Quantitative Aspects of a Theory of Translocation

Abstract

An analysis is made of two aspects of the behaviour of a proposed mechanism of translocation based on the mixing effect within a sieve-tube of streaming transcellular strands of protoplasm passing through the sieve-pores and through a vacuole-like reservoir of sucrose solution in each sieve-element. First, the behaviour of the model is considered when it is transporting a solute (sucrose, for example) in the steady-state condition of constant consumption and supply. It is found that the concentrations of solute in the regions of the model are readily determined at all points of the sieve-tube, and that the gradients of concentration are all equal, the concentrations differing by constant amounts at all points. Transport is analogous to diffusive transfer in that the steepness of the concentration gradient is proportional to the rate of transfer and simple expressions are derived for the net transport of solute and for the apparent diffusion coefficient in terms of the properties of the model. Transfer is found to be rapid over a short path and slower over a longer path; there is a maximum distance beyond which a given rate of transfer cannot take place. Second, an analysis is made of the unsteady behaviour of the model when changing concentrations of solute are introduced into the system. The concept of strand diffusion time is introduced. This is the time taken for the concentration in the strand surrounded by an infinite reservoir to fall to I/e of its initial value. The results of this analysis are used to determine how radioactive solute will become distributed when it is introduced into the steady-state model. If the time over which the translocation of radioactive solute has proceeded is small compared with the strand diffusion time, a wave-like profile of radioactivity with distance is produced, and if large, the profile is of a diffusive kind; intermediate conditions give a profile displaying both characteristics which is termed the transition type. These three types of profile of radioactivity are exemplified by experiments in different plants (Salix, Tropaeolum, and Helianthus), and the experimental profiles are used to estimate (1) the apparent diffusion coefficient of translocated sucrose in the sense of Mason and Maskell, and (2) the permeability constant of the strand-reservoir boundary. The close correspondence between these two sets of figures derived from the radioactive profiles with the experimental values obtained directly is regarded as strong confirmation of the theory.