In order to assess if Ovulaid could realistically serve as an alternative to common ovulation tests, one needs to get an idea of how much hormone is required to trigger the color response, how much yeast is required in the chewing gum, and how long it will take for colour development. Therefore, we created an elaborate model.

Stating the problem and methodology

Problems to address
To best describe and estimate the function of the Ovulaid biosensor, we defined the following 3 problem statements that we seek to address;
1.) To estimate whether the salivary concentration of hormones can generate a significant ligand-induced response for the investigated receptors. If not, what is the lowest concentration of the hormone that can be detected?

2.) To estimate whether the biosensor can distinguish between the base and peak level concentrations of the hormones in the saliva to directly point at the events in the menstrual cycle. How long the gum must be chewed to see a distinct change? Alternatively, how precise should a camera be to be able to distinguish between base and peak level of hormones for a given time period of chewing?

3.) To estimate how the decay rate of yeast and the concentration of substrate in the gum influence the colored catalysis product build-up.

The foundation of our model
To address these problems we formulated our system by numerical integration of ODEs using MATLAB R2019a offered by MathWorks. From this, we were able to derive the concentration of all molecular species at multiple time points and estimate the answers.
We based our model on similar models, already described in the literature. There are existing ordinary differential equations (ODE) models on the endogenous yeast pheromone pathway^{2, 3}, also newer ODE model for biased agonism dynamics of a G protein-coupled receptor⁴, and models that study the intricate changes in individual components like Gβγ¹. We used these existing models as a foundation to design a similar model, but one that is specific for the Ovulaid biosensor.

System Description

The formulation of our set of ODEs is based on a top-down approach from ligand binding to receptors, which activates a signal transduction cascade that ultimately activates gene expression.
When a ligand (estradiol, LH) binds the receptor (GPER, Hu-LHCGR, XLHCGR), the Gα subunit (GPA1-Gαs, GPA1-Gαi) undergoes a conformational change, which causes the Gβγ subunits (Ste4: Ste18) to dissociate. The now released Gβγ then activates a downstream MAPK cascade. The MAPK cascade amplifies and transduces the response from the receptor activation²² by a series of phosphorylation steps, resulting in activation of a transcription factor (Ste12) that then translocates from the cytoplasm to the nucleus and ultimately binds to the promoter of the gene encoding the enzyme (DOPA 4,5-dioxygenase) and activates transcription. Upon transcription and translation, the enzyme catalyzes the substrate (L-DOPA) into the coloured product (Betalains). In Figure 1, we show a representation of our modelling setup, incorporating the assumptions and simplifications written in the paragraph below.

Figure 1: Representation of our modelling setup. Each biochemical species is stated along with its mode of interaction with other species. The curved arrow represent the catalysis reaction while X2* initiates the transcription and the translation of the reporter module (DOPA 4,5-dioxygenase)

Assumptions and simplifications

In formulating the model we made the following assumptions and simplifications:

1.) We assumed that the receptor may be under its inactive conformation R. Furthermore, a receptor may bind to G protein G, and activation of the receptor may cause G to dissociate and undergo the G protein cycle.

2.) We assume the total concentrations (free molecule plus bound molecule) of Receptor, G-protein components, and MAPK components to stay at a constant equilibrium level since the expression of all components in our refactored yeast cells are driven through constitutive promoters, not pheromone-inducible ones. This is mentioned in detail in the project design tab under chassis construction. We thus neglect all feedback signalling between the MAPK activated genes and the upstream signalling components. Moreover, any autoregulatory feedback that Ste12 has via its native promoter is anyhow positive and thus would only strengthen the signalling. This is also done to keep the model simple to prevent unnecessary error propagation from having excessively many ODEs with possibly weakly estimated or even unknown parameters due to experimental limitations and complicated numerical estimations.

3.) The explicit distinction between concentrations in the cytosol and inside of the nucleus are neglected for the sake of simplicity.

4.) Spontaneous receptor activation is neglected, as it is only assumed to happen very rarely compared to ligand-induced activation.

5.) We assume that the ligand concentration in the saliva can be treated as a constant for a certain time scope. This is justified by the notion that even though salivary concentrations of the ligand may be low, the binding of a few ligand molecules to the receptors would make a local dilution of the ligand. The volumetric excess of saliva compared to gum together with the continuous renewal and mixing will smear out any spatial inhomogeneity. This assumption, however, is only true when looking at the time scope of hours, while it would vary over the time scale of a month due to the female reproductive cycle.

