The system is shown in Fig. Oxygen spreads to the cell membrane, where it is either consumed by terminal oxidase or spreads further into the cell interior.
Fig. 1 Schematic Diagram of Cell Structure Model of Escherichia coli
Several processes are able to remove oxygen from E. coli. The oxygen consumed by the inactivation of the \(FNR\) is not released upon its reactivation. Furthermore, the soluble oxidase or oxygenase may contribute to the cytoplasmic oxygen consumption, but this may be minimal.
Then, the only spatial coordinate that we need to consider is the distance \(r\) from the center of the cell.
The derivation process is as follows:
Consider Fick's first Law:
\(\Large J = -D \frac{\partial C}{\partial X}\) \((1)\)
Formula \(J\) is called a diffusion flux. The common unit is \({mol}/{(cm^2\cdot s)}\), \(\frac{\partial C}{\partial X}\) is concentration gradients.
Fig. 2 Schematic Diagram of Fick Diffusion Law
As shown in Fig, Volume elements were taken in the diffusion direction \(A\Delta x\), \(J_x\) and \(J_{x+\Delta x}\) the diffusion flux of the inflow and outflow volume elements respectively. In the time of \(\Delta t\) the accumulation of diffusing material in the volume element is:
\(\large \Delta m=(J_xA-J_{x+\Delta x}A)\Delta t\)
Then
\(\Large \frac{\Delta m}{A\Delta x\Delta t}=\frac{J_x-J_{x+\Delta x}}{\Delta x}\)
When\(\Delta x、\Delta t > 0\), then\(\frac{\partial C}{\partial t}=-\frac{\partial J}{\partial x}\)
Put the (1) into the top formula:
\(\Large \frac{\partial C}{\partial t}=\frac{\partial}{\partial x}(D\frac{\partial C}{\partial x})\)
Assuming that the diffusion coefficient is independent of time, the above equation can be written as:
\(\Large \frac{\partial C}{\partial t}=D\frac{\partial^2C}{\partial x^2}\) \((2)\)
In the spherical coordinate system, by the coordinate transformation:
\( \large \begin{aligned} x & = rsin{\theta}cos{\phi} \\ y & = rsin{\theta}sin{\phi} \\ z & = rcos{\theta} \end{aligned}\)
The each side of volumetric elements are \(dr\), \(rd\theta\), \(rsin{\theta}d\phi\),
Then:
\(\Large \frac{\partial C}{\partial t}=\frac{D}{R^2}\frac{\partial}{\partial r}(r^2\frac{\partial C}{\partial r})\)
Equals to:
\(\Large \frac{\partial C}{\partial t}=D\frac{\partial^2C}{\partial r^2}+\frac{2D}{r}\frac{\partial C}{\partial r}\)
The concentration \(C\) term in the above equation can be rewritten as the concentration difference at radius \(r\) and radius \(0\): \(\Delta c\left(r\right)=c(r)-c_0\)
The temporal characteristic scale of the diffusion is determined by \(\tau\approx\frac{l^2}{D}\), only about \(0.5ms\), We can assume that the oxygen diffusion is in the steady-state, which means
\(\Large \frac{\partial C}{\partial t}(t,r)=0\)
Considering the oxygen consumption rate of E. coli itself, it is concluded that:
\(\Large 0=D\frac{\partial^2\Delta c}{\partial r^2}(r)+\frac{2D}{r}\frac{\partial\Delta c}{\partial r}(r)-\nu(r)\)
In the above formula
\(\Delta c(r)=c(r)-c(0)\) is the difference between the concentration of \(r\) and the concentration of \(r=0\)
According to our experimental hypothesis, the first boundary condition is:
\(\large \Delta c(0)=0\)
Due to the spherical symmetry, no oxygen diffusion occurs over the centre of the cell and we get the second boundary condition:
\(\Large \frac{\partial\Delta c}{\partial r}(t,0)=0\)
The total oxygen consumption of the cell is given by \(J_{tot}(mol/s)\).
