Nonvascular, symplasmic transport of sucrose (Suc) was investigated theoretically in the primary root tip of maize (Zea mays 1.cv WF9 x Mo 17) seedlings. Symplasmic diffusion has been assumed to be the mechanism of transport of Suc to cells in the root apical meristem (R.T. Ciaquinta, W. Lin, N.L. Sadler, V.R. Franceschi [1983] Plant Physiol 72: 362-367), which grow apical to the end of the phloem and must build all biomass with carbon supplied from the shoot or kernel. We derived an expression for the growthsustaining Suc flux, which is the minimum longitudinal flux that would be required to meet the carbon demands of growth in the root apical meristem. We calculated this flux from data on root growth velocity, area, and biomass density, taking into account construction and maintenance respiration and the production of mucilage by the root cap. We then calculated the conductivity of the symplasmic pathway for diffusion, from anatomical data on cellular dimensions and the frequency and dimensions of plasmodesmata, and from two estimates of the diffusive conductance of a plasmodesma, derived from independent data. Then, the concentration gradients required to drive a growth-sustaining Suc flux by diffusion alone were calculated but were found not to be physiologically reasonable. We also calculated the hydraulic conductivity of the plasmodesmatal pathway and found that mass flow of Suc solution through plasmodesmata would also be insufficient, by itself, to satisfy the carbon demands of growth. However, much of the demand for water to cause cell expansion could be met by the water unloaded from the phloem while unloading Suc to satisfy the carbon demands of growth, and the hydraulic conductivity of plasmodesmata is high enough that much of that water could move symplasmically. Either our current understanding of plasmodesmatal ultrastructure and function is flawed, or alternative transport mechanisms must exist for Suc transport to the meristem.Understanding the control of plant growth and development must include an understanding of the transport of photoassimilates from sources into developing sinks. Transport of solutes through the differentiated phloem is explained well by quantitative treatments of Miinch's (1930) pressure flow hypothesis (Christy and Femer, 1973;Tyree et al., 1974a;Ross and Tyree, 1980), and experimental data are in reasonably good agreement with their predictions (cf. Zimmermann and Brown, 1971; Pickard et al.,