From silicon cell to silicon human
Hans V. Westerhoff 1,2, Malkhey Verma1, Frank J. Bruggeman2, Alexey Kolodkin2, Maciej Swat2, Neil
Hayes1, Maria Nardelli1, Barbara M. Bakker3, and Jacky L. Snoep1,2,4
1
Manchester Centre for Integrative Systems Biology, the University of Manchester
2
Netherlands Institute for Systems Biology, VU University Amsterdam
3
Department of Paediatrics, Centre for Liver, Digestive and Metabolic Diseases, University Medical
Centre Groningen, University of Groningen
4
Department of Biochemistry, Stellenbosch University
Summary
This chapter discusses the silicon cell paradigm, i.e. the existing systems biology activity of making
experiment-based computer replica of parts of biological systems. Now that such mathematical
models are accessible to in silico experimentation through the world-wide web, a new future has
come to biology. Some experimentation can now be done in silico, leading to significant discoveries
of new mechanisms of robustness, of new drug targets, as well as to harder validations or
falsifications of biological hypotheses. One aspect of this future is the association of such live
models into models that simulate larger parts of the human body, up to organs and the whole
individual. Reasons to embark on this type of systems biology, as well as some of the challenges
that lie ahead, are discussed. It is shown that true silicon-cell models are hard to obtain. Short-cut
solutions are indicated. One of the major attempts at silicon-cell systems biology, in the Manchester
Centre for Integrative Systems Biology, is discussed in some detail. Early attempts at higher order,
human, silicon-cell models are described briefly, one addressing interactions between intracellular
compartments and a second trying to deal with interactions between organs.
Table of Contents
Summary ................................................................................................................................................. 1
Introduction ............................................................................................................................................ 2
Where Systems Biology is different .................................................................................................... 3
What Systems Biology? ....................................................................................................................... 3
How Systems Biology? ............................................................................................................................ 4
Top-down Systems Biology ................................................................................................................. 4
The silicon cell ..................................................................................................................................... 4
Silicon cell models: advantages and disadvantages ........................................................................... 6
Blueprint modelling ............................................................................................................................ 9
The wisdom of MOSES: domino systems biology ............................................................................... 9
Metabolic Control Analysis models .................................................................................................. 11
The silicon-cell strategy in yeast ....................................................................................................... 12
Silicon cell and differential network-based drug design................................................................... 13
The true silicon cell ........................................................................................................................... 13
Crossing the scales ............................................................................................................................ 15
Different types of modelling ............................................................................................................. 15
Towards the silicon human ................................................................................................................... 17
Acknowledgements............................................................................................................................... 19
References ............................................................................................................................................ 20
Introduction
This chapter addresses how the molecular biology of cell types may be related to their cell biology,
and how both of these may be related to the functioning of a multi-cellular organism. It focuses on
methodologies that make realistic models. These methodologies enable the understanding of
mechanism and control of function. This analysis package is comprehensive, because the authors of
this chapter have invested considerable effort to make it such. Although the endocrine role of
insulin production by beta cells is what the authors have in mind, this application is not made
explicit, in part because too little has been done, and in part because this chapter wishes to inspire
experts to have a fresh go at this.
We shall first address the differences that systems biology may make. Subsequently we shall
describe multiple aspects of our silicon-cell mode of systems biology. We end by speculating how
the approach may lead to a true-to-Life model of how human functions through its interacting
molecules.
Where Systems Biology is different
Genomics and Molecular Biology have focused on the identification of all the individual
macromolecules, their inherent activities, and sometimes their interactions with immediate
partners. Molecular Cell Biology has drawn schemes that indicate which macromolecules interact
with which other macromolecules, either directly or indirectly. Some of these schemes distinguish
between stimulatory and inhibitory interactions. Few of them indicate the strengths of the
interactions and none of them indicate how the strengths of the interactions may depend on other
factors, such as concentrations of other molecules in the network or the concentrations of the
interactors. Probably because of the robustness and adaptability of biological functions, the latter
tend to be regulated through both positive and negative interactions. As a consequence one cannot
come to understanding and predictions without assessing the strength of the interactions
quantitatively. Because insufficient attention has been paid to collecting the intermolecularinteractions data quantitatively and because all data relevant to a certain function have rarely been
integrated into a single frame of reference, network analyses have remained qualitative and thereby
speculative.
On the other hand, mathematical biology has had the tendency to abstract away from the detail and
the actual, because it aimed for generic principles. Of the principles that were found, such as
gradient driven self-organization as possible mechanism for developmental biology, specific
predictions could be falsified. This made self-organization theories irrelevant in the eyes of
experimental developmental biologists (Lawrence 1992; Davidson 2006; Peter and Davidson 2009).
As an alternative paradigm for developmental biology, the concept of the genetic program became
popular, in which the expression of one gene would lead to a protein activating the expression of the
genes of the subsequent phase. Although feedback and feedforward loops are recognizable in the
corresponding networks, it is not clear whether self-organization plays a role (Peter and Davidson
2009).