By \(J_{cyt}(mol/s)\) and \(J_{mem}(mol/s)\),we denote the oxygen consumption in the cytoplasm and at the membrane, respectively. The parameter \(\xi\) determines the fraction of oxygen consumed in the membrane: \(J_{cyt}=(1-\xi)J_{tot}\) and \(J_{mem}=\xi J_{tot}\).
Figure 3 shows the calculated profile of the steady-state concentration difference \(\delta c\) over \(r\)for different values of \(\xi\) and the parameter values shown in Table 1. The model does not account for the unequal equilibrium partition of oxygen between a lipid phase and an aqueous solution. Concentrations of oxygen in the membrane are given as the according equilibrium concentration in an aqueous solution. The diffusion coefficient in the membrane is corrected accordingly (see comment in Table 1).
The largest concentration difference occurs if \(\xi\) is small that is if most of the oxygen is consumed in the cytoplasm and not at the membrane. However, it is a reasonable hypothesis that most of the oxygen consumption is caused by terminal oxidases on the cell membrane, and thus \(\xi\) is expected to be near 1; henceforth, a value for \(\xi = 0.75\) is assumed. The prediction of this model is that an overall concentration difference of around \(0.02\mu M\) is realistic where about a quarter is an intracellular and the rest an extracellular difference.
The parameters in Table 1 are subject to some uncertainties. In particular, the diffusion constants in cytoplasm and membrane are critical parameters whose values are experimentally assessed in artificial situations. Also,the model neglects further possible diffusion barriers as the periplasm and the outer membrane. So, it is possible that the diffusion coefficients are overestimated and that the width of the membrane might need to be increased to include more than just the plasma membrane. The value of \(J_{tot}\) depends on the culture conditions and is growth rate dependent.
As discussed above, any oxygen gradients that are formed will be dependent on the values of diffusion coefficients, geometric parameters and the total oxygen uptake rate. For a set of nominal parameters (Table 2.3), a concentration difference of \(0.02\mu M\) is obtained. For a parameter set with impaired diffusion, a value of \(0.1\mu M\) is predicted.
The term oxygen consumption rate \(v\) in the equation will be determined by the kinetic equation of laccase-reducing oxygen.
This function describes the spatiotemporal behavior between the oxygen concentration \(c(M)\) and the diffusion coefficient \(D(m^2/s)\) and the oxygen consumption \(v(t,r)(M/s)\).
Figure. 3 Concentration difference \(\Delta c\) over \(r\)
Table. 1 Nominal parameters of the reaction-diffusion mode
The above equations can be solved through the toolbox of partial differential equations of MATLAB.
Fig. 4 Simulation Results in 2D Coordinate Area of MATLAB PDE Toolbox
Fig. 5 Simulation Results in 3D Coordinates of MATLAB PDE Toolbox
We also concerned Agent-based modelling, which is a relatively new way to analyse biological systems. It attempts to encapsulate the fact that much of biology is driven by local interactions and its immediate geometry and it is difficult to model this very precisely when using traditional approaches such as differential equations or stochastic processes—a cell is not a bag of chemicals moving around randomly, there is complex structure involved in most processes. These spatial constraints can be captured in great detail using agent-based modelling. Therefore, a realistic geometric space was created to represent a typical E. coil cell, within which, features such as membranes, cytoplasm were located. Into this structure, a population of the key molecules, each represented as autonomous agents,was introduced.
Molecules of oxygen were positioned outside the cell, where they are generated by the simulation to represent the arrival of oxygen in the experimental set-up. Each molecular agent is then programmed to behave as it would in reality. The agents will interact with other appropriate agents under suitable circumstances. The agents move in various ways, some respecting boundaries such as membrane surfaces, others constrained by the biological information available. These behaviors are coded up in the FLAME language. The FLAME system automatically generates a simulation programme in the computer language C which can be run on a supercomputer—or a desktop running any operating system. To begin a simulation, it is necessary to define a starting position for all the agents that describes where they are located in the model and what state they are in—for example, whether they are free or bound to another agent. A convenient starting point is the anaerobic steady state (0% AU) and the simulation begins with the supply of external oxygen molecules. The simulation outputs the detailed locations, state and other information about every agent at every time step.
