An ambitious project of 73 differential equations

Two parts: Model of our own system and modelling database

The modelling part of our project is divided into two parts; the model of our own system and a suggestion of a modelling database being integrated in the iGEM website. Since the Edible coli project aims to make E. coli produce both the essential and the non-essential amino acids in our protein called OneProt, we decided to make a model of the biosynthesis of these amino acids in E. coli in orderto detect bottlenecks in the system. This was a very ambitious project and required a lot of research and time. The biosynthesis of the amino acids consists of over 73 intermediates and thus would require at least 73 ODE's. After a long summer of modelling we came to the realization that since most teams in iGEM need to model pathways every year, it is a shame that every team needs to start from scratch when – most likely – the modelling of the enzymes in their system has already been modelled before in iGEM. This is when we came up with the idea of a modelling database, which would – just like the current parts registry – contain basic modelling “bricks”. These bricks would be uploaded from the teams that have already made them for their own project. Creating this system would allow future teams to make much more interesting and complex models since they could start from where previous teams left off and not from scratch. Below we elaborate on both the model of our own system and this modelling database idea with “proof of concept” examples of how the modelling registry could look and function and how a team would upload their modelling “bricks” to the registry.

Modelling of the biosynthesis of OneProt

Figure 1: The biosynthesis of essential and non-essential amino acids - will open in a new tab due to the size. As mentioned above we wanted to model the biosynthesis of the essential and non-essential amino acids in the attempt to find bottlenecks in the system. We wanted to find out which amino acids would slow down the production of our protein based on the pathway using Michaelis-Menten kinetics and the differential equation solver Berkeley Madonna.

The first step of this process was drawing the pathway of the amino acids, including all enzymes and reactions. This was a huge task and we ended up with the pathway seen in figure 1. Second step consisted of finding all the needed constants of the enzyme reactions in the pathway, including around 170 km and Vmax constants found on BRENDA. and in the literature. A document containing all constants used in our model can be found here.

The last step of the process was implementing the differential equations made using the pathway, Michaelis-Menten kinetics and our constants in a differential equation solver. We chose to use Berkeley Madonna since this solver solve systems quickly and provides the ability to work with “sliders”, which allow us to see the impact of small changes in constants and equations on our system. Our model implemented in Berkeley Madonna can be found here.

What did the model tell us?

Figure 2: Production of OneProt at different TCA levels. The complexity of biological systems makes it impossible to model without making assumptions. As is also the case for us, our model could never have been made without making some assumption. All the assumptions we have made have been noted in the model.

One of the first things we observed after having constructed the model was that a model of this extent is very stiff. Furthermore the complexity of the model also makes it very difficult to predict the outcome of changes.

The model is based on the principle of “sources and sinks”, where sources are the flow into the system and sinks are the flow out of the system. The sources in our case are the Citric acid cycle (TCA) and Pentose phosphate pathway (PPP), which we assume to be constant. The sink is the production of OneProt from amino acids. The production of OneProt has been modeled so that it depends on the concentration of each amino acid and the ratio required of the amino acid.

Figure 3: Example of modelling database. Click the picture for the full page. The model was evaluated by observing if there was a flow through the system. As shown in figure 2, when TCA increases so does the OneProt production.

Though when the TCA is increased beyond a certain point the OneProt production decreases. This trend is a result of the complexity of the system. The availability of the amino acids where analyzed by looking at the flow through the system separately for each amino acid. Thus it was discovered that the limiting amino acid is threonine. By examining the reaction rates towards and away from threonine, it was found that threonine is depleted for the production of isoleucine just as fast as it is produced. The system could potentially be optimized, by increasing the concentration or efficiency of Homoserine kinase.

Modelling database

Figure 4: Example of choosing between models. Click the picture for the full page. Collaborating and helping other teams is a very big part of the iGEM competition. Every year new and better projects are created because it is possible to use what the previous teams have created and use this to make more complex projects – using a collection of bricks to build a new construction. In our opinion this should not only be the case for the wet-lab part of iGEM but also be true for the modelling aspect of iGEM. This is why we suggest making a modelling part registry section on the iGEM page, containing modelling “bricks” created by the iGEM teams all over the world.

To be more specific we want to make it easier to go from pathway to differential equations. This could be achieved by translating the enzymes of the pathways into differential equations only needing the E.C number of the enzyme. As an example we made a proof of concept database on our wiki which is available when using this link. On the iGEM modelling parts registry it should then be possible to search the enzymes using the E.C number of the enzyme, the pathway(s) that the enzyme is a part of, the name of the enzyme or even the most used enzymes (just like the normal parts registry).

Figure 5: Example of model from modelling database. Click the picture for the full page. When the chosen enzyme has been selected, a list of all the teams that have modeled that specific enzyme will be presented. Furthermore the list will contain three columns: Validated, inhibitor and reversible. The idea behind validation is that other teams will be able to validate each other’s modeling. The next column shows whether inhibition has been included in the model, while the last column specifies if the reaction modeled is reversible and whether it has been included.

After choosing the desired team it should then be possible to open a page like this and find the needed information, i. e. name, reaction, differential equation, constants and notes about the differential equation regarding what aspects are included and what aspects are excluded (for example inhibition and the amount of substrates and products). Lastly it should be possible to copy the differential equation with the constants inserted to be able to insert it in the wanted model.

Figure 6: Uploading a model. Click the picture for the full page. Standardization is a very important part of any database and this one is no exception – all uploaded models should include all necessary elements and look the same. This is why it is important to have a specific uploading procedure and why we have made this example of how a team could upload a model to the iGEM modelling part registry.

Link to modelling database