Team:BIT-China/modeling Basic circuits.html
Basic Circuits
Basic Resistance Subsystem Model
Basic circuits contain two subsystems: resistance subsystem and regulation subsystem. Models of these two subsystems were constructed separately.
Main processes include induction of the promoters, transcription and translation of function genes, catalysis of enzymes and acid or alkali production led by enzymes. ODE is used for modeling to describe concentration as function of time. Factors considered are production and degradation, combination and disaggregation and reversible reaction.
Resistance subsystem consists of constitutive promoter J23119, function genes glsA, NhaA and NhaB. J23119 is not influenced by environmental pH, and will lead enzymes production continuously.
Fig. 1 Basic resistance device.
Our model mainly focused on functional genes and enzymes. Assumptions we made are: (1) enzymes will only work in proper pH range and are not activated at other pH level. (2) To prove function of our device, initial intracellular pH is set to ideal value. For acid resistance device (Fig. 1), description of reaction processes are:
Where description and initial value of variables are :
Fig. 2 Name, initial value and description of variables.
Finally, result showed that with application of acid resistance device, pH could be regulated to a suitable range (Fig. 3).
Fig. 3 Intracellular pH is regulated by acid resistance device. To prove the function of circuit, initial pH was set up to 3.0, when glsA was activated. pH can effect the activity of glsA, while glsA conducts gaseous ammonia production. With the enzyme activity changing, pH will be finally stabilized at a suitable level.
For alkali resistance device (Fig.1), NhaB and NhaA genes’ functions were assumed as similar processes to enzyme catalysis. Basing on this assumption, description of the NhaB circuit is:
Consistent with equations above, functions are:
Where description and initial value of variables are:
Fig.4 Name, initial value and description of variables.
As for NhaA, the reaction processes are:
And the functions are:
Where description and initial value of variables are:
Fig.5 Name, initial value and description of variables.
As the result, alkali resistance device could decrease intracellular pH (Fig.6.1, 6.2).
Figure.6.1 Intracellular pH change regulated by alkali resistance circuit led by NhaB. NhaB is not effected by pH, and can assist NhaA to regulate alkaline environment. Here we assumed that initial pH was 9.0 and NhaB had already been activated.
Figure.6.2 Intracellular pH change regulated by alkali resistance circuit led by NhaA. NhaA will be induced at pH 7.0 ~ 9.0, while NhaB will function when NhaA cannot function normally. Here we assumed that initial pH was 8.0 and NhaA had already been activated.
Basic Regulation Subsystem Model
In basic regulation circuit containing acid regulation and alkali regulation device, pH-responsive promoters lead the expression of functional genes. As the products of two functional genes are both enzymes, main processes considered in this model are their translation, degradation and catalysis. We assumed that the H+ or OH- was straightly contacted with the promoters and induced the transcription process.
Acid regulation device consists of acid-responsive promoter P-asr and gene GadA producing enzyme which catalyzes the proton-consuming conversion of glutamate to γ-aminobutyric acid (GABA). GABA can be transported to the environment to regulate acidic micro-environment (Fig.1).
Fig.1 Acid regulation device.
The reaction processes of acid regulation device are described as below:
As for alkali regulation device, gene circuit contains alkali-responsive promoter P-atp2 and functional gene LdhA (Fig.2). LdhA encodes a lactate dehydrogenase which converts pyruvate to lactic acid. Lactic acid will be secreted outside the cell and neutralize the OH-.
Fig.2 Alkali regulation device.
The reaction processes of alkali regulation device are described as below:
To simulate the processes above, we constructed cyclic processes which had four groups of differential equations. pH ranges which were determined by promoters were applied as end conditions to switch among equations.
To examine the function of regulation subsystem, we set up the initial pH to alkaline range.
(1)9.0>pH>7.0 : P-atp2 is induced and leads the production of LdhA, LdhA will catalyze lactic acid production and reduce the pH level. The equations are written as:
Where the initial values and description of variables are shown below (Fig.3).
Fig.3 Name, initial value and description of variables.
(2) 5.0＜pH＜7.0 : With the pH decreasing, both P-atp2 and P-asr are repressed and production of LdhA is stopped. However, remaining LdhA mRNA will continuously translate LdhA till the mRNA is degraded. Environmental pH keeps decreasing.
Where the initial values and description of variables are shown below (Fig.4).
Fig.4 Name, initial value and description of variables.
(3) pH＜5.0 : P-asr promoter is induced and leads production of GadA. GadA will catalyze Glutamate to generate GABA to neutralize hydrogen ion.
Where the initial values and descriptions of variables are shown below (Fig.5).
Fig.5 Name, initial value and description of variables.
(4) 5.0＜pH＜7.0 : This step is similar to step (2). Both promoters are inactivated and the circuit will generate GABA for a short period of time.
Where the initial values and description of variables are shown below (Fig.6).
Fig.6 Name, initial value and description of variables.
The final simulation results of model are shown below (Fig.7). In acidic condition, the acid regulation device will produce GABA and decrease the extracellular pH. When environmental pH turns to be higher than 7.0, alkali regulation device will let lactic acid to neutralize the outside pH. Eventually, the environmental pH will be constrained between two promoters’ responsive range (but with a fluctuation).
Fig.7 Extracellular pH regulated by basic regulation subsystem. In normal fermentation environment, pH will tend to decrease and enter acidic level. Basing on this phenomenon, we assumed that the initial pH was 4.0, and our device was functioning.