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Orthogonal ligand-protein pairs (also known as re-engineered ligand-receptor interfaces or re-engineered enzyme-substrate interactions) are a protein-ligand binding pair made to be independent of the original binding pair. This is done by taking a mutant protein (naturally occurring or selectively engineered), which is activated by a different ...
The Staudinger ligation is a reaction developed by the Bertozzi group in 2000 that is based on the classic Staudinger reaction of azides with triarylphosphines. [15] It launched the field of bioorthogonal chemistry as the first reaction with completely abiotic functional groups although it is no longer as widely used.
The line segments AB and CD are orthogonal to each other. In mathematics, orthogonality is the generalization of the geometric notion of perpendicularity.Whereas perpendicular is typically followed by to when relating two lines to one another (e.g., "line A is perpendicular to line B"), [1] orthogonal is commonly used without to (e.g., "orthogonal lines A and B").
Orthogonal matrices with determinant −1 do not include the identity, and so do not form a subgroup but only a coset; it is also (separately) connected. Thus each orthogonal group falls into two pieces; and because the projection map splits, O(n) is a semidirect product of SO(n) by O(1).
Hence, what is technically a transverse (orthogonal) section with respect to the body length axis of a rat (dividing anterior from posterior) may often be referred to in rat neuroanatomical coordinates as a coronal section, and likewise a coronal section with respect to the body (i.e. dividing ventral from dorsal) in a rat brain is referred to ...
Biorthogonal polynomials are a generalization of orthogonal polynomials and share many of their properties. There are two different concepts of biorthogonal polynomials in the literature: Iserles & Nørsett (1988) introduced the concept of polynomials biorthogonal with respect to a sequence of measures, while Szegő introduced the concept of ...
This definition can be formalized in Cartesian space by defining the dot product and specifying that two vectors in the plane are orthogonal if their dot product is zero. Similarly, the construction of the norm of a vector is motivated by a desire to extend the intuitive notion of the length of a vector to higher-dimensional spaces.
In linear algebra, orthogonalization is the process of finding a set of orthogonal vectors that span a particular subspace.Formally, starting with a linearly independent set of vectors {v 1, ... , v k} in an inner product space (most commonly the Euclidean space R n), orthogonalization results in a set of orthogonal vectors {u 1, ... , u k} that generate the same subspace as the vectors v 1 ...