Team:Imperial College London/Project/Auxin/Results
From 2011.igem.org
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<h2>23rd of August</h2> | <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> 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> | ||
- | <img src=https://static.igem.org/mediawiki/2011/a/ad/ICL_CPEC_assembly_auxin_fragments_and_verifying_PCR.jpg width=200px/> | + | <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/2011/1/18/ICL_Colony_PCR_CPEC.jpg width=500px/> | ||
<img src=https://static.igem.org/mediawiki/2011/4/4f/ICL_Colony_PCR_controls.jpg width=200px/> | <img src=https://static.igem.org/mediawiki/2011/4/4f/ICL_Colony_PCR_controls.jpg width=200px/> | ||
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<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> 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> | ||
- | <img src=https://static.igem.org/mediawiki/2011/7/7a/ICL_Auxin_assembly_digests_run_longer.jpg width=400px/> | + | <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> | <p> Gel 11: Restriction digest of auxin construct with EcoRI, PstI and both for three miniprepped colonies grown from transformed E. coli.</p> | ||
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<h2>26th of August</h2> | <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> Colony PCR results of CPEC assembled PA2652 construct look promising! Will know for sure when sequencing results arrive next week </p> | ||
- | <img src=https://static.igem.org/mediawiki/2011/f/fa/ICL_PA2652_CPEC_colony_pcr2.jpg width=500px/> | + | <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/> | <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> | <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> | ||
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<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>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> | ||
- | <img src=https://static.igem.org/mediawiki/2011/b/b7/ICL_S2.1_results_1.PNG width=800px/> | + | <p> <img src=https://static.igem.org/mediawiki/2011/b/b7/ICL_S2.1_results_1.PNG width=800px/> |
<h2>8th of August</h2> | <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>Today we performed the first PC Salkowski assay successfully. We even took a picture of the gradient:</p> | ||
- | <img src=https://static.igem.org/mediawiki/2011/a/a9/ICL_PC_picture.jpg width=400px/> | + | <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>This was one of the 3 repeats that gave us the following standard curve:</p> | ||
- | <img src=https://static.igem.org/mediawiki/2011/0/07/ICL_PC_results_1.PNG width=800px/> | + | <p> <img src=https://static.igem.org/mediawiki/2011/0/07/ICL_PC_results_1.PNG width=800px/> |
Revision as of 19:44, 29 August 2011
Auxin Results
Chapter 1: Assembly of genetic constructs
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.
Chapter 2: Auxin assays
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:
Chapter 3: effect of auxin on plants
We are not only interested in constructing the auxin-producing pathway in our bacteria but we also want to investigate what effect the auxin has on plants to verify our assumptions about indole 3-acetic acid's effects. This will help us with the human practices aspect of our project and it will also provide a good assay for the functionality of auxin-secreting bacteria.
Root growth on diffent auxin concentrations. Tuesday, 9 August 2011
To look at the effect of auxin on plants, we supplied differing indole 3-acetic acid concentrations to Arabidopsis seedlings in liquid culture.
Si modelled the concentration of auxin secreted by our bacteria to be 10mM. However, according to Joseph et al (1995), increasing exogenous IAA concentrations from 0 - 0.1 nM increases root growth from 0 - 20%. From 0.1 nM to 10microM, the root length and decreases sequentially, while fibrosity increases. The plant dies at concentrations over 10 microM. However ___ state that the optimal auxin concentration lies in between 0.5 microM - 20 microM. Accordingly, we used concentrations starting from 10mM to 0.1nM to test the effect of different auxin concentrations on the length of the roots and their branching. We made the auxin concentrations by serial dilution and added 10ml of concentrated auxin solution to 100ml of half-MS media each. Twenty-five seeds were added to each flask. The seeds were incubated at 23°C and wrapped in aluminium foil to allow the plants to germinate in the dark. They will be allowed to grow in the light in 3 days' time. This follows a protocol described by King et al. (1995). The results are stated in Friday 19th of August and Monday 22th of August
Root growth at different positions where Auxin is applied Wednesday, 10 August 2011
Looking at the effect of auxin on the roots also involves observing its effect on phytogels. On these gels, individual seedlings grow horizontally into a gel containing plant nutrients. These gels enable us to supply the plant with auxin at set distances from the seedling itself. Observing these effects is especially in case our bacteria do not get taken up into roots in nature, which has yet to be investigated. We are using DR:3VENUS seeds. These germinate into plants whose roots respond to auxin uptake by expressing YFP. We hope to be able to get an estimate of the effect of auxin by comparing intensities of fluorescence across plants supplied with different concentrations of auxin.
