Finding Tmax and Cmax in Multicompartmental Models.

Drug absorption data are critical in bioequivalence comparisons, and factors such as the maximum drug concentration (Cmax), time to achieve Cmax (or Tmax), as well as the area under the curve (AUC) are important metrics. It is generally accepted that the AUC is a meaningful estimate of the extent of absorption, and Tmax or Cmax may be used for assessing the rate of absorption. But estimation of the rate of absorption with Tmax or Cmax is not always feasible, as explicit solutions relating Tmax and Cmax to the absorption (ka) and elimination rate (k) constants exist only for the one and not multicompartmental oral model. Therefore, the determination of Tmax or Cmax for multicompartmental models is uncertain. Here, we propose an alternate, numerical approach that uses the point-slope method for the first and second derivative(s) of the concentration-versus-time profiles and the Newton-Raphson iteration method for the determination of Tmax and Cmax We show that the method holds for multicompartmental oral dosing under single or steady-state conditions in the absence of known microconstants, even for flip-flop (ka < ß) models. Simulations showed that the Cmax and Tmax estimates obtained with the Newton-Raphson method were more accurate than those based on the noncompartmental, observation-based method recommended by the US Food and Drug Administration. The %Bias attributable to sampling frequency and assay error were less than those determined by the noncompartmental method, showing that the Newton-Raphson method is viable for the estimation of Tmax and Cmax.

Effect of Extent of Supersaturation on the Evolution of Kinetic Solubility Profiles.

Solubility limited compounds require enabling formulations such as amorphous solid dispersions (ASDs) to increase the apparent solubility by dissolving to a concentration higher than the equilibrium solubility of the drug. This may lead to subsequent precipitation and thus the loss of the solubility advantage. Although higher supersaturation is known to result in faster precipitation, the overall effect of this faster precipitation on the bioavailability is not well understood. The objective of this study is to gain a better understanding of the impact of extent of supersaturation (i.e., dose) on the resulting kinetic solubility profiles of supersaturating dosage forms. Experimental concentration-time curves of two model compounds with different recrystallization tendencies, indomethacin (IND) and naproxen (NAP), were explored under varying sink indices (SIs) by infusing varying volumes of dissolved drug (e.g., in ethanol) into the dissolution medium. The experimental results were simulated with a mechanistic model considering classical nucleation theory and interface controlled growth on the nucleus surface. In the absence of dissolved polymer to inhibit precipitation, experimental and predicted results show that there exists a critical supersaturation below which no precipitation is observed, and due to this supersaturation maintenance, there exists an optimal dose which maximizes the area under the curve (AUC) of the kinetic solubility concentration-time profile. In the presence of dissolved polymer from ASD dissolution, similar trends were observed except the critical supersaturation was increased due to crystallization inhibition by the dissolved polymer. The importance of measuring the experimental "kinetic solubility" is emphasized. However, we show that the true solubility advantage of amorphous solids depends not on the "kinetic solubility" of amorphous dosage forms, typically arising from the balance between the rate of supersaturation generation and the precipitation kinetics, but rather on the critical supersaturation below which precipitation is not observed for a sufficiently long period.

Single-Molecule Analysis of the Supramolecular Organization of the M2 Muscarinic Receptor and the Gαi1 Protein.

G protein-coupled receptors constitute the largest family of transmembrane signaling proteins and the largest pool of drug targets, yet their mechanism of action remains obscure. That uncertainty relates to unresolved questions regarding the supramolecular nature of the signaling complex formed by receptor and G protein. We therefore have characterized the oligomeric status of eGFP-tagged M2 muscarinic receptor (M2R) and Gi1 by single-particle photobleaching of immobilized complexes. The method was calibrated with multiplexed controls comprising 1-4 copies of fused eGFP. The photobleaching patterns of eGFP-M2R were indicative of a tetramer and unaffected by muscarinic ligands; those of eGFP-Gi1 were indicative of a hexamer and unaffected by GTPγS. A complex of M2R and Gi1 was tetrameric in both, and activation by a full agonist plus GTPγS reduced the oligomeric size of Gi1 without affecting that of the receptor. A similar reduction was observed upon activation of eGFP-Gαi1 by the receptor-mimic mastoparan plus GTPγS, and constitutively active eGFP-Gαi1 was predominantly dimeric. The oligomeric nature of Gi1 in live CHO cells was demonstrated by means of Förster resonance energy transfer and dual-color fluorescence correlation spectroscopy in studies with eGFP- and mCherry-labeled Gαi1; stochastic FRET was ruled out by means of non-interacting pairs. These results suggest that the complex between M2R and holo-Gi1 is an octamer comprising four copies of each, and that activation is accompanied by a decrease in the oligomeric size of Gi1. The structural feasibility of such a complex was demonstrated in molecular dynamics simulations.

