Prsentation PowerPoint

1
Dynamics and structure of biological
networksmarseilles - 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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Systems Biology will solve all our Problems
463
luminy, marseilles 17 february 2006
Estimate for whole year
Systems biology growth galactose
metabolism arti?cial life System theory What
is life? Stoicheiometric
analysis (M,R)-systems Mathematical
example Biological example Conclusions Refe
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2005 accounts for more than all the years before
2004 put together!
341 at 26th September
On the evidence of PubMed, Systems biology
started in a small way in 1988
and started its explosive growth in about 2000
3
T. Ideker et al. (2001) Integrated genomic and
proteomic analyses of a systematically perturbed
metabolic network Science 292, 929934
luminy, marseilles 17 february 2006
Systems biology growth galactose
metabolism arti?cial life System theory What
is life? Stoicheiometric
analysis (M,R)-systems Mathematical
example Biological example Conclusions Refe
rences
A. Cornish-Bowden and M. L. Cárdenas (2001)
Complex networks of interactions connect genes
to phenotypes Trends in Biochemical Sciences 26,
463465
4
T. Ideker et al. (2001) Integrated genomic and
proteomic analyses of a systematically perturbed
metabolic network Science 292, 929934
luminy, marseilles 17 february 2006
Doubling time in the presence of galactose (min)
100
200
300
Systems biology growth galactose
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is life? Stoicheiometric
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example Biological example Conclusions Refe
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100
wild type
gal1?
gal7?
gal10?
gal4?
Doubling time in the absence of galactose (min)
gal5?
gal6?
gal2?
gal3?
gal80?
200
A. Cornish-Bowden and M. L. Cárdenas (2001)
Complex networks of interactions connect genes
to phenotypes Trends in Biochemical Sciences 26,
463465
5
T. Ideker et al. (2001) Integrated genomic and
proteomic analyses of a systematically perturbed
metabolic network Science 292, 929934
luminy, marseilles 17 february 2006
Doubling time in the presence of galactose (min)
100
200
300
Systems biology growth galactose
metabolism arti?cial life System theory What
is life? Stoicheiometric
analysis (M,R)-systems Mathematical
example Biological example Conclusions Refe
rences
100
wild type
gal1?
gal7?
gal10?
gal4?
Doubling time in the absence of galactose (min)
gal5?
gal6?
gal2?
gal3?
gal80?
200
A. Cornish-Bowden and M. L. Cárdenas (2001)
Complex networks of interactions connect genes
to phenotypes Trends in Biochemical Sciences 26,
463465
6
T. Ideker et al. (2001) Integrated genomic and
proteomic analyses of a systematically perturbed
metabolic network Science 292, 929934
luminy, marseilles 17 february 2006
Doubling time in the presence of galactose (min)
100
200
300
Systems biology growth galactose
metabolism arti?cial life System theory What
is life? Stoicheiometric
analysis (M,R)-systems Mathematical
example Biological example Conclusions Refe
rences
100
wild type
gal1?
gal7?
gal10?
gal4?
Doubling time in the absence of galactose (min)
gal5?
gal6?
gal2?
gal3?
gal80?
200
A. Cornish-Bowden and M. L. Cárdenas (2001)
Complex networks of interactions connect genes
to phenotypes Trends in Biochemical Sciences 26,
463465
7
T. Ideker et al. (2001) Integrated genomic and
proteomic analyses of a systematically perturbed
metabolic network Science 292, 929934
luminy, marseilles 17 february 2006
Doubling time in the presence of galactose (min)
100
200
300
Systems biology growth galactose
metabolism arti?cial life System theory What
is life? Stoicheiometric
analysis (M,R)-systems Mathematical
example Biological example Conclusions Refe
rences
100
wild type
Galactose 1-phosphate
gal1?
gal7?
gal10?
gal4?
Doubling time in the absence of galactose (min)
gal5?
gal6?
gal2?
gal3?
External galactose
Galactose 6-phosphate
gal80?
