Team:Imperial College London/Project/Auxin/Overview

From 2011.igem.org

(Difference between revisions)

Revision as of 14:24, 30 August 2011

Human Practices

Specifications

The IAM pathway taken for this module is from Pseudomonas savastanoi. This strain of soil dwelling bacteria is a known plant pathogen that uses IAA to infect its target. However, there have been some recent studies that suggest that IAA secretion by bacteria can also lead to positive microbe-plant relations [1]. Therefore, we must carefully analyze what IAA concentration would aid root growth rather than promote gall formation. To achieve this, we will be experimenting with different levels of synthetic auxin on Arabidopsis thaliana. We will also be modelling this module in order to obtain the adequate concentration of IAA excretion from the chassis.

Design

IaaM and IaaH have been codon optimized for both Bacillus subtilis and E. coli through the use of our own codon optimizing software. Also, the genes have been placed under the pVEG promoter which works in B. subtilis and E. coli and we calculated the RBS efficiency for both E. coli and B. subtilis. Furthermore, insulator sequences have been placed in front of the ribosome binding sites so that the genes could be placed under different promoters depending on desired output in different species.

Modelling

Auxin synthesis pathway

The production of auxin by bacteria(E.Coli and/or B.Subtilis) is one main module in our project. In order to choose the appropriate RNA promoter with the optimal strength, the auxin production amount is modelled base on the pathway via the intermediate IAM from the precusor tryptophan.

The result of modelling answers the question: " How much auxin can be produced by the genetically modified bacteria with a typical RNA promoter strength? "

the pathway has two steps:[1]

tryptophan-IAM(IaaM gene - tryptophan-2-monooxygenase)-IAM-IAA (IaaH gene-IAM hydrolase)

A feedback inhibition mechanism exists in the pathway, the production of IAM and IAA inhibits the function of tryptophan-2-monooxygenase, therefore stops the reaction chain

competitive inhibition

E + S ↔ ES → E + P

E + I ↔ EI

the reaction kinetics fits the Michaelis-Menten kinetics model perfectly

a set of ODEs can be used to model the reaction process:

parameters required: k1,k-1,k3,k-3

The rate constants of the reactions inside the pathway are required. All the parameters of the two enzymes involved in this pathway, tryptophan-2-monooxygenase and IAM hydrolase, can be found at the enzyme database Brenda. [2]

Initial a root system

To visualise our modelling result, a root system is demonstrated to show the root growth phenomena(primary root length, branching, root density, etc) in different environmental conditions(external and internal auxin concentration).

Root order:-

Root order describes the branching “generation” of a root system, a root without branching is defined as a zero-order root

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.[3]

initial number of root = n₀

initial cone base radius = r₀

axial insertion angle = α

radial insertion angle = β

To ensure a even distribution of the roots, α and β must be set in the following way:

Tropisms

Root growth depends on the environmental factors, such as gravitation, soil heterogeneities, etc.

Therefore, two more variables are defined to describe the plant adaptation:

α:-

how strong the roots direction changes per 1cm growth ?

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.

the difference of the root systems with different values of N and σ can be shown

Lindenmayer system and root growth modeling

The properties of L-system provides the basic graphic principles to "draw" a root system.

The method to model root growth is to create a root system using Matlab.

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.[4]

-recursive nature

-self-similarity

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.

L-systems are now commonly known as parametric L systems, defined as a tuple.

G = (V, ω, P)

V = a set of symbols containing elements that can be replaced (variables)

ω (start, axiom or initiator) = a string of symbols defining the initial state of the system

P = a set of production rules defining the way variables can be replaced with combinations of constants and other variables.

A production consists of two strings, the predecessor and the successor.

For any symbol A in V which does not appear on the left hand side of a production in P,the identity production A → A is assumed. These symbols are called constants or terminals.

An L-system is context-free if each production rule refers only to an individual symbol and not to its neighbors. Context-free L-systems are thus specified by either a prefix grammar, or a regular grammar.

If there is exactly one production for each symbol, then the L-system is said to be deterministic (a deterministic context-free L-system is popularly called a D0L-system).

If there are several, and each is chosen with a certain probability during each iteration, then it is a stochastic L-system.

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.

Auxin uptake

The modelling of auxin uptake will give prediction of the root system development in the following ways:-

"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 auxin concentration?"

... ...

The auxin distributed in the soil enters the plant mainly by diffusion, if the convection process is neglected, then the diffusion can by described using the following equations (Barber 1995)

θ = volumetric water content of the soil = 0.4

b = buffer power = 100

c = auxin concentration

D₁ = diffusion coefficient of auxin

f = impedance factor = 0.3

s = root surface area per unit volume

F_m = maximal influx = 2.5*10^-7µmol/cm²/s

K_m = Michaelis-Menten constant = 4*10^-4µmol*cm³

t_age = average root surface age

k = decay factor of auxin uptake

An anxin distribution map can be drawn from the equation above.

The values from literature gives the relationship between external auxin concentration and elongation of the roots:-

5*10^-5mol/L → 200 µm elongation in 30 mins

The modelling parameter of growth speed is therefore 9.6*10^-3 m/day

use L-system and turtle command, a zeroth-order root system is demonstrated

As you can see, this demonstration has a more generalised root shape. Arabidopsis, which does not grow in this way,is used in our project. By observing the real roots grow from the plant, the demonstration is modified to give a more reliable and accurate prediction of the root growth. Arabidopsis has a primary root with zeroth order and it is thicker than the branches. Arabidopsis normally grows to the depth of 20~30cm inside the soil and branches once only. The 3D picture shown below predicts the root growth with different elongation rate(with auxin = 0.46cm/day; without auxin = 0.96cm/day). They can be compared with the photo of real root system.

