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Date:         Tue, 8 Sep 1992 17:56:52 +0100
From:         HANS BLOM <ELEMHANS@URC.TUE.NL>
Subject:      e. coli model, again

[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.
Comments: Gated by NETNEWS@AUVM.AMERICAN.EDU