Figure. 6 Initial and final states of the model with no and sufficient oxygen. (A) Initial state of the model with no oxygen supply to the cells. (B) The final state of the model that provides sufficient oxygen to the cell.
It can be found that the oxygen distribution obtained from the agent-based modeling basically matches the solution of our model, which also verifies the accuracy of our model from the side.
On the membrane, we assume that the main biological activities affecting the oxygen concentration are: the consumption of \(Cyo\), \(Cyd\) terminal oxidase.
\(\Large \frac{d[O_2]_m}{dt}=-v_{Cyo}-v_{Cyd}\)
Take into account the process of terminal oxidase \(Cyo\), \(Cyd\) consuming oxygen and reducing it to water.
\(\large QH_2+O_2\xrightarrow{Cyo/Cyd} H_2O+Q\)
\(\Large v_{Cyo}=\frac{d[Cyo]}{dt}={v_{Cyo}^{max}}\cdot\frac{[O_2]}{K_{m,Cyo,O_2}+[O_2]}\cdot\frac{[QH_2]}{K_{m,Cyo,QH_2}+[QH_2]}\)
\(\Large v_{Cyd}=\frac{d[Cyd]}{dt}={v_{Cyd}^{max}}\cdot\frac{[O_2]}{K_{m,Cyd,O_2}+[O_2]}\cdot\frac{[QH_2]}{K_{m,Cyd,QH_2}+[QH_2]}\)
Among them, \(Cyo\), \(Cyd\) was controlled by regulatory factor \(FNR\) and \(ArcA/B\) , Regulatory effects are manifested on parameters \(v_{Cyo}^{max}\), \(v_{Cyd}^{max}\) (Effects of transcription factors on gene expression use \(v^{max}\) to express)
\(\large v^{max}=v^{max'}[1+\sum\limits_{i}TF_i]\cdot\prod\limits_{i}(1-TF_j)\)
For the two terminal oxidases:
\(\large {v_{Cyo}^{max}}={v_{Cyo}^{max'}}[1+TF_{Fnr}+TF_{ArcA,Cyo}]\cdot(1-TF_{Fnr})\cdot(1-TF_{ArcA,Cyo})\)
\(\large {v_{Cyd}^{max}}={v_{Cyd}^{max'}}[1+TF_{Fnr}+TF_{ArcA,Cyd}]\cdot(1-TF_{Fnr})\cdot(1-TF_{ArcA,Cyd})\)
The parameters for the 2 regulators in \(TF_i\) the activity of both of the two.
a. When oxygen is unrestricted, the transcription factors \(FNR\) show its function
Oxygen refrain \(FNR\),and \(FNR\) refrain \(Cyo\)'s \(cyoABCD\) gene's synthesis \(Cyd\)'s \(cydAB\), will \(FNR\) the positive activation effect for both genes was defined as the activity of \(FNR\): \(TF_{Fnr}\)
According to the Hill equation, the following:
\(\Large TF_{Fnr}=\frac{[O_2]^n}{[O_2]^n+K_{Fnr}^n}\), \(([O_2] \in (\varepsilon,+\infty))\)
b. When oxygen is limited, the transcription factor \(ArcA/B\) will play a role.
Oxygen-containing quinone pairs autophosphorylation plays an inhibitory effect to \(ArcB\), \(ArcB\) autophosphorylation can be induced \(ArcA\) in trans phosphorylation, after the trans-phosphorylation of the post \(ArcA\) will limit the \(Cyo\) gene's \(cyoABCD\), and improve \(Cyd\) gene's \(cydAB\).
According to the Hill equation, the following:
\(\Large TF_{ArcA,Cyo}=\frac{[Q]^n}{[Q]^n+K_{ArcA}^n}\)
\(\Large TF_{ArcA,Cyd}=\frac{K_{ArcA}^n}{[Q]^n+K_{ArcA}^n}\)
In the above equation, concentration of oxygen containing quinone \([Q]\), Hydroquinone concentration \([QH_2]\) all effects during oxygen consumption, Through consulting the literature, it is associated with dehydrogenase \(Nuo\) and \(Ndh\).
