Proliferating Active Matter - 1/N

These are some unpolished broad thoughts on my recent focus on growth as a source of activity in condensed matter. I am now transcribing my scientific rants. If given tenure I will resort to writing review papers on my rants. So life goes on.

Let's consider the hydrogen atom of biology: the cell. What do I mean by growth? The changes in size? The changes in density? Ageing? All of it. But I want to talk about proliferation here.

My first introduction to growth as a source of activity was in the context of bacterial range expansion, specifically this work by Hallatschek et al, which explains how two strains of E. Coli. (one labelled by GFP, one by RFP) when plated initially in a well-mixed manner, segregate into sector-like patterns. I was fresh out of undergrad and studying how lambda-phages infect bacteria. Birth and death processes lead to interesting spatiotemporal patterning in these systems and these bacteria being non-motile, the dominant source of motion and activity is growth. How do elongated, nematically aligning, growing colonies of bacteria behave? How does one model them? How do I see sector-like segregation in a continuum theory? What do the sector boundaries look like in this case (a random walk?) I don't have answers to a lot of these questions but Zhihong You's PhD thesis does begin to shed some light on how one goes about approaching such a problem. 

I digress. 

Proliferation. Growth. Usually ignored because of a "separation of timescales" argument in active matter theories that aim to capture biological phenomena from the most in-vivo morphogenesis to the most in-vitro tissue-rheology. Consumption of energy and motion happens in most systems on a much faster timescale than cell-division. This is the separation of timescales assumption. If one wants to study the response and flow of biological systems, proliferation can be kept at bay. Sometimes, biologists can actually "fix" the cells in a specific point of their cell-cycle so that they do not divide. This is controversial in many ways but the most obvious to me is that cell properties change drastically during the cell cycle. Physicists are only studying the properties "averaged" over the cell-cycle. If you fix the cells to be in one stage, you're studying cell-behaviour that is stage-specific. I digress again. But yes, proliferation can be, and usually is, stowed away as a long-time-scale process that is somebody else's problem. I want to be that somebody else.

Now you can argue that plants are a system where proliferation is the only way (in majority of cases) to activity and that I should probably jump a kingdom away from animalia to plantae and study proliferation all I want. But I am trying to convince myself, you, and possibly my funding sources, that animalia is rife with proliferation and we need to stop ignoring it.

Birth-death processes are boring because they impose homogeneity. This is still a sentence that bounces around my head like the DVD logo on old TV screens. This one paper by Cates and company changed my view of the problem: malthusian material undergoing phase separation forms arrested droplets! Not so boring after all. Birth by itself may seem like nothing but a never-ceasing pressure wave but coupled with cell-death it sings a different tune.

Actually Sujit Dutta and friends did a better job of convincing physicists that proliferation is cool. I would recommend reading that review. 

If I am to be that somebody else who thinks about growth as a source of activity, I need to do something about it. I made my first attempt at it recently. I studied "growing nematics" aligning to external fields and found out that jamming and birth-death processes can lead to a strong dependence on initial-conditions in these systems. This doesn't sound like much but it is very surprising to somebody who is used to looking at plots of quantities averaged over initial conditions: they usually don't matter in the grand scheme of things. 

Next up: I will try to understand and report the consequences of breaking density conservation in statistical-mechanics.