Ever been in a sandpit? When I was asked to be in one (called the Applied Maths Sandpit at our new EPS faculty.) I was not sure what it would be. It could be an innocent fun activity in the sand as in the first picture, an unlikely dream holiday at a golf course (as in the second picture), or, most likely, a grueling day which I was not forewarned of (third picture). As it turns out, it was rather nice and, ultimately, useful. There was no sand around, of course! (and neither was there much warm Sun, unsurprisingly for here).
For a start, I met a few brilliant colleagues I did not know existed. Then, in a day of real intense cut-throat Dragon’s den like competition, we pitched our, mostly half-baked, ideas (btw, I am joking about the ‘cut-throat’, after all, we were (applied) mathematicians, not MBA enterpreneurs at the gathering!). Amazingly, at the end of it, our emergently formed motley crew of me, Fred Currell, Thomas Huettemann, Dermot Green and Alessandro Ferraro (All except me from QUB Maths and Physics) have been given resources to recruit and spoil a PhD student for a proposal that makes up the ideas of this post.
So, here comes a very high level, sparse, ambitious, and rough sketch:
Living organisms can be thought of as clusters of cells in communication (typically at gap-junction interfaces). Within interacting communities new cells are born and old ones are removed, through (sometimes programmed) death. There is a strong environmental influence on these processes. On a much smaller scale, quantum-mechanical processes are at work within cells, complicating the picture further. We think real life processes are efficient, fault-tolerant, self-healing and scalable, leading us to hypothise that there must be powerful distributed algorithms somewhere in these networks of cells waiting to be discovered.
Networks are often modelled as a graphs: the cells are nodes and a common surface between two cells facilitates communication. In biological systems, things change and this dynamism in networks is often addressed by failure models, including adversarial and accidental (random) death. The network can react to these changes in various ways and we seek a mathematical framework in which to formulate and analyse the various questions arising.
The team thought of three systems which could be of interest (some of the team already work on these though I know little about them at the moment):
- Volvocine green algae — These capture the evolutionary emergence of multicellularity, including what is believed to be the simplest multi-cellular eukaryotic organism: Tetrabaena socialis.
Rough outline of phylogenetic relationships in volvocine green algae.
- Light harvesting in photosynthetic organisms — the mechanism whereby living organisms harvest energy from light is believed to be one of the clearest biological systems countering the view that life is too “warm and wet” for quantum phenomena to be relevant.
A quantum machine for efficient light-energy harvesting (from the paper)
The tumour spheroid — a simple multicellular mimic of a tumour, this system is amenable to direct laboratory study and is known to show many of the hallmarks of cancer, including the lack of growth regulation mechanisms, meaning it seeks to grow avidly.
A study showing effects on size, shape and growth rate of tumours (from the paper)
The PhD advertisement is here (if you know of suitable candidates): http://www.qub.ac.uk/schools/eeecs/Research/PhDStudy/PhD-2016-17-65/
Talking of Maths sandpits, somebody is already working putting them to work: MathsSandPit.co.uk