The root has a growth rate of 0.96cm/day with the external auxin concentration 5x10-5mol/L, however, this data is selected from 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.

data fitting:-

When the arabidopsis samples are planted, we record the root length and number of branches every day from day 0 to day 20.Then, root length, root growth rate and number of branches are plotted against time and auxin concentration. These three curves are analysed to give the best mathematical equation to describe it, This can be an approximation of the relationship between auxin concentration and root growth. The following graph gives an example of root length against time.

Fabrication

We wish to build a single expression plasmid that can express IaaH and IaaM. While this task can be summarised in one sentence its execution is not as short. The first problem lies in the size of these two enzymes which both exceed 1kbp making their synthesis a problem. We therefore created a new standard for biobrick assembly to tackle this issue. We broke up these large sequences into four fragments that were ordered at the end of week 3. In preparation for the arrival of these fragments (circa 8-10 days) we started to transform our cells with the pVEg+pSB1C3 backbone constructs in order to make enough genetic material for a gibson assembly reaction. This chapter will describe our struggles and successes throughout this grueling and yet rewarding process.

29th of July

Our first transformations were a success! We have managed to transform our competent cell colonies with pSB1C3 containing BBa_K398500 and J23100 promoter to produce cell line 6. We also transformed the cells with part BBa_K316001 to produce cell line 7 and part BBa_K316005 to produce cell line 8. With these cell lines we will be able to make more copies of each part in preparation for the arrival of our synthesized sequences. We are under a tight schedule so efficiency is key.

Also, the cell line with the superfolded GFP integrated in its genome has been plated successfully. We have confirmed that these are the correct cell lines by looking at them under UV light. Their green glow was brighter than we expected.

However, cell line 1 did not grow in the liquid broth media at the same concentration of kanamycin. We will create an assay to ascertain the optimum kanamycin concentration. This is both a bizarre and unexpected result that must be rectified.

30th of July

The previous day, we had obtained the mcpS gene in a pRK415 plasmid from Spain. We then performed a transformation on the competent 5α cell line and obtained the results on this day. Out of the four plates one of them contained transformed cells. We named these cells 10.

1st of August

A month has already passed since we started our project. The experiments that were conducted on this day were a mini-prep on samples 6,7,8 and 10 that were inoculated into an LB broth culture the night before. We used a mini-prep kit to obtain the plasmid DNA that we wanted from the transformed cells. Then, once we obtained the DNA, we started a restriction digest using PstI and EcoRI for 1.5 hours to confirm that the samples from the mini-prep contained the DNA that we wanted (the pSB1C3 backbone with the appropriate promoters).

Sadly, once we tried to visualize the results on a gel, the results were less than satisfactory. Mini-prep 6a and 7b seems to have failed and the rest of the bands do not make much sense. The experiment had to be repeated.

2nd of August

Today we attempted the restriction digest again and the results verified that samples 6,7 and 8 were actually pSB1C3 constructs with the required components. Therefore, the mini-prep experiment had worked and did not need to be repeated. It is a great feeling when everything comes together.

Gel 1&2. Restriction digest of three backbone vectors with EcoRI(E) and PstI(P) to confirm backbone length. Gel1: Lane1-1 kb DNA ladder Lane 2-6a cut with E;Lane 3-6a cut with P; Lane 4-6a cut with E+P;Lane 6-6b cut with E; Lane 7- 6b cut with P; Lane 8- 6b cut with E+P; Lane 11- 7a cut with E; Lane 12- 7a cut with P; Lane 13- 7a cut with E+P; Lane 15- 7b cut with E; Lane 16- 7b cut with P; Lane 17- 7b cut with E+P. Gel 2: Lane 1 - 1kb ladder; lane 2 - 8a cut with E; lane 3- 8a cut with P; lane 4- 8a cut with E+P; lane 6- 8b cut with E; lane 7- 8b cut with P; lane 8 - 8b cut with E+P.

3rd of August

Today we attempted to PCR samples 6, 7 and 8. The PCR did not end up working so well so. The annealing temperature must have been too low because we obtained bands that we did not want. Also, there must have been too little Sybr safe in the gel because the bands that were there were not bright. The PCR will be repeated once again and we will use a temperature gradient for (hopefully) better results.

4th of August

Today we redid the PCR of samples 6, 7, and 8 but with a temperature gradient to improve primer annealing.... and it was a success! So tomorrow we can run the rest of the Dpn1 digested DNA on a gel and gel purify it, then the vectors are ready to be used for DNA assembly once our genes arrive!

Gels 3&4: Temperature gradient PCR of desired backbone with promoter and terminator out of plasmids. Gel 3:Lane 1- 1kb DNA ladder; lanes 2 to 7 - PCR of vector 6 from 57.1°C to 62.6°C; lanes 9 to 15 - PCR of vector 7 from 57.1°C to 62.6°C. Gel 4: lanes 2 to 7 - PCR of vector 8 from 57.1°C to 62.6°C

The backbone sequences have also returned. All of the samples are in order except a one base pair mutation in sample 8 within the pVEg promoter. For now, we are going to amplify it anyways in the hope that the one base pair mutation is just an error that occured during sequencing. Either way, sample 8 is a back-up of sample 7 so there should be no problems either way.

We also started experimenting with the Salkowski reagent. In particular, we tested the S2/1 method and found that the ideal wavelength for measuring the IAA concentration with our apparatus is at 554nm. This was done by scanning between 500nm and 600nm to obtain the individual absorption spectra of each sample. The wavelength at which the absorbance peaked was chosen. This experiment gave us a great standard curve from which we can roughly estimate the amount of IAA in a solution between 2 and 200 μg/ml.

