Supplementary text providing additional details of the computer model I. Diffusive (i.e. not carrier-mediated) membrane permeabilities Protonated IAA. There is a wide range of published values for the permeability of plant lipid membranes to protonated indole-3-acetic acid (IAAH). Many of these must be discounted however, since they do not control for the likely presence of anion carriers 1,2. The only two studies we know of that control for carriers are both by Delbarre and coworkers 3,4. These report permeabilities of 0.14 cm/hr and 0.18 cm/hr respectively for suspension-cultured tobacco protoplasts. We use the model value P IAAH = 0.2 cm/hr. It should be noted that our model value is an order of magnitude lower than the oftcited result of Gutknecht and Walter 5. However, their permeability is found by fitting a straight line to data that comes almost entirely from experiments on artificial bilayers of egg lecithin. We favor measurements made on plant cell membranes, since Bean et al. 6 have shown that the permeability of bilayers to IAAH depends strongly on the composition of the bilayer (their results range between 0.3 cm/hr and 13 cm/hr). Anionic IAA. Following Refs. [ 5 ] and [ 6 ], we assume the IAA - anion has a negligible permeability. II. Carrier-mediated membrane permeabilities Measured permeability values. We begin our discussion of auxin efflux by noting that the PIN proteins are now commonly described as efflux "facilitators" rather than
efflux carriers 7. However, even if PIN's are not carriers, they are components of the efflux machinery, and their patterns of expression and localization are believed to be reliable indicators of auxin efflux 7,8. The permeabilities due to auxin influx carriers (the AUX/LAX gene family 9 ) and to auxin efflux facilitators (the PIN gene family 8,10 ) are not well-known. Perhaps the most useful source of quantitative data is Delbarre et al. 4, who report the diffusive and carrier mediated auxin influx and efflux in suspension-cultured tobacco protoplasts. Based on their data, we estimate an influx carrier permeability of 0.02 cm/hr and an efflux carrier permeability of 0.01 cm/hr. A second useful paper, and the only published value for influx carrier permeability in a plant tissue, is Szponarski et al. 11. They report an influx carrier permeability of 0.011 cm/hr, measured in plasma membrane vesicles derived from mature Arabidopsis leaves (note the surprising agreement with the tobacco protoplast result). Szponarski's result reflects an average over all cells of the leaf, so the permeability in cells specialized for auxin transport is likely to be larger. Considering these facts, permeability values of order 0.1 cm/hr are expected to be reasonable in the root expansion zone. Model permeability values. Table S2 shows the model parameters used for carriermediated transport in the outer root. In the epidermis, we take the influx permeability to be P AUX1 = 0.2 cm/hr and the efflux permeability to be <P PIN2 > = 0.1 cm/hr. The angle brackets indicate an average over the area of the cell membrane. Note that an average is quoted since the efflux carrier permeabilties vary over the cell membrane due to the polar localization of the carriers. The model ratio of influx to efflux permeabilties (2.0) is chosen using an independent fit to the measured speed of basipetal auxin transport in root
tips, about 1 cm/hr 12,13. Blilou et al. 7 describe weak PIN1 expression in the epidermis, co-localized with PIN2. We thus take <P PIN1 > = 0.02 cm/hr. The remaining influx carrier entries in Table S2 are based on Blilou et al. 7. They report strong PIN2 and weak PIN1 expression in the cortex, localized to the apical (i.e. facing the root apex) end of the cells. They also report weak PIN1 expression in the endodermis, localized apically. It should however be noted that there are varying reports on the polarity of PIN2 in the cortex 14,15. We therefore ran model versions with different choices for cortical PIN2 polarity. Surprisingly, model results for the auxin distribution depend only weakly on the localization of PIN2 in the