Effects of apolipoprotein B-100 on the metabolism of a lipid microemulsion model in rats

In previous studies, it was shown that lipid microemulsions resembling LDL (LDE) but not containing protein, acquire apolipoprotein E when injected into the bloodstream and bind to LDL receptors (LDLR) using this protein as ligand. Aiming to evaluate the effects of apolipoprotein (apo) B-100 on the catabolism of these microemulsions, LDE with incorporated apo B-100 (LDE-apoB) and native LDL, all labeled with radioactive lipids were studied after intraarterial injection into Wistar rats. Plasma decay curves of the labels were determined in samples collected over 10 h and tissue uptake was assayed from organs excised from the animals sacrificed 24 h after injection. LDE-apo B had a fractional clearance rate (FCR) similar to native LDL (0.40 and 0.33, respectively) but both had FCR pronouncedly smaller than LDE (0.56, P<0.01). Liver was the main uptake site for LDE, LDE-apoB, and native LDL, but LDE-apoB and native LDL had lower hepatic uptake rates than LDE. Pre-treatment of the rats with 17 alpha-ethinylestradiol, known to upregulate LDLR, accelerated the removal from plasma of both LDE and LDE-apoB, but the effect was greater upon LDE than LDE-apoB. These differences in metabolic behavior documented in vivo can be interpreted by the lower affinity of LDLR for apo B-100 than for apo E, demonstrated in in vitro studies. Therefore, our study shows in vivo that, in comparison with apo E, apo B is a less efficient ligand to remove lipid particles such as microemulsions or lipoproteins from the intravascular compartment. (C) 1999 Elsevier B.V. B.V. All rights reserved.

Fractional polynomial response surface models

Second-order polynomial models have been used extensively to approximate the relationship between a response variable and several continuous factors. However, sometimes polynomial models do not adequately describe the important features of the response surface. This article describes the use of fractional polynomial models. It is shown how the models can be fitted, an appropriate model selected, and inference conducted. Polynomial and fractional polynomial models are fitted to two published datasets, illustrating that sometimes the fractional polynomial can give as good a fit to the data and much more plausible behavior between the design points than the polynomial model. © 2005 American Statistical Association and the International Biometric Society.

Fractional fermion charges induced by axial-vector and vector gauge potentials and parity anomaly in planar graphenelike structures

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A prelude to the fractional calculus applied to tumor dynamic

In order to refine the solution given by the classical logistic equation and extend its range of applications in the study of tumor dynamics, we propose and solve a generalization of this equation, using the so-called Fractional Calculus, i.e., we replace the ordinary derivative of order 1, in one version of the usual equation, by a non-integer derivative of order 0 < α < 1, and recover the classical solution as a particular case. Finally, we analyze the applicability of this model to describe the growth of cancer tumors.