Mathematical and computational modeling of fats and triacylglycerides

Fats and oils are found in many food products; however, their macroscopic properties are difficult to predict, especially when blending different fats or oils together. With difficulties in sourcing specific fats or oils, whether due to availability or pricing, food companies may be required to find alternative sources for these ingredients, with possible differences in ingredient performance. Mathematical and computational modeling of these ingredients can provide a quick way to predict their properties, avoiding costly trials or manufacturing problems, while, most importantly, keeping the consumers happy. This review covers a range of mathematical models for triacylglycerides (TAGs) and fats, namely, models for the prediction of melting point, solid fat content, and crystallization temperature and composition. There are a number of models that have been designed for both TAGs and fats and which have been shown to agree very well with empirical measurements, using both kinetic and thermodynamic approaches, with models for TAGs being used to, in turn, predict fat properties. The last section describes computational models to simulate the behavior of TAGs using molecular dynamics (MD). Simulation of TAGs using MD, however, is still at an early stage, although the most recent papers on this topic are bringing this area up to speed.

Insertion of Molecular Oxygen into a Gold(III)-Hydride Bond

The use of molecular oxygen as an oxidant in chemical synthesis has significant environmental and economic benefits, and it is widely used as such in large-scale industrial processes. However, its adoption in highly selective homogeneous catalytic transformations, particularly to produce oxygenated organics, has been hindered by our limited understanding of the mechanisms by which O2 reacts with transition metals. Of particular relevance are the mechanisms of the reactions of oxygen with late transition metal hydrides as these metal centers are better poised to release oxygenated products. Homogeneous catalysis with gold complexes has markedly increased, and herein we report the synthesis and full characterization of a rare AuIII-H, supported by a diphosphine pincer ligand (tBuPCP = 2,6-bis(di-tert-butylphosphinomethyl)benzene). [(tBuPCP)AuIII-H]+ was found to cleanly react with molecular oxygen to yield a stable AuIII-OOH complex that was also fully characterized. Extensive kinetic studies on the reaction via variable temperature NMR spectroscopy have been completed, and the results are consistent with an autoaccelerating radical chain mechanism. The observed kinetic behavior exhibits similarities to that of previously reported PdII-H and PtIV-H reactions with O2 but is not fully consistent with any known O2 insertion mechanism. As such, this study contributes to the nascent fundamental understanding of the mechanisms of aerobic oxidation of late metal hydrides.

Kinetic interpretation of log-logistic dose-time response curves

A Hill-type time-response curve was derived using a single-step chemical kinetics approximation. The rate expression for the transformation is a differential equation that provides an interpolation formula between the logistic growth curve and second order kinetics. The solution is equivalent to the log-logistic cumulative distribution function with the time constant expressed in terms of a kinetic rate constant. This expression was extended to a full dose-time-response equation by postulating a concentration dependence for the rate constant. This was achieved by invoking a modified form of Haber's law that connects an observed toxic effect with the concentration of the active agent and the elapsed exposure time. Analysis showed that the concept of Concentration Addition corresponds to a special case where the rate constant for the overall transformation rate is proportional to the sum of the rate constants that apply when the agents act individually. Biodiesel "survival" curves were measured and used to test the applicability of the empirical model to describe the effects of inhibitor dosage and binary inhibitor mixtures. Positive results suggest that the proposed dose-response relationship for the toxicity of agents to organisms can be extended to inanimate systems especially in cases where accurate mechanistic models are lacking.

Recent advances and potential applications of modulated differential scanning calorimetry (mDSC) in drug development

Differential scanning calorimetry (DSC) is frequently the thermal analysis technique of choice within preformulation and formulation sciences because of its ability to provide detailed information about both the physical and energetic properties of a substance and/or formulation. However, conventional DSC has shortcomings with respect to weak transitions and overlapping events, which could be solved by the use of the more sophisticated modulated DSC (mDSC). mDSC has multiple potential applications within the pharmaceutical field and the present review provides an up-to-date overview of these applications. It is aimed to serve as a broad introduction to newcomers, and also as a valuable reference for those already practising in the field. Complex mDSC was introduced more than two decades ago and has been an important tool for the quantification of amorphous materials and development of freeze-dried formulations. However, as discussed in the present review, a number of other potential applications could also be relevant for the pharmaceutical scientist.

Molecular Docking and Reaction Kinetic Studies of Chrysin Binding to Serum Albumin

The binding properties of chrysin with serum albumin (SA) were investigated under physiological conditions by calorimetry, circular dichroism (CD) spectroscopy, and molecular modeling. Based on the thermodynamic data, molar reaction enthalpy, reaction order ( n) and the rate constant ( k) were calculated. The results of CD spectroscopy showed that chrysin could bind to SA and the conformation of SA did not have any high-ordered structural change. Computational mapping revealed chrysin binding to the subdomain IB in SA. The chrysin-serum albumin complex was stabilized by hydrophobic force and hydrogen bonding and the reaction was a spontaneous process.