To understand living organisms we need to appreciate with sufficient precision how their
components interact. We need to reckon with a combination of a genetic programme that came
about accidentally in evolution with mechanisms that involved self-organization. This will require
integration of the historical paradigms of mathematical biology and molecular genetics (Westerhoff
and Palsson 2004). It is in this integration that systems biology differs from both mathematical
biology and molecular genetics, and in fact from mainstream physics and biology (Westerhoff,
Winder et al. 2009).
Systems biology also differs from physiology, which describes the functioning of biological systems in
their entirety, without complete reference to the components. Cell physiology helps describe
qualitatively how ATP levels change when muscle is innervated and why this leads to contraction. It
does not explain this in a mode that predicts on the basis of changes in molecular processes.
What Systems Biology?
Systems biology has existed for more than 10 years now. Some of the low hanging fruits have been
picked. This included the discovery of interesting potential patterns of networking (Albert and
Barabasi 2000) and regulation (Alon 2007) based on computational analyses of the completely
sequenced genomes. However even definitive information that two network components can
interact, does not certify that they actually do interact, or that the flow of mass or information flux
between the two components is significant. A transcription factor can interact with a gene only
under the, possibly rare, condition where the former is actually expressed. A metabolite for which
an enzyme has a binding site may only rarely attain concentrations that exceed its binding constant
in the compartment the enzyme resides in. Without dynamic information about the actual states of
the living systems, conclusions about scale-free intracellular networking and about prevalent genenetwork motifs for biological function are preliminary.
Understanding of network function requires the experimental determination of the kinetic or
binding properties of the macromolecular components. Systems Biology should then assemble this
information into a mathematical replica and calculate the fluxes. The latter should then correspond
to what is measured experimentally. Lack of correspondence should be taken as a lead to discovery
of new interactions or parameter values.
How Systems Biology?
Accepting the above ideal scenario for systems biology, one should translate this into something that
is operational. At present this is almost impossible, because too little is known or can be measured
quantitatively. In addition, some parameter values are ‘soft’, i.e. depend on intracellular conditions
that are not quite known. Examples are expression levels and hence Vmax and KM values that depend
on pH or even on the concentrations of other medium components (van Eunen, Bouwman et al.
2010). In addition, it is difficult to measure the property of some enzymes, whereas it can be easier
to do this for others. The strategies for systems biology have not yet been tried out yet. Below we
shall review some such strategies, in particular the ones that relate to the silicon cell.
Top-down Systems Biology
The strategy that is closest to genomics is called top-down systems biology (Alberghina and
Westerhoff 2005). Here the concentrations of all components of a certain class (mRNA, proteins, or
metabolites) are measured in a genome-wide sense, as a function of time, or of conditions. The
components that behave similarly are then grouped together, assuming that correlation indicates a
mechanistic or functional relationship. This may then lead to the proposal that all members of a
group are regulated by the same transcription factor. Such a hypothesis may then be tested by
identification of that transcription factor. It may also lead to the proposal of a temporal sequence of
the action of regulatory molecules, hence to a regulatory pathway. Risks include the confounding of
causes with effects , as well as the fact that regulation does not proceed through a single level of
cellular organization (such as mRNA levels) but tends to involve at least gene expression and
covalent modification through signal transduction, if not metabolism as well.
The silicon cell
The silicon cell approach (Westerhoff 2001; Snoep 2005) is a strong form of the so-called ‘bottom-up
systems biology’. The approach has been elaborated most for metabolic pathways. It consists of
isolating all the enzymes of the pathway that is studied and of determining their kinetic properties,
as well as their Vmax’s. The rate equations of all these enzymes are then put into a computer model,
together with balance equations that give the change in time of the concentrations of all the
metabolites as functions of all the reaction rates. The resulting system of equations is solved
numerically for steady state, or after addition of initial conditions, for time evolution. Thus a
computer replica of a biochemical pathway is created with behaviour identical to real behaviour, if
the model is right.
The above approach may not seem new, but in its precise sense it is: although silicon cell type
models have been made before, in many cases kinetic information was taken from databases for
enzymes assayed under conditions that were not the same for all enzymes, nor corresponded to the
condition in vivo. The silicon-cell models of human erythrocyte glycolysis (Rapoport, Otto et al.
1977), T. brucei glycolysis by (Bakker, Michels et al. 1997), of yeast glycolysis by (Teusink, Passarge et
al. 2000), and of the bacterial phosphotransferase system by (Rohwer, Meadow et al. 2000) are early
examples of what is close to the silicon cell approach. Yet, some of these were imperfect because
the kinetics of the pathway enzymes were determined in cell extracts rather than with purified
enzymes, or the cells were derived from fairly undefined pre-culture (which was however of
immediate relevance for the application, e.g. baker’s yeast).
The silicon cell is a rather loose research program that is greatly stimulated by the JWS-Online
modelling web site (Snoep, Bruggeman et al. 2006). JWS (short for Java Web Simulation project) is a
‘live’ model repository, from which mathematical models of biochemical pathways can be
downloaded in SBML form (Systems Biology Markup Language is the model specification language
through which systems biology models are exchanged between modelling platforms (Hucka, Finney
et al. 2003)). The model repository is ‘live’ in the sense that the models can also be run through a
web interface to JWS-Online, without downloading. A user can therefore be completely ignorant of
modelling and still do experiments in silico. The models come with the standard parameter set
taken from their primary publication, which should correspond to the standard physiological state.
