domain

Confusingly this is also the term that Sun Microsystems use to refer to a group of components that have been grouped together to form a single logical system within an Enterprise 10000 computer.

• The set that a function takes a value from. A function maps one set (its domain) to another (its range or codomain depending on how fussy you are). The domain is defined by the fact that the function assigns a value to every member of it (and to nothing outside it), and assigns exactly one value to every such member. It is symbolized dom, as in dom f.
• An exon, that is an active subregion of a gene, that is not necessarily transcribed, where the gene can have several alternative realizations depending on environmental conditions.
• A region of a magnetized material that is locally all the same polarity. (I think.) If this is not just a fiction of my poor memory, magnetic domains break down at the Curie temperature. (I think.)

1. Domain
2. Kingdom
3. Phylum
4. Class
5. Order
6. Family
7. Genus
8. Species

The domain of a function f:A → B is A.

This is an important point to make: the domain is not the set of values for which an interpretation of the function may make sense. Take, for example, f(x) = (2x + 3). This, believe it or not, is not a full mathematical definition for a function. A more full definition would be f(x):ℜ → ℜ = (2x + 3). In this case, the domain is ℜ, or the set of real numbers. A different function might be g(x):Q → Q = (2x + 3) [Q being the set of rational numbers]. The value of g(x) is equal to the value of f(x), when x is in the domain of both functions, but f and g are in fact different functions; for example, f(√2) is defined but g(√2) is undefined [because the square root of 2 is not a rational number and so not in the domain of g]. Other similar functions might have domains of the integers, or complex numbers, or multiples of √5, or integers modulo n, or p-adic integers, or other sets…

It often happens that the domain of a function is not specified, and in those cases, the obvious logical choice is usually good enough for the task at hand. However, it does make a difference in some special cases, and the strict definition of the domain becomes important.

Compare with range and codomain.

In complex analysis we mainly study functions defined on connected open subsets of C, which is the reason for giving such sets a special name.

We want a domain to be open because while a function may be differentantiable at a single point or at all points in some arbitrary (non-open) set, requiring that a function is differentiable in an open set is a much stronger condition. Such a function is called analytic.

The condition that the set be connected is mainly to avoid trivialities. If a domain could be a union of disjoint sets then a function defined in a domain have quite different properties in the different components, i.e. we could define a function to map z to z² on one component, and constant on another component. Since we want to be able to make statements about the properties of analytic functions throughout the set where they are defined we therefore tend to restrict our attention to functions defined on connected sets.

1. A discrete portion of a protein with its own function. The combination of domains in a single protein determines its overall function.
   
   
2. The highest level of biological classification, superseding kingdoms. The three domains of biological organisms are the Bacteria, the Archaea, and the Eukarya.

From the BioTech Dictionary at http://biotech.icmb.utexas.edu/. For further information see the BioTech homenode.

Protein Domains

A domain on a protein is a compactly folded region in its tertiary structure. Domains tend to be roughly 50 to 300 amino acids in length and are made by folding alpha helices, beta sheets, or a combination of the two together to form a globular unit. This folding allows the formation of multiple hydrogen bonds, which serve to stabilize the protein's structure. Smaller proteins may contain only one domain, while larger proteins can have five or more. Domains are often connected to other domains on the protein by long stretches of polypeptide chains.

Domains can have interesting structural features, such as a region rich in acidic amino acids or have a certain shape such as a leucine zipper. They can also consist of a certain sequence of amino acids that are conserved (nearly identical) in other proteins of the same family or similar proteins in other species. Domains can also be categorized by their function, such as those that allow the protein to act as a kinase or bind a cellular membrane.

Certain domains can be cut and pasted to alter the function of a protein. For example, let's take a protein with a transmembrane domain that allows it to bind to a membrane in the cell. If a molecular biologist removes this domain then the protein can no longer bind to the membrane. Along the same lines, if this domain is introduced into a different protein then it generally gains the ability to bind to the membrane. This process allows researchers to make unique proteins with any combination of functions.

Some important and well-studied protein domains include:

• Kinase domain - Protein kinases are responsible for adding a phosphate group to other proteins. They contain a kinase domain that can bind both ATP and the protein substrate and helps facilitate the transfer of the phosphate group from ATP to the substrate. Some current and experimental anticancer drugs, such as Glivec, work by targeting the kinase domain of certain proteins.
• Transmembrane domain - This domain consists of numerous hydrophobic amino acids and allows a protein to attach to lipid membranes in the cell, including the plasma, nuclear, and mitochondrial membranes.
• Src homology domains (SH2 and SH3) -These domains are involved in the transduction of signals in the cell. SH2 domains allow certain proteins to interact with tyrosine kinase receptors that have been activated by a signal outside the cell. Other proteins then bind to the protein with the SH2 domain, propagating the signal. SH3 domains also help transmit signals, except they bind to proteins with numerous proline residues instead of tyrosine kinases.
• Leucine zipper - Also known as a bZIP domain. It is made up of two alpha helices placed parallel to each other to form a zipper-like structure held together by leucine amino acids. This domain enables a protein to bind to DNA.
• Zinc finger - This domain is actually known as a "motif" because it is only 21 amino acids long. The amino acids are arranged in a loop to look like a finger and there is a zinc molecule present at the "knuckle." It is also involved in DNA binding.

Molecular Biology of the Cell, Alberts, 3rd edition, 1994.

Do*main" (?), n. [F. domaine, OF. demaine, L. dominium, property, right of ownership, fr. dominus master, owner. See Dame, and cf Demesne, Dungeon.]

1.

Dominion; empire; authority.

2.

The territory over which dominion or authority is exerted; the possessions of a sovereign or commonwealth, or the like. Also used figuratively.

The domain of authentic history. E. Everett.

The domain over which the poetic spirit ranges. J. C. Shairp.

3.

Landed property; estate; especially, the land about the mansion house of a lord, and in his immediate occupancy; demesne.

Shenstone.

4. Law

Ownership of land; an estate or patrimony which one has in his own right; absolute proprietorship; paramount or sovereign ownership.

Public domain, the territory belonging to a State or to the general government; public lands. [U.S.] -- Right of eminent domain, that superior dominion of the sovereign power over all the property within the state, including that previously granted by itself, which authorizes it to appropriate any part thereof to a necessary public use, reasonable compensation being made.

© Webster 1913.