Team:HZAU-China/Model
Model
Overview
Due to COVID-19, our lab process is limited. So at this time, the modelling work takes a more important part in our project. We hope our modelling work can achieve several goals as follows. First, we hope our model can predict the possible result before the experiment to tell us whether the design of circuits is doable. Second, we hope we can settle the problems that our team encountered during experiments. Our model can give an instruction on how to justify the circuit to achieve the ideal goal. Finally, we expect our model can provide the theoretical verification and support for our whole project.
In our "Detection & Report" model, we offered the realistic basis of the design of the circuit and explained why we divided the concentration of Streptococcus mutans into three levels. Also, based on the present results of the experiment, we proposed an approach to optimize the design of experiment to satisfy the needs of society. In our "Sterilization" model, we focused on the concentration of the ClyR, a protein that can efficiently kill S. mutans. According to the experiment data, we predicted a proper ClyR concentration which can achieve the ideal effect of sterilization at the lowest value. Meanwhile, in our "Exclusive-OR Gate" model, we successfully gave a prediction on whether the experiment can implement the Exclusive-OR calculation of repair and sterilization module through our model.
More specifically, each model was established to settle the issues that you may concern.
The "Detection and Report" model
What is the theoretical basis for dividing the quantity of S. mutans into three levels?
Can our three levels be realized in reality?
The "Sterilization" model
What is the optimal concentration of ClyR to kill S. mutans in vitro?
What can we do to justify the circuit to get the ideal ClyR concentration?
What about the concentration of ClyR in a more complex oral environment?
The "Exclusive-OR Gate" model
When the sterilization module is closed, will repair module successfully start? And what about the reverse condition?
How much LRAP protein can we produce? Is this quantity enough for repairing the enamel?
Figure 1. The overview of the interaction between the modeling and the experiment.
Detection and Report model
What is the theoretical basis which divides the quantity of S. mutans into three levels?
The aim of establishing this model is to offer a realistic basis for the division of three levels, i.e. "Safe", "Solvable" and "Dangerous" level to better satisfy the demand of human and society.
S. mutans is one of the early colonizers of the tooth surface. It can metabolize sucrose to lactic acid, thus create an acid environment in mouth. And this environment can cause the erosion of enamel. Furthermore, it is believed that an increased number of S. mutans are responsible for the onset of dental decay [1]. Thus, the division principles of the three levels is obvious. When there is no S. mutans or just a small amount of S. mutans which can't be detected by our "Detection Report" module, we regard it as the "Safe" level. According to the literature, the detection threshold is 10 nM [2-3]. While a certain amount of bacteria existing in oral condition which reached the threshold of detection, S. mutans may have the ability to lead the damage to enamel. At this time, we can use our "Sterilization" module to kill bacteria. Therefore, we assume it as a "Solvable" level. A "Dangerous" level is connected to a salivary level of S. mutans greater than 105 CFU per millimeter of saliva, which is generally considered as a high-risk of dental decay [3].
Our "Detection & Report" module utilize the quorum sensing (QS) system to realize the detection function of S. mutans. We adopt Competence-Stimulating Peptide (CSP) as the signal molecule which can indicate the quantity of S. mutans. The mechanism of the QS system as the Figure 2A shows. Therefore, an association between the quantity of S. mutans and CSP concentration is needed. We noticed that the 2014 iGEM team NYMU-Taipei has done the similar work [4].
Can our three levels be realized in reality?
Except for this issue, we still need to predict whether this three levels can be carried out. Many iGEMers has applied the QS system as a switch. Generally, the switch usually just can control two level. However, we proposed a new way to applicate the QS system. We combined two promoters with different sensitivities to CSP. When two promoters respond to a specific concentration of CSP, each promoter can trigger a different expression of florescent protein. Therefore, there will be different mixed color corresponding to different CSP concentration as the Figure 2B shows. In this way, we can achieve the three level?
Figure 2. A) The mechanism of the QS system of S. mutans. B) The schematic diagram of our "Detection and Report" module.
