Model of Oxygen Sensing
Abstract
We built an ODE-based model of the Oxygen Sensing system to simulate the system’s response to oxygen: some genes are expressed with high oxygen concentration, others are inhibited. This system consists of Heme, HAP, and ROX1. This model confirmed that this system shows a response to oxygen. Also, we got some inspiration to improve our system from this model.
Aim
This model aims to confirm that our Oxygen Sensing system will respond to oxygen. Although we can predict that the system can respond to oxygen, quantitative properties are unknown. This model examines the threshold scale of oxygen concentration at which the response occurs. Also, how long it takes to respond to oxygen can be predicted. In addition to estimating the system’s dynamics, it can be used to find out how modifications in the system are reflected in the results. In other words, inspiration to improve the system is obtained from this model.
Model Structure
The model structure of the Oxygen Sensing system (Fig. 1) is based on the HAP-dependent gene networks, which regulate the expression of aerobic/anaerobic genes in Saccharomyces cerevisiae [1]. Under aerobic conditions, an oxygen molecule attaches to a heme. Then two oxyhemes bind to HAP to activate it [2]. The activated HAPs promote the transcription of aerobic genes as well as rox1. The ROX1 protein represses the transcription of anaerobic genes; the rox1 gene itself is also repressed too. Thus, when there is enough oxygen, the expression of aerobic genes is induced; the expression of anaerobic genes is repressed.
Fig. 1 Structure of Oxygen Sensing system
Results
Dynamics of Aerobic genes
It was confirmed, as expected, that aerobic genes in our system are expressed in aerobic conditions (Fig. 2). The graph suggests that the Oxygen Sensing system’s oxygen concentration threshold is around 10^(-2) μM to 1 μM. The change of transcription of an aerobic gene is shown in Fig. 3. It seems that this system works on a 10 minutes scale. Fig. 4 illustrates the change of dynamics in some oxygen levels.
Fig. 2 Relative transcript level of aerobic gene with oxygen level
Fig. 3 Change of relative transcript level of aerobic gene
Oxygen concentration is 200 μM. Blue: simulation Orange: literature data [1]
Fig. 4 Relative transcript level of aerobic gene change for all oxygen concentration
Actually, the oxygen concentration threshold seen in Fig. 2 is too low for our project, so we need a way to change the threshold. We found that when the parameter of
Fig. 5 Effect of change of threshold of aerobic gene transcription
We also simulated what happens when oxygen levels will arise while the system is used (Fig. 6). It was confirmed that this system reacts to an aerobic condition immediately.
Fig. 6 Simulation of reaction to oxygen level rise (aerobic gene)
White background shows anaerobic condition; blue shows aerobic. The right figure shows the relative transcript level of the aerobic gene in color.
Dynamics of Anaerobic genes
The same simulations were executed for an anaerobic gene (Fig. 7 to 11).
Fig. 7 Relative transcript level of anaerobic gene with oxygen level
Fig. 8 Change of relative transcript level of anaerobic gene
Oxygen level is 200 μM
Fig. 9 Relative transcript level of anaerobic gene change for all oxygen concentrations
Fig. 10 Effect of change of threshold of anaerobic gene transcription
Fig. 11 Simulation of reaction to oxygen level rise (anaerobic gene)
Methods
Software
Simulations were executed by Python. Data was processed with WebPlotDigitizer and pandas package. Ordinary differential equations were solved by the scipy.integrate.odeint package. The results of the simulation are illustrated with the matplotlib package.
Differential Equations in Oxygen Sensing system model
Where aero, AERO, anaero, and ANAERO stand for aerobic gene, aerobic gene protein, anaerobic gene and anaerobic gene protein, respectively.
Assumptions
Total concentration of heme and HAP is fixed.
Oxygen concentration depends only on the outside of the system.
Parameters
Parameters for simulating Oxygen Sensing Model are shown in Table 1. Initial values are shown in Table 2.
Table 1 Parameter List for Oxygen Sensing Model
| Parameter | Description | Value |
|---|---|---|
| kinetic constant of binding of heme and oxygen | 0.6109540421254621 | |
| kinetic constant of degradation of oxyheme | 0.3452596258608659 | |
| kinetic constant of binding of HAP and first oxyheme | 0.9412786186693928 | |
| kinetic constant of degradation of HAP-oxyheme complex | 0.11650359730498394 | |
| kinetic constant of binding of HAP and second oxyheme | 0.24742627251341565 | |
| kinetic constant of degradation of HAP-dioxyheme complex | 0.005219852453174578 | |
| maximum transcription speed of aerobic gene | 0.0646956856384373 | |
| kinetic constant of degradation of mRNA of aerobic gene | 0.08283169479647245 | |
| kinetic constant of translation of aerobic gene | 0.516244943234396 | |
| kinetic constant of degradation of protein of aerobic gene | 0.7806670774874644 | |
| maximum transcription speed of rox gene | 0.5753566210841502 | |
| kinetic constant of degradation of mRNA of rox gene | 0.2723775159554356 | |
| kinetic constant of translation of rox gene | 0.8489915633363949 | |
| kinetic constant of degradation of ROX protein | 0.08259737550807678 | |
| maximum transcription speed of anaerobic gene | 0.3441405000323726 | |
| kinetic constant of degradation of mRNA of anaerobic gene | 0.8777518472662488 | |
| kinetic constant of translation of anaerobic gene | 0.34894962768856763 | |
| kinetic constant of degradation of protein of anaerobic gene | 0.09248353394217268 | |
| HAP threshold for aerobic gene transcription | 0.01186678500660332 | |
| HAP threshold for rox gene transcription | 0.9998851604125119 | |
| ROX threshold for rox gene transcription | 0.19378003852297565 | |
| ROX threshold for anaerobic gene transcription | 0.8933557054497672 |
Table 2 Initial Values List
| Parameter | Value |
|---|---|
| heme | 0.8330727120045917 |
| HAP | 0.9024138200264148 |
| others | 0 |
Parameters acquiring
- Parameters were acquired using GA for two steps.
