Team:Monash Australia/Modelling
From 2010.igem.org

Contents 
Introduction
The three key enzymes we require are outlined in the image Figure 1 (left), SAM synthase, ACC synthase and ACC oxidase. SAM synthase converts methionine into SAdenosylLMethionine (SAM), using ATP for an adensoyl group. The second step involves ACC synthase, which cleaves the amino butyrate from SAM, releasing 1aminocyclopropane1carboxylic acid (ACC). Released ACC is then processed by ACC Oxidase which converts ACC to ethylene by cleaving the carboxylic acid off as carbon dioxide and its neighboring carbon with the amino group as cyanide gas. By using such a system to produce ethyene gas we can potentially reduce costs involved with current production methods by reducing temperature requirements by 30 fold.
Kinetic modelling of the ethylene generator
The program tinkercell was used to model the synthesis of ethylene in our E.coli cells. Where, in addition to the qualitative representation (figure 2 & 4) the program allowed, simulation of the model could be exercised inorder to measure the flux of metabolites – with respect to time  in the system given the input of values pertaining to substrate/enzyme concentration, and reaction rates were inputted. Figure 2 or Model 1 was designed to include fixed concentrations at a steady state ratio of 1:1:1. This design ensured sensible approximate values of ethylene output were obtained given the correctness of enzyme rates and other parameters used.
Adapting on to model 1, quantitative data in silico corresponding to mRNA transcription, protein translation, and degradation were implimented into a more complex design  giving model 2. As a result, more realistic outputs of ethylene could be found. This design could then be used to compare and contrast actual ethylene values obtained experimentally. Hence the effiency of our E.coli cells could then be calculated. Depending on the effiency value, certain factors and variables could be changed in order to attempt to reach our tinkercell output.
Another use of the tinker cell model is that it would allow us to understand the pathway in which we chose to take our project. That is, with low concnetrations of ethylene produced, possiblity of the use of the system as a form of plant communicating system would be strongly favoured. In contrast if ethylene produced was found to be in high concentration then the system could strongly possibly used in plastic productions. Therefore the tinkercell program also gives an indication of which direction this particular Monash iGEM project could take given the prospects it carries.
Objectives
To determine the maximum output of ethylene To estimate HCN levels and assess potential damage to cell
Start with a simple model and progress to a more complex one. This allows us to more accurately predict ethylene production
Model 1
Introduction to Model 1
This relatively simple model  as represented in figure 2  was designed to be the starting point of our kinetic modelling. This uncomplicated system could then be used to obtain an ethylene output. This design comprised only of three enzymes and lacked the transcription and translation stages. The enzymes involved were SAM synthetase, ACC synthase and ACC oxidase  also known as EFE (ethylene forming enzyme). These enzymes were present at fixed concentrations (10, 100, 1000 and 3000 uM) and in a 1:1:1 ratio. Although basic, this model in essence was able to give reasonable output values for ethylene produced. Therefore with fixed enzyme concentrations the rate at which ethylene is produced depends on the Vmax of the specific enzymes.
This specific rate is defined by the MichaelisMenton Equation:
kcat*[substrate]*[enzyme] Rate =  km + [substrate]
Assumptions for Model 1
 A 1:1:1 steady state of enzymes. No product inhibition.
Substrates (ATP, LMethionine etc) kept at a constant value due to homeostatic mechanisms in E.coli.
 The best value (km, kcat etc) was always chosen to ensure maximum yield of ethylene.
Parameters and Values used
Met concentration  150 uMATP concentration  9600 uM
O2 concentration  442 uM
SAMsynth Km(Met) 92 uM
ACCsynth Km(AdoMet/SAM) 37 uM
EFE Km(ACC) 12 uM
SAMsynth turnover rate (kcat) 1.5 per second
ACCsynth turnover rate (kcat) 18 per second
EFE turnover rate (kcat)  5.9 per second
Graphs and results
Using Tinkercell a graphical representation of 'Model 1' was generated (Figure 3) using deterministic stimulation. In this figure a graphical representation of the rates  generated internally by Tinkercell's mathematical alogarithms  of ethylene production are shown for each fixed enzyme concentration assumed. As a result not only is production of ethylene shown to be increasing linearly with time, but at a greater rate with increasing concentration of enzyme (SAM synthetase, ACC synthase, EFE) used.

Model 2
Model 2 explores the more complicated adaptation of model 1 by incorporating the transcription, translation, and degradation rates of protein and mRNA into the final design. As a result a more realistic model of what would really be happening in the cell leading to ethylene production could be achieved. Of all the sources studied, it was decided that values from the Elowitz repressilator model would be most sensible and relevant to our system. Therefore the degradation, transcription and translation rates were adapted from this model onto ours to factor in fluctuations in concentrations of our three enzymes, as unlike in model 1, enzyme concentration would not realistically be in a 1:1:1 ratio. Therefore using these values, model 2 was able to more realistically follow the metabolic pathway of ethylene production where fluctuations in enzyme concentration were taken into consideration – rather than having them fixed as in model 1.
Elowitz Degradation Values
mRNA degradation rate  0.00577 mRNA per second Enzyme degradation rate  0.001155 enzymes per second R0011 PoPs or transcription rate  0.5 mRNA per second Translation rate 0.117 enzymes per secondGraphs and results
The rate at which mRNA is produced can be seen to start off at a rapid rate. However as time goes on the mRNA can be seen to reach a steady state.
The production of ethylene in this graph looks realitively accurate, however due to the confunding aspects of excess enzyme production, it is unclear if this graph truly represents the total ethylene output. However it can be assumed that the first few seconds accurately portray the ethylene output.