In adsorption study, isotherms and kinetics of adsorption process provide pieces of information underlying the mechanisms and dynamics of the process. Several equilibrium and kinetic models are usually employed for performing the experimental design of an adsorption system. In this chapter, the Langmuir, Freundlich, Sips, Liu, Redlich-Peterson nonlinear equations, as well as other unusual isotherm models (Hill, Khan, Radke-Prausnitz, Toth) are discussed. For the kinetics of adsorption, the pseudofirst-order, pseudo-second-order, general-order, Avrami fractionary order, and Elovich chemisorption models are explained. The importance of statistical parameters such as coefficient of determination (R 2 ), adjusted coefficient of determination (R 2 adj ), and standard deviation (root of mean square error) are highlighted. The usage of linearized and nonlinearized equations are illustrated and explained. Some common mistakes commonly committed in the literature using linearized equilibrium and kinetic adsorption models as well as other polemic points in adsorption research are pointed out. Analytical techniques together with thermodynamical data of enthalpy and entropy changes are needed to ascertain if an adsorption process is a chemical or a physical process.

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We examined the effect of Niemann-Pick disease type 2 (NPC2) protein and some late endosomal lipids [sphingomyelin, ceramide and bis(monoacylglycero)phosphate (BMP)] on cholesterol transfer and membrane fusion. Of all lipid-binding proteins tested, only NPC2 transferred cholesterol at a substantial rate, with no transfer of ceramide, GM3, galactosylceramide, sulfatide, phosphatidylethanolamine, or phosphatidylserine. Cholesterol transfer was greatly stimulated by BMP, little by ceramide, and strongly inhibited by sphingomyelin. Cholesterol and ceramide were also significantly transferred in the absence of protein. This spontaneous transfer of cholesterol was greatly enhanced by ceramide, slightly by BMP, and strongly inhibited by sphingomyelin. In our transfer assay, biotinylated donor liposomes were separated from fluorescent acceptor liposomes by streptavidin-coated magnetic beads. Thus, the loss of fluorescence indicated membrane fusion. Ceramide induced spontaneous fusion of lipid vesicles even at very low concentrations, while BMP and sphingomyelin did so at about 20 mol% and 10 mol% concentrations, respectively. In addition to transfer of cholesterol, NPC2 induced membrane fusion, although less than saposin-C. In this process, BMP and ceramide had a strong and mild stimulating effect, and sphingomyelin an inhibiting effect, respectively. Note that the effects of the lipids on cholesterol transfer mediated by NPC2 were similar to their effect on membrane fusion induced by NPC2 and saposin-C.

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