From silicon cell to silicon human

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7 Νοε 2013 (πριν από 4 χρόνια και 3 μέρες)

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F
rom 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
Jacky 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, Univer
sity Medical
Centre Groningen, University of Groningen

4
Department of Biochemistry, Stellenbosch University



Summary


T
his 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 hard
er

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. R
easons 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
.
S
hort
-
cut

solution
s

are
indicated.

One of the major a
ttempts 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 intracell
ular
compartments

and
a second trying to deal with
interactions between organs
.

Keywords:

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

Table of Contents

Summary

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

1

Introduction

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

2

Where Systems Bi
ology 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 modelling

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

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 true 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 the
ir

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 t
he endocrine
role of
insul
in

production by beta cells is w
hat the authors have in mind, this application is not made
explicit, in par
t because too little has been done
,

and in part because this chapter wishes to inspire
experts to have a fresh go at thi
s.

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
-
Lif
e 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
,
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 strength
s

of the
interactions and none of them indicate how the strength
s

of the interactions may depend on other
factors, such as concentrations of ot
her 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 c
onsequence 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 because all data relevant to a certain function have rarely been
integrated into a single frame of reference
, n
etwork analyses have remained qualitative and thereby
speculative.


On the other hand,
mathematic
al biology has had the tendency to abstra
ct away from
the
detail
and
the actual, because it aimed
for

generic principles.
Of

t
h
e

principles
that were
found, such as
gradient driven
self
-
organization

as possible mechanism for developmental biology,
specific

predictions c
ould 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
be
came
popular
, in which the expression of one gene would lead to a protein activating the ex
pression of the
genes of the subsequent phase
.
Although
feedback

and feedforward

loops
are recogniz
able in the
corresponding networks
,
it is not clear whe
ther
self
-
organization plays a role
(Peter and Davidson
2009)
.

T
o 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
in
tegration 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 a
nd 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 e
xplain this in a mode that predicts on the basis of changes in molecular processes
.


What Systems B
iology?

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.

H
owever
even
definitive information that two network components can
interact, does not certify that the
y 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 resid
es in
.
Without dynamic information about the ac
tual states of
the living systems
, c
onclusions about scale
-
free intracellular
network
ing

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

th
is

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 S
ystems
B
iology
?

Accepting the above ideal scenario for systems biology
, one should translate this into som
e
thing that
is operational
. At present this is almost impossible, because too little is known
or

can be measured
quantitatively.
I
n 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 th
e concentration
s of other medium
components

(van Eunen, Bouwman
et al
.
2010)
.

In addition, it is difficult to measure th
e property of some enzymes
, whereas it can be easier
to do this for others.
T
he strateg
ies

for systems biology ha
ve

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 B
iology

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
-
wid
e 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
grou
p 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 pa
thway
. 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 t
ends
to i
nvolve 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 equation
s

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
numeri
cally 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

correspond
ed

to
the
condition

in vivo
.
T
he silicon
-
cell model
s

of

human erythrocyte glycolysis

(Rapoport, Otto et al.
1977)
,

T. brucei

glycolysis by

(Bakker, Mich
els et al. 1997)
, of
yeast

glycolysis by
(Teusink, Passarge et
al. 2000)
, and of the bacterial phosphotransfe
rase system

by
(Rohwer, Meadow et al. 2000)

are early

example
s

of

what is close to
the silicon cell approach
. Yet
,
some of these were

imperfect be
cause

the kinetics
of the pathway

enzymes were determined
in cell extract
s

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

we
b

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 wi
th the standard parameter set
taken from

their primary publication, which should correspond to the standard physiological state.
Parameter valu
es 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
importan
t 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 vi
a a direct link within Bio
M
odels.

Its models
have a more systemat
ic
annotation

facility
(Le Novere, Bornstein et al. 2006)
.


The way JWS
-
O
nline

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 sci
entific 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 contro
l

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 numb
er 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 m
ost important
in the future.

In Figs 1, 3 and 5 of this
chapter

we give
jus three
examples of silicon cell

models.
M
ore
such models
are in
JWS
-
O
nline
,
e.g. accessible through

http://jjj.mib.ac.uk/index.html

.

When going th
rou
gh the
models in the JWS repository the read
er will find some diversity. However, s
he/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 co
mputer
-
replica than others,
or
because
some
authors have not submit
ted the
ir models t
o JWS Online
.

Reasons
for

the relative
abu
ndance of metabolic and
especially

glycolytic models

are that in metabolism

the law of
conservation of the elements has direct consequences
: A
t steady state
,

what flows into any node of
the network must be equa
l 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 acti
ve 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
metab
olites 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 structur
ing

are underrepresented, as
are metabolic pathways

that are subject to adaptation through gene
-
expression

regulation
.