200
A. Cornish-Bowden and M. L. Cárdenas (2001)
Complex networks of interactions connect genes
to phenotypes Trends in Biochemical Sciences 26,
463465
8
luminy, marseilles 17 february 2006
6  December  2004
Philip Ball Arti?cial cells take
shape Bacterium-sized protein factories are
a step along the road to synthetic
life. Primitive cells similar to bacteria have
been created by us researchers. These synthetic
cells are not truly alive, because they cannot
replicate or evolve. But they can churn out
proteins for days, and could be useful for drug
production, as well as advancing the quest to
build arti?cial life from scratch...
Systems biology growth galactose
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is life? Stoicheiometric
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example Biological example Conclusions Refe
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The work is very clever, according to David
Deamer, a chemist at the University of
California, Santa Cruz, who has also tried to
devise arti?cial protocells. These guys are on
the right track, he says, Its a big step
forward.
V. Noireaux and A. Libchaber (2004) A vesicle
bioreactor as a step toward an arti?cial cell
assembly Proceedings of the National Academy of
Sciences of the USA 101, 1766917674.
9
Our civilization seems to be suffering a second
curse of Babel just as the human race builds a
tower of knowledge that reaches to the heavens,
we are stricken by a malady in which we ?nd
ourselves attempting to communicate with
luminy, marseilles 17 february 2006
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one another in countless tongues of scienti?c
specialization The only goal of science appears
to be analytical, i.e. the splitting up of
reality into ever smaller units and the isolation
of individual causal trains
Ludwig von Bertalanffy
10
We are living through a period in which the main
activity in biological research is the
accumulation of more and more facts,
luminy, marseilles 17 february 2006
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is life? Stoicheiometric
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example Biological example Conclusions Refe
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11
We are living through a period in which the main
activity in biological research is the
accumulation of more and more facts,
luminy, marseilles 17 february 2006
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is life? Stoicheiometric
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example Biological example Conclusions Refe
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but is this leading to increased under-standing
of the nature of life? Do we, in fact, understand
life any better than at the time of Erwin
Schrödinger in 1944?
Today we no longer study Life in our
laboratories. (François Jacob, 1970)
E. Schrödinger (1944) What is life? Cambridge
University Press
12
Despite the current emphasis on the accumulation
of facts, the facts being accumulated do not
neces-sarily include the things we need to know
in order to integrate them all into a system of
interacting enzymes.
luminy, marseilles 17 february 2006
Systems biology growth galactose
metabolism arti?cial life System theory What
is life? Stoicheiometric
analysis (M,R)-systems Mathematical
example Biological example Conclusions Refe
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In particular, a great deal of genetic
information is being obtained in the absence of
any studies of the kinetic or regulatory
properties of the enzymes coded by the genes.
For the moment, therefore, the absence of useful
kinetic information is forcing us to pay
attention to the purely structural
(stoicheiometric) properties of metabolic
networks.
13
At present one of the most effective ways of
studying large metabolic networks is to analyse
their elementary ?ux modes.
luminy, marseilles 17 february 2006
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is life? Stoicheiometric
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y
a
x
c
(assuming that reactions 3 and 4 can operate in
reverse)
b
z
J. Stelling, S. Klamt, K. Bettenbrock, S.
Schuster and E. D. Gilles (2002)
Metabolic network structure determines key
aspects of functionality and regulation
Nature 420, 190193
A. Cornish-Bowden and M. L. Cárdenas (2002)
Metabolic balance sheets Nature 420,
129130
14
At present one of the most effective ways of
studying large metabolic networks is to analyse
their elementary ?ux modes.
luminy, marseilles 17 february 2006
Systems biology growth galactose
metabolism arti?cial life System theory What
is life? Stoicheiometric
analysis (M,R)-systems Mathematical
example Biological example Conclusions Refe
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y
y
a
x
c
x
b
z
z
In this simple system there are just two or three
elementary ?ux modes.
A. Cornish-Bowden and M. L. Cárdenas (2002)
Metabolic balance sheets Nature 420,
129130
15
why are living systems designed as they are?
luminy, marseilles 17 february 2006
We need a better understanding of what life is
Systems biology growth galactose
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example Biological example Conclusions Refe
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Quino, Argentina
and we need to understand how living systems
maintain their organization in the face of wear
and tear of components and changes in the
environment.
