From silicon cell to silicon human

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23 Οκτ 2013 (πριν από 4 χρόνια και 2 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
,
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 Biochemistry, Stellenbosch University



Summary


T
his chapter
discusses
the silicon cell paradigm
, i.e. the systems biology of making experiment
-
based

comput
er 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
,
new drug targets
, as well as to hard 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
indic
ated.

One of the major attempts
at silicon
-
cell systems biology
,
in the Manchester Centre for Integrative Systems Biology
,

is discussed
in some detail
.
Early attempts at higher order
, human

silicon
-
cell
models are described briefly,
one
addressing intera
ctions between intracellular compartments and
a second trying to deal with
interactions between organs, including the pancreas.



Table of Contents

Summary

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

1

Why Systems Biology?

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

2

The natu
re of biological complexity

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

3

The theoretical complexity of Biology

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

3

The actual complexity of Biology

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

4

Where Systems Biology is dif
ferent

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

6

What Systems Biology?

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

7

How Systems Biology

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

8

Top
-
down S
ystems Biology

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

8

The silicon cell

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

8

Blueprint modelling

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

11

The
wisdom of MOSES: domino systems biology
................................
................................
.......

12

Metabolic Control Analysis models

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

13

The silicon
-
cell strategy in yeast
................................
................................
...............................

14

Silicon cell a
nd differential network
-
based drug design

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

14

The true silicon cell

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

15

Towards the silicon human
................................
................................
................................
..........

16



Why Systems Biology
?


Although it has become possible to characterize almo
st all molecular components, no
comprehensive function of any living organism has yet been understood in terms

of a fully predictive
biology.

Thereby the implicit promise behind much of the life science
s
, i.e. that we are working
towards completely rational therapies of all our diseases,
seems to be broken
.

This broken promise becomes bitter as m
olecular biology, cell biology and genomics
thrive in their
su
ccesses. P
rogress
from almost
complete ignorance
a century ago to the

accumulated data
and
understanding
of today
, has been
enormous
. However
,
the distance between where we are now
and where w
e should be
,

seems to have increased even more. With every new paper about p53, we
understand less of its
function
(Lazebnik 2002)
.

We do not see the forest for the trees and the
information about the individual trees has

been growing
e
xponentially.

Reasons are the enormous
complexity of the subject
matter and
,

perhaps, a
wrong approach
to

that complexity.


The nature of biological complexity


The theoretical complexity of Biology

When setting up or deciding about the fun
ding of research programs it becomes increasingly
important to ensure that they follow
a sensible

strategy.
When aiming to understand the common
basis of all physical forces in terms of
an as yet unidentified
gauge
boson

(Higgs 1964)
, it

makes
little

sense to
study a pendulum in one’s backyard. One probably needs to
make

ele
mentary particles
collide at
huge
energies, requir
ing

an enormous
accel
erator

at vacuum
.
Thus
, an enormous project
emerges, involving lots of laboratories all over the world.
M
ost of what the
se laboratories

do has to
b
e

done in a single context, using c
ommon

standards.


Biology and

molecular biology lack the tradition of
Big Science; they
have been

more like cottage
industries.

Indeed, there have been and there remains to be
good reason
s for

work
ing

on certain
parts of living organisms, for instance on the structure
of an important protein
(MacPherson, Xu et
al. 1998)
, on the genes
down
stream binding sequences for a transcription factor, or on the
mechanisms by which chromatin mo
dification may affect Lyonization
(Monkhorst, de Hoon et al.
2009)
: the structures and molecular mechanisms are
both
fascinating and important scientifically.
An
at least
equally important
aim

of biology however is the understanding of Life, of functions that
contribute to Life, or of malfunctions that lead to disease. In a perhaps too literal r
eading of
the
word Biology, this is what biologists
are supposed to d
o, i.e. figure out the
words

and laws

that
gauge
Life.

