IGEM:Imperial/2010/Modelling: Difference between revisions
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===Results=== | ===Results=== | ||
====Model pre-A==== | ====Model pre-A==== | ||
This is the result for the simulation of simple production of Dioxygenase. | This is the result for the simulation of simple production of Dioxygenase. It can be seen that the concentration will tend towards a final value of around 8.5*10^-6 (units!!!). This final value is dependent on the production rate (which we have just estimated!). | ||
[[Image:Model_pre_A_result.jpg|450px|thumb|center|alt=A|Results of the Matlab simulation of Model preA]] | [[Image:Model_pre_A_result.jpg|450px|thumb|center|alt=A|Results of the Matlab simulation of Model preA]] | ||
====Model A==== | ====Model A==== | ||
*'''Initial Concentration''' | *'''Initial Concentration''' |
Revision as of 08:25, 16 August 2010
Have a look at this link: Synthetic Biology (Spring2008): Computer Modelling Practicals
Have a look at Cell Designer to easily generate images of the system.
Example on how Valencia 2006 team used SimulLink to simulate their project: Valencia 2006 PowerPoint presentation
Objectives
Week 6
Day | Monday | Tuesday | Wednesday | Thursday | Friday | Weekend |
---|---|---|---|---|---|---|
Date | 09 | 10 | 11 | 12 | 13 | 14-15 |
Objective | Find constants | Find protein production constants and TEV reaction rate constants | ||||
Completion | We didn't manage to complete the task | The orders of magnitude established - ready to run simulations |
Week 7
Day | Monday | Tuesday | Wednesday | Thursday | Friday | Weekend |
---|---|---|---|---|---|---|
Date | 16 | 17 | 18 | 19 | 20 | 21-22 |
Objective | Implementing the constant ranges in the output model. Comparing the results between the models. | Start modelling the protein display signalling to find the concentrations | ||||
Completion |
Week 8
Week 9
Week 10
Output amplification model
Motivation: We have come up with a simple concept of amplification of output done by enzymes. Before the final constructs are assembled within the bacterial ogranism, it is beneficial for us to model the behaviour of our design.
The questions to be answered:
- How beneficial use of amplification is? (compare speeds of response of transcription based output to amplified outputs)
- How many 'amplification levels' are beneficial to have? (if too many amplification steps are involved, the associated time delay with expressing even amplfiied output may prove it not to be beneficial.
- Does mixing of amplfication levels have a negative infleunce on output? Is it better to use TEV all the way or HIV1? Modelling should allows us to take decision which design is more efficient.
First attempt
Second attempt
Implementation in Matlab
The Matlab code for the different stages of amplification and diagrams can be found here.
Kinetic constants
Quality | GFP | TEV | split TEV | split GFP |
---|---|---|---|---|
Km and Kcat | Doesn't apply | TEV constants (Km and kcat) | 40% of whole TEV | Doesn't apply |
half-life or degradation rate | Half-life of GFP in Bacillus = 1.5 hours - ref. Chris | ? | ? | Half-life shorter than GFP |
production rate in B.sub | ? | ? | ? | ? |
Conclusions
We couldn't obtain all the necessary constants. Hence, we decided to make educated guesses about possible relative values between the constants as well as varying them and observing the change in output.
As the result, we concluded that the amplification happens at each amplification level proposed. It's magnitude varies depending on the constants. There doesn’t seem to be much difference in substitution of TEV with HIV1.
Modified version
Michaelis Menten kineticsdoes not apply
We cannot use Michaelis-Menten kinetics because of its preliminary assumptions, which our system does not fulfil. These assumptions are:
- Vmax is proportional to the overall concentration of the enzyme.
But we are producing enzyme, so Vmax will change! Therefore, the conservation E0 = E + ES does not hold for our system.
- Substrate >> Enzyme.
Since we are producing both substrate and enzyme, we have roughly the same amount of substrate and enzyme.
- Enzyme affinity to substrate has to be high.
Therefore, the model above is not representative of the enzymatic reaction. As we cannot use the Michaelis-Menten model we will have to solve from first principle (which just means writing down all of the biochemical equations and solving for these in Matlab).
Changes in the system
GFP is not used any more as an output. It is dioxygenase acting on the catechol (activating it into colourful form). Catechol will be added to bacteria, it won't be produced by them. Hence, basically in our models dioxynase is going to be treated as an output as this enzyme is recognised as the only activator of catechol in our system. This means that change of catechol into colourful form is dependent on dioxygenase concentration.
Models:
Model preA: Production of Dioxygenase
This model includes transcription and translation of the dioxygenase. It does not involve any amplification steps. It is our control model against which we will be comparing the results of other models.
Model A: Activation of Dioxygenase by TEV enzyme
The reaction can be rewritten as: TEV + split Dioxygenase <-> TEV-split Dioxygenase -> TEV + Dioxygenase. This is a simple enzymatic reaction, where TEV is the enzyme, Dioxygenase the product and split Dioxygenase the substrate. Choosing k1, k2, k3 as reaction constants, the reaction can be rewritten in these four sub-equations:
- [T'] = -k1[T][sD] + (k2+k3)[TsD] + sT - dT[T]
- [sD']= -k1[T][sD] + k2[TsD] + ssD - dsD[sD]
- [TsD'] = k1[T][sD] - (k2+k3)[TsD] - dTsD[TsD]
- [D'] = k3[TsD] - dD[D]
These four equations were implemented in Matlab, using a built-in function (ode45) which solves ordinary differential equations. The Matlab code for this module can be found here.
