Prsentation PowerPoint

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Dynamics and structure of biological networks
marseilles - luminy, 1417 february 2006
María Luz Cárdenas Towards an understanding of
life
Athel Cornish-Bowden Making systems biology work
cnrs, marseilles
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Dynamics and structure of biological networks
marseilles - luminy, 1417 february 2006
  Organizational invariance and metabolic closure
Letelier et al (2006) Organizational invariance
and metabolic closure Analysis in terms of (M,
R) systems J. Theor. Biol. 238 949-961.
María Luz Cárdenas Athel Cornish-Bowden
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Introduction What is life? (M,R)
Systems Infinite Regression Robert
Rosen Enzymes as mathematical functions Metaboli
c closure What have we accomplished?
Science is impelled by two main factors
technological advance and a guiding vision
(overview) Carl R Woese (2004) A new biology
for a new century Microbiol. Mol.
Biol. Rev. 68, 173186
According to Carl Woese, one of the important
biologists of the 20th century, progress in
science is impelled by two main factors
technological advance and guiding vision
Without an adequate technological advance the
pathway of progress is blocked and without an
adequate guiding vision there is no pathway,
there is no way ahead
This presentation is in the context of a search
for the way ahead, looking for a guiding vision
that can allow Systems Biology (very much in
fashion), to achieve real success in the 21st
century, and not to follow the fate of the
cybernetics in the last century, which didnt
live up to its promise.
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The question of what is life may appear too
philosophical, but in reality if we want to
succed in modifying the living world for medical
or biotechnological purposes, we ought to
understand better what is the essence of a living
being.
Introduction What is life ? (M,R)
Systems Infinite Regression Robert
Rosen Enzymes as mathematical functions Metaboli
c closure What have we accomplished?
We think that Systems Biology as it is being
developed today is too much obsessed with the
accumulation of data, and that it is not leading
us to a better comprehension of the essence of
life.
In addition, today the question about the nature
of life has renewed interest, for several
reasons i) Studies of the origin of life on
earth ii) The search for traces of life on
another planets iii) The ambition to create
artificial life iv) The wish to study living
organisms as global systems
Among others an essential ingredient that is
missing in biology is the idea of metabolic
closure, that is, the fact that metabolism
produces metabolism, which produces metabolism.
The notion of metabolic closure will be analysed
in terms of the theory of (M,R) systems of Robert
Rosen. Starting from this theory we have shown
that it is possible to find objects de?ned by the
remarkable property
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What is metabolism?
Introduction What is life? (M,R)
Systems Infinite Regression Robert
Rosen Enzymes as mathematical functions Metaboli
c closure What have we accomplished?
Why is its understanding important for arriving
at a definition of life?
Proteins are the principal actors that allow the
flux of matter and energy through the metabolic
networks
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What is really metabolism?
Introduction What is life? (M,R)
Systems Infinite Regression Robert
Rosen Enzymes as mathematical functions Metaboli
c closure What have we accomplished?
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Metabolism
But the enzymes are not a gift of heaven they
are a product of metabolism
A living being can be considered as a
metabolism-repair system, or (M,R)-system,
that is capable of preserving its integrity of
organisation in spite of the changes in its
environment and in spite of the finite lifespan
of all of its components.
They are continuously degraded and synthesized,
and for this the cell brings into play complex
machineries involving numerous macromolecules
(RNA, proteins) and control mechanisms.
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Introduction What is life? (M,R)
Systems Infinite Regression Robert
Rosen Enzymes as mathematical functions Metaboli
c closure What have we accomplished?
Life as (M,R)-systems
The theory of (M,R)-systems was formulated by
the theoretical biologist Robert Rosen. According
to him life can be considered as a
Metabolism/Repair System (an (M,R)-system)
In fact, in most cases it is not really a
repair, but a replacement of enzymes that need
to be replaced because of ordinary wear and tear,
or because they are no longer needed, and the
component aminoacids need to be recovered.
Rosen R. (1958) A relational theory of
biological systems Bull. Math. Biophys. 20,
245-341 Rosen R. (1972) Some relational cell
models the metabolism repair system. In Rosen
R. (Ed) Foundations of Mathematical Biology.
Academic Press, NY Rosen R. (1991) Life
itself. Columbia University Press, NY Rosen R.
(2000) Essays on Life itself Columbia
University Press, NY
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No man-made machine that exists at present or
that can be conceived at our current level of
technology and understanding has this property.
Introduction What is life? (M,R)
Systems Infinite Regression Robert
Rosen Enzymes as mathematical functions Metaboli
c closure What have we accomplished?
When parts wear out, as they inevitably do, they
need to be repaired or replaced by an agency
external to the machine itself.
This is true no matter how we de?ne a machine
whether an individual tool like an axe, an
assembly of parts like an aeroplane, or an entire
factory. At no level of de?nition does the
machine make itself or maintain itself without
external help.
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Introduction What is life? (M,R)
Systems Infinite Regress Robert Rosen Enzymes
as mathematical functions Metabolic
closure What have we accomplished?
