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Model- iGEM Chalmers-Gothenburg 2018

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Modeling Objective

Before elaborating on the modeling part of this iGEM project, a good question to ask is why would we model our project? In general, creating a mathematical model for synthetic biology can give precious insight into a complex system, which ideally leads to predictive power over the outcome of this system and allows the improvement of the experimental design.

As described by Ledley (1960), modeling is a cyclical and dynamic process where the formulation of the model is repetitively changed to account for new literature data, experimental data and previous modeling outcomes. This new formulation yields a new outcome, which in turn can serve as a basis for a new modeling cycle or an improvement of the experimental design (see figure 1).

**Figure 1:** “the pentagon of research” (Ledley, 1960)

Modeled Elements

In this project, several aspects can be modeled. Because the yeast is modified to produce anti-cancer proteins as a response of an engineered pheromone sensing feedback loop, one model of interest is the pheromone production and signaling cascade and its corresponding anti-cancer protein production (see blue dotted line in figure 2). Another model consists of the anti-cancer protein effect on the cancer cells, specifically the effect on the cell cycle of the cancer cells (see green dotted line in figure 2). While these models are based purely on reaction kinetics, the third element to model is more complex: the growth of, and interaction between all the types of involved cells in the gut (see orange dotted line in figure 2). Thus including the probiotic S. boulardii and the cancer cells but also the key microbiome species and the healthy gut cells. All these types of cells interact by competing for metabolites and through the anti-cancer protein. The community interaction model thus includes metabolic models of all cells and the two first models. To read all about the construction of these models, please consult the PUT LINK TO MODELING DESIGN PAGE

Responsive image — **Figure 2:** Model overview; different models used in the simulation of the cancer treatment. Blue: α pheromone kinetic model, green: cell-cycle kinetic model, orange: community interaction model.

To give an overview of the modeling done in this project, the core consists a community interaction model supported by two kinetic models. The community interaction model is a dynamic Flux Balance Analysis (dFBA) framework, consisting of three blocks: an FBA block with genome scale metabolic models, a dynamic block consisting of a system of differential equations based on exchange metabolite mass balances, and a kinetic block with kinetic uptake expressions for the exchange reactions of the metabolic models. The dFBA iteratively computes and adjusts the boundaries of each exchange metabolite of every metabolic model, based on Michaelis-Menten kinetics. The kinetic models additionally provide kinetic input to the dFBA for the production of pheromones and anti-cancer proteins and the efficacy of the anti-cancer protein. Both the kinetic and interaction models are formulated using values and parameters from literature. The modeling output enables us to improve our experimental design, which can yield different experimental results that can in turn be used to improve the model. This cyclic flow of information is illustrated as a flowchart in figure 3.

**Figure 3:** Flow chart representing the exchange of information between and within the models and how they are integrated with literature and experiments

Kinetic Model - Cell Cycle

In order to determine and compare the efficiency of p28 and myrosinase on cancer cell proliferation, one ODE model for each anti-cancer agent is built. The first model includes p28 and its effect on the p53 levels in the cell. The other model includes the enzymatic activity of myrosinase and the effect of sulphoraphane on cell survival. The cell cycle model is based on the work of Hamada et al. (2009) and consists of three parts; p53 dynamics, cell cycle arrest and apoptosis. The cell cycle arrest and apoptosis parts of the model were implemented according to Hamada et al. (2009) (figure 4) based on the models created by Bagci, Vodovotz, Billiar, Ermentrout, & Bahar (2000) and Aguda (1999). The construction of these two models is described in details on the modeling design page PUT LINK HERE TO OTHER MODELING PAGE

**Figure :** Simplified schematic of the effect of sulforaphane and p28 on the cancer cell

To test the effect of p28 and myrosinase on cell proliferation, the models were run for anti-cancer agent concentrations between 0 and 200 μM. For simplification, the concentration of sulforaphane was set directly and the conversion of glucosinolate by myrosinase was left out from the simulations. For each concentration of anti-cancer agent, cell proliferation was calculated based on a 1000 realizations evaluated for 86,400 time steps, corresponding to 24 hours. The results are shown in the figure below.