The
se

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 syst
ems 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, Pa
ssarge et al. 2000)
), the cell cycle

(Conradie, Bruggeman et al. 2010)

and oscillations in NF
κ
B signaling
(Ihekwaba, Wil
kinson 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 bioche
mical
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 wh
ich were u
sed
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 feedbac
ks. 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 suc
h 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
:
T
he number of parameter
s

exceed
s

the number that could be determined experimentally at the
re
qui
red level of accuracy, or, more often, the parameters refer to abstract properties that c
annot

be m
easured 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

hypothes
is about

mechanism
, but this has been rare
.


More often
, parameter values
could be found for which the model fit
ted

the experimental behavio
u
r
, but
there was no assurance
that
those parameter values correspond
ed

to reality. For instance the mode
l

w
ould
fit the data if a
lower th
an actual

V
max

was inserted for an enzyme (such as hexokinase in
Teusink, Wal
sh et al.,
1998)
. The fitted model
w
ould 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.
P
henomenological 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 howeve
r; 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

component
s’

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 explan
atory for
,

observed functional behaviour.


Silicon
cell models

are realistic and suitable for a falsification
/validation

strategy.

This is a

prime utility of
silicon cell

ty
pe of models,
i.e. scientific va
lidation/falsif
ication of p
r
op
o
sed 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 a
nother type of understanding,


i.e. that
of the ability to
predict
.
If

the prediction fails to correspond to reality
,

e
xperimental follow
-
up can
lead to

improved understanding. In other words, silicon cells are the tools that are ultimat
ely
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 silico
n 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, t
his 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 glycol
ysis

(Teusink, Walsh et al. 1998)
.

Silicon cell models have two additiona
l advantages. One is that their parameters are ‘hard’ in the
sense that they correspond to properties of real molecules
.

Th
is

means that, onc
e known,
the
parameter values should not change anymore unless the model is wrong
, or the properties of the
molec
ules 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 t
o make the fit optimal

(Novak, Csikasz
-
Nagy et al. 1998)
. For
large models this ca
n become increasingly bothersome. The second additional advantage

of silicon
cell

models

is that because
they are

formulated
in terms of

real entities, mode
ls

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
all
ow

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
the
refore
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 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 requires an awful lot of careful
experimentation to determine all the kinetic parameters. In addition it re
quires
all

components to
be assayed, which is impossible for realistic systems, first because they contain too many
components and second because ther
e is always a component that is
most difficult to isolate or
assay.

A second
dis
advantage is that
it
is excruciatingly slow and not always maximally exciting. For
instance,
the silicon cell

approach suggest
s that having made such a model for

an

organism

for a
particular experimental

condition
, one should
start all over
again if on
e is interested in a different
organism or a different condition; the organism may then ex
press different isoenzymes
. However
,
repeating the procedure for the different condition, one may obtain the same result in terms of true
understa
nding 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 difference
s

in networking of essentially the same mo
lecules

( 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 belon
g to
gether
, such as metabolic pathways

in their cl
assic
al
definition.
Strategies
for a more rational definition of what pathways silicon cell models should
begin to fo
c
us on are being developed (Westerhoff et al., 20
09
).



Bluep
rint 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 related organism a
nd
then

chan
ges
this in the light of
what is
already
know
n

of the molecular properties of the
organism
under study
.
Comparing

the predictions of this adjusted blueprint model with physiological
behaviour

measured experimentally, one then prioritize
s

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
forese
eable time, and one

needs to start with
a
part of the intracellular network. Ways to divide the
intracellular network into modules th
a
t

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 metabo
lite

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

assay
s
,

or by modular kinetic analysis

(Ciapaite,
Van Eikenhorst et al.
2005)
, how the
se

processes depend on the concentration of the
key
metabolite.
Start
ing

with the
most important synthesis process and the most important degradation process, it

then formulates a
ATP
ADP

AMP

Glycolysis


Nucleotide
Synt
hesis




Drug Efflux



Maintenance




DNA repair



Growth


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 inter
mediate

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 t
o

invoke

either
an
additional proce
s
s

or
an
additional metab
o
lic 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 energetic
s
.

Fig. 3 shows
a modelling

result that comes f
rom

this approach, i.e. a perhaps somewhat paradoxical dynamic
behaviour of the
ATP
level up
o
n 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
s
eek t
o

limit

the network size, but

to

reduc
e
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
e
la
s
ticity coefficients

(Kacser and Burns 1973; Westerhoff and Kell 1987; Reder 1988;
Westerhoff and Kell 2009)
. El
a
sticity 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

w
h
ich enable
d

them to calculate the elast
icity

coeffic
ients,

because the
y had

measured

the intracellu
lar concentrations of some metabolites by NMR

(Nuclear Magnetic R
esonance)

(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 t
o determine its
k
i
netic 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 t
o

a function
-
driven
strategy
,

i
.e. to sel
e
ct a function of interest,
estimate

which enzymes

are most involved
in that
function,
isol
ate and characterize those enzymes
,

and the
n

make a silicon cell

model

(Westerhoff et
al., 20
09
)
. 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 fu
nction, 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 bioch
e
mically, but it will not
be
able to
define that action biologically.