Parameter values can be altered and then the changes of concentrations and fluxes can be
calculated as functions of time. In addition, systems properties such as the magnitudes and the
control of steady state fluxes and concentrations can be calculated. Before acceptance of models,
JWS Online checks that they reproduce simulations and calculations they express a claim to in their
original publication. Because this reproduction is rarely complete, this model repository has an
important function in quality control. BioModels, with which JWS collaborates, is another model
repository with an even larger set of mathematical models, most of which can also be simulated in
the JWS Online simulator via a direct link within BioModels. Its models have a more systematic
annotation facility (Le Novere, Bornstein et al. 2006).
The way JWS-Online is populated with models is not completely systematic yet, because there is too
little funding for JWS-Online per se. Consequently, the first generation of models in JWS-Online,
were made by the small JWS-silicon cell community. The second generation consists of models
published in the high quality scientific journals (e.g. FEBS Journal) that became interested in the
quality control aspects of JWS-Online. As part of their refereeing procedure, models in submitted
papers are put into a (non-public) version of JWS, and the models are run to check that they produce
every Figure and Table in the submitted manuscript. Perhaps surprisingly, this quality control
mechanism finds faults with more than 90 % of the submitted manuscripts. Only if the paper is
accepted, the model becomes part of JWS Online (unless the authors do not want it to). In addition,
there is a number of models that have been contributed to JWS-Online by authors interested in
getting their model used by colleagues through JWS-Online or getting their citation numbers
increased. It is the second and the third modes of contribution that should become most important
in the future.
In Figs 1, 3 and 5 of this chapter we give jus three examples of silicon cell models. More such models
are in JWS-Online, e.g. accessible through http://jjj.mib.ac.uk/index.html . When going through the
models in the JWS repository the reader will find some diversity. However, she/he will also
recognize that the variety of models is not representative for biology or even cell biology. This is
because until now some parts of cell biology have led to more computer-replica than others, or
because some authors have not submitted their models to JWS Online. Reasons for the relative
abundance of metabolic and especially glycolytic models are that in metabolism the law of
conservation of the elements has direct consequences: At steady state, what flows into any node of
the network must be equal to what flows out. This helps tremendously when defining the models
and the associated experiments> This has led to such metabolic models being much more concrete
and complete than signal transduction and gene expression models. Moreover, silicon cell models
require accurate experimental data. Until recently, these were obtained either in extracts of cells, or
with enzymes purified from wild-type cells. In both cases, highly active enzymes are analyzed most
readily and hence the pathways that carry most flux can be approached most successfully.
Most models in JWS-Online are of the bag-of-enzymes type, i.e. they assume that enzymes convert
metabolites that are present in well defined pools and that there is no direct transfer of metabolites
between enzymes, i.e. no metabolite channelling. Likewise, enzyme sequestration by binding to
other macromolecules, macromolecular crowding, and active structuring are underrepresented, as
are metabolic pathways that are subject to adaptation through gene-expression regulation. These
issues are underrepresented, but they are not absent. In particular the silicon cell model of the
E.coli phosphotransferase system (Rohwer, Meadow et al. 2000) is rich in these complications: it
addresses signal transduction, transport, channelling and macromolecular crowding. Gene
expression regulation and DNA structure regulating gene expression are modelled in (Snoep, van der
Weijden et al. 2002). Many models are about steady states and the approaches to steady states.
However, in biology systems with steady states as the main attractor, dominate and the rather large
numbers of models in JWS-Online that deal with oscillations may actually over-represent oscillatory
systems. They include yeast glycolytic oscillations (e.g. (Wolf, Passarge et al. 2000)), the cell cycle
(Conradie, Bruggeman et al. 2010) and oscillations in NFκB signaling (Ihekwaba, Wilkinson et al.
2007).
Silicon cell models: advantages and disadvantages
What is the advantage of having a silicon-cell type model, a ‘computer replica’, of a biochemical
pathway? If perfect, such a model is just as complex as reality, hence it does not correspond to the
abstraction and simplification of reality that is often associated with ‘understanding’. Mathematical
biology has long made models of biological systems that aimed at this type of ‘understanding’. Why
not stay with those models of mathematical biology?
