1. E. coil Concentration determined model
1.1 Background

Optimizing the concentration of E. coli on the patch is crucial for the secretion of the hEGF protein and efficient skin cell repair. Insufficient E. coli can result in inadequate secretion of hEGF, leading to incomplete skin cell repair. On the other hand, an excessive amount of E. coli can lead to the overproduction of hEGF, causing unnecessary waste and increased costs. Moreover, a high concentration of hEGF may promote excessive collagen expression, which can potentially result in fibrosis and scarring during the in vitro treatment of skin wounds[1].

1.2 Purpose

The purpose of this model is to determine the minimum density of E. coli on the patch that effectively controls the concentration of hEGF protein, ensuring optimal conditions for complete skin cell repair.

1.3 Assumptions

The default for this experiment is that E. coli is in a stable phase without any growth, replication, or spreading behavior.

1.4 Method

The First-order kinetic equations are commonly used to describe gene expression[2]. So we use first-order kinetic equations to modeling of transcription, translation, degradation, and secretion processes to assess the protein production and secretion capacity of plasmid DNA in E. coli.

1.4.1 First-Order Kinetic Equations

Using the following equations to describe the transcription, translation, degradation, and secretion processes(Figure 1,Table 1).

Figure 1. The First-order kinetic equations of this model

Table 1. The parameters of equations

1.4.2 Data and Modeling

The parameters in the First-order kinetic equations are referenced[3], The following diagram(Figure 2)shows the Integrate ODEs and core code.

Figure 2. Code of First-order kinetic equations
1.5 Result

After modeling the above process, the Figure 3 shows the ability of plasmid DNA to produce hEGF protein secreted by 1 nmol/mL.

Figure 3. Curve of secreted protein content
1.5.1 E. coli concentration calculation

According to the research by S. Sivakesava et al[4], the common concentration of human epidermal growth factor (hEGF) used for therapeutic repair of skin wounds is 130 μg/mL. Because the molecular weight of hEGF is 6.22 kDa, corresponding 6220 g/mol.Subsequent calculation of the molar concentration needed to secrete the protein sp(hEGF) is as follows:Molar concentration (nmol/mL) = Mass concentration (μg/mL) / Molecular weight (g/mol),Using the given values, the calculation is:Molar concentration (nmol/mL) = 130 μg/mL / 6220 g/mol = 20.9 nmol/mL.

The protein production time was set at 180 min, during which 1 nmol/mL of DNA could produce 1350.96 nmol/mL of secreted protein sp.Therefore, it is necessary to calculate 20.9 / 1350.96 = 0.01547 nmol/ml DNA. According to Avogadro's constant: 1 mole = 6.02 x 10^23 molecules, so the DNA copy number is calculated as follows: 6.02 x 10^23 x 0.01547 x 10^-9 = 9.3132 x 10^12 copies/ml. The specified concentration of Escherichia coli is 9.3132 x 10^12 copies/ml.

1.5.2 Conclusion and Future Improvements.

Thus,the specified concentration of Escherichia coli on the patch should be used on patches is 9.3132 x 10^12 copies/ml.

The experiment did not consider the growth, replication, and spread of E. coli, which msy resulted in a lack of accuracy in representing the actual conditions. Subsequently, we plan to incorporate the following formula and introduce variables such as E. coli(DNA) growth rate (α0) at different time points. After considering the growth of E. coli, the production capacity of secreted proteins is shown in the figures below.

Because we cannot accurately measure the change in the growth rate of E. coli during patch production and use, more accurate experimental data are needed to improve this model, but E. coli in the stable phase can use this model to determine the concentration of E. coli on the patch.

2. Facial acne recognition assessment model
2.1 Background

To effectively manage costs and ensure precision in acne treatment, it is essential to consider the impact of high concentrations of hEGF, which can stimulate increased collagen expression, potentially leading to fibrosis and scar formation.

2.2 Purpose

Therefore, a stratified approach to treatment and repair should be implemented for acne-affected areas, utilizing patches with varying concentrations of E. coli based on the severity of the condition. To facilitate this graded approach, a software program is employed to assess the degree of acne severity on the human face, categorizing it into different grades such as Mild, Moderate, and Severe. These grades are then associated with specific categories of treatment and repair patches, each containing varying concentrations of E. coli. Additionally, the design of the patch surface may differ to correspond with the severity category, providing a comprehensive and tailored approach to acne management.

2.3 Assumptions

In our analysis, we focused exclusively on four variables: color, texture, size, and characteristics, utilizing them as criteria to assess the severity of acne. Based on our initial hypothesis, we categorized the acne scores into three distinct levels.

2.4 Method and result
2.4.1 Identification of Facial Acne Sites

We employed web services (https://ai.meitu.com/algorithm/faceTechnology/skinanlysis)[5] to identify the locations of acne on the face. These resources provided robust method and served as a foundation for our modeling ideas. We adapted and enhanced these procedures to introduce our own evaluation methods. The following photos are from a classmate's relatives. They have already signed an informed consent form, explicitly granting us permission to use their photographs.

