Homogeneous differential equationA differential equation can be homogeneous in either of two respects. A first order differential equation is said to be homogeneous if it may be written where f and g are homogeneous functions of the same degree of x and y. In this case, the change of variable y = ux leads to an equation of the form which is easy to solve by integration of the two members. Otherwise, a differential equation is homogeneous if it is a homogeneous function of the unknown function and its derivatives.
Ionotropic glutamate receptorIonotropic glutamate receptors (iGluRs) are ligand-gated ion channels that are activated by the neurotransmitter glutamate. They mediate the majority of excitatory synaptic transmission throughout the central nervous system and are key players in synaptic plasticity, which is important for learning and memory. iGluRs have been divided into four subtypes on the basis of their ligand binding properties (pharmacology) and sequence similarity: AMPA receptors, kainate receptors, NMDA receptors and delta receptors (see below).
Delay differential equationIn mathematics, delay differential equations (DDEs) are a type of differential equation in which the derivative of the unknown function at a certain time is given in terms of the values of the function at previous times. DDEs are also called time-delay systems, systems with aftereffect or dead-time, hereditary systems, equations with deviating argument, or differential-difference equations. They belong to the class of systems with the functional state, i.e.
NMDA receptorThe N-methyl-D-aspartate receptor (also known as the NMDA receptor or NMDAR), is a glutamate receptor and ion channel found in neurons. The NMDA receptor is one of three types of ionotropic glutamate receptors, the other two being AMPA and kainate receptors. Depending on its subunit composition, its ligands are glutamate and glycine (or D-serine). However, the binding of the ligands is typically not sufficient to open the channel as it may be blocked by Mg2+ ions which are only removed when the neuron is sufficiently depolarized.
Stochastic differential equationA stochastic differential equation (SDE) is a differential equation in which one or more of the terms is a stochastic process, resulting in a solution which is also a stochastic process. SDEs have many applications throughout pure mathematics and are used to model various behaviours of stochastic models such as stock prices, random growth models or physical systems that are subjected to thermal fluctuations. SDEs have a random differential that is in the most basic case random white noise calculated as the derivative of a Brownian motion or more generally a semimartingale.
Ketogenic amino acidA ketogenic amino acid is an amino acid that can be degraded directly into acetyl-CoA, which is the precursor of ketone bodies and myelin, particularly during early childhood, when the developing brain requires high rates of myelin synthesis. This is in contrast to the glucogenic amino acids, which are converted into glucose. Ketogenic amino acids are unable to be converted to glucose as both carbon atoms in the ketone body are ultimately degraded to carbon dioxide in the citric acid cycle.
Basal metabolic rateBasal metabolic rate (BMR) is the rate of energy expenditure per unit time by endothermic animals at rest. It is reported in energy units per unit time ranging from watt (joule/second) to ml O2/min or joule per hour per kg body mass J/(h·kg). Proper measurement requires a strict set of criteria to be met. These criteria include being in a physically and psychologically undisturbed state and being in a thermally neutral environment while in the post-absorptive state (i.e., not actively digesting food).
Precursor (chemistry)In chemistry, a precursor is a compound that participates in a chemical reaction that produces another compound. In biochemistry, the term "precursor" often refers more specifically to a chemical compound preceding another in a metabolic pathway, such as a protein precursor. Drug precursor In 1988, the United Nations Convention Against Illicit Traffic in Narcotic Drugs and Psychotropic Substances introduced detailed provisions and requirements relating the control of precursors used to produce drugs of abuse.
Isocitrate lyaseIsocitrate lyase (), or ICL, is an enzyme in the glyoxylate cycle that catalyzes the cleavage of isocitrate to succinate and glyoxylate. Together with malate synthase, it bypasses the two decarboxylation steps of the tricarboxylic acid cycle (TCA cycle) and is used by bacteria, fungi, and plants. The systematic name of this enzyme class is isocitrate glyoxylate-lyase (succinate-forming). Other names in common use include isocitrase, isocitritase, isocitratase, threo-Ds-isocitrate glyoxylate-lyase, and isocitrate glyoxylate-lyase.
Flavin adenine dinucleotideIn biochemistry, flavin adenine dinucleotide (FAD) is a redox-active coenzyme associated with various proteins, which is involved with several enzymatic reactions in metabolism. A flavoprotein is a protein that contains a flavin group, which may be in the form of FAD or flavin mononucleotide (FMN). Many flavoproteins are known: components of the succinate dehydrogenase complex, α-ketoglutarate dehydrogenase, and a component of the pyruvate dehydrogenase complex.
Partial differential equationIn mathematics, a partial differential equation (PDE) is an equation which computes a function between various partial derivatives of a multivariable function. The function is often thought of as an "unknown" to be solved for, similar to how x is thought of as an unknown number to be solved for in an algebraic equation like x2 − 3x + 2 = 0. However, it is usually impossible to write down explicit formulas for solutions of partial differential equations.
Glutamate (neurotransmitter)In neuroscience, glutamate is the dianion (divalent anion) of glutamic acid in its role as a neurotransmitter (a chemical that nerve cells use to send signals to other cells). It is by a wide margin the most abundant excitatory neurotransmitter in the vertebrate nervous system. It is used by every major excitatory function in the vertebrate brain, accounting in total for well over 90% of the synaptic connections in the human brain. It also serves as the primary neurotransmitter for some localized brain regions, such as cerebellum granule cells.
