Team:ZJUT-China/Model
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Team:ZJUT-China/Model
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Team:ZJUT-China/Model
Formaldehyde metabolism model
Purpose and Description
Metabolic pathway is the core content of our project. Based on the understanding of the mechanism of metabolic pathway, this model simulates the formaldehyde metabolic pathway in order to achieve better metabolic effects by adjusting parameters. The following picture showed the relationships between substances. Through this model, we have a better understanding of the metabolism and transformation of substances in cells.
The formaldehyde in the Room enters our device and will be absorbed by the engineered bacteria cultured in the device. Then formaldehyde enters the metabolic pathway. The 1/2/3/4 labels indicated in the figure are the sequences of metabolism. The final metabolite CO2 was released into the external environment to reduce the damage of bacteria caused by the accumulation of intermediate metabolites such as formic acid.
Enter is the rate of formaldehyde entering the cell which is assumed to depend on the concentration of formaldehyde. rHCHO is the concentration of formaldehyde in the room. The following equation showed the rate of formaldehyde entering cells:
$$ \frac{d[HCHO]}{dt}=kf*[rHCHO] $$
The following equation describes the rate of combine1. Because there are two substrates involved in the reaction, we use the Ordered-Bi-Bi Equation to describe it.
combine1:
$$ \frac{d[HMG]}{dt}=\frac{Vm}{(Ksa*Kmb/([GSH]*[HCHO]))+(Kma/[GSH])+(Kmb/[HCHO])+1} $$
| Name | Description |
|---|---|
| HMG | product |
| GSH | substrate A |
| HCHO | substrate B |
| Vm | Maximum reaction rate when substrate A and substrate B reach saturation |
| Kma | The Michaelis constant of A when the concentration of B reaches saturation |
| Kmb | The Michaelis constant of B when the concentration of A reaches saturation |
| Ksa | The dissociation constant of substrate A bound to an enzyme |
The rate equations of combine2/3 are similar.
combine2:
$$ \frac{d[FG]}{dt}=\frac{Vm}{(Ksa*Kmb/([NAD+]*[HMG]))+(Kma/[NAD+])+(Kmb/[HMG])+1} $$
| Name | Description |
|---|---|
| FG | product |
| NAD+ | substrate A |
| HMG | substrate B |
combine3:
$$ \frac{d[CO2]}{dt}=\frac{Vm}{(Ksa*Kmb/([NAD+]*[HCOOH]))+(Kma/[NAD+])+(Kmb/[HCOOH])+1} $$
| Name | Description |
|---|---|
| CO2 | product |
| NAD+ | substrate A |
| HCOOH | substrate B |
The hydrolysis step is simpler, in which formic acid is formed and glutathione is regenerated. This is hydrolysis rate equation:
$$ \frac{d[HCOOH]}{dt}=kf*[FG] $$
Simulation Result
From the figure above, we can see that the concentration of indoor formaldehyde represented by the blue dash line gradually drops, while the concentration of formaldehyde which is represented by the blue solid line in bacteria goes through a process of first rising and then falling. Intermediate metabolites are not accumulated in bacteria, and finally discharged into the room in the form of CO2.
By simulating the metabolism of formaldehyde, we can know how to maximize the rate of formaldehyde metabolism without harming the bacteria themselves.This has implications for the design of our hardware. See the hardware section for details on hardware design. Our hardware consists of an intake device and an enrichment device.Through this model, we can adjust the air intake rate of the device to achieve better formaldehyde removal effect.
Light control model
Purpose and Description
On the basis of last year, we designed the following light-controlled model. Users can crack the engineered bacteria by turning on our built-in blue light after the engineered bacteria finishing their tasks, so as to eliminate biological pollution. In the figure below, light is designed as a switch regulated by two tasks which can control the lysis of cells by influencing the expression of lacI gene and then the expression of lysis gene.