Ultimately this aim may require an even Bigger Science that that required for the Higgs
boson. For the human is likely to be much more complex than the relationship between the four
fundamental forces, and much more important f
or mankind as well.

Genomics has contributed a number of mind shattering understandings of the living state. One is
that the genome sizes of living organisms that we find interesting (e.g. humans, yeast,
Escherichia
coli
) are quite substantial,
amounting
to
the thousands

of genes
. This
might suggest

that to
understand such organisms
, one
should ultimately repeat the stud
y of a component

more than
a
thousand times. Already in this sense, Biology is complex. Rather than the, say 3, elementary
particles th
at may feature at some relevant level in Physics, or the
118 that do so in Chemistry, one
is here dealing with at least 30 000 such element
ary particles

for the human.


Be that as it may, one could engage in an extensive structural Biology initiative and

overexpress,
purify, crystallize and then determine the X
-
ra
y structure of each of the 30 0
00 proteins
(Matthews
2007)
.

This is much and
highly

difficult work, because
most

proteins
of

a

genome

differ

in structure
and
function. This
feature

corresponds to the complexity that is often associated with biology,
i.e.
much
, much

detail

and

little generality
,
i.e.
a seemingly endless project of data collecting
.

However, if Chemistry would ha
ve been satisfied with determining the structures and material
properties of all the elements, this would not have led to as much

understanding of the world as
C
hemistry has contributed now. Most substances that affect the world are not elements but
compounds and much of the relevance of
material
chemistry
resides in

the elements react
ing

with
each other
to
form new entities
;

an infinite number of these
.


Simila
rly, the macromolecules of Biology function exclusively through their interactions with other
macromolecules. T
he cell division cycle is one of the most fundamental and characteristic processes
of Life. Mathematical models exist, in
which
a

numbers of pr
oteins

interact
,

effecting covalent
modification and degradation

of each other
. This entails cell cycling. None of the proteins in
isolation would cycle, but the ensemble of interaction proteins does.

And indeed a phenomenon
such as the transition of

th
e cell through cert
ain characteristic
points of the cell cycl
e appears to be
controlled by multiple proteins
(Conradie, Bruggeman et al. 2010)
.
Oxi
dative phosphorylation is the
main source of the ATP that drives virtually
e
very process sufficiently away from equilibrium to
provide flux that is
relevant for Life. The ATPase responsible for the synthesis of the ATP is driven by
protons tumbling down t
heir across the inner mitochondrial membrane

(Mitchell 1961)
. The
process would run in the

wrong

direction if only this enzyme were involved. The mitochondrial
electron transfer chain is essential to crank up that
ele
ctrochemical gradient
. None of the
participating proteins in isolation would
catalyze the synthesis of ATP; only their network does.

Similarly
,

beta
-
cell function in the sense of the secretion of insulin in response to increased
levels

of
glucose, would not happen if only t
he glucose sensing system were
in place or only the insulin
production machinery.

These are
a mere

three example
s

of
the fact that
functions of living
or
ganisms
depend critically in the interactions between

component
s.


In a
n additional
sense

all biological functions
ultimately
depend on interactions
. A
ll functions
depend on the maintenance of the living sta
te they are part of, which in t
urn depends on a minimum
number of interacting gene products.

This principle
of Life is reinforced by the smallest genome size
of living organisms
being not smaller than some 4
00 genes
(Fraser, Gocayne et al. 1995; Glass,
Assad
-
Garcia et al. 2006)
. The significance of this is that

the smallest form of Life does
not consist of
100 organisms of four genes each but that all genes have to be together in a single organism for any
of the genes to survive [
pace

(Dawkins 1976)
].

This means that all 400 genes have t
o interact with
each other for
each of them

to be viable.

The number of potential binary interactions of 30000 components is almost a billion, and if
interactions c
an
involve any number of components, the
number
of theoretically possible
interactions

(30 000!
=10
121202
, i.e. a
1 with more than 120000

zeros
)

exceeds

the n
umber of atoms
in the Universe

(which is on the order of 10
80

)
(Noble 2006)
.



