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The auxin transport canalisation hypothesis has been proposed by Sachs in 1981

[189], stating that initial auxin fluxes between cells are reinforced by a feedback be-

tween auxin and its transporters, eventually leading to distinct routes (canals) of strong auxin flux. This hypothesis has been useful in understanding the formation of vascular tissue, including leaf veins, where auxin and its transport routes lay out the path for

subsequent tissue differentiation [184]. Since PINs are important in establishing auxin

flux directionality, this idea would imply a feedback between auxin and PINs, causing PINs to accumulate where the auxin flux is highest and polarise in the direction of the flux. This source-sink PIN polarisation pattern can indeed be observed using imaging

in understanding the mechanistic basis of auxin transport canalisation, with an often posed question towards how cells could sense auxin flux in order to polarise efflux

transporters in the direction of flux [117]. As well, the notion that auxin forms maxima

in the SAM during the process of phyllotaxis, inferred from the indirect observation that the synthetic DR5 auxin response reporter is activated at the sites of incipient

leaf formation [235], seems to contradict the canalisation hypothesis, since the forma-

tion of auxin maxima would require PIN polarisation towards higher auxin instead of lower auxin. It has to be noted, however, that DR5 reporters do not respond to auxin concentration directly, but to auxin dependent gene expression.

With these open questions in mind, and the difficulty of measuring auxin concentration directly, the use of computer models to formulate and test hypotheses underlying auxin transport dynamics is useful and has indeed helped to understand better some of

the complex aspects in PAT [63,106,232]. Therefore, the following chapter has its

focus on this theoretical approach. During the next chapter, computer models of auxin transport that have already been published are reviewed and their assumptions and the impact that they have on our current understanding of auxin biology are discussed in detail.

CHAPTER

3

Computer models in auxin biology

In auxin biology there are, despite many advances over the last decades, still many open questions. In the last chapter, some of these advances have been presented. The integration of auxin transport with auxin signalling, leading to the regulation of physiological and developmental processes, and the interplay of auxin with other hor- mones such as cytokinin, strigolactones or ethylene, have been reviewed. We already saw that auxin transport plays a crucial role within this complex network of intertwined processes, since it ensures that auxin is available at places where its action is nec- essary, that auxin is depleted from parts of tissues in order to produce concentration gradients (as is the case in phyllotactic patterning in the SAM), and it allows information to be transmitted from one place to another.

Some of these open questions are: how is regulated auxin transport from cell to cell established in plant tissues, resulting in specific transport patterns such as in the es- tablishment of maxima in the root and shoot meristems, or in distinct canals of auxin transport in the context of canalisation? How are such transport patterns established in cells? We saw that the chemiosmotic hypothesis of auxin transport, now widely

accepted and refined by the discovery of several auxin carriers [47,58], hints towards

the dependency of auxin transport on the interplay and polarisation of auxin transport proteins. On the other hand, the last chapter also discussed mechanisms by which auxin regulates its transporters, both on transcriptional and post-translational levels (see section 2.3.1). How can these regulation mechanisms arrive at sometimes dif- ferent results, especially at flux-oriented (canalisation) versus up-the-gradient auxin

transport (as in phyllotaxis)? How do cells ’know’ where to transport auxin and how does concerted transport between cells in a tissue emerge? And how do the dynam- ics of auxin transport within tissues influence higher level features such as shoot or root branching? There are also problems on a methodological level: it is, for instance, extremely difficult to measure auxin content in living cells or cell compartments. How- ever, there are methods to infer auxin gradients in tissues from the visualisation us- ing DR5:GFP, an auxin responsive promoter element fused to the Green Fluorescent

Protein (GFP) gene [151]. Still, precise quantifications of auxin concentrations are not

possible with these methods, since DR5 does not report auxin concentrations directly, but responds to auxin dependent downstream gene expression.

As a response in order to understand better the dynamics and underlying processes of auxin transport, many computer models have been developed over the last years, tar- geting these open questions mainly at the tissue and whole plant scales. This chapter gives a review of the progress and implications of these models to date and discusses important knowledge gaps in auxin transport modelling that lead to the development of a new model of auxin transport dynamics at a single cell level, which will be described in the following chapters.

3.1

Computational modelling in biology

Computational modelling is a powerful tool to broaden our understanding of complex processes by formulating, quantifying, simulating and testing the mechanistic rules (such as the relationship between chemical or biological entities) upon which the be- haviour of the whole system of interest hypothetically rests. While modelling does not prove a mechanism, it potentially increases the strength of an explanation by explor- ing the consequences of one or several mechanisms and the importance of underlying assumptions, thereby guiding future empirical experiments, the results of which then

can feed back into the modelling process [170], an integration of theoretical and ex-

perimental approaches in biology that is often referred to as systems biology [96].

Mathematical and comptuational modelling are often distinguished, because mathe- matical modelling explicitly defines the relationship entities, thereby unambiguously characterizing the system of interest formally, while computational modelling provides executable models based on algorithms which simulate how the system progresses