Re: metabolism and repair

[Judith Rosen <***>]

Hi David,

I'd say you've mostly got it. The only area that isn't covered by your "three stages of growth" scenario is the construction of self (which is different from reproduction). In a prokaryote, reproduction is a less complex process so the entailments which the repair capability possess aren't as visible as they are in more highly evolved life forms. In a multicellular organism, however, it becomes starkly visible. The self-construction element refers to both embryonic development and to life-cycle-changes type of self-construction. All those things emanate from the genetic or "genome" half of the genome/phenome duality. Metabolism emanates from the other half. But, as RR pointed out; these two are linked. They cannot exist without the existence of the other half of the duality.   The significance of the "(M,R)-System" model is that it turns out to be valid for more than just cells. One of my father's "A-Ha" moments was to realize that this model represents any living system, including multicellular ones like human beings. That's significant because it means that the encoding and decoding process also hold; they are accurate in describing the essential functional entailments of life in an organism. This is the main strength of relational approaches.

On page 204 of Anticipatory Systems, RR goes on to describe some of the information that comes out of the encoding and decoding that he used to derive this model:
Robert Rosen wrote: "These (M,R)-systems possess many remarkable properties. Let us consider a few of them. One of the most obvious is intimately connected with the repair aspect of such systems. Let us suppose that by some means we remove a metabolic component f from the system. The associated repair component [there is a mathematical symbol here which looks like "omega" to me, with f associated to it in a way I can't create on my keyboard] remains present and, if it receives its inputs, can continue to produce copies of f. Thus, the damage initially done to the system in in fact reparable. However, in order for this to be possible, it must be the case that the inputs to [symbol "omega of f" again, meaning "the repair component for f"-- which I will substitute from here on out, when this symbol arises again] do not depend on f; i.e., that the removal of f from the system should not affect the inputs to [the repair component for f] or any of their necessary antecedents. If this is the case, then as we have seen, [the repair component for f] will repair the damage. Let us call a component f with this property "re-establishable"; a component without this property will be "non-re-establishable". Re-establishability of a component f thus depends entirely on two things; (a) the manner in which the metabolic components are inter-connected, and (b) on the domains of the repair components [omega of f].

It can easily be shown that every (M,R)-System must contain at least one non-re-establishable component. That is, there must be at least one way of damaging such a system which cannot be repaired by the system. Moreover, we can show that there is an inverse relation between the number of such non-re-establishable components and their importance for the functioning of the system as a whole. For instance, if there should be exactly one non-re-establishable component, then the removal of that component will cause the entire system to fail. In other words, although such a system can repair almost all such injuries, the single one which it cannot repair is lethal to every component.

Let us consider another kind of result which is unique to the theory of (M,R)-Systems. We have argued that the repair components perform functions usually regarded as nuclear or genetic, in cells. One of the decisive features of genetic activity in real cells pertains to the replication of the genetic material. Thus it would be most important to show that, already within the (M,R)-System formalism as we have defined it, and without the need for making any further ad hoc assumptions, a mechanism for such replication was already present. This is what we shall now proceed to show; namely that already within our formalism, there exists machinery which can replicate the repair components. Let us see how this comes about."

He then goes into the mathematics of proving this, via the mathematics he already used (which I didn't include) to establish the nature of the repair and metabolic "mappings". Just to prove my oft-asserted point that one does not need to read or understand the math to get the ideas, I'm going to skip to the next prose-based part:

"By pursuing this kind of argument in more general settings, we obtain conditions under which replication maps exist for the repair components of any arbitrary (M,R)-Systems. To our knowledge, this kind of result is unique; there is no other situation in which replicative capacity can be made to follow from repair activity without the intervention of ad hoc assumptions. Thus it appears that this replicability is a relational result; i.e. independent of any particular physical mechanism or realization.

[Note: I have the last sentence of the paragraph above marked in my book because it is absolutely HUGE in its implications. The ramifications from that sentence alone is enough to blow mechanism out of the scientific water.]