Examples of such mathematical biology models include the Turing type of models which were used
to show that self-organization might explain pattern formation in developmental biology (Glansdorff
& Prigogine, 1972; Gierer & Meinhardt, 1972). These models each contained a simple network with
positive and negative feedbacks. Using simple parameter values their predictions were calculated
and shown to lead to pattern formation. Most often no attempt was made to produce a precise
correspondence between simulation results and experimental data. Where such attempts were
made and the predictions of the model did not fit experimental observations, the parameters in the
model would be adjusted until a statistically satisfactory fit was obtained. In principle the fitted
parameter values could then be verified experimentally, but this is rarely undertaken in practice:
The number of parameters exceeds the number that could be determined experimentally at the
required level of accuracy, or, more often, the parameters refer to abstract properties that cannot
be measured directly. Even if a parameter value could be measured and was shown not to
correspond to what was assumed in the model, then other parameter values would be adjusted so
as to obtain a renewed fit between model prediction and experimental system behaviour. Only if
such fitting would prove completely impossible the model could serve the important function of
falsifying a hypothesis about mechanism, but this has been rare. More often, parameter values
could be found for which the model fitted the experimental behaviour, but there was no assurance
that those parameter values corresponded to reality. For instance the model would fit the data if a
lower than actual Vmax was inserted for an enzyme (such as hexokinase in Teusink, Walsh et al.,
1998). The fitted model would be wrong mechanistically, even though it would appear to explain
the phenomenon of interest, such as pattern formation.
The resulting model could still be used, but then as a phenomenological, descriptive model.
Phenomenological models have a long and successful history in both physics and engineering. In
physics, because of greater simplicity, subsequent experimental testing was possible and often led to
reformulation in terms of a more detailed, mechanistic model, and then validation or falsification. In
engineering the models were considered useful also without such validation, because the purpose of
a model was the description of the behaviour of the system, not necessarily an explanation of how
that behaviour was actually achieved. Most of biology is different however; it is much more
complex than physics, actual detail matters (see above), and it often wishes to relate physiological
behaviour of the system to its components’ properties. The latter is important for metabolic
engineering and therapeutic purposes.
Now we get to the answer to the question why one could not stay with the usual models of
mathematical biology. The reason is that they do not enable one to validate that proposed
mechanisms are actually operative in, and explanatory for, observed functional behaviour. Silicon
cell models are realistic and suitable for a falsification/validation strategy. This is a prime utility of
silicon cell type of models, i.e. scientific validation/falsification of proposed understanding of
systems.
Although silicon cell models do not themselves constitute understanding in the sense of
simplification to what is most important, they do instantiate another type of understanding, i.e. that
of the ability to predict. If the prediction fails to correspond to reality, experimental follow-up can
lead to improved understanding. In other words, silicon cells are the tools that are ultimately
required for the continued development of our understanding of biological systems.
In addition, silicon-cell models can contribute considerably to understanding by enabling
computational experiments. Complex actual mechanisms may be elucidated more readily by
interrogating a computer replica of reality through computational biology, than by experimental
biology. Fig. 1 illustrates how this has worked already. It shows that the silicon cell model of yeast
glycolysis was rather unrobust with respect to the activity of the glucose import system; as shown in
Fig. 1B only a slight increase in that activity, could lead to a ‘metabolic explosion’, i.e. to a continued
increase in the concentrations of some metabolites. Because real yeast is robust in this respect, but
a mutant is not, this led us to understand an aspect of the ‘turbo’ organization of many catabolic
pathways that could lead to fragility and then to a hypothesis on how a regulatory interaction for
which no function was known and which had not been included in the silicon cell, might be quite
important for yeast glycolysis (Teusink, Walsh et al. 1998).
Silicon cell models have two additional advantages. One is that their parameters are ‘hard’ in the
sense that they correspond to properties of real molecules. This means that, once known, the
parameter values should not change anymore unless the model is wrong, or the properties of the
molecules involved change. Fitted, phenomenological models have the disadvantage that for every
new experiment the entire model should be refitted to all existing experiments, allowing all
parameter values to be adjusted so as to make the fit optimal (Novak, Csikasz-Nagy et al. 1998). For
large models this can become increasingly bothersome. The second additional advantage of silicon
cell models is that because they are formulated in terms of real entities, models that address
adjacent parts of cell function tend to be formulated in the same terms, or in terms that can be
readily translated into one another. Thereby, the silicon cell strategy should allow for the assembly
of some of its models into larger models. Related to this, the silicon cell initiative furthers
standardization. Many modellers like to see their models used by others in a wider context and are
therefore willing to standardize them. The development of SBML (Hucka, Finney et al. 2003) is a sign
of this, but the silicon cell initiative tends to go further in certain aspects. Whereas SBML is a
standardization of a model description format, we aim for a standardization of model construction
protocols.
Fig. 1. Non robustness of a silicon cell for yeast glycolysis. Development in time of a number of
concentrations. A: the normal state (see www.jjj.bio.vu.nl for the model (Teusink, Passarge et al.
2000)). B: the same but after increasing the Vmax of glucose uptake from 95 to 150; the
concentrations of pyruvate and fructosebisphophate fail to reach steady state.
The silicon cell strategy also has many disadvantages. One is that it requires an awful lot of careful
experimentation to determine all the kinetic parameters. In addition it requires all components to
be assayed, which is impossible for realistic systems, first because they contain too many
components and second because there is always a component that is most difficult to isolate or
assay.