Observing figure 7, it can be seen that the effect of sulforaphane seems to be stronger than that of p28. It should be noted, however, that the effect of myrosinase might be less strong than that of sulforaphane since it will be limited by the concentration of glucosinolate in the colon. Moreover, it should also be considered that the results from the α pheromone model suggest that the cells will produce more p28 than myrosinase at a given cell concentration.

Kinetic Model - α Pheromone

In order to simulate the α pheromone system and the production of anti-cancer agent, a model by Kofahl & Klipp (2004) is implemented. The model describes the α pheromone pathway from receptor activation to the production of the transcription factor Ste12. The system described by the model is illustrated in figure 8.

Schematic of alpha pheromone sensing — **Figure 8:** Schematic of engineered alpha pheromone sensing

In this project, Bar1 is removed from the genome of the yeast. Because of this, the concentrations and rate of changes of Bar1 and all of its deriviatives included in the model by Kofahl & Klipp (2004) was set to zero. To get the anti-cancer agent production as a function of the α pheromone concentration in the environment, additional reactions where added to the model. The additional reactions include production of anti-cancer agent mRNA and protein as well as production of α pheromone. For more details about the construction of this model, please consult the model design page PUT LINK TO MODELING DESIGN PAGE

To investigate how changes in the α pheromone concentration affect the anti-cancer agent production, the model was run for initial concentrations of α pheromone between 0 and 1000 nM. Figure 12 shows the maximum concentrations of p28 and myrosinase obtained as a function of initial α pheromone concentration.

**Figure 12:** Maximum concentrations of p28 and myrosinase as functions of initial α pheromone concentration

Figure 12 suggests that the anti-cancer agent production peaks at an initial concentration of approximately 20 nM of α pheromone. This would mean that the highest concentration of anti-cancer agent is obtained when the concentration of α pheromone in the environment is around this value. A value of 20 nM can seem low considering that we do not want production of anti-cancer agent unless several yeast cells have accumulated. However, it should be taken into account that as the yeast cells produce α pheromone, it will disperse in the colon making the effective α pheromone concentration lower than the one produced.

Community dynamic Flux Balance Analysis

The first step in designing a community dFBA framework is to determine which cell types are to be included. Firstly, our community dFBA framework must contain the genome scale metabolic models for colorectal cancer cells, human gut cells, and S. boulardii, since they are key aspects of our project. The question of how to model the complex system that is the gut microbiome was a trickier problem. We decided to use GEMs of three representative species, in terms of composition and biosynthetic capabilities, which were taken from a gut microbiome study by Shoaie et al. (2013). In this paper, the authors generated genome scale metabolic models for three key gut microbiome member species: Bacteroides thetaiotamicron, Eubacterium rectale and Methanobrevibacter smithii, which represent the main phyla Bacteroidetes, Firmicutes, and Euryarchaeota, respectively. Below is a schematic depicting the system modeled by our community dynamic Flux Balance Analysis framework. Note that the schematic corresponds to a scenario of a healthy person without colorectal cancer.

**Figure :** Exchange of metabolites between the key microbiotic species in the colon and the engineered probiotic yeast S. boulardii

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**Figure :** Interaction between the engineered probiotic yeast S. boulardii and the cancer cells

We developed COM-dFBA, short for COMmunity dynamic Flux Balance Analysis, a simple framework for carrying out dFBA simulations for complex communities, such as the one shown above. COM-dFBA makes use of the RAVEN toolbox functionalities, and consists of six original functions and one script, which can be found in our GitHub repository under the folders COM-dFBA/Scripts. To understand the workings of COM-dFBA it is important to know that the chore of this simulation is an iterative cycle consisting of three blocks. First the dynamic block solves a system of ODEs based on mass balances for each biomass and exchange metabolite concentration. This yields a list of concentrations that are used as an input for the kinetic block, which is a system of equations based on Michaelis-Menten kinetics. This kinetic block computes the maximum uptake rates of all metabolites for each organism, which are then implemented as boundaries for the GEMs. Next, the FBA block runs a standard flux balance analysis simulation for each GEM based on the new uptake boundaries, which are defined, as previously mentioned, by kinetic parameters and metabolite availability.