Figure 4. Picture after identifying the acne area

Using the existing web services, we are able to identify and precisely locate each acne area based on characteristics such as color and texture. These areas are marked with green boxes(Figure 4).

2.4.2 Evaluation and Marking of Acne Areas

Subsequently, a Python script is employed to grade the severity of acne within each marked area, categorizing them as Mild, Moderate, or Severe(Figure 5). Detailed evaluation criteria will be outlined later. Following our assessment methodology, each acne area undergoes evaluation and is marked with red letters (as depicted in the image). Based on the assessment outcomes for each area, we will select a biological patch with a specified concentration of E. coli for targeted treatment.

Figure 5. Picture of the acne area after grading

Table 2. Characteristics and calculation methods used for grading acne areas[6]

Each segment is meticulously assessed, and its score is subsequently multiplied by the respective section's weight(Color:0.6,Texture:0.2,Shape:0.1,Size:0.1) to yield the ultimate score [7]. A score falling below 60 is classified as 'Mild,' while a score ranging between 60 and 80 is categorized as 'Moderate.' Any score surpassing 80 is denoted as 'Severe.' This classification system adheres to stringent academic rigor.

2.5 Future work

Our original intention was to transform this model into a web-based application, thereby enabling patients to autonomously upload images for acne diagnosis. Nonetheless, owing to the intricate nature of server setup and web development, we have yet to conclude this task. In our forthcoming endeavors, we shall conclude web development, bolster each facet of the application, and ascertain that all users can seamlessly, effectively, and precisely undertake their acne diagnosis, facilitating their therapeutic processes. Furthermore, in our future work, we intend to establish a more intricate grading system for assessing acne severity and further optimize the program to guarantee that patients receive precise gradings, thereby furnishing a foundation for their treatment.

3. Modeling of Silver Ion Sterilization and E. coli Degradation of Fatty Acids
3.1 Background

Eliminate P. acnes by using silver ions while also utilizing modified Escherichia coli to absorb and break down the fatty acids produced by P. acnes. During the treatment process, silver ions will come into contact with both the Propionibacterium and biological patches, but due to the barrier of bacterial cellulose, the silver ions concentration on the E. coli side will be lower than that on the Propionibacterium side.

3.2 Purpose

To model and determine the initial concentration of E. coli that produces FadL and FadD proteins, as well as the initial concentration of silver nitrate that kills E. coli and P. acnes, we make sure that the independent variables are the concentrations of fatty acids and P. acnes, and that the patch time t remains constant.

3.3 Assumptions

When studying the degradation of fatty acids by E. coli, we assume that the absorption of fatty acids is proportional to the concentration of E. coli. That is because it is difficult to determine the rate coefficient of gene expression in E. coli.

3.4 Method
3.4.1 The growth of E. coli and P. acnes

The growth of E. coli and P. acnes follows the rule of the logistic function. In this way, we use the logistic model and the inhibition coefficient of silver ions to predict the changes in E. coli and P. acnes concentration over time.

It is clear that N refers to the concentration of either E. coli or P. acnes[8], while t represents time. The rate of growth is indicated by the symbol r, and K denotes the maximum capacity that certain bacteria can reach. Additionally, α is a coefficient that represents the inhibitory effect of silver ions, and Ag refers to the concentration of silver ions[9,10].

3.4.2 The process of E. coli absorbing fatty acids

Based on the results of our wet lab experiments(Figure 6), we can build a linear model for the relationship between the number of E. coli and the concentration of fatty acids.

Figure 6. FadL+FadD fatty acid absorption capacity
3.4.3. The diffusion of silver nitrate solution and fatty acids

represents the concentration on the higher side, t represents time, D is the diffusion coefficient, and B represents the concentration on the lower side.

3.5 Result

After modelling, we find that When Ag+ concentration is 2.3 mmol/L, E. coli remains after 4 hours, but if Ag+ concentration is 2.4 mmol/L, P. acnes and E. coli can be all be killed.And we screened the suitable initial value of E. coli concentration, silver ion concentration and time taken for treatment(Table 3).

Table 3. Value of E. coli concentration, silver ion concentration and time

Figure 7. The concentration of bacteria, Ag+ and fatty acids on both sides

After 4 hours of treatment, the concentration of P. acnes and E. coli can be both down to 0 mmol/L. The fatty acid concentration on the side of P. acnes can be down to 8.1e-4 mmol/L, and the fatty acid concentration on the side of E. coli can be down to 2.3e-4 mmol/L(Figure 7).

3.6 Future Improvement

There can be further experiments on the process of calculating the coefficient of the E. coli secreting process and then improving the linear model.


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