Topics in Current Genetics, Vol. 13
L. Alberghina, H.V. Westerhoff (Eds.): Systems Biology
DOI 10.1007/b137122 / Published online: 13 May 2005
 Springer-Verlag Berlin Heidelberg 2005
What is systems biology? From genes to function
and back
Hans V. Westerhoff and Jan-Hendrik S. Hofmeyr
Abstract
The essence of the grand contributions of physiology and molecular biology to biology
is discussed in relation to what may be needed to understand living systems.
Unanswered is the link between function and molecular behaviour, and emergence
of function from the nonlinear interactions, respectively. Systems biology should
focus on properties that emerge in nonlinear interactions from the molecular level
up, which are crucial for biological function. Pre-genomics approaches such as
Metabolic and Hierarchical Control Analysis have already contributed concepts
and conclusions to systems biology. Their combination with the genome-wide
analyses should now lead to substantial progress in the understanding of life. An
aspect of biology at odds with traditional physics and chemistry is the circular
causation that occurs in all living systems. By analyzing this phenomenon quantitatively,
systems biology can already deal with certain types of circular causation
by dissection.
1 What came before?
1.1. Physiology
The experts differ on whether systems biology has been around for a while or if it
is a relatively new science. Both sides may be right, as we shall argue in this chapter.
Perhaps biology started in earnest when human beings marvelled over spermatozoa
as seen under a microscope, trying to recognize the homunculus (little
man) in them (i.e. supposing that a complete system should be there). Or perhaps
biology started with the study of human anatomy, where scientists and artists alike
marvelled at the high level of organization in terms of well-defined and fairly
autonomous organs, with functions that could almost be understood. Although
they were studying biological systems, these disciplines have been called physiology
rather than systems biology. They engage in discourses of nature where the
word `discourse' is significant in the sense of often being argumentation-driven
rather than just data-driven.
Physiology is attractive precisely because it relates directly to function. Indeed,
should function be understood, then dysfunction should be understood as well, and
avenues towards the treatment of disease should open up. The discourses of
120 Hans V. Westerhoff and Jan-Hendrik S. Hofmeyr
physiology were often based on rather loose principles however, which appeared
to lack generality and were always open to ad hoc exceptions. If physiology was
at all based on `laws' of nature, these laws tended to be empirical, such as the law
of Haeckel (phylogeny being a recapitulation of ontogeny) and the scale-free relation
between respiration rate and biomass. This physiology was often little more
than descriptive, useful nonetheless when features would be recurrent. After all,
proper diagnosis and then treatment based on experience with previous cases is
still one of the most successful qualities of human medicine.
For some time, it seemed that the laws or principles of physiology might be
akin to the early formulations of the second law of thermodynamics. This law
started off as an empirical law, which appeared to be liable to falsification in any
new system under study. The second law of thermodynamics gained enormous
standing when it could be derived from the realization that much matter consists
of large numbers of rather ill-organized particles, which due to their randomness
caused systems to produce entropy, provided that entropy was redefined in terms
of an average of molecular properties (cf. Westerhoff and Van Dam 1987).
1.2 Molecular biology
A remarkable event occurred when Mendel observed regularities when crossing
plants, which could be deduced to very simple rules governing the behaviour of
quasi particles, later called genes. Apparently, the appearance of a plant system
was determined by underlying agents (possibly material). Later, the discovery of
the DNA structure with its facile explanation of much of genetics, provided more
of a basis to this, however, by then the real biological revolution had already taken
place.
The biological revolution had been preceded by the chemical revolution where
it had been recognized that the dead world of physics was particle-based. Essentially,
this referred to a quantum nature of matter, in the sense that matter comes in
different types, all with different properties. These properties are discontinuous,
i.e. gold differs from silver and there is not necessarily matter with properties
halfway in-between. For instance, when hydrogen is made to react with oxygen,
the result has completely new properties. The concepts of atoms and molecules
revolutionized the ways in which one analyzed the world and for many years the
chemical industry delivered many new materials with new and useful properties.
Chemistry was perhaps the first clear systems science.
It was soon observed that many of the same molecules that occurred in inorganic
matter also occurred in living systems. The new science of chemistry had
many ties with biology. No chemical elements were discovered that were unique
to living matter. And in fact many chemical molecules for which properties and
structure were determined ex vivo had a biological origin. Boiling living matter in
hydrogen chloride frees a large number of small molecules, including nucleosides
and amino acids, all of which inspired organic chemistry into making more similar
molecules that could be useful to mankind.
What is systems biology? From genes to function and back 121
This phase in scientific history suggested that life was perhaps little more than a
collection of such molecules. It also inspired biochemistry into a search for the reaction
pathways through which those molecules were synthesized. And indeed,
rapid progress ensued, up to the elucidation of the molecular basis of life. A major
step was the recognition that virtually every chemical reaction in living organisms
was catalyzed by a protein and that, therefore, the chemical pathways in life could
be delineated by isolating and characterizing the proteins that catalyzed the subsequent
steps. Next steps were the discovery of a correspondence between those
very same processes and the genes discovered by genetics, and the subsequent
identification of genes with parts of the long linear information carrying molecules
of DNA. The connection between genetics and biochemistry led to the recognition
that life could be studied successfully at the molecular level. This was expressed
in the term `molecular biology', which had an emphasis on the principle that DNA
is expressed through RNA into protein, which then catalyzes molecular processes.
The primary structure of genes could be elucidated, the corresponding amino acid
sequence deduced, the 3-dimensional structure of the corresponding protein could
be determined, and action and the mechanism of action of many proteins could be
established. Indeed, of every macromolecule, and of every process in living organisms
everything could be determined and explained, or so it seemed. This became
the triumph of molecular biology and biochemistry combined.
1.3 Systems molecular biology?
So, here we are. We will (soon) be able to determine the identity and concentrations
of molecules in living organisms. We must surely be close to understanding
life and curing its diseases!
While physiology had come close to describing function without really understanding
it in solid physical chemical terms, molecular biology now seemed to understand
life in precisely those terms, or, at least to do so for the molecules in life.
There was an issue with molecular biology, as with physiology, that it might remain
an incomplete science and, therefore, it remained a limited scientific discipline
in most of the previous century. Living organisms are specified by so many
genes and proteins that it seemed that molecular biology could never fully characterize
a living system. As a consequence, demonstrated failures of molecular biology
to understand living systems could always be attributed to the existence of
still unknown factors.
This is where genomics caused yet another revolution. With the sequencing of
entire genomes and with the ability to study their expression at the level of transcriptome,
proteome, and metabolome, every molecular factor became identifiable.
And indeed, much activity went into complete identification of transcriptomes,
proteomes, and metabolomes. Complete inventories of systems were and
are made. Molecular biology became a complete science; no elusive factors remained
and scientific explanations by molecular biology became falsifiable, or so
it seemed.
122 Hans V. Westerhoff and Jan-Hendrik S. Hofmeyr
Some equated this new molecular biology with systems biology, as it comprised
the complete molecular identification of the system of any living organism.
With the success of molecular biology in helping us to understand the mechanisms
of the individual molecules of life, the extension of molecular biology to the complete
set of molecules of life would surely help us comprehend life. Understanding
30,000 times 1/30,000th part of life would surely amount to the understanding of
life itself or would it? Is systems biology nothing more than molecular biology of
entire systems? Should it be named `systems molecular biology' (Westerhoff and
Palsson 2004)?
2 Limits to systems molecular biology
2.1 Data floods
A number of caveats with respect to such optimism soon emerged. One of these
might prove to be technical only: there is too much data. Data on transcriptomics,
proteomics, and metabolomics are now being accumulated at higher rates than that
they can be analyzed and structured.
Bioinformatics comes to the rescue here, and so is the ever-increasing power of
digital computers. Moreover, the number of types of molecules is limited and for
understanding the essence of life, we need perhaps not understand all possible
conditions. Furthermore, a better specification of the biological issue one actually
wishes to address, and a return to hypothesis-driven research might limit the
amount of data needed for analysis significantly. Therefore, molecular biology,
genomics plus bioinformatics might still be able to do the job.
2.2 Nonlinearity
A second caveat relates to something that is already well known: much of biological
function stems from inherent strong nonlinearity. The word nonlinearity is here
used in a broad sense and deserves appreciable specification. We shall make this
specification by the use of some simple algebra. We ask the less mathematically
oriented reader to bear with us; it will be well worth to study this example, because
it gives the crux of why systems biology is more than the new clothes of the
emperor!
We consider molecules of type x and molecules of type y and first assume that
a functional property of interest, f, depends linearly on both x and y:
cybxaf ++= (1)
x could be the number of molecules of X, y the number of molecules of y, a and b
their respective molecular masses and c the mass of the rest of the cell; f being the
mass of the total. The linear dependence of f on both x and y independently has the
important property that one can study the dependence of f on X and Y independently
and then understand how f behaves by just superimposing the dependencies.
What is systems biology? From genes to function and back 123
For, denoting changes by delta's, one can first determine experimentally how
function changes when only x changes and, thus, determine the value of a.
a
x
f
=


