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Plasma membrane H+-ATPase regulation is required for auxin gradient formation preceding phototropic growth

Phototropism is a growth response allowing plants to align their photosynthetic organs toward incoming light and thereby to optimize photosynthetic activity. Formation of a lateral gradient of the phytohormone auxin is a key step to trigger asymmetric growth of the shoot leading to phototropic reorientation. To identify important regulators of auxin gradient formation, we developed an auxin flux model that enabled us to test in silico the impact of different morphological and biophysical parameters on gradient formation, including the contribution of the extracellular space (cell wall) or apoplast. Our model indicates that cell size, cell distributions, and apoplast thickness are all important factors affecting gradient formation. Among all tested variables, regulation of apoplastic pH was the most important to enable the formation of a lateral auxin gradient. To test this prediction, we interfered with the activity of plasma membrane H+-ATPases that are required to control apoplastic pH. Our results show that H+-ATPases are indeed important for the establishment of a lateral auxin gradient and phototropism. Moreover, we show that during phototropism, H+-ATPase activity is regulated by the phototropin photoreceptors, providing a mechanism by which light influences apoplastic pH.


Supplementary Material and Methods
Supplementary Figure

RNA extraction and quantitative RT-PCR
50 Hypocotyls from 3 day-old etiolated seedlings were dissected using a dissection scissor under green safe light and immediately immersed into liquid N2. RNA extraction and quantitative real time PCR were performed as described in (Lorrain et al. 2009), except that 170 ng of RNA were used for the reverse transcription reaction.
Primer efficiency was preliminary determined using a dilution serie of the cDNA preparation. Primers sequences are given in table S2. Data from three technical and three biological replicates were then analyzed and normalized with the value of the expression levels of AUX1 of one of the replicate.

The model
To investigate lateral auxin gradient formation underlying phototropic bending in Arabidopsis thaliana hypocotyls, we constructed an auxin flux model that tracks auxin relocation as a function of different topological as well as biophysical parameters. The geometry of the model includes a transverse cross section through the hypocotyl explicitly featuring cellular compartments as well as apoplastic compartments. This cross section was determined using microscopy data and an overview on the modeled domain is given in Fig. 1A.
The model is based on a system of ordinary differential equations simulating the flux contributions between neighboring compartments. Free diffusion is assumed between the apoplast compartments, while we consider protonation state dependent auxin diffusion and active auxin efflux based on carriers, i.e. those of the PIN and PGP families, on the interface between cellular compartments and the apoplastic space. We did not consider active IAA influx contributions resulting from AUX/LAX for the following reasons that are explained in the main manuscript.
Apart from the fluxes within the cross section, we explicitly allowed for exchange with the apoplastic space just above and below the considered cross section. Since gradient formation is assumed to happen locally (Iino 2001;Preuten et al. 2013), auxin concentrations in the apoplast just above and below are kept constant, thereby functioning as an auxin source or sink depending on auxin redistribution in the modeled cross section. Our simulations have shown that this exchange with surrounding cross sections has a cushioning effect on the strength of gradients predicted by our model: For example, setting the exchange between the modeled cross section and cross sections above and below to zero results in qualitatively similar results but stronger gradients (increasing gradient strength from 12% for vacuolated cells to 82%). And although this documents a considerable effect of coupling strength on gradient strength, the fact that the qualitative behavior in both extremes is similar lets us not further pursue this parameter.
In addition, we incorporate the fact that the stele is the major mode of basipetal auxin transport and therefore has to be considered an auxin source. Further incorporating the fact that auxin transport in the stele is faster than in the apoplast (Kramer 2006), for our model we assume that auxin concentrations in the stele are high and kept constant.
The model thereby neglects a potential contribution of modulated auxin biosynthesis within cells of the modeled cross section. This assumption seems to be confirmed by phototropism assays in two auxin biosynthesis mutants that were previously shown to be defective for shade-induced auxin-dependent hypocotyl elongation sav3 and yuc1yuc4 (Tao et al. 2008;Won et al. 2011) but show normal phototropic responses (see Fig S8). Nevertheless, considering the redundancy in the TAA1/TAR and YUC gene families, a contribution of local auxin biosynthesis cannot be ruled out completely.
In this framework we define a lateral auxin gradient as follows: First, due to the type of manipulations we use in the simulations (e.g. side-directed pH manipulation, sidedirected PIN localization changes) the modeled cross section can be divided in shaded and lit side just like for hypocotyls in experiments. Under this assumption, a gradient is defined as difference in intracellular auxin concentrations comparing epidermal cells on lit and shaded side by building ratios between the two. Whenever their ratio differs from '1' a gradient has formed. Its steepness is expressed in terms of percentage difference in auxin concentration between the two sides.

