Abstract
We present here explicit mathematical formulas for calculating the concentration, mass, and velocity of movement of the center of mass of the plant growth regulator auxin during its polar movement through a linear file of cells. The results of numerical computations for two cases, (a) the conservative, in which the mass in the system remains constant and (b) the non-conservative, in which the system acquires mass at one end and loses it at the other, are graphically presented. Our approach differs from that of Mitchison's (Mitchison 1980) in considering both initial effects of loading and end effects of substance leaving the file of cells. We find the velocity varies greatly as mass is entering or leaving the file of cells but remains constant as long as most of the mass is within the cells. This is also the time for which Mitchison's formula for the velocity, which neglects end effects, reflects the true velocity of auxin movement. Finally, the predictions of the model are compared with two sets of experimental data. Movement of a pulse of auxin through corn coleoptiles is well described by the theory. Movement of auxin through zucchini shoots, however, shows the need to take into account immobilization of auxin by this tissue during the course of transport.
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Martin, M.H., Goldsmith, M.H.M. & Goldsmith, T.H. On polar auxin transport in plant cells. J. Math. Biol. 28, 197–223 (1990). https://doi.org/10.1007/BF00163145
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DOI: https://doi.org/10.1007/BF00163145