[Hans Blom (920908)]
Bill Powers (920907.0900)
You say
I puzzled mightily over your e. coli Pascal model until I went
back and read your description: "In my model, coli has neither a
counter (memory) nor a sensor to sense gradients. I assume it is
too primitive for either." What I was puzzled about was the lack
of sensing of the gradient -- there can be no control system
without sensing.
Agreed. There can be no control system without sensing. But a control
system can operate without sensing _a gradient_. My simulation shows
just that. You can improve the quality of control by setting the
minimum step size to zero. Try it and see coli stay at its optimum
spot for what I think is an indefinite period (that is, if it gets
there at all).
I was saying to myself, "Why, this is just a random-walk genera-
tor -- how could it ever go up or down a gradient?" The answer
is, of course, that it can't, except by accident. This is why it
always escapes off the screen eventually.
No. The demonstration shows that it can, strange enough, walk down a
gradient even if the gradient cannot be sensed. Change the minimum
step size to zero and coli does _not_ escape off the screen eventually
but stays at the optimum radius once it gets there. Initially actions
are almost random, eventually control is perfect.
Your model is much too simple; the real e. coli (the intestinal
bacterium) does have such rate-of-change chemical sensors, and
does vary the interval between tumbles according to the time rate
of change of concentration.
I understood that it had a chemical sensor, and I modeled that. I did
not understand that it had stereo-sensing, so no modeling of that. In
my model, the interval between tumbles (= step size) varies with the
sensed concentration minus the optimal (reference) concentration. My
implementation may be different (varying step sizes vs. a counter that
determines the step size; i.e. my time scale is different), I think it
does the same thing. A time rate of change, i.e. a memory, is not re-
quired in my simulations. Remember that my attempt in these simula-
tions was to show the 'origin' of control: how simple can a system be
and yet control (well enough).
Greg Williams (920907 - 2)
P.S. Shouldn't you tell Hans B. about how E. coli actually
controls, based on Koshland's work? He seems to think it is
conjectural, not empirically based.
Thanks for the reminder. I immediately abstracted away the real thing.
I shouldn't call it a simulation of E. coli. It is not. It is an
attempt to construct the simplest controller thinkable: one sensor,
one goal, one comparator, one actuator, and the simplest possible
modulation of actuator action by the error.
Bill Powers (920907.2030)
From the way the model behaves, there seems to be some positive
feedback in it -- the bigger the error, the larger the steps. So
when the error gets above some amount, there's a runaway effect.
I don't see what's causing it.
No, it's the other way around: the large steps are normal. Steps get
smaller when coli gets closer to its goal. At the goal, they have zero
length (or are very small) so that coli stays there (for some time).
It is as if - very loosely speaking - my coli has discovered how to
freeze Brownian motion into stasis at places where it feels at home.
(Oh, how I antropomorphize!)
A question: is, in my simulation, the feedback _positive_ or
_negative_? Would it matter if coli consistently stepped into the
direction exactly _opposite_ to the direction it goes now?
Did you see my post in which I described Koshland's findings
about how e. coli is actually organized?
Yes, and thank you very much for that inspiration. As I said, I ab-
stracted away the real thing and started to theorize, wondering how
such a tiny thing, not much larger than a big protein molecule,
actively moves around its world. Maybe its 'natural laws' aren't much
more complicated than the simple, random movement that we know as
Brownian motion. How simple can you get? An animal is usually defined
as a living entity that can move by itself. What is the simplest
animal (with respect to movement)? And from that: what is the simplest
type of control? Sometimes people 'flow along' with the river of life
and let things happen. Sometimes people are in control and _make_
things happen. Are these two mutually exclusive or are there inter-
mediate states? Now it seems that there are, at least in my simulat-
ion.