For the smallest genome we know,
the numbers are 400
!, amounting to 10
866
.
Because these numbers exceed the number of genes
astronomically, and because 30 000 would be manageable for a larg
e

research program but 10
121202

would not

be
,
the problem in the complexity of Biology resides less in the
large
number of
components
than

in the importance of
the
ir

interactions for function.


The actual complexity of Biology

Are living organisms so complex as to depend on more than 10
8
66

interactions? If so, then the
experimental assessment of the strengths of the
se interactions would be impossible
within
the life
time of the human species
,

and
well beyond possible resourcing.
Likewise the mathematical
modelling of the corresponding networks would require computers that cannot be envisaged to be
built or even powe
red. In this section we shall
show that the complexity is far smaller than
suggested by this astronomical number.

Living organisms engage in diverse functions that are often much more sophisticated tha
n

the
functioning of an ideal gas.
It might seem tha
t this sophistication might require the enormous
complexity calculated above.
However,
the p
art of non equilibrium thermodynamics
that deals

with
self
-
organization,

has shown otherwise:
through the
nonlinear
interactions of a
very
limited number
of compo
nents,
highly

complex patterns can emerge

(Glansdorff and Prigogine 1971)
, which

are
reminiscent of the patterning in developmental biology

(Gierer and Meinhardt 19
72)
.
This means
that although many
biological
functions are complex, they might depend on few components and
interactions

(Turing 1952)
.

This n
ow constitutes a paradox. I
f generati
ng strong complexity requires so few components and
interactions,
why
do living organisms
require
so many
(>400)
components and
, do they require as
many as
the
400!
possible
i
nteractions

between these components
?

This paradox is profound and
affects muc
h of the methodology of the Life Sciences. On the one hand

some
life scientists view
biology as a can of worms, every new case requiring a
de novo

acquisition of experimental
information where conclusions can only be drawn empirically and where there is n
o role for the
application of generic laws and principles.
On the other hand, (other) life scientists wish the science
of biology to become a predictive science, where the application of more generic principles and laws
to actual cases suggests hypotheses

that are then tested experimentally

and rigidly
. When projected
into the extreme, the former group sees biology as a can of >400!
w
orms, whereas the latter sees it
as in essence just 4 or 5 general principles being instantiated in large nu
mber of

special

cases.

We
shall here argue that neither view is correct, i.e. that biology is neither simple nor maximally
complex, and that a
n

additional
line of thinking i.e. hysteresis through evolution, is unique for the
life sciences and thereby leads to an entire
ly new methodology

(Boogerd, Bruggeman et al. 2007;
Westerhoff, Winder et al. 2009)
.

By accounting for the minimal requirements for Life, for the number of different chemical
compounds

required
,
for the fact that

bio
chemical synthesis
occurs in sequences
of
a simple
chemical reactions,
and for the required microenvironment for
catalysis
(Westerhoff and Welch
1992)
, one finds
that Life requires more than
hundred reaction steps
(Westerhoff, Winder et al.
2009)
.

In

linear
biochemical pathways

each
protein interact
s

with two other proteins through
an
intermediary metabolite, leading to a number of
(indirect) protein
-
protein
interactions that is equal
to the

number of enzymes.
Because of the requirement of free energy transduction, and because of
convergence of reactions, the actual number of such interactions would be a bit higher.
When
metabolite channelling is absent, one should
not count
only in terms o
f gene products.
The
interactions that underpin the chemistry of living organisms are protein
-
metabolite interactions.
If
there are only linear pathways one then has 2 times
n

enzyme
-
metabolite interactions when there
are
n

enzymes. For the 30 000
-
gene
human this would mean some 60

000

real interactions rather
than the
10
121202

theoretical ones (see above).

