Representation theoryRepresentation theory is a branch of mathematics that studies abstract algebraic structures by representing their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures. In essence, a representation makes an abstract algebraic object more concrete by describing its elements by matrices and their algebraic operations (for example, matrix addition, matrix multiplication).
EndocytosisEndocytosis is a cellular process in which substances are brought into the cell. The material to be internalized is surrounded by an area of cell membrane, which then buds off inside the cell to form a vesicle containing the ingested material. Endocytosis includes pinocytosis (cell drinking) and phagocytosis (cell eating). It is a form of active transport. The term was proposed by De Duve in 1963. Phagocytosis was discovered by Élie Metchnikoff in 1882.
Lie algebra representationIn the mathematical field of representation theory, a Lie algebra representation or representation of a Lie algebra is a way of writing a Lie algebra as a set of matrices (or endomorphisms of a vector space) in such a way that the Lie bracket is given by the commutator. In the language of physics, one looks for a vector space together with a collection of operators on satisfying some fixed set of commutation relations, such as the relations satisfied by the angular momentum operators.
Biochemical cascadeA biochemical cascade, also known as a signaling cascade or signaling pathway, is a series of chemical reactions that occur within a biological cell when initiated by a stimulus. This stimulus, known as a first messenger, acts on a receptor that is transduced to the cell interior through second messengers which amplify the signal and transfer it to effector molecules, causing the cell to respond to the initial stimulus. Most biochemical cascades are series of events, in which one event triggers the next, in a linear fashion.
Irreducible representationIn mathematics, specifically in the representation theory of groups and algebras, an irreducible representation or irrep of an algebraic structure is a nonzero representation that has no proper nontrivial subrepresentation , with closed under the action of . Every finite-dimensional unitary representation on a Hilbert space is the direct sum of irreducible representations. Irreducible representations are always indecomposable (i.e. cannot be decomposed further into a direct sum of representations), but the converse may not hold, e.
Receptor tyrosine kinaseReceptor tyrosine kinases (RTKs) are the high-affinity cell surface receptors for many polypeptide growth factors, cytokines, and hormones. Of the 90 unique tyrosine kinase genes identified in the human genome, 58 encode receptor tyrosine kinase proteins. Receptor tyrosine kinases have been shown not only to be key regulators of normal cellular processes but also to have a critical role in the development and progression of many types of cancer.
PinocytosisIn cellular biology, pinocytosis, otherwise known as fluid endocytosis and bulk-phase pinocytosis, is a mode of endocytosis in which small molecules dissolved in extracellular fluid are brought into the cell through an invagination of the cell membrane, resulting in their containment within a small vesicle inside the cell. These pinocytotic vesicles then typically fuse with early endosomes to hydrolyze (break down) the particles. Pinocytosis is variably subdivided into categories depending on the molecular mechanism and the fate of the internalized molecules.
Group representationIn the mathematical field of representation theory, group representations describe abstract groups in terms of bijective linear transformations of a vector space to itself (i.e. vector space automorphisms); in particular, they can be used to represent group elements as invertible matrices so that the group operation can be represented by matrix multiplication. In chemistry, a group representation can relate mathematical group elements to symmetric rotations and reflections of molecules.
Domain (biology)In biological taxonomy, a domain (dəˈmeɪn or doʊˈmeɪn) (Latin: regio), also dominion, superkingdom, realm, or empire, is the highest taxonomic rank of all organisms taken together. It was introduced in the three-domain system of taxonomy devised by Carl Woese, Otto Kandler and Mark Wheelis in 1990. According to the domain system, the tree of life consists of either three domains such as Archaea, Bacteria, and Eukarya, or two domains consisting of Archaea and Bacteria, with Eukarya included in Archaea.
Synaptic plasticityIn neuroscience, synaptic plasticity is the ability of synapses to strengthen or weaken over time, in response to increases or decreases in their activity. Since memories are postulated to be represented by vastly interconnected neural circuits in the brain, synaptic plasticity is one of the important neurochemical foundations of learning and memory (see Hebbian theory). Plastic change often results from the alteration of the number of neurotransmitter receptors located on a synapse.
