Principles of Metastasis

I have recently become interested in the dynamics of metastatic spread, and together with colleagues at Moffitt Cancer Center, I have started to work on mechanistic models that look at the impact of the topology of the vascular network (e.g. here and here). When coming into this field I was surprised by the lack of work along these lines, and found that most people were delving deep into the genome of cancer cells to find the answers of why, where and how metastases appear.

I was therefore positively surprised to hear of the work of the late Dr. Leonard Weiss, who did a lot of work on metastases throughout his long career. In his work we find the physical perspective of metastatic spread that is almost completely absent in this gene-centric era. The other day I finally received his book "Principles of Metastases" from 1985, which I still believe to be highly relevant. A review will be posted when I've finished reading it, which should be soon.

The dynamics of cross-feeding

Many functions carried out by microbes, such as degradation of man-made toxic compounds, require the joint metabolic effort of many bacterial species. In such bacterial communities the success of each species depends on the presence or absence of other species and chemical compounds, effectively joining the components of the community into a microbial ecosystem. A common mode of interaction in such ecosystems is cross-feeding or syntrophy, whereby the metabolic output of one species is being used as a nutrient or energy source by another species.

I have together with my colleague Torbjörn Lundh formulated and analysed a mathematical model of cross-feeding dynamics. We show that under certain assumptions about the system (e.g., high flow of nutrients and time scale separation), the governing equations reduce to a second-order series expansion of the replicator equation. By analysing the case of two and three species we derive conditions for co-existence and show under which parameter conditions one can expect an increase in mean fitness.

The paper was recently published in Bulletin of Mathematical Biology:

http://link.springer.com/content/pdf/10.1007%2Fs11538-013-9828-3