From silicon cell to silicon human

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7 Νοε 2013 (πριν από 3 χρόνια και 8 μήνες)

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From silicon cell

to silicon human



Hans V. Westerhoff
1,2
, Malkhey Verma
1
, Frank J. Bruggeman
2
, Alexey Kolodkin
2
, Maciej Swat
2
, Neil
Hayes
1
, Maria Nardelli
1
, Barbara M. Bakker
3
, and Ja
cky L. Snoep
1,2,4


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, Universi
ty 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 sili
co

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 targ
ets
, 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
in
dividual. 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 a
t 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
comp
artments

and a second trying to deal with interactions between organs
.

Keywords:

Bottom
-
up
Systems Biol
ogy, computational, networks, modelling
, in silico experimentation,
metabolic control
,
pharmacodynamics and systems biology
, regulation

Table of Contents

Summary

................................
................................
................................
................................
.................

1

Introduction

................................
................................
................................
................................
............

2

Where Systems Biology is different

................................
................................
................................
....

3

What Systems Biology?

................................
................................
................................
.......................

4

How Systems Biology?

................................
................................
................................
............................

4

Top
-
down Systems Biology

................................
................................
................................
.................

4

The silicon cell

................................
................................
................................
................................
.....

5

Silicon cell models: advantages and disadvantages

................................
................................
...........

6

Blueprint modell
ing

................................
................................
................................
............................

9

The wisdom of MOSES: domino systems biology

................................
................................
.............

10

Metabolic Control Analysis models

................................
................................
................................
..

12

The silicon
-
cell strategy in yeast

................................
................................
................................
.......

12

Silicon cell and differential network
-
based drug design

................................
................................
...

13

The t
rue silicon cell

................................
................................
................................
...........................

14

Crossing the scales

................................
................................
................................
............................

15

Different types of modelling

................................
................................
................................
.............

16

Towards the silicon human

................................
................................
................................
...................

17

Acknowledgements

................................
................................
................................
...............................

20

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 m
ake 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. Alt
hough 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 ha
ve 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 l
ead to a true
-
to
-
Life model of how
the
human

being

functions through its
interacting molecules.


Where Systems Biology is different

G
enomics

and Molecular Biology have focused on the identification of all the individual
macromolecules
,
the
ir 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 indir
ectly. 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 concentr
ations 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 interacti
ons. 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
intermolecular
-
interactions

data
quantitatively and b
ecause 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 awa
y 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 b
e 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 pa
radigm

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 combin
ation 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 system
s 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 predict
s 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 actuall
y 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 whic
h
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 abo
ut scale
-
free intracellular networking and about prevalent gene
-
network 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
o
f 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
V
max

and
K
M

values that depend
on
pH or even on the concentrations of other medium components
(van Eunen, Bouwman
et al
.
20
10)
. 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, i
n 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, prote
ins, 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 the
n 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
V
max
’s. The rate equations

of all these enzymes a
re 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
nume
rically 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 mode
l 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 si
licon 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
‘l
ive’ model repository
, from which mathematical models

of biochemical pathways

can be
downloaded in SBML

form (Systems Biology Markup Language is the model specif
ication 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, wh
ich 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 t
his 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
-
silico
n 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 the
ir 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 tha
t 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 u
ntil 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 d
efining 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 pathw
ays 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 t
here 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
ar
e 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, B
ruggeman et al. 2010)

and oscillations in NF
κ
B 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 bioc
hemical
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 lo
ng 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
-
organ
ization

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 th
e 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 i
s 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 fit
ting 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, bu
t there was no assurance
that those parameter values corresponded to reality. For instance the model would fit the data if a
lower than actual

V
max

was inserted for an enzyme (such as hexokinase in Teusink, Walsh et al.,
1998). The fitted mo
del 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 lo
ng 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 v
alidate 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 p
rime 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 sen
se 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
compu
tational 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 i
llustrates 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 sho
wn 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 unders
tand 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 i
n 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 anym
ore 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 expe
riments, 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 addres
s
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 constru
ction
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 V
max

of glucose

uptake from 95 to 150
; t
he
concentrations of pyruvate and fructosebisphophate fail to reach steady state.


The silicon cell

strategy also has many disadvantages. One is that it requi
res 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 i
s 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 fu
nctions 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 s
ilicon 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 blue
-
print procedure

starts from the silicon
-
cell model that is already available of a relate
d 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 pri
oritizes 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 ce
ll

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 mo
dules 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)
.





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 per
forming
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
ATP
ADP

AMP

Glycolysis


Nucleotide
Synthesis




Drug Efflux



Maintenance




DNA repair



Growth


first model with the intermediate in the middle and the two processe
s 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, w
hich 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)
.

0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Time (min)
Adenine nucleotides (mM)
AMP
ATP
ADP
AXP
Glucose added

0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Time (min)
Adenine nucleotides (mM)
AMP
ATP
ADP
AXP
Glucose added

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 suc
h 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 limite
d 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 preci
se 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
s
trategy 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
Integrat
ive 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 parti
ally 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.


Ethanol
determination
Expt. based
FBA
Exo
Meta
bolome
Nonlinear
FBA
Threads
A.
Experimental
design and
pathway
finding
B. Component
characterizat
-
ion
C. Pathway
modelling
D. Validation
E. Discovery
Protein
purification,
Characteriz
,
Determination,
V
max
Proteomics
Flux
prediction
Pathway
ranking
Pathway
modelling
Improving
model
Under
-
standing
Flux
Paths
New
component
functions
Network
functioning
New
functions
Inter
-
actions
Interactions
Mechanisms
Behaviour
Turbidostat
experiment
Standard
FBA
Endometa
bolomics
Isotope
fluxes
Concentr
prediction

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 b
iologically. 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 scann
ed for the molecule that had the
strong
est 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 effectivenes
s 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 a
re 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
-
p
rint 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 s
hifts into the nucleus and binds to response element, causing
a
transcriptional response (Figure 5).