Si corrected the estimated auxin secretion of our bacteria to 0.0001 to 0.01 mM. Accordingly, we set up the auxin concentration gradient experiment with 0.0001, 0.001 and 0.01 mM of IAA. We injected a small volume of IAA dissolved in 70% ethanol at set distances from seeds, which were subsequently put onto the gel. Five replicates were set up for each concentration. On each plate, the seed seeds are sown at distances of 2,4,6,8, and 10 cm from the point where IAA is applied. Roots grow perpendicular to the line on which IAA and seeds are applied. The plates are kept in low light for 3 days in order to prevent photooxidation of auxin and also in 4 C to simulate the winter hibernation. The plates are later put in light for another 6 days to see root growth.
The split root experiment (Friday 12 and Monday 15 August 2011)
To visually compare the difference of the root growth between the applying and non applying of IAA in the same plant, we set up a split root experiment (which had been recommended to us by Dr Alex Milcu). This experiment extends beyond the scope of normal controls as the same plant is subjected to two different treatments. We supplied the following concentrations of IAA to one half of the roots: 0 microM (control), 0.1 microM, 1 microM and 10 microM, while the other half is grown in phytogel containing no IAA. 3 replicates were set up for each concentration. 7-day old seedling of A thaliana DR:3VENUS were used for this set up. This strain responds to auxin by expressing YFP. The plates are sealed and kept in the incubating room for 2 weeks in order to observe the length of the grown root.
Friday, 19 August 2011
We imaged the plants that had been incubated with differing concentrations of IAA using confocal microscopy. Plants incubated with 0.1mM of IAA showed strongly enhanced lateral root growth but also stunted growth.
A Z stack through an Arabidopsis root tip incubated with 0.1mM indole 2-acetic acid.
This did not occur at lower concentrations. However, fluorescence was still clearly visible:
Root of A. thaliana seedling incubated with 1uM indole 3-acetic acid.
At even lower concentrations, fluorescence was much weaker:
Incubated at 0.01nM.
Effect of auxin concentrations results Monday, 22 August 2011
The results shows that from low (0.1nM) to high concentrations (0.1mM)the root legth and the number of the leaves decrease seqeuntially and the plants all die at 10mM. This is an important information for the modelling team since auxin only operates well at liquid concentrations less than 0.1nM. To find the optimal concentrations of auxin for maximal root growth and splitting. We extend the contrations from 0.1 nM lower down from 10 pM, 1 pM, 0.1 pM and 0.01 pM. Hopefully we could produce the bell shape curve graph for both the root's length and its fibrousity
Effect of auxin concentrations in phytogel Tuesday, 23 August 2011
In order to modelling the effect of auxin concentrations on Arabidopsis and build the macros on lateral root initiation and elongation, root length should be measured day by day. This could not be done in liquid media since taken the plant out of liquid media makes the plant prone to fungal contamination. Also the resources we have, e.g. number of shakers, amounts of Venus Arabidopsis seeds are not enough to build up repeats to measure root length everyday. Therefore we decide to grow Arabidopsis in phytogel which is less reliable than the liquid media
Soil erosion experiment Thursday,
In order to see which root architecture, the length and the dispersion, is the best to hold up the soil to prevent soil erosion and retain the moisture inside the soil. We then vary the concentrations from 0.01 pM to 0.1mM as the same as the effect of different auxin concentrations experiment. These different auxin concentrations allow the roots to show different architectures. The experiments are planned up as shown in the diagrams below.
- The material for making the slope is the ...x... pot
- The soil chosen is called M2 which composes of Medium compost without sand and gravel which eliminates the error due to different mixtures which contributes to different soil contents.
- The pressure of water is made by
Modeling
Auxin synthesis pathway
- the pathway has two steps
tryptophan-IAM(IaaM gene - tryptophan-2-monooygenase)-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-monooygenase, therefore stops the reaction chain
- competitive inhibition
E + S ↔ ES → E + P
E + I ↔ EI
- the reaction kinetics fits the Michaelis-Menten model perfectly
a set of ODEs can be used to model the reaction process
- parameters required: k1,k-1,k3,k-3
Initial a root system
- 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.
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, to 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
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 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
- 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
- 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 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
Fm = maximal influx = 2.5*10-7 µmol/cm2/s
Km = Michaelis-Menten constant = 4*10-4 µmol*cm3
tage = 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*10-5 mol/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. li>
- 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.
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. li>