cortex (Tables S3 and S4). The reason is that cortical cells do not express an influx carrier (see Discussion in main text), and so do not accumulate much auxin as compared with the epidermis. The cortical contribution to the net auxin flux is thus relatively weak. A cell with no carrier localized to the plasma membrane is assigned a carrier permeability of zero. For example, the pin2 mutantis modeled using the values in Table S2, with the exception that all PIN2 permeabilities are set equal to zero. Fluorescence immunolabelling shows no AUX1 signal in either the cortex or the endodermis of the Arabidopsis outer root 7,16. We therefore assign zero influx carrier permeability to cells of both the cortex and endodermis. III. Diffusion coefficients Intracellular diffusion coefficient. We do not know of any direct measurements of the cytoplasmic or vacuolar diffusion of IAA (indole-3-acetic acid). Since the vacuole is
mostly water, we expect the vacuolar diffusion coefficient of IAA to be comparable to the known aqueous value, D aq = 0.024 cm 2 /hr 17. In the cytoplasm, comparable small molecules have diffusion coefficients in the range of 10% to 40% of their aqueous value 18. The model used here does not treat the vacuole as a distinct cellular compartment. The proper choice for the diffusion coefficient of IAA inside model cells thus depends on whether IAA can freely enter the central vacuole, and on the fraction of the cell volume occupied by the vacuole. We assume IAA can enter the vacuole (although the carrier family is unknown) 19-21, and so take D = D aq inside model cells. For completeness, however, we have verified that an auxin-impermeable vacuole does not significantly change the model results (data not shown). Apoplastic diffusion coefficient. The permeability of the apoplast to small molecules is not homogeneous, having significant restrictions at Casparian bands, and also possibly within the root meristem 22-24. However, these restrictions are not present in the zone of the Arabidopsis root tip studied here. Following Refs. [ 25 ] and [ 26 ], we take the apoplastic diffusion coefficient of IAA to be 0.1 D aq. IV. Membrane voltage and ph The ph and membrane voltage of plant cells have been thoroughly studied, for examples see Refs. [ 27-29 ]. We use the following representative values: cytoplasm ph c = 7.2, apoplast ph w = 5.3, and cell membrane voltage V = -120 mv (negative inside).
V. Mathematical and numerical methods Our model extends the techniques of Goldsmith et al. 30 and Kramer 31 to the case of a three dimensional array of rectangular cells (see Fig. 2.A). The main difference with the model cells of Ref. [ 31 ] is that we do not include a separate vacuole. To simplify the model, we generally assume the tonoplast is sufficiently permeable to auxin that the cell interior can be treated as a single compartment 19-21. As a check, we do conduct some runs with auxin-impermeable vacuoles and verify that they do not cause significant changes (data not shown). The tissue is divided into a rectangular array of boxes (called "control volumes" in Ref. [ 32 ]). The interior of each cell is a set of (usually 5) contiguous boxes, with the remaining boxes making up the apoplastic space. A nonuniform box size allows us to resolve the 0.5 m thick walls, despite cell lengths up to 400 m. The auxin flux between adjacent boxes within each cell, and between boxes in the apoplastic space, is governed by the discrete approximation to Fick's law for diffusion. J 1 2 = D c 2 c 1 L (1) where J 1->2 is the net flux from box 1 to box 2, c j is the concentration of auxin in box j (including both protonated and anion forms), D is the diffusion coefficient of auxin in the compartment, and L is the center-to-center distance between the boxes. The net flux across the cell membrane is governed by the uniform-field approximation 33. The net flux across any one segment of the cell membrane (i.e. between one cell box and one apoplast box) is J 1 2 = J diff + J PIN + J AUX1, where J diff, J PIN, and J AUX1