8th of August

Today we ran a gel of the PCRd backbone DNA extracted from the previous gel to make sure that the DNA was pure. The gel results were succesful. We also transformed cells with the pure DNA to check that the Dpn1 digestion worked properly.

Gel 5: Gel extracted backbone vector DNA run on a gel to confirm purity. Lane 1- 1 kb DNA ladder; Lane 2- vector 6a; Lane 3- vector 6b; Lane 4- vector 7a; Lane 5- vector 7b; Lane 6- vector 8a; Lane 7- vector 8b.

9th of August

Transformations of auxin fragment 1 (20) and auxin fragment 4 (24) were successful. We obtained plenty of colonies to choose from on both the ampicillin and kanamycin plates. Also, the DpnI digest transformations created bacteria that had no resistance to chloramphenicol.

However, sample 8 has to be repeated because in the "rest" plates there were 1 or 2 colonies on each.

10th of August

Today we attempted to perform a midi-prep on the DNA fragments that had arrived from Germany. The experiment failed and we were not able to obtain a decent yield of DNA. Oh well, got to try again.

12th of August

After the failed results and the rather lethargic week we attempted to get our minds back to gear. The visit to Syngenta the day before was a moment of respite that allowed us to perform two mini-preps that worked. However, there was an issue when we digested our plasmid (pCR2.1) with MlyI. The genes had been placed in a plasmid that contains multiple MlyI sites which would make the gel extraction more difficult. We used Serialcloner to make a virtual cut and then used the predicted image to guide us. In the end we obtained a band for 20b and 24a in the right location (or so we hope!).

Gel 6: gel of MlyI restriction digest of the synthesised genes. Lane 1-Marker; Lane 2-20a; Lane 3-20b; Lane 4-22a; Lane 5-22b; Lane 6-23a; Lane 7-23b; Lane 8-24a.

15th of August

We gel extracted several gene fragemtns that were transformed yesterday.

16th of August

The transformations we did the previous day were a success and the last two remaining fragments were also mini-prepped. We will attempt the Gibson assembly. If all goes well, we'll have E. coli excreting auxin by Friday!

19th of August

Gel 7: Gel extracted DNA fragments for assembly of auxin expressing plasmid. Lane 1&2 - Auxin fragment 1; Lane 3 - Auxin fragment 4; Lane 4&5 - Auxin fragment 3; Lane 6&7 - Auxin fragment 2; Lane 8&9 - pVEG backbone vector

22nd of August

Today we obtained some disappointing results. It seems like the vector is just religating during the Gibson reaction. Maybe the sequences of the two ends of the vectors are too homologous for Gibson to work. Either way, we will be attempting CPEC today and hopefully we will obtain some bands that we can purify and transform bacteria with.

23rd of August

First try of CPEC assembly assembly of the auxin construct seems to have been successful by looking at the gel electrophoresis results of colony PCR and CPEC product PCR with sequencing primers. We expect sequencing results to arrive tomorrow for an accurate assessment, however a preliminary test of colony supernatant with the salkowski reagent showed promosing results with one colony which turned bright red, indicating the presence of auxin.

Gel 8: The first two lanes show that CPEC assembly of four auxin fragments at ~1kb each in a backbone of about 2kb. Lane one contains the assembled construct at ~6 kb and lane 2 contains the negative control assembly of backbone vector with no insert at ~2kb. The following two lanes show the analytical PCR of the CPEC assembled product with standard biobrick primers to PCR our the assembled auxin fragments. The first well shows the auxin assembly at ~4kb and the second (negative control) shows no PCR product because no insert is present. Gel 9: Colony PCR with standard biobrick primers of CPEC assembled auxin fragments showing the desired assembly size of about 4 kb. Gel 10: Colony PCR of negative control colonies (backbone vector 8 only and no insert) and positive control colony PCR of the same vector 8 but the entire plasmid. This result shows that the DpnI digest of PCRd backbone vector 8 was not completely efficient as some complete plasmid remains, but this residual amount did not hinder assembly.

25th of August

A restriction digest of the mini-prepped auxin assembled constructs with EcoRI and PstI show clearly the assembled auxin insert drop out of the backbone vector.

Gel 11: Restriction digest of auxin construct with EcoRI, PstI and both for three miniprepped colonies grown from transformed E. coli.

Testing

How much auxin will we be producing? More importantly, has the module actually worked?! This chapter will look into the methods that we have decided to use in order to measure the amount of auxin in a solution. We have decided to use qualitative methods such as the Salkowski reagent (changes colour which is always good) as well as quantitative methods such as HPLC and GC-MS for more accurate results. Cross our fingers and hope this works!

26th of August

Colony PCR results of CPEC assembled PA2652 construct look promising! Will know for sure when sequencing results arrive next week

Gel 12: Colony PCR of 19 colonies picked from cells transformed with CPEC assembled PA2652 construct, about half have the correct size insert, these will be inoculated and miniprepped. Gel 13: Two more colony PCRs which were unsuccesfull, followed by five colony PCRs from negative control colonies (assembly of backbone vector without insert)showing backbone vector (6a) in one. The next well is a positive control colony PCR with plasmid 6a. The final two wells are analytical PCRs of the CPEC assembly and negative control with sequencing primers showing the correct size band for the assembled insert.

5th of August

After successfully testing the S2/1 method we also attempted the PC method which is both more exact and more specific for IAA. However, it only works at a lower range of concentrations of IAA and will therefore be useless if our bacteria end up excreting more than 20 μg/ml of IAA into the solution. Either way, we now have two standard curves which can be used to measure the amount of IAA in a solution. We are ready for the synthetic genes to arrive!

