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Band et al., (2010). Root gravitropism is regulated by a transient lateral auxin gradient controlled by a tipping-point mechanism.

January 2013, model of the month by Vladimir Kiselev
Original model: BIOMD0000000413, BIOMD0000000414

By definition, gravitropism is a turning or growth movement by a plant or fungus in response to gravity. Gravitropism in plants had become an object of significant attention already in the beginning of the 19th century. One of the first mentions of it was by Thomas Andrew Knight: “... whatever position a seed is placed to germinate, its radicle invariably makes an effort to descend towards the center of the earth ...” [1]. The basic understanding of the mechanism of gravitropism appeared later following a large amount of experimental observations. Charles Darwin in his distinguished work on the power of movements in plants [2] concluded: “... it is the tip alone which is acted on, and that this part transmits some influence to the adjoining parts, causing them to curve downwards ...”. However, the first complete model of gravitropism was independently proposed by Nikolai Cholodny (in 1927) and by Frits Warmolt Went (in 1928), both based on their experimental observations [3]. The main innovation in their experiments was the detection of hormone Auxin in plants. It was shown for the very first time that: 1) plants had altering concentration of Auxin in their roots (stems); 2) rate of the root (stem) growth depended on the concentration of Auxin; 3) Auxin redistribution was due to both gravity and unidirectional light. Even though the Cholodny-Went model was a groundbreaking element in the study of gravitropism, the action of Auxin on molecular level has not been properly described until recently.

Figure 2

Figure 3 A model for the control of root elongation and growth in a direction defined by the gravity vector. (a) Auxin (IAA) is transported down to the root tip. Here it is redistributed to the root cortex and epidermis, and transported back up the root to the elongation zone, where it regulates the rate of cell elongation. (b) If the root is oriented orthogonal to the gravity vector (gravity stimulus), then the direction of the gravity vector can be detected by the sedimentation of statoliths in cells in the root cap. This, in turn, could lead to the asymmetric redistribution of Auxin to the lower side of the root, where elongation is inhibited and the root consequently bends down in the direction of the gravity vector. Figure taken from [5].

In the paper of Band et al.[6], Aux/IAA-based reporter (DII-VENUS) is used in conjunction with a mathematical model (BIOMD0000000413) to quantify Auxin redistribution following a gravity stimulus.

DII-VENUS reporter was composed of a constitutively expressed fusion of the Auxin-binding domain (DII) of Aux/IAA protein to a fast-maturating variant of yellow fluorescent protein (YFP) VENUS. Since Auxin triggers a degradation of the reporter, DII-VENUS can be directly related to endogenous Auxin levels.

Firstly, the degradation of DII-VENUS was quantified by its exposition to a range of concentrations of exogenous Auxin. Reduction of the reporter concentration was measured based on the YFP signal. Time series of DII-VENUS degradation show a clear relationship between Auxin abundance and reporter signal (Figure 3).

Figure 4

Figure 4 Schematic model of the network of interactions that relate the DII-VENUS reporter to Auxin. Figure taken from [6].

The model was then used to determine the Auxin redistribution dynamics upon a gravity stimulus. The total flux of Auxin in the root was assumed to be constant (was shown experimentally) and various piecewise linear profiles of Auxin redistribution (Figure 5) were tested by comparison with experimental results (Figure 6).

The best fit between the model and experimental data shown in Figure 6 was observed when Auxin redistribution profile had a form represented on Figure 7.

Figure 7 Figure 8

Figure 7 Dynamic changes in Auxin distribution between upper and lower root tissues following a gravity stimulus, corresponding to the best fit of the model to the experimental data. Figure taken from [6].

Figure 8 Experimental data showing the rate at which root tips reorientate after a gravitropic stimulus. Roots were grown vertically and then rotated through 90 degrees at t = 0. Figure taken from [6].

