Team:Valencia Biocampus/Modeling

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    	    <li class="active"><a href="#Modeling">Modeling overview</a></li> 
	    <li><a href="#BiobricksModeling">Briobicks Modeling</a></li>
	    <li><a href="#Single">Single worm behaviour</a></li>
            <li><a href="#Group">Group behaviour</a></li>
            <li><a href="#Pseudomonas">Wormboys in action</a></li>
            <li><a href="#System">System performance</a></li>
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== Modeling ==

The main goal in our modeling project is to accurately predict the behaviour of our system in several issues, from the mounting of bacteria on <i>C. elegans</i> to the performance of our worms reaching the place of interest. In order to do that, we use several modeling techniques.
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<br>The movement of <i>C. elegans</i> 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.
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<br>The workflow is the following:
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<br><i>Add diagram showing the steps done</i>
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[[File:Primer_paso.jpg]][[File:Segundo_paso.jpg]][[File:Tercer_paso.jpg]][[File:Cuarto_paso.jpg]][[File:Quinto_paso.jpg]]

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== Biobricks modeling ==

In this section, clumping and PHA production are modeled and fitted to a equation. These things will be considered in other sections.
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== Clumping ==

== PHA production ==

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== <i>C. elegans</i> behaviour ==

In the first place, we model <i>C. elegans</i> behaviour in the absence of chemoattractant and bacteria. When no chemotactic source is present, <i>C. elegans</i> 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 <i>Matlab</i> or <i>R</i>. Simulation is used to test the fiability of the model. The equations are the following:
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<br> <i>Add equations</i>
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<br>Simulations were performed in <i>Matlab</i>, proceeding as described in (Pierce-Shimomura <i>et al.</i>, 1999). We contact with the authors but they could not provide us the code, so we developed our own script based on the article, obtaining similar results.
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<br> <i>Add simulations</i>
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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, <i>C. elegans</i> moves in a similiar fashion as <i>E. coli</i> (Bargmann, 2006), a mechanism called <i>the pirouette model</i> (Pierce-Shimomura <i>et al.</i>, 1999). Following this model, we defined the turning rate as a function of <i>dC/dt</i>. Simulations were performed as expected, showing a bias in the random walk:
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<br> <i>Add simulations</i>
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----
Bargmann CI (2006) <i>Chemosensation in </i>C. elegans. Wormbook <br> 
Berg HC (1993) <i>Random walks in biology</i>. Princeton, NJ: Princeton UP.<br>
Pierce-Shimomura JT, Morse TM, Lockery SR (1999) <i>The Fundamental Role of Pirouettes in </i>C. elegans<i> Chemotaxis</i>. The journal of Neuroscience, 19(21):9557-9569<br> 

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== Group behaviour ==

In practice, a single <i>C. elegans</i> is not employed to perform the task but a group of worms. In this case, the random walk equations obtained for a single worm behaviour can be transformed into partial differential equations (PDEs) to depict the distribution of the population, as the ones describing a diffusion process.
<br><i>Mathematical demonstration of macroscopic RW as a diffusion process. Link?</i>
<br>The equations are the following:
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<br> <i>PDEs</i>
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<br>However, in our case we face a diffusion system with drift, in which the last term arises from the biased movement of <i>C. elegans</i>. To obtain a PDE that reflects this behaviour, we employed difference equations using Taylor series and apropiate limits
<br><i>Mathematical demonstration of C. elegans chemotactic behavior using PDEs from biased random walk employing the pirouette model. Link? Propeties as mean or SD calculated from the equation?</i>
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<br> <i>PDEs. Parameters, as diffusion coefficient (D) or drift force (b) can be calculated form (Pierce-Shimomura, 1999)</i>
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<br>Now, we can predict the behavior of a set of worms in presence of a chemoatractant. Simulations were run using <i>Matlab</i>. As seen, the distribution
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<br><i>Add simulation</i>
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== Wormboys in action ==

Once defined the behaviour of a set of worms with no bacteria attached, we can model the action of microorganisms while they are riding <i>C. elegans</i>. In our model, bacterial substrate and worm chemoatractant are the same molecule, so it is consume while <i>C. elegans</i> is moving through the place. This alters the pattern of the molecule of interest, modifying the trajectory of the nematode. To take into account this feature of the system, a reaction term is added in the previous equation.
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<br><i>PDE</i>
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== 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.


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