Team:Monash Australia/Modelling

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Figure 1: Yang cycle. In red - the reaction we wish to model in silico.


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. In addition to experimental data, with a model, theoretical data can be obtained to extrapolate quantitative data corresponding to mRNA, protein and ethylene outputs under set parameters and assumptions in silico. As a result, using the given theoretical model outputs as a benchmark, manipulations to the parameters and assumptions set can be made in vitro/in vivo in order to achieve higher outputs in future studies of the 'ethylene generator'.

Aims of the Kinetic Modelling

-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

Figure 2: A visual construction of Model 1 using Tinkercell

This relatively simple model - as represented in figure 2 - was designed so 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 invloved 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. This ensured that the model was plain yet ultimately obtained a resonable yet simple ethylene output. 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 Michaelis-Menton Equation:

             km + [substrate]

Assumptions for Model 1

- A 1:1:1 steady state of enzymes.

- No product inhibition.

-Substrates (ATP, L-Methionine 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 uM

ATP 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

Figure 3: Ethylene Production at different steady state concentration

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

Figure 4: A visual construction of Model 2 using Tinkercell, where transcription and translation are taken into account

Model 2 explores the more complicated version of our kinetic modelling. It aims to incorporate the transcription and translation rates of the cell into the final design. This calculation begins to become more difficult due to problomatic degradation, transcription and translation rates. These values were obtained from the Elowitz repressilator model. Of the many sources browsed it was determined that this source seemed to be the most accurate and hence its values were used. Therefore the transcription and translation rates of mRNA and proteins constantly changes the final concentration of the three enzymes. This changing concentration of enzymes then produces ethylene at a more reliable rate. As a result this model is expected to produce a more accurate representation of the ethylene producing pathway.

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 second

Graphs and results

Figure 5: Production of mRNA in the cell
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.

Figure 6: Production rate of the three different enzymes
Due to the polycystronic translation of the mRNA all the three enzymes are produced in a 1:1:1 ratio. To begin the enzymes are produced at a realitively fast rate however as time proceeds they fail to reach a steady state. In E.coli it is known that all enzymes eventually reach a steady state otherwise energy and resources would be depleated. Hence this graph indicates plausible for approximately the first 10 seconds of production. After that the data looks unrealistic and implausible in an E.coli cell.

Figure 7: Ethylene production at floating enzyme concentration

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.



Met --> SAM (AdoMet)

Met sam.jpg


Sam acc.jpg

ACC --> Ethylene

Acc eth.jpg

More to come soon!