Figure 1

Figure 1 There are four distinct layers of regulation in Auxin-mediated gene expression (steps 1–4). Members of the Auxin response factor (ARF) family are transcription factors that bind to Auxin-responsive elements (AREs) in the promoters of primary Auxin-responsive genes, mediating their transcription (step 1). Aux/IAAs are early Auxin-response proteins that bind ARFs, thereby inhibiting ARE-mediated gene transcription (step 2). Aux/IAAs are targets of 26S proteasome-mediated degradation, and this degradation is directed by the ubiquitylation (Ub) of Aux/IAAs (step 3). Ubiquitin-mediated proteolysis of Aux/IAA is stimulated by the binding of Auxin to the F-box protein TIR1 (step 4). Figure taken from [4].

Nowadays, the main Auxin function on molecular level is thought to be the regulation of transcription of genes containing Auxin responsive elements (ARE) [4]. Auxin acts by promoting an interaction between its receptors, TIR1-containing proteins, and Aux/IAA repressor proteins resulting in their ubiquitination and degradation (Figure 1). As a result transcription of genes containing ARE is not inhibited through binding of Aux/IAA proteins to ARFs (Auxin response factors). In contrast, at lower Auxin concentrations, Aux/IAA repressor proteins are not degraded and can inhibit expression of genes containing ARE by interaction with ARFs (Auxin response factors) [Figure 1].

Upon a gravity stimulus Auxin redistribution occur at an apex of the root, providing higher flux of Auxin in the root bottom part. Higher Auxin concentrations result in higher expression of genes containing ARE, slowing down the growth and the elongation of the cells. Due to the cell size asymmetry in the top and in the bottom part of the root, it begins to bend downwards [Figure 2].

Figure 3

Figure 3 Quantification of the dose- and time-dependent degradation of the DII-VENUS signal by exogenous Auxin concentrations; solid lines show the fitted model results. Figure taken from [6].

Secondly, a mathematical model was constructed, which was used to obtain more insights into the Auxin functionality (Figure 4). The set of parameters in the model was calibrated using DII-VENUS degradation data (Figure 3).

Initial model consisted of four differential equations [BIOMD0000000413]. However, making a quasi-steady state assumptions, the model was reduced to one differential equation BIOMD0000000414. The simplified model fitted the DII-VENUS degradation curves well.

Figure 5 Figure 6

Figure 5 An example of the Auxin influx to lower and upper sides of the root. The temporal variations in the Auxin influx is chosen to be piecewise linear. Figure taken from [6].

Figure 6 The fold change in DII-VENUS ratio (upper/lower tissue signals) plotted against time following a gravitropic stimulus. Black crosses show experimental data points, and lines show the fitted simulation results: Red, blue, and green lines are, respectively, the signal from the lower side, the signal from the upper side, and the ratio.Figure taken from [6].

Figure 7 shows that Auxin redistributes within 5 minutes of the gravity stimulus. In contrast, root bending occurs in ~10-20 minutes after the stimulus. These results are in agreement with the general concept of Auxin functionality: Auxin is the main regulator of the root curvature.

The time point when the Auxin influx returns to equal levels (~100 minutes), correspond to bending angle of the root tip of ~40° (Figure 8). This postulates that roots may use a “tipping point” mechanism that reverses asymmetric Auxin flow at the midpoint (~40°) of root bending. The phase after the midpoint is driven by newly synthesized downstream targets of Auxin response machinery.

This work shows how DII-VENUS reporter, in conjunction with a mathematical model, can efficiently provide kinetic information about Auxin redistribution upon a gravity stimulus.

Bibliographic references

  1. Knight TA. On the direction of the radicle and germen during the vegetation of seeds. Philosophical Transactions of the Royal Society of London. 1806; 96, 99–108.
  2. Darwin C and Darwin FE. The Power of Movements in Plants London: John Murray. 1880.
  3. Chen et al. Gravitropism in Higher Plants. Plant Physiology. 1999, 120(2):343-350
  4. Teale et al. Auxin in action: signalling, transport and the control of plant growth and development. Nature Reviews. Molecular Cell Biology. 2006, 7(11):847-859
  5. Leyser, O. Plant hormones: Ins and outs of auxin transport. Current Biology : CB. 1999, 9(1):R8-R10
  6. Band et al. Root gravitropism is regulated by a transient lateral auxin gradient controlled by a tipping-point mechanism. Proceedings of the National Academy of Sciences. 2012, 109(12):4668-4673