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Classical oscillator composed of three genes encoding repressor protein

2022 SZU-China has designed a timed suicide switch mediated by a classical synthetic gene oscillator. In the negative feedback loop, the oscillator is composed of three genes encoding repressor protein -- TetR from the Tn10 transposon, cI from bacteriophage lambda, and LacI from the lactose operon -- each repressor protein is attached to an LVA degradation tag located at the carboxy terminus. The concentration of each kind of repressor protein changed cyclically: lacI inhibited the expression of tetR, tetR inhibited the expression of cI, and cI inhibited lacI expression.

Usage and Biology

Gene oscillation is a gene regulation mechanism, and the amplitude and period of oscillation reflect the gene expression. Its principle is that three gene modules whose encoded repressors inhibit each other are connected in series to form negative feedback, and the periodic change of the content of repressor is realized by the inhibition and deinhibition of gene modules. The oscillator contains three repressor proteins: TetR from the Tn10 transposon, λ cI from bacteriophage λ, and LacI from the lactose operon. Each repressor carries an LVA degradation tag at the C-terminus. The oscillator device is encoded on a low copy plasmid pSB3C5.

Assembly

The oscillator and the effector form a timed suicide switch.

The engineered bacteria with a timed suicide switch were placed in an IPTG-rich medium or in a dormant state before being applied in fields. The purpose of being placed in IPTG is to continuously activate the PlacI and make the oscillator unbalanced and stagnant， in which circumstance MazF does not express.

After being applied to the field, the oscillator is re-activated with the release of IPTG and the resuscitation of the engineering bacteria. The contents of three repressor proteins changed cyclically: lacI inhibited the expression of tetR, tetR inhibited the expression of λ cI, and λ cI inhibited lacI expression. That is, the three promoters PlacI, PtetR, and PλcI were alternately activated.

As for the effector, MazE was constitutively expressed and maintained at a certain concentration in the cytoplasm, while the expression of MazF was inhibited by tetR and showed a fluctuating increase. In a simplified model, MazE and MazF bind at the ratio of 1:1, resulting in toxin inactivation. When the concentration of toxin MazF is higher than that of antitoxin MazE, the extra toxin MazF plays the role of endonuclease to cut mRNA and kill the engineered microorganisms.

Modeling

Assumption

In order to establish the oscillator model, the following assumptions are necessary for the model:

Assumption 1: The amount of DNA in the same cell is constant and the physiological behavior is same. The DNA in the same cell can be expressed at the corresponding gene fragment.

Assumption 2: Transcription and translation processes are carried out under saturation conditions. In the process of transcription and translation, polymerases, ribosomes, amino acids and nucleotides are present in large amounts.

Assumption 3: Degradation of protein and mRNA as well as reactive degradation. That is, proteins and mRNA can be degraded directly without intermediate products.

Assumption 4: Transcription rate can be modelled by Hill equation. That is because the transcription rate of each gene is determined by the concentration of its protein product, and the repressor protein binds to the regulatory region of the gene faster than transcription and translation.

Assumption 5: The Hill coefficient approximates the number of cooperative ligand binding sites on the receptor, and ligand molecules bind to a receptor simultaneously.

Assumption 6: The translation rate of each gene is equal.

Modeling

The expression processes of the 3 genes lacI,tetR and cI are described as follows:

For the transcription process, the ODE for transcription rate is described as follows:

Hill equation：

To carry out dimension reduction and simplify the analysis of this system, we normalize the ODEs

Results

We set the oscillator model parameters as:

First, we set the initial number of mRNA molecules and the number of protein molecules to be both 0. The oscillator model was simulated for 1000 minutes. Note that only the curve representing the number of cI protein molecules is visible, as all plotted concentrations are identical and overlap. From the simulation results, it can be seen that the peak value is 288 molecules at 8 minutes, and the steady state is reached at 28 minutes, where the number of protein molecules is maintained at 210 molecules.

We set the initial mRNA molecules and protein molecules to $$m_{lacI}(t = 0)=m_{tetR}(t = 0) = m_ {cI} (t = 0) = 0$$, $$p_ {tetR} = 10, p_ {lacI} = p_ {cI} = 0 $$, The oscillator model was then simulated for 1000 minutes, and the simulation results are shown in Figure 12. It is clear that after a period of time in the oscillator system, the system reaches a steady state with the peak value is 3000 molecules of the 3 proteins and the peak-to-peak period is 175 min.

It is clear that after a period of time in the oscillator system, the system reaches a steady state with the peak value is 3000 molecules of the 3 proteins and the peak-to-peak period is 175 min.

In order to change the peak amplitude of the oscillator model and the peak when the steady state is reached, we also explored the effect of different initial conditions on the oscillator model. In addition, we used 3D representation that plotted the simulation of the oscillator system for 1000 minutes (Figure 13), to fully understand the behavior of the oscillator system. Figure 13(a). shows that the system will rapidly reach the steady state under different initial protein numbers for 1000 minutes, unless all concentrations are the same, the system will begin to approach the limit cycle, and the steady state simulation is shown in red. Figure 13(b). shows the changes in TetR and LacI protein concentrations during the simulation. Figure 13(c). shows the curve of the region near the steady state near the limit cycle of Figure 13(b). Figure 13(d). shows that when the oscillator system is greater than 800 minutes, except for the steady state (indicated in red), it is related to the limit cycle. Figure 13(e). shows that for more than 200 minutes, the closer the initial conditions are to the same, the longer it takes for the system to reach the limit cycle.

Sequencing

Sequence and Features