**Figure :** Detailed extract of the modeling overview as presented in figure [...]

To investigate the effect of our engineered organism, we set up three distinct in silico experiments:

S. boulardii and Cancer
Gut microbiome and Colon
Gut microbiome, Colon, and S. boulardii

Experiments were run for 200 or 500 hours, depending on what was being investigated. Perhaps the most interesting setup is found in experiment number one, where we can see the interaction dynamics between S.boulardii and colorectal cancer. The rationale behind experiment number two is to provide a control to compare against experiment number three, where we introduce the engineered S.boulardii to the gut microbiome environment.

Results Simulation 1: S. boulardii & Cancer Cells

In this simulation we aim to investigate the interaction between a growing colorectal cancer and our engineered yeast. As can be seen on the top subplot, both the colon cancer and S. boulardii biomass are near zero at the starting time point. The cancer begins to grow in its characteristic exponential fashion, while the yeast accumulates and begins producing alpha pheromone. Just before the 50 hour mark, enough alpha pheromone accumulates to trigger the production of the anti cancer protein Myrosinase. This causes the growth rate of the cancer to slow down, resulting in a global maximum of cancer biomass between 200 and 250 hours. After this phase there is enough myrosinase in the environment to “overtake” the growth rate of cancer, and we see cancer biomass begin to drop until it reaches zero just after 400 hours. S. boulardii approaches a steady state of around 12 g/L at the end of the simulation. The observed behavior of the alpha pheromone concentration, specifically after the peak around hour 50, is due to the fact that less alpha pheromone can be synthesized once myrosinase production begins. This seems reasonable considering there are amino acid and protein pool constraints. The production level of myrosinase relative to alpha pheromone concentration is validated by the myrosinase kinetic model. The system of ODEs defined by the exchange metabolite mass balances was solved for 1342 time steps, and the simulation took approximately 4.92 hours to complete. This simulation was run using MATLAB 2017b on the Hebbe computer cluster, which is part of the Chalmers Center for Computational Science and Engineering. The Hebbe cluster is built on Intel 2650v3 CPU's, and the system consists of a total 315 compute nodes (total of 6300 cores) with 26 TiB of RAM and 6 GPUs.

Results Simulation 2: Gut Microbiome & Colonocytes

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Results Simulation 3: Gut Microbiome, Colonocytes & S. boulardii

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Integrated modeling

The purpose of the mathematical models created in this project is to make an impact on the course of the project and to be able to make inferences about the biological systems that we introduce into yeast. Although the models all have areas for improvement, the modeling made an impact on the overall project and the work in the wet lab. In this section we explain in what ways it did so.

Proof of concept

First and foremost, the kinetic and genome scale models implemented in this project could be used as proof of concept and for illustrations of how our product will work in practice.

When it comes to the kinetic models, the kinetic model of the α pheromone system illustrates how the feedback loop of α pheromone works. It shows how the concentration of α pheromone in the environment induces the MAPK cascade that in turn leads to the production of anti-cancer agent. The cell cycle models with p28 and myrosinase tell us how the anti-cancer agents potentially affect the cell cycle. They also illustrate how p28 and sulforaphane can lead to the induction of apoptosis and thereby effectively kill cancer cells.

For the genome scale models, the results from the simulations of the gut microbiota with and without S. boulardii indicate that the yeast has no dramatic effects on the composition of the gut microbiota. It demonstrates how S. boulardii can survive alongside gut microbial species while also not harming the patient. Moreover, simulations with S. boulardii , suggest that S. boulardii can produce myrosinase without depleting its amino acid resources. This means that the yeast can kill cancer cells while also growing.

α pheromone threshold

The α pheromone model gave additional insight into our anti-cancer agent production system. The results from the simulations indicate that the initiating threshold of α pheromone for the production of anti-cancer agent is lower than expected. Based on these findings, we should look into the system more closely and consider to use a weaker version of the FUS1 promoter. This is of importance since we do not want our S. boulardii to produce anti-cancer agent unless yeast cells has accumulated as a consequence of the presence of cancer cells.

