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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 ...
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
Durotaxis is the directional movement of a cell along a stiffness gradient. Electrotaxis (or galvanotaxis) is the directional movement of motile cells along the vector of an electric field. It has been suggested that by detecting and orienting themselves toward the electric fields, cells can move towards damages or wounds to repair them.
The simplest definition for a potential gradient F in one dimension is the following: [1] = = where ϕ(x) is some type of scalar potential and x is displacement (not distance) in the x direction, the subscripts label two different positions x 1, x 2, and potentials at those points, ϕ 1 = ϕ(x 1), ϕ 2 = ϕ(x 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.
In vector calculus, a conservative vector field is a vector field that is the gradient of some function. [1] A conservative vector field has the property that its line integral is path independent; the choice of path between two points does not change the value of the line integral. Path independence of the line integral is equivalent to the ...
Morphogenesis of Drosophila fruit flies is intensively studied in the laboratory. A morphogen is a substance whose non-uniform distribution governs the pattern of tissue development in the process of morphogenesis or pattern formation, one of the core processes of developmental biology, establishing positions of the various specialized cell types within a tissue.