As Figure 2A shows, the phosphorylated ComE acts as an activator for both promoters. In the presence of the activator, we derived from the promoter activity function [5]that in addition to the maximum transcription rates of the two promoters themselves and the affinity between the phosphorylated ComE and the DNA binding site will influence the promoter activity, but also the concentration of phosphorylated ComE will influence the promoter. However, due to lack of parameters of the ComDE system and our experimental data are insufficient, we were unable to obtain precise parameters to acquire a quantitative relationship. So our model try to explore this issue from a qualitative point of view. We want to help our team better understand the working mechanism of the whole system. We assume that when the concentration of CSP reaches the threshold, different CSP concentrations correspond to different steady-state concentrations of phosphorylated ComE. This means that the activity of the promoter changes with the steady-state content of the phosphorylated ComE, which leads to the mixing of the two colors expressed in different ratios (Figure 3B). And the advice from the modelling group is that our team can mutate the promoter [6] . In this way, we can regulate the parameters of the promoter to justify the color that our circuit produced. Then make the mixed color fit the original design and reality basis of our project.
Figure 3. A schematic that proves our "solvable" pattern and "dangerous" pattern are distinguishable.
Summary
In the "Detection & Report" model, we explained the basis of three levels of classification, showing that it is consistent with the real situations. At the same time we made an exploratory prediction on our report system and proved that it can report three different colors. However, if we want the circuit to be perfectly fit the reality, the guidance model gives is to adjust the attributions of the promoter accordingly.
Sterilization model
What is optimal concentration to kill S. mutans in vitro?
The ClyR is a chimeric lysin which is relatively newly discovered [7]. There are few literatures or parameters describing its properties. Thus, we use our model to depict the properties of this substance [8]. Besides, we expected to find the quantitative association between the concentration of ClyR and the growth rate of S. mutans and then acquire the ideal concentration to kill the bacteria in vitro.
To figure out this association, we utilize our own time-kill experiment data (Figure 4.). From the data, we estimated the S. mutans growth rate (which can be positive or negative) as a linear regression coefficient of the change in bacterial density over time. Then we get a series of points. Each point represents the bactericidal effect of a particular concentration. By simulating a curve based on a Hill function which can be called as the pharmacodynamic function for these points, we can obtain the optimum concentration. The pharmacodynamic function we use is described as follows [9].
$$\psi(c)=\psi_{\max }-\mu(c)\quad\quad(r2.1.1)$$
$$\mu(c)=E_{\max } \frac{\left(c / \mathrm{EC}_{50}\right)^{\kappa}}{1+\left(c / \mathrm{EC}_{50}\right)^{\kappa}}\quad\quad(r2.1.2)$$
$$\psi(c)=\psi_{\max }-\frac{\left(\psi_{\max }-\psi_{\min }\right)(c / \mathrm{zMIC})^{\kappa}}{(c / \mathrm{zMIC})^{\kappa}-\psi_{\min } / \psi_{\max }}\quad\quad(r2.1.3)$$
Figure 4. A) Estimating growth rates.Dashed lines represent linear regressions of the logarithm of the OD600 at different antimicrobial concentrations. The coefficient of the linear regression corresponds to the net bacterial growth rate. B) Fitting the pharmacodynamic function to estimated growth rates.
Click me to show the parameters!
Our mathematical model instructed us that the concentration around 20 nM has the best effect. Besides, according to our model, we predict that the MIC value of ClyR is 0.097 nM and the κ value is 1.138. We hope that the parameters we predicted by modelling will help future teams when they try to understand the properties of the ClyR.
What can we do to justify the circuit to get the ideal ClyR concentration?
Having figured out the optimum concentration, we are concerned with how it should be achieved. We intend to solve this problem by adjusting the value of the RBS upstream of the ClyR. The results are shown in the Figure 5. Precise quantification is difficult for complex biological systems, so we believe that the regulatory result of the RBS B0030, is roughly within the optimal concentration range for the experiments.
