Team:BIT-China/modeling Fine-regulation circuits.html
Fine-regulation Circuits
Basing on basic regulation circuit, three fine-regulation circuits are designed for application in different fermentation situations. Recombinases are constructed downstream pH-responsive promoters to invert direction of constitutive promoter J23119, achieving automatic switch between acid and alkali production.
Main processes in these models are similar to basic regulation circuit model, including induction of the promoters, transcription, translation, catalytic process of enzymes and the effects of products on environmental pH. We also considered reversible reaction and materials’ production and degradation.
To simulate the inversion function of recombinase, we set several groups of equations and made cyclic processes. By determining some key values of pH, the model could switch different groups of equations.
The assumption we made are:
(1) J23119 is firstly in the direction of alkali production, as normal fermentation environment tends to be acidic.
(2) P-atp2 promoter is directly induced by hydroxyl ion, while P-asr promoter is directly induced by hydrogen ion.
(3) To prove the function of circuits, initial pH is set up to 8.0, where circuit led by p-atp2 has already be activated. This process is regarded as the first step of the model.
Cre/Flp Regulation Circuit
Fig.1 The gene circuits of Cre/Flp regulation system
The first fine-regulation circuit is led by recombinases Cre and Flp (Fig.1). The cyclic processes are described as followed:
(1) When pH is higher than 7.0, P-atp2 is induced and activates the production of Cre, which inverts J23119 from alkali production to acid production. Environmental pH begins to decrease.
(2) When pH is between 5.0 and 7.0, both P-asr and P-atp2 promoters are repressed. Because acid production circuit is open, pH level keeps declining.
(3) When pH is around 5.0, p-asr promoter is induced and leads production of Flp, which starts to change the direction of J23119 to alkali production. However, J23119 will not activate downstream functional gene when being inverted, thus, the inverting process causes a time lapse in alkali production. Meanwhile, although the concentration of J23119 toward acid production is decreasing, there are still parts of J23119 functioning. Accordingly, pH will tend to decrease slightly.
(4) When pH is lower than 5.0, after the time lapse, alkali production is activated, and production of Flp is led by P-asr promoter.
(5) When pH returns to the range of 5.0 to 7.0, p-asr promoter is repressed, and J23119 keeps conducting acid production.
(6) When pH increases and reaches around 7.0, p-atp2 is induced again, and the system will go through a time lapse similar to step (3). pH level keeps raising higher than 7.0.
(7) When pH is higher than 7.0, after time lapse in step (6), acid production is activated again, while production of Cre is controlled by P-atp2 promoter. The latter processes are similar to step (1).
Basing on processes above, the reaction equations are described as followed:
(1)
(2)
The description of variables are shown below (Fig.2).
Fig.2 Name and description of variables in model
And groups of differential equations are:
(1)
Fig.3 Initial value of variables
(2)
Fig.4 Initial value of variables
(3)
Fig.5 Initial value of variables
(4)
Fig.6 Initial value of variables
(5)
Fig.7 Initial value of variables
(6)
Our results show that with the application of Cre/Flp regulation circuit, pH Controller could achieve automatic switch in acid and alkali devices and stabilize environmental pH level. (Fig.8)
Fig.8 Extracellular pH regulated by Cre/Flp regulation circuit. The final pH level fluctuates in the range where both promoters are repressed. To prove function of the circuit, initial environmental pH was set up to 8.0, indicating that our regulation circuit had already been induced.
Bxb1 Regulation Circuit
The second fine-regulation circuit is led by recombinase Bxb1 (Fig.9). Bxb1 can invert the constitutive promoter to both sides, thus, the eventual pH level is determined by strength of both acid and alkali.
Fig.9 The gene circuits of Bxb1 regulation system.
The processes of the regulation circuit are described as followed:
(1) At first, because normal fermentation pH tends to be acidic, J23119 is in the direction of GadA production (alkali device).
(2) In alkaline environment (pH＞7.0), P-atp2 is induced and produces Bxb1, which switches the direction of J23119 to generate LdhA (acid device).
(3) Bxb1 will switch J23119 to both sides, and eventually the inversion efficiency of Bxb1 to both sides are the same.
(4) The final environmental pH is determined by strength of acid and alkali produced by LdhA (for acid) and GadA (for alkali).
Here we assumed that Bxb1 had reached stable condition, where the inversion efficiency of Bxb1 to both sides are the same.
Basing on processes above, the reaction equations are described as followed:
Results proved that with the application of Bxb1 regulation circuit, pH Controller could regulate environmental pH to the level determined by the strength of acid and alkali (Fig.10).
Fig.10 pH level change led by Bxb1 regulation circuit. In alkaline environment, p-atp2 is induced, activating downstream Bxb1 to invert the direction of J23119. Bxb1 can invert the constitutive promoter to both sides, thus, the eventual pH level is determined by strength of both acid and alkali.
FimE Regulation Circuit
The last fine-regulation circuit is led by recombinase FimE (Fig.11). This recombinase can only invert the promoter for one time.
Fig.11 The gene circuits of FimE regulation system.
The processes of the circuit are described as followed:
(1) Similar to Bxb1 circuit, the initial direction of J23119 points to GadA.
(2) When pH raises higher than 7.0, P-atp2 is induced and produces recombinase FimE.
(3) FimE will change the direction of J23119 to acid production. The circuit will generate acid till stable condition.
The reaction processes are:
The differential equations are:
Results proved that with the application of FimE regulation circuit, pH Controller could regulate environmental pH to the level determined by the strength of acid (Fig.12). LdhA could be replaced by other functional genes which could produce acid with different strength.
Fig.12 pH level change led by FimE regulation circuit. In alkaline environment, P-atp2 is induced, activating downstream FimE to invert the direction of J23119. J23119 conducts the transcription of LdhA which catalyzing lactic acid production. Eventually, extracellular pH is determined by strength of acid.