Team:ETH Zurich/Modeling/Microfluidics
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* [[Team:ETH_Zurich/Modeling/Parameters#Microfluidics_Model|v<sub>max,AcAl</sub>]] is the maximum reaction rate, i.e. the rate the toxic molecule degradation reaction occurs with at saturation point, and | * [[Team:ETH_Zurich/Modeling/Parameters#Microfluidics_Model|v<sub>max,AcAl</sub>]] is the maximum reaction rate, i.e. the rate the toxic molecule degradation reaction occurs with at saturation point, and | ||
* [[Team:ETH_Zurich/Modeling/Parameters#Microfluidics_Model|K<sub>M,AcAl</sub>]] is the Michaelis Menten constant, i.e. the Acetaldehyde concentration at which the reaction rate is half of [[Team:ETH_Zurich/Modeling/Parameters#Microfluidics_Model|v<sub>max,AcAl</sub>]] | * [[Team:ETH_Zurich/Modeling/Parameters#Microfluidics_Model|K<sub>M,AcAl</sub>]] is the Michaelis Menten constant, i.e. the Acetaldehyde concentration at which the reaction rate is half of [[Team:ETH_Zurich/Modeling/Parameters#Microfluidics_Model|v<sub>max,AcAl</sub>]] | ||
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+ | === Estimation of [[Team:ETH_Zurich/Modeling/Parameters#Microfluidics_Model|v<sub>max,AcAl</sub>]] === | ||
--- Degradation of toxic molecule --- | --- Degradation of toxic molecule --- | ||
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Revision as of 16:28, 17 September 2011
Microfluidics Model |
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In our first spatiotemporal model, we wanted to find out if an Acetaldehyde gradient would be formed at all. The idea was to generate it as an equilibrium of Acetaldehyde diffusion out of the reservoir into our channel and Acetaldehyde degradation by the cells in it. In order to answer this question, we modeled a spatiotemporal reaction-diffusion system in 3D with COMSOL Multiphysics. |
OverviewIn our inital model, we chose a 5 cm long cylindrical channel with a radius of 1 mm (or equivalently 2 mm diameter). This channel is connected to a reservoir filled with medium and acetaldehyde. For the purpose of modeling the diffusion and degradation of acetaldehyde in the channel, we assumed that the reservoir has constant acetaldehyde concentration (or equivalently has infinite size). |
DiffusionFirst of all, we have to model diffusion of Acetaldehyde from the reservoir to the closed end of the microfluidics channel. The relevant partial differential equation is the one for isotropic diffusion, i.e. diffusion that is uniform in all directions: For the relevant diffusion parameter, DAcAl, see the microfludics model section on the parameters page. |
DegradationCell DensityIn order to able to determine how much Acetaldehyde our smoColi cells are able to degrade, we first need to determine the cell density of the immobilized cells in agarose. For this calculation, we assume we have a cell culture with OD600 with which we fill the channel. Parameter-wise, to determine the relative cell density in the channel voume, we need to know:
A parameter we can choose suitably is the dilution of the cells in agarose, cDilution. Then we can calculate the relative cell density in the smoColi-agarose-filled microfluidics channel: Enzymatic DegradationNow that we know what the cell concentration in the channel is, we can model the degradation of the toxic molecule by the cell culture in agarose. This process, together with diffusion of more toxic molecules from the reservoir, will finally generate the toxic molecule gradient. In our enzymatic degradation model, we assume diffusion into the cells is fast compared to the degradation process. The degradation process then is modeled using Michaelis-Menten enzyme reaction kinetics: The constants are the usual ones for Michaelis-Menten-type reactions:
Estimation of vmax,AcAl--- Degradation of toxic molecule --- |
SimulationTo see if we can indeed create an acetaldehyde gradient, we first solved for the gradient steady state in the channel. We chose an acetaldehyde concentration of 100 mg/l for the reservior in these simulations. Steady StateWe can see that the diameter does not influence the mean dynamics of the acetaldehyde gradient. We note that there may be stochastic behavior for very thin channels, since there will be only very few cells. For the channel diameter we chose a mean field approximation should be sufficient though as the amount of cells involved in the degradation is sufficiently high. DynamicsWe were also interested in finding out the time scale which is needed to create the gradient. Therefore we also analyzed the dynamics in a spatiotemporal reaction (degradation) - diffusion simulation. |