- Parameters
to and were acquired by fitting to CYC1 gene expression [4]. - Parameters
to and to were acquired by fitting to ANB1 gene expression (Barba-Aliaga et al, 2020).
Model of Pathogen Detection
Abstract
We built an ODE-based model of the Pathogen Detection system to simulate the system’s response to AHL, a sign of quorum sensing. This model confirmed that this system shows a reaction to AHL. Also, we found some inspiration to improve our system from this model.
Aim
This model aims to confirm that our Pathogen Detection system will respond to AHL. Although we can predict that the system will react to AHL, quantitative properties are unknown. This model examines the sensitivity of the system to AHL. Also, we can estimate how long it takes to detect pathogens to start quorum sensing. In addition to estimating the system’s dynamics, it can be used to find out how modifications in the system are reflected in the results. In other words, inspiration to improve the system can be obtained from this model.
Model Structure
The model structure of the Pathogen Detection system (Fig. 1) is based on MOBILE HEALTH PATHOGEN DETECTOR, iGEM project of Tsinghua, 2013 [5]. The AHL-receptor(for example, LuxR, LasR, or QscR) gene is constantly expressed, and the AHL-receptor is degraded. However, an AHL-receptor binds to an AHL and then forms a dimer when there is AHL. The dimer works as an activator of the reporter gene, and the pathogen infection can be detected.
Fig. 1 Structure of Pathogen Detection system
Results
It was confirmed that reporter genes are expressed when there are AHL above a certain level (Fig. 2). The graph suggests that the Pathogen Detection System’s AHL concentration threshold is around 1 nM. The changes of transcription in each concentration of AHL are shown in Fig. 3. It seems that this system works on an hourly scale. Fig. 4 illustrates the change of dynamics in some AHL levels.
Fig. 2 Relative transcript level of reporter gene with AHL level
Fig. 3 Change of relative transcript level of reporter gene in some AHL
Fig. 4 Relative transcript level of reporter gene change for all oxygen concentration
In addition to these results, we found that the threshold of AHL can be changed by changing parameter 
Fig. 5 Effect of change of threshold of transcription
Methods
Software
Simulations were executed by Python. Data was processed with WebPlotDigitizer and pandas package. Ordinary differential equations were solved by the scipy.integrate.odeint package. The results of the simulation are illustrated with the matplotlib package.
Differential Equations in Pathogen Detection system model
where REC, REC-AHL, 2REC-AHL, rep, and REP stand for AHL-receptor protein, the complex of REC and AHL, dimer of REC-AHL, reporter gene, and reporter protein, respectively.
Here, the translation speed of the AHL-receptor is constant. It is because transcription of the AHL-receptor gene is independent of any other component of this system. When transcription speed is
This can be solved analytically and can be transformed as follows.
where C is the initial concentration of the mRNA. After enough time, the concentration of the mRNA is
.
So, the concentration of the mRNA is constant; thus, the translation of the AHL-receptor gene is consistent.
Assumptions
AHL concentration depends only on the outside of the system.
Parameters
Parameters for simulating Pathogen Detection Model are shown in Table 1. Initial values but AHL concentration is zero.
Table 1 Parameter List for Pathogen Detection Model
| Parameter | Description | Value |
|---|---|---|
| Translation speed of AHL-receptor: product of concentration of mRNA of AHL-receptor(constant) and kinetic constant of translation. | 0.7870499458517503 | |
| kinetic constant of binding of AHL-receptor and AHL. | 0.9573065629284075 | |
| kinetic constant of degradation of AHL-receptor.0.03890052751468431 | 0.03890052751468431 | |
| kinetic constant of degradation of REC-AHL. | 0.00028000229309455005 | |
| kinetic constant of dimerization of REC-AHL. | 0.981485150959217 | |
| kinetic constant of degradation of 2REC-AHL. | 0.008309553360096644 | |
| maximum transcription speed of reporter gene | 0.6698325396098914 | |
| kinetic constant of degradation of mRNA of reporter gene. | 0.9236434348059123 | |
| kinetic constant of translation of reporter gene | 0.9659567837071746 | |
| kinetic constant of degradation of reporter protein. | 0.999689414279895 | |
| 2REC-AHL threshold for reporter gene transcription | 0.8247785216842671 |
Parameters acquiring
- Parameters were acquired using GA.
- Parameters were acquired by fitting to data which shows relative FP level by some concentration of AHL.
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