Team:UFRGS Brazil/Modeling
Model
One of our major concerns regarding this project is to ensure that our bacteria won’t escape the environment designed for them. Although alginate beads can be a very tight structure for bacterial imprisonment, one cannot expect that it will solve all of our problems. Nonetheless, even if these organisms escape, a second containment mechanism must be engaged to avoid any ecological damage, since these beings will be disposed in a natural environment. With the help of computational resources, our team was able to devise two different approaches to help to solve this issue.
1. Alginate beads and diffusion
Bacteria uses its flagella to swim through fluid media. Since E.coli K12 is motile, one of the reasons it could escape from the beads is by diffusion. So, to understand how this would affect our project, we searched for ways of modeling this process.
Using the mathematical relations proposed by Licata et. al, we can calculate the diffusion coefficient of bacterial cells in porous media, being \(v\) the velocity of the cell, \(a\) the pore size, \(\alpha\) the tumbling frequency, the mean projection of adjacent bond and \(x\) a dimensionless parameter.
$$x = {\omega a \over v}$$ $$D = {\frac{v a}{3 (1 - \alpha ) x} [1 - (1 + x) {e}^{-x} + \alpha {e}^{-x} (\mathrm{e}^{-x} - 1 + x)]} $$
This equation considers several parameters that we can not control but are dependent on the bacteria and its surroundings: this includes \(v\) and \(\omega\). The average pore size, represented by \(a\), is a parameter that we can measure by electron microscopy and thus is a variable that we can fix, so as \(\alpha\).
Considering electron microscopy analysis made by our team (figure 2), we found the average pore size on our alginate beads is 22.5 \(\mu m\) and its average diameter is 3 \(mm\). With the aid of an in-house python script, we solved the expression fixing \(a\) as 22.5 \(\mu m\), as found in microscopy data and \(\alpha\) as \(1 \over 3\), with tumbling frequency \({s}^{-1}\) and velocity v(\(\mu m \over s\)) as variables. Using gnuplot to plot the graph (figure 2), we can see that the diffusion constant varies from 0 to 120 \(\mu {m}^{2} \over s\). Bacteria can portray different cell velocity and different tumbling frequency, but considering the worst-case scenario, when v is the highest (30 \(\mu m \over s\))(Maeda et. al) and diffusion constant is the highest (120 \(\mu {m}^{2} \over s\)) , we can solve the equation of diffusion over a distance as: $$t = {{x}^{2} \over 6D}$$
Where \(x\) is our sphere radius (1.5 \(mm\)) and \(D\) is the diffusion coefficient from our worst-case scenario. So, the time bacteria diffuses through porous media is 0.003 seconds, showing that our methodology of generating alginate spheres needs to be reassessed, focusing on reducing pore size and increasing sphere diameter. If we could reproduce a pore size of 28.7 \(Å\), as in Fundueanu et. al, while decreasing diameter to 220 \(\mu m\) our bacteria would need 10 seconds to diffuse through the bead, even this being a pore size 10,000 times smaller than a bacteria. This shows that only this diffusion approach is not enough to represent the complexity of the matter, leaving as a perspective the use of integrated models to ensure a better representation of experimental data.
2. Kill-Switch design and improvement
Bearing in mind the possibility of leakage, a biologically designed containment system must be put into action, not allowing contamination by genetically modified bacteria in the water being treated. To do so, we adapted an already existing biological circuit, consisted of three major players: lacI, cI and MazF toxin.
Since this BioBrick doesn’t have any RBS, and a cI CDS containing a barcode (which has been demonstrated problematic by team 2010 UC Davis), we corrected these two issues, creating and alternate and functional version (BBa_K3215014).
2.1 A Kill Switch with "memory" time repressed by IPTG - Corrected
Firstly, in order to improve and design a BioBrick, we established a mathematical model to analyse the efficiency of the already existing one. To do so, we started by creating some kinetic rate laws.
2.1.1 Kinetic rate laws
With our first kinetic rate law, we showed how the concentration of extracellular glucose varies with time, considering an already stationary phase of bacterial growth:
$$\frac{d[Glucose]}{dt} = {{-k}_{Glu}}$$
Where \({k}_{Glu}\) (\(1 x {10}^{-6} M.{min}^{-1}\)) is the extracellular glucose decay rate. Since there is no bacterial growth, we assumed a constant variation of glucose.