Life as (M,R)-systems
So, unlike man-made machines, living systems have
the capacity of auto-organisation (or
autoconservation) and in that sense they are
autonomous systems
This capacity of autoconservation of living
organisms raises a major theoretical problem,
because the degradation of components (or their
repair), as well as their synthesis, always
involves the action of a series of interdependent
macromolecules, which depend in their turn on
another series, as they also need to be replaced,
in a process involving other enzymes, also
subject to wear and tear
So, there is a problem of infinite regress.
How do living organisms escape from the in?nite
regress, maintaining their identities almost
inde?nitely?
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Introduction What is life? (M,R)
Systems Infinite Regression Robert
Rosen Enzymes as mathematical functions Metaboli
c closure What have we accomplished
Life as (M,R)-systems
Consequently the main problem is how to explain
the constancy of organisation without in?nite
regress.
The theory of (M,R) systems proposed by Robert
Rosen constitutes an effort to solve this
problem. The idea is that metabolic networks
must satisfy logical regularities that go beyond
the thermodynamic and stoichiometric constraints,
and that derive from the circular nature of
biological organisation (metabolic closure).
This theoretical frame is unique, because it
tries to understand biological organisation in a
non-reductionist way.
The essential idea is to identify enzymes with
mathematical functions (mappings) and to
associate the idea of constancy of organisation
with procedures for selecting functions.
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Algebraic formulation of (M,R) Systems
Introduction What is life? (M,R)
Systems Infinite Regression Robert
Rosen Enzymes as mathematical functions Metaboli
c closure What have we accomplished?
In metabolism, each reaction is catalysed by an
enzyme. For example valyl-tRNA synthetase
catalyses the following transformation
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AMP pyrophosphate L-valyl-tRNAVal
ATP L-valine tRNAVal
For arriving at an algebraic formulation of
metabolism, each enzyme can be viewed in a
general way as an operator, M, that transforms a
set of molecules (input materials) into another
one (output materials)
Mi
b1 b2 b3
a1 a2 a3
The catalyst Mi acts formally as a mathematical
mapping, because it transforms some variables
(from the admissible set of input materials) into
other variables belonging to the set of
admissible output materials.
Mi ((a1 ,,a2 , a3)) (b1, b2, b3)
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Algebraic formulation of (M,R) Systems
Introduction What is life? (M,R)
Systems Infinite Regression Robert
Rosen Enzymes as mathematical functions Metaboli
c closure What have we accomplished?
For arriving an an algebraic formulation of
metabolism, each enzyme can be viewed in a
general way as an operator, M, that transforms a
set of molecules (input materials) into another
one (output materials)
Mi
b1 b2 b3
a1 a2 a3
The catalyst Mi acts formally as a mathematical
mapping, because it transforms some variables
(from the admissible set of input materials) into
some other variables belonging to the set of
admissible output materials.
Rosen generalized this mathematical model for a
single metabolic reaction to take account of the
complete network that constitute metabolism.
Thus, he interpreted the overall metabolism as a
type of generalized enzyme or operator (mapping),
Mmet, that transforms a set of input molecules
(a1, a2, a3, ap) of set A in a set of output
molecules (b1, b2, b3, bq) of set B.
Mmet
B b1, b2, b3, bn
A a1, a2, a3, an
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Introduction What is life? (M,R)
Systems Infinite Regression Robert
Rosen Enzymes as mathematical functions Metaboli
c closure What have we accomplished?
What about the Repair or replacement System?
In order to keep its organisation the system
ought to know how it is organised the network
must contain the information.
This could be possible if the knowledge of the
nature of metabolites b could allow the net to
deduce the identity of all the metabolites a as
well as the identity of all the catalysts and
to be able to replace them.
We can formalise the notion of replacement by
considering that what it is needed is an
operator, called a selector and denoted by f,
that using as input the metabolic state of the
organism (the collective result of all the
biochemical reactions) generates f
F(b) f, with the condition that b f(a) (for
some a of A)
In order to have a fully organizationally
invariant (M,R) system, f must also be generated
from the mathematical structure. The solution to
this problem constitutes the kernel of Rosens
work.
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Formally what is needed is a function b with a
property like b(f) F. Thus b is a procedure
that, given a metabolism f, produces the
corresponding selector F.
The operation of an organizationally invariant
(M,R) system corresponds to the following three
mappings acting in synergy (f, F, b)
b
F
f
Map(A, B)
A
B
Map (B, Map(A, B))
f (a) b, F(b) f, b(f) F
Metabolism is interpreted as a mapping f that
transforms an instance a ? A of the huge set A of
possible molecules on the left-hand sides of
equations into an instance b ? B.
Replacement (repair in Rosens terminology) is
a procedure, denoted by F, that, starting with b
? B as input, produces f according to F(b) f
with the condition b f(a) for some a ? A.
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b
F
f
Map(A, B)
A
B
Map (B, Map(A, B))
f (a) b, F(b) f, b(f) F
For b to exist it is required that the equation
F(b) f, for every F must have one and only one
solution, a most demanding condition if M
Map(A, B).
