Team:LINKS China/Model
Background
We have successfully produced tyrian purple dyes from tryptophan using two-cell systems. However, we hope to produce these natural colorants in a one-cell system, as it reduces the complexity of dye production (less bacteria to deal with, less experimenting needed, less human input is required, etcetera); furthermore, a one-cell system would save us resources, time, and work if we were to produce these dyes at an industrial scale.
Metabolic pathway of tyrian purple/indigo production. Trp may be converted in two ways: 1) Trp is converted to indole by tnaA then converted to indigo by FMO. 2) Trp is first halogenated to 6-Br-Trp fre-sttH, then converted to 6-X-Indole by tnaA and finally to tyrian purple by FMO.
In order to obtain tyrian purple as pure as possible in a one-cell system, trp needs to be first converted to 6-Br-Trp so that tnaA-FL-Fmo utilizes 6-Br-Trp as substrate to produce tyrian purple instead of utilizing trp to produce indigo; otherwise, if both trp and 6-Br-Trp are present, then the outcome would be a mixture of indigo and tyrian purple. This means that fre-sttH must be expressed first and halogenate most trp before tnaA-FL-Fmo is expressed. To attain such a mechanism, trp-regulated riboswitch designed by Liu et al., 2021 [1] was utilized.
Design
(A) Design of our one-cell system. cI will inhibit tnaA-FL-Fmo expression to prevent it from converting trp into indigo. Fre-sttH converts trp into 6-Br-Trp. (B) Working principle of the riboswitch. Riboswitch is a special mRNA containing cI sequence. Riboswitch has a stem-loop structure at 5’ masks the RBS and effectively prevents the binding of ribosomes when no trp is bound to. When trp binds to riboswitch, a conformational change occurs. RBS is no longer masked and allows ribosomes to bind, which move downstream and translate the downstream coding sequence (cI proteins).
A constitutive promoter enables constitutive transcription of the mRNA of the riboswitch along with a lambda cI sequence. When trp is high in concentration, it likely binds to the riboswitch causing a conformational change in the mRNA structure, which exposes RBS to ribosomes, enabling translation of cI monomers. cI monomers then dimerize to form cI dimers, and bind on the pR promoter, inhibiting tnaA-FL-Fmo expression (note: only cI dimers can inhibit expression, cI monomers cannot). When trp is low in concentration (i.e, when most trp is converted into 6-Br-Trp), there is a high chance that the ligand does not bind to the riboswitch, thus RBS will not be exposed to ribosomes. As a result, new cI proteins will not be translated, which removes cI inhibition. Consequently, tnaA-FL-Fmo is expressed and 6-Br-Trp can be converted into tyrian purple.
Aims of our model
Our model has two major aims:
1. To simulate a one-cell tyrian purple production system incorporating our riboswitch. The simulation will show whether our riboswitch functions according to our design or not. If our riboswitch works as we expected, then in theory production of tyrian purple by a one-cell system will be feasible.
2. To determine key variables that we can modify to make our tyrian purple production better. This will help us decide what biological components we should use in our future experiment designs (for example, if the model shows higher translation rates of cI proteins leads to higher percentage tyrian purple production, then we may use a stronger RBS in our design).
Modeling Process
Our modeling process begins by describing the rate of change of the riboswitch (along with the cI sequence) concentration through the ordinary differential equation (ODE):
where [RS] is the riboswitch concentration, kTX1 is the transcription rate of the constitutive promoter, [DNA1] is concentration of plasmid 1, kDegm is the degradation rate of mRNA.
The riboswitch may be present in three different states, including: ligand-free state (when no trp is bound to the riboswitch), off-state (when trp is bound to the riboswitch yet no conformational change occurred), and on-state (when the riboswitch has undergone conformational change). The relationship between these three states can be described as:
Among these, [Trp] is tryptophan, [RSoff ] is the off-state riboswitch, and [RSon] is the on-state riboswitch. These reversible reactions can then be expressed as ODEs:
Where ka and ka-1 are the association rate and dissociation rate between trp and the riboswitch respectively.
Among these, kon is the rate at which the riboswitch turns on, and koff is the rate at which the riboswitch turns off.
Since the off-state riboswitch may revert back into trp and ligand-free state riboswitch, the concentration of the latter reactant will be influenced by ka-1[RSoff].