This estimate of 60 000
may be a bit

conservative because there are also reactions that have more
than one substrate
,
e.g. those
invo
l
ving

free
-
energy or redox coenzymes.
However, even though
one might then
require 10
5

interactions
, this

number is astronomically smaller than the theoretical
number

of 10
121202
.

There are other reasons why Life is less complex than it could have been.
Lookin
g at equal
-
size
spheres we find that any one can only interact with six others at the same time
.

In a multi
-
tissue
organism not all genes are expressed in all tissues. In microorganisms not all genes are expressed at
the same time. Yet,
this

differentia
l expression
in space and time
gives evolutionary advantage.
T
he
total number of genes expressed
at any one time in any
human
tissue might

well be as low as

4

000
.
This
decreases

the number of binary interactions to some 10 million, i.e
.

very many, but p
erhaps not
too many fo
r a
very
large research program

of Big Biology
.

M
ore important than the

precise
magnitude of the
se

number
s

however
, is the
suggestion

that
living organisms are not as complex as
the theoretical number of
400
! suggest
ed
.

Why then did
not Life

grow so complex

as it could have
?

Evolution presumably
began

at a suboptimal state and then moved to a variety of more optimal
states, adapted to ecological niches.

Because of strong selection pressure there has been limited
horizo
ntal evolution, i.e. at each intermediary stage of optimality, there have been insufficient
mutations to sample all possibilities of improvement.
If evolution is see
n

as the movement down
from the top of a mountain,
then it cannot be predicted which side

of the mountain, hence in which
of the many valleys surrounding the mountain, evolution ends up. E
volution cannot be seen as a

Markov process
, i.e. t
he state that is achieved ultimately is not determined completely by the
ecological niche and the possibi
lities of chemistry and physics
. I
t is also determined by accidental
‘choices’ during the process of evolution. An example is the fact that all amino acids
in proteins
are
of the L
-
stereoisomeric form, whereas mirror organisms with all D
-
amino acids woul
d have been
equally
viable in terms of

physics and chemistry.

The difference with physics
, or at least with the
classical picture thereof, is that in biology one cannot expect to solve a Sch
ö
dinger type of equation
for minimum energy solutions and find bio
logical reality after evolution
as the

theoretical minimum

energy state
.


Living systems
are not at equilibrium or even near equilibrium. Even when relatively simple, linear
dynamic relations exist, those relations differ from those that could be derived
from near
-
equilibrium non
-
equilibrium thermodynamics
(Westerhoff and Van Dam 1987)
.

Often the system is
‘pumped up’ to a steady state far away from equilibrium by continuous expenditure of free energy
harvested from food
. The
properties
of such a state

do not correspond to the non
-
mechanistic
properties near equilibrium
(Onsager 1931)
. They

reflect mechanisms and regulation
(Keizer 1987)

that may have been selected by evolution. Yet, within a basin of attraction (a valley in the
mountainous landsca
pe), evolutionary optimization may have occurred to some extent
. P
rovided
that certain limitations imposed by evolutionary history
(such as L
-
amino acids)
are taken into
account
, one may be able to

predict the behaviour of the system. In addition in diffe
rent
species

some of the evolutionary pressures are identical and hence some generic principles may
apply
across species
. And then, because of the conservative nature of evolution discussed above, there is
substantial

homology, which also has the effect
of significant predictability (e.g. the prediction that a
newly observed bacterial species will have DNA with four bases).

Our conclusion is that
experimental

insight
into how biological systems happen to work r
educes the
potentially
astronomical complexit
y to perhaps manageable
,

actual complexity. The understanding
of Life will not come from
a grand min
imization
plus

simplicity principle applied to all degrees of
freedom of living systems
(Westerhoff, Winder et al. 2009)
.
I
t will require analysis in terms fo
r

the
actual components of
,

and the actual interactions in actual living organisms.
Therewith
e
xperim
e
n
tal biology

is a

crucial compo
nent, of
systems biology

(Alberghina and Westerhoff 2005)
.