Synthesis processes
$$\text {Gene} \stackrel{K_{\text {mT7RNAp}}}{\longrightarrow} mRNA_{\text {T7RNAp}}\quad\quad(r2.2.1)$$
$$\text mRNA_{T7RNAp} \stackrel{K_{\text {T7RNAp}}}{\longrightarrow} mRNA_{T7RNAp}+T7RNAp \quad\quad(r2.2.2)$$
$$\text {Gene} \stackrel{K_{\text {mClyR}}}{\longrightarrow} mRNA_{\text {ClyR}} \quad\quad(r2.2.3)$$
$$\text mRNA_{ClyR} \stackrel{K_{\text {ClyR}}}{\longrightarrow} mRNA_{ClyR}+ClyR \quad\quad(r2.2.4)$$
Degradation processes
$$m R N A_{T 7 R N A \mathrm{p}} \stackrel{k_{mT7RNAp}}{\longrightarrow} \varnothing\quad\quad(r2.2.5)$$
$$T 7 R N A p \stackrel{k_{T 7 R N A p}}{\longrightarrow} \varnothing\quad\quad(r2.2.6)$$
$$m R N A_{ClyR} \stackrel{k_{\text {ClyR}}}{\longrightarrow} \varnothing\quad\quad(r2.2.7)$$
$$\text { ClyR } \stackrel{k_{\text {ClyR}}}{\longrightarrow} \varnothing\quad\quad(r2.2.8)$$
Ordinary differential equations involved in sterilization model
$$\frac{d\left[m R N A_{T 7 R N A p}\right]}{d t}=K_{m T 7 R N A p}-k_{m T 7 R N A p}\left[m R N A_{T 7 R N A p}\right]\quad\quad(f2.2.1)$$
$$\frac{d[T 7 R N A p]}{d t}=K_{T 7 R N A p}\left[m R N A_{T 7 R N A p}\right]-k_{T 7 R N A p}[T 7 R N A p]\quad\quad(f2.2.2)$$
$$\frac{d\left[mRNA_{\text {ClyR}}\right]}{d t}=K_{\text {mClyR}}-k_{\text {mClyR}}\left[m R N A_{\text {ClyR}}\right]\quad\quad(f2.2.3)$$
$$\frac{d[\text {ClyR} ]}{d t}=K_{\text {ClyR}}\left[mRNA_{\text {ClyR }}\right]-k_{\text {ClyR }}[\text { ClyR } ]\quad\quad(f2.2.4)$$
Figure 5. ClyR concentrations varying with different RBSs.
Click me to show the parameters!
Will this concentration still work in a more complex oral environment?
Because the optimal concentrations we obtained only consider the in vitro condition, this is quite different from the actual situation. We need to know the decrease of ClyR content when considering the process of secretion and diffusion from the cell into the biofilm of S. mutans. Therefore, we developed a model that was as realistic as possible to test whether the sterilization concentration was still effective.
First, we will illustrate the hypothesis of our model. We assumed that S. mutans was cultured in 100mL BHI medium (added glucose). To simplify the model, we approximated the BHI as an aqueous solution. Besides, based on the fact that S. mutans cannot use glucose to synthesize the main component of the biofilm [16], extracellular polysaccharide (EPS), we assumed that the composition of the biofilm of S. mutans remains unchanged over time. Moreover, S. mutans can use glucose for growth. So we use the Monod equation (f2.3.1) to describe the growth rate of S. mutans at different glucose substrate concentrations [23].
