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Team:KULeuven/Modelling/Vanillin Receptor
From 2009.igem.org
Vanillin diffusion
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 equation
Continuity equation: <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.
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.
