# Computational systems biology

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```					   1st FEBS Advanced Lecture Course                                                                           Agenda
The modelling process
Continuation procedure and
Computational Systems Biology.                                                                  bifurcation analysis
Applications in pharmaceutical                                                                  Multiple target intervention
analysis for M. tuberculosis
industry
The Pathway Editor
Computational systems biology in
Igor Goryanin, Gosau, March, 2005                                                               Edinburgh

Computational systems biology
Organism
Arthur C Clarke
Cell and molecular biology

“Any sufficiently advanced                                                                    Genome                        Metabolic                           Cell
technology is indistinguishable from                                                         Annotation                    Biochemistry                      Physiology

magic”
Network
Is Computational Systems                                                                                         Reconstruction                                                        Quantitative
Analytical
Biology/Modelling                                                                                                                                                                        Methods
Microbial
An “Esoteric knowledge” ?                                                                                           Model

The way to understand biological                                                                                                                                               Modeling techniques

systems?                                                                                                               New
Or a tool to solve practical problems?                                                                            Independent
Experimental
Information

Covert et al., Trends Biochem Sci. 2001

Static Models                                                                   Quantitative Kinetic Models
Only connectivity (topology) of the interactions                                      Kinetic models - time dependency incorporated
Visualised as connection or interaction graph
Kinetic behaviour (rate laws) added to static model
Types
Metabolic (Metabolomics, metabonomics)                                           Kinetic constants by fitting to experimental data
Genetic Regulation (Microarrays)                                                 Mathematical model
Protein-Protein Interactions (Proteomics)                                           Time variation of all concentrations and fluxes can be simulated
Model analyses possible: sensitivity, linear stability, bifurcation,
D-glucose                                                                          and asymptotic analysis
R1       HPr-P                                              Repressor
2.7.1.69
HPr R 12                                        β α
σ β ’α
x y                          Mathematical Model                                                                                Numerical Simulation
D-glucose 6-phosphate
Ligand Receptor
R 2                                                     Activator
[R ]′    = −k1[R ][L ] + k2[RL ] − k3[ R ][ I ] + k4 [RI ]                       250
Ligand-Receptor Complex

Inhibitor            [RL ]′     = k1[R ][L ] − k2[RL ]

+
5.3.1.9                                                                                                                                                                                 200

OPERON                        [RI ]′   = k3[R ][ I ] − k4 [RI ]
D-fructose 6-phosphate
150

R 19        R3                                                                                              [L ]′    = −k1[R ][L ] + k2[RL ]
ATP                                                                              Kinetic Model        [I ]′    =   −k3[R ][I ] + k4 [RI ]
100

50
2.7.1.11                                                             R + L ⇔ R⋅ L         L0       =   [L ] + [RL ]
[I ] + [RI ]
0
D-fructose 1,6-bisphosphate                                                        R + I ⇔ R⋅ I         I0
R0       =   [R ] + [RL ] + [RI ]
0      2,000   4,000
Time
6,000   8,000   10,000

Metabolic network                 Protein interaction network   Genetic network        Static model
Bioinformatics, 1999, Vol 15, 749-758,
The modelling process                                        Some general information
Defining the biological scope for the model
Creating the model                                               Dynamical system
Static model development
Entities and Interactions between them
Data acquisition, mining, curation, and storage                           dx
Semi-Quantitative model development
≡ x' = f ( x, α )
Collection of all available data about kinetics and                       dt
time dependencies.                                             x(t): vector of time- dependent state variables
Kinetic model development                                        α: vector of parameters
Fitting experimental data to determine kinetic
parameters
Model validation                                               Ordinary differential equation (ODE) with
Examining to see if model makes ‘plausible’ predictions
Simulation, visualisation, analysis, and biological              parameters
interpretations
Examine results looking for new biology
Planning of future experiments
To enhance model and verify predictions
To replace some in vivo and in vitro experiments

Numerical continuation of equilibria                          Numerical continuation of equilibria
Equilibrium solution:                                            Stable equilibria can be found by
x (t ) ≡ x 0     f ( x0 ,α ) = 0       , i.e.                   integration
 ∂ f1         ∂ f1 
Jacobian matrix                 ∂x     ...
∂x n 
 1                           Unstable equilibria
fx =  .      ...    . 
 ∂f n   ...
∂f n              Can be computed by numerical
 ∂x1

∂x n 
             continuation
is stable if all nearby orbits converge to x0
If all eigenvalues of f x ( x0 ) have negative
real part.

