Designing optimal mixtures using generalized disjunctive programming: Hull relaxations

A general modeling framework for mixture design problems, which integrates Generalized Disjunctive Programming (GDP) into the Computer-Aided Mixture/blend Design (CAMbD) framework, was recently proposed (S. Jonuzaj, P.T. Akula, P.-M. Kleniati, C.S. Adjiman, 2016. AIChE Journal 62, 1616–1633). In this paper we derive Hull Relaxations (HR) of GDP mixture design problems as an alternative to the big-M (BM) approach presented in this earlier work. We show that in restricted mixture design problems, where the number of components is fixed and their identities and compositions are optimized, BM and HR formulations are identical. For general mixture design problems, where the optimal number of mixture components is also determined, a generic approach is employed to enable the derivation and solution of the HR formulation for problems involving functions that are not defined at zero (e.g., logarithms). The design methodology is applied successfully to two solvent design case studies: the maximization of the solubility of a drug and the separation of acetic acid from water in a liquid-liquid extraction process. Promising solvent mixtures are identified in both case studies. The HR and BM approaches are found to be effective for the formulation and solution of mixture design problems, especially via the general design problem

G\mathcal{G}-SELC: Optimization by sequential elimination of level combinations using genetic algorithms and Gaussian processes

Identifying promising compounds from a vast collection of feasible compounds is an important and yet challenging problem in the pharmaceutical industry. An efficient solution to this problem will help reduce the expenditure at the early stages of drug discovery. In an attempt to solve this problem, Mandal, Wu and Johnson [Technometrics 48 (2006) 273--283] proposed the SELC algorithm. Although powerful, it fails to extract substantial information from the data to guide the search efficiently, as this methodology is not based on any statistical modeling. The proposed approach uses Gaussian Process (GP) modeling to improve upon SELC, and hence named $\mathcal{G}$-SELC. The performance of the proposed methodology is illustrated using four and five dimensional test functions. Finally, we implement the new algorithm on a real pharmaceutical data set for finding a group of chemical compounds with optimal properties.Comment: Published in at http://dx.doi.org/10.1214/08-AOAS199 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

The study of probability model for compound similarity searching

Information Retrieval or IR system main task is to retrieve relevant documents according to the users query. One of IR most popular retrieval model is the Vector Space Model. This model assumes relevance based on similarity, which is defined as the distance between query and document in the concept space. All currently existing chemical compound database systems have adapt the vector space model to calculate the similarity of a database entry to a query compound. However, it assumes that fragments represented by the bits are independent of one another, which is not necessarily true. Hence, the possibility of applying another IR model is explored, which is the Probabilistic Model, for chemical compound searching. This model estimates the probabilities of a chemical structure to have the same bioactivity as a target compound. It is envisioned that by ranking chemical structures in decreasing order of their probability of relevance to the query structure, the effectiveness of a molecular similarity searching system can be increased. Both fragment dependencies and independencies assumption are taken into consideration in achieving improvement towards compound similarity searching system. After conducting a series of simulated similarity searching, it is concluded that PM approaches really did perform better than the existing similarity searching. It gave better result in all evaluation criteria to confirm this statement. In terms of which probability model performs better, the BD model shown improvement over the BIR model

Drug-Phospholipid Complex-loaded Matrix Film Formulation for the Enhanced Transdermal Delivery of Quercetin

A novel quercetin-phospholipid-complex(QPLC)-loaded matrix film for improved transdermal delivery of quercetin was developed. The QPLC formulation, prepared using a solvent-evaporation method, was optimized using a central-composite design. The optimized QPLC formulation was characterized by particle size and zeta potential analysis, thermal analysis, Fourier transform infrared spectroscopy (FTIR), and proton nuclear magnetic resonance spectroscopy (1H-NMR). QPLC formulation was functionally evaluated for solubility and in vitro dissolution of quercetin. Matrix films of pure quercetin (Q-MF)or QPLC QPLC-MF) were prepared using a solvent casting method. The prepared Q-MF and QPLC-MF were characterized for weight uniformity, folding endurance, moisture content, and moisture uptake. The films were also functionally characterized for in vitro diffusion of quercetin through a dialysis membrane and ex vivo permeability of quercetin across rat skin. Finally, the anti-inflammatory activity of the films was evaluated on carrageenan-induced paw edema in Wistar albino rats. The experimental design identified the optimal formulation and process variables for the preparation of QPLC. The validation of the obtained model using these values confirmed the suitability and robustness of the model. The physical-chemical characterization of the prepared QPLC supported the formation of a stable complex. The solubility analysis of QPLC showed a 22-fold increase in quercetin aqueous solubility, compared to pure quercetin. The dissolution results exhibited a significantly higher rate and extent of quercetin dissolution from QPLC compared to that of pure quercetin. The permeability of quercetin from Q-MF and QPLC-MF across rat skin mirrored those obtained from the dissolution studies. Topical application of QPLC-MF exhibited a significant (p\u3c0.05) inhibition of carrageenan-induced paw edema in rats compared to that of Q-MF. This study provides a promising combination approach, i.e., phospholipid-based complexation and transdermal film formulation for improved transdermal delivery of quercetin and similar pharmacologically active phytoconstituents

