Team:Edinburgh/Model
Cell-Free model of a biosensor based on ArsR transcription factor expressing a fluorescent RNA aptamer
Modelling an Arsenic cell-free biosensor.
iGEM 2020 competition was impacted by the COVID-19 pandemic, therefore our access to a lab was limited to only 3 weeks of wet-lab results. To help reduce the trial and error process of building different construct for our cell-free biosensors, we decided to build a mathematical model of the biosensor based on the ArsR transcription factor expressing an RNA fluorescent aptamer. The obtained data helped us in decreasing the time needed to calibrate the different components of the reaction and helped us to better understand how the ArsR transcription factor works. It resulted in testing of the BBa_K3380600 and BBa_K3380603 constructs in the lab. Further paragraphs go into greater detail, explaining how the model was built and what data is provided.
ArsR transcription factor.
The elements of the Arsenic biosensor are derived from the plasmid R773 present in Escherichia Coli. The ars operon consists of four genes: three structural genes ArsA, ArsB, ArsC and a regulatory gene ArsR. The structural genes comprise an anion-translocating ATPase that can pump out the oxyanions of arsenic (As) and antimony (Sb) (Wu and Rosen 1991). Thus, conferring the cell resistance to As and SB. Furthermore, the ArsR protein is a trans acting transcription factor that dimerizes and binds to DNA, preventing the polymerase from binding to the promoter and therefore repressing the transcription. Upon addition of As(III) or Sb(III), the dimers unbind the DNA, allowing the polymerase to resume transcription. It is important to mention that one of the drawbacks of the system is the relative high background expression of the genes, probably as a result of the feedback loop (Merulla and van der Meer 2016).
iGEM 2020 Team Edinburgh Arsenic biosensor model.
Our model was built taking into account the repression mechanism of ArsR transcription factor. We planned to build a construct as seen in Figure 1. Under a strong class III T7 RNA polymerase that would have a ArsR binding site, expressing the iSpinach fluorescent RNA aptamer flanked by the F30 tRNA scaffolds to improve stability. The ArsR transcription factors would be supplied by the cell-free extract of Cupriavidus Metallidurans. Upon addition of the DNA construct BBa_K3380603 , ATP, NTPs, DFHBI fluorophore and T7 RNA polymerase, the ArsR monomers would dimerise and repress the transcription of the fluorescent RNA aptamer. However, when supplemented with arsenic, the iSpinach would be transcribed, binding to the fluorophore and outputting fluorescence to indicate the presence of the arsenic atoms.
Figure 1. Schematic representation of the BBa_K3380603 construct.DNA construct under the As responsive BBa_K190015 promoter expressing BBa_K3380150 iSpinach fluorescent RNA aptamer (in green) flanked by F30 tRNA scaffolds to protect from RNAse degradation.
Based on the principles described above, we built an ordinary differential equations (ODE) model. It is mainly based on the work of Berset et al. 2017 that describe a mechanistic model of ArsR Arsenic regulation in a cell, moreover it also takes into account the unspecific binding of ArsR to DNA.
Assumptions, Reactions and Participating species.
Several assumptions have been made to make the system less complicated while keeping the mainframe.
1) All the rates and constants used in the model are measured in cells.
2) Diffusion rate in the cell free system is equal to the diffusion rate in an E.coli cell (kf=106 M-1).
3) Total number of promoters is conserved.
4) ArsR fully represses transcription (no background transcription).
5) Degradation of an ArsR dimer bound to arsenite will lead to that arsenite being added to the intracellular pool of free arsenite.
6)The degradation rate of an ArsR dimer is one-half of the monomer degradation rate.
7) Any ArsR-DNA complex is protected from degradation.
8) Only ArsR dimers can bind the operator and interact with arsenite. ArsR monomers can only bind non specificsites or dimerize.
9) ArsR dimers with one or two arsenite bound molecules have the same affinity for the unspecific sites and for the operator (ArsR binding site).
10) All species in the cell extract, besides ArsR monomers, number of unspecific sites (U) number of T7 RNA Polymerase and molecules of arsenic are zero at the moment of DNA addition.
11) All the genomic DNA has been degraded; therefore, the Unspecific binding site equals to 10% from the amount of initial DNA template concentration.