Rosen never clarified the nature of b, nor gave
the limits within which his model is valid.
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Introduction What is life? (M,R)
Systems Infinite Regression Robert
Rosen Enzymes as mathematical functions Metaboli
c closure What have we accomplished?
What have we accomplished?
We have clarified the formulation of (M,R)
systems in terms of mappings and sets of
mappings
We have shown in a logical way that it is
possible to have a selector F that is going to
choose, out of all possible metabolisms, the one
that has originated the particular set b in a
certain instant.
however, Rosens original model is too general.
And, additional restrictions are required for
the system to have organisational invariance.
Thus we have clarified i) the conditions in
which the model of Rosen is valid, and ii) the
nature of b
We have produced the first mathematical example
of an (M,R) system (to be presented in next talk)
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Introduction What is life? (M,R)
Systems Infinite Regression Robert
Rosen Enzymes as mathematical functions Metaboli
c closure What have we accomplished?
What have we accomplished and what does it mean?
We have shown how to generate self-referential
objects f with the remarkable property of being
able to act as function, argument and result
f( f ) f
Which represents exactly what metabolism is
All this may constitute a small step towards
explaining the circular organization of living
organisms.
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Humberto Maturana Francisco Varela Their
theory of autopoiesis has some points in common
with Robert Rosens (M,R) systems, but it puts
less emphasis on the abstract mathematics, and
more on the structural organization of living
organisms and the necessity to enclose them with
membranes.
Both theories claim that reproduction and
evolvability are not the essential de?ning traits
of living systems
J. Letelier et al (2003) Autopoietic and (M,R)
systems J. Theor. Biol. 222, 261272
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f ( f ) f
Ouroboros
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Groupe en train de travailler
Jorge Soto-Andrade
Juan-Carlos Letelier
Athel Cornish-Bowden
Flavio Guíñez Abarzúa
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The Ouroboros, the dragon forming a cycle,
feeding on its own tail, symbolizes the eternal,
cyclic nature of the universe.
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Introduction Quest ce que la Vie ? Systèmes
(M,R) Regression à lin?ni Robert Rosen Les
enzymes comme des fonctions mathématiques Clôture
métabolique Quest ce quon a appris ?
So, what has been achieved?
Maybe a small step towards explaining the
circular organization of living organisms.
This allows closure of the loop of that would
otherwise lead to in?nite regress.
f ( f ) f
Nonetheless, much remains to be done. Robert
Rosen worked for 40 years without resolving all
the problems we cannot expect to have resolved
them all either.
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R. Rosen (1991) Life Itself, Columbia University
Press, New York R. Rosen (2000) Essays on Life
Itself, Columbia University Press, New York
R. Rosen (1972) Some relational cell models the
metabolism-repair system in Foundations of
Mathematical Biology (ed. R. Rosen) Academic
Press, New York
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What is metabolism, and why is it important for
arriving at a de?nition of life?
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1
E
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Metabolism
Rosen sees life as a metabolism-repair system, or
(M,R)-system, capable of maintaining its
organizational integrity in spite of changes in
its environment and in spite of the ?nite
lifetimes of its component enzymes.
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Introduction What is life? (M,R)
Systems Infinite Regression Robert
Rosen Enzymes as mathematical functions Metaboli
c closure What have we accomplished?
So, in simple words, Rosen saw metabolism as a
mathematical operation that transforms metabolic
components of a set a in components of a set b.
In order to keep its organisation the system
ought to "know" how it is organised the network
must contain the information.
This could be possible if the knowledge of the
nature of metabolites b could allow the net to
deduce the identity of all the métabolites a as
well as the identity of all the catalysts and
to be able to replace them.
We can formalise the notion of replacement by
considering that what it is needed is an
operator, called a selector and denoted by f,
that using as input the metabolic state of the
organism (the collective result of all the
biochemical reactions) generates f
F(b) f, with the condition that b f(a) (for
some a of A)
In order to have a fully organizationally
invariant (M,R) system, f must also be generated
from the mathematical structure. The solution to
this problem constitutes the kernel of Rosen's
work.
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Rosen sees a metabolism as a mathemati-cal
operation that transforms all of the left-hand
sides of all of the component processes into all
of the right-hand sides.
In order to maintain its organization the system
needs to know how it is organized the network
itself must contain the informa-tion needed to
replace any part of itself that needs to be
replaced.
This would be possible if knowledge of all the
right-hand sides allowed all of the left-hand
sides to be deduced, together with the identities
of all the catalysts.
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99 of biologists have never heard of Robert
Rosen, but if we ignore these and just consider
the exceptions
Biologys Newton (Don Mikulecky, 2001)
The work of Rosen will keep scholars busy for
decades (John Casti, 2002)
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Essential problems with Robert Rosens work
Bringing Rosens ideas to a broader audience will
involve describing them intelligibly,
illustrating them with intelligible examples, and
de?ning their range of validity.