According to the literature, we found that the glucose content in saliva ranged from 0.15 to 3.82 mg/dL [24]. We used the maximum value of 3.82 mg/dL as the glucose substrate concentration for the model. Then we calculate the values of some of the parameters. The culture system was 100mL and the volume of glucose in the medium was calculated using the relationship between the density and mass. The volume of glucose is Vg=2.48 ml. By reviewing literature, we obtained the volumetric relationship between S. mutans and its extracellular polysaccharide (EPS) [18], Veps=1.8Vcell. Based on these, we can calculate the volume fraction of different substances in the system which can help us to calculate the effective diffusion coefficient (we will mention it later).
$$B= \frac{\mu_{\max } \cdot {C_{g}} \cdot B_{0} }{k_{s}+C_{g}} \quad \quad (f2.3.1)$$
$$\varepsilon _{EPS}=\frac{1.8 V _{cell}\cdot N}{V_{H} +V_{g}+2. 8 V_{c e l l} \cdot N} \quad \quad(f2.3.2)$$
$$\varepsilon _{cell}=\frac{ V _{cell}\cdot N}{V_{H} +V_{g}+2. 8 V_{c e l l} \cdot N} \quad \quad(f2.3.3)$$
$$\varepsilon _{H}=\frac{ V _{H}}{V_{H} +V_{g}+2. 8 V_{c e l l} \cdot N} \quad \quad(f2.3.4)$$
$$\varepsilon _{g}=\frac{ V _{g}}{V_{H} +V_{g}+2. 8 V_{c e l l} \cdot N} \quad \quad(f2.3.5)$$
Second, the translocation model. Based on the 2017 Sydney_Australia team [19]. We applicate its translocation model to our project. According to the team's calculations, the maximum transit rate is V1=934.2 aa/(min site). What's more, the amount of transporter protein in E. coli is 500. Thus, we can get the translocation rate of each E. coli cell is V2=467100 aa/min. Since ClyR consists of 254 amino acid residues, we can conclude Vt=3.05x10-11 nM/min through the formula (f2.3.6), where the V means the volume of medium.
$$V_{t}=\frac{V_{2}\ \cdot 10^{9}}{A \cdot N_{A}\cdot V} \quad \quad (f.2.6)$$
Third, the diffusion model. Diffusion coefficient in water, the average density of protein is 1.37g/mL according to the literature. Since we assume that ClyR is a simple spherical structure, we can obtain Rmin by formula (f2.3.7), which is the minimum radius of a sphere that can contein a specific mass of protein. However, due to the asymmetric binding of the protein surface to water, the Stokes radius R is commonly used to describe the radius of the protein. Usually, the R/Rmin ratio in proteins will be no less than 1.2 [20]. Therefore, we obtained the diffusion coefficient of ClyR in water D = 6.6x10-5/a cm2/s according to formula (f2.3.8).
Effective diffusion coefficient, during the diffusion process of ClyR through the biofilm, it is hindered by EPS, so its diffusion rate is slower compared to water. In this model, based on the study of Westrin and Axelsson [21], we declare the diffusion coefficient of ClyR in biofilm as the effective diffusion coefficient "De". We obtained "De" by formula (f2.3.9).
Diffusion quantity, to simplify the model, we assume that the diffusion of ClyR in biofilm satisfies Fick's second law. However, it hard to obtain the concentration of ClyR in different depths of biofilm, for this reason we consider the variation of the concentration of ClyR with the position “L” going into the biofilm as a uniform variation. By calculating the formula (f2.3.10) [21], we acquired the concentration of C2 with the change of time(f2.3.11).
$$\frac{4}{3} \pi R_{min}^{3} =\frac{M}{\rho N_{A} } \quad \quad (f2.3.7)$$
$$D=\frac{k T}{6 \pi \eta R} \quad \quad (f2.3.8)$$
$$D_{e}=\frac{\left(1-\varepsilon_{c}-\varepsilon_{E}\right)^{3}D}{\left(1+\varepsilon_{c} / 2\right)\left(1-\varepsilon_{c}+\varepsilon_{E}\right)^{2}}\quad \quad(f2.3.9)$$
$$\varepsilon_{w} \frac{d C_{2} }{d t}=D e \cdot \frac{d^2 C_{1} }{d L^{2}} \quad\quad(f2.3.10)$$
$$\frac{\mathrm{d} C_{2} }{\mathrm{d} t}=\frac{2.08\times 10^{-2} \cdot C_{1}}{a} \quad \quad(f2.3.11)$$
Fourth, the sterilizing effect of ClyR. We assume that ClyR has no receptor in biofilm, so that ClyR cannot be degraded (or the natural degradation time is too long). Therefore, we conclude that the property of ClyR is unaffected in biofilm. And the bactericidal effect of different concentrations is consistent with the effect of the same concentration of ClyR in non-biofilm conditions.
