Time-evolution of highly localized positive-energy states of the free Dirac electron

Highly localized positive-energy states of the free Dirac electron are constructed and shown to evolve in a simple way under the action of Dirac's equation. When the initial uncertainty in position is small on the scale of the Compton wavelength, there is an associated uncertainty in the mean energy that is large compared with the rest mass of the electron. However, this does not lead to any breakdown of the one-particle description, associated with the possibility of pair-production, but rather leads to a rapid expansion of the probability density outwards from the point of localization, at speeds close to the speed of light.

Direct electrochemistry of human and rat NADPH cytochrome P450 reductase

The diflavo-protein NADPH cytochrome P450 reductase (CPR) is the key electron transfer partner for all drug metabolizing cytochrome P450 enzymes in humans. The protein delivers, consecutively, two electrons to the heme active site of the P450 in a carefully orchestrated process which ultimately leads to the generation of a high valent oxo-heme moiety. Despite its central role in P450 function, no direct electrochemical investigation of the purified protein has been reported. Here we report the first voltammetric study of purified human CPR where responses from both the FMN and FAD cofactors have been identified using both cyclic and square wave voltammetry. For human CPR redox responses at -2 and -278 mV (with a ratio of 1e(-):3e(-)) vs NHE were seen at pH 7.9 while the potentials for rat CPR at pH 8.0 were -20 and -254 mV. All redox responses exhibit a pH dependence of approximately -59 mV/pH unit consistent with proton coupled electron transfer reactions of equal stoichiometry. (c) 2006 Elsevier B.V. All rights reserved.