6.) Shaw et al. 2019¹ simplifies the rephosphorylation of the G-alpha unit by assuming the responsible kinase and cellular phosphate concentrations to stay at a constant level. We thus treat the rate of G-alpha rephosphorylation; simply as a constant time the concentration of G-alpha.

7.) As the yeast MAPK pathway and its downstream effects are quite complicated, we simplify it based on Shaw et al. 2019. The interaction of Gβγ with Ste5 and subsequent recruitment of the MAPK cascade (Ste11, Ste7 and Fus3) is represented as an artificial enzyme X1, which is dormant unless activated by binding of Gβγ, in which case it is labelled X1*. X1* then phosphorylates the transcription factor STE12 labelled X2 to its active state X2*, which in turn binds to the inducible promoter pFIG1 to initiate the transcription and translation of the reporter module.

8.) We have made assumptions for the binding of the activated transcription factor to the promoter and the catalysis of the substrate to the reporter. We assume that the binding and unbinding happens sufficiently fast as that these processes can be treated by their equilibrium equations (especially, when we simulate in time units of minutes. See point 11.). More specifically, this means that promoter activity is expressed as a rate constant times its bound fraction and that the enzymatic activity of the reporter-enzyme is treated as Michaelis Menten kinetics. This was done as it allows for better parameter estimations from literature. Apart from this everything is written as kinetic equations and is thus not assumed to be at equilibrium.

9.) We approximated transcription and translation to happen at a constant rate, that we estimated from the time it would take a single RNA polymerase/ribosome to respectively transcribe/translate a gene/ mRNA of a given length. We assume that the RNA polymerase is bound with a probability being equal to the bound fraction of X2* to the promoter and that the ribosome is always bound to a free mRNA.

10.) We treat the movement of substrate and reporter in and out of the cell as describable by a simple diffusion equation. In this respect, the surface area of the cells are taken to be constant and the substrate and the reporter are assumed to be uniformly distributed throughout the gum. Again this is done to keep the model simple and because we would first need to experimentally determine exactly how the yeast cells would treat the cross-membrane transport of substrate and reporter.

11.) We incorporated two different models with respect to the diffusion wherein 1. We take the diffusion of the substrate into account such that the concentration of substrate inside the cell and in the gum varies with time 2. The diffusion occurs so quick that the concentration of substrate inside the yeast stays constant over time as we assume that the concentration of substrate in the gum is so high compared to what is taken up by the yeast that it too stays constant over time. The set of equations without diffusion have the advantage, that it is easier to work with as high diffusion rates requires low time steps when simulating, which can result in long calculating time, but the disadvantage that the final concentration of product can overshoot the initial concentration of substrate when run for too long. Which set to use thus depends on the situation, but we will try to use the set with diffusion to secure conservation of substrate/product concentrations.

12.) We assume the yeast cells to be identical with respect to internal levels of molecules and molecular rates. This is done for the sake of simplicity but is also largely justified by the assumption that the yeast all come from the same strain, and the assumption that the ligand, substrate, and reporter are at any time uniformly distributed in the gum.

13.) When treating the total amount of reporter produced, we assume that the reporter can be seen evenly if it is located in the gum itself or inside of a cell in the gum. Thus, the total reporter concentration would be equal to the amount of reporter produced summed over all cells. We thus assume that the reporter does not diffuse away from the gum during chewing. We are well aware that this is a strong assumption, but we find the issue too complicated to include in a mathematical model given the complexity of physical deformation of the gum and gum-saliva-mixing while chewing. Instead, we would like to make an estimate of how big a percentage of reporter would be lost during chewing and then use this estimate in our judgement whether we have enough reporter or not.

14.) We know that the density of Saccharomyces cerevisiae in YPD is 2e+8 cells/mL. It was considered that the yeast cells are dried and then incorporated into the chewing medium wherein we assume that the volume YPD medium is replaced by the volume of chewing gum medium. In the model, the cells are assumed to not divide for the sake of simplicity and moreover, since yeast would be in a dried state in the chewing gum before taken into the mouth and thus it is not in a proliferative state initially. We also assume that the total volume of yeast cells is much lower than the total volume of Gum.

