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Team:ETH Zurich/GFP
From 2013.igem.org
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<h1>The digital bacterial-based minesweeper</h1> | <h1>The digital bacterial-based minesweeper</h1> | ||
| - | We created a 2D spatio-temporal model of the Colisweeper bacterial game | + | We created a 2D spatio-temporal model of the Colisweeper bacterial game to evaluate our network and design. For the simulation, we used COMSOL Multiphysics. Most of the model parameters are derived from literature, and the rest are fitted. |
Note: For parameter values and references click on a parameter or see the [[Team:ETH_Zurich/Parameter| parameters section]]. | Note: For parameter values and references click on a parameter or see the [[Team:ETH_Zurich/Parameter| parameters section]]. | ||
<h1>Reaction-Diffusion Model</h1> | <h1>Reaction-Diffusion Model</h1> | ||
| - | In our first | + | In our first spatio-temporal model, we wanted to find out if (1) a suitable AHL gradient form at all and (2) validate the model with experimental data. Essentially we model the receiver cells (''E. coli'' DH5α strain) being transformed with a plasmid containing GFP. Subsequently, we simulate a 2D spatio-temporal reaction-diffussion system with COMSOL Multiphysics. |
<br clear="all"/> | <br clear="all"/> | ||
<h1>AHL: Reaction-Diffusion Equation</h1> | <h1>AHL: Reaction-Diffusion Equation</h1> | ||
<br> | <br> | ||
| - | + | The change of AHL concentration over time is influenced by two processes: (1)local chemical reactions and (2)diffusion; which causes the molecule to spread over the agar plate (Fig. 1). <br><br> | |
[[File:Rxn_Diff_AHL.png|500px|center|thumb|<b>Figure 1: General partial differential equation for AHL reaction-diffusion.</b> D(AHL('''r''',t),'''r''') is the diffusive term, R(AHL('''r''',t)) is the reaction term'']] | [[File:Rxn_Diff_AHL.png|500px|center|thumb|<b>Figure 1: General partial differential equation for AHL reaction-diffusion.</b> D(AHL('''r''',t),'''r''') is the diffusive term, R(AHL('''r''',t)) is the reaction term'']] | ||
<br clear="all"/> | <br clear="all"/> | ||
| - | For | + | For diffusion, we have a partial differential equation (Fig. 2) which describes density fluctuations over time and space. ''D<sub>AHL</sub>(AHL(r,t),r)'' denotes the collective ''diffusion coefficient'' for AHL at location r. However, we assume that the ''diffusion coefficient'' does not depend on the density, i.e., ''D<sub>AHL</sub>'' is a constant. The value reported in the literature for the ''diffusion constant'' corresponds to measurements performed in water at 25<sup>o</sup>C. Since diffusion in our system happens in agar, we scaled the ''diffusion constant'' by a factor C<sub>agar</sub> (Fatin-Rouge et al., 2004). <br><br> |
[[File:Diff_AHL.png|500px|center|thumb|<b>Figure 2: Diffusive term for AHL</b>]] | [[File:Diff_AHL.png|500px|center|thumb|<b>Figure 2: Diffusive term for AHL</b>]] | ||
<br clear="all"/> | <br clear="all"/> | ||
| - | For the reaction component, the change of AHL concentrations | + | For the reaction component, the change of AHL concentrations over time is given by an ordinary differential equation (ODE), that comprises production and linear degradation. The synthesis of the signalling molecule depends on the product of ''luxI'' gene. Now for the degradation, we consider that AHL degrades at different rates depending on the localization, i.e. cytoplasmic or extracellular. Given that the intracellular degradation is driven by enzymatic degradation, whereas the extracellular decay is a non active process. Our model also includes a dilution factor due to the cell growth (Fig 3). <br><br> |
| - | [[File:Reaction_Term_AHL.png| | + | [[File:Reaction_Term_AHL.png|450px|center|thumb|<b>Figure 3: Reaction term for AHL</b>]] |
<br clear="all"/> | <br clear="all"/> | ||
Revision as of 12:54, 12 September 2013
The digital bacterial-based minesweeper
We created a 2D spatio-temporal model of the Colisweeper bacterial game to evaluate our network and design. For the simulation, we used COMSOL Multiphysics. Most of the model parameters are derived from literature, and the rest are fitted. Note: For parameter values and references click on a parameter or see the parameters section.
Reaction-Diffusion Model
In our first spatio-temporal model, we wanted to find out if (1) a suitable AHL gradient form at all and (2) validate the model with experimental data. Essentially we model the receiver cells (E. coli DH5α strain) being transformed with a plasmid containing GFP. Subsequently, we simulate a 2D spatio-temporal reaction-diffussion system with COMSOL Multiphysics.
AHL: Reaction-Diffusion Equation
The change of AHL concentration over time is influenced by two processes: (1)local chemical reactions and (2)diffusion; which causes the molecule to spread over the agar plate (Fig. 1).
For diffusion, we have a partial differential equation (Fig. 2) which describes density fluctuations over time and space. DAHL(AHL(r,t),r) denotes the collective diffusion coefficient for AHL at location r. However, we assume that the diffusion coefficient does not depend on the density, i.e., DAHL is a constant. The value reported in the literature for the diffusion constant corresponds to measurements performed in water at 25oC. Since diffusion in our system happens in agar, we scaled the diffusion constant by a factor Cagar (Fatin-Rouge et al., 2004).
For the reaction component, the change of AHL concentrations over time is given by an ordinary differential equation (ODE), that comprises production and linear degradation. The synthesis of the signalling molecule depends on the product of luxI gene. Now for the degradation, we consider that AHL degrades at different rates depending on the localization, i.e. cytoplasmic or extracellular. Given that the intracellular degradation is driven by enzymatic degradation, whereas the extracellular decay is a non active process. Our model also includes a dilution factor due to the cell growth (Fig 3).