Having the variation of extracellular glucose with time, we can relate it with the concentration of intracellular cyclic AMP, in a mass balance equation:
$$[cAMP] = {{K}_{cAMP}(\frac{{K}_{Sat}}{[Glucose] \psi + {K}_{Sat}})}$$
Where \({K}_{Sat} (1x{10}^{-2} M \)) is the saturation of extracellular glucose conversion to intracellular \(cAMP\) constant; \(\psi\)(10) is a correction factor, which arose from factors such as difference of concentration between levels of extracellular and intracellular glucose, glucose-6-Phosphate production, cell concentration, etc...; and \({K}_{cAMP}\) (\(1x{10}^{-4} M\)) is the maximum intracellular \(cAMP\) concentration. This equation was achieved by defining the maximum concentration of \(cAMP\) found in E. coli, and with that information, we related it with the levels of extracellular glucose:
This graph shows us that \(cAMP\) concentration varies within a range of millimolar glucose variation, which correlates with data found in the literature.
For the concentration of the \({mRNA}_{lacI}\), we have:
$$\frac{d[{mRNA}_{lacI}]}{dt} = {{V}_{mRNA-lacI} \quad - \quad [{mRNA}_{lacI}]{k}_{d,mRNA-lacI}}$$
Where \({k}_{d,mRNA-lacI}\) (0.3 \({min}^{-1}\)) is the degradation rate constant of \({mRNA}_{lacI}\), and \({V}_{mRNA-lacI}\) is the rate of lacI mRNA formation, given by:
$${V}_{mRNA-laci} = {{k}_{mRNA-lacI} \omega 1 [{G}_{lacI}]}$$
In which \({k}_{mRNA-lacI} (5 {min}^{-1})\) is the mRNA transcription rate constant, \([GlacI] (2.54x{10}^{-9} M)\) is the lacI coding sequence concentration, and \(\omega 1\) is the percentage of transcription complexes bound to the lacI CDS promoter:
$$\omega 1 = {\frac{[RP:s:Pc]}{[Pc]}}$$
Where \([RP:s:Pc]\) is the concentration of the RNA Polymerase-sigma factor-promoter complex, and \([Pc] (2.54x{10}^{-9} M)\) is the promoter concentration. Since all of these values are constant, \(\omega 1\) is also constant. All concentrations of the components of this equation can be found in the next section, regarding the mass balance equations.
For the lacI protein:
$$\frac{d[lacI]}{dt} = {{V}_{lacI} \quad [lacI] {k}_{d,lacI}}$$
Having \({k}_{d,lacI} (0.3 {min}^{-1})\), the protein degradation constant, and \({V}_{lacI}\), the rate of lacI protein production:
$${V}_{lacI} = {{k}_{lacI}[{mRNA}_{lacI}]}$$
Where \({k}_{lacI} (5 {min}^{-1})\) is the mRNA translation constant.
Following, we have the variation ofthe concentration of \({mRNA}_{cI}\), which, in a similar way of thinking in relation to lacI mRNA, is given by:
$$\frac{d[{mRNA}_{cI}]}{dt} = {{V}_{mRNA-cI} \quad - \quad [{mRNA}_{cI}] {k}_{d,mRNA-cI}}$$
With \({k}_{d,mRNA-cI} = 0.3 {min}^{-1}\); and the rate of cI mRNA formation being:
$${V}_{mRNA-cI} = {{k}_{mRNA-cI}\eta 1 \eta 2 \eta 3 [{G}_{cI}]}$$
Having \({k}_{mRNA-cI} = 5 {min}^{-1}\) and the concentration of cI promoter \([GcI] = 2.4x{10}^{-9} M\). The three constants (\(\eta 1\), \(\eta 2\), and \(\eta 3\)) are related to the percentages of RNA Polymerase-sigma factor-promoter complex (like for \(\omega 1\)), of CRP-cAMP-DNA complex and of free lac operator regions (this part lacks operator region 2), respectively:
$$\eta 1 = {\frac{[RP:s:Plac]}{[Plac]}}$$
$$\eta 2 = {\frac{[CRP:cAMP:E]}{[E]}}$$
$$\eta 3 = {(\frac{[{O1}_{f}]}{[O1]}) (\frac{[{O3}_{f}]}{[O3]})}$$
Again, all concentrations of the components of these equations can be found in the next section, regarding the mass balance equations, together with \(\omega 1\).