(2)
Similarly one can determine the value of b:
b
y
f
=


(3)
When both x and y change one can then simply calculate the change in function
from a, b and the actual changes in x and y, through:
ybxaf += (4)
For the mass of a dead cell this might work. But it may not work for many other
functions. For instance, it would not work for the mass of a living cell. For, the
change in amount of a certain enzyme x would lead to a change in the rate of the
reaction it catalyzes and, therefore, to a change in metabolite concentrations and
because the cell is an open system a corresponding change in total mass. The latter
change could well depend on whether or not the amount of a second enzyme y is
also changed at the same time. In the latter case, the total change in mass should
not equal the change in mass of enzyme x plus the change in mass of enzyme y.
Looking at the living cell from a structural point of view, one might, inadvertently,
come to the view that total structure is a linear property: determine the
structure of all proteins independently and call these structures x, y, etc., multiply
each structure with the number of molecules of the corresponding protein (a, b,
etc.). Do this for all proteins and add up all the results so as to obtain the total
structure of the cell (one should of course add spatial coordinates for where in the
cell the structure sits). The approach seems reasonable, and is valuable perhaps as
a first order approach. Yet, one quickly realizes that it may still be incorrect even
if one only focuses on the structure and not on the dynamics and functioning of
the cell. The approach should fail for instance if two proteins (e.g. subunits of a
single protein) interact with each and form a complex of a more compact structure,
or if chaperons are involved, or if they interact with each other and cause the synthesis
of ATP, which causes the phosphorylation of a kinase, the expression of
many genes and, therefore, altered levels of many other proteins.
Let us now look at a case where there is no linear relationship between function
and the molecules x and y, e.g.:
2
* yxdf = (5)
Even though this equation is even simpler than the linear one (fewer parameters,
i.e. only d rather than a, b, and c), it produces many complications. First, the dependence
of function (f*) on x is no longer constant but depends on y:
2*
yd
x
f
=


(6)
and, hence, cannot be determined once and for all: The functioning of x depends
on the activity of y.
For the dependence of function on y the situation is even worse: it depends on
x, on y, as well as upon the change in y:
124 Hans V. Westerhoff and Jan-Hendrik S. Hofmeyr
( ) yxdyxdyxdyyxd
y
f
+=-+=


2
* 22
(7)
In addition, a change in function due to a change in both x and y cannot be understood
as the sum of the change in function due to the change in x and the change
in function due to the change in y:
( ) ( )
yyyxdxydy
y
f
x
x
f
yxdyxydxydyxdyyxdf
++=


+


++++=
)2(
**
22*
2
222
(8)
the difference between the two amounting to:
( )2
2
**
* yxdyxydy
y
f
x
x
f
fSB +=


-


-= (9)
Only detailed modelling/calculation can relate the functioning of x and y independently
to their functioning together.
In the above, x and y were treated as independent molecules. Often they are not
independent. And a change in x may also cause y to change. Then already for the
linear dependence there is a complication:
x
y
ba
x
f