A model for pH determination during alcoholic fermentation of a grape must by Saccharomyces cerevisiae

A model to predict accurately pH evolution during alcoholic fermentation of must by Saccharomyces cerevisiae is proposed for the first time. The objective at least is to determine if the pH measurement could be used for predictive control. The inputs of the model are: the temperature, the concentrations in sugars, ethanol, nitrogen compounds, mineral elements (magnesium, calcium, potassium and sodium) and main organic acids (malic acid, citric acid, acetic acid, lactic acid, succinic acid). In order to avoid uncertainties coming from the possible precipitation, we studied this opportunity on a grape must without any tartaric acid, known as forming complexes with potassium and calcium during the fermentation. The model is based on thermodynamic equilibrium of electrolytic compounds in solution. The dissociation constants depend on the temperature and the alcoholic degree of the solution. The average activity coefficients are estimated by the Debbye–H¨uckel relation. A fictive diacid is introduced in the model to represent the unmeasured residual species. The molality of hydrogen ions and thus the pH are determined by solving a non-linear algebraic equations system consisted of mass balances, chemical equilibrium equations and electroneutrality principle. Simulation results showed a good capacity of the model to represent the pH evolution during fermentation

Mixed valency in cerium oxide crystallographic phases: Determination of valence of the different cerium sites by the bond valence method

We have applied the bond valence method to cerium oxides to determine the oxidation states of the Ce ion at the various site symmetries of the crystals. The crystals studied include cerium dioxide and the two sesquioxides along with some selected intermediate phases which are crystallographically well characterized. Our results indicate that cerium dioxide has a mixed-valence ground state with an f-electron population on the Ce site of 0.27 while both the A- and C-sesquioxides have a nearly pure f^1 configuration. The Ce sites in most of the intermediate oxides have non-integral valences. Furthermore, many of these valences are different from the values predicted from a naive consideration of the stoichiometric valence of the compound

Mathematical Modelling of Hydrophilic Ionic Fertiliser Diffusion in Plant Cuticles: Lipophilic Surfactant Effects

The agricultural industry requires improved efficacy of sprays being applied to crops and weeds to reduce their environmental impact and increase financial returns. One way to improve efficacy is by enhancing foliar penetration. The plant leaf cuticle is the most significant barrier to agrochemical diffusion within the leaf. It has been noted that a comprehensive set of mechanisms for ionic active ingredient penetration through plant leaves with surfactants is not well defined and oils that enhance penetration have been given little attention. The importance of a mechanistic mathematical model has been noted previously in the literature. Two mechanistic mathematical models have been previously developed by the authors, focusing on plant cuticle penetration of calcium chloride through tomato fruit cuticles. The models included ion binding and evaporation with hygroscopic water absorption, along with the ability to vary the active ingredient concentration and type, relative humidity and plant species. Here we further develop these models to include lipophilic adjuvant effects, as well as the adsorption and desorption of compounds on the cuticle surface with a novel Adaptive Competitive Langmuir model. These modifications to a penetration model provide a novel addition to the literature. We validate our theoretical model results against appropriate experimental data, discuss key sensitivities and relate theoretical predictions to physical mechanisms. The results indicate the addition of the desorption mechanism may be one way to predict increased penetration at late times and the sensitivity of model parameters compares wells to those present in the literature

Dissolution Rates of Mangosteen (Garcinia mangostana L.) Pericarps Extract Granules in Synthetic Human Gastrointestinal Fluid

Mangosteen (Garcinia mangostana L.) pericarps contain prenylated xanthone derivates, which exhibit some pharmacological activities, such as antiinflammatory, antihistamine, antibacterial, antivirus, antifungal, antioxidant, and antiulcerogenic. The purpose of this research was to study the dissolution rates of mangosteen pericarp extract granules in synthetic human gastrointestinal fluid at various pH and temperatures, which include experimental and modeling works. The granules were prepared by wet granulation of methanol extracts of mangosteen pericarps with addition of 25% w/v Arabic gum and 5% w/v maltodextrin. Dissolution rate study was performed by dissolving 0.5 g granules in 500 mL of 0.02M phosphate buffer solution with constant agitation at various pH (5.5, 6, 6.5, 7 and 7.5) and temperatures (30, 37 and 40oC) for two hours. Every 20 minutes, a liquid sample was withdrawn from the system for xanthone analysis. The results showed that mangosteen pericarps granules dissolution rates increased with pH under acidic condition. At pH 7.5 (basic condition), the dissolution rate was faster than that at pH 7. As expected, the dissolution rates were higher at higher temperatures. The semi empirical Korsmeyer-Peppas model showed its superiority over other models to predict the mangosteen pericarps granules dissolution rates. However, the mass transfer model proposed in this work also agreed well with the experimental data with error percentages closely similar to that of Korsmeyer-Peppas model