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Team:Valencia Biocampus/Modeling
From 2013.igem.org
Modeling
The main goal in our modelling project is to accurately predict the behaviour of our system in several issues, from the mounting of bacteria on C. elegans to the performance of our worms reaching the place of interest. In order to do that, we use several modeling techniques.
The movement of C. elegans in the presence of a chemoattractant in order to carry our bacteria to that source is the main issue of our project, so we consider modeling this aspect and employing it as scaffold for the whole modeling project. Several layers show up that it must be modeled in different ways. In our approach, we mathematically describe each layer, from the simplest to the most complex, integrating each one.
Biobricks modeling
Modeling of the biobricks performance
C. elegans behaviour
In the first place, we model C. elegans behaviour in the absence of chemoattractant and bacteria. When no chemotactic source is present, C. elegans moves randomly. This behaviour can be modeled as a random walk (Berg,1993) and can be simulated in several steps using a programming language, such as Matlab. The equations of this model are the following:
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Simulations were performed in Matlab, proceeding as described in (Pierce-Shimomura et al., 1999). We developed our own script based on the article, obtaining similar results.
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Chemotaxis of a single worm
However, we are interested in the movement of the nematode in a gradient of a chemoattractant. In presence of a chemotactic source,C. elegans moves in a similiar fashion as E. coli (Bangmann, 2006), a mechanism called the pirouette model (Pierce-Shimomura et al., 1999). Following this model, we defined the turning rate as a function of dC/dt. Simulations were performed as expected, showing a bias in the random walk:
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Bangmann CI (2006) Chemosensation in C. elegans. Wormbook
Berg HC (1993) Random walks in biology. Princeton, NJ: Princeton UP.
Pierce-Shimomura JT, Morse TM, Lockery SR (1999) The Fundamental Role of Pirouettes in C. elegans Chemotaxis. The journal of Neuroscience, 19(21):9557-9569
Group behaviour
In practice, a group of C. elegans are employed to perform the task. In this case, the random walk equations obtained for a single worm behaviour can be transformed into partial differential equations (PDEs) as the ones describing a diffusion process.
Mathematical demonstration of macroscopic RW as a diffusion process. Link?
The equations are the following:
PDEs
System performance
The main objective of the project is employing the equations to describe a new, theoretical, solid-batch biorreactor and comparing it versus liquid-batch biorreactor.