Numerical continuation                                      Numerical continuation of equilbria
In generic one parameter problems,
eigenvalues on the imaginary axis
appear in two ways:
Simple zero eigenvalue
Corresponds to a fold (LP) bifurcation
Conjugate pair of simple pure
imaginary eigenvalues
Corresponds to a Hopf (H) bifurcation
Parameter continuation. Bifurcations                                Numerical continuation
Allows to compute branches of objects, e.g.
branches of equilibria, if a parameter varies.
Allows to detect bifurcation points and
analyze them.
Allows to start new branches and branches
of new objects, switch parameters etc.
Allows to continue bifurcation points if a
second parameter is freed.
Software
Matcont (Matlab)
Auto (general package)
DBsolve 7 (As a Systems Biology workbench)

TB statistics                                                      Target analysis for M. tuberculosis
There are 40 million cases
of TB each year,                                                    Pulmonary tuberculosis is a chronic infection of the lungs,
leading in many cases to progressive tissue destruction and
i.e. 20,000 new cases of                                         death.
active TB every day                                              The causative organism is Mycobacterium tuberculosis. The
initial stages of infection are thought to involve invasion,
About one third of the                                              followed by release of large numbers of extra-cellular
human population –                                                  bacteria and tissue destruction. Reactivation of the disease
is often many years after the initial TB infection.
roughly 2 billion people - are                                   Current regimens for the treatment of pulmonary TB
infected with TB, often in a                                     involve extended therapy with multiple antibiotics
latent form                                                      Despite this, multiply drug resistant strains (MDR-TB) are
increasingly common. New agents are required which are
2 million people die each                                           active against MDR-TB
year from TB,                                                       The greatest improvements to current therapy and
commercial attractiveness would be realized by drugs which
i.e. between 5,000 and 6,000                                     are active against persisting organisms
people a day .

The glyoxylate pathway                                               Why to model glyoxylate pathway?
The glyoxylate pathway (also called the glyoxylate bypass            ICL genes have been shown to be up-regulated,
or shunt) comprises the activities of isocitrate lyase (ICL)         suggesting that ICL activity may be part of a wider
and malate synthase (MS).
strategy for intracellular survival by pathogenic
It acts as an alternative route for isocitrate metabolism in         microorganisms.
the tricarboxylic acid (TCA) cycle, bypassing the steps in
which two molecules of carbon are lost as CO2.                       Both enzymes ICL and MS could be potential targets
This enables organisms possessing this pathway to utilize            for chemotherapeutic agents aimed at persisting
acetyl-coA as the only input into the TCA cycle and hence            organisms.
permits growth on fatty acids and lipids, which are                  Small molecule inhibitors with adequate
degraded to acetyl-coA by beta-oxidation.                            pharmacokinetics are required to fully validate this
The glyoxylate pathway is present in bacteria and plants             hypothesis and there may be broader spectrum
but has not been demonstrated in higher mammals.                     applications for such novel inhibitors.
Gene disruption of icl in M. tuberculosis results in a strain,       It would be advantageous to construct a
which is unable to cause a persistent, chronic infection
mathematical model of the glyoxylate pathway. The
analysis of simultaneous in silico inhibitions could be
used to assess potential targets for drug
intervention.
ICL                  MS                                                 ICL                 MS
Glyoxylate                                                             Glyoxylate
System properties of overexpression inhibition

Reaction rate (mM/min)
Reaction rate (mM/min)
4 (MD 1.1.1.37)
Mal
4 (MD 1.1.1.37)
OA                                                                                                                                                                                                             Mal                                        OA                                                             A
CoA                                       -
12
7                                                                                             CoA                                                -                                                       12
10                                                                                    v2               7    3 (MS 4.1.3.2)                                  6                   1 (TCA flux)                                    10                                                                                    v2
8                                                                                                                                                                                                                               8
7 3 (MS 4.1.3.2)                                                                                  6                                                                                                                                                                                                                     -                               AcCoA                                                                         6
unstable
1 (TCA flux)                                                              6
unstable              stable 1                                v3                                       GlOx                                                                                              4                                                       stable 1                         v3
4
0                                                                                                                    -                   2 (ICL 4.1.3.1)                                                               2       0
-                                                                                                                                                                  2                                                                                                         Suc                                                           ICit
AcCoA
GlOx                                                                                                                                              0                            1
GlOx (mM)
2                                3
-
GlOx (mM)
2                         3
8                                                                                                                                                                                                                                                                                                               8
-                                                                 5 (IDH 1.1.1.42)                                                                                                                                                                                                                                            5 (IDH 1.1.1.42)
Suc                                                                                                                ICit
A
D

Reaction rate (mM/min)