Where Systems Biology is different


G
enomics and Molecular Biology have focused on the identification of all the individual
macromolecules and on their inherent activities. Cell Biology has drawn schemes of macromolecular
networks in exclusively qualitat
ive terms. As a consequence, we largely lack the
data
describing the
intermolecu
lar interactions quantitatively
, and n
etwork analyses have remained qualitative and
thereby speculative.

On the other hand,
mathematic
al biology has had the tendency to abst
ract
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 could be falsified
. This

made

self
-
organization theories
irrelevant

in the
eyes of experimental developmental biologists
(Lawrence 1992; Davidson 2006; Peter and Davidson
2009)
.

As an alternative paradigm for developmental biology, the
concept of the
genetic program
be
came
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
recognized,
it is not clear whe
ther
self
-
organization plays a role
(Peter and Davidson 2009)
.

T
o understand
living organisms
we need to appreciate

how
their components interact.
We need to
reckon with a
combination of a genetic
programme that came about accidentally in evolution

with

mechanisms that involved self
-
organization. This will require integration of the historical paradigms
of mathematical biology and molecular genetics
(Westerhoff and Palsson 2004)
.
It is in this
integration that systems biolog
y differs from
both
mathematical biology and molecular genetics.

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
d
escribe

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 comp
letely
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 transcrip
tion factor may interact with a gene

only
under the

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 en
zyme resides 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.
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
’s, 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 the property of some enzyme
s, 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.


Top
-
down Systems B
iology

The strategy that is closest to genomics is called top
-
down syste
ms biology. Here the concentrations
of all components of a certain class (mRNA, proteins, or metabolites) are measured in a genome
-
wide sense, as a function of time, or of conditions.
The

components that behave similarly,

are then
grouped
together, assu
ming that
correlation

indicates a mechanistic or functional relationship
. This
may

then lead to the proposal that all members of a group are regulated by the same transcription
factor. Such a hypothesis
may

then be tested by identification of that transc
ription 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 throu
gh a single level of cellular organization (such as mRNA levels) but
t
ends
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
syst
ems 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 en
zymes
are

then put into a computer model,
together with balance equations that give the change in time of the concentrations of all the
metabolites as functions of all the reaction rates. The resulting system of equations is solved
numerically for steady
state, or after addition of initial conditions, for
time evolution
. Thus a
computer replica of a biochemical pathway is created

with identical behaviour if the model is right.

The above approach
may

not
seem
new
, but in its precise sense it is
: although s
ilicon 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 of yeast glycolysis by Teusink
et al.


(Teusink, Passarge et al.
2000)

is
an example

of

what is close to

the silicon cell approach
. Yet
, it is imperfect be
cause

the
kinetics
of the pathway enzymes were determined for enzymes extracted from cells grown under
conditions that differed from those of the cells
used for the

lim
i
ted validation of the concentration
s
and fluxes predicted by the model.

The silicon cell is a rather loose research program that is greatly stimulated by the JWS modelling
we
b

site
(Snoep, Bruggeman et al. 2006)
.
JWS is a ‘live’

model repository
, from which mathematical
models of biochemical pathways can be download
ed in SBML form.

The model repository is ‘live’ in
the sense that the models can
also
be run through a web interface
, without downloading them
.
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 values can be altered and then the
changes of concentrations and fluxes can be calculated as functions of time. I
n addition
,

systems
properties such as the
magnitudes and
the control of steady state fluxes and concentrations can be
calculated.

BioModels, with which JWS collaborates, is another model repository
with an even
larger set of mathematical models, but th
ese are not accessible to through
-
web experimentation
in
silico
.
Its models
have a more systemat
ic annotation facility
(Le Novere, Bornstein et al. 2006)
.

