Generalized quantum Fokker-Planck, diffusion and Smoluchowski equations with true probability distribution functions

Traditionally, the quantum Brownian motion is described by Fokker-Planck or diffusion equations in terms of quasi-probability distribution functions, e.g., Wigner functions. These often become singular or negative in the full quantum regime. In this paper a simple approach to non-Markovian theory of quantum Brownian motion using {\it true probability distribution functions} is presented. Based on an initial coherent state representation of the bath oscillators and an equilibrium canonical distribution of the quantum mechanical mean values of their co-ordinates and momenta we derive a generalized quantum Langevin equation in $c$-numbers and show that the latter is amenable to a theoretical analysis in terms of the classical theory of non-Markovian dynamics. The corresponding Fokker-Planck, diffusion and the Smoluchowski equations are the {\it exact} quantum analogues of their classical counterparts. The present work is {\it independent} of path integral techniques. The theory as developed here is a natural extension of its classical version and is valid for arbitrary temperature and friction (Smoluchowski equation being considered in the overdamped limit).Comment: RevTex, 16 pages, 7 figures, To appear in Physical Review E (minor revision

O-GlcNAcylation and oxidation of proteins: is signalling in the cardiovascular system becoming sweeter?

O-GlcNAcylation is an unusual form of protein glycosylation, where a single-sugar [GlcNAc (N-acetylglucosamine)] is added (via β-attachment) to the hydroxyl moiety of serine and threonine residues of nuclear and cytoplasmic proteins. A complex and extensive interplay exists between O-GlcNAcylation and phosphorylation. Many phosphorylation sites are also known glycosylation sites, and this reciprocal occupancy may produce different activities or alter the stability in a target protein. The interplay between these two post-translational modifications is not always reciprocal, as some proteins can be concomitantly phosphorylated and O-GlcNAcylated, and the adjacent phosphorylation or O-GlcNAcylation can regulate the addition of either moiety. Increased cardiovascular production of ROS (reactive oxygen species), termed oxidative stress, has been consistently reported in various chronic diseases and in conditions where O-GlcNAcylation has been implicated as a contributing mechanism for the associated organ injury/protection (for example, diabetes, Alzheimer's disease, arterial hypertension, aging and ischaemia). In the present review, we will briefly comment on general aspects of O-GlcNAcylation and provide an overview of what has been reported for this post-translational modification in the cardiovascular system. We will then specifically address whether signalling molecules involved in redox signalling can be modified by O-GlcNAc (O-linked GlcNAc) and will discuss the critical interplay between O-GlcNAcylation and ROS generation. Experimental evidence indicates that the interactions between O-GlcNAcylation and oxidation of proteins are important not only for cell regulation in physiological conditions, but also under pathological states where the interplay may become dysfunctional and thereby exacerbate cellular injury