A second disadvantage is that it is excruciatingly slow and not always maximally exciting. For
instance, the silicon cell approach suggests that having made such a model for an organism for a
particular experimental condition, one should start all over again if one is interested in a different
organism or a different condition; the organism may then express different isoenzymes. However,
repeating the procedure for the different condition, one may obtain the same result in terms of true
understanding of function, as one had obtained for the original conditions and organism. On the
other hand, quite similar organisms may have entirely different functions or mechanisms which they
may achieve by differences in networking of essentially the same molecules ( compare (Haanstra,
van Tuijl et al. 2008) to (Teusink, Walsh et al. 1998)). This issue now leads to comparative systems
biology.
A third disadvantage is that until now, the actual silicon cell models have been about parts of cell
function that were considered to belong together, such as metabolic pathways in their classical
definition. Strategies for a more rational definition of what pathways silicon cell models should
begin to focus on are being developed (Westerhoff et al., 2009).
Blueprint modelling
Blueprint modelling tries to deal with this demotivating feature of having to redo silicon cell models
of related organisms and with the motivating feature of comparative systems biology. The blueprint procedure starts from the silicon-cell model that is already available of a related organism and
then changes this in the light of what is already known of the molecular properties of the organism
under study. Comparing the predictions of this adjusted blueprint model with physiological
behaviour measured experimentally, one then prioritizes which parts of the blueprint model need
to be detailed further.
The wisdom of MOSES: domino systems biology
Intracellular networks are vast and virtually completely connected. In principle, a true silicon cell
model is a model of the total expressed genome. This is impossible to achieve, at least for the
foreseeable time, and one needs to start with a part of the intracellular network. Ways to divide the
intracellular network into modules that can be considered separately, are highly important therefore
(Schuster, Kahn et al. 1993; van der Gugten and Westerhoff 1997; Hartwell, Hopfield et al. 1999;
Schuster 1999).
Growth
Nucleotide
Synthesis
Maintenance
ATP
ADP
Glycolysis
AMP
Drug Efflux
DNA repair
Figure 2: Several modules linked by their consumption, production or other interactions (e.g.
allosteric) with the adenine nucleotide pool.
‘Domino systems biology’ begins at a key metabolite and then uses pre-existing knowledge
concerning the pathways and processes that synthesize this metabolite and the processes that
consume it. It determines, by using pre-existing pathway models from silicon cell, by performing
new in vitro enzyme kinetic assays, or by modular kinetic analysis (Ciapaite, Van Eikenhorst et al.
2005), how these processes depend on the concentration of the key metabolite. Starting with the
most important synthesis process and the most important degradation process, it then formulates a
first model with the intermediate in the middle and the two processes around it. It then predicts
how activation of the processes affect the concentration of the intermediate at steady state and the
fluxes, and compares this with the results of corresponding experiments. Failure of the model to
predict the latter type of observations, is then used to invoke either an additional process or an
additional metabolic intermediate. By incorporating a next additional process or metabolite one
adds the next domino stone.
Micro-Organism Systems biology: Energy and Sacharomyces cerevisiae (MOSES), is a research
program that develops domino systems biology for yeast. Fig 2 shows the example for when one
takes ATP as the central intermediate, which is relevant because for cellular energetics. Fig. 3 shows
a modelling result that comes from this approach, i.e. a perhaps somewhat paradoxical dynamic
behaviour of the ATP level upon activation of the glycolytic pathway producing ATP (Somsen,
Hoeben et al. 2000).
4.5
Adenine nucleotides (mM)
4
AMP
ATP
ADP
AXP
3.5
3
Glucose added
2.5
2
1.5
1
0.5
0
-0.2
-0.1
0
0.1
0.2
0.3
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0.8
0.9
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Time (min)
4.5
Adenine nucleotides (mM)
4
AMP
ATP
ADP
AXP
3.5
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Glucose added
2.5
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-0.1
0
0.1
0.2
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Figure 3: Adenine nucleotides dynamics for glucose perturbation by integration of glycolysis
and maintenance modules. AXP=ATP+ADP+AMP.
Metabolic Control Analysis models
Another strategy to enable precise modelling does not seek to limit the network size, but to reduce
the types of questions that are addressed by the model. Metabolic Control Analysis is such an
approach. It only addresses the control of fluxes and concentrations, not their magnitudes. It is
possible to calculate the flux and concentration control coefficients from enzyme kinetic properties
called elasticity coefficients (Kacser and Burns 1973; Westerhoff and Kell 1987; Reder 1988;
Westerhoff and Kell 2009). Elasticity coefficients contain limited information about the enzymes
that participate in the pathway and can hence be estimated in the absence of the full information.
Galazzo & Bailey pioneered this approach experimentally, using a fair number of rather precise rate
equations which enabled them to calculate the elasticity coefficients, because they had measured
the intracellular concentrations of some metabolites by NMR (Nuclear Magnetic Resonance)
(Galazzo and Bailey 1990). They found much but non-exclusive control of the flux by the glucose
transport system, but this was partly the result of a proposed inhibition of the transporter by
glucose-6-phosphate, for which there is no direct experimental evidence.
