Microbes that see the future

Quite a few stories have come out recently about microorganisms that use one type of stress as a signal that they should prepare themselves for another stress. For example, an Escherichia coli bacterium on a piece of the salad you ate for lunch (let’s hope normal E. coli, not the pathogenic sort) may find itself traversing your digestive tract.  One of the first things it can observe about its new environment is that the temperature has gone up; soon afterwards, the level of oxygen goes down.  It turns out that the transcription of genes associated with dealing with oxygen starvation is induced by an increase in temperature.  It seems that E. coli has evolved a response that anticipates oxygen starvation when it sees a temperature elevation.  Another study found that when E. coli encounter lactose they upregulate the genes required for dealing with maltose (but not vice versa), mirroring the order in which the bacteria are likely to see these sugars as they traverse our guts.  In an artificial setting in which sugars are offered one after the other, wild-type E. coli grew better than a strain in which this anticipatory response is broken; in other words, the anticipatory response provided a fitness advantage.  There have been similar findings in other settings, for example the response of yeast to the conditions it encounters during the process of wine production.  Human pathogens such as Vibrio cholerae and Candida albicans appear to have responses like this as well.

Tzachi Pilpel and colleagues have contributed much to the idea that this so-called “predictive” behavior might be a general phenomenon.  In a recent paper, they set out to develop a theoretical framework for analyzing the costs and benefits of an anticipatory response (Mitchell and Pilpel, 2011, A mathematical model for adaptive prediction of environmental changes by microorganisms.  PNAS doi:10.1073/pnas.1019754108).  The problem here is simple: when a cell upregulates a set of genes that it doesn’t immediately need, it starts paying a cost.  Some time later, the genes start to be useful, and it gains an advantage.  How far ahead can you start paying the cost, and still find the advantage worthwhile?  And if the gap between the first signal and the second signal is variable, how fast does that erode your ability to gain an advantage from anticipation?

The general form of this problem may be familiar to you from the discussions people have about retirement planning. [Or perhaps it isn’t, if you live in a country where retirement planning is less of an obsession than it is in the US — every time I log into my bank account I get a screen asking me whether I’m saving enough for retirement.  The answer is always “probably not”, which is disheartening.  Then again, that’s what happens when you tell the calculator that you plan to live forever.]  When you start saving for retirement, you pay a cost; you reduce your standard of living now in an attempt to improve your standard of living later.  But, of course, you don’t know exactly how long you need your retirement savings to last.  So what’s the right amount to save?  I think people probably solve this problem less efficiently than bacteria.

The mathematics of marriage, or, less happily ever after

An article I recently ran across in PLoS One (Rey J-M, 2010 A Mathematical Model of Sentimental Dynamics Accounting for Marital Dissolution. PLoS ONE 5: e9881 doi:10.1371/journal.pone.0009881) sets out to provide a mathematical framework for understanding why many marriages fail.  I’d say that qualifies as a topic of general interest, though many might doubt the ability of mathematics to offer insight.  As so often with mathematical treatments of complex problems, one of the key benefits of creating the model is that it forces you to make explicit your assumptions.

Rey’s basic assumptions are these:

1. The initial level of mutual affection, x(0), has a natural tendency to decline at a constant rate, r. Rey calls this, pessimistically or realistically depending on your point of view, the second law of thermodynamics for relationships.

2. Efforts made by a couple (c) can increase the level of mutual affection (x) with a certain efficiency (a)

3.  Effort has a cost, D.  The cost is not monotonic; some efforts are pleasurable. The cost of effort is at a minimum (and negative) at a particular level of effort, c*, and goes up from there.

4.  There is a utility function, U (the happiness you derive from your relationship), that increases with the level of mutual affection but eventually plateaus.

Friday Feature: A natural curve

As your Friday treat, here is an amazing image Felice Frankel made for Walter Fontana’s group, as a cover suggestion for their recent paper on curvature in metabolic scaling (Kolokotrones T, Van Savage, Deeds EJ, Fontana W. 2010. Curvature in metabolic scaling. Nature 464 753-6.PMID: 20360740). There’s a lot of substance to this image, and it’s really too bad that the issue of Nature the paper ended up in happened also to be the one that celebrated the 10th anniversary of completing the human genome.  Some things are hard to compete with.

So what’s going on here?  In this paper, Kolokotrones et al. take on the ancient assertion that basal metabolic rate scales as body mass to the pth power, and the huge debate over what, in that case, p might be.  Some say 3/4; others 2/3; others, that it all depends. To all of these, Kolokotrones et al. respond “well… kinda”.  Using a new data set that (among other things) permits better correction for temperature, they show that the best fit for a log/log plot is not a straight line, but a curve.  This, for the first time, makes sense of both the smallest animals and the largest: the orca (top right) has always been an outlier before.  It now becomes clear why it has been hard to identify a single value for p — it depends where you take the tangent to the curve.

Building better biology

The very first paper from Ron Milo’s lab (Bar-Even A, Noor E, Lewis NE, Milo R. Design and analysis of synthetic carbon fixation pathways. Proc Natl Acad Sci U S A. 2010 107 8889-94. PMID: 20410460)  is out in PNAS — congratulations, Ron!

This is a nicely done theoretical/computational study asking whether it is possible to increase the overall efficiency of photosynthesis.  People have tried to increase the efficiency of RuBisCo, the primary enzyme that performs the carbon fixation step but unsurprisingly (well, I’m not surprised, don’t know about you) this turns out to be hard.   Bar-Even et al. point out that there are many different carbon fixation strategies in nature, and in a gedankenexperiment we might call “virtual gene shuffling” they ask whether one could re-assort naturally occuring enzymes from different pathways to create a new, hybrid pathway with better efficiency.