are due to the diffusive membrane permeability of the protonated auxin molecule, PIN family carriers, and AUX1 carriers respectively. c J diff = P 2 IAAH 1+10 c 1 ph 2 pk 1+10 ph 1 pk (2) f ( φ)c J PIN = P 2 PIN 1+10 f (φ)c 1 (3) ph 2 + pk 1+10 ph 1 + pk f (φ)c J AUX1 = P 2 AUX1 1+10 f ( φ)c 1 ph 2 + pk 1+10 ph 1 + pk (4) f (x) = x e x 1 (5) where ph and pk have their usual meanings, the P j are membrane permeabilities, and φ = ± FV/RT where V is the membrane potential, F is the Faraday constant, R is the gas constant, T is the temperature, and the + sign is used if box 1 is interior to box 2 (by definition, the cytoplasm is interior to the cell wall). It is instructive to substitute the parameter values into Eqns. (2) through (5) and sum to find an expression for the net auxin influx across a membrane segment J w c = ( 0.24 P IAAH + 3.57 P AUX1 + 0.034 P PIN )c w (6) ( 0.0040 P IAAH + 0.045 P AUX1 + 4.68 P PIN )c c where the subscript w denotes the wall, the subscript c denotes the cytoplasm, and a negative flux would be out of the cell. Note that the influx carrier permeability enters the top line of Eqn. (6) with a prefactor nearly 15 times larger than the diffusive permeability. Thus, although P IAAH and P AUX1 are of the same order of magnitude (see Secs. I and II above), the carrier dominates diffusive influx in all model cells where it is expressed. There is a common misconception that, because protonated auxin is
membrane permeable, influx carriers play only a supplemental role in auxin distribution. A quantitative treatment shows that this is not the case. The flux of auxin between the simulation boxes is described by a coupled set of thousands of differential equations. These differential equations are discretized using an explicit scheme as described in Chapter 4 of Ref. [ 32 ]. The equations are solved using the program AuxSim3D, written by the author and run on a PowerBook G4. VI. Assessing the speed of transport. The speed of auxin transport in the elongation zone is assessed in the following way. Figure S7a shows the auxin concentration in the central elongation zone, 500 m proximal to the source of auxin (see model figure, main text), as a function of time. The initial condition is a root empty of auxin. Starting at time zero, a constant, asymmetric auxin source is applied to the distal apoplast of the model root epidermis. After about 5 min, the auxin concentrations in the CEZ have reached a steady state. There are several ways one might assign a speed to this auxin pulse. Our preferred method is to divide the distance traveled (0.05 cm in this case) by the time it takes the auxin concentration to reach half its steady-state value. For data in Fig. S7a, these times are 0.031 hr along the bottom flank of the root and 0.034 hr on the top flank. These give speeds of 1.60 cm/hr and 1.46 cm/hr respectively.
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Table S1: t-test: Two-Sample Assuming Equal Variances Variable 1 Variable 2 t Critical twotail P(T<=t) two-tail J0951>>axr3 J0951 2.131451 0.017821 J0951>>axr3 Col x C24 2.119905 0.012917 J0951>>axr3 UAS axr3 2.079614 0.012219 J0951>>axr3 Col 2.144789 0.022356 Col x C24 Col 2.085962 0.483661 Col x C24 UAS axr3 2.051829 0.61051 C24 Col x C24 2.093025 8.42E-09 C24 Col 2.100924 9.08E-10 C24 UAS axr3 2.059537 7.24E-09 C24 J0951 2.093025 0.522109 Two sample student s t-test assuming equal variance was performed on 5-7 day old roots in three separate experiments. The null hypothesis here is that the means are equal ( P> 0.05), and the alternative hypothesis is that they are not (P< 0.05). The results presented in this table are representative of the three separate experiments. Table S2 Carrier-mediated permeability values. Tissue layer <P PIN1 > <P PIN2 > (cm/hr) PIN polarity P AUX1 (cm/hr) (cm/hr) epidermis 0.02 0.1 To base 0.2 cortex 0.02 0.1 To apex 0 endodermis 0.02 0 To apex 0 Carrier-mediated permeabilities and PIN polarity used in the model of wildtype elongation zone tissues. Angle brackets indicate a mean over the area of the cell membrane. "To apex" indicates that PIN permeability is highest on the portion of the cell membrane facing the root apex.