Model parameters
The model comprises three different types of parameters. First there is a set of kinetic constants that are inherently necessary to translate auxin fluxes into mathematical expressions. Although these constants ideally would be determined experimentally, many of them are difficult to measure and therefore have to be treated as free parameters (Kramer 2007). An overview on these parameters is given in Table S1.
All of the listed parameters apart from the decay rate µ had been part of a sensitivity analysis in which we varied each reported value separately by ±1 and ±2 orders of magnitude. During this analysis it turned that the dissociation constants I and as well as the membrane permeability of membranes for auxin ( diff ) are rather negligible because varying them had no strong impact on the forming gradients. Instead, the model was sensitive to changes of the remaining three parameters, transport capacities of PIN carriers I , transport capacity of PGP carriers , and the diffusion constant of auxin D IAA . It responded approximately linearly to changes of these parameters with pumping capacities increased by 2 orders of magnitude resulting in gradients of about 70% concentration difference between sides and a change of 2 orders of magnitude in the diffusion rate resulting in gradients increased by about 50% as compared to the reported diffusion constants.
The second class of considered parameters are topological parameters. And although the cross section shown in Fig. 1A is generated copying an experimentally determined hypocotyl cross section (determined using microscopy data) that has to be considered a naturally occurring topology, it remains open if the inherent asymmetries of this topology introduce a non-negligible bias into the model. We therefore tested the impact of these asymmetries and other features of this topology by comparing it to a range of altered topologies shown in Fig. 1E (including different cell size distributions).
In addition to shape and cell size distribution across layers (which at the same time influence cell volumes and thereby impact resulting auxin concentrations), the distribution of apoplast thicknesses across the different cell layers has to be considered as another important topological parameter because the thickness of the apoplastic space modifies auxin storage capabilities as well as possible auxin travel distances in the apoplast (again influencing apoplastic volumes and thereby impacting resulting auxin concentrations). To choose plausible thickness distributions for the simulations we relied on data gathered by Derbyshire and colleagues (Derbyshire et al. 2007). And in order to match the reported thickness distributions with the size of our seedlings, we used the growth stages IIa-c (Hayashi et al. 2010;Steinacher et al. 2012;Derbyshire et al. 2007). In addition to these reported distributions we tested different artificial and homogeneous apoplast thickness distributions of 100 nm, 400 nm, and 800 nm throughout all layers to avoid introducing unnecessary bias by potential peculiarities of the reported distributions.
Here, especially the efflux carriers of the PIN family are of interest since they are known to show polar distributions as well as knock out experiments show a significant defect in phototropism (Friml et al. 2002;Ding et al. 2011;Christie et al. 2011). In addition to the PINs we explicitly incorporated potential contributions of carriers of the PGP family as well since they as well have been implicated to be of potential importance for phototropism (Noh et al. 2003;Christie et al. 2011;Nagashima et al. 2008). With respect to modeling auxin fluxes the other carriers and especially the carriers belonging to the AUX/LAX family were neglected due to their negligible effect on phototropism (Fig. S1).
Lastly, auxin fluxes are impacted by compartmental pH (Kramer & Bennett 2006;Kramer 2006;Krupinski & Jönsson 2010;Steinacher et al. 2012). Here, predominantly extracellular pH distributions are of interest because the natural occurring auxin indole-3-acetic acid (IAA) is a weak acid with a pK a value of 4.8 (Delbarre et al. 1996). This means that for an assumed apoplast pH of around 5.5 (Kramer 2006;Krupinski & Jönsson 2010;Yu et al. 2000;Bibikova et al. 1998;Kurkdjian & Guern 1989), the protonation state of IAA crucially depends on the exact pH value (e.g. at pH 5.5 only ~16% of the IAA are protonated while at pH 4.8 already 50% are protonated, Fig. 1C). And considering that only protonated IAA is able to permeate cell membranes, the pH and protonation state potentially have a significant impact on auxin uptake by the cells. In this regard, we considered pH as an exogenous variable, i.e. one that follows an assumed distribution (e.g. homogeneous apoplastic pH throughout the whole cross section during model equilibration and differential distributions as described during the simulations of gradient formation during photo stimulation). In other words, this means that the model does not consider inherent means on how photo stimulation impacts pH, e.g. by the hypothesized photo stimulus dependent regulation of H + -ATPases or other yet uncovered means of regulation.
Especially the hypothesis about a phototropin based regulation of H + -ATPase provides a possible link between phototropism and apoplastic pH and could be included in a future version of the model inspired by the implementation by Steinacher and colleagues for a link between H + -ATPase activity and pH .

Model equations
The

Simulations
The model was implemented in MATLAB® version 2012b relying on the ode23tb numerical integrator which is an implementation of an explicit Runge-Kutta scheme (Bogacki & Shampine 1989). Simulation runs were conducted in a two step process; first a run for 2.5h of simulated time (here, timescales are set via the time-dependent diffusion and permeability rates) allowing the system to reach steady state under dark conditions (i.e. no polar PIN or heterogeneous pH distributions) before in another run of 4h simulated time the respective differential pH and PIN distributions are applied.
Within these 4h of simulated time, all simulations reached a steady state, usually already after about 1.5h-2h. Here, this time window fits well auxin gradient formation timescales seen in root gravitropism (Band et al. 2012), which can be seen as a gradient formation process similar to the one underlying phototropism and therefore indicating that at least the timescales in the simulations a well in line with naturally occurring events.

Supplemental figure legends
Supplementary Figure