Team:Imperial College/SingleCell

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Single Cell Modelling Overview

These models extensively describe the intracellular interactions of our Genetically Engineered Artificial Ratio (G.E.A.R.) system. The models were built using Simbiology, a MATLAB toolbox. They have provided us with timescale information and their results have allowed us to review our assembly strategies in the wet lab. Experiments conducted in the wet lab fed back into the model and improved the accuracy of our parameters. We are very proud to present you our models, the fruit of weeks of very hard work!

The first stage of our modelling process was to construct a single cell in silico model of our circuit. Our model was built using mass action kinetics in Simbiology (Matlab toolbox) and built up reaction by reaction.

We first separated the models into 3 modules: Quorum Communication, STAR-antiSTAR Comparator and Growth Regulation.


We constructed the four quorum systems that we considered viable choices for our system (cin, rhl, lux and las) to allow us to directly compare the expected behaviour and plan our growth module experiments accordingly. We designed the overall model for the Rhl and Cin systems (Chen et al., 2015) as they have been previously shown to operate with minimal crosstalk.

Assumptions
We used numbers obtained from Chen et al for C4 and C14 production. This is a high level production term that ignores parts of the central dogma. We made this assumption due to the limited data on the enzymatic kinetics of the autoinducer synthases.

Rhl
The Rhl system consists of an autoinducer synthase RhlI (that produces C4 AHL) and a transcriptional regulator RhlR that dimerises to activate a pRhl promoter which activates STAR transcription.

Cin
The Cin system consists of an autoinducer synthase CinI (that produces C14 AHL) and a transcriptional regulator CinR that dimerizes to activate a pCin promoter which induces Anti-STAR production.



Reactions



Communication module:

\[\varnothing\rightarrow C14\] \[\varnothing\rightarrow C4\] \[RNA_{pol} + g_{C4R} \rightarrow RNA_{pol} + g_{C4R} + mRNA_{C4R}\] \[RNA_{pol} + g_{C14R} \rightarrow RNA_{pol} + g_{C14R} + mRNA_{C4R}\] \[mRNA_{C4R}\rightarrow C4R\] \[mRNA_{C14R}\rightarrow C14R\] \[C14+C14R \rightarrow C14_{complex}\] \[C4+C4R \rightarrow C4_{complex}\] \[C4\rightarrow\varnothing\] \[mRNA_{C4R}\rightarrow\varnothing\] \[C4R\rightarrow\varnothing\] \[C4_{complex}\rightarrow\varnothing\] \[C4_{dimer}\rightarrow\varnothing\] \[C14\rightarrow\varnothing\] \[mRNA_{C14R}\rightarrow\varnothing\] \[C14R\rightarrow\varnothing\] \[C14_{complex}\rightarrow\varnothing\] \[C14_{dimer}\rightarrow\varnothing\]



Simulation Results



The results indicate that the species within this module reach steady states at time points unique to that species.



Figure 1: Production of C4 AHLs and C14 AHLs against time



Figure 2: Production of C4R and C14R regulatory proteins against time



Figure 3: C4:C4R and C14:C14R complex formation against time


Using STAR (Short Transcription Activating RNA) technology, we were able to develop a novel method of comparing the sizes of two populations from their quorum signal concentrations.

We used RNAstruct developed by Matthews Lab to help aid the development of the ANTISTAR. This software allowed us to determine the secondary structure and free energy to optimize the way in which our ANTISTAR sequence was designed. This was done so that our ANTISTAR sequence would have as high an affinity to the STAR sequence as was possible.



Figure 4: Secondary structure of our ANTISTAR sequence



To calculate the kinetics of the RNA interactions that occur within this module we adapted a method developed by Eric Winfree known as DNA strand displacement kinetics (Zhang and Winfree, 2009).



Reactions



Comparator module:

\[C14_{dimer} + Promoter_{Cin} \rightleftharpoons Promoter_{Cin+C14}\] \[RNA_{pol} + Promoter_{Cin+C14} \rightleftharpoons RNA_{pol} + Promoter_{Cin+C14} + antiSTAR\] \[RNA_{pol} + Promoter_{Cin} \rightleftharpoons RNA_{pol} + Promoter_{Cin} + antiSTAR\] \[C4_{dimer} + Promoter_{Rhl} \rightleftharpoons Promoter_{Rhl+C4}\] \[RNA_{pol} + Promoter_{Rhl+C4} \rightleftharpoons RNA_{pol} + Promoter_{Rhl+C4} + STAR\] \[RNA_{pol} + Promoter_{Rhl} \rightleftharpoons RNA_{pol} + Promoter_{Rhl} + STAR\] \[antiSTAR + STAR\rightleftharpoons STAR_{complex}\] \[C4_{dimer}\rightarrow\varnothing\] \[C14_{dimer}\rightarrow\varnothing\] \[RNA_{pol}\rightarrow\varnothing\] \[STAR\rightarrow\varnothing\] \[antiSTAR\rightarrow\varnothing\] \[STAR_{complex}\rightarrow\varnothing\]



Simulation Results:

Induced production of STAR and ANTISTAR was shown to be much higher than their basal production.



