Two populations of protein molecules detected by small-angle neutron and X-ray scattering (SANS and SAXS) in lyophilized protein:lyoprotector (disaccharide) systems.

Two protein interaction peaks are observed in pharmaceutically-relevant protein (serum albumin) : disaccharide 1 : 1 and 1 : 3 (w/w) freeze-dried systems for the first time. In samples with a higher disaccharide content, the protein-protein distances are longer for both populations, while the fraction of the protein population with a shorter protein-protein distance is lower. Both factors would favor better stability against aggregation for disaccharide-rich protein formulations. This study provides direct experimental support for a "dilution" hypothesis as a potential stabilization mechanism for freeze-dried protein formulations.

Water Distribution on Protein Surface of the Lyophilized Proteins With Different Topography Studied by Molecular Dynamics Simulations.

Water play an important role in many structural and physicochemical properties of lyophilized proteins. Molecular dynamics simulations were employed to study the explicit water distributions on four structurally diversed proteins: insulin-like growth factor 1 (IGF1), immunoglobin G1 (IgG1), human serum albumin (HSA), and collagen. The MD simulations were combined with the literature data on water vapor sorption isotherms. To account for the heterogeneity of protein surface, the water molecules were classified into different groups according to the binding strengths. A mechanistic mathematical model was built to describe the type-II vapor sorption isotherms and successfully applied to all four model protein systems. Although commonly used Brunauer-Emmett-Teller (BET) theory has a good fitting to the experimental vapor sorption isotherms, the basic "monolayer" concept is not consistent with reality - covering too limited protein surface. Experimentally, several physicochemical properties did show a break point near the BET "monolayer" level. This study demonstrates that the water content threshold or BET "monolayer" is consistent with the onset of water cluster (n≥3) formation. Based on water distributions at different amino acid sidechains as well as the backbones, a simple formula was derived based on primary sequence and fractions of ordered secondary structures (i.e. alpha helix and beta sheet) to predict the BET "monolayer". We find that proteins with helical structural elements are more stable upon changes in water content compared to other protein architectures.

Eyes on Lipinski's Rule of Five: A New "Rule of Thumb" for Physicochemical Design Space of Ophthalmic Drugs.

The study objective was to investigate molecular thermodynamic properties of approved ophthalmic drugs and derive a framework outlining physicochemical design space for product development. Unlike the methodology used to obtain molecular descriptors for assessment of drug-like properties by Lipinski's Rule of 5 (Ro5), this work presents a retrospective approach based on in silico analysis of molecular thermodynamic properties beyond Ro5 parameters (ie, free energy of distribution/partitioning in octanol/water, dynamic polar surface area, distribution coefficient, and solubility at physiological pH) by using 145 marketed ophthalmic drugs. The study's focus was to delineate inherent molecular parameters explicitly important for ocular permeability and absorption from topical eye drops. A comprehensive parameter distribution analysis on ophthalmic drugs' molecular properties was performed. Frequencies in distribution analyses provided groundwork for physicochemical parameter limits of molecular thermodynamic properties having impact on corneal permeability and topical ophthalmic drug delivery. These parameters included free energy of partitioning (ΔGo/w) calculated based on thermodynamic free energy equation, distribution coefficient at physiological pH (clog DpH7.4), topological polar surface area (TPSA), and aqueous solubility (Sint, SpH7.4) with boundaries of clog DpH7.4 ≤4.0, TPSA ≤250 Å2, ΔGo/w ≤20 kJ/mol (4.8 kcal/mol), and solubility (Sint and SpH7.4) ≥1 µM, respectively. The theoretical free energy of partitioning model streamlined calculation of changes in the free energy of partitioning, Δ(ΔGo/w), as a measure of incremental improvements in corneal permeability for congeneric series. The above parameter limits are proposed as "rules of thumb" for topical ophthalmic drugs to assess risks in developability.

Water Distribution and Clustering on the Lyophilized IgG1 Surface: Insight from Molecular Dynamics Simulations.

