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Reaction-Diffusion System of 6 equations on 2D/3D shape (biological cell)

Posted Aug 26, 2018, 6:04 p.m. EDT Chemical, Chemical Reaction Engineering, Biosciences 1 Reply

Aaron Hagström
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Hello All, I am trying to simulate reaction-diffusion systems on a biological cell. I modeled it as a kind of a half-sphere in 3D and as a circle in 2D.

However, everytime I perform calculation, I get an unvarying color map. It is either all green or it shows color variation, but all values are virtually the same to 5 or 6 decimal digits.

Why might this be? Attaching 2D model for now. I am not entirely sure what might be the best initial conditions and parameters. Could that be the problem?

3D Hagstrom1.mph -1 surface-reaction module -1 dilute reaction

2D -6 coefficient-form PDE

1 Reply Last Post Aug 27, 2018, 1:47 a.m. EDT
Lasse Murtomäki
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Posted: 6 years ago Aug 27, 2018, 1:47 a.m. EDT

Hi

The model you attached apparently is in axisymmetric 2D geometry. If you draw a circle at some distance from the rotation axis, you actually get a torus.

The other question is that why should there be a spatial concentration distribution because your reaction is homogeneous and an impermeable boundary surrounds it?

Yet another question is the time span. In small domains diffusion has no meaning because the average distance a species travels by diffusion is d ~sqrt(D·τ) (Einstein 1905). Hence, time a species needs to lead a distance d is τ ~d²/D. Your domain radius is 0.08 cm and when the diffusion coefficient is of the order of 5·10^-6 cm²/s, τ ~1280 s. It is roughly the same as your simulation time; I am confused by the dimensions of the model, some variables dimensionless, some with dimension (such as the domain size).

If diffusion were meaningful in cells, our metabolism would be much slower due to diffusion limitation. I have thought that our cell size is just the right in order life to evolve.

I wish I did not completely misunderstood what you have done :)

Best regards Lasse

Hi The model you attached apparently is in axisymmetric 2D geometry. If you draw a circle at some distance from the rotation axis, you actually get a torus. The other question is that why should there be a spatial concentration distribution because your reaction is homogeneous and an impermeable boundary surrounds it? Yet another question is the time span. In small domains diffusion has no meaning because the average distance a species travels by diffusion is d ~sqrt(D·τ) (Einstein 1905). Hence, time a species needs to lead a distance d is τ ~d²/D. Your domain radius is 0.08 cm and when the diffusion coefficient is of the order of 5·10^-6 cm²/s, τ ~1280 s. It is roughly the same as your simulation time; I am confused by the dimensions of the model, some variables dimensionless, some with dimension (such as the domain size). If diffusion were meaningful in cells, our metabolism would be much slower due to diffusion limitation. I have thought that our cell size is just the right in order life to evolve. I wish I did not completely misunderstood what you have done :) Best regards Lasse

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