Urea co-inclusion compounds of 13 cis-retinoic acid for simultaneous improvement of dissolution profile, photostability and safe handling characteristics

13-cis Retinoic acid (cis-RA), a synthetic retinoid used in the treatment of severe acne, is known to exhibit extremely low aqueous solubility and high photosensitivity. In this study, urea, a well-known adductor for linear compounds, was successfully employed for the adduction of cis-RA — a substituted cyclic organic compound. Formation of urea inclusion compounds was confirmed by FTIR, DSC and XRD. A modified Zimmerschied calorimetric method was employed for the estimation of the minimum amount of rapidly adductible endocyte (RAE) required for adduction of cis-RA in urea. Urea–cis-RA-RAE inclusion compounds containing varying proportions of guests were prepared and their thermal behaviour studied by DSC. The inclusion compounds were found to have an improved dissolution profile as demonstrated by an overall increase in the dissolution efficiency. An accelerated photostability study, conducted as per Q1B ICH guidelines, revealed that co-inclusion of cis-RA in urea delayed photo-degradation of the drug when compared with that of the pure drug. The results suggest the possibility of exploiting co-inclusion of the drug in a urea host lattice for improved solubility, stability and reduced handling problems for cis-RA.

Study on thermal decomposition characteristics of AIBN

It is found that the results such as observed in the differential scanning calorimeter (DSC), which show the major thermal decomposition (TD) of a self-reactive material, lack the detail to reveal what happens at the initial stage of a reaction. The reaction at this stage is corresponding to the handling condition of storage or transportation, often possibly having the potential to be developed to a runaway reaction. This paper examined and compared the thermal behaviors of AIBN at various working conditions in calorimeters and Dewar vessels. The mechanism that affects the initial reaction and self-heating behavior of the given material was clarified. Near its onset decomposition temperature, physical processes, such as sublimation or melting interfered the initial reaction of AIBN. The mutuality of the physical effect and the chemical reaction made AIBN behave differently under different measuring conditions, and as the result, quasi-autocatalysis or TD possibly occurs in the same sample at the handling temperature range. The heat accumulation storage tests in two Dewar vessels presented completely different self-heating behaviors due to this mechanism and heat transfer capability of the vessels.

Thermal characteristics of lysine tri-isocyanate and its mixture with water

The thermal reactivity of lysine tri-isocyanate (LTI, 2-isocyanatoethyl-2,6-diisocyanato caproylate) and its mixture with 1% water was investigated after the occurrence of a runaway reaction at a plant. By using a sensitive thermal calorimeter, C80, and an adiabatic calorimeter, ARC, an onset reaction of LTI was observed at 70-100 degrees C and it became vigorous at 175-200 degrees C. The reaction is considered as co-polymerization at this stage, which causes a second decomposition reaction at 200 degrees C if the heat generation is accumulated in the vessel. On the other hand, the presence of water can catalyze LTI at much lower onset temperature and lead to a moderate reaction at 50 degrees C since carbamine is produced and in turn it induces decarbonization of the LTI molecule with significant release of CO2 gas which was detected by a gas chromatography and an FT-IR gas analyzer.

Semiempirical Equations for Modeling Solid-State Kinetics Based on a Maxwell−Boltzmann Distribution of Activation Energies: Applications to a Polymorphic Transformation under Crystallization Slurry Conditions and to the Thermal Decomposition of AgMnO4 Crystals

Many solid-state reactions and phase transformations performed under isothermal conditions give rise to asymmetric, sigmoidally shaped conversion-time (x-t) profiles. The mathematical treatment of such curves, as well as their physical interpretation, is often challenging. In this work, the functional form of a Maxwell-Boltzmann (M-B) distribution is used to describe the distribution of activation energies for the reagent solids, which, when coupled with an integrated first-order rate expression, yields a novel semiempirical equation that may offer better success in the modeling of solid-state kinetics. In this approach, the Arrhenius equation is used to relate the distribution of activation energies to a corresponding distribution of rate constants for the individual molecules in the reagent solids. This distribution of molecular rate constants is then correlated to the (observable) reaction time in the derivation of the model equation. In addition to providing a versatile treatment for asymmetric, sigmoidal reaction curves, another key advantage of our equation over other models is that the start time of conversion is uniquely defined at t = 0. We demonstrate the ability of our simple, two-parameter equation to successfully model the experimental x-t data for the polymorphic transformation of a pharmaceutical compound under crystallization slurry (i.e., heterogeneous) conditions. Additionally, we use a modification of this equation to model the kinetics of a historically significant, homogeneous solid-state reaction: the thermal decomposition of AgMnO4 crystals. The potential broad applicability of our statistical (i.e., dispersive) kinetic approach makes it a potentially attractive alternative to existing models/approaches.

