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Modelling the 3D whole cell biosensor
Posted 25 apr 2015, 07:57 GMT-4 Microfluidics, Chemical Reaction Engineering Version 5.0 3 Replies
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Hi friends,
I have been trying to learn the COMSOL to do the modelling for whole cell biochips. I have this problem which involves reaction- diffusion equation. So basically my chip is an electrode and which can sense the product of an enzyme reaction. whereas the enzyme reaction is taking place inside the cells which are kept on top of the chip separated by a distance l. The first boundary condition is at x=0 (at the electrode) which says that the flux due to electrochemical oxidation reaction is equal to diffusion flux (of the product). where as the second boundary condition says at x=l , there is no outflux.
I am trying to do it but getting mostly errors.. Can someone help me solve this.
I have been trying to learn the COMSOL to do the modelling for whole cell biochips. I have this problem which involves reaction- diffusion equation. So basically my chip is an electrode and which can sense the product of an enzyme reaction. whereas the enzyme reaction is taking place inside the cells which are kept on top of the chip separated by a distance l. The first boundary condition is at x=0 (at the electrode) which says that the flux due to electrochemical oxidation reaction is equal to diffusion flux (of the product). where as the second boundary condition says at x=l , there is no outflux.
I am trying to do it but getting mostly errors.. Can someone help me solve this.
3 Replies Last Post 25 apr 2015, 14:26 GMT-4
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Posted:
10 years ago
From your description I don't fully understand your equations but it seems to me perhaps you are underconstraining the system and it can't converge. What controls the incident rate of flux of the reagent?
You've set that the flux of reaction product equals the flux of the reagent but that, it seems, is automatically taken care of by the continuity equation in the bulk and so I don't see that does anything -- in fact it may be a form of overconstraint.
What you want, I think, is to specify a specific reagent boundary condition, for example flux density or concentration, to drive the reaction.
Pardon me for being rather rusty on this stuff but I'll do my best. Consider where I have a local reaction equation:
A + B <-> AB
The stationary continuity equation for this is (1D):
-d/dx flux A = -d/dx flux B = d/dx flux AB
So if A is disappearing then B is disappearing and AB is appearing. No extra boundary condition required.
Then you can have some sort of reaction rate, for example:
d/dx flux AB = (A B - AB0) / [ tau ( A + B ) ]
where AB0 is the equilibrium product of A and B.
This is 3 equations for 3 unknowns but you need to provide some sort of boundary conditions for A or flux A, B or flux B, AB or flux AB.
I could be wrong here and I likely made a few mistakes but I think your boundary condition is clearly a concern.
You've set that the flux of reaction product equals the flux of the reagent but that, it seems, is automatically taken care of by the continuity equation in the bulk and so I don't see that does anything -- in fact it may be a form of overconstraint.
What you want, I think, is to specify a specific reagent boundary condition, for example flux density or concentration, to drive the reaction.
Pardon me for being rather rusty on this stuff but I'll do my best. Consider where I have a local reaction equation:
A + B <-> AB
The stationary continuity equation for this is (1D):
-d/dx flux A = -d/dx flux B = d/dx flux AB
So if A is disappearing then B is disappearing and AB is appearing. No extra boundary condition required.
Then you can have some sort of reaction rate, for example:
d/dx flux AB = (A B - AB0) / [ tau ( A + B ) ]
where AB0 is the equilibrium product of A and B.
This is 3 equations for 3 unknowns but you need to provide some sort of boundary conditions for A or flux A, B or flux B, AB or flux AB.
I could be wrong here and I likely made a few mistakes but I think your boundary condition is clearly a concern.
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Posted:
10 years ago
Hi..
In this problem..
the reaction is E+S--> P.. So the enzyme is fixed (inside the cell), the cell consume the substrate S and generate product P.. Now this product diffuses to the electrode and get oxidized electrochemically and give rise to a current.. Now my boundary conditions are
at x=0 (on the surface of electrode) Ks.P(0,t) =Dp.dP/dx, where Ks is reaction constant and Dp is diffusion coefficient.
at x=l dP/dx= 0
In this problem..
the reaction is E+S--> P.. So the enzyme is fixed (inside the cell), the cell consume the substrate S and generate product P.. Now this product diffuses to the electrode and get oxidized electrochemically and give rise to a current.. Now my boundary conditions are
at x=0 (on the surface of electrode) Ks.P(0,t) =Dp.dP/dx, where Ks is reaction constant and Dp is diffusion coefficient.
at x=l dP/dx= 0
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Posted:
10 years ago
That seems good to me. Are you using a symmetry boundary for the 2nd boundary?