\(\Large \frac{d[QH_2]}{dt}=v_{Nuo}+v_{Ndh}+v_{Syn,QH_2}+v_{SDH}-v_{Cyo}-v_{Cyd}-μ[QH_2]-v_{CueO}\)
\(\Large \frac{d[Q]}{dt}=v_{Cyo}+v_{Cyd}-v_{Nuo}-v_{Ndh}-v_{SDH}-μ[Q]\)
(\(v_{SDH}\) refers to the rate of succinate production, the purpose of this model was to construct a low-oxygen environment, whereas E. coli had a very low succinate production under anaerobic conditions. So, hypothesis \(v_{SDH}\approx0\))
Dehydrogenase \(v_{Nuo}\) and \(v_{Ndh}\)'s adduction effect to \(NADH\) and \(FADH_2\) is as follow:
\(\large Q+NADH/FADH_2\xrightarrow{Nuo/Ndh} NAD^+/FAD^++[QH_2]\)
\(\Large v_{Nuo}=\frac{d[Nuo]}{dt}=v_{Nuo}^{max'}\cdot\frac{[Q]}{K_{m,Nuo,Q}+[Q]}\cdot\frac{[NADH]}{K_{m,Nuo,NADH}+[NADH]}\)
\(\Large v_{Ndh}=\frac{d[Ndh]}{dt}=v_{Ndh}^{max'}\cdot\frac{[Q]}{K_{m,Ndh,Q}+[Q]}\cdot\frac{[NADH]}{K_{m,Ndh,NADH}+[NADH]}\)
\(\Large \frac{d[NADH]}{dt}=v_{Emp}+v{PDH}+v{\alpha KGPH}+v_{MDH}-v_{LDH}-v_{ADH}-v_{Nuo}-v_{Ndh}-μ[NADH]\)
To achieve a more accurate solution of the above system, we learn from the literature [1]. Consider transcription factors such as \(ArcA/B\) and \(FNR\), respiratory chain reaction and fermentation pathways, as well as catabolite regulation, we simulated the metabolic changes of transcription factor activity and intracellular metabolite concentrations with DO levels in E. coli by predicting the metabolic dynamics at different dissolved oxygen levels. The simulation results show the product concentrations at the time point at which \(10g/l\) of glucose was depleted in a batch culture.
Figure. 7 Curves of the activity of the two transcription factors with DO values
Figure. 8 Curve of oxygenated quinone concentration change with DO value
Figure. 9 Change curve of hydroquinone concentration with DO value
Figure. 10 Change curve of oxygen consumption of \(Cyo\) and \(Cyd\) rate with DO value
Therefore, we assume that the consumption of oxygen by the terminal oxidase is fixed in the case of DO determination.
Combined with the proxy-based modeling mentioned earlier, it is known that the main oxygen distribution within E. coli is concentrated around the cell wall. Through finding the literature, we found that the oxygen association sum constant of leghemoglobin under physiological pH conditions is approx \(120 \mu M^{-1}S^{-1}\), The equilibrium constant is approximately \(5.6 S^{-1}\). Therefore, it can be assumed that the oxygen consumption of intracellular bean hemoglobin at this time is much greater than the oxygen consumption of E. coli itself. Therefore, we hypothesized that the intracellular biological activities affecting oxygen concentrations mainly include:
Laccase consumption, mehoglobin consumption.
\(\Large \frac{d[O_2]}{dt}=-v_{CueO}-v_{Lb}\)
A similar catechol can be oxidized by laccase
\(\large [QH_2]+[O_2]\xrightarrow{CueO}[H_2O]+[QH]+[Q]\)
\(\Large v_{CueO} = \frac{d[CueO]}{dt} = \frac{v_{CueO}^{max}\cdot[O_2]}{K_{m,CueO,O_2}+[O_2]} \cdot \frac{[QH_2]}{K_{m,CueO,QH_2}+[QH_2]}\)
Bean Haemoglobin reduces the oxygen concentration by binding to oxygen and transporting it, and since we do not know the specific mechanism, consider the prediction with the BP neural network model.