8th of August

Today we performed the first PC Salkowski assay successfully. We even took a picture of the gradient:

This was one of the 3 repeats that gave us the following standard curve:

26th of August

Today we have determined that the Salkowski reagent that we are currently using is not specific enough to detect indole-3 acetic acid. Instead, it is reacting with random indoles found within the supernatant and the cell samples. After working the entire day in order to obtain a conclusive answer on whether the cells are producing auxin or not has led to a frustrating result where the current reagent's only use is that of a very elaborate cell density measurement system, ergo useless. We will attempt HPLC next week as well as do some further reading on what we might have done wrong.

Implementation

Indole-3 acetic acid (IAA) is one of the most well studied phytohormones and is also known more commonly under the name Auxin. IAA is known as a key player in the regulation of plant growth and is also a known morphogen implicated in a vast array of processes ranging from embryo patterning to isodiametric expansion (fruit growth).

However, the topic of auxin producing soil bacteria in the rhizosphere has been given little attention so far. We believe that plant-microbe interactions mediated through IAA could be tapped into to modulate the plasticity of the root architecture. In this module, we will be attempting to express Tryptophan monooxygenase (IaaM) and Idoleacetimide hydrolase (IaaH) in Escherichia coli. We are aware that E. coli would not be a suitable chassis for field work and we have taken this into account when we made our DNA sequences.

The effect on plants

To observe how indole 3-acetic acid influences plants, we will be working with the plant model organism Arabidopsis thaliana. Arabidopsis is well-established for research into plant biology and researchers have established lines that respond to auxin exposure by expressing reporter genes, which are particularly useful for our project.

We will use DR5:GFP and DR5:3XVENUS plants that respond to auxin by expression of GFP and YFP, respectively, to look at the plant response to synthetic auxin and later bacteria-secreted auxin. The DR5 plant lines respond to auxin exposure by expressing GFP and YFP, respectively. This will allow us to monitor how much auxin is taken up and which cells respond to it. We will be using confocal microscopy to evaluate the relative strength of fluorescence expressed by the plant. This will act as an indirect reporter on the auxin concentration supplied as it relies on the plant expressing fluorescence in response to stimulation by the hormone.

Initially, we will be supplying the plants with synthetic auxin and observe the differences in growth and (root) morphology due to differential concentrations of the hormone. In later stages of the project, this will be followed by exposing the plants to E. coli cells expressing auxin.

References:
[1] Stijn Spaepen, Jos Vanderleyden, and Roseline Remans, “Indole-3-acetic acid in microbial and microorganism-plant signaling,” FEMS Microbiology Reviews 31, no. 4 (July 2007): 425-448.