Reaction rate (mM/min)
-
Simplified kinetic model of (branched) TCA cycle (Scheme) operating                                                                                             10                                                                                                                                         Mal                                        OA                                                    12
v2                                                                  CoA                                       -
10
v2
under anaerobic (or micro aerobic) conditions.. dependence of                                                                                                    8                                                                                                                                                                                                                                           8
glyoxylate (GlOx) consumption (v3) and glyoxylate production (v2)
6                                    unstable                                                                     7    3 (MS 4.1.3.2)                                  6                                                                    6
4
v3                                                                                                     1 (TCA flux)                                     4
stable 0                                                               v3
rates on GlOx concentration at different activities of isocitrate                                                                                                2                            stable 0                                                                                         -                               AcCoA                                                                         2
0                        1                           2                                3                                   GlOx                                                                                                  0                                  1                             2                        3
dehydrogenase (IDH, process 5), isocitrate lyase (ICL, process 2),                                                                                                                                                     GlOx (mM)                                                                           -                   2 (ICL 4.1.3.1)
GlOx (mM)
Suc                                                           ICit
malate synthase (MS, process 3).

Reaction rate (mM/min)
5 (IDH 1.1.1.42)
4 (MD 1.1.1.37)                                                                                                                                                                                                                                                                                                                                        F

Reaction rate (mM/min)
Mal                                                                                                                                              10
9
CoA                                               -                                                                 8
7
v2                                                                         4 (MD 1.1.1.37)
6
5                                                                                                                             Mal                                        OA                                                    11
10
6
4
3                                                                                                                                                   CoA                                       -                                 9                                                   stable 1                         v2
3 (MS 4.1.3.2)                                                                                         1 (TCA flux)                                                                     2                  stable 0                                             v3                                                                                                                                                      8
7
1                                                                                                     7    3 (MS 4.1.3.2)                                  6                   1 (TCA flux)                                     6
0                            1
GlOx (mM)
2                                    3                                                                                                                             5       unstable
-                                              AcCoA                                                                                                                                                                                                                                     -                               AcCoA                                                                         4
GlOx                                                                                                                                                                                                                                                                            GlOx                                                                                              3
2           stable 0                                                               v3
1

Suc
-
2 (ICL 4.1.3.1)               ICit
C                                                                                                 Suc
-                   2 (ICL 4.1.3.1)       ICit
0                                      1
GlOx (mM)
2                         3

-
-
15%                                           NADP                         . A There are 3 steady states: “stable 1” (physiological stable                                                                                                                                                              5 (IDH 1.1.1.42)
35%                                     5 (IDH 1.1.1.42)                   “stable 0” (non physiological zero stable state). B Inhibition
of ICL by 15% results in loss of stability of physiological                                                                                            (Fig. D) The same type of behavior, i.e. loss of stability of physiological steady state and its
“stable 1” steady state. and 35% C Inhibition of ICL by 35%                                                                                            disappearance, can be resulted from overexpression of MS by 300%).
results in disappearance                                                                                                                               (Fig. F) However, physiological steady state can be restored if we inhibited IDH by 50%

Cellular modelling. Hypothesis testing.
Simultaneous ICL/MS inhibition.
4 (MD 1.1.1.37)                                                                                                                                                                                                                            isocitrtae lyase (ICL) and malate synthase (MS) inhibition as a potential drug
Mal
CoA
OA
-                                  The pathway has non-linear                                                                                                                                                    targets for TB
3 (MS 4.1.3.2)
6            1 (TCA flux)                                response.                                                                                                                                                                     The analysis shows that intuition does not work. The glyoxylate pathway is not
-                       AcCoA
GlOx
7                        Suc
-           2 (ICL 4.1.3.1) ICit
linear, but has non-linear response.
-      %Inhibition ICL
8
5 (IDH 1.1.1.42)
Effective inhibition is in the range of >50%ICL and >70%MS, otherwise the
pathway will be still in physiological state
The pathway normal functioning after ICL inhibition (~30%) could be
restored by simultaneous MS inhibition(50%)
1.0                                                                                                                                                                                                                          No intuitive complex                                                                                                                                  Traditional linear
behaviour                                                                                                                                         understanding
ICL                            MS
Glyoxylate
IDH/TCA

0.5                                                                                                                                                                                                                                         4 (MD 1.1.1.37)
L
IC

100
Mal                     OA
• A, C are non physiological                                                  90
of

100                                                              CoA                 -
%Inhibition MS                                                                                                                                   80                              A
ion

% inhibition of MS
80                                                                                                                                                                                                70
7                          6
60                                                                                            1 (TCA flux)                regions
ibit

0.0                                                                                                                                               40                                                                    3 (MS 4.1.3.2)                                                                                                                         60                30% ICL and 50% MS                                          D
inh

80                                                                                                                                                                                                   -              AcCoA                                                                                                                        50
% inh 60
ibition                40                                                                                        20                                                                             GlOx
• B is physiological region                                                   40                         B                                    C
%

20                                                                                                                                           -
of     MS                                                                              0     0                                                                               Suc                 2 (ICL 4.1.3.1)
ICit                                                                                                           30