What is the advantage of having a silicon
-
cell type model, a ‘computer replica’, of a biochemical
pathway? If perfect, such a model is

just as complex as

reality, hence it does not correspond to
the

abs
traction and simplification of reality that
is often associated with

‘understanding’.

Mathematical
biology has long made models of biological systems that focused on obtaining this type of
understanding.
Its

models started with simplifying the system to

what was hypothesized to be the
minimum set of components and properties that suffic
ed

to obtain the behaviour that needed to be
explained. Examples include the Turing type of models where it was shown that self
-
organization
might explain pattern format
ion in developmental biology. If the predictions of such a model
did

not
immediately and precisely fit experimental observations, then the parameters in the model would
be adjusted until a statistically satisfactory fit was obtained.
In principle the fit
ted parameters values
could then be verified experimentally, but this
is
rarely undertaken

in practice
:
Almost always 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, th
e parameters refer to abstract properties that c
annot

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
rene
wed fit between model prediction and experimental system behaviour. Only when such fitting
would
prove impossible the model served the important function of
falsifying a

hypothesis about

mechanism

.

Because of the many degrees of freedom in biology and
the many possible unknown
interactions, they rarely achieved this functionality
. P
henomenological models do show what
mechanisms might explain the behaviour of the biological systems, but they do not show what
mechanisms do

ex
plain that behaviour.
Only s
ilicon cell models also do the latter.

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
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

component
s’

properties
. The latter is
important for metabolic enginee
ring and therapeutic purposes.


The above is not mean
t to detract fro
m the utility of the phenomenological models of mathematical
biology.
Such models
are also useful. However, one should realize that they do not deliver ultimate
test
s

of concepts and
proposed mechanisms.
They are hardly falsifiable.
Silicon cell type of 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
se
d understanding of systems.

Although silicon cell models do not themselves constitute understanding in the sense of
simplification to what is most important
, they

do
instantiate another type of understanding,


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

the

prediction fails to correspond to reality
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 add
ition
,

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 ex
perimental
biology. Fig. 1 illustrates how this has worked already. It shows that the silicon cell model of yeast
glycolysis was rather unrobust with respect to the activity of the glucose import system; as shown in
Fig. 1B only a slight increase in that

activity, could lead to a ‘metabolic explosion’, i.e. to a continued
increase in the concentrations of some metabolites. This led us to understand an aspect of the
‘turbo’ organization of many catabolic pathways that could lead to fragility and then to a

hypothesis
on how a regulatory interaction for which no function was known

and which had not been included
in the silicon cell,

might be quite important for yeast glycolysis

(Teusink, Walsh et al. 1998)
.

Silicon cell models have two additional advantages. One is that their parameters are ‘hard’ in the
sense that they
correspond to properties of real molecules. These means that, onc
e known,
the
parameter values should not change anymore unless the model is wrong. Fitted, phenomenological
models have the disadvantage that for every new experiment the entire model shoul
d be refitted to
all existing experiments
,

allowing all parameter values to be adjusted so as to make the fit optimal.
For large models this can become increasingly bothersome. The second additional advantage is that
because the model is formulated
in te
rms 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.


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 requires all comp
onents 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
begin again if one is interested in a
different organ
ism 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 understanding of function
,

as one had obtained for the original

conditions and
organism. On the other hand, quite similar organisms may have entirely different functions
or
mechanisms
which they may achieve by difference
s

in networking of essentially the same molecules

( compare
(Haanstra, van Tuijl et al. 2008)

t
o
(Teusink, Walsh et al. 1998)
)
.

This issue now leads to
comparative syste
ms biology.


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 f
rom the silicon
-
cell model that is already available of a related organism and
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 wit
h 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 int
o modules tha
t

can be considered separately are highly important therefore
(Schu
ster, 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
performing
n
ew
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.
Starts with the
most important synthesis process and the most important degradation process, it

then formulates a
first model with the intermediate in the middle and
the
two

processes around it.

