No abstract

In this paper, we study the stability of the zero equilibria of the following systems of difference equations: xn+1=axn+byne−xn,yn+1=cyn+dxne−yn and xn+1=ayn+bxne−yn,yn+1=cxn+dyne−xn where a, b, c and d are positive constants and the initial conditions x0 and y0 are positive numbers. We study the stability of those systems in the special case when one of the eigenvalues has absolute value equal to 1 and the other eigenvalue has absolute value less than 1, using centre manifold theory. Copyright © 2016 John Wiley & Sons, Ltd.

No abstract

One aspect in a broad spectrum of possible mechanisms of cariostatic reactions of fluoride is its interaction with the metabolism of oral bacteria. Information on the mechanisms and kinetics of fluoride inhibition of essential enzymes of the glycolytic pathway of the relevant bacteria is lacking. In this work, the isolation and purification of enolase from Streptococcus rattus and its characterization are described. The enzyme has been isolated in a monomeric (22 kilodaltons) and dimeric (49 kilodaltons) form. The Km for 2-phosphoglycerate is 4.35 mM. Fluoride inhibition kinetics have competitive character, while phosphate in concentrations above 2 mM and in the presence of 0.5 mM fluoride alters the inhibition kinetics from competitive to noncompetitive. Without fluoride, 2 mM phosphate has a slight stimulatory effect on the enzyme. Monofluorophosphate has a noncompetitive inhibiting effect on the enzyme. This finding suggests that the effect of phosphate may be due to an additional binding of fluoride to the enolase, resulting in a conformational change of the enzyme.

In this paper, we study the stability of the zero equilibria of two close-to-symmetric systems of difference equations with exponential terms in the special case in which one of their eigenvalues is equal to −1 and the other eigenvalue has an absolute value of less than 1. In the present study, we use the approach of center manifold theory.