Choice of anti-cancer agent

Based on the p28 and myrosinase models, we decided to move on with only myrosinase as the potential anti-cancer agent. The reason for this was that the models indicated that the efficiency of sulforaphane would be better than that of p28. The α pheromone model showed that cells would produce more p28 than myrosinase, which would perhaps favor choosing p28. However, myrosinase has the additional benefit that it can keep producing sulforaphane as long as there is any enzyme and substrate (glucosinolate) present, whereas the anti-cancer potential of p28 is limited by its own concentration. Had the results from the cell cycle models been added to the model of S. boulardii and cancer cells, it is expected that even further conclusions could have been drawn regarding anti-cancer agent efficiency.

S. boulardii content in pill

The simulation of together with the gut microbiota gave an indication of how much yeast to put inside of the final product, i.e. the pill. In the simulations, the inflow of S. boulardii was set to 1 g/L with a total liquid inflow of 0.05 L/h. This gives a daily inflow of 1.2 g of yeast. Therefore, a patient should ingest 1.2 g of yeast every day during treatment. The patient could either take one pill per day or the content could be split into several pills to get an even flow of yeast throughout the day. Since part of the yeast cells will die both in the manufacturing process and on the journey from the patient’s mouth to the gut, this should be considered a lower bound.

Future work

The models created in this project gave us valuable insights into project design and helped us improve our visualised product. While this is true, the modeling could still be subject to improvement. Below, we bring up model improvements that did not fit the time scope of the project.

For all of the kinetic models, optimization was used to find parameter values. However, in the process of optimization, an identifiability analysis should optimally be performed to determine the validity of the outcome. If the work on the α pheromone model and the cell cycle models would continue, this would be the next step. Based on the identifiability analysis it can be decided if more data is needed in order to fit the models to reality and if there are parameter values that cannot be found with optimization.

In the implementation of the cell cycle model, parameter values and initial concentrations were obtained from Hamada et al. (2009). However, these values are based on the dynamics of a normal, healthy cell. For future work, the parameters in the model could be modified in order for the dynamics to better resemble those of a cancer cell. To develop the cell cycle models further, the models could be made more time responsive in the sense that cell proliferation is not only a matter of anti-cancer agent concentration but also something that is affected by exposure time. If the models had been fit to proliferation data available at several time points, they could have been rendered more realistic based on exposure time.

When it comes to the genome scale models, the next step would be to add all of the GEMs implemented in this project, including the gut cell, the cancer cell, the gut microbiota andS. boulardii together in order to get an abstraction of the whole gut system. In addition to this, glucosinolate should be added to the gut inflow to get a better understanding of how the diet can affect the efficiency of myrosinase.

The optimal last step of this modeling project would be to add the results of the α pheromone and cell cycle models to the system of GEMs. In this way, we would obtain a large-scale model that can be used to evaluate the effects of our yeast on cancer cell proliferation and to further improve our product.

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Frydoonfar, H. R., McGrath, D. R., & Spigelman, A. D. (2004). Sulforaphane inhibits growth of a colon cancer cell line. Colorectal Disease, 6(1), 28–31. https://doi.org/10.1111/j.1463-1318.2004.00488.x

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Warso, M. A., Richards, J. M., Mehta, D., Christov, K., Schaeffer, C., Rae Bressler, L., … Das Gupta, T. K. (2013). A first-in-class, first-in-human, phase I trial of p28, a non-HDM2-mediated peptide inhibitor of p53 ubiquitination in patients with advanced solid tumours. British Journal of Cancer, 108(5), 1061–1070. https://doi.org/10.1038/bjc.2013.74

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@@ Line 182: / Line 182: @@
 <figure style="text-align:center;">
 <img src="https://static.igem.org/mediawiki/2018/e/ec/T--Chalmers-Gothenburg--2_model_overview.png" class="img-fluid" alt="Responsive image" align="middle">
-<figcaption><i><b>Figure 2:</b> model overview; different models used in the simulation of the cancer treatment. Blue: α pheromone kinetic model, green: cell-cycle kinetic model, orange: community interaction model.</i></figcaption>
+<figcaption><i><b>Figure 2:</b> Model overview; different models used in the simulation of the cancer treatment. Blue: α pheromone kinetic model, green: cell-cycle kinetic model, orange: community interaction model.</i></figcaption>
 </figure>
-<p>To give an overview of the modeling done in this project, the core consists a community interaction model supported by two kinetic models. The community interaction model is a dynamic Flux Balance Analysis (dFBA) framework, consisting of three blocks: an FBA block with genome scale metabolic models, a dynamic block consisting of a system of differential equations based on exchange metabolite mass balances, and a kinetic block with uptake kinetic expressions for the exchange reactions of the metabolic models. The dFBA iteratively computes and adjusts the boundaries of each exchange metabolite of every metabolic model, based on Michaelis-Menten kinetics. The kinetic models additionally provide kinetic input to the dFBA for the production of pheromones and anti-cancer proteins and the efficacy of the anti-cancer protein. Both the kinetic and interaction models are formulated using values and parameters from literature. The modeling output enables us to improve our experimental design, which can yield different experimental results that can in turn be used to improve the model. This cyclic flow of information is illustrated as a flowchart in figure 3.  </p>
+<p>To give an overview of the modeling done in this project, the core consists a community interaction model supported by two kinetic models. The community interaction model is a dynamic Flux Balance Analysis (dFBA) framework, consisting of three blocks: an FBA block with genome scale metabolic models, a dynamic block consisting of a system of differential equations based on exchange metabolite mass balances, and a kinetic block with kinetic uptake expressions for the exchange reactions of the metabolic models. The dFBA iteratively computes and adjusts the boundaries of each exchange metabolite of every metabolic model, based on Michaelis-Menten kinetics. The kinetic models additionally provide kinetic input to the dFBA for the production of pheromones and anti-cancer proteins and the efficacy of the anti-cancer protein. Both the kinetic and interaction models are formulated using values and parameters from literature. The modeling output enables us to improve our experimental design, which can yield different experimental results that can in turn be used to improve the model. This cyclic flow of information is illustrated as a flowchart in figure 3.  </p>
 <figure style="text-align:center;">
 <img src="https://static.igem.org/mediawiki/2018/8/8a/T--Chalmers-Gothenburg--3_iGEM_modeling_data_flow.png" class="img-fluid" class="img-fluid">
-<figcaption><i><b>Figure 3:</b> flow chart representing the exchange of information between and within the models and how they are integrated with literature and experiments</i></figcaption>
+<figcaption><i><b>Figure 3:</b> Flow chart representing the exchange of information between and within the models and how they are integrated with literature and experiments</i></figcaption>
 </figure>
@@ Line 202: / Line 202: @@
 </figure>
-<p>To test the effect of p28 and myrosinase on cell proliferation, the models were run for anti-cancer agent concentrations between 0 and 200 μM.  For simplification, the concentration of sulforaphane was set directly and the conversion of glucosinolate by myrosinase was left out from the simulations. For each concentration of anti-cancer agent, cell proliferation was calculated based on a 1000 realizations evaluated for 259,200 time steps, corresponding to 72 hours. The results are shown in the figure below.</p>
+<p>To test the effect of p28 and myrosinase on cell proliferation, the models were run for anti-cancer agent concentrations between 0 and 200 μM.  For simplification, the concentration of sulforaphane was set directly and the conversion of glucosinolate by myrosinase was left out from the simulations. For each concentration of anti-cancer agent, cell proliferation was calculated based on a 1000 realizations evaluated for 86,400 time steps, corresponding to 24 hours. The results are shown in the figure below.</p>
 <figure style="text-align:center;">
 <img src="https://static.igem.org/mediawiki/2018/4/45/T--Chalmers-Gothenburg--proliferation.png" alt="Cell proliferation" class="img-fluid">
-<figcaption><i><b>Figure 7:</b> Cell proliferation as a function of anti-cancer agent concentration obtained with simulation during a time period corresponding to 72 hours</i></figcaption>
+<figcaption><i><b>Figure 7:</b> Cell proliferation as a function of anti-cancer agent concentration obtained with simulation during a time period corresponding to 24 hours</i></figcaption>
 </figure>
-<p>Observing figure 7, it can be seen that the effect of sulforaphane seems to be stronger than that of p28. It should be noted, however, that the effect of myrosinase might be less strong since it will be limited by the concentration of glucosinolate in the colon. Moreover, the effect of p28 is likely to be underestimated for an exposure time of 72 hours. The reason for this is that the parameters for the p28 model were found using data obtained with an exposure time of 24 hours. To avoid this, the models could have been optimized to data obtained with the same exposure time. However, it would have been even better if the models had been fit to proliferation data obtained at several exposure times. In that way, the output of the models would become more sensitive to exposure time.  Disregarding that, it should also be considered that the results from the α pheromone model suggest that the cells will produce more p28 than myrosinase at a given cell concentration.</p>
+<p>Observing figure 7, it can be seen that the effect of sulforaphane seems to be stronger than that of p28. It should be noted, however, that the effect of myrosinase might be less strong than that of sulforaphane since it will be limited by the concentration of glucosinolate in the colon. Moreover, it should also be considered that the results from the α pheromone model suggest that the cells will produce more p28 than myrosinase at a given cell concentration.</p>
 <h1 style="text-align: center;">Kinetic Model - α Pheromone</h1>
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-<p>In this project, Bar1 is removed from the genome of the yeast. Because of this, the concentrations and rate of changes of Bar1 and all of its deriviatives included in the model by Kofahl & Klipp (2004) was set to zero. To get the anti-cancer agent production as a function of the α pheromone concentration in the environment, additional reactions where added to the model. The additional reactions include production of anti-cancer agent mRNA and protein as shown in the equations below. For more details about the construction of this model, please consult the model design page <b>PUT LINK TO MODELING DESIGN PAGE</b></p>
+<p>In this project, Bar1 is removed from the genome of the yeast. Because of this, the concentrations and rate of changes of Bar1 and all of its deriviatives included in the model by Kofahl & Klipp (2004) was set to zero. To get the anti-cancer agent production as a function of the α pheromone concentration in the environment, additional reactions where added to the model. The additional reactions include production of anti-cancer agent mRNA and protein as well as production of α pheromone. For more details about the construction of this model, please consult the model design page <b>PUT LINK TO MODELING DESIGN PAGE</b></p>
 <p>To investigate how changes in the α pheromone concentration affect the anti-cancer agent production, the model was run for initial concentrations of α pheromone between 0 and 1000 nM. Figure 12 shows the maximum concentrations of p28 and myrosinase obtained as a function of initial α pheromone concentration. </p>
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-<p>Figure 12 suggests that the anti-cancer agent production peaks at an initial concentration of approximately 20 nM of α pheromone. This would mean that the highest concentration of anti-cancer agent is obtained when the concentration of α pheromone in the environment is around this value.  A value of 20 nM can seem low considering that we do not want production of anti-cancer agent unless several yeast cells have accumulated. However, it should be taken into account that as the yeast cells produce α pheromone, it will diffuse in the colon making the effective α pheromone concentration <b>lower...something...  Is this reasonable? And what about the threshold that we would like to see in the beginning?? (Can we make a connection to the GEM?). Can we say something about the absolute values of anti-cancer agent concentrations?</b> </p>
+<p>Figure 12 suggests that the anti-cancer agent production peaks at an initial concentration of approximately 20 nM of α pheromone. This would mean that the highest concentration of anti-cancer agent is obtained when the concentration of α pheromone in the environment is around this value.  A value of 20 nM can seem low considering that we do not want production of anti-cancer agent unless several yeast cells have accumulated. However, it should be taken into account that as the yeast cells produce α pheromone, it will disperse in the colon making the effective α pheromone concentration lower than the one produced.</p>
 <h1 style="text-align: center;">Community dynamic Flux Balance Analysis</h1>
 <a class="anchor" id="COMdFBA"></a>
-<p>The first step in designing a community dFBA framework was to determine which cell types are to be included. Firstly, our community dFBA framework must contain the genome scale metabolic models for colorectal cancer cells, human gut cells, and <i>S. boulardii</i>, since they are key aspects of our project. The question of how to model the complex system that is the gut microbiome was a trickier problem. We decided to use GEMs of three representative species, in terms of composition and biosynthetic capabilities, which were taken from a gut microbiome study by Shoaie et al. (2013). In this paper, the authors generated genome scale metabolic models for three key gut microbiome member species: <i>Bacteroides thetaiotamicron</i>, <i>Eubacterium rectale</i> and <i>Methanobrevibacter smithii</i>, which represent the main phyla Bacteroidetes, Firmicutes, and Euryarchaeota, respectively. Below is a schematic depicting the system modeled by our community dynamic Flux Balance Analysis framework. Note that the schematic corresponds to a scenario of a healthy person without colorectal cancer.</p>