-    %Inhibition            NADP                    • D is oscillatory (non                                                       20
10                                        30% ICL inhibition only
8                     ICL                 5 (IDH 1.1.1.42)
0           10     20     30    40 50       60 70          80       90   100
% inhibition of ICL

Switch of fluxes between TCA and glyoxylate pathways under condition of simultaneous

Target identification. Success?
decrease in glucose influx and increase in fatty acid influx. IDH activation included

14
Pyr
11
PEP
12
TrPh
13
Glc
TB metabolic model was created
CoA                                                                                E.coli based with TB add-ons                                                                                        two whole cell models E.coli and TB were compared.
9 Synthesis from Glucose                                                                              1) Mal and Suc to ICL (V2)
Analysis
-
10                                                                                                                                                                     2) GlOx and OA IDH (V5)
6 Synthesis from FA                                                                E.coli.
AcCoA
-                                                                                                                                                                  Glc - glucose, TrPh -                                                                               switch of fluxes between TCA and glyoxylate pathways
triosophosphates, Pyr -                                                                            under condition of simultaneous decrease in glucose
4                                                                                                                                            pyruvate, PEP - phosphoenol
Mal                                                                                                       OA
pyruvate, Mal - malonate,
influx and increase in fatty acid influx is provided by
CoA
3
GlOx - glyoxylate, Icit -                                                                          Isocitrate Dehydrogenase (IDH) kinase/phosphotase in
GlOx                                                                                                                             isocitrate, OA -                                                                                   E.coli.
7                                                                                                                       1
oxaloacetate.
-                   -
2 ICL
CoA                                                                                                                                                      Prediction
-                     +                 -                                                                                                                                                                                           TB has an enzyme analogous to the IDH kinase/
Suc                                                                                                       ICit
8
+                       5 IDH           +                                                                                                                                                                                                   phosphotase in E.coli.
15
18
This enzyme could be potential drug target, as well as
Reaction rate (mM/min)

16
14
Flux_through_IDH (v5)
TB probably has an                                                                                 current targets: isocitrate lyase and malate synthase
12
10
8                                                                                                                                                                                           enzyme analogous to                                                                  "Applications of whole cell and large pathway mathematical models in the pharmaceutical industry"
the IDH kinase/
6
4                 Flux_through_ICL (v2)                                                                                                                                                                                                                                          Metabolic Engineering in the Post-Genomic Era, Editors B. Kholodenko and H. Westerhoff, Horizon
2
0                                                                                                                                                                                           phosphotase in E.coli                                                                Bioscience, UK, 2003
0.1                  0.2           0.3         0.4          0.5         0.6                0.7            0.8          0.9                                                  1
% decrease of Glc and increase of FA influx
Why modelling?                                              The Pathway Editor
Knowledge management. Build a high resolution              Visual annotation of metabolic, genetic regulatory, signal
understanding.                                             transduction and other intracellular networks.
integrate and explain data even large scale              Visual annotation of multicellular, tissue and organism level
quantitative study of biological processes as whole      networks for disease knowledge reconstruction and modelling.
systems
identify knowledge gaps                                     a convenient way to represent networks visually and
Hypothesis generation.                                        populate them in a consistent way
design cell for bioengineering problems                        checking biological names
predict the cellular functions                                 kinetic information
different therapeutic, environmental, physiological         generic/specific relationship
and genetic conditions.                                     data quality and confidence
predict intervention consequences                              arbitrary object’s
easy data exchange
Hypothesis testing
pathways stored locally
provide cheaper and faster methods complementary to
in vitro, ex vivo and in vivo experiments or animal            pathways stored in database
models                                                         for enterprise sharing and merging
Rational Design                                               export/import pathways
pathways, cells, biomarkers, organisms                         pathways and model databases
picture formats, including WEB compatible

Editable maps                   Edinburgh Centre for Bioinformatics

More then 75 scientists from
The University of Edinburgh. College of Science & Engineering
The University of Edinburgh. College of Medicine
MRC Human Genetics Unit
Roslin Institute
Heriot-Watt University
National e-Science Centre
In collaboration with Scottish Bioinformatics Research Network (SBRN)

Computational Systems Biology. Edinburgh                     Acknowledgements
Systems Biology modelling support
collaborative projects with academia, pharma and        GlaxoSmithKline
other industries
Systems Biology computational infrastructure                  Discovery Research,
in collaboration with industry (IBM BlueGene, etc)
Research & Development IT
Systems Biology knowledge base
software, methods, and algorithms                        Moscow State University, Russia
databases on pathways, cellular networks, models
Systems Biology teaching                                      Dr Oleg Demin, group
MSc course, PhD programme, seminar series                EMP project, US

Picture of Edinburgh

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