Hence ODE of [RS] is re-written as
Most cI proteins are translated when the riboswitch is at its on-state, which can be described by the ODE:
Among these, [cI] is the concentration of cI proteins, kTL1 is the translation rate of cI proteins, and kDegp is the protein degradation rate.
However, cI translation may still happen when riboswitch is not on (in ligand-free and off-state), but only during rare occasions. These rare occasions are due to translation leakages, which should also be considered in the equation above.
Therefore, equation of [cI] is modified as:
Where kLk is the leakage rate of translation.
According to iGEM team USTC 2010 [2], cI inhibits gene expression from promoter pR only in the form of dimers. cI dimerization is represented by the following equation:
Among these, [cI2] is the concentration of cI dimers, kdm is the rate of cI dimerization.
cI dimers then bind to the pR promoter and inhibit downstream gene expression. We make the assumption that cI binding (regulation) follows the Hill equation.
Therefore, the ODE of tnaA-FL-Fmo mRNA transcription can be written as:
Among these, [mRNAtlf] is the concentration of tnaA-FL-Fmo mRNA, [DNA2] is the concentration of plasmid 2, kTX2 is the transcription rate of the pR promoter when no cI dimers are bound to, kR is the repression constant of cI dimer/repressors, and n is the hill coefficient of cI dimers on the pR promoter.
tnaA-FL-Fmo translation takes place subsequently:
Where [tlf] is the concentration of tnaA-FL-Fmo, and kTL2 is the translation rate of the protein.
We then take fre-sttH, the trp halogenase, into account. We make another assumption that fre-sttH is saturated during the whole process. The reaction velocity, or the rate of change of the product (6-Br-Trp) concentration, can be described by the Michealis-Meten equation. Hence, we can derive the ODE for 6-Br-Trp concentration:
Among these, [6-Br-Trp] is the concentration of 6-Br-Trp, [Trp] is the concentration of trp, Vmaxfs is the maximum reaction velocity achieved by fre-sttH, and Kmfs is the Michealis constant of fre-sttH.
Since the rate of increase of products is equal to the rate of decrease of reactants, we can also derive the ODE for trp concentration:
However, trp is influenced in two other ways. The first way is that off-state riboswitch may revert to trp and ligand-free state riboswitch, which increases trp concentration during the process. The second is that trp-riboswitch binding lowers trp concentration.
Therefore, the above equation can be re-written as:
Finally, trp and 6-Br-Trp are converted into indigo and tyrian purple respectively. Assuming that tnaA-FL-Fmo follows the Michealis-Menten equation, we can derive the ODEs for indigo and tyrian purple concentration change:
In the case of indigo (the above equation), [I] is the concentration of indigo, kcat is the rate constant of trp-tnaA-FL-Fmo complex dissociating to give indigo, and Kmtlf is the Michealis constant of tnaA-FL-Fmo.
The case for tyrian purple is very similar to that of indigo. [TP] is the concentration of tyrian purple in the equation above.
Since the concentrations of trp and 6-Br-Trp are affected by tnaA-FL-Fmo, ODES of [Trp] and [6-Br-Trp] need to be modified.
ODE of [Trp] is re-written as:
And ODE of [6-Br-Trp] is re-written as:
Results and plotting
We used the ODE solver “deSolve” in R to simulate our one-cell system based off the 11 ODEs we wrote and “ggplot2” to plot the dynamics of molecules of interest, and obtained the results below:
As shown by the proteins graph, tnaA-FL-Fmo concentration peaks at the start of the simulation and drops quickly when concentration of cI monomers (cI) and dimers (cI2) increase (tnaA-FL-Fmo expression is being inhibited by cI dimers). Concentration of cI monomers and dimers then fall slowly, and as a result, tnaA-FL-Fmo concentration increases gradually and reaches a plateau.
In the amino acid graph, 6-Br-Trp concentration increases as trp concentration lowers. 6-Br-Trp then decreases starting from Time = 250000 seconds due to tnaA-FL-Fmo concentration increase (6-Br-Trp converted into tyrian purple).
As shown by the dye graph, indigo concentration increases by a small amount at first and then stays constant. Tyrian purple concentration increases at a lower rate than that of indigo at the start then increases quickly after Time = 250000 seconds (when tnaA-FL-Fmo concentration increases), and finally plateaus off at the end.
