Stability of systems of fractional-order differential equations with caputo derivatives

Systems of fractional-order differential equations present stability properties which differ in a substantial way from those of systems of integer order. In this paper, a detailed analysis of the stability of linear systems of fractional differential equations with Caputo derivative is proposed. Starting from the well-known Matignon’s results on stability of single-order systems, for which a different proof is provided together with a clarification of a limit case, the investigation is moved towards multi-order systems as well. Due to the key role of the Mittag–Leffler function played in representing the solution of linear systems of FDEs, a detailed analysis of the asymptotic behavior of this function and of its derivatives is also proposed. Some numerical experiments are presented to illustrate the main results

Comparative in vitro studies on native and recombinant human cationic trypsins - Cathepsin B is a possible pathological activator of trypsinogen in pancreatitis

Hereditary pancreatitis, an autosomal dominant disease is believed to be caused by mutation in the human trypsinogen gene. The role of mutations has been investigated by in vitro studies using recombinant rat and human trypsinogen (TG), In this study we compare the enzymatic properties and inhibition by human pancreatic secretory trypsin inhibitor (hPSTI) of the native, postsynthetically modified and recombinant cationic trypsin, and found these values practically identical, We also determined the autolytic stability of recombinant wild type (Hu1Asn21) and pancreatitis-associated (Hu1Ile21) trypsin, Both forms were equally stable. Similarly, we found no difference in the rate of activation of the two zymogens by human cationic and anionic trypsin. Mesotrypsin did not activate either form. The rate of autocatalytic activation of Hu1Asn21 TG and Hu1Ile21 TG was also identical at pH 8 both in the presence and absence of Ca2+. At pH 5 Hu1Ile21 TG autoactivated about twice as fast as HulAsn21 TG, The presence of physiological amount of hPSTI completely prevented autoactivation of both zymogens at pH 8 and at pH 5 as well. Cathepsin B readily activated both zymogens although Hu1Ile21 TG was activated about 2.5-3 times as fast as Hu1Asn21 TG, The presence of hPSTI did not prevent the activation of zymogens by cathepsin B, Our results underlie the central role of cathepsin B in the development of different forms of pancreatitis

Molecular mechanisms of vaspin action: from adipose tissue to skin and bone, from blood vessels to the brain

Visceral adipose tissue derived serine protease inhibitor (vaspin) or SERPINA12 according to the serpin nomenclature was identified together with other genes and gene products that  were specifically expressed or overexpressed in the intra abdominal or visceral adipose tissue  (AT) of the Otsuka Long-Evans Tokushima fatty rat. These rats spontaneously develop visceral  obesity, insulin resistance, hyperinsulinemia and ‐glycemia, as well as hypertension and thus represent a well suited animal model of obesity and related metabolic disorders such as type  2 diabetes.  The follow-up study reporting the cloning, expression and functional characterization of  vaspin suggested the great and promising potential of this molecule to counteract obesity induced insulin resistance and inflammation and has since initiated over 300 publications, clinical and experimental, that have contributed to uncover the multifaceted functions and molecular mechanisms of vaspin action not only in the adipose, but in many different cells, tissues and organs. This review will give an update on mechanistic and structural aspects of vaspin with a focus on its serpin function, the physiology and regulation of vaspin expression, and will summarize the latest on vaspin function in various tissues such as the different adipose tissue depots as well as the vasculature, skin, bone and the brain