Ordinary differential equations

Taking the above assumptions and simplifications into account, our system consists of:
• 4 receptor states
• 4 non-receptor bound G-protein states
• 4 signal transduction states
• 2 reporter gene expression states
• 5 substrate and the product diffusion state
• 1 state for yeast number
This amounts to a total of 20 ODEs. The model outputs the changes in the concentrations of each individual element with time, while the individual kinetic rate constants, the lowercase k, along with _plus and _minus, was used to denote forward and backward reactions.
Click to download the MATLAB file.

$$1: \frac{d[R]}{dt}= kL_-[LR] - kL_+[L][R]+kG_-[GR]-kG_+[R][G]$$ $$2: \frac{d[LR]}{dt}= -kL_-[LR] + kL_+[L][R]+kG_-[LGR]-kG_+[LR][G] +k_{GTP+}[LGR]$$ $$3: \frac{d[GR]}{dt}= kL_-[LGR] - kL_+[L][GR] - kG_-[GR] + kG_+[R][G]$$ $$4: \frac{d[LGR]}{dt}= -kL_-[LGR]+kL_+[L][GR]-kG_-[LGR]+kG_+[LR][G]-k_{GTP+}[LGR]$$ $$5: \frac{d[G]}{dt}= kG_-[GR]-kG_+[R][G]+kG_-[LGR]-kG_+[LR][G]-k_{GRA-}[G]+k_{GRA+}[a_{GDP}][bg]$$ $$6: \frac{d[a_{GDP}]}{dt}= -k_{hyd-}[a_{GDP}]+k_{hyd+}[a_{GTP}]+k_{GRA-}[G]-k_{GRA+}[a_{GDP}][bg]$$ $$7: \frac{d[a_{GTP}]}{dt}= k_{hyd-}[a_{GDP}]-k_{hyd+}[a_{GTP}]+k_{GTP+}[LGR]$$ $$8: \frac{d[bg]}{dt}= k_{GRA-}[G]-k_{GRA+}[a_{GDP}][bg]+k_{GTP+}[LGR]-k_{X1+}[bg][X1]+k_{X1-}[X1_*]$$ $$9: \frac{d[X1]}{dt}= k_{X1-}[X1^*]-k_{X1+}[bg][X1]$$ $$10: \frac{d[X1^*]}{dt}= -k_{X1-}[X1^*]+k_{X1+}[bg][X1]$$ $$11: \frac{d[X2]}{dt}= k_{X2-}[X2^*]-k_{X2+}[X1^*][X2]$$ $$12: \frac{d[X2^*]}{dt}= k_{X2+}[X1^*][X2]-k_{X2-}[X2^*]$$ $$13: \frac{d[m_E]}{dt}= \frac{\alpha_{transcription}[X2^*]}{[X2^*]+K_D}-\gamma_{mC}[m_E]$$ $$14: \frac{d[p_E]}{dt}= \alpha_{translation}[m_E]-\gamma_{pC}[pE]$$

The model downstream was run with two different alternative strategies wherein 1. Without diffusion, we use equation 19 to calculate the amount of product produced in units of moles while treating the substrate concentration as constant. We do this as diffusion of substrate and product between yeast and gum are assumed to happen instantaneously and the volume of the gum much larger than the total volume of yeast. 2. With diffusion Equation 15 to 19 are included to model the diffusion of substrate and product between yeast and gum

$$15: \frac{d[C_{in}]}{dt}= -P_{yeast}([C_{in}]-[C_{out}])-\frac{k_{cat}[p_E][C_{in}]}{K_M+[C_{in}]}-\gamma_{Cin}[C_{in}]$$ $$16: \frac{d[C_{out}]}{dt}= N_{yeast}P_{gum}([C_{in}]-[C_{out}])-\gamma_{Cout}[C_{out}]$$ $$17: \frac{d[C^*_{in}]}{dt}= -P_{yeast}([C^*_{in}]-[C^*_{out}])+\frac{k_{cat}[p_E][C_{in}]}{K_M+[C_{in}]}-[\gamma_{C*in}][C^*_{in}]$$ $$18: \frac{d[C^*_{out}]}{dt}= N_{yeast}P_{gum}([C^*_{in}]-[C^*_{out}])-\gamma_{C*out}[C^*_{out}]$$ $$19: \frac{dC^*_{tot}}{dt}= N_{yeast}V_{yeast}\frac{k_{cat}[p_E][C_{in}]}{K_M+[C_{in}]}-\gamma_{C*out}[C^*_{out}]$$ $$20: \frac{dN_{yeast}}{dt}= -\gamma_{yeast}N_{yeast}$$

The set of base parameters, including initial species concentrations used for the simulations can be found below. Parameter values were qualitatively fit through scientific literature while retaining source values when possible.

