Re: metabolism and repair

[Judith Rosen <***>]

Interesting-- the fates are with us today, in that John M. brought this up just as I was about to start typing in some passages from "Foundations of Mathematical Biology, Volume II, Cellular Systems". I think some of the answers to various specific questions are in this material.

> John M. wrote: I take 'replication' in two ways: one is that of a
> species in the gender-combination mode, definitely not
> the replication of individuals, what it is not, (2 of
> them - different - produce a 3rd kind, not a replica
> of either) and the 'real one', the prokaryotic
> mitosis, producing identical replicas. Prokaryotes
> don't age, the senedcence does not occur as we know
> it, however outside impact may interfere with their
> 'immortality.

>From page 229, "Theory of a Single Metabolism-Repair System":
Robert Rosen wrote: "If we regard a metabolizing cell as a general input-output system, receiving inputs from its environment and processing them in a characteristic way to produce environmental outputs, we are struck at once by the fact that the lifetime of a cell far exceeds the functional lifetimes of any of its parts. The question we must put ourselves, then, is the following: How is it possible for the overall lifetime of an input-output system to be greater than that of any of its components?

If we think for a moment about the properties of biological cells, we see at once that these cells are continually repairing themselves. Indeed, to simply look at a typical cell under the microscope is to be struck by the fact that the cell is compartmented into two obviously different regions, which we may roughly call nucleus and cytoplasm. On closer investigation, we discover that the cytoplasmic part of the cell is mainly concerned with what we customarily call the metabolic activity of the cell, while one of the basic nuclear functions is concerned with repair. This repair takes the form of a continual synthesis of basic units of metabolic processing (enzymes), utilizing as inputs materials provided by the metabolic activity itself.
--snip (diagrams and math)--
"In order to keep the system functioning beyond the lifetimes of its components, it is necessary to replace components before their lifetimes are exceeded. It is suggested, from analogy with the situation in biological cells, that this be done by appending to the system a number of new components, one for each of the original components.
--snip (more diagrams and math)--
"Our general rule in passing from block diagrams to abstract block diagrams is that components are replaced by mappings, and inputs and outputs by the sets which comprise the domains and ranges of these mappings. --snip--

"Theorem: Every (M,R)-system must contain a non-re-establishable component.
Proof: Choose a re-establishable component, relabeling it M1. By hypothesis its corresponding repair component R1 is not dependent on M1. But since R1 must by hypothesis receive inputs from some component of the system, there must be a component M2 the output of which is an input to R1. If M2 is non-re-establishable we are done; otherwise R2 receives an input from another component M3 distinct from M1, M2. The corresponding repair component R3 must, if M3 is re-establishable, receive an input from a component M4 distinct from M1, M2, M3. Proceeding in this fashion, we must ultimately reach a non-re-establishable component, since the total number of components is finite.

An immediate corollary we can draw from this theorem is the following: 
If an (M,R) system contains a single non-re-establishable component, then that component is central [meaning crucial to the system]. Otherwise we could remove the single non-re-establishable component and be left with an (M,R) system containing only re-establishable components, which contradicts our theorem. [It also contradicts what we know to be the case in living systems.]

The biological significance of this theorem is the following: If we regard a cell as an (M,R) system, then by virtue simply of the fact of the functional interrelationships of the metabolic and repair structures of the cell, there must be metabolic components whose loss or injury is not repairable by the system, even though the repair components are intact. Which components will fail to be repairable depends on the specific relationships that exist between the metabolic and repair components; the same component may be re-establishable in one (M,R) system but may fail to be re-establishable in another (M,R) system containing the same metabolic components interrelated in the same way in exactly the same way. But there must always be one component that is non-re-establishable.

Moreover, there is a certain subtle interplay between re-establishability and centrality that is worthy of mention. It seems evident that an (M,R) system will be most effectively constructed if the relation between the metabolic and repair components is such that the largest possible number of components are re-establishable. But this means, accrding to our corollary, that the non-re-establishable components will be central, or close to it. Thus, a sysstem with a large number of re-establishable components will be able to survive many types of injury essentially unaffected, but certain kinds of injury will cripple the entire system. It may thus be better to allow a large number of non-re--establishable components but such that the damage caused by removal of these components is not so serious. We thus have questions of selective advantage entering into our theory at the outset."

He goes on to describe what the introduction of time does to the qualities of non-re-establishability, particularly in the sense of a time-lag caused by necessary processing time, transport time, etc. The basic qualities remain but a great deal more subtle interplay becomes visible. Nifty!

The rest of this discussion begins to have way too much mathematics for me to type it in. Perhaps I can scan a few pages and either post them on the list (if the posting rules can be gotten around....homework for me) or else I'll post them on my website and post the link here.

Judith

Web address: http://www.rosen-enterprises.com
BioTheory: An electronic journal of general science based on the Relational (Rosennean) Complexity Paradigm
On Sep 9, 2005, at 10:07 AM, John M wrote: