YEAST-AID

# Model

## 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 ( Table 1) changes, the oxygen concentration threshold moves, too. In fact, parameter is operable [3] because it is related to the DNA sequence of the promoter. In addition, the transcript level will fall if is bigger. The simulation suggests that an amplifying circuit is also needed to increase the threshold.

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); it can be changed by editing the binding region of promoter. If our device does not have enough sensitivity, we should lower ; if our device has too many false positives, K should be raised.

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 and degradation kinetic constant is , the differential equation of mRNA of AHL-receptor gene is as follows.

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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