Water has a critical role in the stability of the higher-order structure of proteins. In addition, it is considered to be a major destabilization factor for the physical and chemical stability of freeze-dried proteins and peptides. Physical and chemical aspects of protein/water relationships are commonly studied with the use of water vapor sorption isotherms for amorphous lyophilized proteins, which, in turn, are commonly analyzed using the Brunauer-Emmett-Teller (BET) equation to obtain the parameters, Wm and CB. The parameter Wm is generally referred to as the "monolayer limit of adsorption" and has a narrow range of 6-8% for most proteins. In this study, the water distribution on an IgG1 surface is investigated by molecular dynamics (MD) simulations at different water contents. The monolayer of water molecules was found to have limited coverage of the protein surface, and the true monolayer coverage of the protein globule actually occurs at a hydration level above 30%. The distribution of water molecules on the IgG1 surface is also highly heterogeneous, and the heterogeneity is not considered in the BET theory. In this study, a mechanistic model has been developed to describe the water vapor sorption isotherm. This model is based on the analysis of the hydrogen bonding network extracted from the MD simulations. The model is consistent with the experimental Type-II isotherm, which is usually observed for proteins. The physical meaning of the BET monolayer was redefined as the onset of water cluster formation. A simple model to calculate the onset water level, Wm, is proposed based on the hydration of different amino acids, as determined from the MD simulations.

Predictive Modeling of Micellar Solubilization by Single and Mixed Nonionic Surfactants.

Micellar solubilization is an important concept in the delivery of poorly water-soluble drugs. The rational selection of the type and the amount of surfactant to be incorporated in a formulation require comprehensive solubility studies. These studies are time and material demanding, both of which are scarce, especially during late discovery and early development stages. We hypothesized that, if the solubilization mechanism or molecular interaction is similar, the solubilization capacity ratio (a newly defined parameter) is dictated by micellar structures, independent of drugs. We tested this hypothesis by performing solubility studies using 8 commonly used nonionic surfactants and 17 insoluble compounds with diverse characteristics. The results show a striking constant solubilization capacity ratio among the 8 nonionic surfactants, which allow us to develop predictive solubility models for both single and mixed surfactant systems. The vast majority of the predicted solubility values, using our developed models, fall within 2-fold of the experimentally determined values with high correlation coefficients. As expected, systems involving ionic surfactant sodium dodecyl sulfate, used as a negative control, do not follow this trend. Deviations from the model, observed in this study or envisioned, were discussed. In conclusion, we have established predictive models that are capable of predicting solubility in a wide range of nonionic micellar solutions with only 1 experimental measurement. The application of such a model will significantly reduce resource and greatly enhance drug product development efficiency.

Effect of Water on the Chemical Stability of Amorphous Pharmaceuticals: 2. Deamidation of Peptides and Proteins.

Role of water in chemical (in)stability is revisited, with focus on deamidation in freeze-dried amorphous proteins and peptides. Two distinct patterns for deamidation versus water have been reported, that is, a consistent increase in rate constant with water, and a "hockey stick"-type behavior. For the latter, deamidation is essentially independent of water at lower water contents and accelerates when water content increases above a threshold value. Two simple kinetic models are developed to analyze literature-reported relationships between water content and deamidation rate constants. One model is based on catalytic role of water clusters in enabling proton transfer, which is a critical reaction step. Water clusters are formed when water content increases above a threshold value, while unclustered (and less catalytically-active) water molecules are predominant at lower water levels. The second model considers the dual role of water, as both a destabilizer via catalysis and a stabilizer of protein native structure. Considering that both models emphasize the importance of local structure and that local structure is intrinsically related to fast (and non-cooperative) relaxation modes, it is plausible to expect correlations between local mobility, such as beta-relaxation, and amorphous chemical instability.

Competition of hydrophobic steroids with sodium dodecyl sulfate, dodecyltrimethylammonium bromide, or dodecyl ß-D-maltoside for the dodecane/water interface.

