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We present an exhaustive class of states with quantum backflow -the phenomenon in which a state consisting entirely of positive momenta may have negative current and the probability flows in the opposite direction to the momentum. They are characterized by a general function of momenta subject to very weak conditions. Such a family of states is of interest in the light of a recent experimental proposal to measure backflow. We find one particularly simple state which has surprisingly large backflow -about 41 percent of the lower bound on flux derived by Bracken and Melloy. We study the eigenstates of a regularized current operator and we show how some of these states, in a certain limit, lead to our class of backflow states. This limit also clarifies the correspondence between the spectrum of the regularized current operator, which has just two non-zero eigenvalues in our chosen regularization, and the usual current operator.

The extracellular levels of the neurotransmitter glycine in the brain are tightly regulated by the glycine transporter 1 (GlyT1) and the clearance rate for glycine depends on its rate of transport and the levels of cell surface GlyT1. Over the years, it has been shown that PKC tightly regulates the activity of several neurotransmitter transporters. In the present work, by stably expressing three N-terminus GlyT1 isoforms in porcine aortic endothelial cells and assaying for [32P]-orthophosphate metabolic labeling, we demonstrated that the isoforms GlyT1a, GlyT1b, and GlyT1c were constitutively phosphorylated, and that phosphorylation was dramatically enhanced, in a time dependent fashion, after PKC activation by phorbol ester. The phosphorylation was PKC-dependent, since pre-incubation of the cells with bisindolylmaleimide I, a selective PKC inhibitor, abolished the phorbol ester-induced phosphorylation. Blotting with specific anti-phospho-tyrosine antibodies did not yield any signal that could correspond to GlyT1 tyrosine phosphorylation, suggesting that the phosphorylation occurs at serine and/or threonine residues. In addition, a 23-40% -inhibition on Vmax was obtained by incubation with phorbol ester without a significant change on the apparent Km value. Furthermore, pre-incubation of the cells with the selective PKCα/β inhibitor Gö6976 abolished the downregulation effect of phorbol ester on uptake and phosphorylation, whereas the selective PKCβ inhibitors (PKCβ inhibitor or LY333531) prevented the phosphorylation without affecting glycine uptake, defining a specific role of classical PKC on GlyT1 uptake and phosphorylation. Taken together, these data suggest that phosphorylation that conventional PKCα/β regulates the uptake of glycine, whereas PKCβ is responsible for GlyT1 phosphorylation.