16
What is metabolism, and why is it important for
arriving at a de?nition of life?
luminy, marseilles 17 february 2006
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E
1
E
2
E
3
E
4
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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(No Transcript)
18
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)
19
Essential problems with Robert Rosens work
luminy, marseilles 17 february 2006
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example Biological example Conclusions Refe
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Bringing Rosens ideas to a broader audience will
involve describing them intelligibly,
illustrating them with intelligible examples, and
de?ning their range of validity.
J.-C. Letelier, J. Soto-Andrade, F. Guíñez
Abarzúa, A. Cornish-Bowden and M. L. Cárdenas
(2006) Organizational invariance and metabolic
closure analysis in terms of (M,R) systems
Journal of Theoretical Biology 238, 949961
20
Essential problems with Robert Rosens work
luminy, marseilles 17 february 2006
Rosens work provides an ideal ?eld for
interactions between mathematicians and
biologistsextremely few biologists have the
mathematical expertise to understand his work,
but most mathematicians lack the biological
knowledge necessary for putting it in a proper
context.
Systems biology growth galactose
metabolism arti?cial life System theory What
is life? Stoicheiometric
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example Biological example Conclusions Refe
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Quite early in my professional life, a
colleague said to me in exasperation, The
trouble with you, Rosen, is that you keep trying
to answer questions nobody wants to ask. This is
doubtless true. But I have no option in this and
in any event, the questions themselves are real,
and will not go away by virtue of not being
addressed. This attitude, I know, has estranged
me from many of my colleagues in the scienti?c
enterprise, and has put me far from todays main
stream. But sooner or later, if I am at all
correct, that stream will ?ow my way.
There have been very few attempts to build on it,
and some of those are greeted with horror by
people who really under-stand it, e.g.
Chu and Hos recent paper
in Arti?cial Life is riddled with errors. In
particular, they use a wrong de?nition of Robert
Rosens mechanism. This renders their critical
assessment of Rosens central proof null and
void.
Aloisius Louie, 2005
J.-C. Letelier, J. Soto-Andrade, F. Guíñez
Abarzúa, A. Cornish-Bowden and M. L. Cárdenas
(2006) Organizational invariance and metabolic
closure analysis in terms of (M,R) systems
Journal of Theoretical Biology 238, 949961
21
Essential problems with Robert Rosens work
luminy, marseilles 17 february 2006
Rosen sometimes expressed his view of life by
saying that organisms are closed to ef?cient
causationwhat we have called metabolic closure
or metabolic circularity.
Systems biology growth galactose
metabolism arti?cial life System theory What
is life? Stoicheiometric
analysis (M,R)-systems Mathematical
example Biological example Conclusions Refe
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What does this mean?
It means that the catalysts (enzymes)the
ef?cient causes of metabolismare themselves
products of metabolism.
It emphatically does not mean that there is no
?ux of matterfood transformed into excretain
living organisms, which would be absurd.

No one is saying that organisms are
closed to material causation.
J.-C. Letelier, J. Soto-Andrade, F. Guíñez
Abarzúa, A. Cornish-Bowden and M. L. Cárdenas
(2006) Organizational invariance and metabolic
closure analysis in terms of (M,R) systems
Journal of Theoretical Biology 238, 949961
22
organisms are closed to ef?cient causation
luminy, marseilles 17 february 2006
Systems biology growth galactose
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example Biological example Conclusions Refe
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f
F
A
B
However, shown like this it appears obscure
23
organisms are closed to ef?cient causation
luminy, marseilles 17 february 2006
The enzymes are themselves produced by the system,
Systems biology growth galactose
metabolism arti?cial life System theory What
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example Biological example Conclusions Refe
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Catalysis metabolism is the result of action of
a set of catalysts (enzymes) f on A f is the
ef?cient cause of B
f
F
A
B
Metabolism transformation of a set of
metabolites A into a set B A is the material
cause of B
Rosen used the word repair rather than
replacement, but this can be confusing as repair
has other (more appropriate) meanings in modern
biology.
24
Before trying to discuss a biological example of
Rosens ideas we need to ask whether what he is
demanding is possible even at an abstract level,
as Christopher Landauer and Kirstie Bellman have
denied that it is, claiming that some of his
ideas are simply false.
luminy, marseilles 17 february 2006
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example Biological example Conclusions Refe
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We have developed a purely formal and
mathematical example to show that Landauer and
Bellman are mistaken.