A curious aspect is that both export of importins

and export of liganded receptor are driven by
RanGTP

hydrolysis. Why wo
uld 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 kinet
ic parameters are still unknown. In this model we
asked what would happen if we
decrease
d

∆G

(i.e. the Gibbs free energy difference)
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 nu
clear receptor by importin.





F
ig. 5. Silicon cell model of a nuclear hormone receptor

signalling

network and prediction of the
dependence of transcription activation on the total concentration o
f 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
expre
ssion. 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, metho
ds 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 sc
ales

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 t
otal 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. 2
009)
. M
etabolic Control Analysis (M
CA
)

has been extended to address the multi
-
scale issue of
signal transduction

(Kahn an
d Westerhoff 1991)

and of that metabolism versus gene expression
(Westerhof
f, 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 modell
ing

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 eve
n 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 be
en 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 networ
ks 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 ave
rage. 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 ca
rbon 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 fo
r 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 activ
ation of intracellular networks, what happens in their beginning is co
-
determined 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

lo
ops 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 molecule

numbers in the relevant compartment
s 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 c
entre 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 illustrate
s 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 me
rged 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 incorpor
ated 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 experimenta
lly 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 thresh
old
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 secret
ion 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 provide
d

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 th
ose

predictions would be correct or not, but this is
now

accessible to experimental
validation
.





Fig. 7. Minimali
stic 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 C
-
peptide

kinetics. B. Calcul
ations 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 thou
sands 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 impossibl
e 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 apprec
iate 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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Subjects:

Adenine nucleotides
, 6

annotation, 3

ATP
, 2, 5, 6, 7, 8, 11

balance equations, 3, 8

biochemical pathway, 3

biochemical pathways, 3

BioModels, 3, 10

blue print modelling, 8

blue
-
print model, 7

blue
-
print procedure, 5

Boolean networks, 8

bottom
-
up,
3

Brownian motion, 8

cascade, 8

cell cycle, 3, 10

compartment, 2, 8, 9

compartmentalized, 7

computational experiments, 4

computer replica, 1, 3, 4, 8

control, 1, 2, 3, 6, 7, 9, 10, 11

control coefficients, 6

C
-
peptide, 9

development, 4, 7, 10

domino system
s biology, 8

Domino systems biology, 5

drug targets, 1

drug toxicity, 7

drugs, 7, 10

elasticity coefficients, 6

energetics, 5

ensemble, 8

enzymes
, 2, 3, 6, 8, 10, 11

erythrocytes, 7, 10

falsification, 4

feedback
, 2, 8

feedforward
, 2

free energy, 7, 8

funct
ion
-
driven strategy
, 6

gene expression, 2, 3, 8, 11

gene
-
expression, 3, 11

Genomics
, 2

genomics
-
driven strategy
, 6

glucose, 4, 6, 7, 8, 9, 10

glucose tolerance test
, 10

glucose transport, 6, 10

glycolysis, 3, 4, 6, 10, 11

glycolytic models, 3

gradients, 8

high throughput
, 6

hypercaloric state, 9

importins, 7

inflammation, 7

insulin, 2, 9, 10

interactions between organs, 1

isoenzymes, 5

Java Web Simulation, 3

JWS Online, 3

JWS
-
Online, 3, 7, 9

key metabolite, 5

kinetic assays
, 5, 6

kinetic equations, 8

kineti
c properties, 3, 6

lifetimes, 8

maintenance
, 6

mathematical models, 1, 3, 10

MCISB, 7

metabolic control analysis, 8

Metabolic Control Analysis, 6

metabolic engineering, 4

metabolic pathways, 3, 5, 7, 8, 11

metabolism, 2, 3, 7, 8

middle
-
out, 10

model reposi
tory, 3, 7

modelling, 1, 3, 5, 6, 8

Molecular Cell Biology
, 2

Monte Carlo, 8

MOSES, 5

multi
-
scale model, 9

nuclear hormone receptor, 7, 8

Nuclear receptors, 7

organization, 2, 4, 8, 10

paradigm
, 1, 2, 10

parasite, 7

Partial differential equation, 8

pathway
, 2, 3, 5, 6, 8, 9, 10, 11

pharmacokinetics, 9

phenomenological models, 4, 8

phosphotransferase system, 3, 10

quality control, 3

quasi
-
steady state approach, 8

RanGTP, 7

rate equations, 3, 6

regulation
, 1, 2, 3, 11

response element, 7

robustness, 1, 2, 4

SBML, 3, 4, 10

self
-
organization
, 2, 4

sequestration, 3, 7

signal transduction, 2, 3, 8

signalling, 7, 8, 10, 11

silicon human, 1, 8, 9, 10

simulation, 4, 8

sleeping sickness, 7

Stochastic modelling, 8

systems biology, 1, 2, 3, 5, 6, 8, 10, 11

Systems biol
ogy
, 2, 5

T. brucei
, 3, 7

targets, 7

time scales, 8

tissue
-
tissue interaction, 9

top
-
down systems biology, 2

Top
-
down systems biology, 8

transcription factors, 7

turbo, 4, 10, 11

validation, 4, 9

virtual patient, 9

V
max
, 2, 3, 4

whole
-
body
, 10

world
-
wide w
eb, 1

yeast, 3, 4, 5, 6, 10, 11