Adapted from: Webre et al.
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Did you ever think tiny things like the bacterium have a lot of things to tell us? Well, I didn\’t know like that previously until when I read Webre et al. (2003) and tried to look at it in the background of life itself. Well, why bacteria so special? It is a simple system being a prokaryote, and many poor creatures are used in the laboratory. But, what we are interested in now is the motion of the bacteria, specifically bacterial chemotaxis. Now we are not looking at how it is swimming; instead, we can look at why it is swimming. Like any other organism, it is also swimming to get molecules that will provide nutrients and energy.
Why bacterial chemotaxis so special? Unlike a cow grazing on the field, which can determine in which direction if it is going, it can get more grass; the bacteria can\’t do that. Instead, it is comparing the difference in concentration of nutrients at two different time points. If we are making it in simple words, a cow would be looking at the spatial difference, while a bacteria is looking at the temporal difference. One may ask why it is like that, and the simple answer is that it lacks machinery to look at the spatial gradients. Suppose the reader is not satisfied with this answer. In that case, you are encouraged to read the original paper about chemotaxis, where the authors had described the same question in more detail. Here we are not looking at that level of detail.
What the bacteria does is simple. Suppose the concentration at the time point t is c(t). The bacteria will have a direction to move, and by traveling a characteristic distance, it would reach another point in space at time t+1 where concentration is c(t+1). Then there is a comparison, and if c(t+1)>c(t), the bacterium would continue to move in the same direction. If not, the bacterium would choose a random path and move in that direction; that is, a random walk. The way it is done is simple; if all the bacterium\’s flagella are rotating in one particular order, they will tangle together. If the rotation is in the opposite direction, they will separate apart. It would choose a random path to orient and continue the same pattern when it is separated apart.
So, what our tiny little bacterium is lacking? It is the spatial detail of the concentration function of the nutrients. I don\’t know the topology. It is like a blind person climbing a hill only with the help of an altimeter. On the other hand, if he had a stick or something to estimate the slope, he could\’ve reached the peak in a shorter time. But our tiny little organism doesn\’t have that.
But you may also ask why I would present this as something extraordinary. It is merely that it resembles life very much. What is unknown to the bacteria is precisely the thing strange to us also, the topology. If one ever gets a chance to know about the topology, then things would\’ve been a lot easier for him. Here, one may also feel that I am mixing up things, as in the real-life situation, probability of many possible events unfold at each time point, and course of action collapses that into one possible future event. Then one wouldn\’t even be able to define such a topology here; that is, there are many regions that we can\’t explain. But, simply that\’s why I would tell you that we are like the bacteria in that aspect. That we know where we were at time t, at t+1, we are at another state, and we are comparing the two conditions. It could be explained in a complicated way by defining reward and associated behavior and all. What this evaluation enables us to do is that we can get a sense of whether we are going towards the optima. If it turns out that at t+1, one is not satisfied, then would probably look at other possibilities. However, unlike a pure random walk model, a rational agent would have a prior probability for each option. The likelihood function that gives a posterior chance would weigh each of the course of actions. Thus simply life is a topology, its nature does depend on how you define it, but in a higher dimension, we could perhaps see that. Sometimes it may be similar to the bacteria, that the way it cannot capture the concentration function, we are unable to see the topology.
I know someone would disagree with this. I presented my view, and comments are always constructive because they would refine the thoughts.
abstract thoughts 