+<p>The first step in designing a community dFBA framework is to determine which cell types are to be included. Firstly, our community dFBA framework must contain the genome scale metabolic models for colorectal cancer cells, human gut cells, and <i>S. boulardii</i>, since they are key aspects of our project. The question of how to model the complex system that is the gut microbiome was a trickier problem. We decided to use GEMs of three representative species, in terms of composition and biosynthetic capabilities, which were taken from a gut microbiome study by Shoaie et al. (2013). In this paper, the authors generated genome scale metabolic models for three key gut microbiome member species: <i>Bacteroides thetaiotamicron</i>, <i>Eubacterium rectale</i> and <i>Methanobrevibacter smithii</i>, which represent the main phyla Bacteroidetes, Firmicutes, and Euryarchaeota, respectively. Below is a schematic depicting the system modeled by our community dynamic Flux Balance Analysis framework. Note that the schematic corresponds to a scenario of a healthy person without colorectal cancer.</p>
 <figure style="text-align:center;">
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 <h2 style="text-align: center;">Proof of concept</h2>
 <p>First and foremost, the kinetic and genome scale models implemented in this project could be used as proof of concept and for illustrations of how our product will work in practice.</p>
-<p>When it comes to the kinetic models, the kinetic model of the α pheromone system illustrates how the feedback loop of α pheromone works.  It shows how the concentration of α pheromone in the environment induces the MAPK cascade that in turn leads to the production of anti-cancer agent. The cell cycle models with p28 and myrosinase told us how the anti-cancer agents potentially affect the cell cycle. They also illustrate how p28 and sulforaphane can lead to the induction of apoptosis and thereby effectively kill cancer cells.</p>
+<p>When it comes to the kinetic models, the kinetic model of the α pheromone system illustrates how the feedback loop of α pheromone works.  It shows how the concentration of α pheromone in the environment induces the MAPK cascade that in turn leads to the production of anti-cancer agent. The cell cycle models with p28 and myrosinase tell us how the anti-cancer agents potentially affect the cell cycle. They also illustrate how p28 and sulforaphane can lead to the induction of apoptosis and thereby effectively kill cancer cells.</p>
 <p>For the genome scale models, the results from the simulations of the gut microbiota with and without <i>S. boulardii</i> indicate that the yeast has no dramatic effects on the composition of the gut microbiota. It demonstrates how <i>S. boulardii</i> can survive alongside gut microbial species while also not harming the patient. Moreover, simulations with <i>S. boulardii</i> , suggest that <i>S. boulardii</i> can produce myrosinase without depleting its amino acid resources. This means that the yeast can kill cancer cells while also growing.</p>
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 <p>The optimal last step of this modeling project would be to add the results of the α pheromone and cell cycle models to the system of GEMs. In this way,  we would obtain a large-scale model that can be used to evaluate the effects of our yeast on cancer cell proliferation and to further improve our product.</p>
-<p><b>Future work section from cell cycle model, should it be included in the part above?</b></p>
-<p>In the implementation of the cell cycle model, parameter values and initial concentrations were obtained from Hamada et al. (2009). However, these values are based on the dynamics of a normal, healthy cell. For future work, the parameters in the model could be modified in order for the dynamics to better resemble those of a cancer cell.
-In the process of optimization, an identifiability analysis should optimally be performed to determine the validity of the outcome. If the work on the cell cycle models would continue, this would be the next step. Based on the identifiability analysis it can be decided if more data is needed in order to fit the model to reality and if there are parameter values that cannot be found with optimization.
-To develop the cell cycle models further, the models could be made more time responsive in the sense that cell proliferation is not only a matter of anti-cancer agent concentration but also something that is affected by how long time the cell is exposed to the anti-cancer agent. If the models had been fit to proliferation data available at several time points, they could have been rendered more realistic based on exposure time.
-The optimal last step of this modeling project would be to implement the cell cycle models into the genome scale model to get a large-scale model that can be used to evaluate the effects of p28 and myrosinase on cancer cell proliferation.</p>
 <h1>References</h1>

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