It then predicts
how
activation of the processes affect the concentration of the 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

invo
ke

either
an
additional proce
s
s

or
an
ATP
ADP

AMP

Glycolysis


Nucleotide
Synthesis




Drug Efflux



Maintenance




DNA repair



Growth


additional metab
o
lic intermediate
. By incorporating a next additional process or metabolite one
adds the next domino stone
.

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.


Figure 3:
Adenine
nucleotides dynamics for glucose perturbation by integration of glycolysis
and maintenance modules.


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 questio
ns 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 enzym
e kinetic properties
called
e
la
s
ticity coefficients

(Kacser and Burns 1973
; Westerhoff and Kell 1987; 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
wich
enable
d

them to calculate the elast
icity

coeffic
ients,

because the
y had

measured

the intracellu
lar
concentrations of some metabolites by NMR

(Galazzo and Bailey 1990)
. They found much but non
-
exclusive control of the flux by the glucose transport system, but this was partly the resul
t 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 a
genda
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 to then 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. The resulting
strategy is
illustrated

in Fig. 4.



Fig. 4. The strategy of the Manchester Centre for Integrative Systems Biology 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 a
ction 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
-
bio
logy 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 of the parasite.
However rather than targeting pyruvate kinase, i.e. the enzyme that makes most of the cytosolic
ATP, the network was scanned for the molecule that had
the greatest influence on ATP production.
The glucose transporter came out as
the
number one
target
(Bakker, Westerhoff et al. 2000)
.

An equally important aspect as drug effectiveness is drug toxicity. Accordingly a drug should be
m
aximally 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 hum
an 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 model re
pository
, are mod
el
s of m
ostly 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 pa
thways. 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 factor
s 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 resp
onse element

on the DNA
.
Addition of ligand results in the appearance of NrL in
the cytoplasm. Then, NrL shifts into the nucleus and binds to response el
ement,
c
ausing
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 close but not yet
equiva
lent

to a silicon cel
l model
; man
y kinetic parameters are still unknown. In this mo
d
el we
asked
what would happen if we
decrease
d

∆G

of both processes 100 times (dashed line). We
found
that the high investment of Gibbs free energy would st
i
mu
l
ate transcription at high
concent
ration
ratios of importin 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 r
eceptor signalling network and prediction of the
dependence of transcription activation on the total concentration of importin
(Imp)
in the system and
the free energy driving the transport cycles.

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 would be a multiscale m
odel 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
imila
r
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 computations
to a
n individual

research centre
and
then
to
integra
te 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.


Pharmacokinetics has already studied the human body as a multi
-
compartment problem. Recently it
has been proposed more mechanistic information should be incorporated into pharmacokinetics
(Lave, Chapman et al.
2009)
. We are therefore elaborating the silic
on 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. Ba
sed 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
function of glucose concentration above a certain threshold level, the latte
r 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 nor
mal 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 ins
ulin 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 predict
ed.
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 begin
ning
) 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 interp
lay 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
. Above we
d
iscussed h
ow
ever that the
number
3000!
derives

f
ro
m a failure to appreciate that biolog
ical organization
greatly reduce
s

complex
ity
.
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 thousands of mathematical models that each describe
a part

of the
human. Perhaps the only strategic decision we need to make now, is whether all those models wil
l
have resulted from a cottage industry such that it will be impossible to integrate them with each
other,
or all those models will have been developed in a common context and will merge into a
larger model. The latter possibility should ena
ble each resea
rcher working on her/his

part of the
human to appreciate the implications of her/his findings for the functioning of the human as a
whole.


Acknowledgements

We thank
the BBSRC
, EPSRC (
BBD0190791,
BBC0082191,
BBF0035281, BBF0035521,
BBF0035521, BBF0035361,
BBG5302251,
SySMO P 49

)
,

EU
-
FP7 (BioSim, NucSys, EC
-
MOAN)
and
others (
http://www.systembiology.net/support/

) for support.



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