The silicon-cell strategy in yeast
Of course an alternative to the above approximate approaches is to carry out the silicon cell agenda
as completely as possible. It is indeed one of the main aims of the Manchester Centre for
Integrative Systems Biology to provide a first, fully predictive, and essentially complete, systems
biology of the most important function of an organism, in terms of a silicon cell model. The initial
strategy was to over-express and partially purify each enzyme of yeast and then to determine its
kinetic and interactive properties. This approach was not efficient enough, as high throughput
kinetic assays were only successful for some enzymes. For most others the substrates were not
available commercially, or the enzymes were too unstable.
Therefore it was decided to leave this genomics-driven strategy and to switch to a function-driven
strategy, i.e. to select a function of interest, estimate which enzymes are most involved in that
function, isolate and characterize those enzymes, and then make a silicon cell model (Westerhoff et
al., 2009). The resulting strategy is illustrated in Fig. 4.
Threads
A.
Experimental
design and
pathway
finding
Understanding
Nonlinear
FBA
Standard
FBA
Expt. based
FBA
Ethanol
determination
B. Component
characterization
C. Pathway
modelling
Flux
Pathway
ranking
Paths
Exo
Meta
bolome
Protein
purification,
Characteriz,
Determination,
Vmax
Proteomics
Pathway
modelling
Interactions
component
functions
Flux
prediction
Improving
model
Concentr
prediction
D. Validation
New
Turbidostat
Endometa
experiment
bolomics
Isotope
fluxes
Interactions
Mechanisms
E. Discovery
Network
functioning
Behaviour
New
functions
Fig. 4. The strategy of the Manchester Centre for Integrative Systems Biology (MCISB) toward a
silicon cell, focusing on a single function, i.e. most of the carbon flux through the organism under
study.
Silicon cell and differential network-based drug design
Most drugs have multiple effects on the patient. One reason is that their targets are parts of
molecular networks that connect with other networks. The concept that drugs should be targeted at
single molecules may be good for the ability to define drug action biochemically, but it will not be
able to define that action biologically. For the latter definition the multiple effects of the target
molecule on network performance should be understood. There have been attempts at the
corresponding systems-biology driven drug targeting. One of these has used the silicon cell
approach to find molecular targets for drugs against T. brucei, the causative agent of sleeping
sickness. Indeed, one of the first silicon cells was the glycolytic network of T. brucei (Bakker,
Michels et al. 1997). The functional target was the ATP synthesis by the parasite. However rather
than targeting pyruvate kinase, i.e. the enzyme that makes most of the cytosolic ATP, the network
was scanned for the molecule that had the greatest influence on ATP production. The glucose
transporter came out as the number-one target (Bakker, Westerhoff et al. 2000).
An equally important aspect as drug effectiveness is drug toxicity. Accordingly a drug should be
maximally effective against the parasite but minimally effective against the host. A differential
analysis comparing trypanosomes with human erythrocytes confirmed that the glucose transporter
might be a good target because the glucose transporter of human erythrocytes was calculated to
have little control on ATP synthesis (Bakker, Assmus et al. 2002). However, the human host contains
many more cell types than the erythrocytes and the drug should be ineffective against all host
targets. For further evaluation of drugs, silicon cells of most host tissues should be useful if not
necessary.
The true silicon cell
Until now the words ‘silicon cell’ have been misnomers. All that exists presently, as exemplified by
the collection of models on the JWS-Online model repository, are models of mostly metabolic
pathways. There is no model of entire cells. The name silicon cell stems from the ambition
ultimately to combine silicon-cell models of pathways into models of entire cells.
Cells are compartmentalized and involve more than metabolic pathways. Fig. 5A shows a network
that is not involved in metabolism but in signalling. It represents a blue-print model of nuclear
hormone receptor signalling in various human cell types. Nuclear receptors (NRs) belong to a family
of transcription factors involved in a diverse range of regulatory functions, such as the ones that are
active during development, inflammation and metabolism (Carlberg and Dunlop 2006). A NR is a
protein that is synthesized in the cytoplasm, shuttles between the nucleus and the cytoplasm, and
binds with its response element on the DNA. Addition of ligand L results in the appearance of NRL in
the cytoplasm. Then, NRL shifts into the nucleus and binds to response element, causing
transcriptional response (Figure 5).
A curious aspect is that both export of importins and export of liganded receptor are driven by
RanGTP hydrolysis. Why would the cell spend free energy on these processes that both seem to
work in the wrong direction? We made a model of this network which is on its way to but not yet
equivalent to a silicon cell model; many kinetic parameters are still unknown. In this model we
asked what would happen if we decreased ∆G of both processes by a factor of 100 (dashed line). We
found that the high investment of Gibbs free energy would stimulate transcription at high
concentration ratios of importin to nuclear hormone receptor. This leads us to formulate the
hypothesis that the investment of free energy serves to prevent sequestration of nuclear receptor
by importin.
Fig. 5. Silicon cell model of a nuclear hormone receptor signalling network and prediction of the
dependence of transcription activation on the total concentration of importin (Imp) in the system and
the free energy driving the transport cycles.
Crossing the scales
In the above venture from pathway to cell, we met the complication of an extra compartment.