Parameter	Meaning	Values	Source
k_LH+	LH binding rate	2.17E+06 M^-1 s^-1	Gospodarowicz 1973⁶
k_LH-	LH unbinding rate	2.46E-03 s^-1	Gospodarowicz 1973⁶
k_E2+	E2 binding rate	1.3E+06 M^-1 s^-1	Rich et al. 2002 ⁷
k_E2-	E2 unbinding rate	1.2E−03 s^-1	Rich et al. 2002⁷
k_G+	G protein binding rate	1.00E+08 M^-1 s^-1	Bridge et al. 2010⁵
k_G-	G protein unbinding rate	1.00E-01 s^-1	Bridge et al. 2010⁵
k_GRA+	G protein re-association rate	7.00E+08 M^-1 s^-1	Shaw et al. 2019¹
k_GRA-	G protein dissociation rate	1.30E-03 s^-1	Bridge et al. 2010⁵
k_HYD+	Hydrolysis rate of G_αGTP	1.00E-04 s^-1	Bridge et al. 2010⁵
k_HYD-	Exchange rate of GTP to GDP at G_α	1.00E-04 s^-1	Bridge et al. 2010⁵
k_GTP+	RG dissociation rate	1.00E-02 s^-1	Shaw et al. 2019¹
k_X1+	X1 activation rate to X1^*	2.00E+03 M^-1s^-1	Fitted to Shao et al., 2006^{^^²}
k_X1-	X1^* inactivation rate to X1	2.00E-04 s^-1	Fitted to Shao et al., 2006^{^^²}
k_X2+	X2 activation rate to X2^*	2.00E+03 M^-1s^-1	Fitted to Shao et al., 2006^{^^²}
k_X2-	X2^* inactivation rate to X2	2.00E-04 s^-1	Fitted to Shao et al., 2006^{^^²}
K_dTF	Dissociation constant of TF to the promoter	100e-9	Fitted Le et al., 2018²⁰
α_{Transcription}	Transcription rate	5 bp s^-1	Fitted Maiuri et al., 2011¹⁵
γ_mC	Degradation rate of mRNA	1.925E-3 s^-1	Fitted Martin-Perez and Villén, 2017¹¹
α_Translation	Translation rate	6.6 bp s^-1	Fitted Ikemura 1985¹², Percudani et al. 1997¹³ and Akashi 2003¹⁴
γ_pC	Degradation rate of peptide	1.925E-4 s^-1	Fitted Martin-Perez and Villén, 2017¹¹
γ_yeast	Rate of yeast cell death	1.00E-02 s^-1	Fitted Ovulaid, 2019
Length_{Reporter gene}	Reporter gene length	804 bp	Grewal et al., 2018¹⁰
K_M	Michaelis–Mentens constant reporter catalysis	17e-06 M	Fitted Kovaleva, Rogers and Lipscomb, 2015²¹
k_cat	Rate of catalysis of L-DOPA to Betalains	10.6 s	Fitted Kovaleva, Rogers and Lipscomb, 2015²¹
R_tot	Total receptor concentration	1e-06 M	Hao et al., 2003²⁴
G_tot	Total G protein concentration	1e-06 M	Hao et al., 2003²⁴
L_SalivaLH-	LH concentration at basal level in saliva	17.2 pmol/L	Saibaba et al., 2017¹⁹
L_SalivaLH+	LH concentration at peak in saliva	512.31 pmol/L	Ersyari, Wihardja and Dardjan, 2014⁸
L_SalivaE2+	Estrogen concentration at peak in saliva	40 pmol/L	Chiappin et al., 2007¹⁶
L_SalivaE2-	Estrogen concentration at basal level in saliva	20.6 pmol/l	Chiappin et al., 2007¹⁶
L_SalivaPR+	Progesterone concentration at peak	436 pmol/l	Chiappin et al., 2007¹⁶
L_SalivaPR-	Progesterone concentration at basal levels	22.1 pmol/l	Chiappin et al., 2007¹⁶
L_SerumE2+	Estrogen concentration at peak in serum	200-500 pg/mL	Carmina and Lobo, 2009²³
L_SerumE2-	Estrogen concentration at basal level in serum	20 to 80 pg/mL	Carmina and Lobo, 2009²³
X1_tot	Total X1 concentration	2.5E-07 M	Fitted Shaw et al. 2019 to Shao et al. 2006¹²
X2_tot	Total X2 concentration	2.5E-07 M	Fitted Shaw et al. 2019 to Shao et al. 2006¹²
C_tot	Substrate concentration	1E-00 M	Fitted, Ovulaid 2019
D_E2	Diffusion coefficient of estradiol	5.18E-6 cm²/s	Land, Li and Bummer, 2006¹⁷
D_Betalain	Diffusion coefficient of betalain extraction	18.95E−11 m²/s	Xu et al., 2015¹⁸
P_Gum= 1000*DA_Yeast/T_PMV _gum	Concentration flux parameter for diffusion in &/or out of the gum (factor 1000 is for unit conversion between m^3 and L)	2.5147e-06 s^-1	Fitted, Ovulaid 2019^{^^}
P_Yeast= 1000*DA_Yeast/T_PMV _gum	Concentration flux parameter for diffusion in &/or out of the yeast (factor 1000 is for unit conversion between m^3 and L)	2.9241e+04 s^-1	Fitted, Ovulaid 2019^{^^}
T_PMYeast	Thickness of yeast plasma membrane	7.1 nm	Schneiter et al., 1999²⁵
A_Yeast	Surface area of yeast	9.4219e-11 m ²	Powell, 2003²⁶
V_gum	Volume of gum in Liters	1E-03 L	Fitted, Ovulaid 2019
V_yeast	Volume of yeast cells in Liters	86E-15 L	Fitted M. Milani et al 1998⁹

