A Conversation for Complexity Theory

A "Real Life" example

Post 1

Feral Korzybski

One of the cool things about interconnectivity in a signalling network is the way feedback loops allow the
network to adapt to perturbations from the environment. A couple recent papers on bacterial chemotaxis
provide a neat example of this sort of thing (Barkai & Leibler, Nature 387:913-917 and Alon, Surette, Barkai,
and Leibler Nature 397:168-171). Chemotactic e. coli are able to swim up gradients of nice things (e.g. sugars)
and down gradients of nasty things (e.g. toxins) by changing their relative rates of choosing a new direction
(tumbling) and swimming straight in response to signals from receptors on their cell surface. This is all very
well and good for swimming towards, say, a nice pool of sugar, but some mechanism of attenuation is required
to let the bacteria know when it has reached an area of uniform concentration so that it can stop searching.
The first paper models the components of the chemotaxis pathway (a small collection of proteins that chuck
phosphate groups from component to component between the receptors and the bacterium's flaggellar motor)
as a system of differential equations and suggests that the connectivity of the pathway is sufficient to provide
adaption to a sharp uniform change in sugar concentration. It further predicts that over or underexpressing
most components of the pathway, while changing variables such as adaption time and average path length, has
negligible impact on the precision of adaption. In the second paper, a computer/video tracking system was
used to watch genetically engineered bacteria in which the genes of the chemotaxis pathway could be
tweeked up or down. Although they didn't get a perfect quantitative fit to the model, the general trends
suggested that precision of adaption is indeed a robust property that depends primarily of the connectivity
of the network! One of the really cool things about this is that it provides a safe mechanism for evolutionary
change. Mutations that create a diversity of potentially useful path lengths, adaption times, etc can occur
without compromising the ability of the bacteria to adapt to environmental changes.

A "Real Life" example

Post 2


Let's see if I understand this (bear with me, I'm not a biochemist!)

This suggests that the e.coli's evolvability (it's stability, yet sensitivity to change and accuracy of adaptation) is a function of the connectivity of interacting phenotypes - the components of the chemotaxis pathway - rather than (or aswell as) the connectivity of mutually switching genes in the genome.

A "Real Life" example

Post 3

Feral Korzybski

Sorry, I think I was a bit hasty and wound up re-using the same terms to mean three or four different things. Let me see if I can sort it out. The simplest experiment we can do to watch chemotaxis is to uniformly raise the concentration of sugar in the solution that our e. coli is swimming in. Since the e. coli does not expect sugar distribution to change suddenly like this, its interpretation of the sudden rise in sugar concentration is that there is a big pool of sugar in the direction it was swimming in (an analogous case is if I were walking north in a pitch black room and suddenly smelled frying bacon, I would assume that there was some bacon frying to the north of me and I had just gotten close enough to smell it, discarding the hypothesis that I had suddenly been surrounded by frying bacon). In response to this assumption, the e. coli changes its swimming behavior, trying to home in on the new source of sugar. Eventually, it realizes that the sugar concentration, although higher than before, is uniform in every direction, and it resumes its original swimming behavior. In order to make this sound confusing, we say that the e. coli has "adapted" to the new sugar concentration. So for this short time-scale case of a single e. coli adapting to a change in sugar concentration,
the network we are interested in is made up of the protein components of the chemotaxis pathway. We can observe some properties of this system that depend very much on how many copies of each protein are present in a cell (for example, how long it takes the e. coli to "adapt" back to it's normal swimming behavior, the average path length during its normal swimming behavior, etc) while other properties are "robust" over many different copy numbers of the different proteins in the network (for example, "precision of adaption", which is how closely the swimming behavior after adaption to the higher sugar concentration resembles the original swimming behavior, is relatively unperturbed by tweaking of the pathway components). So in the short term case, we can say that the connectivity of the network is sufficient to give us the robust property of precise adaption. If we now turn to a long term case (say, a population of billions e. coli over the course of ten years (about two-million generations), which could be sufficient time for evolution to optomize the chemotaxis system for a given environment) we can make a prediction about how the system can evolve. Let's assume that the really critical property is that the e. coli be able to adapt to new basal levels of sugar (i.e. we assume neurotic e. coli that are dashing all around unless the sugar concentration is at some very specific value are at a disadvantage) but that a certain average path-length is optimal for a given environment (i.e. a far-ranging search pattern might be optimal for an environment that tended to have rich pools of sugar distributed sparsely over a large area). Let us also only consider mutations in the regulatory genes of the system (which control protein copy number) and not mutations in the genes coding for the proteins themselves. If adaption depended on the copy number of some or all of the pathway components, we can imagine that it would take the population quite a while to evolve the optimal chemotaxis system for the environment because they would have to optomize both precision of adaption and path length (this would be especially difficult if a mutation benificial to one criterion were detrimental to the other!). On the other hand, if adaption is robust over many different copy numbers, then the population is "free" to experiment with many different path-lengths without having to worry about their ability to adapt to different sugar concentrations. If this model turns out to hold, then it would suggest that one of the advantages to having so much crosstalk between different biological pathways is that it allows for this mechanism of rapid evolution! Hopefully this was a little bit clearer this time, or at least confusing in a different way. If you'd like to see some more interesting signalling and metabolic pathways, the Kegg encyclopedia, at http://www.genome.ad.jp/kegg/kegg2.html is a great resource (its entry for the chemotaxis pathway is at http://www.genome.ad.jp/kegg/regulation/eco02030.html). Science magazine has just launched a "signal transduction knowledge environment" (at http://www.stke.org/) which could wind up being a very good resource for this sort of thing, but at the moment it's pretty sparse.

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