\(\Large v_{Lb}=\frac{d[Lb]}{dt}=k_2[O_2]\)
Among these, the initial concentration of leghemoglobin \([Lb]_0\) was controlled by the promoter strength, \([Lb]_0=k_3[Lb]\), \(k_3\) is directly proportional to the promoter intensity
The parameters \(k_2\) in the above equation are obtained from the BP neural network model.
Since the experiments were performed with the addition of a concentration \(0.1mmol/L\) IPTGof IPTG inducer. Judging from the above assumptions, \([Lb]_0=k_3[Lb]\). It is assumed that the inducer concentration determines the promoter intensity. That is, the concentration of the IPTG inducer that we added determines \(k_3\). Then we can think that the data is obtained is in the case of fixed values \(k_3\). We assume \(k_3\), \([Lb]_0\) are fixed value, so there are:
\(\Large v_{Lb}=\frac{d[Lb]}{dt}=k_2[O_2]\)
\(\Large \frac{d[O_2]}{dt}=-v_{Lb}-v_{CueO}\)
We want to get the values for the parameters \(k_2\),that is the relationship between \(v_Lb\) and \(O_2\) We experimentally measured the fluorescence intensity of the different plasmids. During the previous model building process, we assumed that the intracellular oxygen consumption was only affected by laccase and leghemoglobin, ignoring the consumption of oxygen by E. coli during growth. According to the experimental results we measured, E. coli proliferation mainly consumed oxygen in the early stage, and the later laccase and leghemoglobin began to play a role, so what we need is the later data measured in the modeling process.
a. The relationship between the fluorescence intensity and \([DO]\):
According to the fluorescence intensity measured in our experiment, the following equation:
\(\Large \frac{d[AU]_{CueO+grow}}{dt}-\frac{d[AU]_{grow}}{dt}=v_{CueO}\)
But, \(\frac{d[AU]}{dt}\) is the curve-tangent slope of the time-dependent curve of the fluorescence intensity measured by our experiment. Therefore, we can obtain a series of data based on the experimental data \((v_{CueO},AU)\). According to our model, we made the graphs \(v_{CueO}-[DO]\). Combining the two, we can get a range of data \(([DO],AU)\). By using the BP neural network method, we can predict the relationship between the two.
b. The relationship between \(v_{Lb}\) and \([DO]\)
According to the fluorescence intensity measured in our experiments:
\(\Large v_{Lb}=\frac{d[AU]_{CueO+grow+Lb}}{dt}-\frac{d[AU]_{CueO+grow}}{dt}\)
\(\Large v_{Lb}=\frac{d[AU]_{CueO+grow+Lb}}{dt}-\frac{d[AU]_{CueO}}{dt}-\frac{d[AU]_{grow}}{dt}\)
\(\Large v_{Lb}=\frac{d[AU]_{grow+Lb}}{dt}-\frac{d[AU]_{grow}}{dt}\)
Analyzing as above, we can get a series of data of \((v_{Lb},AU)\). According to the data \(([DO],AU)\) that we have obtained previously, We can get a series of data \((v_{Lb},[DO])\). By using the BP neural network method, we can predict the relationship between the two.
Because there are various errors in the experimental and modeling process, the data has positive and actual errors.
We obtained by calculating: \(k_2=0.647s^{-1}\)
We simulated the relationship curve of the rate of oxygen consumption by laccase with DO values on Matlab by combining transcription factors such as \(ArcA/B\) and \(FNR\), respiratory chain reaction and fermentation pathways, and catabolite regulation.
Figure. 11 Curve of laccase oxygen consumption rate to change with DO value
Experimental parameters:
Table. 2 Comprehensive list of the kinetic parameters.
Table. 3 Total concentrations
* The parameter values were tuned in the present model.
The values were converted into [\({μmol}/{gDCW}\)] using cell density 564 [\({gDCW}/L\) cell volume] (Reference[19]).
The values were converted into [\({μmol}/{gDCW}\)], where the cell concentration was assumed to be a certain value (Reference[19]).