@@ Line 19: / Line 19: @@
 <h2>Modelling</h2>
+<h2>Auxin  synthesis pathway</h2>
+<p>    The production of auxin by bacteria(E.Coli and/or B.Subtilis) is one main module in our project. In order to choose the appropriate RNA promoter with the optimal strength, the auxin production amount is modelled base on the pathway via the intermediate IAM from the precusor tryptophan.
+<p>    The result of modelling answers the question: <i>" How much auxin can be produced by the genetically modified bacteria with a typical RNA promoter strength? "</i>
+<p>    the pathway has two steps:[1]
+<p>  <em>tryptophan-IAM(IaaM gene -  tryptophan-2-monooxygenase)</em><em>-</em><em>IAM-IAA (IaaH  gene-IAM hydrolase)</em><br />
+<p>    A feedback inhibition mechanism exists in the pathway, the  production of IAM and IAA inhibits the function of tryptophan-2-monooxygenase,  therefore stops the reaction chain</p>
+<br>
+<ul>
+      <b><li>competitive inhibition</li></b>
+</ul>
+<p>  E + S &harr; ES &rarr; E + P <br />
+<p>  E + I &harr; EI<strong></strong></p>
+<br>
+<ul>
+      <b><li>the reaction kinetics fits the Michaelis-Menten kinetics model perfectly <strong></strong></li></b>
+</ul>
+<p>    a set of ODEs can  be used to model the reaction process:
+<p>  <img src="https://static.igem.org/mediawiki/2011/1/13/Equ.png" width="360" height="270" />
+<br>
+<ul>
+      <b><li>parameters required: k1,k-1,k3,k-3 </li></b>
+</ul>
+<p>    The rate constants of the reactions inside the pathway are required. All the parameters of the two enzymes involved in this pathway, tryptophan-2-monooxygenase and IAM hydrolase, can be found at the enzyme database <i>Brenda</i>. [2]
+<p>  <img src="https://static.igem.org/mediawiki/2011/7/71/ICL_Auxin1.png" alt="" width="359" height="271" /></p>
+<h2>Initial a root system</h2>
+<p>    To visualise our modelling result, a root system is demonstrated to show the root growth phenomena(primary root length, branching, root density, etc) in different environmental conditions(external and internal auxin concentration).
+<br>
+<ul>
+      <b><li>Root order:- </li></b>
+</ul>
+<p>    Root order describes the branching &ldquo;generation&rdquo; of a root system, a root  without branching is defined as a zero-order root</p>
+<p>    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.[3]
+<p>    <img src="https://static.igem.org/mediawiki/2011/0/02/ICL_Auxin2.png" alt="" width="175" height="131" />
+       <img src="https://static.igem.org/mediawiki/2011/7/76/ICL_Auxin3.png" alt="" width="200" height="122" />
+<p>    initial number of  root = n<sub>0</sub><br />
+<p>    initial cone base  radius = r<sub>0</sub><br />
+<p>    axial insertion  angle = &alpha; <br />
+<p>    radial insertion angle = &beta;</p>
+<p>    To ensure a even distribution of the roots, &alpha; and &beta; must be set in the following way:
+<p>  <img src="https://static.igem.org/mediawiki/2011/0/06/ICL_AuxinEqn6.png" alt="" width="119" height="22" /> <br />
+<p>  <img src="https://static.igem.org/mediawiki/2011/3/35/ICL_AuxinEqn7.png" alt="" width="57" height="19" /> <br />
+<p>  <img src="https://static.igem.org/mediawiki/2011/6/60/ICL_AuxinEqn8.png" alt="" width="71" height="19" /></p>
+<br>
+<ul>
+      <b><li>Tropisms </li></b>
+</ul>
+<p>    Root growth depends on the environmental factors, such as gravitation,  soil heterogeneities, etc.
+<p>    Therefore, two more variables are defined to describe the plant  adaptation:
+<p>    <b>&alpha;:-</b>
+<p>    how strong the roots direction changes per  1cm growth ?
+<p>    larger value indicates a more deflected root and a more twisted root system
+<p>    <b>N:-</b>
+<p>    the number of trials for the roots to find the optimal angles &alpha; and &beta; for the rotation
+<p>    for the downward movement
+<p>    N can be any real number, if N = 1.5, if means that N can be either 1 or 2.</p>
+<br>
+<ul>
+      <b><li>the difference of the root systems with different values of N and σ can be shown </b>
+<p>  <img src="https://static.igem.org/mediawiki/2011/4/4a/ICL_Auxin4.png" alt="" width="491" height="249" />
+<p>  <img src="https://static.igem.org/mediawiki/2011/8/89/ICL_Auxin5.png" alt="" width="521" height="259" /></li>
+</ul>
+<h2>Lindenmayer system and root growth modeling</h2>
+<p>    The properties of L-system provides the basic graphic principles to "draw" a root system.
+<p>    The  method to model root growth is to create a root system using Matlab.
+<br>
+<p>    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.[4]
+<p>      <i>-recursive nature</i>
+<p>      <i>-self-similarity </i>
+<br>
+<p>    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.
+<br>
+<p>    L-systems are now commonly known as <em>parametric</em> L systems, defined as a tuple.
+<p>    G = (<em>V</em>, ω, <em>P</em>)<br />
+<p>    V = a set of symbols containing elements that can be  replaced (<em>variables</em>)<br />
+<p>    ω (<em>start</em>, <em>axiom</em> or <em>initiator</em>) = a  string of symbols defining the initial state of the system
+<p>    P = a set of production rules defining the way variables can be replaced with combinations of constants and other variables.
+<p>    A production consists of two strings, the <em>predecessor</em> and the <em>successor</em>. <br />
+<p>    For any symbol A in V which does not appear on the  left hand side of a production in P,the identity production A → A is assumed. These symbols are called <em>constants</em> or <em>terminals</em>. </p>
+<br>
+<p>    An L-system is <em>context-free</em> if each production  rule refers only to an individual symbol and not to its neighbors. Context-free L-systems are thus  specified by either a prefix grammar, or a regular grammar.
+<p>    If there is  exactly one production for each symbol, then the L-system is said to be <em>deterministic</em> (a deterministic context-free L-system is popularly called a <em>D0L-system</em>).
+<p>   If there are several, and each is chosen with a certain probability during each iteration, then it is a <em>stochastic</em> L-system.</p>
+<br>
+<ul>
+      <b><li>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.</li></b>
+</ul>
+<h2>Auxin uptake</h2>
+<p>    The modelling of auxin uptake will give prediction of the root system development in the following ways:-
+<p>    <i>"What is the primary root growth rate?"</i>
