···
Thanks for the compliment, but so far
as I know, the only original idea in what I wrote is that it might
be possible for the autocatalytic “pile-up” of product in a tight
space to evolve into the kind of “signal” we consider in control
loops (I’m thinking of synaptic transmitter chemicals as an
example). It might be worth publishing if I could find an argument
that autocatalytic systems with such pile-ups would be more likely
to survive in the autocatlytic ecology than would more distributed
loops, but it never occurred to me to try to publish.
Other than that, the near inevitability of quasi-stable feedback
structures in a non-equilibrium energy flow is well-known (e.g.
Prigogine), and I got the inevitability of autocatalytic loops
from Kauffman, though he probably got it from elsewhere as well.
Actually, Kauffmann's argument is rather simple and striking at
the same time, so I’ll repeat it here (Boris has already seen it).
There are 92 natural elements, plus a few more when the Earth was
new. For arithmetical simplicity, let’s say there are 100
elements. Potentially, any two of these (including two of the
same) could join to form a compound. But we know that most such
pairings either never happen or happen very rarely. For the sake
of argument, let’s say that X+Y->XY occurs for only 9% of the
possible pairs. All of the di-atomic molecules produced in such
reactions will occur at least occasionally in a 2-D or 3-D
environment in which the components can move around freely. We can
call this environment “the soup”.
With 100 elements there are 10,000 possible di-atomic molecules,
of which we hypothesised above that only 900 can actually exist.
Including the elemental atoms, that makes 1000 entities that could
possibly combine into more complex molecules. There are now
1,000,000 possibilities for such reactions. If 9% of those
actually can occur, there could be 90,000 new species of
molecules, plus the 1000 we knew about before. And these 91,000
could combine in 8,281,000,000 different ways, of which we assume
only a few could actually occur. And we can continue this
development past the trillions and quadrillions of possibilities,
so that we should expect at least billions of different species of
molecules to exist after a not very long time.
All of these complex molecules can break down in a reaction
inverse to the one that built them (and in other ways, too). If a
reaction X+Y->XY occurs, so does XY->X+Y. If the soup
happened to be in equilibrium, there would be some fixed
relationship among the relative proportions of X, Y, and XY. If X
and Y are highly reactive, there would be lots of XY and very
little remaining X and Y, but if X and Y join only with
difficulty, the reverse would be true.
A catalyst is an entity whose presence increases to probability or
the speed of a reaction. Z catalyses X+Y->XY if that reaction
goes faster or is more likely to occur at all in the presence of Z
than in its absence. If there is a Z, therefore, the relative
proportions of X, Y, and XY in the soup will be tilted in favour
of there being more XY and less X and Y. If, on the other hand, Z
catalyses the breakdown reaction XY-X+Y, there will be more X and
Y and less XY than if Z were absent.
It may be very unlikely that any particular molecule will act as a
catalyst for any particular reaction. Let’s suppose that the
probability is one in a million. If we look at 1000 different
molecules that might catalyze that reaction, the probability that
at least one of them will catalyse it goes up to roughly one in a
thousand. And if there are a thousand such reactions that one of
these thousand molecules might catalyze, the probability is much
higher (1/e?). But we just talked about there being a million
possible reactions when there are 1000 different molecules, and at
the next stage there are 8 trillion possible reactions and 91,000
possible catalysts. The likelihood that at least one molecule
catalyzes at least one reaction soon gets arbitrarily close to
1.0. And when that happens, the probability is very high that
there are thousand or millions of cases in which some molecule
catalyzes some reaction.
You can see where this is going. When there are enough catalysed
reactions in the soup it becomes almost inevitable that some of
the products of the reactions will serve as catalysts for other
reactions, and then that chains of catalysis develop, and then
that at least one reaction in a chain produces a reaction product
that catalyses a reaction at some other point in the chain,
forming an autocatalytic loop. And when the probability is near
1.0 that some autocatalytic loop has formed, it is highly probable
that there are others, and that there will be cases in which more
than one loop has a reaction that uses the same resource input or
produces the same product, thus creating cross-linking among the
loops. The former case is Tsokolov’s negative feedback example.
Anyway, that is the core of Kauffmann's argument in "At Home in
the Universe".
Martin
This is brilliant Martin, thank you so much for
that illumination. I really hope you get these ideas published
soon!
Warren
On Wed, Oct 23, 2013 at 8:31 PM, Martin
Taylor mmt-csg@mmtaylor.net
wrote:
Matti,
Thanks for this. It ties in with a conversation I've been
having with Boris about the role of autocatalytic systems
in the origin of life.
I have to disagree with Tsokolov on one point, though. In
any non-equilibrium energy flow, there are likely to be
many quasi-stable negative feedback systems (a simple
vortex is an example). I agree with Referee 1 that this
cannot be the defining characteristic of life. What can be
the defining characteristic, in my view, is the existence
of perceptual control. A control system stabilizes
something “inside” – a “perception”-- by exerting more
power on the “outside” than the outside exerts on the
inside. The asymmetry of the negative feedback loop is
critical.
Although interacting autocatalytic loops can create
negative feedback loops, the nature of those loops differs
from that of the feedback loops involved in control. A
control loop stabilizes the strength of something we might
call a signal at a given location. An autocatalytic loop
produces more instances of the types of entity (e.g.
molecular species) that are catalysts in the loop or are
byproducts of the autocatalytic reaction. These instances
can float away anywhere. They don’t pile up in the way
that a signal value “piles up” in a positive feedback
loop, and when the ecology of interacting autocatalytic
loops does produce a negative feedback loop (which need
not oscillate) that stabilizing effect is on the numbers
of instances of the types of entities in the loop, not in
the value of a “signal” at some specific place.
Nevertheless, I think that the interaction of
autocatalytic loops is likely to be the first stage in the
development of true control loops. The “pile-up” of
instances could become equivalent to a signal if some part
of the loop is confined to a limited physical region.
I disagree with Referee 1 about viruses, inasmuch as every
living thing can live only in an appropriately supportive
environment, and reproduces only insofar as it
participates in an autocatalytic ecology. That goes just
as much for humans as it does for a virus. The difference
is that so far as I know, viruses do not have perceptual
control loops.
Martin
On 2013/10/20 5:38 PM, Matti Kolu wrote:
[From Matti Kolu
(2013.10.20.2340 CET)]
Trying again, this time
with the paper attached…
A Theory of Circular Organization and
Negative Feedback: Defining Life in a
Cybernetic Context
Sergey Tsokolov
Abstract
All life today incorporates a variety of
systems controlled by negative
feedback loops and sometimes amplified by
positive feedback loops. The first
forms of life necessarily also required
primitive versions of feedback, yet
surprisingly little emphasis has been given
to the question of how feedback
emerged out of primarily chemical systems.
One chemical system has been
established that spontaneously develops
autocatalytic feedback, the
Belousov-Zhabotinsky (BZ) reaction. In this
essay, I discuss the BZ reaction
as a possible model for similar reactions
that could have occurred under
prebiotic Earth conditions. The main point
is that the metabolism of
contemporary life evolved from primitive
homeostatic networks regulated by
negative feedback. Because life could not
exist in their absence, feedback
loops should be included in definitions of
life.
ASTROBIOLOGY Volume 10, Number 10, 2010 Mary
Ann Liebert, Inc.DOI:
10.1089/ast.2010.0532
--
Dr Warren Mansell
Reader in Psychology
Cognitive Behavioural Therapist & Chartered Clinical
Psychologist
School of Psychological Sciences
Coupland I
University of Manchester
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Email: warren.mansell@manchester.ac.uk
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