Ordinary differential equations as follows
$$\frac{d C_{1}}{d t}=V_{t}-\frac{D e}{\varepsilon \omega} \cdot Q_{1}+\frac{D e}{\varepsilon \omega} \cdot Q_{2} \quad \quad (f2.3.12)$$
$$\frac{d C_{2}}{d t}=\frac{D e}{\varepsilon_{\omega}} \cdot Q_{1}-\frac{D e}{\varepsilon_{\omega}} \cdot Q_{2} \quad \quad(f2.3.13)$$
$$\frac{d B}{d t}=\frac{\mu_{\max } \cdot C_{g} \cdot B}{k_{s}+C_{g} }-\psi \left(C_{2}\right)\quad \quad(f2.3.14)$$
Figure 6. The growth of S.mutans varying with diffferent values of "a" in complex environment.
Because of the uncertainty of "a", it's hard for us to judge the effect of a value on the growth of S. mutans. From the literature, the maximum value of "a" is only 2.44 [20]. For this situation, we want to choose a higher value of "a" to reflects the growth of S. mutans. So we simulate for 500 minutes with diffferent "a" values.
From the Figure 6, S.mutans grow at first. Then because of the accumulation of ClyR in biofilm, the growth of S.mutans was inhibited. The values of "a" selected by us all have this trend, but the inhibition time is different. So we can know that the values of "a" has effect on the growth of S.mutans. Even if we can not define the value of "a", we can get a conclusion that when the value of "a" between 1.2 and 3.6, our sterilization module can work in a complex environment.
Click me to show the parameters!
Summary
In Sterilization model, we used the data provided by the experiment. A pharmacokinetic curve is simulated based on the data, depicting the properties of ClyR in vitro and giving the ideal sterilization concentration. At the same time, it gives experiment guidance on how to select the appropriate RBS to achieve this concentration. In addition, we simulated the real environment of the oral cavity and demonstrate that at this ideal concentration, ClyR is still effective in killing Streptococcus mutans in the biofilm after secretion and diffusion processes.
Exclusive-OR Gate
When the repair module is closed, will sterilization module successfully start? And what about the reverse condition?
How much LRAP protein can we produce? Is this quantity enough for repairing the enamel?
We use the "Exclusive-OR Gate" conception to describe the work pattern of the switching conversion between repair and sterilization module. Its mechanism as the Figure 7 shows which can be explained as "must have one module or the other but not both".
Figure 7. Mechanism of Exclusive-OR gate of sterilization module and repair module.
Synthesis processes as follows
$$\text {Gene} \stackrel{K_{\text {mT7RNAp}}}{\longrightarrow} mRNA_{\text {T7RNAp}}\quad\quad(r3.1)$$
$$\text {Gene} \stackrel{\beta _{1}}{\longrightarrow} mRNA_{\text {T7RNAp}}\quad\quad(r3.2)$$
$$\text mRNA_{T7RNAp} \stackrel{K_{\text {T7RNAp}}}{\longrightarrow} mRNA_{T7RNAp}+T7RNAp \quad\quad(r3.3)$$
$$\text {Gene} \stackrel{K_{\text {mtetR}}}{\longrightarrow} mRNA_{\text {tetR}} \quad\quad(r3.4)$$
$$\text {Gene} \stackrel{K_{\text {mClyR}}}{\longrightarrow} mRNA_{\text {ClyR}} \quad\quad(r3.5)$$
