Team:TorontoMaRSDiscovery/Modeling

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Contents

Objective

Model

The construct that needs to be modelled is shown below. Our submission this year may/may not have all of the parts assebled.

BioBrick.png

The construct is represented by the reactions shown below Click here for excel file. The reaction framework was mainly generated using the SynBioSS Designer (a great modelling tool!), which also provides "default" parameter values. These parameter values have been gathered from various literature sources, and should be taken as approximations on the appropriate order of magnitude. All units were taken to be (1 / molarity^n-1 * s), where n is the order of the reaction. For example, for the reaction 2 lacI --> lacI2, n = 2, thus the rate constant has the units 1/molality*s.

The pathways for the expressed proteins, eCFPt and Encapsulin, need to be modelled in more detail. For example, in this basic model eCFPt is degraded via a first order reaction and Encapsulin makes a dimer complex. However, in reality fluorescent proteins have been shown to degreade via Micheales-menton kinetics and Encapsulin is thought to make a complex of about 60 monomers. These issues will be addressed in future work.


Reaction Rate Constant
Constitutive Expression
--> lacl4 1E-10
--> tetR2 1E-10
Multimerization
2 lacI --> lacI2 1.00E+09
lacI2 --> 2 lacI 10
2 lacI2 --> lacI4 1.00E+09
lacI4 --> 2 lacI2 10
2 tetR --> tetR2 1.00E+09
tetR2 --> 2 tetR 10
2 Enc --> Enc2 100
Encapsulation
Enc2 + eCFPt --> Enc2:eCFPt 100
Transcription
RNAp + BBa_R0010 + LacI_binding_site --> RNAp:BBa_R0010:LacI_binding_site 10000000
RNAp:BBa_R0010:LacI_binding_site --> RNAp + BBa_R0010 + LacI_binding_site 0.057
RNAp:BBa_R0010:LacI_binding_site --> RNAp:BBa_R0010:LacI_binding_site* 0.1
RNAp:BBa_R0010:LacI_binding_site* --> RNAp:DNA_eCFPt + BBa_R0010 + LacI_binding_site 30
RNAp:DNA_eCFPt --> RNAp + mRNA_eCFPt 0.035
RNAp + BBa_R0040 + TetR_1 + TetR_2 --> RNAp:BBa_R0040:TetR_1:TetR_2 10000000
RNAp:BBa_R0040:TetR_1:TetR_2 --> RNAp + BBa_R0040 + TetR_1 + TetR_2 0.057
RNAp:BBa_R0040:TetR_1:TetR_2 --> RNAp:BBa_R0040:TetR_1:TetR_2* 0.1
RNAp:BBa_R0040:TetR_1:TetR_2* --> RNAp:DNA_Enc + BBa_R0040 + TetR_1 + TetR_2 30
RNAp:DNA_Enc --> RNAp + mRNA_Enc 0.0375
Translation
rib + mRNA_eCFPt --> rib:mRNA_eCFPt 100000
rib:mRNA_eCFPt --> rib:mRNA_eCFPt_1 + mRNA_eCFPt 33
rib:mRNA_eCFPt_1 --> rib + eCFPt 0.1154
rib + mRNA_Enc --> rib:mRNA_Enc 100000
rib:mRNA_Enc --> rib:mRNA_Enc_1 + mRNA_Enc 33
rib:mRNA_Enc_1 --> rib + Enc 0.1234
Protein-DNA
lacI4 + nsDNA --> lacI4:nsDNA 1000
lacI4:nsDNA --> lacI4 + nsDNA 1.6225
lacI4 + LacI_binding_site --> lacI4:LacI_binding_site 1.00E+09
lacI4:LacI_binding_site --> lacI4 + LacI_binding_site 0.005
tetR2 + nsDNA --> tetR2:nsDNA 1000
tetR2:nsDNA --> tetR2 + nsDNA 1.6225
tetR2 + TetR_1 --> tetR2:TetR_1 1.00E+09
tetR2:TetR_1 --> tetR2 + TetR_1 0.005