Following, we have that:
$$\frac{d[cI]}{dt} = {{V}_{cI} - [cI] {k}_{d,cI}}$$
Where \({k}_{d,cI} = 0.3 {min}^{-1}\), and \({V}_{cI}\):
$${V}_{cI} = {{k}_{cI}[{mRNA}_{cI}]}$$
With \({k}_{cI} = 5 {min}^{-1}\). To address the concentration of MazF mRNA, we assumed that:
$$\frac{d[{mRNA}_{MazF}]}{dt} = {{V}_{mRNA-MazF} \quad - \quad [{mRNA}_{MazF}]{k}_{d,mRNA-MazF}}$$
In which the degradation rate constant, \({k}_{d,mRNA-MazF} = 0.3 {min}^{-1}\), and the MazF mRNA formation rate is given by:
$${V}_{mRNA-MazF} = {{k}_{mRNA-MazF}\epsilon 1 \epsilon 2 [{G}_{MazF}]}$$
Where \({k}_{mRNA-MazF} = 5 {min}^{-1}\), \([GMazF] = 2.54x{10}^{-9} M\), having the two constants relations, \(\epsilon 1\) and \(\epsilon 2\), given by:
$$\epsilon 1 = {\frac{[RP:s:PcI]}{[PcI]}}$$
$$\epsilon 2 = {(\frac{[{OcI 1}_{f}]}{[OcI 1]}) (\frac{[{OcI 2}_{f}]}{[OcI 2]})}$$
Where \(\epsilon 2\) is the fraction of both free cI operator regions.
The last two differential relations of this first Kill-Switch model are given by:
$$\frac{d[MazF]}{dt} = {{V}_{MazF} \quad - \quad [MazF]{k}_{d,MazF}}$$
Where \({k}_{d,MazF} = 0.3 {min}^{-1}\), and \({V}_{MazF}\) is:
$${V}_{MazF} = {{k}_{MazF}[{mRNA}_{MazF}]}$$
In which \({k}_{MazF} = 5 {min}^{-1}\). Although the differential equations were set, we still need to figure how to relate some of the variables found in them to values already established. To do so, several mass balances equations were deduced, resulting in multiple nonlinear systems of equations that need to be solved in order to integrate these functions. For this model, we considered the concentrations of IPTG constant, since it was designed to provide bacterial survival in our medium. List of parameters used in this section:
2.1.2 RNA Polymerase and promoters
For these first mass balances reactions, we considered the concentrations of RNA Polymerase (RP), sigma factor (s), a constitutive promoter (Pc) and nonspecific DNA (D), together with their free concentrations:
Relations: $$[RP] = {[{RP}_{f}] + [RP:Pc] + [RP:D] + [RP:s] + [RP:s:Pc] + [RP:s:D]}$$ $$[s] = {[{s}_{f}] + [RP:s] + [RP:s:Pc] + [RP:s:D]}$$ $$[Pc] = {[{Pc}_{f}] + [RP:Pc] + [RP:s:Pc]}$$
Where: $$[RP:s] = {{K}_{ns} . [{RP}_{f}] . [{s}_{f}]}$$ $$[RP:Pc] = {{K}_{npc} . [{RP}_{f}] . [{Pc}_{f}]}$$ $$[RP:D] = {{K}_{nd} . [{RP}_{f}] . [D]}$$ $$[RP:s:Pc] = {{K}_{nspc} . [RP:s] . [{Pc}_{f}]}$$ $$[RP:s:D] = {{K}_{nsd} . [RP:s] . [D]}$$
List of parameters used in this section:
2.1.3 Glucose regulation
Here we have cAMP Receptor Protein (CRP), cyclic AMP (cAMP) and complex CRP-cAMP binding site (E), together with their free concentrations:
Relations: $$[CRP] = {[{CRP}_{f}] + [CRP:E] + [CRP:cAMP] + [CRP:D] + [CRP:cAMP:E] + [CRP:cAMP:D]}$$ $$[cAMP] = {[{cAMP}_{f}] + [CRP:cAMP] + [CRP:cAMP:E] + [CRP:cAMP:D]}$$ $$[E] = [{E}_{f}] + [CRP:E] + [CRP:cAMP:E]$$
Where: $$[CRP:cAMP] = {{K}_{ca} . [{CRP}_{f}] . [{cAMP}_{f}]}$$ $$[CRP:E] = {{K}_{ce} . [{CRP}_{f}] . [{E}_{f}]}$$ $$[CRP:D] = {{K}_{cd} . [{CRP}_{f}] . [D]}$$ $$[CRP:cAMP:E] = {{K}_{cae} . [CRP:cAMP] . [{E}_{f}]}$$ $$[CRP:cAMP:D] = {{K}_{cad} . [CRP:cAMP] . [D]}$$
List of parameters used in this section:
2.1.4 IPTG regulation
For the IPTG regulation, four major components take place: the repressor lac (Rep, which equals to two molecules of lacI), IPTG, and operator regions (O1 and O3, since O2 is not present in BBa_R0010).
