Two ␣-amylase genes from the thermophilic alkaliphile Anaerobranca gottschalkii were cloned, and the corresponding enzymes, AmyA and AmyB, were investigated after purification of the recombinant proteins. Based on their amino acid sequences, AmyA is proposed to be a lipoprotein with extracellular localization and thus is exposed to the alkaline milieu, while AmyB apparently represents a cytoplasmic enzyme. The amino acid sequences of both enzymes bear high similarity to those of GHF13 proteins. The different cellular localizations of AmyA and AmyB are reflected in their physicochemical properties. The alkaline pH optimum (pH 8), as well as the broad pH range, of AmyA activity (more than 50% activity between pH 6 and pH 9.5) mirrors the conditions that are encountered by an extracellular enzyme exposed to the medium of A. gottschalkii, which grows between pH 6 and pH 10.5. AmyB, on the other hand, has a narrow pH range with a slightly acidic pH optimum at 6 to 6.5, which is presumably close to the pH in the cytoplasm. Also, the intracellular AmyB is less tolerant of high temperatures than the extracellular AmyA. While AmyA has a half-life of 48 h at 70°C, AmyB has a half-life of only about 10 min at that temperature, perhaps due to the lack of stabilizing constituents of the cytoplasm. AmyA and AmyB were very similar with respect to their substrate specificity profiles, clearly preferring amylose over amylopectin, pullulan, and glycogen. Both enzymes also hydrolyzed ␣-, ␤-, and ␥-cyclodextrin. Very interestingly, AmyA, but not AmyB, displayed high transglycosylation activity on maltooligosaccharides and also had significant ␤-cyclodextrin glycosyltransferase (CGTase) activity. CGTase activity has not been reported for typical ␣-amylases before. The mechanism of cyclodextrin formation by AmyA is unknown.

The p-moment exponential stability of non-instantaneous impulsive Caputo fractional differential equations is studied. The impulses occur at random moments and their action continues on finite time intervals with initially given lengths. The time between two consecutive moments of impulses is the Erlang distributed random variable. The study is based on Lyapunov functions. The fractional Dini derivatives are applied.

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