Use of isothermal heat-conduction microcalorimetry (IHCMC) for the evaluation of synthetic biomaterials

Isothermal heat-conduction microcalorimetry (IHCMC) allows measurement of extremely small rates of heat flow-on the order of 0.1 microwatt. This provides, for example, the ability to directly observe-and quantitate in a few days-rates of degradation as low as 1% per year at body temperature, in solid material samples of a few grams. Also, one method of IHCMC data analysis allows direct determination of the reaction-rate constant at the temperature of interest, thereby avoiding possible errors due to rate mechanism changes with temperature, an issue that needs to be considered when the Arrhenius method is used. IHCMC can also be used to measure transient phenomena, such as heat of adsorption, and initial metabolic responses of cellular entities to biomaterials. The purposes of this review article are to (a) explain the basic principles, attractive features, limitations, and methods of IHCMC; (b) describe biomaterials applications to date--including studies of the stability of ultra-high-molecular-weight polyethylene and implant-grade calcium sulfate, setting reactions of dental adhesives, and macrophage response to biomaterial particles; (c) provide a discussion of issues and concerns that should be addressed in order to maximize the utility of IHCMC in biomaterials studies; and (d) suggest a number of possible future biomaterials applications for this technique.

Decomposition of solids accompanied by melting--Bawn kinetics

The book "Chemistry of the Solid State", edited by W.E. Garner more than 50 years ago, contained a chapter (Chapter 10) by C.E.H. Bawn which dealt with the kinetics of the thermal decompositions of solids that are accompanied by some melting. Rate equations were derived and this model has become known as the Bawn model or as "Bawn kinetics". This kinetic model has proved particularly useful in pharmaceutical stability studies. The isothermal curves of extent of decomposition, alpha, against time for this model are sigmoidal and the problems of distinguishing this model from other sigmoidal models (Prout-Tompkins, Avrami-Erofeev) have been examined. Under programmed temperature conditions, distinguishability becomes even more difficult.

Application of isothermal microcalorimetry in solid state drug development

Microcalorimetry is an analytical technique that has found numerous applications within the pharmaceutical environment. In the realm of pharmaceutics, especially solid state pharmaceutics, the technique has proved to be an invaluable tool. This review addresses the solid state applications of microcalorimetry within the pharmaceutical industry, with a specific focus on stability, compatibility and amorphicity determinations.

The detection of amorphous material in a nominally crystalline drug using modulated temperature DSC--a case study

Two batches (1 and 2) of an experimental drug (L7) which have shown marked differences in their chemical stability profiles were examined with a view to identifying the presence of small quantities of amorphous material using modulated temperature DSC (MTDSC). The external morphological characteristics of the two batches were similar although marked differences were seen in the moisture uptake profiles. MTDSC studies indicated that while no evidence for a glass transition could be seen for Batch 1, a T(g) and accompanying relaxation endotherm were observed for Batch 2. Comparison with a glassy form of the drug indicated that the amorphous content was in the region of 5-6% w/w in Batch 2. Dynamic moisture sorption studies indicated that while Batch 2 showed a higher uptake profile than Batch 1, addition of 5% w/w amorphous material to Batch 1 led to the establishment of a very similar profile to that seen for Batch 2. It was concluded that Batch 2 contains amorphous material which is responsible for the greater moisture uptake (and by implication poor chemical stability) of this sample and that the glass transition of this fraction may be characterised using MTDSC.

Pharmaceutical applications of the Prout-Tompkins rate equation

More than 50 years ago, a paper by E.G. Prout and F.C. Tompkins was published in the Transactions of the Faraday Society. The paper dealt with the kinetics of the thermal decomposition of crystals of potassium permanganate, and suggested a rate equation, which has become known as the Prout-Tompkins equation, for use in the kinetic analysis of solid state reactions. The paper has been extensively cited in the literature. Applications of the Prout-Tompkins equation in pharmaceutical stability studies are reviewed in this short review.

Determination of the kinetics of degradation of 13-cis-retinoic acid and all-trans-retinoic acid in solution

The degradations of 13-cis-retinoic acid and all-trans-retinoic acid in an organic solvent were determined with an HPLC assay. The degradation curves at 70, 50 and 37 degrees C all showed autocatalytic characteristics for both isomers. For this kind of complex reaction, the usual method cannot be used to estimate the shelf-lives and half-lives at room temperature. In this work a new method was developed to directly calculate the shelf-lives and half-lives. From this equation the activation energy was found to change as the multiple step reaction progressed.