C. Landauer and K. Bellman (2002) in Theoretical
Biology Organisms and Mechanisms, AIP Conference
Proceedings Vol. 627, pp. 5970.
25
Arithmetic modulo 12 is very familiar in everyday
life (so much so that usually we do it without
thinking)
luminy, marseilles 17 february 2006
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example Biological example Conclusions Refe
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What time is it now?
What time will it be exactly 24 hours from now?
27.30 (half past twenty-seven)?
Or in other words, 3 24 3 (modulo 12)
26
Hypothesis starting from any integer i in the
set 0, 1, 2, 3 11 and applying the operation
j i x n mod 12, for some value of n it will be
possible to deduce i from j, in other words the
operation of multiplication by n modulo 12 is
invertible. Note that this is not a general
property of operations on sets, which are
generally not invertible indeed, Landauer and
Bellman claim that they can never be invertible.
luminy, marseilles 17 february 2006
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example Biological example Conclusions Refe
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27
Does it work for n 4?
luminy, marseilles 17 february 2006
0 x 4 mod 12 0
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1 x 4 mod 12 4
2 x 4 mod 12 8
3 x 4 mod 12 0
Already it fails we have two solutions for j 0
4 x 4 mod 12 4 5 x 4 mod 12 8 6 x 4 mod 12
0 7 x 4 mod 12 4 8 x 4 mod 12 8 9 x 4 mod 12
0 10 x 4 mod 12 4 11 x 4 mod 12 8
and it fails more generally only three j values
are allowed, so it is not possible to invert the
operation of multiplication by 4 modulo 12.
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Does it work for n 3?
luminy, marseilles 17 february 2006
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example Biological example Conclusions Refe
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Essentially the same problem as with n 4 only
four possible j values, and hence multiple ways
of solving for the set i that generates a
particular set j.
29
Results of j i x n mod 12 for all possible i
and n
luminy, marseilles 17 february 2006
  i  0 1 2 3 4 5 6 7 8 9 10 11
n
    0 0 0 0 0 0 0 0 0 0 0 0 0
    2 0 2 4 6 8 10 0 2 4 6 8 10
    5 0 5 10 3 8 1 6 11 4 9 2 7
    6 0 6 0 6 0 6 0 6 0 6 0 6
    7 0 7 2 9 4 11 6 1 8 3 10 5
    8 0 8 4 0 8 4 0 8 4 0 8 4
    9 0 9 6 3 0 9 6 3 0 9 6 3
    10 0 10 8 6 4 2 0 10 8 6 4 2
    1 0 1 2 3 4 5 6 7 8 9 10 11
    11 0 11 10 9 8 7 6 5 4 3 2 1
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The operation is invertible for n 7 (and also
for n 5)
luminy, marseilles 17 february 2006
0 x 7 mod 12 0
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1 x 7 mod 12 7
2 x 7 mod 12 2
3 x 7 mod 12 9
31
luminy, marseilles 17 february 2006
Systems biology growth galactose
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example Biological example Conclusions Refe
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We now turn to a more biological example
32
Consider an organism whose entire metabolic
activity consists of the production of a molecule
ST from precursors S and T.
luminy, marseilles 17 february 2006
This process requires a catalyst, M.
Systems biology growth galactose
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example Biological example Conclusions Refe
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However, this is not a gift from heaven. It needs
to be produced by the organism itself, so it is
better to treat it explicitly as a reactant.
J.-C. Letelier, J. Soto-Andrade, F. Guíñez
Abarzúa, A. Cornish-Bowden and M. L. Cárdenas
(2006) Organizational invariance and metabolic
closure analysis in terms of (M,R) systems
Journal of Theoretical Biology 238, 949961 (a
pdf ?le is available)
33
Consider an organism whose entire metabolic
activity consists of the production of a molecule
ST from precursors S and T.
luminy, marseilles 17 february 2006
This process requires a catalyst, M.
Systems biology growth galactose
metabolism arti?cial life System theory What
is life? Stoicheiometric
analysis (M,R)-systems Mathematical
example Biological example Conclusions Refe
rences
However, this is not a gift from heaven. It needs
to be produced by the organism itself, so it is
better to treat it explicitly as a reactant.
The only possible starting materials are those we
have already in the system, S, T and ST, or else
a new external source U.
