## Mating pheromone pathway model

We expected to use mRFP intensity to predict the sweetness based on our system. So we needed an insight into relationship between mRFP and sweetness. But lots of factor can impact the signal output so that we decided to divide our system into two parts, **single cell model** and **yeast growth model**.

### Single cell model

#### Purpose

To simulate RFP intensity under different sweetness, we needed to set a model in a single cell firstly. By establishing this model, we could learn about how the sweetness signal transmit in the in yeast coupling pheromone pathway^{[3]}, and know each step of the signal transmit in detail, which provides supports for regulating the signal and improving our bio-meter.

#### Single cell model:

In single cell model, we pay main attention to the signal transduction in pheromone pathway based on^{[4]}.And in order to simulate the signal transduction in mathematical way conveniently, we set some hypothesizes of this model:

#### Method and discussion

In order to simulate our project systematically, we divided our whole system into four blocks: (a) the activation of T1R2/T1R3 receptor; (b) the activation of G-protein cycle; (c) the cascade reaction of MAPK; and (d) the expression of RFP. And the simulating process and result of each part were shown below.

1. The activation of T1R2/T1R3 receptor:

In this process, T1R2/T1R3 receptor has four different states. And the receptor transfer between these states under the different sweetener-binding conditions. The equations of this process were shown as follow:

Parameter | Description | Value |
---|---|---|

k_{1} |
Rate constant of sweetness binding on receptor | 0.0012 |

k_{2} |
Rate constant of activated receptor | 0.6 |

k_{3} |
Rate constant of downregulated receptor | 0.24 |

k_{4} |
Rate constant of receptor degradation | 0.024 |

The result of T1R2/T1R3 receptor’s activation was shown below(Fig. 10). It demonstrated that T1R2/T1R3 receptor could respond to different concentration of ligand.

#### 2. The activation of G-protein cycle:

After upstream signal was produced, the activated G exchanges GTP in place of GDP^{[5]}. Then the G and G_{βγ} dimer are dissociated from receptor and then active downstream pathway. Here, we selected the G_{βγ} dimer as the output of this part. And the equations of this process were listed as follow:

(The parameters of this part were listed in Table 2)

Parameter | Description | Value |
---|---|---|

k_{5} |
Rate constant of G_{αβγ}'s dissociated |
0.0036 |

k_{6} |
Rate constant of G_{αβγ}'s Synthetized |
2000 |

k_{7} |
Rate constant of G_{βγ}'s bind with Ste5 |
0.1 |

k_{8} |
Rate constant of G_{βγ}'s unbind with Ste5 |
5 |

The result of G-protein cycle’s activation was shown below (Fig. 12). According to the figure, we indicated that our system could transduce upstream signal accurately.

#### The cascade reaction of MAPK:

All proteins in this part belong to the category of kinase and the signal was transmitted through phosphorylation. Finally, Fus3 activates the expression of Ste12 which was regarded as the output of this part. And all equations in this process were listed as follow:

(The parameters of this part were listed in Table 3)

Parameter | Description | Value |
---|---|---|

k_{7} |
Rate constant of G_{βγ}'s bind with Ste5 |
0.1 |

k_{8} |
Rate constant of G_{βγ}'s unbind with Ste5 |
5 |

k_{9} |
Rate constant of Ste11's Phosphorylated | 10 |

k_{10} |
Rate constant of Ste7's double Phosphorylated | 47 |

k_{11} |
Rate constant of Fus3's double Phosphorylated | 345 |

k_{12} |
Rate constant of double Phosphorylated Fus3's dissociation. | 140 |

k_{13} |
Rate constant of double Phosphorylated Fus3's synthesis. | 260 |

k_{14} |
Rate constant of Fus3's dephosphorylated | 50 |

k_{15} |
Rate constant of double pp-Fus3's bind with Ste12 | 18 |

k_{16} |
Rate constant of double pp-Fus3's unbind with Ste12 | 10 |

The result of the cascade reaction of MAPK was shown as follow (Fig. 14).

