Lead thermodynamic solubility

At the hit triage stage, it is most common to be able to characterize sets of compounds in a kinetic solubility assay. In the assessment and utilization of these data, the potential disconnects between kinetic and thermodynamic solubility must be considered. Low kinetic solubility for a series of compounds should lead a project team to be concerned about the behavior of compounds in biological assays and buffers, as well as the potential for optimizing drug-like properties in that series. Conversely, while high kinetic solubility is a desirable property, chemists should still remain cognizant of the need to assess thermodynamic solubility as compounds are further optimized. 

Adding compounds solubilized in DMSO to aqueous medium as part of a discovery solubility assay can lead to two types of solubility assay with different uses. At one extreme, the quantity of DMSO is kept very low (<1%). At this low level of DMSO, the solubility is only slightly affected by the DMSO content. For example, data from a poster by Ricerca Ltd. [11] suggest that a DMSO content of 1% should not elevate apparent solubility by more than about 65%. At 5% DMSO, this group reported an average solubility increase of 145% due to the DMSO content. Solubility in an early discovery assay containing one percent DMSO can however exceed thermodynamic solubility by much more than 65%. However, this is very likely due to the time scale. Studies by the Avdeef (plon Inc.) group show a close approximation of early discovery solubility (quantitated by UV) to literature ther-... 

PURPOSE AND RATIONALE Solubility assays are gaining growing attention in drug discovery, because many pharmaceutically active compounds can be adjusted to in vivo testing merely with co-solvents. Furthermore, in vitro assays may also lead to false results, simply for precipitation of a compound in the assay media. Solubility assays vary in one main point they are either performed from solids or stock solutions. A nomenclature has been established in the literature which tries to distinguish between these methods. Determinations from stock solutions are often called kinetic solubility whereas thermodynamic solubility stands for solubility of solids (Kerns). Thermodynamic solubility takes the crystal lattice forces into account. Batch to batch variations, polymorphism... 

The actual in vitro measurements of thermodynamic solubility correspond to the idealized titration regime conditions only to some extent. The closest method seems to be a labor-intensive shake-flask experiment requiring relatively large amounts of a dry crystalline drag and long equilibration times. Moreover, each pH point requires a separate measurement in different buffer. Different buffers usually represent different ionic conditions and may lead to internal inconsistency of the solubility profile thus obtained. The buffer issue deserves an entire subsection of this review and will be discussed later. The real question is whether this investment of resources is worthwhile. The answer depends on who is asking the question. A drag-development... 

As with turbidimetric assays, many of the direct UV absorbance assays are set up to determine kinetic solubility. However, the UV absorbance method also lends itself well to thermodynamic solubility determination by extending the period of sample agitation prior to filtration to 24 h or more. This offers a number of advantages. The solubility data generated are less dependent on the physical form of the initial material precipitated from DMSO and are much closer to thermodynamic solubility values determined later in discovery and in early development. As such, it gives more consistent solubility data through the discovery phase and enables a better quality early assessment to be made of the likely difficulties or otherwise of progressing a lead series into development. 

In the lead identification and lead optimization phases of discovery, there is greater focus on thermodynamic solubility measurements. Thermodynamic solubility assays are designed to determine the solubility of the stable crystalline form of the compound, since this is the physical form that will be sought in the development phase for orally administered drugs. As such, thermodynamic solubilities provide discovery projects with a better risk assessment of likely formulation issues in development. Thermodynamic solubilities, unlike kinetic solubilities, are less dependent on the initial physical form of the compound and being less time critical also tend to be more reproducible. This is particularly important from a molecular design perspective where chemists are seeking to modify molecular structure to improve solubility. 

Attempting to measure a thermodynamic solubility of compounds which will then be used under these screening conditions, will not necessarily give a useful picture of the compounds performance. They will not reflect the more transient nature of the compound that is present in nonequilibrium systems. The presence of organic solvents changes the dielectric constant of an aqueous solution and thus helps to solvate lipophilic compounds in particular, and will give an increased solubility for some series of compounds across the Biopharmaceutics Classification System (BCS) [4]. This is an important consideration in the ultimate use of the solubility data, and a lack of full solubility of the analyte at the test concentration will lead to an underestimation of the compound s true activity. Measuring the solubility of the compounds in close approximation to the assay conditions to which they will be exposed will be more relevant. Indeed, if sensitivity is not an issue, then the quantities, concentrations, and incubation conditions used should reflect those available in the discovery assays. 

Setchenow coefficients for hydrocarbons and for volatile solutes In sea water the osmotic coefficient and density of sea water as a function of temperature and salinity. Thermodynamic solubility products of minerals In brines the activity coefficient of carbon dioxide In sea water speclatlon calculations on copper, zinc, cadmium, and lead In sea water excess Gibbs energies of mixing of electrolyte solutions at 25 C and pairwise and triplet Interaction terms for electrolyte solutions in terms of various models. 

