TY - JOUR
T1 - Mathematics of experimentally generated chemoattractant gradients.
AU - Postma, Marten
AU - van Haastert, Peter J.M.
PY - 2009/1/1
Y1 - 2009/1/1
N2 - Many eukaryotic cells move in the direction of a chemical gradient. Several assays have been developed to measure this chemotactic response, but no complete mathematical models of the spatial and temporal gradients are available to describe the fundamental principles of chemotaxis. Here we provide analytical solutions for the gradients formed by release of chemoattractant from a point source by passive diffusion or forced flow (micropipettes) and gradients formed by laminar diffusion in a Zigmond chamber. The results show that gradients delivered with a micropipette are formed nearly instantaneous, are very steep close to the pipette, and have a steepness that is strongly dependent on the distance from the pipette. In contrast, gradients in a Zigmond chamber are formed more slowly, are nearly independent of the distance from the source, and resemble the temporal and spatial properties of the natural cAMP wave that Dictyostelium cells experience during cell aggregation.
AB - Many eukaryotic cells move in the direction of a chemical gradient. Several assays have been developed to measure this chemotactic response, but no complete mathematical models of the spatial and temporal gradients are available to describe the fundamental principles of chemotaxis. Here we provide analytical solutions for the gradients formed by release of chemoattractant from a point source by passive diffusion or forced flow (micropipettes) and gradients formed by laminar diffusion in a Zigmond chamber. The results show that gradients delivered with a micropipette are formed nearly instantaneous, are very steep close to the pipette, and have a steepness that is strongly dependent on the distance from the pipette. In contrast, gradients in a Zigmond chamber are formed more slowly, are nearly independent of the distance from the source, and resemble the temporal and spatial properties of the natural cAMP wave that Dictyostelium cells experience during cell aggregation.
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M3 - Article
C2 - 19763986
AN - SCOPUS:74049118336
VL - 571
SP - 473
EP - 488
JO - Methods in molecular biology (Clifton, N.J.)
JF - Methods in molecular biology (Clifton, N.J.)
SN - 1064-3745
ER -