When two compartments have different volumes, processes in the one compartment are likely to
have different kinetics from processes in the other. Even in a single compartment, time scales may
be diverse. One origin of this is in the gene expression cascade. The concentrations of the enzymes
in metabolic pathways may adjust to changes at the level of metabolism through regulated gene
expression. Because the lifetimes of proteins are mostly longer than the lifetimes of many
intermediary metabolites, the dynamics of gene expression are often quite a bit slower than the
dynamics of metabolic changes. The methodology of rate and balance equations that has mostly
been used in the silicon cell up to now, can deal with a full range of dynamics. However for
conceptual purposes, and for the purpose of more rapid computation, methods that summarize the
behaviour of more detailed, faster scales into behaviour at the often more relevant , slower and less
detailed scales, are important (de la Fuente, Snoep et al. 2002).
A well known issue at the faster time scales is that of the dynamic behaviour of enzymes. This can
be described at the level of the free substrate [S], the free enzyme [E] and the enzyme-substrate
complex [ES], or at the level of the total substrate and the total enzyme concentration. The latter
has the advantage that total enzyme is set by the dimension of gene expression not by metabolism.
Even though the quasi-steady state approach (QSSA) to enzyme kinetics is a fair way to deal with
this usually, there are recent methods for dealing with the cases where enzyme and substrate
concentrations are comparable and the QSSA fails (de la Fuente, Snoep et al. 2002; Hardin, Zagaris et
al. 2009). MCA has been extended to address the multi-scale issue of signal transduction (Kahn and
Westerhoff 1991) and of that metabolism versus gene expression (Westerhoff, Koster et al. 1990;
Westerhoff 2008), also experimentally (Snoep, van der Weijden et al. 2002; Hardin, Zagaris et al.
2009).
When moving up from the cell level, to the whole body, additional scales appear, such as the scale of
the circulation, which is important for the organism action of beta-cells. The coupling of models of
the silicon cell type should again help at those scales. We shall discuss this below.
Different types of modelling
This chapter is motivated by the question how molecular issues in beta cells might be put in the
perspective of their biological function. Since their biological function is at the level of the whole
human, this involves the crossing of temporal and spatial scales from molecules to the whole
mammalian body. Apart from, but sometimes related to, the scales at which one is considering
these issues, there are different modelling methodologies. Above we have discussed a few, i.e. top-
down systems biology, blue print modelling, domino systems biology, metabolic control analysis, and
silicon cell. Three of these five modelling methodologies involve balance equations and kinetic
equations. Metabolic control analysis uses less than this (Westerhoff and Kell 1987; Reder 1988),
but is limited to control aspects. Top-down systems biology tends to lead to phenomenological
models describing patterns. There are quite a few other modelling methodologies that we have not
discussed until now. This is because this chapter is devoted to describing the methods that we find
most important for obtaining a useful mathematical representation of the human that enables to
relate her function to her molecules.
This is not to say that other modelling methods are not more useful for other important problems,
or even that they will not be important for some aspects of the silicon human. For instance, flux
balance analysis as a modelling method may help establish where to look first for important
pathways (Westerhoff et al., 2009). However, it ultimately suffers from the fact that we do not
know what the relevant objective functions are. A sole objective function of maximum yield of ATP
is likely to be irrelevant for most human cells.
Modelling cells in terms of Boolean networks may be quite helpful for initial understanding, but
suffers from the limitation that in reality the intracellular networks are based on ensembles of
molecules and not on individual chains of molecules. Therefore only after it has been shown that
parts of the intracellular networks do indeed act as switches, one could engage this method.
Transcription does not yield a single mRNA molecule that is then transcribed into a single enzyme
which then makes a single molecule of the product. The difference matters for Life, which critically
depends on the ability to deal with the challenges imposed by the second law of thermodynamics.
The latter depends on the laws of larger numbers and entropy (Westerhoff & Van Dam, 1987).
Boolean networks have no problem with violating the second law of thermodynamics. Bayesian
networks are a more subtle alternative to Boolean networks, allowing for event probabilities in
between 0 and 1. Living systems operate in states that are steady or steady on average. Thereby
part of the essence is not how they move from one state to the next, but how a single state is
functioning. For sure, when a glucose molecule enters a tumour cell, its C1 carbon atom has a
certain probability to end up in carbon dioxide and a different probability to end up in lactate. One
would be interested in how these probabilities are influenced by the expression of glycolytic genes.
This is a matter of a steady-state balance between rates, the implications of which for metabolite
concentrations are modelled best by rate and balance equations. Bayesian networks operate by
forward logics, i.e. what happens can only be determined by the present and not by the future.
Already shortly after activation of intracellular networks, what happens in their beginning is codetermined by what has happens at their end. At steady state the end of the pathway just coexists
with its beginning: the former depends on feedback loops through the latter, one of the reasons why
the first step is not completely rate limiting. Bayesian networks do not seem to accommodate this
essential, feedback property of living cells.
One interpretation of ‘computer replica’ of the living organism, would indeed model the system in
terms of all its individual molecules as they are interacting. This would inspire a gigantic Monte
Carlo simulation including the quasi Brownian motion through Cartesian and chemical space. This
however would generate models that are more complex than can be calculated in the lifetime of the
Planet, even after introducing the simplifications offered by biological organization discussed above.
