Team:NYMU-Taipei/modeling/m3

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Using the above-described module, we can change the level of threshold by putting different efficacies and numbers of terminators in our circuit. It is reasonable for use to introduce the rule of probability for predicting the result. The higher the efficacy of terminator is, the less likely the coding sequence is to be transcribed. And the more terminators put behind the promoter, the lower the transcription probability is, as the rule of probability multiplication has shown (eq.). Here, we use modelling to verify this concept and figure out the best combination of terminators for our circuit.</p>
Using the above-described module, we can change the level of threshold by putting different efficacies and numbers of terminators in our circuit. It is reasonable for use to introduce the rule of probability for predicting the result. The higher the efficacy of terminator is, the less likely the coding sequence is to be transcribed. And the more terminators put behind the promoter, the lower the transcription probability is, as the rule of probability multiplication has shown (eq.). Here, we use modelling to verify this concept and figure out the best combination of terminators for our circuit.</p>
       <h1>Models and mathematic equations</h1>
       <h1>Models and mathematic equations</h1>
 +
      <p>If we build some terminator in front of the lysine gene mRNA, the concentration of lysis protein won’t increase easily and thus killing the S. mutans in a short time. Although the threshold of concentration of lysine gene that would kill S. mutans is fixed, we can still regulate the velocity of lysine protein reach this threshold by using different amount of terminator with different efficiency.<br>$$\frac{d[lysine \; gene \; mRNA]}{dt}=\beta \frac{[comE]^n}{K_d+[comE]^n} (1-a)^x - [lysine \; gene \; mRNA] K_m$$
 +
$$\frac{d[lysine \; protein]}{dt}= K_t [lysine \; gene \; mRNA] - K_p [lysis \; protein]$$
 +
This is the simulation of lysine gene mRNA and the lysine protein. The circuit is activated by nlmC promoter, which is turned on by comE molecule. The term $(1-a)^x$ is how the terminator works, lowering the probability that the promoter can successfully transcript the lysine gene mRNA. Note that in addition to using same terminator, we can try combinations of different terminators. The meaning of parameters is shown as below:<br><br>
 +
1.&nbsp; $\beta$:max nlmC promoter activity<br>
 +
2.&nbsp; $K_d$:promoter-TF dissociation constant<br>
 +
3.&nbsp; $K_m$:Lysine gene mRNA degradation<br>
 +
4.&nbsp; $K_t$:Translation efficiency<br>
 +
5.&nbsp; $K_p$:Lysine protein degradation<br>
 +
6.&nbsp; $n$:hill coefficient<br>
 +
7.&nbsp; $a$:terminator efficiency<br>
 +
8.&nbsp; $x$:amount of terminator
 +
 +
      </p>
       <h1>Result and model validation</h1>
       <h1>Result and model validation</h1>
       <h1>Reference</h1>
       <h1>Reference</h1>

Revision as of 05:37, 27 September 2014

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Threshold model

Purpose

1. To determine the relationship between S. mutans population and the amount of CSP, competence stimulating peptide.
2. To verify if gene expression level under different combination of terminators can be shown in mathematic equations.
3. To find out the type and the amount of terminators to put behind promoter, so that we can have a proper threshold for lysine-protein-producing gene (see control-sensor).

Background

As we have shown you in competition model, it is better to control the population of S. mutans in a proper amount. To achieve this goal, we design a S. mutans population sensing promoter and a threshold in our circuit, and therefore won’t start the killing module, the lysine-protein-producing gene, until S. mutans exceed the optimal amount we have set.

NlmC is a S. mutans population sensing promoter. Studies have shown that nlmC is triggered by a transcription factor which is only produced when receptor binds to CSP, a quorum sensing chemical released by every S. mutans[1]. The more S. mutans there are, the higher the concentration of CSP is in the environment, and therefore, the more likely the coding sequence behind the downstream promoter, nlmC, is to be transcribe[2]. However, the certain and quantified connection between the amount of S. mutans and CSP concentration is not well understood. Therefore, we use modelling to do a regression and find out the relation by using an experimental data[3].

Nevertheless, using population sensing promoter only doesn’t meet our needs, for we want to have the killing module transcribed only when the amount of S. mutans exceed a certain level. And since the RBS in M102, the phage we plan to manipulate, is not well studied, changing RBS that have different ribosome binding strength is not suitable for our circuit to create a threshold. And therefore we have to find another way to attain the objective. It is well known that terminators have its own efficacy and is possible to have some leakage[4]. As a result, if we put terminators between promoter and coding sequence, the circuit will not be transcribed until the concentration of transcription factor reach a certain level and raise the terminator leakage probability.

Using the above-described module, we can change the level of threshold by putting different efficacies and numbers of terminators in our circuit. It is reasonable for use to introduce the rule of probability for predicting the result. The higher the efficacy of terminator is, the less likely the coding sequence is to be transcribed. And the more terminators put behind the promoter, the lower the transcription probability is, as the rule of probability multiplication has shown (eq.). Here, we use modelling to verify this concept and figure out the best combination of terminators for our circuit.

Models and mathematic equations

If we build some terminator in front of the lysine gene mRNA, the concentration of lysis protein won’t increase easily and thus killing the S. mutans in a short time. Although the threshold of concentration of lysine gene that would kill S. mutans is fixed, we can still regulate the velocity of lysine protein reach this threshold by using different amount of terminator with different efficiency.
$$\frac{d[lysine \; gene \; mRNA]}{dt}=\beta \frac{[comE]^n}{K_d+[comE]^n} (1-a)^x - [lysine \; gene \; mRNA] K_m$$ $$\frac{d[lysine \; protein]}{dt}= K_t [lysine \; gene \; mRNA] - K_p [lysis \; protein]$$ This is the simulation of lysine gene mRNA and the lysine protein. The circuit is activated by nlmC promoter, which is turned on by comE molecule. The term $(1-a)^x$ is how the terminator works, lowering the probability that the promoter can successfully transcript the lysine gene mRNA. Note that in addition to using same terminator, we can try combinations of different terminators. The meaning of parameters is shown as below:

1.  $\beta$:max nlmC promoter activity
2.  $K_d$:promoter-TF dissociation constant
3.  $K_m$:Lysine gene mRNA degradation
4.  $K_t$:Translation efficiency
5.  $K_p$:Lysine protein degradation
6.  $n$:hill coefficient
7.  $a$:terminator efficiency
8.  $x$:amount of terminator

Result and model validation

Reference

  1. Li, Y.-H., et al., A quorum-sensing signaling system essential for genetic competence in Streptococcus mutans is involved in biofilm formation. Journal of bacteriology, 2002. 184(10): p. 2699-2708.
  2. Liu, T., et al., ComCED signal loop precisely regulates nlmC expression in Streptococcus mutans. Annals of Microbiology, 2014. 64(1): p. 31-38.
  3. van der Ploeg, J.R., Regulation of bacteriocin production in Streptococcus mutans by the quorum-sensing system required for development of genetic competence. Journal of bacteriology, 2005. 187(12): p. 3980-3989.
  4. Chen, Y.-J., et al., Characterization of 582 natural and synthetic terminators and quantification of their design constraints. Nature methods, 2013. 10(7): p. 659-664.