12) The model calculates the reactions for a cell volume equal to 1 femtoL
Based on the assumptions enumerated above we outlined the species that would be present in the model (Figure 2).
Figure 2. Schematic representation of species present in the model.DNA construct under the As responsive BBa_K190015 promoter expressing BBa_K3380150 iSpinach fluorescent RNA aptamer (in green) flanked by F30 tRNA scaffolds to protect from RNAse degradation. The notation of each species is written on the right of the species description. The green numbers represent species, while purple numbers represent the species concentrations that were changed throughout the simulations.
In total 20 species including the expressed transcript of iSpinach fluorescent RNA aptamer. The species would interact according to the mechanism of ArsR transcription factor repression explained by Berset et al. 2017. Figure 3 summarises the reactions that can take place.
Figure 3. Schematic representation of species and reactions taking place in the model.The binding reactions are indicated by green arrows, the repression is shown with red lines and the degradation (ф) is shown with dotted black line. All the reactions are ordered and indicated with blue numbers. These reactions correspond to the reactions enumerated below. ArsR represents ArsR transcription factor monomers, U represents unspecific binding, As represent arsenic molecules, ABS represents ArsR binding sites, the purple claw like protein represents the T7 RNA polymerase. The miSpinach in green represents the mRNA of green fluorescent RNA aptamer.
Involving all the species enumerated. Therefore, the reactions that were accounted for are as follows:
ArsR + ArsR ⇌ ArsR2 #ArsR2 formation by ArsR dimerization
ArsR + U ⇌ ArsR:U #ArsR unspecific binding
U+ ArsR2 ⇌ ArsR2:U #ArsR2 dimer unspecific binding
As+ ArsR2 ⇌ ArsR2:As #ArsR2 dimer binding As
As+ ArsR2:As ⇌ ArsR2:As2 #ArsR2 dimer with As bound, binding another As
U+ ArsR2:As ⇌ ArsR2:As:U #ArsR2 dimer with As bound, binding unspecific
U+ ArsR2:As2 ⇌ ArsR2:As2:U #ArsR2 dimer with two As bound, binding unspecific
ABS+ ArsR2 ⇌ ABS:ArsR2 #ArsR binding site (ABS) binding ArsR2 dimer
ABS+ ArsR2:As ⇌ ABS:ArsR2:As #ABS binding ArsR2 dimer with As bound
ABS+ ArsR2:As2 ⇌ ABS:ArsR2:As2 #ABS binding ArsR2 dimer with two As bound
ABS + T7RNAP ⇌ ABS:T7RNAP # T7 RNA polymerase binding the promoter(transcription)
ABS:ArsR2 +T7RNAP ⇌ ABS:ArsR2:T7RNAP #dimer binding to the ABS (repression)
ABS:ArsR2:As +T7RNAP ⇌ ABS:ArsR2:As:T7RNAP #dimer bound to As binding to ABS (transcription)
ABS:ArsR2:As2 +T7RNAP ⇌ ABS:ArsR2:As2:T7RNAP #dimer bound to As2 binding ABS (transcription)
These reactions allowed us to build a set of Steady State Ordinary Differential Equations to study the effects of different inputs on the As biosensor construct
Ordinary Differential Equation
d[ArsR2]/dt= kf[ArsR2] – kb[ArsR2]
d[ArsR]/dt= 2kb[ArsR2] – 2kf[ArsR2]
d[ArsR:U]/dt= kf[ArsR][U] – kb1[ArsR:U]
d[ArsR2:U]/dt= kf[U][ArsR2] – kb2[ArsR2:U]
d[ArsR2:As]/dt= kf[As][ArsR2] – kb3[ArsR2:As]
d[ArsR2:As2]/dt= kf[As][ArsR2:As] – kb4[ArsR2:As2]
d[ArsR2:As:U]/dt= kf[U][ArsR2:As] – kb5[ArsR2:As:U]
d[ArsR2:As2:U]/dt= kf[U][ArsR2:As2] – kb6[ArsR2:As2:U]
d[ABS:ArsR2]/dt= kf[ABS][ArsR2] – kb7[ABS:ArsR2]
d[ABS:ArsR2:As]/dt= kf[ABS][ArsR2:As] – kb8[ABS:ArsR2:As]
d[ABS:ArsR2:As2]/dt= kf[ABS][ArsR2:As2] – kb9[ABS:ArsR2:As2]
d[ABS:T7RNAP]/dt= = kf[ABS][T7RNAP] -kb10[ABS:T7RNAP]
d[ABS:ArsR2:T7RNAP]/dt= kf[ABS:ArsR2][T7RNAP]- kb11[ABS:T7RNAP]
d[ABS:ArsR2:As:T7RNAP]/dt= kf[ABS :ArsR2:As][T7RNAP]-kb12[ABS:ArsR2:As:T7RNAP]
d[ABS:ArsR2:As2:T7RNAP ]/dt = kf[ABS:ArsR2:As2][T7RNAP]-kb13[ABS:ArsR2:As2:T7RNAP]
Transcription
(d[mRNA])/dt= Tr* [ABS]*([ ABS:ArsR2:As2:T7RNAP]+[ ABS:ArsR2:As:T7RNAP]+[ ABS:T7RNAP])/(1+[ ABS:ArsR2:T7RNAP]+[ ABS:T7RNAP]+[ ABS:ArsR2:As2:T7RNAP]+[ ABS:ArsR2:As:T7RNAP] )