+=


(10)
i.e. the functioning of x is not only given by a, but also by how x affects function
through y and by b.
The paradigm of molecular biology is to determine a and b. It sees these as
universal constants. a and b are the clothes of the emperor. Using the first equation,
it then predicts how the molecules determine the functioning of the system.
(8 shows that the prediction will be wrong whenever function depends nonlinearly
on the molecular behaviour. New clothes for the emperor may not even help: the
emperor should engage in a whole new game of redressing himself depending on
the active and dynamic conditions he is in).
Again, where are we? Molecular biology determines x and y of the above equations,
and perhaps the extents to which they change. Physiology can determine f*
and its changes. The urge is to understand why f* changes when x and y change.
The paradigm that the functional behaviour of the system can be understood from
the changes in x and y by just determining a and b, is only true in linear systems.
Therefore, the issue now is whether biological systems are linear, or more precisely,
whether important functional properties of biological systems are linearly
related to the properties of their molecules. And the issue is whether the molecular
properties are independent of one another.
2.3 Nonlinearities and dependencies prevail in real life
There was a time where linear relations were quite popular. Substrate concentrations
were assumed to be far below the KM's of their enzymes such that enzyme
kinetics in vivo should be linear. Looking at the `live' database of a number of
What is systems biology? From genes to function and back 125
metabolic pathways (cf. www.siliconcell.net ) one readily notes that this assumption
is not realistic for the pathways that have been studied to sufficient detail experimentally.
Often the substrate concentration is around the KM, so that rates depend
non-linearly on concentrations. And, in many cases kinetics is cooperative in
terms of substrate concentrations, providing another reason for nonlinearity. And,
almost per definition product inhibition, which occurs frequently, is nonlinear.
Indeed, Michaelis-Menten, Monod, and Hill's equations for enzyme and
growth kinetics respectively are less than first-order in their dependence on concentration.
Quite a few reactions depend on the concentration of more than one
compound, e.g. when ATP is co-substrate in kinase reactions. Then the rate is bilinear
or sub-linear, i.e. does not fulfil the linear superposition of two linear equations.
Also approximations of kinetic relations in cell function reckon with nonlinear
dependencies being the rule rather than the exception. Biochemical Systems
Theory (Savageau 1976) uses power laws for this description with the clear intention
that the powers need not equal 1. Mosaic non-equilibrium thermodynamics
(MNET; Westerhoff and Van Dam 1987) uses linear relationships between the
logarithms of concentrations and reaction rates, which translate into nonlinear dependencies
of rate on concentrations (cf. Wu et al. 2004).
How does function depend on gene dosage? For non-redundant essential genes
it is clear that function disappears upon a complete knockout. Most such genes (or
rather the mutations therein) are recessive, however, this implies that half the gene
dosage bestows the organism with full rather than half function: function tends to
vary hyperbolically not linearly with gene dosage (Kacser and Burns 1973). The
related issue of how pathway flux depends on enzyme activity can be addressed
relatively strictly by Metabolic Control Analysis (MCA) and leads to a rather
similar answer: pathway flux varies much less than proportionally with enzyme
concentration.
There are a number of cases were it is quite obvious that simply adding the behaviour
of molecules in isolation will not reproduce their behaviour in vivo. One is
that the molecules that are involved in the cell-cycle oscillation and the molecules
that are involved in glycolytic oscillations would not themselves oscillate in isolation.
The oscillation only arises when many molecules of the network are present
(see chapter by Novak et al.). Yeast glycolysis would not operate as steadily as
observed experimentally if the TPS1 regulatory feedback with trehalose phosphate
inhibiting hexokinase would not be active (Teusink et al. 1998). More generally,
reaction rates through metabolic pathways can only attain steady state when they
become equal to one another, which they can only do if the enzymes interact with
each other, mostly by sensing the concentrations of the metabolites between them.
ATP synthesis by the H+
-ATPase is only possible when the enzyme occurs in a
system with electron­transfer chain linked proton pumps that generate an electrochemical
potential difference for protons that is sufficiently high. If the latter are
absent, ATP hydrolysis will occur. The difference between ATP synthesis and
ATP hydrolysis is crucial for life.
Clearly, the more realistic assumption should be that relationships are nonlinear.
Rather than assuming linearity of the dependence of reaction rates on the concentrations
of their substrates and products, we use the paradigm that kinetics in
126 Hans V. Westerhoff and Jan-Hendrik S. Hofmeyr
vivo is massively nonlinear in terms of metabolite concentrations. And, we reckon
that just adding knowledge of the individual molecules outside the context of the
systems in which they act, will not lead us to understand their functioning in the
living organism: outside the system the y's are different, making the prediction of
how x affects function, fail. This compromises `molecular systems biology' and
suggests that something is needed in addition to the massive determination of the
properties of all the molecules of the living cell, individually.
3 Systems biology: Neither the biology of systems nor the
biology of all molecules individually
We are able to analyze function of living organisms by physiology without too
much reference to molecules. We are also able to determine the properties and
concentrations of most molecules that are active in living cells. However, because
of the aspect of nonlinearity addressed above, adding all the bits of knowledge
about the individual molecules will not lead us to understand the functioning of
the living cell. And, on the other hand physiology only understands life in terms of
more descriptive properties that are not clearly related to molecular events.
What is needed is a science, which we shall call `systems biology' that connects
physiology to genome-wide molecular biology, i.e. a science that addresses
specifically how and why the system of macromolecules differs functionally from
the sum of the individual behaviours of the molecules that constitute the system.
Because of the importance of nonlinearities for function, this science is complex,
whether we like it or not. Where physics has profited much from simplification often
down to linear first-order approximations, systems biology is inherently more
complicated as mostly it cannot engage in such linearization, for fear of approximating
away its very essence, i.e. the properties that arise precisely due to the
nonlinearity of the relations.
The tendency of Non-Equilibrium Thermodynamics to focus on areas where
flux-force relations are quasi-linear may seem to make it more appropriate from
the physics perspective than from the perspective of systems biology, were it not
for the fact that a linear description in a lin-log (Westerhoff and Van Dam 1987;
Wu et al. 2004) or a log-log world corresponds to a nonlinear world in the true
coordinates, and that MNET did away with Onsager's reciprocity relations. Indeed,
linear flow-force relations of non-equilibrium thermodynamics are perfectly
consistent with the occurrence of oscillations (Cortassa et al. 1991).
The feature we noted above, i.e. that the dependence of function on a molecular
property may depend on the intensity of that property itself and on the intensity of
other molecular properties, has the implication that systems biology properties
may be much more a conglomerate of special properties that are only valid in a
subset of conditions than general properties. In a linear world, many completely
general, condition-independent properties should be expected to dominate, but not
so in a nonlinear world, although there may still be some such general properties.
What is systems biology? From genes to function and back 127
And then, one should not forget that systems biology refers to `biology', i.e. to
functioning of living systems. This implies that it may not deal with the most general
of all nonlinear systems, but mostly with the subset of systems that are found
in biology. Accordingly, there is an emphasis on systems that are robust with respect
to chemical and even evolutionary fluctuations (cf. Carlson and Doyle 2002;
Westerhoff and Van Dam 1987). Explosive systems with unbounded reaction rates
are unlikely to be common in the living cell.
Is systems biology new then? Well, No and Yes at the same time. Scientists
have long studied cases where new properties arose in molecular interactions
(Westerhoff and Palsson 2004). Below, we will discuss show this systems biology
avant la lettre reached beyond both molecular biology and physiology. We will
show how systems biology combines both these disciplines with at least three others,
and perhaps even more. We will illustrate how systems biology has already
solved issues about biology that many physiologists and molecular biologists were
not even able to recognize as issues because of the limitations of their paradigms.
And, we will suggest some ways in which parts of systems biology may be developed
further.
4 Systems biology avant la lettre
4.1 Self-organization
The molecular biology paradigm sees the cell as a bag of structures kept together
by a plasma membrane. The biochemistry paradigm adds that many of the structures
correspond to proteins that catalyze or regulate chemical processes. However,
macroscopically, and even microscopically, most living organisms do not
quite look like amorphous bags of enzymes; rather, they are well structured, the
top differing greatly from the bottom and perhaps the left being a mirror image
rather than a replica of the right. How do these structures form? Early development
of organisms is a case in point, where elaborate spatial structure arises from
an apparently spherically symmetrical egg. The apparent breaking of symmetry
also occurs in the dimension of time. In a continuous environment, heart cells begin
to beat, cell cycles begin to run. The issue connotes with an issue of energetics,
i.e. how chemical free energy could be converted into and from spatial free
energy such as in muscle contraction, in chemicomotion of macromolecules, and