Table 1 defines a list of all the parameters used in the model with their abbreviation as used in the MATLAB code file, their full name defining the abbreviation, the values assigned to them along with their unit in column 3 along with their origin as mentioned in column 4.

^{^} Shao et al., 2006 observes that upon saturated pheromone induction (1 μM α-factor), the level of the activated G-protein climbs up rapidly, reaches its peak at ∼30 s, and then gradually declines to a bottom at ∼7.5 min before it gradually increases again. Shao then plots the downstream responses to α-factor induction: the activated Ste12 (that is X2* in our case) as a result of the 1 uM ligand induction. To fit the model to a realistic response, we fitted the constants kX1_plus, kX1_minus, kX2_plus, kX2_minus, X1_tot, X2_tot such that X2* shows roughly the same response as STE12 in Shao et al., 2006, when induced by 1 uM of the ligand.
^{^^} The values of P_Gum and P_Yeast from the table led to almost instant diffusion in and out of the yeast cells & the gum, which made the code numerically unstable. In our simulations, we divided both values with a factor of 1000 except in figure15. In the plots below we observe the diffusion of substrate and product between yeast and gum match even with the modified values without a loss of generality indicating that the equilibration of concentrations between the two happens almost instantly compared to the other processes.

Simulation Results

Determining steady states
We seek to find the steady state for each biochemical species considered in our project which is the receptors constituents and the downstream pathway elements. These steady states are prior to ligand induction and the exceptions are; the reporter substrate, product and yeast number.
To do so, the system was simulated until the relative difference between the latest concentration of each considered species and the concentration just before that point was less than 1e-10 (Equation 21). We then saved the last found values for a steady-state and used it as an initial condition for all later simulations. This procedure, to determine steady states, was repeated for each receptor (GPER and LHCGR) respectively.

Relative difference = (A(i) - A(i-1))/ A(i-1) < 1e-10 (Equation 21)

Here, A specifies arbitrary species and i specifies time index. It is noted that both of the receptors had quite similar affinities towards the ligand since the dissociation constant for both the receptor have a similar order of magnitude (KdER: 9.2308e-10 and KdLH:1.1336e-09). Since the signal transduction pathway for both the Estrogen- and the LH receptor is the same, we don’t expect any big differences between the two to arise, except due to the different concentrations of Estrogen and LH.

Salivary hormone concentrations are sufficient for color production
For ligand induction, it was evident that picomolar concentrations of hormones are enough to induce a response, which corresponds to the salivary levels. We then simulated the system at basal level concentration (E2:20.6 pmol/L and LH:17.2 pmol/L) and the peak level concentration (E2:40 pmol/L and LH:512.31 pmol/L for both ligands without taking the diffusion of the substrate and the product into account. This yielded results that showed that the biosensor has a significant ligand-induced constitutive expression even at the basal level of hormones which would lead to the production of a colored product (Figure 2-5 & Figure 8-11).

Hormone level change would be measurable for LH receptor
For the biosensor to give a conclusive result, it is extremely important for a reporter module of the biosensor to be able to distinguish between the basal level and the peak level of the hormones.
For estrogen, it is difficult to differentiate between the reporter module expression at basal and peak levels because the concentration of ligand only undergoes a 2-fold change during the menstrual cycle (Figure 6). This means, that even though we would have colour production, the color-change would not be measurable, as seen in Table 2.
For LH on the other hand, the concentration of ligand has a 29-fold increase at the peak level when compared with the basal level (Figure 12). Therefore, a clear distinction can be made in the reporter gene expression as seen in Table 2. The model suggests that the LHCGR based biosensor can clearly indicate the change in hormonal levels such that the biosensor can be used to point at the events in the menstrual cycle (Figure 14). It is important to note that even low concentration of ligands are enough for the biosensor to produce colour if kept active for long enough.

