ACTOR A ENTREVISTAR: OLGA DIAZ MUNICIPIO: TENJO

Although the modeling approach has allowed us to correctly simulate the LRE phenotypes upon many modifications of boundary permeabilities, in particular the similar LRE defects caused by both gain- and loss-of-function of PIP2;1, some experimental data, which disagreed with model simulations, suggest that estimates of crucial parameter values are inaccurate and require further modifications.

The delayed LRE observed in pip1;1 and pip2;4 mutants is contradictory to the model prediction. Since PIP1;1 and PIP2;4 are exclusively expressed in the overlaying tissue (Figure 9a, b and 11f, g), they should contribute to the boundary permeabilities k2 and k4,

which affect the water fluxes into the overlaying tissue (Figure 12). Furthermore, boundary permeability k2 is reduced during LRE due to auxin accumulation, whereas k4 is not regulated

by auxin. Therefore, the simulation of LRE phenotype in pip1;1 or pip2;4 mutant involves the value changes of model parameters including initial k2 (k2init, distinguished from minimum k2

as a result of auxin repression), k4 and rate of decrease of k2 due to auxin (k2g). Simulations by

Leah Band (University of Nottingham) revealed that reducing k2init and k4 causes faster

emergence whereas reducing k2g causes delayed emergence (Table 2). The faster emergence

in pip1;1 or pip2;4 predicted by the current model considered the effects of reducing k2init and

k4 dominating over reducing k2g, but the delayed LRE observed in pip1;1 and pip2;4 mutants

implied that reducing k2g should have a more pronounced effect than reducing k2init and k4 on

emergence time. Taking this into account, the model prediction of emergence time in pip1;1

or pip2;4 mutant would be greatly improved with slight reductions of k2init and k4 (e.g.

k2init=k4=0.6) and a very small value of k2g (Table 2). However, the meaning of such

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individual overlaying-tissue PIPs to boundary permeabilities k2init and k4 during LRE and the

relationship between changes in k2init and k2g (the degree of k2g reduction is associated with

how much k2init would be reduced) is still lacking. Although quantitative analysis of PIP

proteins in the whole root could give some hints (Monneuse et al., 2011), this data cannot be simply used to assess the contribution of individual PIPs to boundary permeabilities during LRE for two main reasons: (1) protein abundance is not equal to its real-time activity (for example, PIP2;2 is more abundant than PIP2;1 in the whole root whereas PIP2;1 appears to function more dominantly at the particular LR formation sites); (2) one isoform could have different expression levels in LRP and overlaying tissues and, therefore, exert different contributions to boundary permeabilities (such as PIP1;2 and PIP2;7). Nevertheless, the currently available data on transcript and protein levels of PIP1;1 and PIP2;4 could be employed for subsequent simulations. In addition, optimal estimates of these parameters could be identified from the simulation which most nicely agrees with the experimental data.

Table 2 The influence of different boundary permeabilities (k2init and k4) and the decreasing rate of

k2init (k2g) on the predicted emergence time.

k2init k2g k4 Emergence time

Wild type 1 0.0028 1 28 hours

Partial contribution of PIP(s) to kx*

& auxin influences k2init

0.6 0.0028 0.6 22.7 hours

Partial contribution of PIP(s) to kx

& auxin no longer influences k2init

0.6 0 0.6 44.7 hours

Full contribution of PIP(s) to kx

& auxin no longer influences k2init

0.2 0 0.2 17 hours

* kx represents k2init and k4.

The significance of boundary permeability k3-mediated water flux during LRE may have been

overlooked in the current model. k3-dependent water flux is predicted to flow from

primordium into the stele (it is commonly known that water moves towards the stele where long-distance transport occurs), and plays the least important role in affecting the emergence time (Péret et al., 2012). However, the spatio-temporal expression of PIP2;8 at LR formation

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sites and retarded LRE observed in pip2;8 mutants suggest that k3-dependent water transport

could be equally important as other water fluxes. This raises the possibility that the direction of water flux between stele and primordium driven by the water potential difference may revert at LR formation sites, namely from stele into primordium, to meet the water requirement in the rapidly growing LRP for cell expansions. Although the experimental data supporting this speculation is challenging to obtain, the observations in this work will direct the parameter modification towards strengthening the importance of k3 and considering

dynamic changes of water potential difference between primordium and stele.

In addition to optimization of the current parameters, new factors might be required to further develop the mathematical model. The regulatory signals other than auxin (e.g. the inducer of

PIP2;8 expression) could be integrated. Furthermore, since the current tissue-scale model provides the simplest representation of LRE, considering the growing primordium and the overlaying tissue as two homogeneous fluid-like compartments and lumping the effects of cell-wall extension and cell-to-cell reorganization into the boundaries surrounding each tissue region (Péret et al., 2012), it would be important to build a cell-scale, three-dimensional model. Such a model would facilitate the simulations of the emergence time and, more importantly, help to better understand the complexity of LRE biomechanics.

2.2.5 Mutations in PIPs do not affect LR number under normal growth