in transmembrane electric potentials.
Although preceded by many others, the Brussels school led by Prigogine attracted
much attention when addressing these issues (Nicolis and Prigogine 1977).
It turned out that small fluctuations, which could themselves break symmetry
could be amplified in come cases and lead to a less symmetric final state (both in
space and in time) than the initial state. Because in particle physics there should be
time invariance and conservation of momentum at the level of individual particles,
this still produced a paradox. However, part of this paradox had been resolved before
by statistical thermodynamics showing that in systems of many particles
128 Hans V. Westerhoff and Jan-Hendrik S. Hofmeyr
some system configurations recognized as single macroscopic states actually corresponded
to many more underlying microscopic states than other such macroscopic
configurations. Therefore, the former are more likely to be observed. If one
were to observe an unlikely macroscopic state first (e.g. because it had been preprepared
by earlier processes), then it should be highly likely that one would see
that macroscopic state change to the more likely one. This is what we have learnt
to call spontaneous processes. We note that this phenomenon is a property of systems
of particles much more than of the particles themselves.
For these transitions between macroscopic states to occur, it is important that
the system of particles can move between its microscopic configurations, to then
act as if it were searching for the most probable macroscopic state. The movements
between the microscopic configurations are called `fluctuations'. They derive
from the continuous bombardment of particles from the environment with energies
of all sorts, at least at temperatures above zero Kelvin. The fluctuations
cause a progression of a system through its many configurations, which is a random
walk in terms of the microscopic states, but a much biased random walk in
terms of macroscopic states. In macroscopic terms, it seems that the system exhibits
a preference for the most probable macroscopic state, i.e. for the macroscopic
state that has most microscopic configurations. The latter macroscopic state then is
the final `steady' state and such a state is then stable with respect to fluctuations,
i.e. after fluctuations the system will return to that macroscopic state. It is this stability
against fluctuations (and even of processes themselves) that is at the basis of
many systems biology properties, such as robustness and the flux and control
properties of dynamic systems including biological ones (cf. Westerhoff and Van
Dam 1987). For now it is important that this very stability is a property of systems
not of their components.
The above statistical thermodynamic argument is often formulated in terms of
spontaneous processes producing entropy, where entropy is associated with less
ordered states, or chaos. Living organisms are different in this respect as they
typically produce order out of chaos, or at least maintain order. Life is, therefore,
at the basis of quite a significant extension of thermodynamics where it was made
clear that Gibbs (Katchalsky and Curran 1967), or rather metabolic (Westerhoff
and Van Dam 1987) free energy has to be destroyed to keep life processes going,
whilst some of the input free energy is transduced to free energy in the new biomass.
Because this is essentially about life and biology and because it critically
depends on the system nature of biology, this has perhaps been the first type of
system(s) biology.
Living systems, therefore, need to operate away from equilibrium, yet not so far
away that they expend all input free energy and fail to retain some of it for building
their own structures. For true symmetry breaking it was shown that systems
need to be further away from equilibrium than where the first order Onsager approximation
applies (Nicolis and Prigogine 1977; Cortassa et al. 1991). Moreover,
for such phenomena to occur, more than two components, asymmetrical thermokinetics,
and nonlinear kinetics are needed. Such symmetry breaking or `selforganization'
can only happen in systems of molecules not in individual mole-
cules.
What is systems biology? From genes to function and back 129
4.2 Perpetuation
Symmetry breaking of the above, far-from-equilibrium thermodynamic type has
the disadvantage that it is non-robust: it depends on the nature of the first fluctuation.
If the bifurcation is to lead from spherical to left-handed symmetry for instance,
one should expect an equal probability to have an outcome of right-handed
symmetry. At a fifty percent error rate, this symmetry breaking would be a highly
unreliable mechanism. Because many such symmetry breaking steps need to be
made, this should result in little fitness vis--vis biological evolution. Indeed, experimental
results now suggest that there is much less absolute symmetry breaking
in biology than was once assumed.
First, most eggs are not quite symmetrical but exist in the context of asymmetrical
environment set up by the maternal organism. Probably self-organization
mechanisms serve to consolidate symmetry breaking and developmental decisions
that have been set in motion by robust asymmetries. The latter are set in place by
pre-existing biological matter. Indeed, perpetuation is a major characteristic of life
as we know it. New cells are not created de novo somewhere in the middle of the
maternal cell, then to be excreted as a newborn cell. Rather, the mother cell grows
in volume and surface area and then either splits into two equal parts, or a small
part of the mother cell pinches off and becomes the daughter cell. New proteins
are synthesized on old ribosomes, new mRNA is synthesized by old RNA polymerase,
and half the DNA of cells already existed in the mother cell. This perpetuation
aspect of life makes the issues of symmetry breaking and selforganization
much less acute. There is far less self-organization than anticipated
earlier on; much of what happens is perpetuation and then division. Selforganization
processes serve to maintain and stabilize decisions made through per-
petuation.
4.3 Chemiosmotic coupling
The maternal organism may convey its own asymmetry to its daughter cell in this
mass action way. However, asymmetry can also be conveyed catalytically. Proteins
are asymmetrical and are inserted asymmetrically into membranes. Accordingly
a cytochrome oxidase catalyzing the macroscopically scalar reaction of oxygen
reduction by cytochrome c can couple this reaction to vectorial proton
movement by virtue of its asymmetrical 3-D organization. A substantial fraction
of the free energy in food is transduced to free energy in new biomass through the
electrochemical potential difference for protons across the mitochondrial inner
membrane. This involves a transition from chemical free energy, which is a scalar
property, through a vectorial property back to a scalar property. Hence, it involves
two changes of symmetry, the former of which involves cytochrome c oxidase.
For the present chapter, it is important that of necessity, this process requires a
system, i.e. cannot be carried out by a single macromolecule: it requires a primary
proton pump generating the electrochemical potential difference of protons, a
closed membrane and a secondary proton pump converting the protonmotive free
130 Hans V. Westerhoff and Jan-Hendrik S. Hofmeyr
energy into ATP hydrolytic free energy. Indeed, the chemiosmotic coupling concept
by Peter Mitchell (1961) was a second important case of systems biology
avant la lettre.
4.4 Non-equilibrium thermodynamics
Many biological free-energy transduction processes have been described in terms
of non-equilibrium thermodynamics. Where thermodynamics was once thought to
be devoid of mechanistic detail, and indeed this was proclaimed to be an asset, it
was shown that the very essence of processes that are significantly removed from
equilibrium is that their thermodynamics does depend on mechanisms (Keizer
1987). MNET was developed precisely to relate systems performance to the
mechanism of free-energy transduction, including those leading to incomplete
coupling (Westerhoff and Van Dam 1987).
4.5 Systems biology avant la lettre: Metabolic Control Analysis; laws
of systems biology
Non-equilibrium thermodynamics approximates rate equations by linear functions
of logarithms of concentrations. This enables analytical solutions at steady state
(Katchalsky and Curran 1967). In this approach, however, the parameters are
treated as phenomenological and little emphasis is placed on their relationship
with parameters that reflect details of mechanisms. Hill's (1977) analysis of complex
biological reactions catalyzed by single enzymes showed that although their
rate equations obeyed some general format, their parameter values and form also
reflected mechanism. For systems of reactions, MNET (Westerhoff and Van Dam
1987) elaborated this and showed how quantitative analysis of biological freeenergy
transduction systems could lead to conclusions about the functioning of
mechanisms such as imperfect coupling and back-pressure.
Biochemical Systems Theory (BST) approximates rate equations with power
laws. For linear reaction chains, this again enables analytical solutions of the system
equations for steady state (Savageau 1976). There is no emphasis on how the
powers relate to underlying mechanisms; the emphasis is on qualitative systems
behaviour, i.e. on physiology in the above definition. In addition, BST and MNET
result in descriptions and sometimes tendencies for systems to behave in certain
ways, but not in general principles or `laws'.
Metabolic Control Analysis (MCA) is both less and more ambitious than BST
and MNET. First it does not aim at describing the entire dependence of functional
properties on process properties. It focuses on the infinitesimal dependence of
functions on those properties. The disadvantage of this is that MCA only considers
small changes in the system. The advantage is that in this, MCA is not an approximation
but exact, and that as a corollary thereof, MCA has derived some
general principles for metabolic systems, i.e. some systems biology `laws'. We
shall here illustrate one of these, i.e. the summation law for the control of flux
What is systems biology? From genes to function and back 131
through a metabolic pathway by the various reaction steps in that pathway. As in
biology almost all reactions are catalyzed by enzymes, the control by a reaction
step is related to the control by proteins and to the control by gene expression. The
control of the steady-state flux J through a metabolic pathway, such as in Fig. 1,
by enzyme i is quantified in terms of the so-called control coefficient of that enzyme
vis--vis that flux:
ijnjei
J
e
j
i ed
Jd
C
=