Generally speaking, BP neural network is a "universal model + error correction function". Each time, the training results and the expected results are analyzed, and then the weight and threshold are modified, and the model that can output and the expected results can be obtained step by step.
Here, the input layer is the input side of the information, and there may be many in the actual network. The hidden layer, which is the processing end of the information, is used to simulate a computational process. Output layer: the output side of the information, which is what we want to result from. Based on our experiments, the input layer will currently be composed of the dissolved oxygen concentration, the promoter strength, and the reducing substrate concentration, and the output layer is used to measure the low oxygen environment.
We hope to train the model to reach several key parameters that determine the E. coli oxygen consumption process to predict the low oxygen environment inside it.
Training function we use the Levenberg-Marquardt (or gradient descent algorithm), and the activation function selects the Sigmoid.
Since our team initially chose to use the neural network model for parameter prediction, we encountered many problems in how to apply the BP neural network and the neural network code writing. At the same time, the division of data sets, data import, and parameter adjustment consume a lot of time. In order to facilitate the future iGEM teams to get started more simple and convenient and use BP neural network to complete some modeling work, we specially developed a BP neural network prediction GUI (graphical user interface) with Matlab's own guide function based on MATLAB compilation environment. Through this GUI, we only need to import the data needed to be trained and the data needed to be predicted, and we can export the prediction results of the BP neural network through simple parameter debugging. Since the guide function of the old version of Matlab will be replaced by the app designer function, in order to increase the universality of the software developed by our team, our team chose to develop the BP neural network prediction GUI development with the app designer function again. We packaged the graphical user interface we developed into an APP with a simple installation to the Matlab. In addition, our team considering we developed software can only run in the condition of Matlab, in order to be able to run in no Matlab environment, we also uploaded to be able to run without Matlab environment MCR, at the same time install MCR and our team to develop the software, can be without Matlab environment can also work normally. We have significantly increased the convenience of the software by installing it into a standalone desktop APP.
The software interface layout of the Guide version is as follows:
After the neural network training:
The software interface layout of the App designer version is as follows:
The neural network training results after using different algorithms are as follows:
Click here to view
the detailed code!
Due to the impact of the epidemic, the experimental progress of our project has been greatly affected. In fact, the amount of data required for neural network prediction is relatively large, and our team is difficult to obtain enough data under the influence of the epidemic. According to the data measured in the experiment, we found that the data samples are small and linear. We found that these meet the prerequisites for the application of the grey prediction model, so we considered using the Gray Forecast Model to process our experimental data.
Grey Forecast Model is a forecasting method that establishes a mathematical model and makes predictions through a small amount of incomplete information.
Grey system theory is a theory to study and solve grey system analysis, modeling, prediction, decision-making and control Grey prediction is the prediction of grey system. At present, some commonly used prediction methods (such as regression analysis) require large samples. If the samples are small, they often cause large errors, making the prediction target invalid. Grey prediction model needs less modeling information, is easy to operate, and has high modeling accuracy. It is widely used in various prediction fields, and is an effective tool to deal with small sample prediction problems. Especially, it has a unique effect on the analysis and modeling of systems with short time series, few statistical data and incomplete information, so it has been widely used.
1. Definition of grey system:
Grey system refers to a system containing both known and unknown information.
2. Definition of Grey Forecast Model:
A model for forecasting the grey system.
Grey Model (GM model for short) is generally expressed as GM (n, x) model, which means that x variables are modeled by n-order differential equations.
3. Purpose of Grey Forecast Model:
The discrete data scattered on the time axis is regarded as a group of continuously changing sequences, and the unknown factors in the gray system are weakened and the influence of known factors is strengthened by means of accumulation and subtraction. Finally, a continuous differential equation with time as a variable is constructed, and the parameters in the equation are determined by mathematical methods to achieve the purpose of prediction.
4. Characteristics of Grey Forecast Model:
There is no need for a large number of data samples, the short-term prediction effect is good, and the calculation process is simple.
5. Deficiency of Grey Forecast Model:
The prediction effect of nonlinear data samples is poor.
