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Team:KULeuven/Modelling/Vanillin Receptor
From 2009.igem.org
Vanillin diffusion
intro
Because the VirA protein sensor domain is located in the cytoplasmic region, it senses intercellular vanillin concentration. Because the objective of this project is to regulate the extracellular vanillin concentration we investigate the relation between the intercellular and extracellular vanillin concentration. It will be shown that on the time-scale we are interested in, intracellular and extracellular concentration are equal.
We can approximate the relationship with following continuity equation (equilibrium in cytoplasm and extracellular):
<math>d[V_inter]/dt = V_production-k_diffusion(V_inter-V_extra)</math>
V_inter: intercellular concentration V_extra: extracellular concentration V_production: production of vannilin k_diffusion: speed of diffusion in and out cell
rewriting the above equation gives <math>V_extra = V_intra+1/k_diffusion*(d[V_inter]/dt - V_production)</math>
If the k_diffusion is big, on the time-scale we are interested in, we are not interested in phenomena which occur within 1 minute, V_extra and V_intra can be regarded as equal.
simulation
The following more exact treatise will try to determine the time scale on which the vanillin concentration reaches equilibrium conditions (V_extra = V_inter). The process is described by following (more general) continuity equation:
<math> d[V]/dt = V_production+k_degradation*V+d[D_V*d[V]/dx]/dx</math>
V: Vanillin concentration V_production: Vanillin production k_degradation: speed of degradation but will here be considered 0 D_V: diffusion coefficient of vanillin
Inner Membrane thickness: 8 nm
Outer Membrane thickness: 12 nm
Periplasm thickness: 10 nm
We neglect the outer membrane because the porins make the membrane permeable.
