Two main mechanisms have been proposed so far to explain RI. Since then it has been recognized as a general morphogenetic process involved in a wide range of systems, including fish epiboly ( Warga and Kimmel, 1990), fly gastrulation ( Clark et al., 2011), amphibian and fish neural folding ( Kee et al., 2008), regeneration of hydra ( Kishimoto et al., 1996), and in mammalians during gastrulation ( Yen et al., 2009), gut development ( Yamada et al., 2010), and ear development ( Chen et al., 2002). RI was first described during the uniform expansion of the ectoderm in the animal pole region during amphibian gastrulation ( Keller, 1980). During epiboly, the number of cell layers in a multilayered epithelium is reduced by cell intercalation, a process called radial intercalation (RI). This study provides insight into the fundamental process of radial intercalation and could be applied to a wide range of morphogenetic events.Īcquiring shape and form in multicellular organisms involves deformation of epithelial sheets through bending (invagination), extension through narrowing (convergent extension), and expansion via thinning (epiboly). This mechanism is robust against fluctuations of chemoattractant levels and expression patterns and explains expansion during epiboly. We identify the chemoattractant as the complement component C3a, a factor normally linked with the immune system. The mechanism is explored by computational modeling and tested in vivo, ex vivo, and in vitro. This role of chemotaxis in tissue spreading and thinning is unlike its typical role associated with large-distance directional movement of cells. Using amphibian epiboly, the thinning and spreading of the animal hemisphere during gastrulation, here we provide evidence that radial intercalation is driven by chemotaxis of cells toward the external layer of the tissue. Minute to Radian Conversion Table Minute ġ5 ' = 15 × 0.0002908882 rad = 0.Radial intercalation is a fundamental process responsible for the thinning of multilayered tissues during large-scale morphogenesis however, its molecular mechanism has remained elusive. As such, when angle measures are written, the lack of a symbol implies that the measurement is in radians, while a ° symbol would be added if the measurement were in degrees. Although the symbol "rad" is the accepted SI symbol, in practice, radians are often written without the symbol since a radian is a ratio of two lengths and is therefore, a dimensionless quantity. Although he described the unit, Cotes did not name the radian, and it was not until 1873 that the term "radian" first appeared in print.Ĭurrent use: The radian is widely used throughout mathematics as well as in many branches of physics that involve angular measurements. The concept of the radian specifically however, is credited to Roger Cotes who described the measure in 1714. History/origin: Measuring angles in terms of arc length has been used by mathematicians since as early as the year 1400. One radian is equal to 180/π (~57.296) degrees. An angle's measurement in radians is numerically equal to the length of a corresponding arc of a unit circle. It is a derived unit (meaning that it is a unit that is derived from one of the seven SI base units) in the International System of Units. Radianĭefinition: A radian (symbol: rad) is the standard unit of angular measure. History/origin: The term "minute" is derived from the Latin "pars minuta prima" which means the "first small part." The minute was originally defined as 1/60 of an hour (60 seconds), based on the average period of Earth's rotation relative to the sun, known as a mean solar day.Ĭurrent use: The minute, as a multiple of the second, is used for all manner of measurements of duration, from timing races, measuring cooking or baking times, number of heart beats per minute, to any number of other applications. Under Coordinated Universal Time, a minute can have a leap second, making the minute equal to 61 rather than 60 seconds. Definition: A minute (symbol: min) is a unit of time based on the second, the base unit of the International System of Units (SI).
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