ST
S
J.-C. Letelier, J. Soto-Andrade, F. Guíñez
Abarzúa, A. Cornish-Bowden and M. L. Cárdenas
(2006) Organizational invariance and metabolic
closure analysis in terms of (M,R) systems
Journal of Theoretical Biology 238, 949961 (a
pdf ?le is available)
T
34
luminy, marseilles 17 february 2006
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ST
S
J.-C. Letelier, J. Soto-Andrade, F. Guíñez
Abarzúa, A. Cornish-Bowden and M. L. Cárdenas
(2006) Organizational invariance and metabolic
closure analysis in terms of (M,R) systems
Journal of Theoretical Biology 238, 949961 (a
pdf ?le is available)
T
35
From stoicheiometric considerations it is evident
that M must be identical to STU, so let us write
it that way.
luminy, marseilles 17 february 2006
Systems biology growth galactose
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example Biological example Conclusions Refe
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But the repair enzyme R must also be subject to
wear and tear.
ST
STUST
STU
S
STUS
J.-C. Letelier, J. Soto-Andrade, F. Guíñez
Abarzúa, A. Cornish-Bowden and M. L. Cárdenas
(2006) Organizational invariance and metabolic
closure analysis in terms of (M,R) systems
Journal of Theoretical Biology 238, 949961 (a
pdf ?le is available)
T
36
From stoicheiometric considerations it is evident
that M must be identical to STU, so let us write
it that way.
luminy, marseilles 17 february 2006
U
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SUST
SUSTU
But the repair enzyme R must also be subject to
wear and tear.
SU
ST
STUST
STU
S
STUS
T
37
With each new en-zyme we need a new repair
enzyme, which needs its own repair enzyme, and so
ad in?nitum.
luminy, marseilles 17 february 2006
U
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SUST
SUSTU
SU
ST
To avoid introducing endless new precur-sors,
suppose that R is of the same general type as the
other molecules and has the structure SU.
STUST
STU
Now we have a com-plete (M,R) system.
S
STUS
T
Drawing in the style of the ?rst slide in this
section will make it look less complicated.
38
U
decays
Here we have three molecules created by
metabolism, ST, STU and SU, of which ST is the
product of the metabolism, and SU and STU are
catalysts.
ST
luminy, marseilles 17 february 2006
SU
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decays
STU
S
U
T
With three molecules and three reactions to be
catalysed, we have 333 27 possible assignments
a truly gigantic number if we regard it as a
surrogate for a model of more realistic size,
e.g. 89110 2.7 10214 for the model of
Escherichia coli mentioned earlier.
However, if we introduce a rule forbidding
autocatalysis in either direction so a
metabolite cannot catalyse its own formation or
its own removal, then we have a more manageable
four possibilities instead of 27.
39
U
decays
ST
luminy, marseilles 17 february 2006
SU
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decays
STU
S
U
T
However, if we introduce a rule forbidding
autocatalysis in either direction so a
metabolite cannot catalyse its own formation or
its own removal, then we have a more manageable
four possibilities instead of 27.
40
So, what has been achieved?
luminy, marseilles 17 february 2006
For the ?rst time we have provided an example of
an (M,R) system.
Systems biology growth galactose
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example Biological example Conclusions Refe
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We have disproved a claim by Landauer and Bellman
that Rosens central idea of metabolic
circularity is incorrect.
We have, moreover, determined the limits within
which organizational invariance is possible.
It allows closure of the loop that would
otherwise lead to in?nite regress.
Maybe this constitutes a step towards explaining
the circular organization of living organisms.
41
So, what has been achieved?
luminy, marseilles 17 february 2006
Organizational invariance can be summarized by a
bizarre equation in which f acts in turn as
function, argument and result
Systems biology growth galactose
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example Biological example Conclusions Refe
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Why not f(f) 2f? (Sylvain Blanquet, 2005)
Literature is mostly about having sex, and not
much about having children. Life is the other way
round.
David Lodge, 1965
We need to have a far better understanding of
what constitutes life, and of how organisms
organize themselves, before systems biology
moves beyond the level of tinkering.