+<p>    <i>"What does the root system look like after a certain period of time?"</i>
+<p>    <i>"How does arabidopsis respond to different auxin concentration?"</i>
+<p>    ... ...
+<br>
+<p>    The auxin distributed in the soil enters the plant mainly by diffusion, if the convection process is neglected, then  the diffusion can by described using the following equations (Barber 1995)<br />
+  <img src="https://static.igem.org/mediawiki/2011/c/c7/ICL_AuxinEqn9.gif" alt="" width="521" height="39" /><br />
+<p>  &theta; = volumetric water content of the soil = 0.4<br />
+<p>  b =  buffer power = 100<br />
+<p>  c = auxin concentration<br />
+<p>  D<sub>1</sub> = diffusion coefficient of auxin<br />
+<p>  f =  impedance factor = 0.3<br />
+<p>  s =  root surface area per unit volume <br />
+<p>  F<sub>m</sub> = maximal influx = 2.5*10<sup>-7 </sup>&micro;mol/cm<sup>2</sup>/s <br />
+<p>  K<sub>m</sub> = Michaelis-Menten constant = 4*10<sup>-4 </sup>&micro;mol*cm<sup>3</sup><br />
+<p>  t<sub>age</sub> = average root surface  age <br />
+<p>  k = decay factor of auxin uptake</p>
+<p>    An anxin  distribution map can be drawn from the equation above.</li>
+<br>
+<p>    The  values from literature gives the relationship between external auxin concentration and elongation of the roots:-
+<p>    5*10<sup>-5 </sup>mol/L &rarr; 200 &micro;m elongation in 30 mins <br />
+<p>    The modelling parameter of growth speed is therefore 9.6*10<sup>-3</sup> m/day</p>
+<p>    use  L-system and turtle command, a zeroth-order root system is demonstrated</li>
+<p>  <img src="https://static.igem.org/mediawiki/2011/6/67/ICL_Auxin6.jpg" alt="" width="295" height="329" /></p>
+<br>
+<p>    As you can see, this demonstration has a more generalised root shape. Arabidopsis, which does not grow in this way,is used in our project. By observing the real roots grow from the plant, the demonstration is modified to give a more reliable and accurate prediction of the root growth. Arabidopsis has a primary root with zeroth order and it is thicker than the branches. Arabidopsis normally grows to the depth of 20~30cm inside the soil and branches once  only. The 3D picture shown below predicts the root growth with different elongation rate(with auxin = 0.46cm/day; without auxin = 0.96cm/day). They can be compared with the photo of real root system.
+<p>  <img src="https://static.igem.org/mediawiki/2011/thumb/0/0c/Ttt.png/800px-Ttt.png" alt="" width="800" height="644" /><br />
+<br>
+<p>    The root has a growth rate of 0.96cm/day with the external auxin concentration 5x10-5mol/L, however, this data is selected from 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.
+<ul>
+<p>  <b><li>data fitting:-</li></b>
+</ul>
+<p>    When the arabidopsis samples are planted, we record the root length and number of branches every day from day 0 to day 20.Then, root length, root growth rate and number of branches are plotted against time and auxin concentration. These three curves are analysed to give the best mathematical equation to describe it, This can be an approximation of the relationship between auxin concentration and root growth. The following graph gives an example of root length against time.
+<p>  <img src="https://static.igem.org/mediawiki/2011/7/7e/Plot1.PNG" alt="" width="506" height="582" />
 <h2>Fabrication</h2>
+<p>We wish to build a single expression plasmid that can express IaaH and IaaM. While this task can be summarised in one sentence its execution is not as short. The first problem lies in the size of these two enzymes which both exceed 1kbp making their synthesis a problem. We therefore created a new standard for biobrick assembly to tackle this issue. We broke up these large sequences into four fragments that were ordered at the end of week 3. In preparation for the arrival of these fragments (circa 8-10 days) we started to transform our cells with the pVEg+pSB1C3 backbone constructs in order to make enough genetic material for a gibson assembly reaction. This chapter will describe our struggles and successes throughout this grueling and yet rewarding process.</p>
+<h2>29th of July</h2>
+<p>Our first transformations were a success! We have managed to transform our competent cell colonies with pSB1C3 containing BBa_K398500 and J23100 promoter to produce cell line 6. We also transformed the cells with part BBa_K316001 to produce cell line 7 and part BBa_K316005 to produce cell line 8. With these cell lines we will be able to make more copies of each part in preparation for the arrival of our synthesized sequences. We are under a tight schedule so efficiency is key.</p>
+<p>   <img src=https://static.igem.org/mediawiki/2011/c/c8/ICL_Transformation_6.jpg width=300px/>
+<p>   <img src=https://static.igem.org/mediawiki/2011/e/e0/ICL_Transformation_7.jpg width=300px/>
+<p>   <img src=https://static.igem.org/mediawiki/2011/5/59/ICL_Transformation_8.jpg width=300px/>
+<p>Also, the cell line with the superfolded GFP integrated in its genome has been plated successfully. We have confirmed that these are the correct cell lines by looking at them under UV light. Their green glow was brighter than we expected.</p>
+<p>However, cell line 1 did not grow in the liquid broth media at the same concentration of kanamycin. We will create an assay to ascertain the optimum kanamycin concentration. This is both a bizarre and unexpected result that must be rectified.</p>
+<h2>30th of July</h2>
+<p>The previous day, we had obtained the mcpS gene in a pRK415 plasmid from Spain. We then performed a transformation on the competent 5α cell line and obtained the results on this day. Out of the four plates one of them contained transformed cells. We named these cells 10.</p>
+<p>   <img src=https://static.igem.org/mediawiki/2011/3/3c/ICL_Transformation_10.jpg width=400px/>
+<h2>1st of August</h2>
+<p>A month has already passed since we started our project. The experiments that were conducted on this day were a mini-prep on samples 6,7,8 and 10 that were inoculated into an LB broth culture the night before. We used a mini-prep kit to obtain the plasmid DNA that we wanted from the transformed cells. Then, once we obtained the DNA, we started a restriction digest using PstI and EcoRI for 1.5 hours to confirm that the samples from the mini-prep contained the DNA that we wanted (the pSB1C3 backbone with the appropriate promoters).</p>
