Reaction diffusion model

[suman Gare]

Hello, 

I want develop a reaction diffusion model in Morpheus. In work I want to take two type of cells one is secreting a chemical other cell is up taking it. That interaction lead to the change the status of second cell. and they are moving in a spatial environment. Can you you help in constructing a model for this. 

[Lutz Brusch]

Dear Suman,

thank you for this question, this is easy to do in Morpheus. I attach such a model (xml) which you can open in the Morpheus-GUI to inspect and change all aspects. 

There are two cell types (besides medium): cell_secreting (which secretes U with flux p into the Global/Field U.external) and cell_receiving (which takes U up from U.external with rate d and accumulates it in U.internal, when U.internal exceeds U.threshold=500 then cell_receiving changes its state U.superthreshold from 0 to 1). The chosen CPM settings let cells of different types repel each other and let cell_receiving chemotax upward the U.external gradient.

The attached figure shows an intermediate state where U.external is shown on a white-yellow-red scale with isolines in the background. Receiving cells are color-coded by their U.internal as given by the color bar. The number (0 or 1) in each receiving cell is the state of U.superthreshold.

Please also read the descriptions of related models like autocrine chemotaxis (https://identifiers.org/morpheus/M0031) and the cAMP dynamics during dictyostelium aggregation (https://identifiers.org/morpheus/M0034). 

You can extend that model by different motility modes and by new cell behavior once U.superthreshold has switched to 1. Also the field U.external may get extra reaction terms (for an example see: https://identifiers.org/morpheus/M0012).

Best,

Lutz

[suman Gare]

Hello,

Thanks for your help. I have a question about how the diffusion equation is solved in morpheus. If I want to include the boundary conditions for each cell separately how to do that. 

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Thanks and Regards

Suman Gare

Research Scholar

Indian Institute of Technology, Hyderabad

Ph. No: +919494786284

[Lutz Brusch]

Hello,

the diffusion solver allows for heterogeneous diffusion coefficients as expressions of any other symbol (please see https://morpheus.gitlab.io/post/2023/01/09/morpheus-2.3-release-notes/#fields) such that you can set it different (e.g. to zero) inside versus outside of cells (and individually for each cell or each cell type). 

You may also limit secretion to the surface of cells with a MembraneProperty inside CellType (please see https://identifiers.org/morpheus/M5482).

However, the 2D models are often constructed as a projection of the z-dimension in the actual 3D system onto the x-y plane. In 3D, molecules are also secreted along the top and bottom (in z) membranes of the cell and can diffuse in the medium above or below the cell. In 2D, that corresponds to secretion and uptake inside the 2D cross section of the cell and to diffusion of molecules "through" the 2D cross section of the cell.

The overall domain boundary can also get different boundary conditions for fields of cells, for this please see the In-App documentation panel in the GUI.

Best,

Lutz