Adequate production of the plant hormone auxin or indole-3-acetic acid (IAA) from genetically modified (GM) Escherichia coli could efficiently promote plant root growth. However, IAA is toxic to plants if its concentration is too high. Therefore it is important to predict the IAA expression level with a certain promoter, and then adjust the promoter strength to ensure the IAA produced by our E.coli will optimally increase root growth.

IAA increases root growth in terms of root length and number of branches. In order to study how different concentrations of IAA effect root growth patterns, modelling tools were combined with wet lab results to predict and visualise Arabidopsis root growth.

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2.1 Objective

Determine the IAA expression level of a single E. coli cell with IAA promoter strength 4.536 RNA/min/μg substrate DNA, and then predict the number of bacteria to be placed in the seed coat to induce optimal root growth.

2.2 Description

The genetically engineered IAA pathway involves two genes, IaaM and IaaH, both of which are constitutively expressed. The IaaM gene encodes tryptophan-2-monooxygenase (T-2-monase) that catalyses the conversion of tryptophan (Trp) to indole-3-acetamide (IAM), which is then hydrolysed to release indole-3-acetic acid (IAA) by the hydrolase iaaH [3]. At the same time, the synthesised IAM and IAA will competitively inhibit the enzyme activity of tryptophan-2-monooxygenase, thereby inducing a negative feedback loop on the expression of IAA. The enzymatic reactions involved in the pathway are illustrated in Figure 1 below.

Figure 1 [1]: IAA synthesis pathway

In addition, based on research carried out at the University of Colorado [4], tryptophan is also negatively controlled inside bacteria. Therefore the tryptophan synthesis pathway should be integrated into the above model. Furthermore, in order to reduce the numbers of parameters, as most of the parameters in Figure 1 are not available to us, the IAA pathway is then simplified into two Michaelis Menten equations, which are combined with the tryptophan pathway and constitutive gene expression for T-2-monase and iaaH. The whole tryptophan IAA pathway model is described in Equation 1 [5], and the parameters are defined in the parameters section below.

In this model, we made the following assumptions:

(1) We neglect the short time delay due to synthesis of Trp-T-2-monase (substrate-enzyme (ES) complex), IAM-iaaH (ES complex), IAM-T-2-monase (inhibitor-enzyme (EI) complex) and IAA- T-2-monase (inhibitor-enzyme (EI) complex) and assume that these species reach their equilibrium almost instantaneously.

(2) The degradation rate of IAA is extremely low (7 days according to the experiments) compared to bacterial growth rate. Therefore we used bacterial growth rate as the IAA degradation rate in this model.

(3) During the modelling of the IAA pathway, we found that the rate-determining species for IAA synthesis is IAM, not the enzyme iaaH, since the production of IAM is inhibited by itself and IAA.

2.3 Result and discussion

Figure 2 below represents the output of our model. It shows how the concentration of each protein species varies with time. It shows the simulation of the enzymatic reaction for each of the species, with initial concentrations of O_F = 1.54×10^-4 µM, M_F = 3.78×10^-4 µM , E = 0.378 µM, Trp = 4.1 µM and all others = 0 [4].

Figure 2(a): The evolution of IAM vs. time. Figure 2(b): The evolution of IAA vs. time Figure 2(b) shows IAA expression level is 72.35 µM, therefore each bacterium produces 7.24×10^-14 µmole at steady state with bacterial cell volume equal to 10^-15 dm³. From wet lab experiments) we know that the optimal concentration of IAA to promote root growth is 0.1 nM, and the volume of Arabidopsis seed with seed coat approximately equals 4.2×10^-9 m³ [7]. Therefore the number of bacteria required to be present in the root to maximally increase root growth of roots is 5 under optimal bacterial growth conditions. .

In conclusion, we obtained the concentration of IAA produced by the IAA DNA construct (72.25 μM). From this value, we calculated the number of bacteria that would need to enter the root under ideal growth conditions and ignoring death and division of bacteria, which was found to be 5 bacteria for Arabidopsis. This value varies due to the variation in seed size of different of plants. Since bacterial cells can be lost from the plant and not all the bacteria from the seed coat will enter the plant, the number of bacteria required in the seed coat will be higher than this. Furthermore, the modelling of root growth in the next part helped us visualise the root growth.