As described in previous sections, solution phase interactions play an important role in co-crystal solubility. The influence is greater than for single component crystals (or their hydrates) since each co-crystal component will modify solution behavior to different extents depending on their interactions with the environment. Kinetic studies are useful when informed by co-crystal thermodynamic solubilities and their solution phase dependence. Simply adding a cocrystal to a solution and measuring drug concentration as a function of time may fail to capture important properties of the co-crystal and lead to inaccurate assessment of its performance. 

The data given in Tables 1.9 and 1.10 have been based on the assumption that metal cations are the sole species formed, but at higher pH values oxides, hydrated oxides or hydroxides may be formed, and the relevant half reactions will be of the form shown in equations 2(a) and 2(b) (Table 1.7). In these circumstances the a + will be governed by the solubility product of the solid compound and the pH of the solution. At higher pH values the solid compound may become unstable with respect to metal anions (equations 3(a) and 3(b), Table 1.7), and metals like aluminium, zinc, tin and lead, which form amphoteric oxides, corrode in alkaline solutions. It is evident, therefore, that the equilibrium between a metal and an aqueous solution is far more complex than that illustrated in Tables 1.9 and 1.10. Nevertheless, as will be discussed subsequently, a similar thermodynamic approach is possible. 

Reaction of PdCl4 with KNCS leads successively to a precipitate of Pd(SCN)2 and the soluble salt K2Pd(SCN)4 (square planar, Pd-S 2.31-2.39 A). This reacts with Ph3As to form the S,S-bonded Pd(SCN)2(AsPh3)2 (kinetic product), which on heating gives the thermodynamically more stable N,N-bonded isomer ... 

The rates of multiphase reactions are often controlled by mass tran.sfer across the interface. An enlargement of the interfacial surface area can then speed up reactions and also affect selectivity. Formation of micelles (these are aggregates of surfactants, typically 400-800 nm in size, which can solubilize large quantities of hydrophobic substance) can lead to an enormous increase of the interfacial area, even at low concentrations. A qualitatively similar effect can be reached if microemulsions or hydrotropes are created. Microemulsions are colloidal dispersions that consist of monodisperse droplets of water-in-oil or oil-in-water, which are thermodynamically stable. Typically, droplets are 10 to 100 pm in diameter. Hydrotropes are substances like toluene/xylene/cumene sulphonic acids or their Na/K salts, glycol.s, urea, etc. These. substances are highly soluble in water and enormously increase the solubility of sparingly. soluble solutes. 

The comparison of I —> N and N —> I may also be explained by the buffered pH in the diffusion layer and leads to an interesting comparison between a process under kinetic control versus one under thermodynamic control. Because the bulk solution in process N —> I favors formation of the ionized species, a much larger quantity of drug could be dissolved in the N —> I solvent if the dissolution process were allowed to reach equilibrium. However, the dissolution rate will be controlled by the solubility in the diffusion layer accordingly, faster dissolution of the salt in the buffered diffusion layer (process I—>N) would be expected. In comparing N—>1 and N —> N, or I —> N and I —> I, the pH of the diffusion layer is identical in each set, and the differences in dissolution rate must be explained either by the size of the diffusion layer or by the concentration gradient of drug between the diffusion and the bulk solution. It is probably safe to assume that a diffusion layer at a different pH than that of the bulk solution is thinner than a diffusion layer at the same pH because of the acid-base interaction at the interface. In addition, when the bulk solution is at a different pH than that of the diffusion layer, the bulk solution will act as a sink and Cg can be eliminated from Eqs. (1), (3), and (4). Both a decrease in the h and Cg terms in Eqs. (1), (3), and (4) favor faster dissolution in processes N —> I and I —> N as opposed to N —> N and I —> I, respectively. 

Aqueous solubility, potency and permeability are three factors under medicinal chemistry control that must be optimized to achieve a compound with acceptable oral absorption. Typically, a lead (chemistry starting point) is deficient in all three parameters. The inter-relationships of these three parameters has been described in a series of publications from Pfizer researchers [7, 8]. Figure 9.1 depicts graphically the minimum acceptable solubility as a function of projected clinical potency and intestinal permeability. A minimum thermodynamic aqueous solubility of 52... 

For a given solid material, a progressive reduction of particle size corresponds to increases in the surface/volume ratio and the escaping tendency of the molecules until the nature of the surface dominates the properties of the material. Two related thermodynamic consequences of this effect are an increase of solubility in any solvent and an increase of vapor pressure as the size of the particle is reduced. For a spherical particle of radius r, thermodynamic arguments lead to the Thomson-Freundlich equation [19] ... 

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