The Grey Forecast Model is a developed and relatively perfect model. Here we do not introduce the mathematical principle of the grey prediction model, but mainly introduce that we use the grey prediction model to fit the parameter curve in Model II and the growth curve of Escherichia coli.
The change curve of measured unit fluorescence intensity with time is shown in the following figure:
Figure. 12
Figure. 13 Fitting Results of Derivative Value of Fluorescence Intensity Change Curve of Plasmid with Laccase
Figure. 14 Fitting results of derivative of fluorescence intensity change curve of empty plasmid with nirB
Similarly, using the Grey Forecast Model, we can fit the growth curve of Escherichia coli, so that we can predict the OD value of Escherichia coli at any time for our calculation.
The growth curve of Escherichia coli measured by experiment is shown in the following figure:
Figure. 15
Figure. 16 Fitting results of growth curve of Escherichia coli with laccase
Figure. 17 Fitting results of growth curve of Escherichia coli added with nirB
We uploaded the code for implementing the grey prediction model on Matlab to Gitlab, and interested teams can download the reference.( Click here!)
At the beginning of the model building, we did not consider the consumption of oxygen by physiological activities such as the metabolism of E. coli itself, but after considering only the transmembrane diffusion of oxygen and the oxygen consumption of internal function modules, we found that the model did not fit very well. By looking up the literature, we found that terminal oxidases on E. coli membranes also have effects on oxygen consumption, and therefore, we reconstructed model II. In order to simplify the complexity of the model, we consulted the relevant literature, calculated and simplified the existing model in the literature, we ignored some processes that the actual oxygen consumption is not obvious, and finally realized the construction of model II. We made the prediction of intracellular low oxygen by combining oxygen transmembrane diffusion and E. coli itself oxygen consumption, and compared it with our detection modules, and successfully built and predicted the low oxygen environment.
The calculation from model one revealed that the oxygen on the membrane surface hardly changes significantly.
Due to the impact of the epidemic this year, our school has experienced a month of closed management since May, during which we were unable to go to the laboratory for experiments. Due to the epidemic, the school asked us to return home in June in advance, which also led to our inability to carry out experiments in the summer vacation. After meeting the requirements of the school to return to school, we immediately returned to school to carry out experiments. The members of our team were everywhere, and the epidemic situation varied in different places. Our earliest students also came back on August 12. For three months, we were unable to conduct the experiment because of the outbreak. Therefore, the development of our experimental part was not very satisfactory, and finally there were very few data that could model the part to perform the operations. Therefore, we can only measure whether the low oxygen system we built met the conditions by indirect judgment. We judged whether the low-oxygen environment construction was successful by attaching the fluorescent protein, and by observing the intensity of the fluorescent protein. The results for the final fluorescent protein also indicate a successful implementation of intracellular hypoxia.
The fluorescence intensity shows that the functions of laccase and leghemoglobin have been realized. We have observed a significant increase in fluorescence intensity. Compared with the empty plasmid introduced only nirB, the fluorescence intensity has increased by up to 30000 AU, indicating that our function module works normally. Because the characterization of leghemoglobin in Escherichia coli cells is relatively difficult, it is difficult to measure the relevant data of leghemoglobin. We consider further experiments to measure a large number of data to fit the parameters of the leghemoglobin we need. However, this step takes a lot of time, which is difficult to achieve in our current work. The experimental data can show that the leghemoglobin works normally. We try to calculate the relevant parameters of leghemoglobin through further measurement experiments in the future.
We separately measured the curve of fluorescence intensity versus time when laccase worked.
Figure. 18 Fluorescence intensity versus time after laccase addition
The working curve of laccase in the case of laccase working alone, simulated by computer, is
Figure. 19 Computer simulated oxygen consumption rate of laccase
We measured the curve of fluorescence intensity with time in the case of laccase and leghemoglobin co-culture
The working curve in the case of co-culture of laccase and leghemoglobin simulated by computer is
The curve of fluorescence intensity of leghemoglobin with time is
The working curve of leghemoglobin simulated by computer is
It can be found that the results predicted by the model are roughly consistent with the experimental measurement results.
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