at any moment. The surface corresponds to eq 10 with the values of the coefficients specified in Table 5. Other details are as given in Figure 15.

Nonequilibrium concentration−lipophilicity profiles for individual phases of a 10-compartment system of alternating aqueous and core phases at a constant time of distribution.(2089) Other details as in Figure 15. The compartment numbers are shown near the respective curves. The aqueous phases are denoted by the odd numbers and the bilayers are marked by even numbers, as in Figure 14 in section .

Growth inhibition of Ctenomyces mentagrophytes by alkyl amines (c_X is the minimum inhibitory concentration)(2093), relative to the lipophilicity, expressed as the partition coefficient P. The dotted curve corresponds to the bilinear equation 9, and the full curve represents eq 11 for the mixed period of distribution (i = 2). The optimized coefficient values are given in Tables 8 and 9, respectively.

Reactivity dependence of the concentrations in compartment 4 of a four-compartment, water−bilayer−water−bilayer model that were corrected for the contribution of lipophilicity to show only the reactivity portion of this form of the disposition function (eq 13). The exposure time is increasing from top to bottom. Other details are as given in Figure 22.

Dependencies(2112) of the concentration c in the fifth compartment of the system of alternating aqueous and bilayer phases on the partition coefficient P for (A) pure unidirectional transport, (B) transport combined with protein binding, and (C) transport influenced by protein binding and metabolism, after the following times of distribution (in time units): 3.2 (green), 10 (blue), 32 (red), and 100 (black). Calculated using eq 14, with the parameters as in Figure 24A (B_i = 1) and k_i = 1/(time unit).

Steady-state concentration−lipophilicity profiles for (A) aqueous compartment 7 and (B) bilayer 8 of a catenary system of alternating aqueous and bilayer phases, relative to the elimination rate constant k.(2115) The elimination terms only contain k, in (time unit)⁻¹: 10⁻⁴ (curve 1), 10⁻² (curve 2), 1 (curve 3), 10 (curve 4), 10² (curve 5), and 10³ (curve 6). Other details are as shown in Figure 26.

Relationship(2124) between the concentration c of the protein-bound chemical, the partition coefficient P, and the exposure time of distribution t for a pseudo-equilibrium situation: (A) projection into the plane c−P, (B) projection into the plane c−t, and (C) overall view. The values were calculated using eq 25 multiplied by P, with c₀ = 1 unit, β = A = 1, B = 0.1, C = 0.01, and D = 0. Individual curves in projection A are valid for log t = −4 (curve 1), −3 (curve 2), −1.75 (curve 3), −0.5 (curve 4), 0.75 (curve 5), 1.25 (curve 6), 1.75 (curve 7), 2.75 (curve 8), 3.75 (curve 9), and 4.75 (curve 10). Individual curves in projection B are valid for log P = −4 (curve 10), −3 (curve 9), −2 (curve 8), −1 (curve 7), 0 (curve 6), 1.25 (curve 5), 2.5 (curve 4), 3.75 (curve 3), 5 (curve 2), and 6 (curve 1).(2124)

Growth-inhibiting activity of lincomycin derivatives(2190) against Sarcina lutea in the agar diffusion test, as a function of acidity, given as the negative logarithm of the dissociation constant K_a, and lipophilicity, parametrized by the 1-octanol/water partition coefficient P.(34) The surface corresponds(20) to eq 29. The fitted activities of the trans derivatives (not shown) form a similar surface, raised by 0.283 logarithmic units. The outlier did not conform to the smooth surface. More details are given in the text.

Dependence of the inhibitory activity of α-bromoalkanoic acids against V. cholerae on the 1-octanol/water partition coefficient P and the pH values of the medium. Toxicities (T) are given as the inverse values of the minimum killing concentrations. The surface corresponds to eq 34, with the optimized values of adjustable coefficients given in Table 11.(2224)

Structure-based subcellular pharmacokinetics and related sciences. Two-sided arrows indicate mutual influence; one-sided arrows indicate supportive roles.