How can we graph resilience?

I’m interested in understanding resilience, which measures how biological systems can be stressed out of shape and then bounce back to their original form, or break and enter a new state.  Our first two papers on this subject looked infections in flies, mice and humans.

(http://dx.doi.org/10.1371/journal.pbio.1002436, http://dx.doi.org/10.1371/journal.pbio.1002435)

My idea was that we could make maps of the paths sick individuals trace as they move from health, through sickness and back to health through recovery.  My group found that sick individual trace loops through “disease space” and that sicker individuals take larger loops; for example if we look at how red blood cells and parasites change over the course of an malaria infection in mice the mice trace a path over time moving from the thin to the thick area of the curve.  First the parasites grow, without changing RBC number, then the RBCs crash while the mouse starts to clear the parasites and then the mouse starts to recover.  The colors show what is happening in each part of the graph.  The green part denotes “comfort”.  Blue denotes sickness and yellow recovery.  We are especially interested in the recovery part of disease space because that is what we want to happen when we get sick.

RBC by parasites

To figure out how whether sick individuals were deviating from the safe path of resilience, we used a trick suggested to us by our co-author Ann Tate; instead of plotting the graph on Cartesian coordinates, we transformed the data to polar coordinates.  What this means is that instead of giving each point an (x,y) position, we defined the point by an angle and a radius.  The advantage of this is that the non-resilient mice had statistically different radii, which made them easy to identify using relatively small amounts of data.

I am satisfied, for now, with the way I can display these data in print.  I think there are better ways to do show of the data when I’m are standing in front of my poster at a meeting or when a stranger in the airplane seat next to us asks me what I do.  Instead of waving my hands in the air or drawing on a napkin, I plan to come prepared with props that I will describe in the next few posts.

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