42
references A. Cornish-Bowden, M. L. Cárdenas,
J.-C. Letelier, J. Soto-Andrade F. Guíñez
Abarzúa (2004) Understanding the parts in terms
of the whole Biology of the Cell 96, 713717
http//bip.cnrs-mrs.fr/bip10/biolcell.htm J.-C.
Letelier, J. Soto-Andrade, F. Guíñez Abarzúa, A.
Cornish-Bowden M. L. Cárdenas (2006)
Organizational invariance and metabolic closure
analysis in terms of (M,R) systems Journal of
Theoretical Biology 238, 949961
http//bip.cnrs-mrs.fr/bip10/rosen.htm J.-C.
Letelier, T. Kuboyama, H. Yasuda, M. L. Cárdenas
A. Cornish-Bowden (2005) A self-referential
equation, f(f) f, obtained by using the theory
of (M,R) systems overview and applications pp.
115126 in Algebraic Biology 2005 (ed. H. Anai
K. Horimoto) Universal Academy Press, Tokyo
http//bip.cnrs-mrs.fr/bip10/algebraic.htm R.
Rosen (1972) Some relational cell models the
metabolism-repair system in Foundations of
Mathematical Biology (ed. R. Rosen) Academic
Press, New York R. Rosen (1991) Life Itself,
Columbia University Press, New York R. Rosen
(2000) Essays on Life Itself, Columbia University
Press, New York
luminy, marseilles 17 february 2006
Systems biology growth galactose
metabolism arti?cial life System theory What
is life? Stoicheiometric
analysis (M,R)-systems Mathematical
example Biological example Conclusions Refe
rences
43
Dynamics and structure of biological
networksmarseilles - luminy, 1417 february 2006
María Luz Cárdenas Towards an understanding of
life
Athel Cornish-Bowden Making systems biology work
cnrs, marseilles
44
acornish_at_ibsm.cnrs-mrs.fr cardenas_at_ibsm.cnrs-mrs.f
r http//bip.cnrs-mrs.fr/bip10/homepage.htm
45
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46
organisms are closed to ef?cient causation
luminy, marseilles 17 february 2006
The enzymes are themselves produced by the system,
Systems biology growth galactose
metabolism arti?cial life System theory What
is life? Stoicheiometric
analysis (M,R)-systems Mathematical
example Biological example Conclusions Refe
rences
Catalysis metabolism is the result of action of
a set of catalysts (enzymes) f on A f is the
ef?cient cause of B
f
F
A
B
Metabolism transformation of a set of
metabolites A into a set B A is the material
cause of B
Rosen used the word repair rather than
replacement, but this can be confusing as repair
has other (more appropriate) meanings in modern
biology.
47
aristotles four causes
luminy, marseilles 17 february 2006
Systems biology growth galactose
metabolism arti?cial life System theory What
is life? Stoicheiometric
analysis (M,R)-systems Mathematical
example Biological example Conclusions Refe
rences
What makes a table?
This table is made of metal.
Material cause
Having four legs, a ?at top and a rigid structure
makes this a table.
Formal cause
Factory workers employed by Ikea made this table.
Ef?cient cause
Final cause
Having a surface suitable for putting my computer
on makes this a table.
It is the ef?cient cause that corresponds to the
modern (Humean) idea of a cause. The others are
not really causes at all as we would understand
the word today.
48
aristotles four causes
luminy, marseilles 17 february 2006
Some authors consider that cause is an
inappropriate translation of Aristotles word
and prefer just to transliterate it as
aitia. It corresponds not so much with the modern
meaning of cause, but with the answers one can
give to the question of what makes something what
it is (rather than what causes it).
a?t?a
Systems biology growth galactose
metabolism arti?cial life System theory What
is life? Stoicheiometric
analysis (M,R)-systems Mathematical
example Biological example Conclusions Refe
rences
What makes a metabolite?
Metabolites are made of metabolites.
Material cause
Formal cause
Being the product of an enzyme-catalysed reaction
makes glucose 6-phosphate a metabolite.
Metabolites are made by the action of enzymes.
Ef?cient cause
Final cause
Final causes are banished from modern
sciencethere is no creator, and hence
teleological thinking is not allowed. Products of
technology do have ?nal causes, because they are
made for reasons organ-isms, and the components
of organisms, have no ?nal causes.
There is thus no cause
beyond the ef?cient cause organisms are closed
to ef?cient causation.
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