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Hierarchical representation
for a biological theory of the functional organization (MTIP
: Mathematical Theory of Integrative Physiology)
We previously
saw that MTIP is an action and organization theory, at once
topological and geometrical. In fact, we can start from a
principle of functional interaction between biological structures
and from a principle of hierarchical organization of the folowing
structures : nucleus, cell, tissue and organ. The association
of these interactions lead to the observed functional organization.
I also previously mentionned the two propriteties of interactions,
the non-symmetry and the non-locality, which played an essential
role in the human being development.
How can we represent those interactions which are non-symmetrical
and non-local actions of a structure on an other one ? Which
process are connected to them ?
The first way consists in using graph theory in order to represent
the functional hierarchy induced from the mix of interactions.The
second way, complementary to the first one, consists in using
the field theory so as to represent through time and space
positioned action, non-symmetrical, namely a exchanged product
between structural units between source and well. A fiel in
mathematics is a variable quantity in all points in the space.
In a given moment and in a given point of the physical space
(the source), an operator spreads, in a subsequent moment,
this quantity toward an other point (the well). This abstract
description of the action dynamic offers one interest which
is to implicitly take into account of the living system anatomy,
while making explicit the propagation fathered by transformations
which take place in the source.
One question ensues from this : why do functional interactions
appear ?
Before reaching adulte state, the organism passes througha
development phase in which its structural oragnization and
its functional organization are altering. It exists a geneticala
program which manages this evolution. But why this program
acts as it is observed ? Against the finalism, this philosophical
doctrine which imposes a final reason to the existence of
each structure, we must understand why an association between
two structures exists while it makes the system more complex
and that each unit is, by its own, potentially self-sufficient.
Now, contrary to what generally is obtained in physical systems,
I showed both physicaly and mathematicaly(1)
that a biological system is all the more stable since it is
complex(2)
: there is stabilisation by structure associations (what I
called the stabilizing auto-association principle, or PAAS,
general organizational principle in biology which describes
why two structures tend to associate themselves, carrying
out a new function). In biological terms, the compulsory conservation
of the homeostasy during the development leads to structure
association so as to the stability of the physiological dynamic
increases. The PAAS leads to a mathematical construction of
the biological system : associated units exist because their
functional process associated to an other one become more
stable and that an environmental perturbation, that used to
destroy them before, can't do it anymore [see
the diagram].
So, the theory I propose consists in a general principle,
the PAAS, in the necessary existence of elementary functional
interaction, and in a organised mathematical construction
of the structural units from functional interactions. The
hierarchical organization according to space and time scales
is a fundamental element of that theory.
This organization permits to obtain a classification of the
biological datas according to criterions (space and time),
necessary for their integrated comprehension. The elementary
physiological mechanisms are then classified according to
a hierarchical graph which can be mathematicaly studied. We
can next obtain a real integration of functional process observed.
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To go further… (well-informed
publici)
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Functional organization and fiel with n
levels
 Theory
Formalism |
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[1] In particular when
it's a matter of two biochimical ways (Chauvet and Costalat,
1995), but also in more complex cases, as for example the
cerebellum dynamic (Chauvet and Chauvet 1999). The PAAS is
a constant, a general organizational principle in biology.
.
(2) It is the contrary in the physical systems
(except from conditions to respect) : the explanation of the
difference with biological systems rests on the causality
type : evenemential for biological systems, non-evenemential
for physical systems.
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