Table S3 Variation due to changes in the cortical localization of PIN2. PIN2 polarity in Lateral auxin Fraction of all Fraction of cortex gradient in CEZ auxin in the auxin pulse that (c bottom /c top ) apoplast reaches the CEZ To apex 4.41 0.06 0.54 To base 4.61 0.06 0.58 To epidermis 4.46 0.05 0.66 To endodermis 4.63 0.06 0.49 Changes to the wildtype entries of Table 1 resulting from various choices for the polarity of PIN2 in the model cortex. Top row is the version presented in the main text. Table S4 Cytoplasmic auxin concentrations. Cortical Mean auxin concentration in PIN2 polarity epidermis cortex endodermis To apex 3.43 0.278 0.160 To base 3.38 0.153 0.241 To epidermis 4.24 0.081 0.189 To endodermis 2.87 0.067 0.261 Model results for the partitioning of auxin between the three cell layers of the outer root, given different choices for the polarity of PIN2 in the cortex. Auxin concentrations have arbitrary units.
Swarup et al Fig S1 Col 0 3.0 6.0 J0951>Aux1 0 3.0 6.0 0.5 3.5 6.5 0.5 3.5 6.5 1.0 4.0 7.0 1.0 4.0 7.0 1.5 4.5 7.5 1.5 4.5 7.5 2.0 5.0 8.0 2.0 5.0 8.0 2.5 5.5 24 2.5 5.5 24 Fig. S1 Seedlings were grown vertically for four days on MS plates and the plates were then turned at an angle of 90. Photographs were taken every 30 minute up to 8 hours and then at 24 hours after the change in the direction of the gravity vector. The figure illustrates results from wildtype (Col.) and J0951>AUX1 lines and are representative of data collected for all other lines which is summarised in Fig. 1i.
Swarup et al Fig S2 a Auxin concentration (arb. units) 0.15 0.12 0.09 0.06 0.03 0 0 1 2 3 4 5 t (min) b Auxin concentration (arb. units) 0.15 0.12 0.09 0.06 0.03 0 0 1 2 3 4 5 t (min) Fig. S2 Time-dependence of the epidermal auxin concentration. Cytoplasmic auxin concentration in two epidermal cells located 500 microns proximal to the lateral root cap. The concentrations on lower and upper sides of the roots are depicted in blue and red, respectively. (a) To assess the speed of the auxin pulse, the initial condition was a root with no auxin. (b) To visualize the gravitropic signal, the initial condition was a vertical root (concentrations were equilibrated to a uniform distal auxin source before time zero). An auxin gradient is supplied to the distal epidermal apoplast beginning at time zero.
Swarup et al Fig S3 a b c d e f Fig. S3 Root gravitropism requires AUX1 to be expressed in more than 5 elongating epidermal cells. Comparison of HA-AUX1 localisation in gravitropic (top) vs agravitropic (bottom) aux1 1092 >>Aux1 seedlings. Immunolocalisation was performed with anti HA primary antibody and Alexa Fluor 555 coupled secondary antibody (b & e). Background staining was performed with Sytox Green (a & c). Scale bar 40 m.
Swarup et al Fig S4 120 % root growth compared to control 100 80 60 40 20 0 Col a1-22 axr3 C24 Col x C24 UAS axr3 M0013 M0013>>axr3 J0951 J0951>>axr3 Fig. S4 Disrupting auxin perception in epidermal cells results in increased auxin resistance Seedlings were grown vertically on MS plates for five days and were then transferred on fresh MS, MS + 2,4-D (10-7 M) or MS + IAA plates (2.5 x 10-7 M) for further two days. The delta root growth in presence or absence of auxin was measured and expressed as percent root growth compared to MS control. Error bars represent standard deviation.
Swarup et al Fig S5 J0951 0 3.0 6.0 J0951>>axr3 0 3.0 6.0 0.5 3.5 6.5 0.5 3.5 6.5 1.0 4.0 7.0 1.0 4.0 7.0 1.5 4.5 7.5 1.5 4.5 7.5 2.0 5.0 8.0 2.0 5.0 8.0 2.5 5.5 24 2.5 5.5 24 Fig. S5 Seedlings were grown vertically for four days on MS plates and the plates were then turned at an angle of 90. Photographs were taken every 30 minute up to 8 hours and then at 24 hours after the change in the direction of the gravity vector. The figure illustrates results from wildtype (Col.) and J0951>axr3-1 lines and are representative of data collected for all other lines which is summarised in Fig. 6m.