The U.S. opioid epidemic: One disease, diverging tales

Synthetic and semisynthetic opioids are pivotal in pain management and tackling opioid addiction. Semisynthetic opioids, including morphinans (morphine derivatives), oxycodone, oxymorphone, hydrocodone, and hydromorphone, have improved pharmacokinetic profiles compared to morphine. Additionally, heroin and 6-MAM (6-Monoacetylmorphine) show better CNS penetration than morphine due to heightened lipid solubility. Hydromorphone, a potent opioid, undergoes hepatic metabolism to form the active...

The divergence of a vector field at a point is the net outward flow of the flux out of a small volume through a closed surface enclosing the volume, as the volume tends to zero. More practically, divergence measures how much a vector field spreads out or diverges from a given point. For an outgoing flux, conventionally, the divergence is positive. The diverging point is often called the "source" of the field. Meanwhile, the negative divergence of a vector field at a point means that the vector...

Opioid receptors, including the mu (μ, MOR), delta (δ, DOR), and kappa (κ, KOR) types, belong to the rhodopsin family of G protein-coupled receptors. These receptors are located throughout the central and peripheral nervous systems and in non-neuronal tissues such as macrophages and astrocytes. Opioid receptor ligands can be categorized into agonists or antagonists. Highly selective agonists include [d-Ala2, MePhe4, Gly(ol)5]-enkephalin or DAMGO for MOR, [D-Pen2,...

The divergence and Stokes' theorems are a variation of Green's theorem in a higher dimension. They are also a generalization of the fundamental theorem of calculus. The divergence theorem and Stokes' theorem are in a way similar to each other; The divergence theorem relates to the dot product of a vector, while Stokes' theorem relates to the curl of a vector. Many applications in physics and engineering make use of the divergence and Stokes' theorems, enabling us to write...

The seminal work of Ohno in 1970 popularized the idea of gene duplication and divergence. DNA sequence comparison studies reveal that a large portion of the genes in bacteria, archaebacteria, and eukaryotes was  generated by gene duplication and divergence, indicating its critical role in evolution.
The duplicated copies of the gene are called Paralogs. Paralogs with similar sequences and functions form a gene family. Across several species, a large number of gene families are...

The divergence of a vector is a measure of how much the vector spreads out (diverges) from a point. For example, an electric field vector diverges from the positive charge and converges at the negative charge. The divergence of an electric field is derived using Gauss's law and is equal to the charge density divided by the permittivity of space. Mathematically, it is expressed as