Fig 1.
Theoretical and simulation results predict that auxin influx carriers facilitate periodic patterning and promote auxin maxima.
(A) Snapshots of simulation results showing periodic distribution of auxin inside and outside cells for higher (left, I = 100 μM s-1) and lower (right, I = 0.001 μM s-1) influx carriers levels along a ring of vascular tissue composed of 60 cells surrounded by the apoplast. Cytosolic (blue) and apoplastic (green) auxin concentrations at time t = 17.5 are shown. The red circular line represents the ring of cells in the tissue. Insets depict the same results projected into a 2D plane. Space is represented in arbitrary units [AU]. Influx and efflux carriers distributions are described in S1 Text. (B) Simulation (boxplot) and theoretical estimation (κ, depicted by solid lines; see S1 Text) results of the inverse value of the number of cells between cytosolic auxin maxima at different influx carriers levels (I). Each boxplot depicts the results for 30 simulations with different initial auxin distributions (Materials and Methods). Simulations were done for rings of 60 cells. The bottom and the top of the boxes represent the first and third quartile, enclosing the 25%-75% data range, the red line within the box stands for the median, and the low and high whiskers enclose the 1.5×(25%-75%) data range. The theoretical estimation is performed through linear stability analysis for a ring of 60 and 1200 cells (black and blue lines, respectively). Theory and simulations show that influx impairment enlarges the periodicity of the pattern, increasing the distance between consecutive auxin maxima. (C) Phase diagram obtained from theoretical linear stability analysis on a ring of 60 cells on the parameters space of amount of influx carriers (I) and apoplastic diffusion coefficient (D). The solid line divides the space in two regions (Methods): in the H region (white, above the solid line) the homogeneous state is linearly stable and no periodic pattern can be formed from small perturbations of it. In the P region (colored, below the solid line) the homogeneous state is linearly unstable and a periodic pattern can arise. The dashed black line corresponds to an analytical approximation to the solid black line (S1 Text, Eq S34). The color scale shows the theoretical estimation of the inverse value of the average number of cells between cytosolic auxin maxima (κ). The horizontal dashed-dotted white line depicts the line along which simulations are presented in panels A and B. For low apoplastic diffusion D, periodic patterning can still occur at low influx parameter values I, while high influx values are necessary for patterning at higher apoplastic diffusion coefficients. Main parameter values: E = 105 μM s-1, D = 2 s-1, Dca = 15 s-1 and auxin threshold for transporters activation θI = θP = 10 μM. Other parameter values can be found in S1 Text.
Fig 2.
Auxin influx carrier quadruple mutants show fewer vascular bundles in the inflorescence stem due to an increased spacing of vascular bundles and to a decreased number of cells in the provascular ring.
(A) WT 14-week-old plant (left) and aux1lax1lax2lax3 quadruple mutant 14-week-old plant. (B) Basal shoot cross section of WT shoot inflorescence stem. (C) Basal shoot cross section of aux1lax1lax2lax3 quadruple mutant shoot inflorescence stem. (D-F) Boxplots of VB number (D), vascular unit size (E), and total cell number across the provascular ring (F) for WT and aux1lax1lax2lax3 mutant vascular rings. For the total cell number quantification along the shoot stem section, the ring of cells formed by the interfascicular fiber cells and the procambial cells within the vascular bundle were taken into account. The vascular unit size measures the spacing of VBs position and was defined as the number of procambial cells along the ring within a VB plus the number of interfascicular fiber cells up to the next VB in this ring. Note that the vascular unit size is enlarged in influx mutant plants, being consistent with the theoretical predictions shown in Fig 1. (G) Percentage of expected contribution of VB spacing (red) and total cell number (blue) to the change in VB number in the aux1lax1lax2lax3 mutant, computed by using Eq 2. All plants were grown under short day conditions. In panels D-G, n = 24 for Col-0 and n = 18 for quadruple mutant plants. Scale bars: 250 μm. *: p-value≤ 0.01; ***: p-value≤ 0.0001.
Fig 3.
Influx carrier mutants show impaired xylem differentiation in Arabidopsis shoot stem.