$$\text mRNA_{tetR} \stackrel{K_{\text {tetR}}}{\longrightarrow} mRNA_{tetR}+tetR \quad\quad(r3.6)$$
$$\text mRNA_{ClyR} \stackrel{K_{\text {ClyR}}}{\longrightarrow} mRNA_{ClyR}+ClyR \quad\quad(r3.7)$$
$$\text {Gene} \stackrel{K_{\text {LRAP}}}{\longrightarrow} mRNA_{\text {LRAP}}\quad\quad(r3.8)$$
$$\text {Gene} \stackrel{\beta_{3}}{\longrightarrow} mRNA_{LRAP}\quad\quad(r3.9)$$
$$\text mRNA_{LRAP} \stackrel{K_{\text {LRAP}}}{\longrightarrow} mRNA_{LRAP}+LRAP \quad\quad(r3.10)$$
$$\text where,K_{mT7RNAp}=\frac{\beta_{1}}{1+\frac{k_{d1}}{ComE}}, K_{mClyR}=\frac{\beta_{2}}{1+\frac{k_{d2}}{T7RNAp}}, K_{\text {metR}}=\frac{\beta_{3}}{1+\frac{{tetR}}{k_{d3}}}$$
Degradation processes as follows
$$m R N A_{T 7 R N A \mathrm{p}} \stackrel{k_{mT7RNAp}}{\longrightarrow} \varnothing\quad\quad(r3.11)$$
$$T 7 R N A p \stackrel{k_{T 7 R N A p}}{\longrightarrow} \varnothing\quad\quad(r3.12)$$
$$m R N A_{t e t R} \stackrel{k_{\text {tetR}}}{\longrightarrow} \varnothing\quad\quad(r3.13)$$
$$\text { tetR } \stackrel{k_{\text {tetR}}}{\longrightarrow} \varnothing\quad\quad(r3.14)$$
$$m R N A_{ClyR} \stackrel{k_{\text {ClyR}}}{\longrightarrow} \varnothing\quad\quad(r3.15)$$
$$\text { ClyR } \stackrel{k_{\text {ClyR}}}{\longrightarrow} \varnothing\quad\quad(r3.16)$$
$$m R N A_{m L R A P} \stackrel{k_{m L R A P}}{\longrightarrow} \varnothing\quad\quad(r3.17)$$
$${L R A P } \stackrel{k_{\text {LRAP}}}{\longrightarrow} \varnothing\quad\quad(r3.18)$$
$${LRAP-LAA } \stackrel{k_{\text {LRAP-LAA}}}{\longrightarrow} \varnothing\quad\quad(r3.19)$$
The difficulty we met is that we are not sure when the sterilization module is open whether the repair module can be successfully inhibited and how much time it will take. Just imagine the situation when there is existing too much S. mutans, our Tooth Fairy will switch to the sterilization mode, the production of tetR protein may be too few to inhibit the Ptet promoter. The result we get through the ODEs as the Figure 8 shows.
Ordinary differential equations as follows
$$\frac{d\left[m R N A_{T 7 R N A p}\right]}{d t}=K_{m T 7 R N A p}-k_{m T 7 R N A p}\left[m R N A_{T 7 R N A p}\right]\quad\quad(f3.1)$$
$$\frac{d[T 7 R N A p]}{d t}=K_{T 7 R N A p}\left[m R N A_{T 7 R N A p}\right]-k_{T 7 R N A p}[T 7 R N A p]\quad\quad(f3.2)$$
$$\frac{d\left[mRNA_{\text {tetR}}\right]}{d t}=K_{\text {mtetR}}-k_{\text {mtetR}}\left[m R N A_{\text {tetR}}\right]\quad\quad(f3.3)$$
$$\frac{d[\text {tetR} ]}{d t}=K_{\text {tetR}}\left[mRNA_{\text {tetR }}\right]-k_{\text {tetR }}[\text { tetR } ]\quad\quad(f3.4)$$
$$\frac{d\left[m R N A_{L R A P}\right]}{d t}=\beta_{3}-k_{m L R A P}\left[m R N A_{L R A P}\right]\quad\quad(f3.5)$$
$$\frac{d\left[m R N A_{L R A P}\right]}{d t}=K_{m L R A P}-k_{m L R A P}\left[m R N A_{L R A P}\right]\quad\quad(f3.6)$$
$$\frac{d[L R A P]}{d t}=K_{L R A P}\left[m R N A_{L R A P}\right]-k_{L R A P}[L R A P]\quad\quad(f3.7)$$
Figure 8. Changes in LRAP protein concentration over time in the case of Exclusive-OR gate.