,,..,.1,
log
log
(11)
where log stands for logarithm with any base. ei refers to the catalytic activity of
the ith
step in the pathway and can in simple cases be replaced by either the Vmax or
the concentration of the enzyme catalyzing that reaction. Technically speaking, the
d here stands for a partial derivative, with the conditions that the other process activities
are held constant and the steady state is re-attained. The logarithmic derivative
is taken at the physiological state and can be replaced by the normal derivative
provided that the result is then multiplied by the ratio of enzyme activity
to flux.
The control coefficient quantifies the importance of the ith
step in the pathway
for the pathway flux. Taking the molecular biology point of view to the extreme
one might wish to determine this flux control coefficient in vitro for every enzyme
individually and then assume that that control coefficient should be approximately
the same in vivo. With the enzyme in isolation, the flux through the enzyme is directly
proportional to its concentration, which implies that the flux control coefficient
equal 1. For a pathway of n enzymes, this should imply that all enzymes
should be flux-limiting and that the sum of all flux control coefficients should
equal n. MCA falsifies this conjecture: it has a law that says that the sum of the
flux control coefficients for any flux over all processes equal 1:
1
1

=
n
i
J
ei
C (12)
Contemplating a two-step metabolic pathway, it is simple to see how this relates to
the issue that systems biology deals with nonlinear systems in which processes are
dependent:
21
1
2
1
e
J
de
dJ
J
e
de
dJ






-= (13)
i.e. the functional property flux (J) neither depends on the molecular properties e1
and e2 independently, nor on either of them linearly. The more intuitive explanation
for this is that when one increases the activity of one enzyme in the pathway
to see if it is flux limiting, one simultaneously makes the other enzymes more flux
limiting.
Laws of MCA address the sum totals of control coefficients with respect to flux
and concentration, as well as relationships between control coefficients and enzyme
properties called elasticity coefficients. The latter laws are called connectivity
theorems and relate to the stability of the system against fluctuations (cf.
above and Westerhoff and Van Dam 1987). They are often called theorems but
132 Hans V. Westerhoff and Jan-Hendrik S. Hofmeyr
would equally qualify as `laws' of systems biology, as they indeed address the difference
between properties of the systems and properties of the molecules in isola-
tion.
The enzyme properties that are important in the connectivity laws are the elasticity
coefficients. They denote the extent to which a reaction step, hence the enzyme
that catalyzes it, responds to changes in its metabolic environment. For the elasticity
of enzyme 1 of Fig. 1 with respect to the concentration (z2) of metabolite Z2:
2
11
log
log
2 z
v
Z 

 (14)
For the case that enzymes 1 and 2 of the pathway are product insensitive, but enzyme
1 is sensitive to the concentration of metabolite Z2, one finds for the control
of the steady state flux through enzyme 1:
13
3
1
22
2
zz
zJ
C