Figure 5: Basal vs Induced STAR production



Figure 6:Basal vs induced AntiSTAR production

STAR:ANTI STAR Complex formation occurs continuously whereas STAR: STAR Target complex formation is dependant on the copy number of the STAR target (in this case it was 30 represented by a psB3k3 plasmid backbone.



Figure 7:STAR:AntiSTAR Complex formation



Figure 8:STAR:STAR Target Complex formation


We constructed 4 different models for each of our growth regulators.

Auxotrophy (LeuB)

LeuB codes for an enzyme in the biosynthetic pathway of leucine in E. coli. The gene has been used before as a control method in co-culture. When using LeuB, we would need to use a strain that is auxotrophic for leucine and a growth medium lacking leucine. This system would require an inverter for it to operate so we incorporated a Tet inverter into the model.



Reactions



LeuB module:

\[Promoter_{AD1} + STAR\rightleftharpoons Promoter_{AD1+STAR}\] \[RNA_{pol} + Promoter_{AD1+STAR}\rightarrow RNA_{pol} + Promoter_{AD1+STAR} + mRNA_{TetR}\] \[RNA_{pol} + Promoter_{AD1}\rightarrow RNA_{pol} + Promoter_{AD1} + mRNA_{TetR}\] \[mRNA_{TetR}\rightarrow TetR\] \[TetR_{pre}\rightarrow TetR\] \[Promoter_{Tet} + STAR\rightleftharpoons Promoter_{Tet+TetR}\] \[RNA_{pol} + Promoter_{Tet+TetR}\rightarrow RNA_{pol} + Promoter_{Tet+TetR} + mRNA_{LeuB}\] \[mRNA_{LeuB}\rightarrow LeuB_{pre} \] \[LeuB_{pre}\rightarrow LeuB \] \[mRNA_{RNApol}\rightarrow\varnothing\] \[RNA_{pol}\rightarrow\varnothing\] \[mRNA_{TetR}\rightarrow\varnothing\] \[ TetR_{pre}\rightarrow\varnothing\] \[TetR\rightarrow\varnothing\] \[mRNA_{LeuB}\rightarrow\varnothing\] \[ LeuB_{pre}\rightarrow\varnothing\] \[LeuB\rightarrow\varnothing\]



Simulation Results



The figure shows successful repression of LeuB by the Tet system.



Figure 9: Effect of tet repressor on the production of LeuB



Antibiotic resistance (Chloramphenicol resistance)


Cat, encoding Chloramphenicol acetyltransferase, which is an enzyme that confers resistance to the antibiotic chloramphenicol. We decided to use chloramphenicol because it is a bacteriostatic rather than a bactericidal antibiotic. When using Cat, chloramphenicol would be added to the growth medium. This system would require an inverter for it to operate so we incorporated a Tet inverter into the model.

Reactions



Chloramphenicol resistance module:

\[Promoter_{AD1} + STAR\rightleftharpoons Promoter_{AD1+STAR}\] \[RNA_{pol} + Promoter_{AD1+STAR}\rightarrow RNA_{pol} + Promoter_{AD1+STAR} + mRNA_{TetR}\] \[RNA_{pol} + Promoter_{AD1}\rightarrow RNA_{pol} + Promoter_{AD1} + mRNA_{TetR}\] \[mRNA_{TetR}\rightarrow TetR\] \[TetR_{pre}\rightarrow TetR\] \[Promoter_{Tet} + STAR\rightleftharpoons Promoter_{Tet+TetR}\] \[RNA_{pol} + Promoter_{Tet+TetR}\rightarrow RNA_{pol} + Promoter_{Tet+TetR} + mRNA_{CAT}\] \[mRNA_{CAT}\rightarrow CAT_{pre} \] \[CAT_{pre}\rightarrow CAT \] \[mRNA_{RNApol}\rightarrow\varnothing\] \[RNA_{pol}\rightarrow\varnothing\] \[mRNA_{TetR}\rightarrow\varnothing\] \[ TetR_{pre}\rightarrow\varnothing\] \[TetR\rightarrow\varnothing\] \[mRNA_{CAT}\rightarrow\varnothing\] \[ CAT_{pre}\rightarrow\varnothing\] \[CAT\rightarrow\varnothing\]



Simulation Results



Figure 10: Effect of tet repressor on the production of CAT



Gene product 2

Gp2 is a gene from the E. coli bacteriophage T7 phage, which slows down cell growth by binding reversibly to the E. coli RNA polymerase complex, thus inhibiting transcription. T7 phage infection is characterised by the hindrance of bacterial growth, and Gp2 has been suggested as a potential antimicrobial agent.