The surface tension lowering abilities of insoluble steroids, progesterone and testosterone, were examined at the dodecane/water interface in the presence and absence of surfactants, sodium dodecyl sulfate, dodecyltrimethylammonium bromide, and dodecyl maltoside. In the absence of these surfactants, the steroids significantly lowered the interfacial tension while exhibiting no activity at the air/water and air/dodecane surfaces. Further, in mixtures of surfactants and steroids, significant enhancement of interfacial tension lowering was observed. At a sufficiently high concentration of surfactant, no further lowering of tension was observed in the presence of the steroids. The synergistic effects on interfacial tension of steroids and surfactants were characterized by the free energy of transfer to the interface of each solute based on a two-dimensional solution equation of state. Assuming no significant interaction between the steroids and the surfactants in the interface, predictions of interfacial tensions were made based on the calculated free energies of transfer and interfacial area occupied. Good agreement was found between the predicted values and experimental values for interfacial tension. The results of these studies show that progesterone and testosterone, molecules not normally thought of as surface active, exhibit significant interfacial activity and can successfully compete with surfactants for the dodecane/water interface.

Determination of intraliposomal pH and its effect on membrane partitioning and passive loading of a hydrophobic camptothecin, DB-67.

The purpose of this work was to study the effect of pH on the liposomal encapsulation of a model camptothecin anti-tumor agent, DB-67, by considering the state of ionization and bilayer membrane/water partitioning of the drug as a function of pH. A novel fluorescence method was developed to monitor intravesicular pH in liposomal formulations containing entrapped DB-67 by using the drug itself as a pH indicator. Fluorescence spectra were recorded in aqueous buffers and liposomes and used to estimate the ionization constant of the A-ring phenol of DB-67 (pKappa(a2)) and shifts in ionization constants ( pKappa (a1) and pKappa(a2) ) due to membrane binding. Bilayer/water partitioning studies by equilibrium dialysis were employed to show that DB-67 is highly membrane bound over the entire pH range examined though binding decreases with an increase in pH. The observed ionization constants of membrane-bound DB-67 obtained from the equilibrium dialysis experiments were consistent with observations from fluorescence measurements and previous permeability results. The pH dependence of DB-67 loading using a passive loading technique was found to reflect the pH dependence of membrane binding of the drug. This results in poor encapsulation efficiency of DB-67 at high pH, necessitating further development of formulation strategies to improve loading efficiency.

Empirically augmented density functional theory for predicting lattice energies of aspirin, acetaminophen polymorphs, and ibuprofen homochiral and racemic crystals.

PURPOSE: Lattice energies of drug crystals are closely associated with many important physicochemical properties including polymorphism of the crystals. Current quantum mechanical methods that can be applied to calculate the lattice energy of most drug crystals are not capable of fully considering the van der Waals interaction energy, a dominant component in the lattice energy. Herein, we report the results of using empirically augmented quantum mechanical methods for predicting the lattice energies of selected drug crystals. METHODS: Long-range van der Waals energies were evaluated by atom-atom pairwise C ( 6 ) R (-6 ) functions that were damped at short interatomic distance where interatomic interactions could be better evaluated by density functional theory (DFT). The atomic C ( 6 ) coefficients were taken from literature, and three damping functions were tested. For the quantum mechanical calculations, different basis sets were tested with aspirin as the model system. Basis set superposition error (BSSE) was considered. In addition to aspirin, acetaminophen Form I and Form II, and s(+)- and (+/-)-ibuprofen were calculated and the results were compared to experimental values. Experimentally determined single crystal structures were optimized prior to both empirical and DFT energy calculations. RESULTS: Lattice energies calculated by the empirically augmented quantum mechanical methods are in very good agreement with experimental values, suggesting the approach is acceptable. The results also indicate that the long-range van der Waals or dispersion energy is a significant part of the lattice energy, which cannot be accurately estimated by the DFT methods alone. CONCLUSIONS: Due to the empirical nature for estimating the dispersion energy, choosing the right empirical parameters is crucial. The methods and parameters tested seem to be able to produce reliable values of lattice energies of the drug crystals.

Predicting Lattice Energy of Organic Crystals by Density Functional Theory with Empirically Corrected Dispersion Energy.