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3.1 Objective

1. Create a graphic program to demonstrate the growing process of the Arabidopsis root system, based on the principles of Lindenmayer system and plant physiology.

2. Use Matlab data fitting tools to develope relations between IAA concentration and growth rate and number of branches.

3.2 Description

We used computational tools to visulise the root growth phenomena (primary rootlength, branching, root density, etc) in different enviromental conditions, and specifically considered root order and root length. Root order describes the branching “generation” of a root system; a root without branching is defined as a zero-order root. Root growth depends on environmental factors, such as gravitation and soil heterogeneities.

3.2.1 Tropisms

A root system starts with a single root tip of a zero-order root. Then the root grows away from the plant stem in a conical way.[10]

Root growth depends on environmental factors, such as gravitation and soil heterogeneities. Therefore, two more variables are defined to describe the plant adaptation:[10]

σ:-

- how strong the roots direction changes per 1 cm growth

- a larger value indicates a more deflected root and a more twisted root system

N:-

- the number of trials for the roots to find the optimal angles α and β for the rotation

for the downward movement

- N can be any real number, if N = 1.5, if means that N can be either 1 or 2.

Figure 3: The difference of the root systems with different values of N and σ

3.2.2 Lindenmayer system and root growth modelling

An L-system is a parallel rewriting system, namely a variant of a formal grammar, most famously used to model the growth processes of plant development, but also able to model the morphology of a variety of organisms, due to the two main properties: recursiveness and self-similarity [11]. Plant models and natural-looking organic forms are easy to define, as by increasing the recursion level the form slowly 'grows' and becomes more complex.

Using L-systems for generating graphical images requires that the symbols in the model refer to elements of a drawing on the computer screen. It interprets each constant in an L-system model as a turtle command.

3.2.3 Root Growth

The modelling of IAA uptake can give predictive answers to questions such as these:

"What is the primary root growth rate?"

"What does the root system look like after a certain period of time?"

"How does Arabidopsis respond to different IAA concentrations?"

We modified a MATLAB program developed by Daniel Leither's research group [6] to demonstrate the 3D root system based on the principles of Lindenmayer system (turtle commands) and the root growth modelling toolbox developed by Daniel Leitner et al from BOKU (Universität für Bodenkultur Wien, University of Natural Resources and Life Sciences, Vienna).[12]

3.2.4 Data fitting

We took growth rate parameters from the literature and analysed the raw data from our wet lab to give more accurate and suitable parameters for our project. Arabidopsis plants were planted and root length and number of branches recorded every three days from day 0 to day 9. Root length, daily root growth rate and number of branches were plotted against time and IAA concentration.

3.3 Result and Discussion

3.3.1 Visualisation of a root system

The values from the literature give the relationship between external IAA concentration and elongation of the roots as 5*10^-5 mol/L → 200 µm elongation in 30 min. The modelling parameter of growth speed is therefore 9.6*10^-3 m/day.[9]

We observed real roots grow patterns and modified our simulation to give a more reliable and accurate prediction of root growth. Arabidopsis has a primary root with zeroth order and it is thicker than the branches. Arabidopsis normally grows to the depth of 20-30 cm inside the soil and branches only once. The 3D picture shown below predicts the root growth with different elongation rate (with IAA = 0.96 cm/day; without IAA = 0.46 cm/day [10]). They can be compared with the photo of a real root system.

Figure 4: 3D visalisation of the arabidopsis root system. The graph Figure 4(a)(b) shows the demonstration of the Arabidopsis root system in different IAA concentration conditions with a growth time of 20 days as our simulation results. Figure 4(c)(d) are the actual photos of real Arabidopsis plants taken from the literature and our wet lab.

Figure 5: The graphic analysis of the 3D root system. By taking cross and longitudinal sections of the root system at different positions, Figure 5(a) is the root length distribution (by fraction) against the root depth.Figure 5(c) is the surface area distribution map. This graph will give the guidance of placing GM E. coli inside the soil. E. coli should be placed at the depth with the maximal root surface area (6 cm) inside the soil for the maximal uptake efficiency.

The root has a growth rate of 0.96 cm/day with the external IAA concentration 5x10^-5 mol/L, however, this data is selected from the literature. To get an accurate growth rate which is particularly fitting our project, we decided to do data fitting analysis to the Arabidopsis we plant.