+<p>Sadly, once we tried to visualize the results on a gel, the results were less than satisfactory. Mini-prep 6a and 7b seems to have failed and the rest of the bands do not make much sense. The experiment had to be repeated.</p>
+<h2>2nd of August</h2>
+<p>Today we attempted the restriction digest again and the results verified that samples 6,7 and 8 were actually pSB1C3 constructs with the required components. Therefore, the mini-prep experiment had worked and did not need to be repeated. It is a great feeling when everything comes together.</p>
+<p>   <img src=https://static.igem.org/mediawiki/2011/4/4c/ICL_restriction.digest.backbone.vectors.jpg width=400px/>
+<p>   <img src=https://static.igem.org/mediawiki/2011/1/14/ICL_restriction.digest.backbone.vectors.2.jpg width=400px/>
+<p>Gel 1&2. Restriction digest of three backbone vectors with EcoRI(E) and PstI(P) to confirm backbone length. Gel1: Lane1-1 kb DNA ladder Lane 2-6a cut with E;Lane 3-6a cut with P; Lane 4-6a cut with E+P;Lane 6-6b cut with E; Lane 7- 6b cut with P; Lane 8- 6b cut with E+P; Lane 11- 7a cut with E; Lane 12- 7a cut with P; Lane 13- 7a cut with E+P; Lane 15- 7b cut with E; Lane 16- 7b cut with P; Lane 17- 7b cut with E+P. Gel 2: Lane 1 - 1kb ladder; lane 2 - 8a cut with E; lane 3- 8a cut with P; lane 4- 8a cut with E+P; lane 6- 8b cut with E; lane 7- 8b cut with P; lane 8 - 8b cut with E+P.</p>
+<h2>3rd of August</h2>
+<p>Today we attempted to PCR samples 6, 7 and 8. The PCR did not end up working so well so. The annealing temperature must have been too low because we obtained bands that we did not want. Also, there must have been too little Sybr safe in the gel because the bands that were there were not bright. The PCR will be repeated once again and we will use a temperature gradient for (hopefully) better results.</p>
+<h2>4th of August</h2>
+<p>Today we redid the PCR of samples 6, 7, and 8 but with a temperature gradient to improve primer annealing.... and it was a success! So tomorrow we can run the rest of the Dpn1 digested DNA on a gel and gel purify it, then the vectors are ready to be used for DNA assembly once our genes arrive!</p>
+<p>   <img src=https://static.igem.org/mediawiki/2011/6/6f/ICL_temp.gradient.PCR.6a.6b.7a.7b.jpg width=500px/>
+<p>   <img src=https://static.igem.org/mediawiki/2011/b/b0/ICL_PCR.temp.gradient.8a.8b.jpg width=400px/>
+<p>Gels 3&4: Temperature gradient PCR of desired backbone with promoter and terminator out of plasmids. Gel 3:Lane 1- 1kb DNA ladder; lanes 2 to 7 - PCR of vector 6 from 57.1°C to 62.6°C; lanes 9 to 15 - PCR of vector 7 from 57.1°C to 62.6°C. Gel 4: lanes 2 to 7 - PCR of vector 8 from 57.1°C to 62.6°C</p>
+<p>The backbone sequences have also returned. All of the samples are in order except a one base pair mutation in sample 8 within the pVEg promoter. For now, we are going to amplify it anyways in the hope that the one base pair mutation is just an error that occured during sequencing. Either way, sample 8 is a back-up of sample 7 so there should be no problems either way.</p>
+<p>We also started experimenting with the Salkowski reagent. In particular, we tested the S2/1 method and found that the ideal wavelength for measuring the IAA concentration with our apparatus is at 554nm. This was done by scanning between 500nm and 600nm to obtain the individual absorption spectra of each sample. The wavelength at which the absorbance peaked was chosen. This experiment gave us a great standard curve from which we can roughly estimate the amount of IAA in a solution between 2 and 200 μg/ml.</p>
+<h2>8th of August</h2>
+<p>Today we ran a gel of the PCRd backbone DNA extracted from the previous gel to make sure that the DNA was pure. The gel results were succesful. We also transformed cells with the pure DNA to check that the Dpn1 digestion worked properly.</p>
+<p>   <img src=https://static.igem.org/mediawiki/2011/5/55/ICL_PCRgelextraction.jpg width=400px/>
+<p>Gel 5: Gel extracted backbone vector DNA run on a gel to confirm purity. Lane 1- 1 kb DNA ladder; Lane 2- vector 6a; Lane 3- vector 6b; Lane 4- vector 7a; Lane 5- vector 7b; Lane 6- vector 8a; Lane 7- vector 8b.</p>
+<h2>9th of August</h2>
+<p>Transformations of auxin fragment 1 (20) and auxin fragment 4 (24) were successful. We obtained plenty of colonies to choose from on both the ampicillin and kanamycin plates. Also, the DpnI digest transformations created bacteria that had no resistance to chloramphenicol.</p>
+<p>   <img src=https://static.igem.org/mediawiki/2011/0/03/ICL_Transformation_20.jpg width=400px/>
+<p>   <img src=https://static.igem.org/mediawiki/2011/c/ca/ICL_Transformation_24.jpg width=400px/>
+<p>However, sample 8 has to be repeated because in the "rest" plates there were 1 or 2 colonies on each.</p>
+<p>   <img src=https://static.igem.org/mediawiki/2011/e/e2/ICL_Transformation_8_DpnI.jpg width=400px/>
+<h2>10th of August</h2>
+<p>Today we attempted to perform a midi-prep on the DNA fragments that had arrived from Germany. The experiment failed and we were not able to obtain a decent yield of DNA. Oh well, got to try again.</p>
+<h2>12th of August</h2>
+<p>After the failed results and the rather lethargic week we attempted to get our minds back to gear. The visit to Syngenta the day before was a moment of respite that allowed us to perform two mini-preps that worked. However, there was an issue when we digested our plasmid (pCR2.1) with MlyI. The genes had been placed in a plasmid that contains multiple MlyI sites which would make the gel extraction more difficult. We used Serialcloner to make a virtual cut and then used the predicted image to guide us. In the end we obtained a band for 20b and 24a in the right location (or so we hope!).</p>
+<p>   <img src =https://static.igem.org/mediawiki/2011/f/f8/ICL_Results_of_MlyI_restriction_digest.PNG width=400px/>
+<p>Gel 6: gel of MlyI restriction digest of the synthesised genes. Lane 1-Marker; Lane 2-20a; Lane 3-20b; Lane 4-22a; Lane 5-22b; Lane 6-23a; Lane 7-23b; Lane 8-24a.</p>
+<h2>15th of August</h2>
+<p>We gel extracted several gene fragemtns that were transformed yesterday. </p>
+<p>   <img src=https://static.igem.org/mediawiki/2011/4/4a/ICL_gelextractionsofgenepartsforassembly.jpg width=400px/>
+<h2>16th of August</h2>
