Team:BIT-China/Model/GPCRpathway

BIT-CHINA

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:

1. We assumed that T1R2/T1R3 receptor does not have synergistic effect when it binds with sweeteners.

2. We hypothesized that the number of binding sweetener are consistent when binding to T1R2/T1R3 receptor or pheromone receptor.

3. We supposed that the combining rate and the initial binding concentration of sweetener are as same as pheromone receptor’s.

4. There is no influence between cell growth and protein expression in a single cell.

5. Only concern conservation relations of protein concentration in a single cell. The protein involving in the signal transduction is not considers its production or degradation.

Method and discussion

Fig 8． Sweetness testing pathway in Sugar Hunter

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:

Fig. 9 The mechanism of T1R2/T1R3 receptor’s activation

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:

(T1R2/3: the T1R2-T1R3 receptor. All parameters of this part were listed in Table 1)

Table 1． The value of parameters in activation of T1R2/T1R3 receptor
Parameter	Description	Value
k₁	Rate constant of sweetness binding on receptor	0.0012
k₂	Rate constant of activated receptor	0.6
k₃	Rate constant of downregulated receptor	0.24
k₄	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.

Fig. 10． The simulating result of receptor’s activation under the different concentration of ligand

2. The activation of G-protein cycle:

Fig. 11 The process of G-protein cycle’s activation

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)

Table 2． The value of parameters in G-protein cycle’s activation
Parameter	Description	Value
k₅	Rate constant of G_αβγ's dissociated	0.0036
k₆	Rate constant of G_αβγ's Synthetized	2000
k₇	Rate constant of G_βγ's bind with Ste5	0.1
k₈	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.

Fig. 12． The result of G-protein cycle’s activation under the different concentration of ligand

The cascade reaction of MAPK:

Fig. 13 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)

Table 3． The value of parameters in cascade reaction of MAPK
Parameter	Description	Value
k₇	Rate constant of G_βγ's bind with Ste5	0.1
k₈	Rate constant of G_βγ's unbind with Ste5	5
k₉	Rate constant of Ste11's Phosphorylated	10
k₁₀	Rate constant of Ste7's double Phosphorylated	47
k₁₁	Rate constant of Fus3's double Phosphorylated	345
k₁₂	Rate constant of double Phosphorylated Fus3's dissociation.	140
k₁₃	Rate constant of double Phosphorylated Fus3's synthesis.	260
k₁₄	Rate constant of Fus3's dephosphorylated	50
k₁₅	Rate constant of double pp-Fus3's bind with Ste12	18
k₁₆	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).

Fig. 14 The result of Ste12’s activation under the different concentration of ligand

4. Expression of mRFP:

Fig. 15 The process of RFP’s expression

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)

Table 4． The value of parameters in RFP expression
Parameter	Description	Value
k₁₇	Rate constant of mRFP_mRNA Synthetize	0.382
k₁₈	Rate constant of mRFP_mRNA Degradation	8.39
k₁₉	Rate constant of nascent RFP synthetize	0.012
k₂₀	Rate constant of mature mRFP synthetize	0.0012
k₂₁	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).

Fig. 16． The result of RFP intensity under different concentration ligand Our modeling result exhibited that different concentration of ligand could result in different RFP intensity, which demonstrated that our system could response to the different signal strength specifically. And it also demonstrated that our system could work in a single cell in theory.

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.

1. The condition of cell was divided into two states, activated and non-activated, and there is no conversion between two states. Each state of cell consume the nutrition independently.

2. Only the activated state could combine sweetener.

3. The nutrition in culture was limited.

4. Each group cell had same growth condition.

Then we set the ODEs as following:

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

Table 5． The value of parameter in yeast growth part
Parameter	Description	Value
r₁	Rate of non-active yeast growth	1
r₂	Rate of active yeast growth	2
n₁	Culture time for non-active yeast	30
n₂	Culture time for active yeast	30
s₁	Rate constant of nutrition consumption for non-active yeast	0.45
s₂	Rate constant of nutrition consumption for active yeast	2

Result

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

Fig. 17 The result of yeast cell growth model

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).

Fig. 18 The simulation result of RFP intensity in population level.

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.

Table 6． The result of sweetness measurement using Sugar Hunter at 16 hours
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:

1. Sweetness of all sweeteners could be transformed into the different concentration of standard sucrose (10% dissolving in water) with the same sweetness.

2. The bind between different ligands and GPCR will not impact signal transduction in pheromone pathway.

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.

Fig. 20． The relationship between sweetness and ideal ligand

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．)

Table 7． The sweetness of sweetener measured by people taste
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．

Fig. 21． The modeling result of RFP intensity induced by different sweeteners

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:

(1) Through molecular simulation to discover the combination constant of sweetener binding process.

(2) The correct factor is to be considered the molecular weight, binding sites and combination numbers of the sweetener.

(3) Combine the protein expression and cells growth together. Consider the interaction between two models.

SUMMARY

Based on our models, we successfully got following results:

1. We simulated the structure of T1R2/T1R3 receptor and bound it with different sweeteners to observe the combining situation of different sweeteners through molecular docking.

2. We constructed the signal transduction model to simulate pheromone response pathway in two different levels and proved that our system could work as we expected.

3. We also provided an ideal relationship between RFP intensity and sweetness based on the wet lab data and our signal transduction model , which also demonstrated that our system could detect different range of sweetness. Although sweeteners are various, but we still can taste all of them and sense different sweetness due to the powerful sweetness receptors, T1R2/T1R3. Based on our model, we successfully proved that using sweetness receptor as a “meter” and coupling the signal pathway to determine the sweetness in yeast cell is available. Last, let’s set foot on the trip of beating sweet-monsters in parallel space with our

Sugar Hunter!!!

References

1. Dubois G E. Molecular mechanism of sweetness sensation.[J]. Physiology & Behavior, 2016, 164(Pt B):453.

2. Nie Y, Vigues S, Hobbs J R, et al. Distinct contributions of T1R2 and T1R3 taste receptor subunits to the detection of sweet stimuli.[J]. Current Biology Cb, 2005, 15(21):1948-52.

3. Richardson, Kathryn. Mechanisms of GPCR signal regulation in fission yeast[J]. University of Warwick, 2014.

4. Kofahl B, Klipp E. Modelling the dynamics of the yeast pheromone pathway.[J]. Yeast, 2004, 21(10):831.

5. Audet M, Bouvier M. Restructuring G-Protein- Coupled Receptor Activation [J]. Cell, 2012, 151(1):14-23.

6. Carocho M, Morales P, Icfr F. Sweeteners as food additives in the XXI century: A review of what is known, and what is to come[J]. Food & Chemical Toxicology An International Journal Published for the British Industrial Biological Research Association, 2017, 107.

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