The Influence of External Real and White Noise on the LOTKA-VOLTERRA Model

The behaviour of a marginally stable predator-prey system, the LOTKA -VOLTERRA model is analyzed under the influence of parameter fluctuations. The cases of white and real noise are studied separately. It is shown that for white noise no stationary solution exists, but even for time tending to infinity explosion occurs only with zero probability. In the case of real noise the class of noise processes that permit a stationary solution is characterized by their spectral density. It turns out that this class consists of all stationary processes that do not contain the eigenfrequencies of the LOTKA -VOLTERRA system. It is shown that for all other real noise processes a resonance phenomenon occurs and the solutions grow unboundedly.     

The active sites of cellulases are involved in chiral recognition: a comparison of cellobiohydrolase 1 and endoglucanase 1

The cellulases cellobiohydrolase 1 (CBH 1) and endoglucanase 1 (EG 1) from the fungus Trichoderma reesei are closely related with 40% sequence identity and very similar in structure. In CBH 1 the active site is enclosed by long loops and some antiparallel β-strands forming a 40 Å long tunnel, whereas in EG 1 part of those loops are missing so that the enzyme has a more common active site groove. Both enzymes were immobilized on silica and these materials were used as chiral stationary phases for chromatographic separation of the enantiomers of two chiral drugs, propranolol and alprenolol. The CBH 1 phase showed much better resolution than did the EG 1 phase, suggesting that the tunnel structure of the protein may play an important role in the chiral separation. The chiral compounds were found to be competitive inhibitors of both enzymes when p-nitrophenyl lactoside (pNPL) was used as substrate. (S)-enantiomers showed stronger inhibitory effects and also longer retention time on the stationary phases than the (R)-enantiomers. The consistency between kinetic data and retention on the stationary phases clearly shows that the enzymatically active sites of CBH 1 and EG 1 are involved in chiral recognition.