=
(15)
When enzyme 1 is well regulated by metabolite Z2, the corresponding elasticity
1
2z
 is quite high in absolute magnitude. Through the above equations, this has the
effect that enzyme 1 exerts no control on its own steady state reaction rate; all that
control may then reside in enzyme 3 of figure 1. In this way, MCA can illustrate
that the in vitro control a macromolecule has of its own activity, may be absent in
the physiological situation of the intact system. The other factors, residing in different
macromolecules, may control its function. This brings home the key issue
of systems biology that important aspects of cell function reside in the interaction
properties (the elasticity coefficients) rather than in the properties of the individual
molecules. It also reinforces the role of MCA as an important theoretical tool in
systems biology.
4.6 Circular causality and emergence
Biochemistry and molecular biology reinforced the use of the scientific methods
of contemporary physics and chemistry in biology, methods which arose from and
are still closely tied to the Newtonian view of the world. The Newtonian perspective
can be reconciled with three of the four Aristotelian causes, i.e., the state of
the system at time t+t can be explained as the effect of a material cause corresponding
to the state of the system at time t, an efficient cause corresponding to
the mathematical form of the recursive state transition function, and a formal
cause corresponding to the initial state at time t0 and other parameter-values.
However, as argued by Rosen (see e.g. Rosen 1991), there is no place in this view
for the fourth Aristotelian causal category, namely that of final cause. The reason
What is systems biology? From genes to function and back 133
S Z1 PZ3Z2e1 ene4E3e2
Fig. 1. Metabolic pathway, with feedback from the second metabolite on the first reaction.
We shall assume all reaction irreversible and not product inhibited.
for this is that whereas material, efficient and formal causes all work in the forward
direction, final cause works backwards, which in the Newtonian framework
would imply the future affecting the present. From the perspective of physics,
chemistry and molecular biology, final cause is, therefore, illegitimate.
Final explanations are closely linked to the concept of function, which is indispensable
for many explanations in mainstream biology, and is, despite its uncertain
status in formal arguments, often invoked as an inspiration for finding phenomena
and even mechanisms. Today many biologists regard evolution and
selection of the fittest as an acceptable basis for the use of final causation as part
of a scientific explanation. The more frequent type of argument is that a certain
mechanism is in place because it leads to a higher growth rate or to a higher
growth efficiency. The background for this argumentation is often left implicit but
is taken to be that because the mechanism improves growth rate, it should have
been selected for in evolution, which explains why it is present in the organism
under study: ultimately the explanation is then effectively rephrased in terms of
formal causation. Common examples of application of final cause include statements
such as the occurrence of multidrug resistance proteins at the blood-brain
barrier, because it helps to keep toxins out of the brain. Recent examples in systems
biology include the flux balance analysis of Palsson and colleagues (Reed et
al. 2003). Here fluxes are calculated on the basis of earlier experimental results on
metabolic pathway genes specifying the metabolic network, and on the assumption
of maximal growth rate (which thereby acts as a final cause). The correspondence
of the calculated fluxes with experimental fluxes is taken to indicate the
correctness of the pathway model.
The first three Aristotelian causes appear to be more solid than final cause. On
the other hand, one can see particularly in biology that the implementation of final
causes in scientific research can be useful, provided that the final cause (such as
the assumed requirement to be optimal in terms of growth rate) is mentioned explicitly.
If then, later, it turns out that an organism has not been optimized for
growth rate, the argumentation drops for that particular organism but may remain
in place for others. After all, other parts of science, with mathematics as a champion,
operate on the basis of axioms, which are assumed material causes, and it is
accepted that such sciences are useful only for phenomena that obey those axioms.
However, biology may not yet be quite ripe for the acceptance of final cause.
First it needs to be certified for every final cause that it has indeed been brought
134 Hans V. Westerhoff and Jan-Hendrik S. Hofmeyr
into play in evolutionary selection. Although, it may seem that evolution is able to
select for any odd property that could in theory enhance survival potential, this is
not so. For instance, lions born with jet engines would be much more successful in
hunting, but such lions could certainly not emerge through biological evolution.
An understanding of whether natural selection could have indeed selected for a
presumed function again requires insight in the functioning of the entire biological
system: it requires systems biology. For as long as insufficient systems biology is
in place, it is perhaps still better to weed out the implicit use of final (forward)
causation that is all too frequent in a biology that pretends to follow rationality
only.
The above sketches the way mainstream biology currently attempts to cope
with final causation. Contemporary physics and chemistry, on the other hand, are
quite strict in eradicating final causes in their scientific arguments. Even more
strongly they consider as illegitimate the circular causation implied in explanations
in which we say that A causes B, B causes C and C causes A. However,
Rosen (1991) argued persuasively that it is exactly this type of causation that distinguishes
living organisms from non-living systems. In brief, Rosen demonstrated
that for living systems to be able to fabricate themselves autonomously (i.e. be
autopoetic in the sense of Maturana and Varela 1980) they need to be organised in
a way such that all efficient causes are inside the system. Using the formalism of
category theory, he developed a relational biology with which this living organisation
can be described.
There are other types of circular explanation that have more to do with causation
in the Humean sense of one event causing another subsequent event; these
also have potential value in biology. Examples are found in induction of gene expression
and in the cell cycle: lactose uptake in E. coli causes an increase in intracellular
allolactose, which binds lac repressor and causes induction of the lac operon
which causes enhanced expression of lactose permease, which causes
enhanced uptake of lactose, etc. Accordingly, lactose uptake causes (more) lactose
uptake. In glycolytic oscillations, activation of phosphofructokinase causes an increase
in AMP which causes a further such increase. The ensuing stronger drop in
ATP and increase in fructose bisphosphate causes the lower part of glycolysis to
make more ATP, which then again stimulates phosphofructokinase which then
again decreases ATP and increases fructose bisphosphate which stimulates the
lower part of glycolysis. Here phosphofructokinase activation causes phosphofructokinase
activation, be it with a time delay; oscillations being the consequence.
Because life is a self-sustaining phenomenon, it has mechanisms in place that
cause effects that in turn cause their causes. Although this may not fall within the
accepted paradigm of the physical chemical sciences, the phenomenon of circular
causation may be so essential to biology that it should be dealt with. As mentioned
above, Rosen (1991) has shown how to deal with organisation that leads to circular
fabrication. Below we shall show a way that deals with circular event-causality
by dissecting it into two or more parts, employing mathematical methodologies.
What is systems biology? From genes to function and back 135
4.7 Networks and hierarchies in life
The identification of most genes encoding the metabolic enzymes of some organism
has enabled methodologies for the systematic mapping of metabolic networks.
The method first identifies the genes that encode enzymes, then identifies the
chemical reactions these enzymes catalyze, and then writes for each enzyme
which chemical compounds it produces and consumes, and at which stoichiometry.
The stoichiometries for each reaction are then denoted as the column of a huge
stoichiometry matrix N. The multiplication of N with a vector v of all reaction
rates then gives the time dependence of the concentrations of all chemical substances
(dm/dt) inside the cell:
vN
dt
dm
= (16)
One then tries to determine which combinations of reaction rates should make the
right-hand side of the equation equal zero; those are the rates that are compatible
with steady states. Technically, these rates are in the Kernel of matrix N, and they