Impact of phase separation morphology on release mechanism of amorphous solid dispersions.

Amorphous solid dispersions (ASDs) can phase separate in the gel phase during dissolution, lowering the chemical potential and thus the driving force for drug release. The purpose of this study is to explore the connection between amorphous phase separation in the hydrated ASD and its resulting release rate. Poorly soluble model compounds - indomethacin (IND) and ritonavir (RTV) - were formulated as ASDs using PVP as carrier. Rotating disk dissolution studies with varying drug loading levels of IND-PVP and RTV-PVP showed that the drug release was fastest at an intermediate drug loading level. This was in part due to faster erosion of the ASD at lower drug loading levels. More interestingly, at low drug loading levels, PVP and the drug co-eroded, while at high drug loading levels, PVP was released preferentially. In the case of RTV-PVP, the loading level corresponding to this transition was correlated with the change in phase separation morphology as probed by confocal fluorescence imaging studies. At low drug loading levels, the hydrophobic domains were discrete domains while at high drug loading levels, hydrophobic domains were continuous. Our results suggest that at low drug loadings, release is mediated by erosion of the polymer along with embedded drug rich droplets, whereas at high drug loadings, formation of a drug-rich domain continuous morphology leads to preferential release of the polymer-rich domains. The transition from hydrophobic discrete to hydrophobic continuous morphology occurs at the percolation threshold. We discuss the two mechanisms of phase separation and its impact on the drug release from ASDs in the context of the ternary phase diagram.

Hepatic clearance concepts and misconceptions: Why the well-stirred model is still used even though it is not physiologic reality?

The liver is the most important drug metabolizing organ, endowed with a plethora of metabolizing enzymes and transporters to facilitate drug entry and removal via metabolism and/or biliary excretion. For this reason, much focus surrounds the development of clearance concepts, which are based on normalizing the rate of removal to the input or arterial concentration. By so doing, some authors have recently claimed that it implies one specific model of hepatic elimination, namely, the widely used well-stirred or venous equilibration model (WSM). This commentary challenges this claim and aims to provide a comprehensive discussion of not only the WSM but other currently applied hepatic clearance models - the parallel tube model (PTM), the dispersion model (DM), the zonal liver model (ZLM), and the heterogeneous capillary transit time model of Goresky and co-workers (GM). The WSM, PTM, and DM differ in the patterns of internal blood flow, assuming bulk, plug, and dispersive flows, respectively, which render different degrees of mixing within the liver that are characterized by the magnitudes of the dispersion number (DN), resulting in different implications concerning the (unbound) substrate concentration in liver (CuH). Early models assumed perfusion rate-limited distribution, which have since been modified to include membrane-limited transport. The recent developments associated with the misconceptions and the sensitivity of the models are hereby addressed. Since the WSM has been and will likely remain widely used, the pros and cons of this model relative to physiological reality are further discussed.

Allosteric modulation in monomers and oligomers of a G protein-coupled receptor.

The M2 muscarinic receptor is the prototypic model of allostery in GPCRs, yet the molecular and the supramolecular determinants of such effects are unknown. Monomers and oligomers of the M2 muscarinic receptor therefore have been compared to identify those allosteric properties that are gained in oligomers. Allosteric interactions were monitored by means of a FRET-based sensor of conformation at the allosteric site and in pharmacological assays involving mutants engineered to preclude intramolecular effects. Electrostatic, steric, and conformational determinants of allostery at the atomic level were examined in molecular dynamics simulations. Allosteric effects in monomers were exclusively negative and derived primarily from intramolecular electrostatic repulsion between the allosteric and orthosteric ligands. Allosteric effects in oligomers could be positive or negative, depending upon the allosteric-orthosteric pair, and they arose from interactions within and between the constituent protomers. The complex behavior of oligomers is characteristic of muscarinic receptors in myocardial preparations.