In addition it would depend on the initial conditions of all the individual molecules, which one could
never determine. It would also be impossible to trace the behaviour of every individual molecule,
without perturbing it; this problem is not unique to quantum mechanics. The silicon cell project
models mostly in terms of ensemble-averaged concentrations, whenever this is feasible on the basis
of statistical mechanical considerations (Westerhoff and Van Dam 1987). Stochastic modelling does
become important when molecules numbers in the relevant compartments are below 100. This is
rare, though occasionally important. Partial differential equation based modelling is needed when
gradients within compartments become important (Kholodenko 2006).
Towards the silicon human
In the context of the human, the ambition is even greater, i.e. to combine models of cells into
models of tissues and then to combine models of tissues into body-wide models. Because the cell
models would still be in terms of molecular activities, the result would be a multi-scale model
relating whole body function to molecular activities in time and space. Here, the silicon-cell project
will become a silicon organism project, with variations such as the virtual physiological human and
the digital human projects. The idea is similar to that of integrating pathway models. Relatively
autonomous models of organs are to be combined. One thought is to leave the coordination of each
organ model including the corresponding computations to an individual research centre and then to
integrate the models dynamically through web services. Although perhaps slow, this would have the
advantage of maximum responsibility of a group over a part of the whole model, ensuring quality
control. Fig. 6 illustrates this approach, where of course the beta cell component model will play an
important role. Another thought has models for parts of the system uploaded to JWS-Online by the
respective research groups, these models being automatically merged into the complete model,
available to all participating groups.
Pharmacokinetics has already studied the human body as a multi-compartment problem. Recently it
has been proposed that more mechanistic information should be incorporated into
pharmacokinetics (Lave, Chapman et al. 2009). We are therefore elaborating the silicon cell
approach for tissue-tissue interaction in the whole human body. We thereby focus on the part of
Fig. 6 that is depicted in Fig. 7A. The pancreatic beta-cells, shown schematically on the left, are
connected with a model for C-peptide kinetics. Based on experimentally measured C-peptide levels
in a patient we are able, using this model, to estimate the dynamic and static component of the
insulin secretion, the former being a function of the glucose concentration above a certain threshold
level, the latter being a function of the rate of increase of the glucose concentration. Fig. 7B and C
give the results of calculations for two different silicon humans (i.e. different mechanistic parameter
values for the two models) of insulin secretion rates in the normal and in the hypercaloric state. Fig.
8 A illustrates a complementary model for glucose and insulin dynamics. It allows for estimation of
the insulin sensitivity of a virtual patient, a numerically calculated measure quantifying the interplay
between insulin level, and the ability of the organism to balance its glucose concentration. The figure
shows that provided individuals can be characterized in terms of a few mechanistic parameter
values, implications of food intake for insulin dynamics can be predicted. At this stage, it is unclear
whether those predictions would be correct or not, but this is now accessible to experimental
validation.
Fig. 7. Minimalistic whole body silicon-cell model relevant for insulin, glucose and c-peptide
dynamics and some of its predictions. A. The scheme referring to the insulin release model and Cpeptide kinetics. B. Calculations of insulin secretion after administration of glucose for a silicon
human subject to a normal (the line that is the highest in the beginning) and a hypercaloric diet. C.
The same calculations for a different silicon human.
Fig. 8. Another minimal whole-body silicon-cell model relevant for insulin and glucose dynamics and
some of its predictions. A. The scheme referring to interplay between insulin and its effect on glucose
utilization and storage. B. Calculations of glucose absorption profile during an oral glucose tolerance
test (bottom plot) and fitted glucose time course (top plot).
To many, the idea of a silicon human seems too complex to even think about. This may however
derive from a failure to appreciate that biological organization greatly reduces complexity
(Westerhoff, 2010). Moreover, the silicon human is already developing. Models of important
aspects of the heart (Noble 2006) and of the liver cell (Vera, Bachmann et al. 2008) are constructed.
30 years from now we will avail of thousands of mathematical models that each describe a part of
the human. Perhaps the only strategic decision we need to make now, is whether all those models
will have resulted from a cottage industry such that it will be impossible to integrate them with each
other, or all those models will have been developed in a common context and can be merged into a
larger, more complete model. The latter possibility should enable each researcher working on
her/his part of the human to appreciate the implications of her/his findings for understanding the
functioning of the human as a whole. And, because there will be simultaneous top-down and
‘middle-out’ (Noble, 2006) strategies towards mathematical models of the human, we also have
another choice. Either the results of these three methodologies will be developed independently of
each other and the results will be in different languages. Or, some time is spent now to ensure that
ultimately they become continuous with each other. The choice is (y)ours.
Acknowledgements
We thank the BBSRC, EPSRC (BBD0190791, BBC0082191, BBF0035281, BBF0035521,
BBF0035521, BBF0035361, BBG5302251, SySMO P 49 ), EU-FP7 (BioSim, NucSys, EC-MOAN)
and other funders (http://www.systembiology.net/support/ ) for support of this rather
encompassing activity.
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