Hormone	Concentration (pmol/L)	Amount coloured product (~*10^-5moles) 60 mins	Amount coloured product (~*10^-5moles) 120 mins	Amount coloured product (~*10^-5moles) 180 mins
Estrogen	Base: 20.6	0.25	1.75	5.10
	Peak: 40	0.25	2.25	5.50
LH	Base: 17.2	0.20	1.75	5.00
	Peak: 512.31	0.75	3.10	7.00

Table 2

Mobile camera will determine the necessary time for color development
An important parameter for the biosensor to work is the change in the reporter expression over time, and the change in reporter expression will be measured as a color-change. From the table above, it can be seen that this change happens approx. linearly (Figure 6, 12 & 14).
The measuring device for the color-change will be a mobile application, that works by a camera. The resolution of this camera will, therefore, determine the lower boundary for how long the biosensor should be activated by hormones to produce a measurable color-change.

Diffusion of color across the membrane assumed to happen instantly
We first tried to run our model with the diffusion of substrate and reporter product across the cell membrane with the original values for P_gum and P_yeast in the table, but the simulation gave unreliable results due to diffusion happening almost instantly (Figure 15). When simulated over a really small dt, it showed that the concentration inside and outside the cell are equilibrated almost instantly. We, therefore, considered whether to use the set of differential equations without diffusion and assume diffusion to be instant or the set with diffusion but with lowered values of P_gum and P_yeast. To make sure the substrate/product concentrations were conserved, we chose the latter approach as noted below Table1.

Yeast Cell death and substrate concentration simulation
It is important to highlight that the concentration of substrate and the number of yeast cells are two arbitrary values that can be modulated depending upon the strategy employed for the implementation of the biosensor as a diagnostic tool. The above simulations assume no death of yeast and no decay of substrate or product (Figure 2-14). This corresponds to having our biosensor in a closed system (Eppendorf). In order to simulate the gum, we wanted to include the death of yeast and decay of substrate and product. We performed the yeast survivability assay in collaboration with the Danish chewing gum company Fertin Pharma which showed that we must expect the yeast to survive the salivary conditions but at the same time the loss in yeast cells due to chewing cannot be ignored. It was difficult to quantify the decay constant in time experimentally and we were not successful. The model for LH peak level value was however simulated with an estimated decay constants to show the correlation between the change in the coloured product concentration and the yeast decay rate wherein the decay rate of 1E-02 saturates the colour at 2.75*10-8 moles in around 10 minutes, while the decay rate of 1E-04 shows a curve reaching approximately 3.50*10-5 moles in 3 hours (Figure 16).

In the future, we would need to experimentally determine conditions such as sufficient substrate concentration and yeast decay, which we were only able to approximate for the current version of this model. Given these constant, we could finetune the system in its entirety to fit the biosensor in the diagnostic tool (Figure 16).

Estrogen

Figure 2: The concentration (uM) v/s time (mins) graph comparing the simulation of GPCR constituents at the basal levels (left, 20pmol/L) and the peak levels (right, 40pmol/L) of estrogen respectively.

Figure 3: The concentration (uM) v/s time (mins) graph comparing the simulation of heterotrimeric constituents (G protein, Gα subunits: G_αGDP, G_αGTP and Gβγ)at the basal levels (left, 20pmol/L) and the peak levels (right, 40pmol/L ) of estrogen respectively.

Figure 4: The concentration (uM) v/s time (mins) graph comparing the simulation of activated MAPK (X1^*) and the activated transcription factor (X2^*) at the basal levels (left, 20pmol/L) and the peak levels (right, 40pmol/L ) of estrogen respectively.

Figure 5: The concentration (uM) v/s time (mins) graph comparing the simulation of transcription (mE) and the translation (pE) when the activated transcription factor (X2^*) binds to the promoter pFIG1 and initiates the expression of reporter module; at the basal levels (left, 20pmol/L) and the peak levels (right, 40pmol/L ) of estrogen respectively.

Figure 6: The concentration (moles*10^-5) v/s time (mins) graph comparing the simulation of coloured catalysis product (C^*_total) at the basal levels (left, 20pmol/L) and the peak levels (right, 40pmol/L ) of estrogen respectively.

Figure 7: The no. of yeast cells (*10^8) v/s time (mins) graph comparing the simulation yeast decay rate that was considered to be 0 for the first simulation with the basal levels (left, 20pmol/L) and the peak levels (right, 40pmol/L ) of estrogen respectively.

Luteinizing hormone

Figure 8: The concentration (uM) v/s time (mins) graph comparing the simulation of GPCR constituents at the basal levels (left, 17.2pmol/L) and the peak levels (right, 512.31pmol/L) of LH respectively.

