Modeling work
2023 SDU-CHINA
Introduction
01 EsaI/R-AHL Quorum Sensing (QS) system
02 SWITCH: Grow or Produce?
03 Calculate The Optimal Working Hours
04 Correlation analysis of microplastics
References
Firstly, we examined the intricate interaction mechanism between the EsaR protein and AHL (3-O-C 6-HSL). For enhanced precision control, we introduced 19 point mutations in EsaR and predicted the subsequent three-dimensional structures using the AlphaFold2 algorithm. Concurrently, a comprehensive quantitative analysis of binding affinity was conducted using the AutoDock software.
Secondly, we described the mechanism of the SWITCH dual promoter system and simulated the temporal changes of gene expression intensity using this system.
Thirdly, by segmenting the lifecycle of E. coli into distinctive phases, we probed into the dynamic and static costs associated with each stage, along with the dynamic revenue during the production process. A pivotal aim of this segment was to ascertain the optimal stopping point for achieving the maximum return on investment.
Lastly, we conducted a Pearson correlation analysis based on microplastics data sourced from soil samples across diverse regions in China. This was done to better comprehend the relationship between microplastic pollution and other social indicators.
In the EsaI/R-AHL Quorum Sensing (QS) system, the interaction between EsaR protein and AHL (3-O-C 6-HSL) directly influences the sensitivity of the promoter to AHL, thereby determining the response timing of the QS switch.
To achieve precise control over the QS system, we introduced 19 different point mutations into EsaR. Using the AlphaFold2 algorithm [1, 2], we predicted the three-dimensional structures of these mutated variants.
Furthermore, we employed AutoDock software to quantitatively analyze their binding affinity with AHL [3-8]. This research will provide crucial data for the subsequent optimization of the QS switch, allowing for more accurate temporal control of gene expression.
The table below presents the results of our molecular dynamics simulations conducted on 19 EsaR protein mutants. The data clearly reveal that among all the studied EsaR mutants, EsaR/125V/170V has the strongest binding affinity with AHL, while the 34W/67K mutant exhibits the weakest binding ability.
Based on these variants with different binding affinities, we can select suitable mutants to meet our sensitivity requirements for the QS system.
| EsaR or Mutant | The binding energy with AHL (kcal/mol) |
|---|---|
| EsaR | -7.5 |
| 21D | -7.3 |
| 34W | -5.3 |
| 46T | -7.3 |
| 50A | -7.0 |
| 54G | -7.0 |
| 55T | -7.0 |
| 58M | -6.0 |
| 67K | -5.3 |
| 69Y | -5.5 |
| 82S | -6.9 |
| 98A | -7.1 |
| 101V | -6.9 |
| 106T | -7.2 |
| 125V | -7.5 |
| 170V | -7.5 |
| 177R | -7.2 |
| 185K | -7.1 |
| 218R | -7.2 |
| 242F | -7.4 |
We are employing a SWITCH dual promoter system to regulate the metabolic state in bacteria. Herein, we use differential equations to model the transitional dynamics of this switch. Throughout the simulation, it’s presumed that AHL is generated at a foundational level at a consistent rate, while the concentration of EsaR2 is unchanging. Additionally, the initial state of the SWITCH is established with all PesaR/S being bound to EsaR2, resulting in a zero exposed concentration of PesaR/S.
In our switch system, the growth metabolism genes are represented by PesaR/S, and the production genes are represented by EsaR2 - PesaS. Hence, we primarily explore the variations over time of these two molecules through a system of differential equations, representing the operating principle of our switch.
The parameters and sources to use in our model
This graph illustrates the quantitative changes in two molecules over time, representing the expression sequence of the genes connected to the two promoters.
The results demonstrate that our switch dual promoter system indeed can switch the expression of different genes at specific times, as we envisioned.
Additionally, we employed genes labeled with fluorescent proteins to validate our dual-promoter switch. By fitting the experimental data to the differential equations we previously outlined, we obtained curves related to the changes in small molecule concentration. This also confirmed that our dual-promoter switch system possesses excellent switch control capabilities. The fit between the modeled results and experimental findings is highly consistent.
In this section, we categorize the lifecycle of E. coli into three stages based on gene expression timing: the growth phase, the production phase, and the lysis phase. In each stage, the purpose of the E. coli differs. We will use sets of differential equations to represent these three stages. By calculating the dynamic and static costs, as well as the dynamic revenue during the production process, we aim to measure our total profit. This helps us identify the optimal stopping point, at which we can achieve the maximum return on investment.
All data used in this section are sourced from either literature or the experimental records of this project. Here, we simulate the proliferation of E. coli based on the logistic equation model and utilize polynomial fitting for the lysis process. By calculating the cost consumption and the revenue from PHB at each moment, we aim to find the optimal fermentation termination time.
| ITEM | MEANING | VALUE | UNITS |
|---|---|---|---|
| k1 | E. coli PHB production rate | 2.9e-12[6] | g L-1 min-1CFU-1 |
| k2 | Rate of glucose consumption by E. coli in the first stage (growth phase) | 3.44e-13 | g L-1 min-1CFU-1 |
| k3 | Rate of glucose consumption by E. coli in the second stage (productive phase) | 5.43e-13 | g L-1 min-1CFU-1 |
| k4 | Rate of glucose consumption by E. coli in the late stage (lysis phase) | 2.37e-13 | g L-1 min-1CFU-1 |
| k5 | E.coli lysis constant | 2.52 | - |
| k6 | E.coli lysis constant | -19938 | - |
| k7 | E.coli lysis constant | 2.4498×10e+7 | - |
| K | The carrying capacity of E.coli | 68627256 | CFU mL-1 |
| r | The intrinsic growth rate | 0.01843 | min−1 |
| N0 | Initial number of E. coli | 1302355 | CFU mL-1 |
| T1 | The time of E. coli starts producing PHB | 450 | min |
| T2 | The moment when E. coli begins to cleave | 880 | min |
| A | Other fixed costs | 80 | yuan |
| R1 | Unit price of glucose | 0.00484 | yuan/g |
| R2 | Unit price of PHB | 0.145 | yuan/g |
| R3 | The electricity bill for an hour of fermenter work | 0.5 | yuan/h |
| N | The number of E.coli | - | CFU |
First, we converted experimentally measured OD into CFU for calculation, using the following standard curve [7]:
(Where only glucose is consumed and the number of E. coli continually increases)
(Where the rate of glucose consumption changes and PHB production begins, with no change in the number of E. coli)
(Where E. coli begins to lyse, glucose continues to be consumed, and each E. coli still produces PHB).
When dynamic costs exceed dynamic revenue, our profit will decrease. Below is the result of our modeling:
At the 3,778th minute, the dynamic revenue falls below the dynamic costs, so operations should ideally be halted.
By the 4,104th minute, all bacteria have died.
The total profit amounts to 85.00776820637935 yuan.
In addition, based on the experimental data obtained from simulated fermentation, we modeled the changes in glucose concentration and derived a function representing glucose changes over time. This can provide data references for our hardware—the glucose automatic monitoring and supplementation system based on human-computer interaction. Meanwhile, based on the modeled glucose concentration indications, we can provide predictions for software testing. In the same vein, we will optimize our model according to updates from both hardware and software, aiming to achieve more accurate model parameters.
In this section, based on the data we obtained from testing microplastics in soil samples collected from various regions in China, as well as some microplastics data gathered from the internet [8-10], we conducted a Pearson correlation analysis between the abundance of microplastics and other data from these regions.
References