(A-B) VB magnification of a shoot basal cross section for WT (A, C and E) and aux1lax1lax2lax3 quadruple mutant (B, D and F) 14-weeks old plants grown in short day conditions. Light blue dots indicate undifferentiated cell layers in procambium tissue between phloem and xylem differentiated cells. First differentiated xylem cell is indicated by white arrow. The undifferentiated cell layers comprise both the procambial cells and the meristematic xylem cells (round cells with undifferentiated walls between the procambium and the xylem). Note that above the procambial cells appear some undifferentiated cells with different shape than the procambial cells. This round shape is more characteristic from xylem cells while the cell walls are not differentiated. Therefore, we quantify them as undifferentiated cells, which can comprise both, procambial and meristematic xylem cells. White squares highlight interfascicular fiber cells. Scale bar: 100 μm. (G) Frequency distribution of the number of undifferentiated cell layers, for WT and aux1lax1lax2lax3 mutants (n = 24 VB).
Fig 4.
Vascular pattern and xylem differentiation phenotypes in long day and short day conditions for influx aux1lax1lax2lax3 and efflux pin1pin2 mutants.
Basal shoot cross section of aux1lax1lax2lax3 (A, D), WT (B, E) and pin1pin2 (C, F) plants grown in long day conditions (A-C) and in short day conditions (D-E). WT and the aux1lax1lax2lax3 plants grown in long day conditions showed no statistical significant differences in number of VBs, total cell number, nor average vascular unit size (S11 Fig, n = 18 for WT, n = 15 for aux1lax1lax2lax3). Scale bars: 500μm. VB detail of aux1lax1lax2lax3 (G, J), WT (H, K) and pin1pin2 (I, L) shoot inflorescence stem grown in long day conditions (G-I) and in short day conditions (J-L). Light blue dots indicate undifferentiated cell layers in procambium tissue between phloem and xylem differentiated cells. First differentiated xylem cell is indicated by white arrow. White brackets highlight the interfascicular fiber cells (if). Black brackets highlight the xylem cells (xy). Scale bars: 200 μm. Frequency distribution of the number of undifferentiated cell layers in long day conditions for the three genotypes is shown in S11 Fig.
Fig 5.
Modeling shows that influx carriers diminish differences in the concentration of auxin in the apoplast.
(A) Snapshots of simulation results showing periodic distribution of auxin inside and outside cells for higher (left, I = 100 μM s-1) and lower (right, I = 0.001 μM s-1) influx carriers levels along a ring of vascular tissue composed of 30 cells surrounded by the apoplast. Cytosolic (blue) and apoplastic (green) auxin concentrations at time t = 17.5 are shown. The red circular line represents the ring of cells in the tissue. Insets depict the same results projected into a 2D plane. Space is represented in arbitrary units [AU]. The number of auxin maxima is the same in both cases. (B-E, F-I) Simulation results showing the number of cytosolic auxin maxima over the total number of cells (B,F), the amplitude of the pattern of auxin (C,G), the averaged auxin maxima levels (D,H) and the averaged auxin values along the vascular ring (E,I) in the cytosol (top panels, blue boxplots) and in the apoplast (bottom panels, green boxplots) as a function of the amount of influx carriers I (B-E) and of efflux carriers E (F-I). Each boxplot depicts the results for 30 simulations with different initial auxin distributions (Methods). Simulations in B-I were done for rings of 60 cells until time t = 17.5. Depicted boxplot components are the same as in Fig 1B. Other details of panels (B, F) are the same as in Fig 1B. Vertical line in (F) indicates the critical parameter value (in this case, the efflux carriers levels E) above which the pattern can not emerge, derived from linear stability analysis. Dotted lines in (E,I) panels correspond to the theoretical auxin homogeneous steady states given by Eqs S9 and S35. See Materials and Methods and S13 Fig for more details on the computation of the amplitude and average levels. All parameter values as in Fig 1 except for passive influx Dca = 50 s-1. E = 105 μM s-1 for A-E panels, while I = 100 μM s-1 for F-I panels.
Fig 6.
A model of apoplastic and cytoplasmic auxin control of xylem differentiation.
(A) Auxin cytoplasmic signaling is required for xylem differentiation [16,46,57–59]. Our computational analysis predicts apoplastic (extracellular) auxin as an inhibitor of this differentiation. Both efflux and influx carriers increase cytoplasmic auxin concentration at auxin maxima, while they antagonistically regulate apoplastic auxin concentration. Arrows stand for activation, while blunt arrows for inhibition. (B) Cytoplasmic (blue) and apoplastic (green) auxin concentrations in two cells (rectangles with rounded corners). Lighter blue and green account for decreased cytoplasmic and apoplastic concentrations respectively. The predicted differentiation phenotypes of WT, influx and efflux mutants are depicted on the right. Xylem differentiated cells are depicted with blue borders.