d[mIspinach]/dt= [mRNA] – kdeg[mRNA]
Furthermore, to facilitate the calculations and aid in tracking the species concentrations in the model we build a stoichiometric matrix (available on GitHub ) which was based on the detailed reactions of each species derived from the ODE system outlined above ( also available on GitHub ).
Parameters and Initial conditions
Most of the parameters for the As biosensor model such as degradation rates were taken from the Berset et al. 2017 paper. Moreover, the binding constants were also taken from the same paper as seen in the table below. However we introduced several changes, the mRNA degradation rate for egfp in the cell was 7.63x10^-3, we decreased that to 7.63x10^-10 because the degradation is much slower in the cell-free extract due to less RNAses being present. The T7 RNA polymerase concentration was set at 200 nM per cell, which is close to the estimations of Marshall and Noireax 2019 for a cell-free system. The ArsR transcription factors monomers was set at 2x10^4 nM per cell, as an approximation of the possible number of ArsR monomers present in the cell-free system. The T7 RNA polymerase transcription rate (Tr) and the its dissociation rate from the promoter was taken from the work of Skinner et al. 2004 which was estimated to be 43 nt s^-1 and 2.9 s^-1 respectively.
Results and Sensitivity Analysis
To study the impact of different DNA concentrations on the transcription of the RNA aptamer we performed a sensitivity analysis by increasing and decreasing DNA concentrations as it can bee seen below.
As expected, the increase in DNA concentration leads to an increase in number of iSpinach transcripts. All the results that had a DNA concentration increase, had an increase in the transcripts output, with the biggest increase being +800% followed by 400%. Also, as expected, when decreasing the DNA, the amount of transcripts is also decreased. However, there was an interesting result, the increase of 1000% of DNA did not result in a similar increase of transcripts number. It was actually lower than most other results. This could be explained by several factors. Firstly, there should be a threshold at which the present T7 RNA polymerase molecules in the sample would not be able to proceed to transcription fast enough to record an increase in transcripts output, and perhaps that was the case. Moreover, the actual decrease in output could be the cause of ArsR transcription factors binding, and repressing the transcription. Because the high concentration of DNA, the binding of transcription factors could be higher, thus repressing transcription. Moreover, a small amount of unspecific binding could also be the cause of higher repression by the ArsR transcription factors.
Therefore we tried increasing the unspecific binding and indeed the transcription outputs also increase as seen in the image below. The unspecific binding sequestered some of the transcription factors allowing for more transcripts produced.
Similarly, we tried changing the concentration of T7 RNA polymerase to asses its effects on the system. As seen from the image below, the change in T7 RNA polymerase did not make a difference on the transcripts outputs. As expected, only when the T7RNA polymerase concentration was decreased to 0, no transcription was recorded. This phenomenon could be explained by the DNA concentration bottleneck, the T7RNA polymerase proceeds to transcription fast enough, however it does not have enough DNA to transcribe from. Therefore we also increase the DNA concentration by 300% to see it's effects. Indeed, the transcription increased, suggesting that the DNA concentration needs to be much higher for bigger transcripts output by the system.