For the latter definition the
multiple
effect
s

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 cell
s

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
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 effectiv
eness is drug toxicity
. Accordingly a drug should be
maximally effective against the parasite

but minimally ef
fective 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 cell
s

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 re
pository
, are mod
el
s of mostly metabolic
pathways
. There is no model of entire cells.

The name silicon cell stems fro
m the ambition
ultimately to combine silicon
-
cell models of pathways into models of entire cells.


Cells are co
mpartmentalized

and involve more than metabolic pathways
. Fig. 5A shows a ne
t
work
that is not involved in metabolism

but in signalling
. It represents

a

blue
-
print model

of nuclear
horm
one 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 N
R
L in
the cytoplasm. Then, N
R
L shifts into the nucleus and binds to response el
emen
t,
c
ausing
a
transcriptional response
(Figure 5).

A

curious
aspect
is that both export of importins

and export of liganded receptor are driv
en

by
RanGTP

hydrolysis
. Wh
y wo
u
ld 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
equiva
lent

to a silicon cell

model
; man
y kinetic parameters are still unknown. In this mo
d
el 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 st
i
mu
l
ate transcription at high
concentration
ratios of impo
rtin t
o

nuclear hormone receptor
.
This leads us to formulat
e

the hypothesis that the investment

of free energy serves to prevent
sequestration

of

nuc
l
ear 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 of importin
(Imp)
in the system and
the free ene
rgy

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.
E
ven in a single compartment, time scales

may
be di
verse
. 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 pro
tei
ns are mostly longer than the lifetimes of
many
intermediary metabolites,
the dynamics of gene expression are of
ten

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 concentratio
n. The latter
has the advantage that total enzyme is set by the dimension of gene expression

not by metabolism
.
Even t
h
ough 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)
.

M
etabolic Control Analysis (M
CA
)

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

(Kahn and Weste
rhoff 1991)

and

of that
metabolism versus gene expression

(Westerhoff, Kost
er 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 issue
s

in beta cells
might

be p
ut in the
perspective of t
heir 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
e
quations
. Metabolic control analysis uses less than this

(Westerhoff and Ke
ll 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 t
hat

enables to
relate her function to her mo
lecules.

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 an
alysis as a modelling method
may

help

establish where to look first for important
pathways

(Westerhoff et al., 2009)
. However, it ultimately suffers
fro
m 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
whi
ch then makes a single molecule

of the product. The difference matter
s 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 diff
erent 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
concentrat
ions 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 co
-
determined by what has happens at their end. At stea
dy

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 cal
culated in the lifetime of the
P
lanet, 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 co
u
ld
never determine. It would also be impossible to trace the behaviour of every individual molecule,
without perturbin
g 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 consider
ations
(Westerhoff and Van Dam 1987)
. Stochastic modelling

does
become important when molecule

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 im
portant
(Kholodenko 2006)
.


Towards the silicon human



In the
context of the human
, the
ambition

is ev
en greater, i.e. to combine models of cells into
models of tissu
e
s 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 wou
ld be a multi
-
scale model

relating whole body function to molecular activities in time and space. Here, the
s
ilicon
-
cell project
will become a

silicon organism project, with variations such as th
e

virtual
physiological human
and
the digital human projects. The idea is s
imilar
to th
at
of

integrating pathway

models. Rel
atively
autonomous models of organs are
to be
combined. One thought is to leave the coordination of
each

organ model
including the corresponding co
mputations
to a
n individual

research centre
and
then
to
integrate the models dynamically through web services. Although perhaps slow, this would h
a
v
e the
advantage of maximum responsi
bility of a group ove
r a part of the whole model, en
suring quality
control
.

Fig. 6

ill
ustrate
s

this app
roa
ch, w
here of course the be
ta

cell
component
model will p
lay 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 vir
tual 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. 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 C
-
peptide

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 calcula
tions 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

f
ro
m a failure to appreciate that biolog
ical organization

greatly reduce
s

complex
ity

(Westerhoff, 2010)
.
Moreover
, the

silicon h
uman 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
merge
d

into a
larger
, more complete

model. The latter possibility should ena
ble 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 mathemat
ical models of the human, we also have
another choice. Either the results of the
se

three methodologies will be developed independen
tly 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

funder
s (
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 systems 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

function
-
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

kinetic 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 repository, 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 biology
, 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 web, 1

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