There are two other noteworthy features of the above construction. The first is that replication is not an obligatory feature of repair, but depends on the invertibility of a certain mapping. This in turn depends on the character of the entire set H(A, B) with which we are dealing. It may be expected that this condition will not usually be satisfied, and hence that most (M,R)-Systems cannot replicate. Thus as we would expect, replication is a relatively rare and unusual situation.[Which holds true; most body cells of a multicellular organism cannot replicate the whole organism (without a whole lot of scientific tinkering) and many whole organisms cannot reproduce at all; like worker bees or hybrids with unequal genetic inheritance from the two parents, such as a mule.]

The second noteworthy aspect of our construction arises from the relation of the replication map (when it exists) to the other mappings of an (M,R)-system, shown in figure (3.5.13) [which I will exclude because it includes all sorts of notation I can't produce]. Let us notice that the first three maps constitute our original (M,R)-system, in which f represents the metabolic component and [omega f] represents the repair component. But let us now consider the [rest of the diagram and] see that  these three maps themselves constitute an (M,R)-System; but now one in which the original repair component [omega f] plays the role of metabolic component, and the original replication map plays the role of the repair component. From this we see the curious fact that there is nothing intrinsic about the biological qualities of metabolism, repair and replication; our perception of them depends on the total system in which they are embedded. In fact, we can imagine the diagram extended indefinitely on both sides, with any successive triplet of mappings being an (M,R)-system and in which any map could be either a metabolic component, a repair component or a replication map, depending on which triplet was selected as primary. This too is a most remarkable result, of an entirely relational character.

These few results should suffice to give the flavor of the (M,R)-Systems as cellular metaphors. It should be noted that, in formal terms, we may form (M,R)-Systems in any category of sets and mappings (cf. Example 6, Chapter 3.1, above). Indeed, it can be shown that the totality of (M,R)-systems which can be formed in any category is itself a category in a natural way, and can serve as an index of the structure of the original category. Moreover, the property of being an (M,R)-system is preserved invariant by functors  between categories. This fact has some interesting consequences which we cannot go into here; we refer the reader to the original paper for fuller details.

One final feature of the (M,R)-systems may be mentioned. As we have seen, such systems may be formed from any category of sets and mappings, In particular, we may think of the mappings appearing in an (M,R)-system as representing equations of state, or linkage relations, of some natural system. Now we saw in Example 2 above that one natural encoding of a biological genome is in terms of a set of structural or constitutive parameters appearing in such an equation of state. If we do this, then the output of the associated repair mapping can be thought of as precisely such a set of constitutive parameters; we obtain thereby a way of interpreting these repair components, which in fact represent nuclear activity in cells, in terms of the more familiar genetic concepts arising from morphological and biochemical considerations. Once again, we cannot pursue this interesting circle of ideas here, but perhaps the reader can observe from the outline presented above how rich such relational considerations can be."

In the chapter notes, RR suggests that "for a succinct review of the basic ideas, see Chapter 4 of "Foundations of Mathematical Biology",  Volume 2. I'll go take a look at that book and see if there is enough prose to warrant typing any of it in.

Cheers,
Judith


Web address: http://www.rosen-enterprises.com
BioTheory: An electronic journal of general science based on the Relational (Rosennean) Complexity Paradigm
On Sep 8, 2005, at 2:28 PM, David Macy wrote:

> <x-tad-smaller>Hey Jude,</x-tad-smaller>
>  
> <x-tad-smaller>You wrote...</x-tad-smaller>
>  
>  In other words, the kind of functional capability required for repair is almost the same required for reproduction). Repair is a capability for maintenance of, and building/rebuilding, aspects of the organization itself. Metabolism cannot exist without repair in a living system and vice versa.
>  
> <x-tad-smaller>Alright, see when you say this I can almost wrap my mind around it.  I can't really visualize the life cycle of sexual, multi-cellular eukaryote, far too mush entailment you see.  So when you say this I'm picturing a prokaryote alive through a microscope.  I can imagine three "states" of growth: diminishing, breaking even, and growing.  If the cell is growing, at some point (by forces external, internal or both) the cell snaps in two.  Voila!  Reproduction.  The breaking even "state" is where repair is precisely matching degradation.  Actual growth and reproduction is repair with extra metabolic oomph behind it.</x-tad-smaller>
>  
> <x-tad-smaller>How does all that groove (commute)?</x-tad-smaller>
>  
> <x-tad-smaller>David</x-tad-smaller>