tetR2 + TetR_2 --> tetR2:TetR_2 1.00E+09
tetR2:TetR_2 --> tetR2 + TetR_2 0.005
Protein - Effector - DNA
lacI4 + IPTG --> lacI4:IPTG 50000000
lacI4:IPTG --> lacI4 + IPTG 0.1
lacI4:IPTG + LacI_binding_site --> lacI4:IPTG:LacI_binding_site 1.00E+09
lacI4:IPTG:LacI_binding_site --> lacI4:IPTG + LacI_binding_site 0.7
lacI4:LacI_binding_site + IPTG --> lacI4:IPTG:LacI_binding_site 1000000
lacI4:IPTG:LacI_binding_site --> lacI4:LacI_binding_site + IPTG 0.4
lacI4:IPTG + nsDNA --> lacI4:IPTG:nsDNA 1000
lacI4:IPTG:nsDNA --> lacI4:IPTG + nsDNA 1.6225
lacI4:nsDNA + IPTG --> lacI4:IPTG:nsDNA 1000
lacI4:IPTG:nsDNA --> lacI4:nsDNA + IPTG 1.6225
tetR2 + aTc --> tetR2:aTc 50000000
tetR2:aTc --> tetR2 + aTc 0.1
tetR2:aTc + TetR_1 --> tetR2:aTc:TetR_1 1.00E+09
tetR2:aTc:TetR_1 --> tetR2:aTc + TetR_1 0.7
tetR2:TetR_1 + aTc --> tetR2:aTc:TetR_1 1000000
tetR2:aTc:TetR_1 --> tetR2:TetR_1 + aTc 0.4
tetR2:aTc + TetR_2 --> tetR2:aTc:TetR_2 1.00E+09
tetR2:aTc:TetR_2 --> tetR2:aTc + TetR_2 0.7
tetR2:TetR_2 + aTc --> tetR2:aTc:TetR_2 1000000
tetR2:aTc:TetR_2 --> tetR2:TetR_2 + aTc 0.4
tetR2:aTc + nsDNA --> tetR2:aTc:nsDNA 1000
tetR2:aTc:nsDNA --> tetR2:aTc + nsDNA 1.6225
tetR2:nsDNA + aTc --> tetR2:aTc:nsDNA 1000
tetR2:aTc:nsDNA --> tetR2:nsDNA + aTc 1.6225
Degredation
lacI4 --> 0.000289
tetR2 --> 0.000289
mRNA_eCFPt --> 0.0015
mRNA_Enc --> 0.0015
eCFPt --> 0.000289
Enc2 --> 0.000289
Enc2:eCFPt --> 0.000289
Dilution
lacI4:nsDNA --> nsDNA 0.000193
tetR2:nsDNA --> nsDNA 0.000193
lacI4:IPTG --> IPTG 0.000289
tetR2:aTc --> aTc 0.000289
lacI4:IPTG:nsDNA --> IPTG + nsDNA 0.000193
tetR2:aTc:nsDNA --> aTc + nsDNA 0.000193


Simulations

All simulations were carried out using the SimBiology Matlab Toolbox, which was freely available to iGEM teams. The File:SimBiology project file used for the following simulations can be accessed File:Here.

Accumulation of Proteins and Encapsulin-eCFP complex

Uft mod pic1.png Uft mod pic2.png

It can be observed that the expressed proteins and Encapsulin-eCFP complex have some sort of oscillatory behavior, and that the later inverses the former. The Encapsulin and eCFPt proteins concentrations build up while the complex concentation stays low, and then the complex starts to form while the reservoirs of Encapsulin and eCFPt are depleted.

Addition of IPTG and aTc effectors

Uft mod pic3.png Uft mod pic4.png

IPTG and aTc effectors bind lacI4 and tetR2 respectively, preventing them from inhibiting transcription. Predictably, when IPTG and aTc are added to the system (initial amounts changed from 0 --> 100), we observe higher peaks in protein expresssion and complex formation.

Sensitivity Analysis

It is interesting to note which parameters have the greatest effect on the dynamics of the system. Since the parameters in our model are approximations from literature sources, the most sensitive parameters would be leading candidates to be experimentally determined.

File:Uft mod sa1.png

Future Work