may well ones that are biochemically unrealistic for instance by proceeding thermodynamically
uphill. In addition, the number of possible reaction rates that lead
to steady state is very large. Schuster and colleagues added the requirement that all
reactions proceed as allowed by thermodynamics, leading to the so-called elementary
reaction modes of the network (Schuster et al. 2000). By also taking into account
the stoichiometries at which external substrates are utilized and external
products are formed, this enabled Schuster and colleagues to examine whether the
known network was able to produce certain chemical compounds from certain
substrates. Palsson and colleagues added other restrictions such as maximum capacities
and later (see above) maximum efficiency or rate of growth (Reed et al.
2003). This led them to unique solutions for v, which were often close to experimental
observations.
These pieces of work are examples of systems biology, in the sense that they
depend completely on the connectivity of the network; for an individual reaction
such an analysis is impossible. In addition and in contrast to our earlier examples
of systems biology, they rely on most, if not all, of the network being known, i.e.
they are genome-wide.
Both these methods focus on network topology, neither takes kinetics into account.
What they, therefore, obtain is potential flux patterns, i.e. flux patterns that
would materialize if indeed kinetics of all the individual reactions were such that
metabolite concentrations could evolve to steady state values that are consistent
with all those fluxes.
The `central dogma' of molecular biology states that DNA makes mRNA
makes protein makes metabolites. Literally this statement is illustrated in figure 2.
Kahn and Westerhoff (1991) observed that what was meant was actually orthogonal
to the literal interpretation of the statement: DNA does not make mRNA;
rather, RNA-polymerase (efficient cause) makes mRNA (effect) from nucleotide
triphosphates (material cause) using DNA as template (formal cause). Likewise,
136 Hans V. Westerhoff and Jan-Hendrik S. Hofmeyr
gene
mRNA
metabolite
enzyme
function
Fig. 2. The central dogma of molecular biology: DNA gives mRNA gives protein, gives
catalytic activity, gives metabolites and function. 30,000 such diagrams would represent
molecular systems biology in humans.
ribosomes, rather than mRNA, make proteins from amino acids using mRNAs as
templates. These authors then emphasized that in essence cell function is subdivided
in various hierarchical levels, one at the level of mRNA metabolism, one at
the level of protein metabolism and one at the level of intermediary metabolism
(cf. Fig. 3). In essence (though not quite strictly), these levels are not converted
into each other but regulate conversions inside each other. This means that the
stoichiometry matrix N (cf. above) is block-diagonal. This feature enabled the development
of a new version of MCA called Hierarchical Control Analysis, which
led to new laws specific for such hierarchical systems. One of these laws is that:
0=+ J
rd
J
rs CC (17)
acknowledging that transcription of the gene encoding the protein that catalyzes
reaction 1 can also control the flux J, and that (at steady state) this control is
equally strong as the control by the process that degrades this mRNA. The
strength of these controls can readily be 1 and -1 respectively, leading to the effect
that the flux through step 2 of the pathway of Fig. 3 can be strongly controlled by
a process that is quite remote in the cell's network, i.e. the degradation of the
mRNA of enzyme 1. This again illustrates that the processes run by macromolecules
(such as the enzyme catalyzing step 2 in this example) in living systems, are
usually not determined by these macromolecules themselves, but rather by the interactions
of all the macromolecules, i.e. by what makes the system differ from its
components.
Fig. 3 shows how metabolism is not only determined by metabolic control but
potentially also by transcription and translation control. It suggests a hierarchy of
control, transcription presiding over translation, which would again preside over
What is systems biology? From genes to function and back 137
metabolite
mRNA
protein
pdps
rdrs
1 2 J
Fig. 3. Hierarchical organization of cell function, as simplified for the function flux (J)
through a two-step metabolic pathway, leading through reaction 1 from a substrate S, at
fixed concentration, not shown, through the metabolite at a variable concentration, through
a reaction 2 to a product P, at constant concentration, now shown. Only of step 1 it is shown
explicitly that it is catalyzed by a protein, which is synthesized in a `protein synthesis process
`ps' and degraded in a protein degradation process `pd'. The protein is not converted to
the metabolite, hence, the dashed arrow from protein to reaction 1. The synthesis of this
protein occurs in a process that is specified by the corresponding mRNA. This specification,
however, corresponds to an influence not to a conversion of mRNA into the protein,
hence, the dashed line. The mRNA is synthesized in a process called `rs' and degraded
through a process called `rd'. Note that feedback from the lower to the upper levels is not
taken into account here; this is a dictatorial system.
metabolism. Signal transduction networks also consist of various levels of organization
that are not connected by mass flow, just by information flux. Many of the
laws Hierarchical Control Analysis also pertain to signal transduction and, many
more are still being discovered (Hornberg et al. 2005).
The type of control structure in figure 3 has been called a `dictatorial' control
hierarchy. Such dictatorial control systems are highly robust against internal fluctuations,
but not adaptive if anything goes wrong structurally. Most biological systems
appear to be more sophisticated in that the upper level in the hierarchy (i.e.
transcription) is not autonomous but adjusts itself to altered requirements at the
metabolic, i.e. functional level: Transcription regulation often responds to changes
at the metabolic level. For instance, allolactose in E. coli induces the enzyme that
metabolizes it (indirectly, see chapter by Kremling et al.) with the effect that if the
cell sees lactose (and is able to take it up, see above) it will synthesize more of the
enzymes involved in the corresponding catabolic pathway, but only if insufficient
such enzymes are present, i.e. only if allolactose accumulates to some extent. Biologists
have become used to this phenomenon, but perhaps not to the implications
that (i) it compromises the central dogma of molecular biology somewhat
(cf. Fig. 2) in that now metabolism also determines gene expression, and (ii) it
provides biology with circular causation, metabolism being the cause of changes
in gene expression which in turn causes changes in metabolism.
138 Hans V. Westerhoff and Jan-Hendrik S. Hofmeyr
4.8 Systems biology: dealing with the circular causation in biology
Systems with circular causality are shied way from by physics, chemistry, and molecular
biology and for good reasons: such systems are much more difficult to
handle experimentally and their analysis runs the risk of either becoming futile
when the feature of circular regulation is neglected, or becoming inconsistent because
cause and effect are interchanged inappropriately.
Again, by taking the feature of circular regulation into account explicitly, systems
biology has to deal with one of the features that perhaps distinguish biology
most from physics and chemistry. We shall now show how Hierarchical Control
Analysis as one of the systems biology approaches avant la lettre, is able to deal
with the issue of circular regulation. Basically, it does this by cutting away a regulatory
link that causes the regulation to be cyclic, by then analyzing the regulation
of the remaining non-cyclic parts independently, and by then using mathematics to
understand the circularity that occurs in the intact system.
We shall illustrate this for a simplified version of Fig. 3, i.e. Fig. 4, which still
contains the circular regulation but has neglected the level of translation (protein
synthesis and degradation). We shall consider the extent to which enzyme 1 controls
its own flux, i.e. to what extent the flux through enzyme 1 changes when we
activate the Vmax of that enzyme (through a point mutation, or by reducing the concentration
of a non-competitive inhibitor). This increase in its Vmax will cause an
increase in X, which may activate the transcription of gene 1 which will then lead
to an increased amount of enzyme 1; activation of step 1 will have been caused by
activation of step 1 (we, here, consider the feedback loop to be positive; when the
feedback is negative, circular causation is negative, less obvious, but perhaps even
more confusing).
We dissect the overall system into two subsystems, one at the level of mRNA
metabolism and one at the level of the metabolic pathway. We do this by setting
the effect of X on transcription to zero, i.e., by assuming that
0
]log[
log
=



