How many orthonormal bases are needed to distinguish all pure quantum states?

We collect some recent results that together provide an almost complete answer to the question stated in the title. For the dimension d=2 the answer is three. For the dimensions d=3 and d>4 the answer is four. For the dimension d=4 the answer is either three or four. Curiously, the exact number in d=4 seems to be an open problem

DNA damage by lipid peroxidation products: implications in cancer, inflammation and autoimmunity

Oxidative stress and lipid peroxidation (LPO) induced by inflammation, excess metal storage and excess caloric intake cause generalized DNA damage, producing genotoxic and mutagenic effects. The consequent deregulation of cell homeostasis is implicated in the pathogenesis of a number of malignancies and degenerative diseases. Reactive aldehydes produced by LPO, such as malondialdehyde, acrolein, crotonaldehyde and 4-hydroxy-2-nonenal, react with DNA bases, generating promutagenic exocyclic DNA adducts, which likely contribute to the mutagenic and carcinogenic effects associated with oxidative stress-induced LPO. However, reactive aldehydes, when added to tumor cells, can exert an anticancerous effect. They act, analogously to other chemotherapeutic drugs, by forming DNA adducts and, in this way, they drive the tumor cells toward apoptosis. The aldehyde-DNA adducts, which can be observed during inflammation, play an important role by inducing epigenetic changes which, in turn, can modulate the inflammatory process. The pathogenic role of the adducts formed by the products of LPO with biological macromolecules in the breaking of immunological tolerance to self antigens and in the development of autoimmunity has been supported by a wealth of evidence. The instrumental role of the adducts of reactive LPO products with self protein antigens in the sensitization of autoreactive cells to the respective unmodified proteins and in the intermolecular spreading of the autoimmune responses to aldehyde-modified and native DNA is well documented. In contrast, further investigation is required in order to establish whether the formation of adducts of LPO products with DNA might incite substantial immune responsivity and might be instrumental for the spreading of the immunological responses from aldehyde-modified DNA to native DNA and similarly modified, unmodified and/or structurally analogous self protein antigens, thus leading to autoimmunity

Overcoming Endocytosis Deficiency by Cubosome Nanocarriers

The use of lipid-based nanoparticles for the delivery of biomacromolecules has attracted considerable attention due to the current interest in protein-based therapeutics. Cubosomes protect the incorporated therapeutics, which are susceptible to degradation by enzymes, thereby improving their bioavailability, and concomitantly enhance cellular uptake. The cubosome nanoparticles presented herein were loaded with bovine serum albumin (BSA) and characterized by small-angle X-ray scattering and dynamic light scattering techniques, while the BSA encapsulation and its release were evaluated in vitro. The ability of this formulation to increase the cellular uptake of albumin by 2-fold was tested on various types of renal tubular cells and confirmed by in vivo renal uptake experiments in mice. The obtained results show that cubosomes are able to deliver BSA inside the cell through distinct uptake and intracellular routing. These data were substantiated, with evidence of a high cubosome-mediated uptake of BSA in Clcn5 knockout mice characterized by defective receptor-mediated endocytosis. The use of cubosomes as a delivery system thus represents a promising approach to overcome the low endocytic uptake in diseased epithelial cells and to treat dysfunctions of the kidney proximal tubule