The constant expression of LRAP is 64510 nM(Figure 8A). While the sterilization module start, the LRAP concentration is 3017 nM (Figure 8B). However, according to the literature, 3000 nM LRAP is the minimum concentration of restorable enamel[8]. Thus, its derived from our original expectation. Therefore, we propose a new approach to settle this problem. A degradation tag LAA was attached to the LRAP to regulate the expression of LRAP. Through the adjustment, we get a satisfactory result. The constant expression level of LRAP trun to 7157 nM (Figure 9A). There has been literature verified that approximately 6000 nM has the best effect of repair[8]. And the inhibited concentration of LRAP decreased notably to 368.8 nM (Figure 9B). This means the repair module is successfully inhibited.
$$\frac{d[LRAP-LAA]}{d t}=K_{L R A P}\left[m R N A_{L R A P}\right]-k_{L R A P-LAA}[L R A P-LAA]\quad\quad(f3.8)$$
Figure 9. Changes in LRAP-LAA protein concentration over time in the case of Exclusive-OR gate.
When the number of S. mutans does not reach the threshold value of the detection module. The
repair module open while the sterilization module keep closed. We are interested in whether the basal expression of T7 promoter affects the ClyR production. The result we get through the ODEs as the Figure 10 shows. The concentration of ClyR at the state is 2.376 nM (Figure 10). This indicate that when the repair module is open, the steriliazation module could be totally closed.
$$\frac{d\left[m R N A_{T 7 R N A p}\right]}{d t}={\beta_{4} }-k_{m T 7 R N A p}\left[m R N A_{T 7 R N A p}\right]\quad\quad(f3.9)$$
$$\frac{d[T 7 R N A p]}{d t}=K_{T 7 R N A p}\left[m R N A_{T 7 R N A p}\right]-k_{T 7 R N A p}[T 7 R N A p]\quad\quad(f3.10)$$
$$\frac{d\left[mRNA_{\text {ClyR}}\right]}{d t}=K_{\text {mClyR}}-k_{\text {mClyR}}\left[m R N A_{\text {ClyR}}\right]\quad\quad(f3.11)$$
$$\frac{d[\text {ClyR} ]}{d t}=K_{\text {ClyR}}\left[mRNA_{\text {ClyR }}\right]-k_{\text {ClyR }}[\text { ClyR } ]\quad\quad(f3.12)$$
Figure 10. Changes in ClyR protein concentration over time in the case of Exclusive-OR gate.
Click me to show the parameters!
Summary
In "Exclusive-OR Gate" model, we wanted to achieve the function of sterilization without restoration or restoration without sterilization. In order to avoid mixing inclusion or causing unnecessary metabolic stress when repairing enamel. After our simulations, we demonstrated theoretically that we could achieve this function and give effective guidance before the experiments are performed.
References
[1] Giacaman R A, Araneda E, Padilla C. Association between biofilm-forming isolates of mutans streptococci and caries experience in adults[J]. archives of oral biology, 2010, 55(8): 550-554.
[2] Eşian D, Man A, Burlibasa L, et al. Salivary level of Streptococcus mutans and Lactobacillus spp. related to a high risk of caries disease[J]. Rom Biotechnol Lett, 2017, 22(2): 12496-503.
[3] Loesche W J. Microbiology of dental decay and periodontal disease[M]//Medical Microbiology. 4th edition. University of Texas Medical Branch at Galveston, 1996.
[4] https://2014.igem.org/Team:NYMU-Taipei
[5] Aron U. Introduction to Systems Biology: design principles of biological circuits [M]. Chemical Industry Press, 2010.