Calculation of the lattice energy of organic crystals is needed for predicting important structural and physicochemical properties such as polymorphism and growth morphology. Quantum mechanical methods that can be used for calculating typical organic crystals are unable to fully estimate van der Waals energies in a crystal. A method by augmenting the density functional theory with an analytical, nonelectronic approach for accounting for the dispersion energy was tested for selected organic crystals. The results illustrate the feasibility of this method for the prediction of the lattice energy of organic crystals. It is also shown that the dispersion energy is a dominant component of the lattice energy, particularly for those organic crystals that have no hydrogen bonds.

Study of crystal packing on the solid-state reactivity of indomethacin with density functional theory.

PURPOSE: Solid-state reactions are highly anisotropic. Different polymorphs of the same compound may have remarkably different chemical reactivities. It was reported that two polymorphs of indomethacin single crystals, alpha- and gamma-forms, reacted with ammonia gas at dramatically different rates. In this study, the effect of crystal packing on their difference in chemical reactivity was investigated by examining the electronic structures and properties of the crystal forms. METHODS: Ab initio methods, including density functional theory, were used to calculate electronic structures of the alpha- and gamma-forms of indomethacin. In particular, nuclear Fukui functions were obtained to elucidate how a molecule in a crystal may respond to an electronic perturbation that can be caused by a chemical reaction. RESULTS: Different conformers in the two polymorphs showed different electronic structures. The carboxylic group of one symmetrically different molecule in the alpha-form had significantly larger nuclear Fukui functions than those of other molecules of either the alpha- or gamma-form, supporting the experimental observation that the alpha-form was much more reactive with ammonia than the gamma-form. In addition, the large nuclear Fukui functions associated with atoms other than those from the carboxylic group were attributed to the tension of two dislodged aromatic rings. CONCLUSIONS: Electronic calculations were able to provide insightful glimpses into the effect of crystal packing on the solid-state reaction of indomethacin. The nuclear Fukui function, which characterizes the physical stress on an atom due to perturbation in electron density, may provide a powerful means of studying the solid-state reactions of organic crystals at the electronic level.

Face-integrated Fukui function: understanding wettability anisotropy of molecular crystals from density functional theory.

Wettability is one of the anisotropic surface properties of molecular crystals that exhibit the structural variance of chemical moieties on various growth faces. The divergence in liquid-solid interactions at different faces is thought to be related to the inherent responding capacity or sensitivity of a solid surface to the perturbation in electronic structures and atomic positions as a result of the contact by a liquid. Since the Fukui function, according to density functional theory (DFT), is a local function for describing such sensitivity to the structural perturbation and is directly related to local softness, it has been proposed and tested to use an integrated Fukui function over a crystallographic plane for describing the anisotropy of solid-liquid interactions. It is found that the contact angle of a polar solvent, such as water, on a crystal surface shows an intimate connection to the integrated Fukui functions of the surface, illustrating an extension of Pearson's HSAB (hard and soft acids and bases) to crystal systems. The concept of face-integrated Fukui function and the approach to apply the HSAB with the DFT-based concepts may provide a powerful means for describing anisotropic properties, including wettability of organic crystals.

Understanding solid-state reactions of organic crystals with density functional theory-based concepts.

Solid-state reactions are commonly observed in organic crystals, including pharmaceutical and agricultural materials, fine chemicals, dyes, explosives, optics, and many other substances. The fact that these reactions are in general highly anisotropic with regard to the initiation and propagation in a crystal has led to this study for investigating the effect of crystal packing on the reaction mechanism and kinetics of organic crystals. We have used electron density-based concepts, including nuclear Fukui function, developed from density functional theory, for elucidating the effect of electronic structures of different polymorphs on the difference in their chemical reactivity. Two polymorphs of flufenamic acid were studied. The calculation results on major reacting faces of the two forms support their reactivity difference with ammonia gas. In addition, we calculated surface energies of reacting faces to discuss how the mechanical difference may affect the propagation of solid-state reaction.