New Sorption Isotherms Derived from a Gamma Distribution of Binding Constants.

New sorption isotherms for heterogeneous sorbents are derived by combining a Gamma distribution of binding constants with a local isotherm defined by a Langmuir or Hill equation. The new "Gamma isotherms" are expressed as Stieltjes transforms of the distribution and involve generalized exponential integrals. The related energy distributions are asymmetric and present a peak corresponding to the mean binding constant. The advantages of the new isotherms are (1) at low pressures or concentrations, with a Langmuir local isotherm, the global "Gamma-Langmuir" isotherm retrieves Henry's law; (2) contrary to the power Freundlich or hypergeometric Freundlich global isotherms, these Gamma isotherms do not need a redefinition of the standard state; (3) with a Hill local isotherm, the global "Gamma-Hill" isotherm allows a separate estimation of the cooperativity and heterogeneity parameters; and (4) the condensation approximation is a good approximation if the local isotherm is Hill and displays a high degree of cooperativity. The Gamma-Langmuir model is applied to three examples from the literature, with rather different Gamma distributions.

Yesterday, Today, and Tomorrow. Evolution of a Sleeping Beauty: The Freundlich Isotherm.

The name of Herbert Freundlich is commonly associated with a power relationship for adsorbed amount of a substance (Cads) against the concentration in solution (Csln), such that Cads = KCslnn; this isotherm (together with the Langmuir isotherm) is considered to be the model of choice for correlating the experimental adsorption data of micropollutants or contaminants of emerging concern (pesticides, pharmaceuticals, and personal care products), but it also concerns the adsorption of gases on solids. However, Freundlich's 1907 paper was a "sleeping beauty", which only started to attract significant citations from the early 2000s onward; moreover, these citations were too often wrong. In this paper, the main steps in the historical developments of Freundlich isotherm are identified, along with a discussion of several theoretical points: (1) derivation of the Freundlich isotherm from an exponential distribution of energies, leading to a more general equation, based on the Gauss hypergeometric function, of which the power Freundlich equation is an approximation; (2) application of this hypergeometric isotherm to the case of competitive adsorption, when the binding energies are perfectly correlated; and (3) new equations for estimating the Freundlich coefficient KF from physicochemical properties such as the sticking surface or probability. From new data treatment of two examples from the literature, the influence of several parameters is highlighted, and the application of linear free-energy relationships (LFER) to the Freundlich parameters for different series of compounds is evoked, along with its limitations. We also suggest some ideas that may be worth exploring in the future, such as extending the range of applications of the Freundlich isotherm by means of its hypergeometric version, extending the competitive adsorption isotherm in the case of partial correlation, and exploring the interest of the sticking surfaces or probabilities instead of KF for LFER analysis.

Patterns and predictive factors of loss of the independence trajectory among community-dwelling older adults.

BACKGROUND: Independence is related to the aging process. Loss of independence is defined as the inability to make decisions and participate in activities of daily living (ADLs). Independence is related to physical, psychological, biological, and socioeconomic factors. An enhanced understanding of older people's independence trajectories and associated risk factors would enable the develop early intervention strategies. METHODS: Independence trajectory analysis was performed on patients identified in the Unité de Prévention de Suivi et d'Analyse du Vieillissement (UPSAV) database. UPSAV cohort is a prospective observational study. Participants were 221 community-dwelling persons aged ≥75 years followed for 24 months between July 2011-November 2013 and benefits from a prevention strategy. Data were collected prospectively using a questionnaire. Independence was assessed using the "Functional Autonomy Measurement System (Système de Mesure de l'Autonomie Fonctionnelle (SMAF))". Group-based trajectory modeling (GBTM) was performed to identify independence trajectories, and the results were compared with those of k-means and hierarchical ascending classifications. A multinomial logistic regression was performed to identify predictive factors of the independence trajectory. RESULTS: Three distinct trajectories of independence were identified including a "Stable functional autonomy (SFA) trajectory" (53% of patients), a "Stable then decline functional autonomy decline (SDFA) trajectory" (33% of patients) and a "Constantly functional autonomy decline (CFAD) trajectory" (14% of patients). Not being a member of an association, and previous fall were significantly associated of a SDFA trajectory (P < 0.01). Absence of financial and human assistance, no hobbies, and cognitive disorder were significantly associated with a CFAD trajectory (P < 0.01). Previous occupation and multiple pathologies were predictive factors of both declining trajectories SDFA and CFAD. CONCLUSIONS: Community-living older persons exhibit distinct independence trajectories and the predictive factors. The evidence from this study suggests that the prevention and screening for the loss of independence of the older adults should be anticipated to maintaining autonomy.

Temperature dependence of binding and catalysis for human serum arylesterase/paraoxonase.

The influence of temperature upon the hydrolysis of phenyl acetate, catalysed by purified human serum arylesterase/paraoxonase (E. C. 3.1.8.1), was studied in the temperature range 10 °C-40 °C by spectrophotometry in TRIS buffer, pH 8.0, using both initial rate analysis and progress curve analysis. The kinetic parameters (catalytic constant k(cat); Michaelis constant K(m); product inhibition constant K(p)) were determined by nonlinear regression. All parameters increased with temperature, but the ratios k(cat)/K(m) and K(p)/K(m) remained practically constant. Binding of both substrate and reaction product (phenol) was exothermic. A negative entropic term accounted for about 50% of the enthalpy change for both the binding and catalytic steps. Thermodynamic analysis suggested that: (1) the rate-limiting step is the nucleophilic attack of the carbonyl group of the substrate by a water molecule, (2) the active site is preorganized with no induced fit, (3) the enzyme-bound calcium plays an important role in stabilizing both the substrate and the transition state. The practical implications of these results are discussed.

Microcalorimetric study of the inhibition of butyrylcholinesterase by paraoxon.

The inhibition of horse serum butyrylcholinesterase (EC 3.1.1.8) by the organophosphorus compound paraoxon (diethyl 4-nitrophenyl phosphate) was studied by flow microcalorimetry at 37 degrees C in Tris buffer (pH 7.5) using a modification of the kinetic model described by Stojan and coworkers [J. Stojan, V. Marcel, S. Estrada-Mondaca, A. Klaebe, P. Masson, D. Fournier, A putative kinetic model for substrate metabolisation by Drosophila acetylcholinesterase, FEBS Lett. 440 (1998) 85-88]. The reversible steps of the inhibition were studied in the mixing cell of the calorimeter, whereas the irreversible step was studied in the flow-through cell. A new pseudo-first-order approximation was developed to allow the kinetic analysis of inhibition progress curves in the presence of substrate when a significant amount of substrate is transformed. This approximation also allowed one to compute an analytical expression of the calorimetric curves using a gamma distribution to describe the impulse response of the calorimeter. Fitting models to data by nonlinear regression, with simulated annealing as a stochastic optimization method, allowed the determination of all kinetic parameters. It was found that paraoxon binds to both the enzyme and acyl-enzyme, but with weak affinities (K(i) = 0.123 mM and K'(i) = 5.5 mM). A slight activation was observed at the lowest paraoxon concentrations and was attributed to the binding of the substrate to the enzyme-inhibitor complex. The bimolecular inhibition rate constant k(i) = 2.8 x 10(4) M(-1) s(-1) was in agreement with previous studies. It is hoped that the methods developed in this work will contribute to extending the application range of microcalorimetry in the field of irreversible inhibitors.