The nature and validity of the mathematical formulation of Michaelis-Menten type kinetics for enzyme-catalysed biochemical reactions is studied. Almost all previous work has concentrated on isolated reactions, i.e. those without input or other environmental influences. In this paper, we investigate the effects of substrate input on this formulation, in particular, on the nature and validity of the quasi-steady state assumptions.

In this paper we investigate the validity of a quasi-steady state assumption in approximating Michaelis-Menten type kinetics for enzyme-catalysed biochemical reactions that are subject to periodic substrate input.

Coarsening of solutions of the integro-differential equationformula herewhere Ω ⊂ ℝn, J(·) [ges ] 0, ε > 0 and f(u) = u3 − u (or similar bistable nonlinear term), is examined, and compared with results for the Allen–Cahn partial differential equation. Both equations are used as models of solid phase transitions. In particular, it is shown that when ε is small enough, solutions of this integro-differential equation do not coarsen, in contrast to those of the Allen–Cahn equation. The special case J(·) ≡ 1 is explored in detail, giving insight into the behaviour in the more general case J(·) [ges ] 0. Also, a numerical approximation method is outlined and used on tests in both one- and two-space dimensions to verify and illustrate the main result.

Abstract:The present paper focuses on solid lipid particles (SLPs), described in the literature as the most effective lipid drug delivery systems that have been introduced in the last decades, as they actually combine the advantages of polymeric particles, hydrophilic/lipophilic emulsions and liposomes. In the current study, we present our most recent advances in the preparation of alendronate (AL)-loaded SLPs prepared by hot homogenization and ultrasonication using various ratios of a self-emulsifying lipidic mixture of Compritol 888, Gelucire 44/14, and Cremophor A 25. The prepared AL-loaded SLPs were investigated for their physicochemical, morphological and structural characteristics by dynamic light scattering, differential scanning calorimetry, thermogravimetric and powder X-ray diffraction analysis, infrared spectroscopy, optical and scanning electron microscopy. Entrapment efficacy and actual drug content were assessed by a validated HPLC method. In vitro dissolution tests performed in simulated gastro-intestinal fluids and phosphate buffer solution pH 7.4 revealed a prolonged release of AL of 70 h. Additionally, release kinetics analysis showed that both in simulated gastrointestinal fluids and in phosphate buffer solution, AL is released from SLPs based on equal ratios of lipid excipients following zero-order kinetics, which characterizes prolonged-release drug systems.

Magnolol (MG) is a small-molecule neolignan polyphenolic compound isolated from the genus Magnolia. The anti-inflammatory, anti-oxidative, anti-diabetic, anti-tumorgenic, anti-neurodegenerative, anti-depressant and anti-microbial properties of MG are well documented in recent literature. These fascinating multiple biological activities of MG encourage research about the development of new delivery and administration approaches able to maximize its potential benefits. This study describes the amino-functionalization of the SBA-15 (Santa Barbara Amorphous) mesoporous matrix by post-synthesis grafting using APTES (3-aminopropyltriethoxysilane) and the characterization of amino-functionalized mesoporous silica SBA-15 loaded with MG in order to achieve modified drug delivery systems. The amino-functionalization of silica SBA-15 was carried out by grafting by refluxing in dry toluene. The powders obtained were characterized texturally by Brunauer-Emmett-Teller (BET) surface area analysis measurements and morphologically by scanning electron microscopy. MG loading degree in the nanoporous matrix was determined by the HPLC method at λ = 290 nm. Results showed that by grafting the amino groups in the silica SBA-15, we obtained amino-functionalized silica SBA-15 with an ordered structure, with specific surfaces and pore sizes that differ from the original matrix, which was reflected in the amount of MG immobilized and release kinetics profile.