#### 4. Expression of mRFP:

Ste12 could accept signal from upstream pathway, it leads to the activation of relevant promoter *P _{fus}* and expression of downstream gene. There we regarded the expression of RFP as the output. The equations in this process were listed as follow:

(The parameters of this part were listed in Table 4)

Parameter | Description | Value |
---|---|---|

k_{17} |
Rate constant of mRFP_mRNA Synthetize | 0.382 |

k_{18} |
Rate constant of mRFP_mRNA Degradation | 8.39 |

k_{19} |
Rate constant of nascent RFP synthetize | 0.012 |

k_{20} |
Rate constant of mature mRFP synthetize | 0.0012 |

k_{21} |
Rate constant of mature mRFP degradation | 0.018 |

#### Result

Integrating four models of each block, we obtained completed result about signal transduction in single cell. The result was shown as follow (Fig. 16).

### Yeast growth model

#### Purpose

After constructing the model of signal transduction in a single cell, we considered to combine single cell model with the growth of yeast to simulate our system’s practical condition. So in this part, we looked forward to construct a simple model to describe the growth of yeast cells and provided some bases to the next step.

#### Method

##### Practical data measurement

We refered the model established by Imperial College 2016. This model was used to describe the growth condition of two kinds of cell which are competitive in a limit culture.

We re-proposed some hypotheses to fit our system.

Then we set the ODEs as following:

(The parameters of this model were listed in Table 5)

Parameter | Description | Value | |
---|---|---|---|

r_{1} |
Rate of non-active yeast growth | 1 | |

r_{2} |
Rate of active yeast growth | 2 | |

n_{1} |
Culture time for non-active yeast | 30 | |

n_{2} |
Culture time for active yeast | 30 | |

s_{1} |
Rate constant of nutrition consumption for non-active yeast | 0.45 | |

s_{2} |
Rate constant of nutrition consumption for active yeast | 2 |

#### Result

The result of yeast growth model was showed as follow. (Fig. 17)

#### Discussion

Analyzing the trend of the curve, it shown that our model can simulate the growth of yeast in some certain condition. And we considered activated cell as effective bio-meter in our project.

### Combination Model coupling single cell and yeast growth

Based on the above results, we combined these two models together to simulate the performance of whole system in population level. We multiplied the value of Yeast_{active} and the value of RFP_{mature} directly.

And we altered some parameters to fit the experimental data.

The result of this combined model was shown below (Fig. 18).

#### Discussion

Combining two models, we discovered that the RFP intensity is almost the same as base line (value is 0) at the beginning. And after 15 hours, the fluorescence intensity were reflected from single cell level to population level. because the cells entered into stationary phase.

As for the curve after 22 hours, the RFP intensity starts to decrease slowly in all ligand concentration. It may due to the death of cells.

We decided to select the RFP intensity at 22 hours as the final output value of sweetness signal based on our model. In order to avoid the cell growth impacts the RFP intensity, we selected this specific moment as the sampling time.

### SWEETENESS MODEL

#### Purpose

We expected to set a model based on our above model to simulate the RFP intensity of sweetener. Make a comparison between the results of simulation and practical measurement, Our system could not only work like people gustatory sensation system with universality but also is more accurate and less interference than people.

#### Method

Although we finished the GPCR model, the combination rate between the sweetener and receptor had not reported or measured yet. So we needed to measure this data from wet lab.

But because of the instability of our system, we only got a useful group of data. More discussion was established in Project Page. The result was shown (Table 6). Then we utilized these values to optimize our pheromone model.

Group Name | RFP intensity/ unit |
---|---|

2% Sucrose | 42.5 |

0% Sucrose (Control) | 27.5 |

Analyzing previous methods of sweetness measurement, we made two assumptions for this sweetness model:

Based on these, the most significant work is to find out the RFP intensity corresponding to the standard sucrose.

Combining the experimental data, we made a simple calculation and got the RFP intensity of standard sweetness amounting to the fluorescence intensity induced by 750nM ideal ligand in our model.

We set a correction factor K_{corret}=750 on calculation result. Then we reset the input according to following equation:

Then we prefered to predict different sweetness of sweetener. The sweetness data was obtained from previous study^{[7]}. (Table 7．)

Sweetener | Sweetness |
---|---|

Sucrose | 1 |

Aspartame | 200 |

Stevioside | 150 |

Sucralose | 600 |

Glycyrrhizic acid | 170 |

Acesulfame | 200 |

Cyclamate | 30 |

#### Result

The result of simulated RFP intensity induced by different sweeteners was shown in Fig. 20．

#### Discussion

After 22 hours, the peak of all curve were displayed as the pheromone model. And different sweetness also could induce different fluorescence intensity. But this model still need optimization in further, based on the following aspects:

### SUMMARY

Based on our models, we successfully got following results:

Sugar Hunter!!!

#### References