Figure 9: The concentration (uM) v/s time (mins) graph comparing the simulation of heterotrimeric constituents (G protein, Gα subunits: G_αGDP, G_αGTP and Gβγ)at the basal levels (left, 17.2pmol/L) and the peak levels (right, 512.31pmol/L ) of LH respectively.

Figure 10: The concentration (uM) v/s time (mins) graph comparing the simulation of activated MAPK (X1^*) and the activated transcription factor (X2^*) at the basal levels (left, 17.2pmol/L) and the peak levels (right, 512.31pmol/L ) of LH respectively.

Figure 11: The concentration (uM) v/s time (mins) graph comparing the simulation of transcription (mE) and the translation (pE) when the activated transcription factor (X2^*) binds to the promoter pFIG1 and initiates the expression of reporter module; at the basal levels (left, 17.2pmol/L) and the peak levels (right, 512.31pmol/L ) of LH respectively.

Figure 12: The concentration (moles*10^-5) v/s time (mins) graph comparing the simulation of coloured catalysis product (C^*_total) at the basal levels (left, 17.2pmol/L) and the peak levels (right, 512.31pmol/L ) of LH respectively.

Figure 13: The no. of yeast cells (*10^8) v/s time (mins) graph comparing the simulation yeast decay rate that was considered to be 0 for the first simulation with the basal levels (left, 17.2pmol/L) and the peak levels (right, 512.31pmol/L ) of LH respectively.

Comparison of biosensor activity of hormones at basal levels and peak levels

Figure 14: The The concentration (moles*10^-4) v/s time (mins) graph comparing the simulation of coloured catalysis product; at the basal levels (Estrogen:20pmol/L, LH:17.2pmol/L) and the peak levels (Estrogen: 40pmol/L, LH:512.31pmol/L) consecutively.

Diffusion of substrate and colored catalysis product

Figure 15: The concentration (uM) v/s time (mins) graph comparing the simulation of the diffusion of substrate (C_in, C_out) and colored catalysis product (C^*_in, C^*_out) across the cell membrane, showing that the diffusion happens almost instantly. The simulation is made using the original values of P_gum and p_yeast from Table1 and a concentration of 1mM substrate in the gum initially.

Yeast decay rate

Figure 16: Top left: The concentration (moles*10^-8) v/s time (mins) graph comparing the simulation of the colored catalysis product (C^*_total) under the condition where yeast decay rate is 1E-02. Top right: The yeast cell number (*10^8) v/s time (mins) showing the decrease in total yeast cells with time accounting for the loss of yeast at the yeast decay rate of 1E-02. Bottom left: The concentration (moles*10^-5) v/s time (mins) graph comparing the simulation of the colored catalysis product (C^*_total) under the condition where the yeast decay rate is 1E-04. Bottom right: The yeast cell number (*10^8) v/s time (mins) showing the decrease in total yeast cells with time accounting for the loss of yeast at the yeast decay rate of 1E-04.