Implementation in TinkerCell
Another approach to model the amplification module would be to implement it in a program such as TinkerCell (or CellDesigner). It would also be useful to check whether the Matlab model works.
Model B: Activation of Dioxygenase by TEV or activated split TEV enzyme
This version includes the following features:
- 2 amplification steps (TEV and split TEV)
- Split TEV is specified to have a and b parts
- TEVa is forbidden to interact TEVa (though in reality there could be some affinity between the two). Same for interaction between Tevb and Tevb
- Both TEV and TEVs are allowed to activate dioxugenase molecule
- Dioxugenase is assumed to be active as a monomer
- Activate split TEV (TEVs) is not allowed to activate sTEVa or sTEVb (this kind of interaction is accounted for in the next model version)
- There is no specific terms for time delays included
The MatLab code can be found here. Note that no final conclusions should be drawn before realistic estimates for kinetic constants are included. It wasn’t done so far.
Model C: Further improvement
This model is not implemented yet.
This version adds the following features:
- activated split TEV (TEVs) is allowed to activate not only sD but sTEVa and sTEVb
Results
Model pre-A
This is the result for the simulation of simple production of Dioxygenase. It can be seen that the concentration will tend towards a final value of around 8.5*10^-6 (units!!!). This final value is dependent on the production rate (which we have just estimated!).
Model A
- Initial Concentration
The initial concentration of split Dioxygenase, c0, determines whether the system is amplifying. The minimum concentration for any amplification to happen is 10^-4 (units???).
- Changing Km:
Km is indirectly proportional to the "final concentration" (which is the concentration at the end of the simulation), i.e. the bigger the evalue of Km, the smaller the "final concentration" will be. However, the highest "final concentration" seems to be around 5.4*10^-6. Once this value is reached, even very big variation of Km will not change the concentration. Hence, different Km values determine how quickly the amplification will take place.
Model B
Constants for Modelling
Type of constant | Derivation of value |
---|---|
TEV Enzyme dynamics | Enzymatic Reaction:
E + S <-> ES -> E + P Let
We know that Km = (kcat + k2)/k1 Assuming that kcat << k2 << k1, we can rewrite Km ~ k2/k1 From this paper constants for TEV can be found:
These values correspond with our assumption that kcat ~ 0.1 s^-1 and Km ~ 0.01 mM. Hence, we can estimate the following orders of magnitude for the rate constants:
Using these values should be a good approximation for our model. |
Degradation rate
(common for all) |
Assumption: To be approximated by cell division (dilution of media) as none of the proteins are involved in any active degradation pathways
Growth rate (divisions/h): 0.53<G.r.<2.18 Hence on average, g.r.=1.5 divisions per hour => 1 division every 1/1.5=0.6667 of an hour (40mins) To deduce degradation rate use the following formula: τ_(1⁄2)=ln2/k Where τ_(1⁄2)=0.667 hour, k – is the degradation rate k=ln2/τ_(1⁄2) = 0.000289 s^(-1) |
Production rate
(TEV and dioxygenase) |
We had real trouble finding the production rate values in the literature and we hope to be able to perform experiments to obtain those values for (TEV protease and catechol 2,3-dioxygenase). The experiments will not be possible to be carried out soon, so for the time being we suggest very simplistic approach for estimating production rates. We have found production rates for two arbitrary proteins in E.Coli. We want to get estimates of production rates by comparing the lengths of the proteins (number of amino-acids). As this approach is very vague, it is important to realise its limitations and inconsistencies:
LacZ production = 100 molecules/min (1024 AA) Average production ≈ 100molecules/min 720 AA That gives us:
As production rate needs to be expressed in concentration units per unit volume, the above number is converted to mols/s and divided by the cell volume → 2.3808*10^(-10) mol*dm^(-3)*s^(-1)
We will treat these numbers as guiding us in terms of range of orders of magnitudes. We will try to run our models for variety of values and determine system’s limitations. |
Kinetic parameters
of dioxygenase |
Initial velocity of the enzymatic reaction was investigated at pH 7.5 and 30 °C.
Km = 10μM kcat = 52 s^(−1)
Km = 40μM kcat = 192 s^(−1) Consequently, the kcat/Km 4.8 of the mutant was slightly lower than kcat/Km 5.2 of the wild type, indicating that the mutation has little effect on catalytic efficiency. |
Dimensions of
Bacillus subtillis cell |
Dimensions of Basillus subtilis (cylinder/rod shape) in reach media (ref. bionumbers):
This gives: Volume= π∙(d/2)^2∙l=2.793999 μm^3≈ 2.79∙10^(-15) dm^3 |
Split TEV
production rates |
*Assume the both parts of split TEV are half of size of the whole TEV (3054/2=1527 AA)
The whole construct is then: 1617 AA → split TEV production rate ≈ 1.2606*10^(-10) mol*dm^(-3)*s^(-1) |