The As (III) concentrations were also changed to study its impact on the system. By analysing the data, we concluded that the optimal concentration of the As(III) for our system (and for the initial values of other components) is at 200% from the initial concentration. Higher concentrations of As do not result in higher transcripts output, probably due to the bottleneck of DNA concentration and unspecific binding.
The different concentrations of ArsR monomers in the system, revealed an expected result. The transcription is much faster when there is no ArsR transcription factors in the system, furthermore, decreasing the initial concentration of ArsR monomers by 50% also resulted in the second highest transcription. Also, increasing their concentration, results in higher repression and thus yielding less transcripts.
Varying Unspecific binding levels, we observed that it has no impact on the system, even the highest increase of 1000% did not have an impact on the system, therefore we decided to check if the DNA concentration was once again the bottleneck of the system. We increased the DNA concentration form 2.11x10^1 to 2.11x10^5 and 2.11x10^2 respectively. The unspecific binding was set to 2.11x10^5. We discovered that although in the case when thee is lower DNA concentration (2.11x10^2) the transcription is faster with the same amount of unspecific binding. This could be due to high unspecific binding to repressor dimers and monomers and therefore increasing the transcription. Furthermore, more increased DNA amount, as seen before, can results in faster transcription factors binding and therefore, higher transcription. Therefore a higher amount of unspecific binding is also required for having higher transcription and it has an impact on the overall system.
Conclusions
As a conclusion, by performing simulation using this model, our team learned that the biggest impact on transcription is the concentration of DNA and T7 RNA polymerase in the system. As opposed to translation, the transcription is not a rate-limiting factor. Therefore with enough chemical energy, NTPs and other indispensable for in vitro transcription components, the transcription (and thus fluorescent output) can be increased by increasing the DNA and T7 RNA polymerase concentrations. It is also important to remember the impact of ArsR transcription factors concentrations in an Arsenic biosensor. For better repression of the transcription, the cell-extract should contain plenty transcription factors, so that it proceeds to transcription of the fluorescent output only when the As is present. Therefore As concentration is also crucial. Finally, the Unspecific binding also plays a role in this system, a high unspecific binding can result in less powerful repression by the ArsR transcription factors, thus decreasing the biosensor efficiency.
Further work
There is plenty of work that can be done to improve this system. First of all, measurements in the lab of binding constants, degradation rates and other parameters with cell-free system should be performed to render an close to accurate result. Following that, the lab results should be compared with the simulation results and the simulation results should be adjusted accordingly. Moreover, the system could be improved by adding dependency on energy, fluorophores, NTPs concentrations, to give a broader perspective over what happens in the system. Finally, the system could be perfected by adding complexity to it. Once the mainframe will be close to the wet-lab results, a more complex model could give clues for more advanced questions such as suitability for biosensing properties of various cell-free extracts.
References
Berset, Y., Merulla, D., Joublin, A., Hatzimanikatis, V. and Van Der Meer, J.R., 2017. Mechanistic modeling of genetic circuits for ArsR arsenic regulation. ACS synthetic biology, 6(5), pp.862-874.
Marshall, R. and Noireaux, V., 2019. Quantitative modeling of transcription and translation of an all-E. coli cell-free system. Scientific reports, 9(1), pp.1-12.
Merulla, D., and van der Meer, J. R. (2016) Regulatable andmodulable background expression control in prokaryotic syntheticcircuits by auxiliary repressor binding sites.ACS Synth. Biol. 5,36−45
Wu, J. and Rosen, B.P., 1991. The ArsR protein is a trans‐acting regulatory protein. Molecular microbiology, 5(6), pp.1331-1336.
Skinner, G.M., Baumann, C.G., Quinn, D.M., Molloy, J.E. and Hoggett, J.G., 2004. Promoter binding, initiation, and elongation by bacteriophage T7 RNA polymerase a single-molecule view of the transcription cycle. Journal of Biological Chemistry, 279(5), pp.3239-3244.
