An Application of Lorentz Invariance Violation in Black Hole Thermodynamics

In this paper, we have applied the Lorentz-invariance-violation (LIV) class of dispersion relations (DR) with the dimensionless parameter n = 2 and the "sign of LIV" {\eta}_+ = 1, to phenomenologically study the effect of quantum gravity in the strong gravitational field. Specifically, we have studied the effect of the LIV-DR induced quantum gravity on the Schwarzschild black hole thermodynamics. The result shows that the effect of the LIV-DR induced quantum gravity speeds up the black hole evaporation, and its corresponding black hole entropy undergoes a leading logarithmic correction to the "reduced Bekenstein-Hawking entropy", and the ill defined situations (i.e. the singularity problem and the critical problem) are naturally bypassed when the LIV-DR effect is present. Also, to put our results in a proper perspective, we have compared with the earlier findings by another quantum gravity candidate, i.e. the generalized uncertainty principle (GUP). Finally, we conclude from the inert remnants at the final stage of the black hole evaporation that, the GUP as a candidate for describing quantum gravity can always do as well as the LIV-DR by adjusting the model-dependent parameters, but in the same model-dependent parameters the LIV-DR acts as a more suitable candidate.Comment: 18 pages, 7 figure

Substrate entering and product leaving trajectories predict an engulfing dynamic for the major conformational change of the β-lactam acylase

It is still a major challenge to acquire insight into the conformational changes between the ground state and the transition state of an enzyme, although conformational fluctuation within interconverting conformers has been widely investigated (1-4). Here, we utilize different enzymatic reactions in b-lactam acylase to figure out the substrate/product trajectories in the enzyme, thereby probing the overall conformational changes in transition state. First, an auto-proteolytic intermediate of cephalosporin acylase (EC 3.5.1.11) with partial spacer segment was identified. As a final proteolytic step, the deletion of this spacer segment was revealed to be a first-order reaction, suggesting an intramolecular Ntn mechanism for the auto-proteolysis. Accordingly, the different proteolytic sites in the acylase precursor indicate a substrate entering pathway along the spacer peptide. Second, bromoacyl-7ACA can interact with penicillin G acylase (EC 3.5.1.11) in two distinguish aspects, to be hydrolyzed as a substrate analogue and to affinity alkylate the conserved Trpb4 as a product analogue. The kinetic correlation between these two reactions suggests a channel opening from Serb1 to Trpb4, responsible for the main product leaving. These two reaction trajectories relaying at the active centre, together with the crystal structures (5-10), predict an engulfing dynamic involving pocket constriction and channel opening