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These gradients are critical for cellular identity and cell relocation. Similarly, the gradients produced by cells may influence cellular fate by their temporal and spatial characteristics. In certain organisms, the choice of cell fate can be determined by a gradient, a binary choice, or through a relay of molecules released by a cell. [1]
The gradient of a function is called a gradient field. A (continuous) gradient field is always a conservative vector field: its line integral along any path depends only on the endpoints of the path, and can be evaluated by the gradient theorem (the fundamental theorem of calculus for line integrals). Conversely, a (continuous) conservative ...
In the case of the gravitational field g, which can be shown to be conservative, [3] it is equal to the gradient in gravitational potential Φ: =. There are opposite signs between gravitational field and potential, because the potential gradient and field are opposite in direction: as the potential increases, the gravitational field strength decreases and vice versa.
Individual cells within a morphogenetic field in an embryo are flexible: thus, cells in a cardiac field can be redirected via cell-to-cell signaling to replace damaged or missing cells. [6] The Imaginal disc in larvae is an example of a discrete morphogenetic field region of cells in an insect embryo. [7]
Homogeneous regions have spatial gradient vector norm equal to zero. When evaluated over vertical position (altitude or depth), it is called vertical derivative or vertical gradient; the remainder is called horizontal gradient component, the vector projection of the full gradient onto the horizontal plane. Examples: Biology
During early development, morphogen gradients result in the differentiation of specific cell types in a distinct spatial order. The morphogen provides spatial information by forming a concentration gradient that subdivides a field of cells by inducing or maintaining the expression of different target genes at distinct concentration thresholds.
Species richness, or biodiversity, increases from the poles to the tropics for a wide variety of terrestrial and marine organisms, often referred to as the latitudinal diversity gradient. [1] The latitudinal diversity gradient is one of the most widely recognized patterns in ecology. [1] It has been observed to varying degrees in Earth's past. [2]
In biology, a cline is a measurable gradient in a single characteristic (or biological trait) of a species across its geographical range. [1] Clines usually have a genetic (e.g. allele frequency, blood type), or phenotypic (e.g. body size, skin pigmentation) character.