X
v ntranslatiot
X . The control coefficients obtained for this dissected
system are written as lower-case c's. For the control exerted by enzyme 1 on the
metabolic flux this amounts to:
12
2
1
xx
xJ
c


=
(18)
For the dissected control of enzyme 1 on the concentration of metabolite X, one
finds:
121
1
xx
x
c
 =
(19)
What is systems biology? From genes to function and back 139
mRNA
X1 2
t d
Fig. 4. Simplified hierarchical organization of cell function. The transcription and translation
levels have been contracted to a single level overlying the metabolic level, in which
enzyme 1 synthesizes metabolite X and enzyme 2 degrades it. At the upper level mRNA is
synthesized by process `t' and degraded by process `d'. The dashed arrow from mRNA to
enzyme 1 refers to the transcription-translation regulation of the level of enzyme 1. The
dashed level from X to `t' refers to transcription regulation by the level of metabolite X.
The latter regulation makes the network `democratic'.
For the control exerted by transcription on the concentration of mRNA for enzyme
1, it leads to:
t
mRNA
d
mRNA
mRNA
tc
11
1
1
 =
(20)
For the intact system, Hierarchical Control Analysis has shown that for the control
exerted by the Vmax of enzyme 1 on the flux one finds (Kahn and Westerhoff 1991;
Hofmeyr and Westerhoff 2001):
12
1
1
11
ln
ln
11
111
11
111
xx
t
Xt
mRNA
d
mRNA
J
Xt
X
mRNA
t
JJ
Vd
JdJ
V
c
cc
cc
C




-

-
-
=
-
=
-
=



=
(21)
The term:
121
11
11
1
xx
t
Xt
mRNA
d
mRNA
Xt
X
mRNA
t cc




-

==
(22)
is the circular causation term. It quantifies the regulation of enzyme 1 (through
mRNA1) by transcription, multiplied by the regulation of transcription by X, multiplied
by the regulation of X by enzyme 1. If the circular causation term is -1)
this halves the control the Vmax of enzyme 1 exerts on the flux, corresponding to a
case of homeostatic regulation. If the circular causation term is plus 1, or higher,
then the circular causation causes instability and perhaps self-organization, this is
a bifurcation point (cf. chapter by Novak et al.).
140 Hans V. Westerhoff and Jan-Hendrik S. Hofmeyr
This example shows how Hierarchical Control Analysis can deal with circular
causation. An important aspect is that circular causation can have one out of various
possibly strengths. Only for some such strengths, it may become difficult to
analyze the system. But for most others, circular causation can be analyzed quantitatively
and is seen to adjust the robustness, i.e., homeostasis of the system.
5 Concluding remarks
What is systems biology then? And if there was systems biology avant la lettre,
what new is there under the systems biology sun?
Systems biology studies, in a fully scientific manner, the functional properties
that arise in the dynamic nonlinear interactions between the components of living
systems. This implies that it is based both on experimentation and on strict criteria
of scientific testing of theories. There should be no open ends, and the system under
study should be characterized completely, if not immediately then at least ultimately.
Therefore, although in the initial building stages, systems biology may
limit itself to fairly autonomous parts of living cells (cf. www.siliconcell.net): this
is only whilst en route to the analysis of the complete living cell. Systems biology
is tied in strongly with genomics, proteomics, and metabolomics, in the sense of
the ability of measuring all concentrations cell-wide.
Systems biology is a science in and of itself. Hence, it does not boil down to
modelling of part of a living cell, or to measuring all metabolite concentrations in
that cell, however important each may be. Systems biology tries to discover new
principles behind the functioning of living organisms. Genome-wide experiments
and models of parts of living cells are tools in that discovery, not aims in them-
selves.
The systems biology avant la lettre mentioned here has shown that important
principles can indeed be discovered, but that appreciable parts of the living cell
remain to be explored. In addition, the already discovered principles have not yet
been examined in terms of their validity or usefulness for the genome size systems.
And, inspection of the larger systems, in terms of their functionality may indeed
lead to principles that do not reign in the smaller, theoretical systems studied
thus far (as suggested for instance by the study of Reed et al. (2003).
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Hofmeyr, Jan-Hendrik S.
Dept. of Biochemistry, University of Stellenbosch, Private Bag X1, Matieland
7602, Stellenbosch, South Africa
Westerhoff, Hans V.
Institute for Molecular Cell Biology and Swammerdam Institute for Life Sciences,
BioCentrum Amsterdam, De Boelelaan 1087, NL-1081 HV Amsterdam,
EU
hans.westerhoff@falw.vu.nl