+<p>The transformations we did the previous day were a success and the last two remaining fragments were also mini-prepped. We will attempt the Gibson assembly. If all goes well, we'll have E. coli excreting auxin by Friday!</p>
+<h2>19th of August</h2>
+<p>   <img src=https://static.igem.org/mediawiki/2011/f/f4/ICL_gel_extracted_auxin_fragments_and_backbone_for_gibson_assembly.jpg width=500px/>
+<p>Gel 7: Gel extracted DNA fragments for assembly of auxin expressing plasmid. Lane 1&2 - Auxin fragment 1; Lane 3 - Auxin fragment 4; Lane 4&5 - Auxin fragment 3; Lane 6&7 - Auxin fragment 2; Lane 8&9 - pVEG backbone vector
+<h2>22nd of August</h2>
+<p>Today we obtained some disappointing results. It seems like the vector is just religating during the Gibson reaction. Maybe the sequences of the two ends of the vectors are too homologous for Gibson to work. Either way, we will be attempting CPEC today and hopefully we will obtain some bands that we can purify and transform bacteria with.</p>
+<h2>23rd of August</h2>
+<p> First try of CPEC assembly assembly of the auxin construct seems to have been successful by looking at the gel electrophoresis results of colony PCR and CPEC product PCR with sequencing primers. We expect sequencing results to arrive tomorrow for an accurate assessment, however a preliminary test of colony supernatant with the salkowski reagent showed promosing results with one colony which turned bright red, indicating the presence of auxin. </p>
+<p>   <img src=https://static.igem.org/mediawiki/2011/a/ad/ICL_CPEC_assembly_auxin_fragments_and_verifying_PCR.jpg width=200px/>
+<img src=https://static.igem.org/mediawiki/2011/1/18/ICL_Colony_PCR_CPEC.jpg width=500px/>
+<img src=https://static.igem.org/mediawiki/2011/4/4f/ICL_Colony_PCR_controls.jpg width=200px/>
+<p>Gel 8: The first two lanes show that CPEC assembly of four auxin fragments at ~1kb each in a backbone of about 2kb. Lane one contains the assembled construct at ~6 kb and lane 2 contains the negative control assembly of backbone vector with no insert at ~2kb. The following two lanes show the analytical PCR of the CPEC assembled product with standard biobrick primers to PCR our the assembled auxin fragments. The first well shows the auxin assembly at ~4kb and the second (negative control) shows no PCR product because no insert is present. Gel 9: Colony PCR with standard biobrick primers of CPEC assembled auxin fragments showing the desired assembly size of about 4 kb. Gel 10: Colony PCR of negative control colonies (backbone vector 8 only and no insert) and positive control colony PCR of the same vector 8 but the entire plasmid. This result shows that the DpnI digest of PCRd backbone vector 8 was not completely efficient as some complete plasmid remains, but this residual amount did not hinder assembly.</p>
+<h2>25th of August</h2>
+<p> A restriction digest of the mini-prepped auxin assembled constructs with EcoRI and PstI show clearly the assembled auxin insert drop out of the backbone vector.</p>
+<p>   <img src=https://static.igem.org/mediawiki/2011/7/7a/ICL_Auxin_assembly_digests_run_longer.jpg width=400px/>
+<p> Gel 11: Restriction digest of auxin construct with EcoRI, PstI and both for three miniprepped colonies grown from transformed E. coli.</p>
 <h2>Testing</h2>
+<p>How much auxin will we be producing? More importantly, has the module actually worked?! This chapter will look into the methods that we have decided to use in order to measure the amount of auxin in a solution. We have decided to use qualitative methods such as the Salkowski reagent (changes colour which is always good) as well as quantitative methods such as HPLC and GC-MS for more accurate results. Cross our fingers and hope this works!</p>
+<h2>26th of August</h2>
+<p> Colony PCR results of CPEC assembled PA2652 construct look promising! Will know for sure when sequencing results arrive next week </p>
+<p>   <img src=https://static.igem.org/mediawiki/2011/f/fa/ICL_PA2652_CPEC_colony_pcr2.jpg width=500px/>
+<img src=https://static.igem.org/mediawiki/2011/0/01/ICL_PA2652_CPEC_colony_pcr_neg_cntrls.jpg width=250px/>
+<p>Gel 12: Colony PCR of 19 colonies picked from cells transformed with CPEC assembled PA2652 construct, about half have the correct size insert, these will be inoculated and miniprepped. Gel 13: Two more colony PCRs which were unsuccesfull, followed by five colony PCRs from negative control colonies (assembly of backbone vector without insert)showing backbone vector (6a) in one. The next well is a positive control colony PCR with plasmid 6a. The final two wells are analytical PCRs of the CPEC assembly and negative control with sequencing primers showing the correct size band for the assembled insert.</p>
+<h2>5th of August</h2>
+<p>After successfully testing the S2/1 method we also attempted the PC method which is both more exact and more specific for IAA. However, it only works at a lower range of concentrations of IAA and will therefore be useless if our bacteria end up excreting more than 20 μg/ml of IAA into the solution. Either way, we now have two standard curves which can be used to measure the amount of IAA in a solution. We are ready for the synthetic genes to arrive!</p>
+<p>   <img src=https://static.igem.org/mediawiki/2011/b/b7/ICL_S2.1_results_1.PNG width=800px/>
+<h2>8th of August</h2>
+<p>Today we performed the first PC Salkowski assay successfully. We even took a picture of the gradient:</p>
+<p>   <img src=https://static.igem.org/mediawiki/2011/a/a9/ICL_PC_picture.jpg width=400px/>
+<p>This was one of the 3 repeats that gave us the following standard curve:</p>
+<p>   <img src=https://static.igem.org/mediawiki/2011/0/07/ICL_PC_results_1.PNG width=800px/>
+<h2>26th of August</h2>
+<p>Today we have determined that the Salkowski reagent that we are currently using is not specific enough to detect indole-3 acetic acid. Instead, it is reacting with random indoles found within the supernatant and the cell samples. After working the entire day in order to obtain a conclusive answer on whether the cells are producing auxin or not has led to a frustrating result where the current reagent's only use is that of a very elaborate cell density measurement system, ergo useless. We will attempt HPLC next week as well as do some further reading on what we might have done wrong.</p>
 <h2>Implementation</h2>