3.3.2 Data fitting

The data fitting plots are analysed to give an approximation of the relationship between IAA concentration and root growth. The following graph gives an example of root length against time. [8]

Figure 6: Root growth speed decays over time. This graph gives a prediction of the root growth speed (cm/day) for 20 days. The exponential decay constant is 0.048.

Figure 7: Primary root length (mm) vs. time (day) and external IAA concentration (mol/L). The data fitting result gives this plot of the Arabidopsis primary root length. The length increases as the growth time increases, and reaches a maximal depth when the IAA concentration is approximately 1 pM.

Figure 8: Primary root growth rate (mm/day) vs. root growth time (day) We used the data fitting toolbox of Matlab to obtain this figure. The relationship between the growth rate and the IAA concentration can be approximated by a Gaussian equation. The abnormality of the 0.1 nM curve is due to two contaminated samples which stopped growing at 7 mm after day 5. Figure 8 is consistent with the prediction of the decay of the root growth speed given by Figure 6.

Figure 9: Number of lateral branches vs. external IAA (log) concentration. The optimal concentration for lateral root branching = 1 uM-10 nM, at this concentration, the Arabidopsis root gained the most lateral branches.

The result of the data fitting does not coincide with our latest wet lab experimental results, since the optimal external concentration for Arabidopsis is found to be 0.1 nM. The failure of the previous experiment is analysed and gives the guidance for the new experiments in the following ways:

1. Instead of measuring the primary root length and number of lateral branches of Arabidopsis, the growth rate should be tested by measuring the dry mass of the roots.

2. At the early stage of planting, the number of lateral branches is very small, therefore massive percentage errors and standard derivation are produced.

3. Huge error is also introduced by the dilution process of the IAA solution to reach a low concentration level of 10^-13 mol/L.

4. The wet lab result shows that the IAA concentration in phytogel media is negligible after 9 days, the degradation of IAA in an important factor when the root growth is modelled.

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* Link to the Registry Page:

http://partsregistry.org/Main_Page

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[1] Hutcheson SW, Kosuge T (1985) Regulation of 3-indole acetic acid production in Pseudomonas syringae pv savastanoi: Purification and properties of tryptophan 2-monooxygenase. The Journal of Biological Chemistry 260(10): 6281-6287.

[2] Saepen S, Vanderleyden J, Remans R (2007) Indole-3-acetic acid in microbial and microorganism-plant signaling. FEMS Microbiology Reviews 31(4) 425-448.

[3] Cheng Y, Dai C, Zhao Y (2006), Auxin biosynthesis by the YUCCA flavin monooxygenases controls the formation of floral organs and vascular tissues in Arabidopsis. Genes & Dev 1790-199. Doi: 10.1101/gad.1415106

[4] http://mathbio.colorado.edu/mediawiki/index.php/MBW:Modelling_the_Tryptophan_Operon

[5] Santillan M, Mackey MC (2001) Dynamic regulation of the tryptophan operon: a modeling study and comparison with experimental data. PNAS 98(4) 1364-1369.

[6] http://www.ccdb.ualberta.ca/CCDB/cgi-bin/STAT_NEW.cgi

[7] http://www.seedgenes.org/Tutorial.html

[8] Leitner D, Klepsch S, Bodner G, Schnepf A (2009) A dynamic root system growth model based on L-Systems: tropisms and coupling to nutrient uptake from soil. Plant and Soil 332(1-2): 177-192.

[9] Rayle DL, Evans ML, Hertel L (1970) Action of auxin on cell elongation. Proc Nat Acd Sci USA 65(1): 184-191.

[10] Beemster GTS, Baskin TI (1998) Analysis of cell division and elongation underlying the developmental acceleration of root growth in Arabidopsis thaliana. Plant Physiology 116(4): 1515-1526.

[11] Hu H, Cao X, Lin B (2003) Three dimensional Lindenmayer system. The Journal of Engineering Graphics

[12] Leitner D, Schnepf A, Klepsch S, Roose T (2009) Comparison of nutrient uptake between 3-dimensional simulation and an averaged root system model. Plant Biosystems 144(2): 443-447.

[13]Brenda: The Comprehensive Enzyme Information System (http://www.brenda-enzymes.org/)

[14] http://www.jbs.org/content/246/22/6956.full.pdf

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