Where: $$[Rep:IPTG] = {{K}_{rl} . [{Rep}_{f}] . [{IPTG}_{f}]}$$ $$[Rep:O1] = {{K}_{ro1} . [{Rep}_{f}] . [{O1}_{f}]}$$ $$[Rep:O3] = {{K}_{ro3} . [{Rep}_{f}] . [{O3}_{f}]}$$ $$[Rep:D] = {{K}_{rd} . [{Rep}_{f}] . [D]}$$ $$[Rep:IPTG:O1] = {{K}_{rlo1} . [Rep:IPTG] . [{O1}_{f}]}$$ $$[Rep:IPTG:O3] = {{K}_{rlo3} . [Rep:IPTG] . [{O3}_{f}]}$$ $$[Rep:IPTG:D] = {{K}_{rld} . [Rep:IPTG] . [D]}$$ $$[O1:Rep:O3] = {{\lambda}_{13} . {K}_{ro1} . [Rep:O3] . [{O1}_{f}]} = {{\lambda}_{13} . {K}_{ro3} . [Rep:O1] . [{O3}_{f}]}$$ $$[O1:Rep:IPTG:O3] = {{K}_{rlo1o3} . [Rep:IPTG:O1] . [{O3}_{f}]}$$
List of parameters used in this section:
2.1.5 cI regulation
In this section, we have the dimeric cI repressor (cI2, that equals to two cI molecules) and both cI operator regions (OcI1 and OcI2).
Relations: $$[cl2] = {[{cl2}_{f}] + [cl2:Ocl1] + [cl2:Ocl2] + [Ocl1:cl2:Ocl2] + [cl2:D]}$$ $$[Ocl1] = {[{Ocl1}_{f}] + [cl2:Ocl1] + [Ocl1:cl2:Ocl2]}$$ $$[Ocl2] = {[{Ocl2}_{f}] + [cl2:Ocl2] + [Ocl1:cl2:Ocl2]}$$
Where: $$[cl2:Ocl1] = {{K}_{cio1} . [{cl2}_{f}] . [{Ocl1}_{f}]}$$ $$[cl2:Ocl2] = {{K}_{cio2} . [{cl2}_{f}] . [{Ocl2}_{f}]}$$ $$[Ocl1:cl2:Ocl2] = {{K}_{cio2} . {\lambda}_{13} . [cl2:Ocl1] . [{Ocl2}_{f}]} = {{K}_{cio1} . [cl2:Ocl2] . [{Ocl1}_{f}]}$$ $$[cl2:D] = {{K}_{cid} . [{cl2}_{f}] . [D]}$$
List of parameters used in this section:
2.1.6 Results
All codes were written (Python 3.7.4) considering every equation above. The function created depends on 7 variables: (i) glucose concentration; (ii) lacI mRNA concentration; (iii) lacI concentration; (iv) cI mRNA concentration; (v) cI concentration; (vi) MazF mRNA concentration; and (vii) MazF concentration. We considered (iii) - (vii) to be zero, since they are the values we are interested in. On the other hand, we must know the values of (ii) and (iii) (“constants”), because our system can be thought as one that all organisms grew to a stationary level, and only after that the transcription of cI mRNA and MazF mRNA really begun. The only two “real” variables found in this model is glucose and IPTG (intrinsic to each function, since it is constant). Interestingly, the model only works if we consider two more parameters: \({\psi}_{cAMP}\) and \({\psi}_{IPTG}\) which both equal to 1000. The reason they emerged is probably because of factors such as difference between IPTG and cAMP concentrations inside and outside the cells, and also to factors such as experimental discrepancy, since some of the parameters values could have been defined considering different salt concentrations, temperature, etc…
The first experiment was, then, to determine the concentrations of lacI mRNA and lacI, where these values are independent of the glucose and IPTG concentrations:
The values for mRNA lacI \((~1.94x{10}^{-8} M)\) and lacI \((~3.23x{10}^{-7} M)\) are consistent with data from the literature. Both values obtained were incorporated into the next analysis. Now the question to be made is whether if glucose concentration can affect MazF’s IPTG regulation:
These results show us that when the concentration of glucose increases, the influence of IPTG on the system decreases, as expected. What is debatable is whether if glucose could prevent the overall toxicity of the system; in other words, whether the levels of MazF concentration in a glucose containing medium are still below a toxicity threshold. To answer this question and speculate a better Kill-Switch, a new model was created, and the dependence of glucose was removed, together with the removal of one operator region of cI CDS promoter (O3), since the tight lac regulation could be loosen, considering that this regulation might hinder the rise of cI levels, which are essential to prevent MazF mRNA transcription. In our system, the less MazF in the presence of IPTG, the better.
