Posted by: Dan | February 5, 2007

Search Strategies for Intermittent Olfactory Cues

(Entry #1 for the week of science)

Search strategies based on chemical attractants require concentrations of the chemical cues to be greater than the detection threshold. Regardless of whether the seeker is a bacterium in search of nutrients or a bloodhound on the trail – the same concept seems to apply – scents, odors and tastes are indeed nothing more than chemical cues. Massimo Vergassola and colleagues (2007) have an interesting letter out in Nature, which attempts to mathematically describe this search process in terms of an algorithm, ‘Infotaxis’ as a strategy for searching without gradients. Their premise is that:

In the dilute limit, the searcher detects odour in a sporadic sequence of distinct events arising from its encounters with patches of fluid (or air) where turbulent mixing has failed to dissipate the advected odour down to a level below the detectability threshold.

Figure3

Vergassola et al. describe the resulting behavior as a balance between exploration and exploitation, or ‘infotaxis,’ where at each time step, the searcher chooses the direction that locally maximizes the expected rate of information acquisition.

The intuitive idea is that entropy decreases (and thus information accumulates) faster close to the source because cues arrive at a higher rate, hence tracking the maximum rate of information acquisition will guide the searcher to the source much like concentration gradients in chemotaxis.

Remember, that this information is in the form of a binary detection signal (there or not there, with possibly a more subtle ability to detect concentration differences), and that choices are influenced by (de)stabilization of directional biases. In the bacterium, this signal integration is of course very simple, but the detection is no less simple in, say, mammals.

The formulas themselves aren’t so terribly important, but the relevance of this paper to cell migration and molecular biology does interest me. Afterall, it seems that all of biology is permeated by a balance for “exploratory” and “exploitative” behaviors. Stochastic versus deterministic behaviors of motile cells, for instance: growth cone guidance, immune surveillance, etc. Similarly, in evolutionary genetics, non-adaptive vs. adaptive changes over the course of a few generations. This latter example is of course on a very different timescale, but the bias in a certain direction (filling niches, from the molecular to the ecological scales) still permeates. Nothing in biology is completely random or completely predetermined.

References:

  • Vergassola M, Villermaux E, and Shraiman BI. 2007. ‘Infotaxis’ as a strategy for searching without gradients. Nature 445, 406-409 (25 January 2007). Pubmed
  • Berg HC. Random Walks in Biology (Princeton Univ. Press, Princeton, 1993).

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