Cubic reciprocityCubic reciprocity is a collection of theorems in elementary and algebraic number theory that state conditions under which the congruence x3 ≡ p (mod q) is solvable; the word "reciprocity" comes from the form of the main theorem, which states that if p and q are primary numbers in the ring of Eisenstein integers, both coprime to 3, the congruence x3 ≡ p (mod q) is solvable if and only if x3 ≡ q (mod p) is solvable. Sometime before 1748 Euler made the first conjectures about the cubic residuacity of small integers, but they were not published until 1849, after his death.
G protein-coupled receptorG protein-coupled receptors (GPCRs), also known as seven-(pass)-transmembrane domain receptors, 7TM receptors, heptahelical receptors, serpentine receptors, and G protein-linked receptors (GPLR), form a large group of evolutionarily related proteins that are cell surface receptors that detect molecules outside the cell and activate cellular responses. They are coupled with G proteins.
Tetrameric proteinA tetrameric protein is a protein with a quaternary structure of four subunits (tetrameric). Homotetramers have four identical subunits (such as glutathione S-transferase), and heterotetramers are complexes of different subunits. A tetramer can be assembled as dimer of dimers with two homodimer subunits (such as sorbitol dehydrogenase), or two heterodimer subunits (such as hemoglobin). The interactions between subunits forming a tetramer is primarily determined by non covalent interaction.
Quadratic reciprocityIn number theory, the law of quadratic reciprocity is a theorem about modular arithmetic that gives conditions for the solvability of quadratic equations modulo prime numbers. Due to its subtlety, it has many formulations, but the most standard statement is: Let p and q be distinct odd prime numbers, and define the Legendre symbol as: Then: This law, together with its supplements, allows the easy calculation of any Legendre symbol, making it possible to determine whether there is an integer solution for any quadratic equation of the form for an odd prime ; that is, to determine the "perfect squares" modulo .
Protein productionProtein production is the biotechnological process of generating a specific protein. It is typically achieved by the manipulation of gene expression in an organism such that it expresses large amounts of a recombinant gene. This includes the transcription of the recombinant DNA to messenger RNA (mRNA), the translation of mRNA into polypeptide chains, which are ultimately folded into functional proteins and may be targeted to specific subcellular or extracellular locations.
ChemiosmosisChemiosmosis is the movement of ions across a semipermeable membrane bound structure, down their electrochemical gradient. An important example is the formation of adenosine triphosphate (ATP) by the movement of hydrogen ions (H+) across a membrane during cellular respiration or photosynthesis. Hydrogen ions, or protons, will diffuse from a region of high proton concentration to a region of lower proton concentration, and an electrochemical concentration gradient of protons across a membrane can be harnessed to make ATP.
Nuclear magnetic resonance spectroscopyNuclear magnetic resonance spectroscopy, most commonly known as NMR spectroscopy or magnetic resonance spectroscopy (MRS), is a spectroscopic technique to observe local magnetic fields around atomic nuclei. This spectroscopy is based on the measurement of absorption of electromagnetic radiations in the radio frequency region from roughly 4 to 900 MHz. Absorption of radio waves in the presence of magnetic field is accompanied by a special type of nuclear transition, and for this reason, such type of spectroscopy is known as Nuclear Magnetic Resonance Spectroscopy.
Nuclear magnetic resonance spectroscopy of proteinsNuclear magnetic resonance spectroscopy of proteins (usually abbreviated protein NMR) is a field of structural biology in which NMR spectroscopy is used to obtain information about the structure and dynamics of proteins, and also nucleic acids, and their complexes. The field was pioneered by Richard R. Ernst and Kurt Wüthrich at the ETH, and by Ad Bax, Marius Clore, Angela Gronenborn at the NIH, and Gerhard Wagner at Harvard University, among others.
G proteinG proteins, also known as guanine nucleotide-binding proteins, are a family of proteins that act as molecular switches inside cells, and are involved in transmitting signals from a variety of stimuli outside a cell to its interior. Their activity is regulated by factors that control their ability to bind to and hydrolyze guanosine triphosphate (GTP) to guanosine diphosphate (GDP). When they are bound to GTP, they are 'on', and, when they are bound to GDP, they are 'off'. G proteins belong to the larger group of enzymes called GTPases.
Connection (principal bundle)In mathematics, and especially differential geometry and gauge theory, a connection is a device that defines a notion of parallel transport on the bundle; that is, a way to "connect" or identify fibers over nearby points. A principal G-connection on a principal G-bundle P over a smooth manifold M is a particular type of connection which is compatible with the action of the group G. A principal connection can be viewed as a special case of the notion of an Ehresmann connection, and is sometimes called a principal Ehresmann connection.
Beta blockerBeta blockers, also spelled β-blockers, are a class of medications that are predominantly used to manage abnormal heart rhythms (arrhythmia), and to protect the heart from a second heart attack after a first heart attack (secondary prevention). They are also widely used to treat high blood pressure, although they are no longer the first choice for initial treatment of most patients.
Cardiac conduction systemThe cardiac conduction system (CCS) (also called the electrical conduction system of the heart) transmits the signals generated by the sinoatrial node – the heart's pacemaker, to cause the heart muscle to contract, and pump blood through the body's circulatory system. The pacemaking signal travels through the right atrium to the atrioventricular node, along the bundle of His, and through the bundle branches to Purkinje fibers in the walls of the ventricles. The Purkinje fibers transmit the signals more rapidly to stimulate contraction of the ventricles.