2.2 A Kill Switch with "memory" time repressed by IPTG - Improved
Our new Kill-Switch created (BBa_K3215016) differs from the last one in two already explained aspects: absence of a CRP binding region; and absence of one cI CDS operator region (dimeric lacI repressor binding site).
Using the same approach as before, almost every kinetic rate law were used, with the exception of those involved in glucose regulation, which includes glucose concentration rate law, cAMP mass balance relation and \(\epsilon 2\). In addition to that, the set of IPTG regulation mass balance equations was adjusted, considering the removal of O3 region.
2.2.1 IPTG regulation
Relations: $$[Rep] = {[{Rep}_{f}] + [Rep:IPTG] + [Rep:O1] + [Rep:D] + [Rep:IPTG:O1] + [Rep:IPTG:D]}$$ $$[IPTG] = {[{IPTG}_{f}] + [Rep:IPTG] + [Rep:IPTG:O1] + [Rep:IPTG:D]}$$ $$[O1] = {[{O1}_{f}] + [Rep:O1] + [Rep:IPTG:O1]}$$
Where: $$[Rep:IPTG] = {{K}_{rl} . [{Rep}_{f}] . [{IPTG}_{f}]}$$ $$[Rep:O1] = {{K}_{ro1} . [{Rep}_{f}] . [{O1}_{f}]}$$ $$[Rep:D] = {{K}_{rd} . [{Rep}_{f}] . [D]}$$ $$[Rep:IPTG:O1] = {{K}_{rlo1} . [Rep:IPTG] . [{O1}_{f}]}$$ $$[Rep:IPTG:D] = {{K}_{rld} . [Rep:IPTG] . [D]}$$
All the values of each parameter used are shown in Table 4.
2.2.2 Results
Since we don’t have the influence of glucose anymore, the number of variables in this new equation is reduced to six: (i) lacI mRNA concentration; (ii) lacI concentration; (iii) cI mRNA concentration; (iv) cI concentration; (v) MazF mRNA concentration; and (vi) MazF concentration. Once again, we considered (iii) - (vii) to be zero, since they are the values we are interested in. Since glucose concentration does not affect the levels of lacI mRNA and consequently, lacI levels, the same values obtained previously were used. The parameters \({\psi}_{cAMP}\) and \({\psi}_{IPTG}\) were not used anymore, since the absence of glucose/cAMP was removed.
These results show us that, when compared to the last model, this new system has a much higher efficiency in a natural environment that lacks glucose. The removal of O3 region showed a less rigid cI regulation (the levels of MazF in different IPTG concentrations are smaller when compared to the last system), although this fact can be in part attributed to maybe a “leaky transcriptional inhibition” activity promoted by CRP in the last model - when glucose was absent -, leading to a diminution of the levels of cI, and therefore, enhancement of MazF’s.
The major advantage of this new BioBrick is that we can now grow our bacteria in a medium containing glucose, which is way cheaper and easier to produce than other media. We do not consider this “less MazF levels” as an immediate upgrade, for the fact that we don’t know the MazF concentration toxicity threshold established for this system; if this critical value is achieved by inhibition - in low concentrations of glucose - of the last system, one could still use the latter, considering that in a natural environment, the odds to have high levels of glucose \((~5mM)\), which could interfere in bacterial survival, are very low. Bearing that in mind, we can speculate that maybe the best option to contain these organisms is not by the use of a toxin that directly kills the bacteria, since it is much likely subjected to threshold toxin concentrations that may or may be not achieved. On the other hand, using a toxin that arrests cell cycle, rather than a toxin that directly kills a cell, that can be controlled with an inducer and glucose in a more loosen way than before (more cI levels) seems to be a much more prosperous way to deal with our bacteria-leaking problems.
