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When a plant of an apically dominant species such as garden pea (Pisum sativum) is decapitated (its main shoot apex is removed) several previously inhibited buds are released to form new axillary shoots (e.g., Morris et al., 2005; Dun et al., 2006; Waldie et al., 2010). In pea, as well as many other plant species, this outgrowth of the axillary buds after decapitation can be substantially inhibited by the presence of auxin (Sachs & Thimann, 1967). However, this inhibition of bud outgrowth by exogenous auxin is rarely complete, as revealed by investigations of whether auxin treatment of decapitated plants can prevent the earliest developmental stage of bud release (Morris et al., 2005; Beveridge et al., 2009; Ferguson & Beveridge, 2009). Moreover, as auxin cannot move acropetally in buds, it must act indirectly. There is considerable evidence that auxin signalling affects cytokinin and strigolactone concentrations and that these can act directly in buds to affect outgrowth (Brewer et al., 2009; Ferguson & Beveridge, 2009; Dun et al., 2012). In addition, based on auxin canalization theory, the relative flux of auxin down the stem, compared with that from axillary buds, has been suggested to trigger bud outgrowth directly or indirectly (Prusinkiewicz et al., 2009; Balla et al., 2011; Domagalska & Leyser, 2011). Importantly, in all of these potential mechanisms of auxin regulation of bud outgrowth after decapitation, auxin transport and/or concentration in the stem adjacent to axillary buds is considered of critical importance (Prusinkiewicz et al., 2009).
Given the suggested importance of auxin depletion in the stem in stimulating the outgrowth of an adjacent bud after decapitation, it is essential that we test whether changes in auxin flux or concentration in the stem adjacent to axillary buds are actually correlated with the timing of initial bud outgrowth. Our previous study on polar auxin transport and bud outgrowth (Morris et al., 2005) is perhaps the only study that has incorporated the temporal and/or spatial resolution to test this correlation. Bud outgrowth and radiolabelled auxin transport (3H-indole-3-acetic acid) were measured at a fine temporal and spatial scale in tall garden pea plants where the growing buds and the shoot tip were separated by a relatively large distance (Morris et al., 2005). The experiments provided surprising evidence that the initial growth of axillary buds after decapitation is not correlated with a local depletion in stem auxin concentration (Morris et al., 2005). Experimental data indicated that the radiolabelled auxin moves slowly down the plant in a wave; the peak of this auxin wave moves at c. 0.8–1.0 cm h−1. Axillary bud growth commenced almost immediately after decapitation at the node just below the decapitation site (node 7) and within c. 5 h at node 2, which was c. 20 cm below the decapitation site (Morris et al., 2005). This indicates that the trigger for initial bud outgrowth moves down through the stem at c. 4 cm h−1 or faster. The conclusion was drawn that auxin moves too slowly to be the cause of the initial bud outgrowth, and that some other mechanism must be responsible (Morris et al., 2005; Ferguson & Beveridge, 2009). These conclusions are supported by observations that while decapitation promotes bud outgrowth in pea, stem girdling or pharmacological methods that cause equivalent changes in stem auxin content to those caused by decapitation do not always induce bud outgrowth even in wildtype plants (Morris et al., 2005; Ferguson & Beveridge, 2009).
Given that these results do not support the long-standing dogma that changes in auxin concentrations or transport near buds is the initial, albeit indirect, trigger for outgrowth, we decided to use a modelling approach to investigate the process of long-distance auxin transport in more detail. For example, although the peak of the auxin wave moved at c. 0.8–1.0 cm h−1, the front appeared to move faster and the tail slower, and we wanted to test whether this kind of phenomenon might be able to provide an explanation for how changes in auxin concentration may affect bud outgrowth. Long-distance auxin transport studies in pea and Arabidopsis are also not consistent with an auxin transport limitation/canalization hypothesis because stems of these species appear to have a robust ability to transport both normal and relatively large amounts of auxin (Brewer et al., 2009). Again, we need to understand whether the long-distance auxin transport in stems is consistent with a carrier-limited auxin transport system such as is required for canalization. Various models of auxin transport within the apical meristem (e.g., Heisler & Jönsson, 2007; Kramer, 2008), and within and between metamers (Prusinkiewicz et al., 2009) have been presented, but we are not aware of any existing models that represent long-distance auxin transport along a whole stem and which are tested against empirical auxin transport data.
In this paper, we present and contrast two models that represent auxin transport along a stem at different degrees of abstraction. The more detailed intracell model allowed us to explore the effects of different underlying biological assumptions on predicted patterns of auxin transport and signalling. In particular, we identify three contrasting scenarios about underlying processes of auxin transport. These scenarios vary in the extent to which passive transport, active transport and limiting transporter numbers impact on the transport profile observed. We show that each scenario results in different predicted patterns of auxin transport, with varying implications for hormonal signalling, and discuss which scenario is most likely to be relevant to auxin transport in stems, based on the match with experimental data. The scenario that best matches biological data from pea and Arabidopsis is also consistent with our simple segment-based compartment model.
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Fig. S1 Distribution of times taken from one cell to the next for the standard set of model parameter values.
Fig. S2 Plots showing the time taken from one cell to next, tt as the filament proportion, fp, and the delay, d, vary.
Fig. S3 Plots showing how mean and standard deviation and probability density functions for time taken from one cell to the next, tt, vary with different fixed number of particles per transporters, npr.
Fig. S4 An auxin input function of a fixed shape scaled by different fixed amounts to show the predicted effects of changes in auxin input amount on long-distance transport.
Notes S1 Additional information on modelling.
Movie S1 Dynamics of both endogenous and exogenous radio-labelled auxin within a pea stem, simulated with the compartment model.
Movie S2 Visualization of dynamic intracell model of auxin particles moving through cells.
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