We can plot another graph showing the ratio between tyrian purple and indigo concentration:
At first, the ratio between tyrian purple and indigo concentration is less than 1, meaning that indigo concentration is greater than that of tyrian purple. However, the ratio increases throughout and levels off at about 21 in the end.
Discussion
As seen in the results, our model shows that a one-cell system can produce pure tyrian purple close to perfect. Concentrations of cI monomers and dimers are high when there are large amounts of trp, and low when trp is at small amounts, thus showing the effectiveness of our riboswitch design. tnaA-FL-Fmo is translated when trp is in low concentration and when 6-Br-Trp is high in concentration as a result of the riboswitch mechanism, thus producing large amounts of tyrian purple and very little indigo.
Our model also shows that a flaw of our one-cell system: small amounts of indigo will be produced (this is why we stated earlier our one-cell system can produce pure tyrian purple close to perfect, not perfect). According to our results, some amounts of tnaA-FL-Fmo is produced at the start of the simulation, meaning that cI inhibition is not in effect yet. This is because cI monomers and dimers need time to accumulate, as well as riboswitch transcription and cI translation. Hence, there is a period of time, specifically during the start, where cI dimers have not accumulated enough to inhibit tnaA-FL-Fmo expression, leading to indigo “leakage”.
In order to minimize indigo production, we need cI dimers to accumulate as quickly as possible. Therefore, cI transcription and translation rates need to be high, which can lead to quicker tnaA-FL-Fmo inhibition. We can apply a strong promoter and a strong RBS to the riboswitch-cI gene circuit to achieve this.
In addition to the solution described above, we can reduce tnaA-FL-Fmo expression in order to decrease indigo concentration even more. To achive this, we can lower tnaA-FL-Fmo translation rate by using a weak RBS, meaning that less trp will be converted into indigo at the start. The downside, however, is that more time is needed for 6-Br-Trp to be converted into tyrian purple since there is lower tnaA-FL-Fmo concentration.
Looking into the future
Experiment design:
Through our results and discussion, we determined three key variables that we can control to maximize the ratio between tyrian purple and indigo: transcription rate of riboswitch with cI sequence, translation rate of cI, and translation rate of tnaA-FL-Fmo. Hence in our experiment design, we will apply a strong promoter and a strong RBS to our riboswitch gene circuit and a weak RBS to tnaA-FL-Fmo in ourder to achieve our desired outcome—high purity tyrian purple.
Future modeling:
During our experiments, we may be able to gather or test new experimental data for our model, which will help us make our model more accurate. In addition, we may build another model to determine the optimal translation rate of tnaA-FL-Fmo by taking indigo concentration, time, and other factors into consideration.
How can future teams use our model?
Our model provides a riboswitch-sensor design that future teams can use. Our ODEs are not restricted to trp, cI, tnaA-FL-Fmo only: they can be modified for other types of ligands, inhibitors, proteins, and etcetera. Any future team that has sensing and/or inhibition included in their experiment design can use our model to simulate their systems and determine whether their designs are feasible or not.
Teams can download our model r code here
Parameter list
Supplementary information: Determining Vmax and Km of fre-sttH
Part of our measurement is to show how trp is converted into 6-Br-Trp (by tnaA-FL-Fmo) over time. We added about 2.5mM trp in a fre-sttH saturated solution, then measured the concentrations of trp and 6-Br-Trp every 6 hours for 4 times (24h in total). We obtained the raw data and fitted a natural exponential curve (equation) to the data in order to describe the relationship between time and trp concentration (note: we chose the natural exponential equation because it showed the highest R^2 among other equations we tried fitting). After that, we determined the reaction velocity at x-values (times) 6(h), 12(h), 18(h), and 24(h) (i.e. different trp concentrations) by taking the gradients of the natural exponential equation at the above points, thus obtaining 4 reaction velocities with respect to their substrate concentrations. Then, we fitted the Michealis-Meten equation to the calculated data and determined Vmax and Km.
References
- Establishment of a Biosensor-based High-Throughput Screening Platform for Tryptophan Overproduction. Yongfei Liu, Huiling Yuan, Dongqin Ding, Huina Dong, Qinhong Wang, and Dawei Zhang ACS Synthetic Biology 2021 10 (6), 1373-1383. DOI: 10.1021/acssynbio.0c0064
- UTSC 2010, https://2010.igem.org/Team:USTC_Software/detail