Reactions



GP 2 module:

\[Promoter_{AD1} + STAR\rightleftharpoons Promoter_{AD1+STAR}\] \[RNA_{pol} + Promoter_{AD1+STAR}\rightarrow RNA_{pol} + Promoter_{AD1+STAR} + mRNA_{GP2}\] \[RNA_{pol} + Promoter_{AD1}\rightarrow RNA_{pol} + Promoter_{AD1} + mRNA_{GP2}\] \[mRNA_{GP2}\rightarrow GP2_{pre}\] \[GP2_{pre}\rightarrow GP2\] \[GP2 + RNA_{pol} \rightleftharpoons GP2:RNA_{pol}\] \[\varnothing\rightarrow mRNA_{RNApol}\] \[mRNA_{RNApol}\rightarrow RNA_{pol}\] \[mRNA_{RNApol}\rightarrow\varnothing\] \[RNA_{pol}\rightarrow\varnothing\] \[mRNA_{GP2}\rightarrow\varnothing\] \[ GP2_{pre}\rightarrow\varnothing\] \[GP2\rightarrow\varnothing\] \[GP2:RNA_{pol}\rightarrow\varnothing\]





Simulation Results



Figure 11: Basal vs induced production of Gp2





Gene Product 0.4

Gp0.4 is another T7 phage gene which inhibits growth by binding to the FtsZ ring during mitosis, preventing cytokinesis (the final stage of cell division where the two daughter cells separate).



Reactions



GP 0.4 module:

\[Promoter_{AD1} + STAR\rightleftharpoons Promoter_{AD1+STAR}\] \[RNA_{pol} + Promoter_{AD1+STAR}\rightarrow RNA_{pol} + Promoter_{AD1+STAR} + mRNA_{GP2}\] \[RNA_{pol} + Promoter_{AD1}\rightarrow RNA_{pol} + Promoter_{AD1} + mRNA_{GP2}\] \[mRNA_{GP2}\rightarrow GP2_{pre}\] \[GP0.4_{pre}\rightarrow GP0.4\] \[GP0.4 + FtsZ \rightleftharpoons GP0.4:FtsZ\] \[\varnothing\rightarrow mRNA_{RNApol}\] \[mRNA_{RNApol}\rightarrow RNA_{pol}\] \[mRNA_{RNApol}\rightarrow\varnothing\] \[RNA_{pol}\rightarrow\varnothing\] \[mRNA_{GP0.4}\rightarrow\varnothing\] \[ GP0.4_{pre}\rightarrow\varnothing\] \[GP0.4\rightarrow\varnothing\] \[FtsZ\rightarrow\varnothing\]





Simulation Results



Figure 12: Basal vs Induced production of GP 0.4


Once the modules were built they were joined to form cohesive models of our circuit. These were named after the growth regulators used in them and analyzed.

The first thing we did was to compare the time taken for the four different models (GP2,GP0.4,LeuB and CAT) to work as expected. We decided to focus our attention on the GP2 and GP0.4 systems as they were predicted by our models to work the fastest. This was due to the fact that the LeuB and CAT modules required Tet inverters in order.



Sensitivity Analysis

We then performed sensitivity analysis on the GP0.4 and GP2 models. We only analysed the parameters that we can change in lab (transcriptions rates via promoter strength, translation rates via RBS strength, copy numbers and degradation rates via the inclusion of degradation tags). This allows us to identify which parameters should be tweaked in order to balance our system in order to set the population ratios that we want.



Transcription rates



Figure 13: Sensitivity analysis for the transcription rates for the production of GP 0.4 and GP2



Translation rates


Figure 14: Sensitivity analysis for the translation rates for the production of GP 0.4 and GP2



Degradation rates


Figure 15: Sensitivity analysis for the degradation rates in the GP2 and GP0.4 models



Copy Number


Figure 16: Sensitivity analysis for the copy numbers in the GP2 and GP0.4 models







Parameter Sweeps
Our next process was to create a framework in which we could balance our circuit in silico. To do this identified the the parameters indicated by the sensitivity analysis and ran parameter sweep in order to see how this would affect parts of the models. We used known numbers from biobrick parts as we wanted our model to use the materials available to us in the lab.

Transcription rates

By altering promoter strength, we can alter the transcription rates within the models. For example:



Figure 17: Parameter sweep for the transcription rate of C4R (k_mC4R) encompassing the Anderson promoter library



Translation rates
Translation rate can be affect by RBS strength and this can be can be altered through the use of RBS calculators such as the one developed by the Salis Lab.



Copy numbers
Plasmid copy number is influenced by the origin of replication with in the plasmid. By using different origins of replication we can modify the circuit's behaviour, for example pSB3K3 has a copy number of 20-30.



Degradation rates
Degradation affect everything within the cell so it is an ideal parameter to alter in order to modify the circuit's behaviour. This can be done with the addition of degradation tags e.g. LVA tags.



The analysis data was then used in our population level models to balance the system at population level and predetermine the ratio of co-cultures.

Works Cited


Chen, Y., Kim, J., Hirning, A., Josi, K. and Bennett, M. (2015). Emergent genetic oscillations in a synthetic microbial consortium. Science, 349(6251), pp.986-989.

Zhang, D. and Winfree, E. (2009). Control of DNA Strand Displacement Kinetics Using Toehold Exchange. J. Am. Chem. Soc., 131(47), pp.17303-17314.

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