We assume that the growth of engineered bacteria conforms to the single-population model of continuous growth. When t=0 , cell=1. Since each cell contains a lacI gene and a lysis gene, there is t=0,lacI=lysis=cell=1.We correlate the increase and decrease in lacI and lysis with the increase and decrease in the number of cells so as not to cause a situation in which the cells have completely died but the number of genes still keeps rising.
The follwing is the growing equation of the cells:
$$ \frac{d[cell]}{dt}=\frac{r×cell×(K-cell)}{K} $$
| Name | Description |
|---|---|
| cell | the number of cells |
| r | birth rate minus death rate, the net growth rate. Since r value of the bacteria was almost zero at the later stage of stable growth, we added a task to it and made it 0.01 after 30h. |
| K | load capacity |
die is the rate of cell lysis by pro-lysis.kd is parameter of inhibition
$$ die=kd*[pro-lysis]*[cell] $$
mRNA1 is the product of transcription and pro-lacI is the product of translation.The rate of transcription and translation equations of lysis is analogous. The rate of transcription and translation equations of lacI is as follows:
$$ \frac{d[mRNA1]}{dt}=ksc*[lacI] - kd1*[mRNA1] $$
$$ \frac{d[pro-lacI]}{dt}=ksl*[mRNA1] - kd2*[pro-lacI] $$
It is worth noting that since lacI gene expression is affected by light, an extra reaction ld was added to mRNA1. The inhibition effect of light intensity on lacI gene expression is as follows:
$$ ld=kld×[mRNA1]×[light] $$
| Name | Description |
|---|---|
| ld | the inhibition intensity of light on gene expression, the stronger the light, the greater the inhibition intensity of lacI expression, on the contrary, the smaller. No inhibition effect in dark |
| mRNA1 | the number of mRNA1 |
| light | the intensity of light |
The expression of lysis gene is inhibited by pro-lacI and the negative regulation form of Hill equation considering promoter leakage is used to describe the expression rate of lysis gene under the action of inhibiting factor pro-lacI:
$$ \frac{d[mRNA2]}{dt}= \frac{a-k}{1+([pro-lacI]/Xm)^m}+k $$
| Name | Description |
|---|---|
| mRNA2 | lysis transcript |
| pro-lacI | inhibitory factor content |
| a | the promoter's maximum activation capacity |
| k | the amount of promoter leakage |
| Xm | content of pro-lacI when the model change trend changes |
| m | Hill coefficient |
To sum up, in the dark environment, lacI can express repressor (pro-lacI) which will bind to the lactose operon downstream the promoter of lysis , making lysis cannot express normally and thus the engineering bacteria will not split and can work well.
However, under light conditions, the expression products of upstream light regulatory genes do not occur phosphorylation .The promoter of lacI will not start and lacI gene cannot express repressor proteins, so lysis gene is normally expressed and the engineering bacteria cleaved.
The time and duration of the illumination are controllable, so the cleavage of the engineered bacteria can be artificially controlled, achieving what we call the switch effect.
Simulation result
We assume that the engineered bacteria were exposed to light within 30h to 60h. During other periods the engineered bacteria would grow under dark conditions. The curve of each content is shown in the figure above. It can be seen that pro-lacI has a strong inhibitory effect on the expression of lysis gene under dark conditions. Although there is a small amount of expression, it can be neglected during the vigorous and stable periods of bacterial growth. However, under light conditions, lacI gene expression is strongly inhibited, mRNA1 and pro-lacI curves suddenly decrease but lysis expression volume increases and pro-lysis content increases. Due to the decrease of the net growth rate of the engineering bacteria, the lysis efficiency is very high, and the time and duration of such lysis are completely controllable.
Positive feedback amplifier system
Purpose and Description
This model simulates our positive feedback amplifying system PFAS and predicts the inhibitory effect of amplifying pathway on promoter leakage. LuxI1 in the figure below is a formaldehyde-induced gene. To simplify the equation, the formaldehyde content here is set as a constant. Since the leakage of promoter1 was relatively obvious, we applied Hill Equation of promoter induced by inducer and considered the expression of leakage. Promoter0 had a constant activation rate and it could promote luxR1. Pro-luxR, a protein expressed by luxR1, could specifically recognize N-AHL and bind to it to form LN, which was the factor that induced promoter2 activation. Promoter2 activates the expression of luxI2 and luxR2, generating more pro-luxI and pro-luxR. Thus a positive feedback amplification system is formed.