2.3 Tse2 Repressed by Arabinose Kill Switch
To meet the requirements discussed above, a completely new BioBrick was designed: BBa_K3215013.
To start a new model, we had to create new kinetic relations, and adapt those already created.
2.3.1 Kinetic rate laws
For this model, all equations related to lacI and lacI mRNA were removed, together with \({\eta}_{3}\). The new equations for this model are: $$\frac{d[Arabinose]}{dt} = {{-k}_{Ab}}$$ $${V}_{mRNA-cI} = {{k}_{mRNA-cI} {\eta}_{1} \kappa {\eta}_{3} [{G}_{cI}]}$$ $$\kappa = {(\frac{[AraC:{I}_{1}:{I}_{2}] + [AraC:{I}_{1}:Ab:{I}_{2}]}{[{I}_{2}]})}$$ $$\frac{d[{mRNA}_{Tse2}]}{dt} = {{V}_{mRNA-Tse2} \quad - \quad [{mRNA}_{Tse2}] {k}_{d,mRNA-Tse2}}$$ $${V}_{mRNA-Tse2} = {k}_{mRNA-Tse2} \epsilon 1 \epsilon 2 [{G}_{Tse2}]$$ $$ \epsilon 1 = {\frac{[RP:s:PcI]}{[PcI]}}$$ $$ \epsilon 2 = {(\frac{[{OcI1}_{f}]}{[OcI1]})(\frac{[{OcI2}_{f}]}{[OcI2]})}$$ $$\frac{d[Tse2]}{dt} = {{V}_{Tse2} \quad - \quad [Tse2]{k}_{d,Tse2}}$$ $${V}_{Tse2} = {k}_{Tse2}[{mRNA}_{Tse2}]$$
All of the parameters are explained in section 2.1.1. The list of parameters used in this section are:
2.3.2 Arabinose regulation
In this section, we have the AraC protein and DNA binding regions I1, I2 and O2, where I2 is an activator region and O2 a repressor region.
Relations:
Where: $$[AraC:{I}_{1}] = {{K}_{ai1} . [{AraC}_{f}] . [{I}_{1f}]}$$ $$[AraC:{I}_{1}:{I}_{2}] = {{K}_{ai1i2} . [AraC:{I}_{1}] . [{I}_{2f}]}$$ $$[AraC:{I}_{1}:{O}_{2}] = {{K}_{ai1o2} . [AraC:{I}_{1}] . [{O}_{2f}]}$$ $$[AraC:{I}_{1}:Ab] = {{K}_{ai1ab} . [AraC:{I}_{1}] . [{Ab}_{f}]}$$ $$[AraC:{I}_{1}:Ab:{I}_{2}] = {{K}_{ai1abi2} . [AraC:{I}_{1}:Ab] . [{I}_{2f}]}$$ $$[AraC:{I}_{1}:Ab:{O}_{2}] = {{K}_{ai1abo2} . [AraC:{I}_{1}:Ab] . [{O}_{2f}]}$$
List of parameters:
2.3.3 Results
Since this experiment does not depend on lacI and lacI mRNA concentration, this new model operates with 6 variables: (i) arabinose concentration; (ii) glucose concentration; (iii) cI mRNA concentration; (iv) cI concentration; (v) Tse2 mRNA concentration; and (vi) Tse2 concentration. The results are shown below, as a function of concentration of glucose and arabinose, for both cI and Tse2:
Both these results show us the dependence of the system on glucose concentration. When it is subjected to a low glucose concentration, the effect of arabinose becomes much more pronounced. What we can conclude from these experiments is that this system has a very tight cI regulation, which interferes with the rise of Tse2 levels, being difficult to manipulate the concentrations of the intermediates of this biological circuit. Considering all this, we still don’t know if the concentrations of Tse2 for different glucose concentrations, varying arabinose levels, are enough to arrest bacterial growth or not. Furthermore, more experiments should be done to measure the efficiency of this system. Our model showed that this circuit works, but says almost nothing on how it should work in a living system.
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