References

1. Shaw, W. M., Yamauchi, H., Mead, J., Gowers, G. O. F., Bell, D. J., Öling, D., ... & Ellis, T. (2019). Engineering a model cell for rational tuning of GPCR signaling. Cell, 177(3), 782-796
2. Shao, D., Zheng, W., Qiu, W., Ouyang, Q. and Tang, C. (2006). Dynamic Studies of Scaffold-Dependent Mating Pathway in Yeast. Biophysical Journal, 91(11), pp.3986-4001.
3. Kofahl, B. and Klipp, E. (2004). Modelling the dynamics of the yeast pheromone pathway. Yeast, 23(10), pp.831-850.
4. Bridge, L.J., Mead, J., Frattini, E., Winfield, I., and Ladds, G. (2018). Modelling and simulation of biased agonism dynamics at a G protein-coupled receptor. J. Theor. Biol. 442, 44–65.
5. Bridge, L. J., King, J. R., Hill, S. J., & Owen, M. R. (2010). Mathematical modelling of signalling in a two-ligand G-protein coupled receptor system: Agonist–antagonist competition. Mathematical biosciences, 223(2), 115-132
6. Gospodarowicz, D. (1973). Properties of the luteinizing hormone receptor of isolated bovine corpus luteum plasma membranes. Journal of Biological Chemistry, 248(14), 5042-5049
7. Rich, R. L., Hoth, L. R., Geoghegan, K. F., Brown, T. A., LeMotte, P. K., Simons, S. P., ... & Myszka, D. G. (2002). Kinetic analysis of estrogen receptor/ligand interactions. Proceedings of the National Academy of Sciences, 99(13), 8562-8567
8. Ersyari, R. M., Wihardja, R., & Dardjan, M. (2014). Determination of ovulation in women using saliva ferning test. Padjadjaran Journal of Dentistry, 26(3)
9. M Milani et al, Differential Two Colour X-Ray Radiobiology of Membrane/Cytoplasm Yeast Cells, TMR Large-Scale Facilities Access Programme Technical report January 1998 University of Milan, Italy
10. Grewal, P., Modavi, C., Russ, Z., Harris, N. and Dueber, J. (2018). Bioproduction of a betalain color palette in Saccharomyces cerevisiae. Metabolic Engineering, 45, pp.180-188.
11. Martin-Perez, M. and Villén, J. (2017). Determinants and Regulation of Protein Turnover in Yeast. Cell Systems, 5(3), pp.283-294.e5.
12. T. Ikemura, Codon usage and transfer-RNA content in unicellular and multicellular organisms, Mol. Biol. Evol. 2 (1985), pp. 13–34.
13. R. Percudani, A. Pavesi and S. Ottonello, Transfer RNA gene redundancy and translational selection in Saccharomyces cerevisiae, J. Mol. Biol. 268 (1997), pp. 322–330.
14. H. Akashi, Translational selection and yeast proteome evolution, Genetics 164 (2003), pp. 1291–1303
15. Maiuri, P., Knezevich, A., De Marco, A., Mazza, D., Kula, A., McNally, J. and Marcello, A. (2011). Fast transcription rates of RNA polymerase II in human cells. EMBO reports, 12(12), pp.1280-1285.
16. Chiappin, S., Antonelli, G., Gatti, R. and De Palo, E. (2007). Saliva specimen: A new laboratory tool for diagnostic and basic investigation. Clinica Chimica Acta, 383(1-2), pp.30-40.
17. Land, L., Li, P. and Bummer, P. (2006). Mass Transport Properties of Progesterone and Estradiol in Model Microemulsion Formulations. Pharmaceutical Research, 23(10), pp.2482-2490.
18. Xu, H., Peng, Q., Yuan, F. and Gao, Y. (2015). Mathematical Modeling of Betanin Extraction from Red Beet (Beta vulgaris L.) by Solid–Liquid Method. International Journal of Food Engineering, 11(1), pp.17-22.
19. Saibaba, G., Srinivasan, M., Priya Aarthy, A., Silambarasan, V. and Archunan, G. (2017). Ultrastructural and physico-chemical characterization of saliva during menstrual cycle in perspective of ovulation in human. Drug Discoveries & Therapeutics, 11(2), pp.91-97.
20. Le, D., Shimko, T., Aditham, A., Keys, A., Longwell, S., Orenstein, Y. and Fordyce, P. (2018). Comprehensive, high-resolution binding energy landscapes reveal context dependencies of transcription factor binding. Proceedings of the National Academy of Sciences, 115(16), pp.E3702-E3711.
21. Kovaleva, E., Rogers, M. and Lipscomb, J. (2015). Structural Basis for Substrate and Oxygen Activation in Homoprotocatechuate 2,3-Dioxygenase: Roles of Conserved Active Site Histidine 200. Biochemistry, 54(34), pp.5329-5339.
22. Yi, T., Kitano, H. and Simon, M. (2003). A quantitative characterization of the yeast heterotrimeric G protein cycle. Proceedings of the National Academy of Sciences, 100(19), pp.10764-10769.
23. Strauss, J. and Barbieri, R. (2009). Yen & Jaffe's Reproductive Endocrinology. London: Elsevier Health Sciences.
24. Hao, N., Yildirim, N., Wang, Y., Elston, T. and Dohlman, H. (2003). Regulators of G Protein Signaling and Transient Activation of Signaling. Journal of Biological Chemistry, 278(47), pp.46506-46515.
25. Schneiter, R., Brügger, B., Sandhoff, R., Zellnig, G., Leber, A., Lampl, M., Athenstaedt, K., Hrastnik, C., Eder, S., Daum, G., Paltauf, F., Wieland, F. and Kohlwein, S. (1999). Electrospray Ionization Tandem Mass Spectrometry (Esi-Ms/Ms) Analysis of the Lipid Molecular Species Composition of Yeast Subcellular Membranes Reveals Acyl Chain-Based Sorting/Remodeling of Distinct Molecular Species En Route to the Plasma Membrane. The Journal of Cell Biology, 146(4), pp.741-754.
26. Powell, C. (2003). Chitin scar breaks in aged Saccharomyces cerevisiae. Microbiology, 149(11), pp.3129-3137.