I read the above paper. Re-read several parts of it, actually. It may be that this was the first modeling paper I read to discuss pattern formation in cell masses (I've got a couple more waiting in my stacks now), but I found the principles and mechanisms laid out in this paper to be both profound and eye-opening. I didn't care much about how cyclical chemotactic signaling in Dictyostelium affects its cell differentiation, but it was still interesting in light of everything that had been previously discussed (I probably wouldn't have read the paper if it was only about Dictyostellium).
Normally we think about squishiness and stickiness as being separate properties of a material. For example, ice cream is both squishy and sticky but Jello is only squishy. Compared to Teflon, wood is sticky but not squishy. This paper integrated squishiness and stickiness on the cellular levels as the net effective surface energy of a given cell through the lens of physics models of foams. While it is possible that I was just being unobservant, this seems like a major intuitive leap forward. We know that cells interact with one another through various chemical interactions, whether it is simple polar interactions as lipid-rich plasma membrane innately repel each other or more complex composite polar interactions as the proteins embedded in those membranes are differentially attracted to each other. This paper summarized this as sticky cells have a high effective surface energy tied up in interactions with neighboring cells (or media/substrate) that holds them together while squishy cells have a lower effective surface energy and are therefore deformable because there is a lower entropy cost to do so. Essentially, it is easier to fall when you're only held up by a couple of thin supports (a late stage of a Jenga game), but much more difficult to do so when there are lots of solid supports (new Jenga game).
This paper didn't stop there though. It kept going.
Then they discussed chemotactic dynamics when there are 2 types of cells in a confined volume and the differences that may arise:
1) Pressure gradient: with Big cells and Small cells responding equally (to same degree and direction of chemotaxsis) to a given uni-directional chemotactic signal, the Big cells will get pushed in a direction opposite to the chemotactic signal. This occurs because Small cells form a pressure gradient that acts upon the larger surface area of the Big cells to accumulate a pressure differential between the leading and trailing edges (anisotropy). Small cells have a smaller effective surface area per given volume and can therefore tie more energy up in bonds with neighbors in a given volume than large cells, allowing them to cluster together more efficiently and form the pressure gradient.
2) Minority sorting: for this to occur, there must be a difference in the interactions of the 2 cells types such that the energy of interaction of like + like (of either cell type) is greater than the energy of interaction of like + different (also known as differential adhesion). Therefore, if there are fewer Jelly cells than Jam cells, more Jelly cells will have lower surface energy because they will numerically be bordered by more Jam cells and will thus have an entropic incentive to migrate together and get clumpy (although clumps can act like big cells within the pressure gradient). Furthermore, this doesn't just work with unequal cell populations, it'll also work with equal so long as the difference in energy of interactions is large enough.
3) Probability of moving: is energy of new conformation lower than energy of present conformation? If so, the probability that a cell will move to that conformation is greater. This is a lot like chemistry and orbital excitation, but cooler.
So, I thought that the paper was well-written, concise, and very interesting. Read it!
Käfer, J., Hogeweg, P., & Marée, A. (2006). Moving Forward Moving Backward: Directional Sorting of Chemotactic Cells due to Size and Adhesion Differences PLoS Computational Biology, 2 (6) DOI: 10.1371/journal.pcbi.0020056
Music for the Revolution
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