[6] Kannan S, Sams T, Maury J, et al. Reconstructing dynamic promoter activity profiles from reporter gene data[J]. ACS synthetic biology, 2018, 7(3): 832-841.
[7] Xu J, Yang H, Bi Y, et al. Activity of the chimeric lysin ClyR against common Gram-positive oral microbes and its anticaries efficacy in rat models[J]. Viruses, 2018, 10(7): 380.
[8] Foerster S, Unemo M, Hathaway L J, et al. Time-kill curve analysis and pharmacodynamic modelling for in vitro evaluation of antimicrobials against Neisseria gonorrhoeae[J]. BMC microbiology, 2016, 16(1): 216.
[9] Regoes R R, Wiuff C, Zappala R M, et al. Pharmacodynamic functions: a multiparameter approach to the design of antibiotic treatment regimens[J]. Antimicrobial agents and chemotherapy, 2004, 48(10): 3670-3676.
[10] https://2018.igem.org/Team:MIT/Model
[11] Hung D C I, Downey J S, Ayala E A, et al. Characterization of DNA binding sites of the ComE response regulator from Streptococcus mutans[J]. Journal of bacteriology, 2011, 193(14): 3642-3652.
[12] Selinger D W, Saxena R M, Cheung K J, et al. Global RNA half-life analysis in Escherichia coli reveals positional patterns of transcript degradation[J]. Genome research, 2003, 13(2): 216-223.
[13] Sharma A K, Ahmed N, O’Brien E P. Determinants of translation speed are randomly distributed across transcripts resulting in a universal scaling of protein synthesis times[J]. Physical Review E, 2018, 97(2): 022409.
[14] Újvári A, Martin C T. Thermodynamic and kinetic measurements of promoter binding by T7 RNA polymerase[J]. Biochemistry, 1996, 35(46): 14574-14582.
[15] https://2019.igem.org/Team:HZAU-China/Model
[16] Xiao J, Koo H. Structural organization and dynamics of exopolysaccharide matrix and microcolonies formation by Streptococcus mutans in biofilms[J]. Journal of applied microbiology, 2010, 108(6): 2103-2113.
[17] Cross S E, Kreth J, Zhu L, et al. Atomic force microscopy study of the structure–function relationships of the biofilm-forming bacterium Streptococcus mutans[J]. Nanotechnology, 2006, 17(4): S1.
[18] Cai J N, Kim M A, Jung J E, et al. Effects of combined oleic acid and fluoride at sub-MIC levels on EPS formation and viability of Streptococcus mutans UA159 biofilms[J]. Biofouling, 2015, 31(7): 555-563.
[19] https://2017.igem.org/Team:Sydney_Australia/Model
[20] Erickson H P. Size and shape of protein molecules at the nanometer level determined by sedimentation, gel filtration, and electron microscopy[J]. Biological procedures online, 2009, 11(1): 32.
[21] Stewart P S. Theoretical aspects of antibiotic diffusion into microbial biofilms[J]. Antimicrobial agents and chemotherapy, 1996, 40(11): 2517-2522.
[22] Lynch D J, Fountain T L, Mazurkiewicz J E, et al. Glucan-binding proteins are essential for shaping Streptococcus mutans biofilm architecture[J]. FEMS microbiology letters, 2007, 268(2): 158-165.
[23] Kemp C W, Robrish S A, Curtis M A, et al. Application of a competition model to the growth of Streptococcus mutans and Streptococcus sanguis in binary continuous culture[J]. Applied and Environmental Microbiology, 1983, 45(4): 1277-1282.
[24] Yamaguchi M, Mitsumori M, Kano Y. Noninvasively measuring blood glucose using saliva[J]. IEEE Engineering in Medicine and Biology Magazine, 1998, 17(3): 59-63.
[25] https://2016.igem.org/Team:William_and_Mary/Model
[26] Nagano, T., et al. "Mmp-20 and Klk4 cleavage site preferences for amelogenin sequences."Journal of dental research 88.9 (2009): 823-828.
[27] http://parts.igem.org/Part:BBa_C0012.
