Medium Adhesion

11 weeks ago by
Hi all,

I'm wondering if I understand adhesion energy correctly for the adhesion contact plugin. So far, my understanding is that the energy hierarchy dictates behaviour.
For example, in the cell sorting demonstration, if cell type A is highly adhesive to self, one would set the energies hierarchy as A-A=1, A-M (medium) 10, and M-M 0, something like this. Roughly, as long as the hierarchy is correct, the sorting should be robust.
However, I have tested energies where A-M<A-A which should be that cell type A favors binding to medium rather than itself. I would expect cells to disperse into the medium.
Instead, I observe cells still adhering and forming a spheroid under these conditions. There appears to be a fine number for A-M where if A-M<A-A by slightly, cells will still adhere to one another rather than disperse.
The plugins I am using are volume, surface area, contact energy, center of mass ,neighbor tracker, and moment of inertia. I suspect that it is the volume and surface plugins, as they are the only possible energy terms in the probability distribution function.

Example energy for the 3D cell sorting demo.
<Plugin Name="Contact">
<Energy Type1="Medium" Type2="Medium">0</Energy>
<Energy Type1="NonCondensing" Type2="NonCondensing">14</Energy>
<Energy Type1="Condensing" Type2="Condensing">14</Energy>
<Energy Type1="NonCondensing" Type2="Condensing">14</Energy>
<Energy Type1="NonCondensing" Type2="Medium">10</Energy>
<Energy Type1="Condensing" Type2="Medium">10</Energy>
I have run simulations to 30k steps without significant dispersion. All neighbor order is 3.

Have I missed something obvious? Any help would be much appreciated. Thanks!

5 Answers

11 weeks ago by
So your thinking is not entirely correct regarding theory. Here is explanation:

Imagine you have two cells: 1, and 2
    |        |         |
    |    1  |   2    |
When they touch each other and the neighbor order is 1 the the contact energy associated with the interface between them is (per your simulation ) 14

Now, when you separate the two you are creating 2 interfaces (medium-cell1 and medium-cell2)

    -------     -------
    |        |     |         |
    |    1  |     |   2    |
    -------      ------

and each interface will "cost you" 10 units of energy so now you hav a choice - keep one interface and have energy associated with it 14/unit length or have 2 interfaces and have energy associated with the two 10+10=20/unit length

This is why if you want cell dispersion you need to lower then energy between cells and medium to around 7

Let me know if this makes sense

11 weeks ago by
"based solely on A-M=10 and A-A=14"
I think that might be where your thinking is off by a bit. The real situation would be;
      2(A-M)=20 versus A-A=14
When A-A separates it creates two A-M interfaces, each with the same length (or surface) as the single A-A interface length (or surface).
11 weeks ago by
Here is the rule of thumb you should apply:

if you want cells to stick to each other - make sure they have low (in relative terms) adhesion coefficient, if you want them to avoid each other make sure they have high adhesion coefficient (in relative terms). Another rule of thumb: avoid mixing positive and negative energy coefficients .

I think your overall understanding of adhesion energy coefficients is correct but in this particular case you may want to lower cell-medium adhesion

<Energy Type1="NonCondensing" Type2="Medium">2</Energy>
<Energy Type1="Condensing" Type2="Medium">2</Energy>

also it depends what temperature you have used in the system

Also medium-medium energy does not really matter

For completness I am attaching a simulation where dispersion does happen . All I had to do was to drop cell-medium adhesion coefficient

File attached: (7.39 KB)

‘avoid mixing positive and negative energy coefficients.’
Does this mean that all coefficients in contact plugin must be all positive or all negative?
written 11 weeks ago by dali Zan 
11 weeks ago by
Thanks for the reply. I understand that the energies can be set very high/different from one another to get desired dispersion/adherence.
My question is why can I break the cell adhesion hierarchy, established in the plos somitogenesis paper, which states that the order of energy is most important to yield desired behaviour.

A Multi-cell, Multi-scale Model of Vertebrate Segmentation and Somite Formation 

A-M=10 and A-A=14 yields adherence when theoretically, it should yield dispersion. I have tried this at T=10 and T=40. If I increase temperature, dispersion is more favored (due to unfavorable interactions being even more probable) but even at T=10 or 40, cells should disperse over time based solely on A-M=10 and A-A=14. I'm wondering if there's some unaccounted energy term that is also used in calculating the probability, which causes cohesion, aside from the volume and surface constraints used.

Hope that clear it up, thanks!
11 weeks ago by
That makes perfect sense. I knew I missed something obvious. Thank you both very much for the help!
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