Modeling

Overview

An important part of our project is devoted to the concrete realization of a lemon by moulding it from agar gel. It is well explained in the lemon shaping part.

But, before starting more investigations and more experimentations, there is a real need to ensure that our project is feasible. We will tackle these following points :

• By cutting a lemon, there is a slight color yellow / green on the surface and white on the inside. To reproduct this effect, we use a kill-switch system based on oxygen and had been achieved by the team iGEM Paris Saclay 2013. The more we penetrates into the gel, the less oxygen is present, the less kill-switch system is activated, the less bacteria will produce desired color, and the more interior is white. For this, we must ensure that oxygen does not penetrate completely into the lemon.

• A major issue is the development of our bacteria in an agar medium. We noticed that the bacteria inside the gel grew less than those on the outside. Without development of our bacteria, we cannot realize anything.

• To be even closer to the reality, we will imitate the ripening process of a real lemon. We wanted to test if we could get a green color by fusion of two chromoproteins one yellow and one blue.

• Lastly, we obtain the lemon scent by modifying E.coli in order to let it produce pinene, limonene and geraniol but this do not ensure us that we will smell the lemon fragrance.

For all these reasons, modeling is really important for the concrete realization of our artwork and in general in an iGEM project!

Oxygen Diffusion

Is it possible to have a crust on the surface of the lemon by producing a "lemon coloration-like" by our bacteria ?

To answer this question, we note that E.coli can live in an anaerobic environment. Thus, with this property combined with the ease of access to oxygen, we solve the problem by making our E.coli react only in contact with oxygen. Since we just want a crust, it is not necessary that all our bacteria react. Hence the necessity to estimate the penetration of oxygen into the gel. We invite you to discover how we modelled the oxygen diffusion.

Bacterial Growth

Now that we know if bacteria could develop in agar or not, a natural issue is to predict the bacterial growth.

Without spoiling, we can just say that the previous model confirms the intuition we could have : while oxygen can't easily move into the medium, the growth on the surface area is sufficiently more important than into the medium to neglect the latter. More precisely, our bacteria is colorful and the surface will be entirely covered before internal bacteria have time to develop enough to be visible. Finaly, when we could hope to observe internal bacteria due to their color, the surface bacteria have already done an opaque layer.

So, this part aims at predicting over time the bacterial population growth on an ellipsoidal object - a fake lemon in practice -.

More precisely, we have to determine the initial proportion of bacteria threshold from which we are sure that the population will never extinct...if this threshold exists !

Fusion Protein

An important aspect of our project is the color transition from green to yellow, in order to emulate the lemon maturation.

To do this, we use a fusion protein. Before starting the fusion of the two chromoproteins -blue and yellow-, we have checked for their respective compatibility. That's why we will then discuss the structural modeling of the proteins.

Lemon Scent

We need criteria to assess the scent of lemon. For this, we have process as follow:

• We evaluate the evolution of the concentrations of this three fragrances over time.
• Give a procedure for estimating a suitable time interval in which we can say that we got the smell citronel as desired.

Note : Do not be afraid and run away because of seing mathematical formulae : Maths is fun and we have made a real effort to be as precise as possible in order non-mathematicians to understand. For example, in order not to disgust poor mathematical readers of others, we will just add one or two -for the warrior- star(s) to parts which need more mathematical background. Morever, we illustrated our work with figures which could be understood for themselves, without knowing the method to get them.