Promoter1 is regulated by formaldehyde. When there is a certain concentration of formaldehyde in the environment, Promoter1 starts to express luxI1 at a certain rate. Here, we adopt the positive regulation form of Hill equation. The expression rate of luxI1 is as follows:
$$ \frac{d[luxI1]}{dt}= \frac{(α1-ξ1)*[HCHO]^m}{[HCHO]^m+Xm1^m}+ξ1 $$
| Name | Description |
|---|---|
| luxI1 | Induced gene(activated) |
| HCHO | Inducing factor ---- formaldehyde |
| α1 | Maximum boot capacity of promoter |
| ξ1 | Promoter leakage |
| Xm1 | The value of the inducer when the change trend of the promoter leakage amount model changes |
| m | Hill coefficient. The larger the parameter m, the closer the regulation behavior of the regulator to the step switch behavior |
Under the catalysis of pro-luxI, AM and FAACP combine to generate N-AHL, and the reaction rate is
$$ \frac{d[N-AHL]}{dt}= \frac{[pro-luxI]*Vm}{(Ksa*Kmb/([FAACP]*[AM]))+(Kma/[FAACP])+(Kmb/[AM])+1} $$
| Name | Description |
|---|---|
| N-AHL | product |
| FAACP | substrate A -- fatty acyl-acyl carrier protein |
| AM | substrate B -- S-adenosyl methionine |
| Vm | Maximum reaction rate when substrate A and substrate B reach saturation |
| Kma | The Michaelis constant of A when the concentration of B reaches saturation |
| Kmb | The Michaelis constant of B when the concentration of A reaches saturation |
| Ksa | The dissociation constant of substrate A bound to an enzyme |
N-AHL can be specifically recognized by LuxR to generate LN, and their binding rate is:
$$ \frac{d[LN]}{dt}= Vmf*[pro-luxR]*[N-AHL] $$
LN is the compound of LuxR protein and N-AHL.
Promoter2 is regulated by LN, which promotes the gene luxI2 and luxR2 .The positive regulation form of Hill equation is also used to simulate the expression rates of luxI2 and luxR2
$$ \frac{d[luxI2]}{dt}= \frac{(α2-ξ2)*[LN]^m}{[LN]^m+Xm2^m}+ξ2 $$
$$ \frac{d[luxR2]}{dt}= \frac{(α3-ξ3)*[LN]^m}{[LN]^m+Xm3^m}+ξ3 $$
| Name | Description |
|---|---|
| luxI2/luxR2 | Induced gene(activated) |
| LN | Inducing factor |
| α2/α3 | Maximum boot capacity of promoter |
| ξ2/ξ3 | Promoter leakage |
| Xm2/Xm3 | The value of the inducer when the change trend of the promoter leakage amount model changes |
| m | Hill coefficient. The larger the parameter m, the closer the regulation behavior of the regulator to the step switch behavior |
Their expression products combine with the corresponding substrates to stimulate more LN. Thus, the positive feedback system is successfully constructed.
Simulation result
LuxI1 and luxR2 were activated by promoter1 and promoter2 respectively. To some extent, the expression of luxI1 and luxR2 reflecting the promoters' activation capabilities. As can be seen from the above figure, there was a slight lag in luxR2 expression compared with luxI1 at the beginning, but it exceeded luxI1 as it approached 5. We hope to increase this lag to reduce the leakage expression of promoter2. So we analyzed the sensitivity of the parameters, and the results are as follows:
Under the condition of without changing promoter1 parameters, we adjust parameter k of promoter2 which was shown matter the most in the above analysis, to strengthen promoter2's hysteresis in order to lag the expression of lbfdh started by it, so as to reduce the expression products of lbfdh to reduce the burden on the bacteria in their early growing period.
