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
                                                                                                 The Pathway Editor
                                                                                                Computational systems biology in
Igor Goryanin, Gosau, March, 2005                                                               Edinburgh

    Computational systems biology
                   Arthur C Clarke
                                                                                                                                                                         Cell and molecular biology

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

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

                     The way to understand biological                                                                                                                                               Modeling techniques

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

                                                                                             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
          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
                    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 ]

                                                                                               +                                                                                                                                                                                 200

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

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

                                                                     R + L ⇔ R⋅ L         L0       =   [L ] + [RL ]
                                                                                                                         [I ] + [RI ]
      ADP                                                                                                            =
    D-fructose 1,6-bisphosphate                                                        R + I ⇔ R⋅ I         I0
                                                                                                            R0       =   [R ] + [RL ] + [RI ]
                                                                                                                                                                                                         0      2,000   4,000
                                                                                                                                                                                                                                       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
 Model validation                                               Ordinary differential equation (ODE) with
    Examining to see if model makes ‘plausible’ predictions
 Simulation, visualisation, analysis, and biological              parameters
    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.
                                                                           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
                   ICL                  MS                                                 ICL                 MS
                           Glyoxylate                                                             Glyoxylate
                                                                                                                                                                                                                                                                                                                                                                                                    System properties of overexpression inhibition
                                                                          NAD                       NADH
                                                                                                                                                                                                                            Inhibition effect.                                                                                                        NAD             NADH

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

                                                                                                                                                                  Reaction rate (mM/min)

                                                                                                                                                                                                                                                                                                                                                                                                                Reaction rate (mM/min)
                                                                                                                                                                                                                                                                                                                                                      NAD             NADH
                                                                                                                                      NADPH                                                  12                                                                                                                                                                 4 (MD
                             Simplified kinetic model of (branched) TCA cycle (Scheme) operating                                                                                             10                                                                                                                                         Mal                                        OA                                                    12
                                                                                                                                                                                                                                                                                          v2                                                                  CoA                                       -
                             under anaerobic (or micro aerobic) conditions.. dependence of                                                                                                    8                                                                                                                                                                                                                                           8
                             glyoxylate (GlOx) consumption (v3) and glyoxylate production (v2)
                                                                                                                                                                                              6                                    unstable                                                                     7    3 (MS                                  6                                                                    6
                                                                                                                                                                                                                                                                                  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
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              GlOx (mM)
                                                                                                                                                                                                                                                                                                                    Suc                                                           ICit
                             malate synthase (MS, process 3).
                                                                          NAD                       NADH                                                                                                          B                                                                                                                               -

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

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

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

                                                                                  15%                                           NADP                         . A There are 3 steady states: “stable 1” (physiological stable                                                                                                                                                              5 (IDH
                                                                                                                                                             steady state), “unstable” (nonphysiological steady state)
                                                                                  35%                                     5 (IDH                   “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.
                                                                  NAD                 NADH                                                                                                                                                                                                                                Model of glyoxylate shunt was constructed to assess advantage of simultaneous
                                                                               4 (MD                                                                                                                                                                                                                            isocitrtae lyase (ICL) and malate synthase (MS) inhibition as a potential drug
%Overexperssion MS
                                                                                                         -                                  The pathway has non-linear                                                                                                                                                    targets for TB
                                                 3 (MS
                                                                                   6            1 (TCA flux)                                response.                                                                                                                                                                     The analysis shows that intuition does not work. The glyoxylate pathway is not
                                       -                       AcCoA
    7                        Suc
                                                    -           2 (ICL ICit
                                                                                                                                                                                                                                                                                                                          linear, but has non-linear response.
                                                        -      %Inhibition ICL
                                                                                                           5 (IDH
                                                                                                                                                                                                                                                                                                                          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
                                                                                                                                                                                                                                                                                                                                      NAD     NADH
                                                                                                                                                                                                                                                                                                                                                                              ICL                            MS

                                                                                                0.5                                                                                                                                                                                                                                         4 (MD

                                                                                                                                                                                                                                                                                                                              Mal                     OA
                                                                                                                                                                                                                                                                                                                                                                                     • A, C are non physiological                                                  90

                                                                                                                                                                                                                                                                           100                                                              CoA                 -
                                                                                                                                                                                                                                                                                                                  %Inhibition MS                                                                                                                                   80                              A

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

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

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

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

                                                                                                                                                                                                                                                                                                                                 -    %Inhibition            NADP                    • D is oscillatory (non                                                       20
                                                                                                                                                                                                                                                                                                                                                                                                                                                                   10                                        30% ICL inhibition only
                                                                                                                                                                                                                                                                                                                8                     ICL                 5 (IDH
                                                                                                                                                                                                                                                                                                                                                             NADPH                   physiological) region                                                          0
                                                                                                                                                                                                                                                                                                                                                                                                                                                                             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

                                                                                                                                                                                                                                                                                                                           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)
                                   10                                                                                                                                                                     2) GlOx and OA IDH (V5)
                                                                                                                       6 Synthesis from FA                                                                E.coli.
                                                        -                                                                                                                                                                  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
                                                                                                                                                                                                                           GlOx - glyoxylate, Icit -                                                                          Isocitrate Dehydrogenase (IDH) kinase/phosphotase in
                                                                                          GlOx                                                                                                                             isocitrate, OA -                                                                                   E.coli.
                                   7                                                                                                                       1
                                                                  -                   -
                                                                                                                              2 ICL
                                                                                                                                                                  CoA                                                                                                                                                      Prediction
                                                                                          -                     +                 -                                                                                                                                                                                           TB has an enzyme analogous to the IDH kinase/
                                            Suc                                                                                                       ICit
                                                                                  +                       5 IDH           +                                                                                                                                                                                                   phosphotase in E.coli.
                                                                                                                                                                                                                                                                                                                              This enzyme could be potential drug target, as well as
    Reaction rate (mM/min)

                                                 Flux_through_IDH (v5)
                                                                                                                                                                                                                           TB probably has an                                                                                 current targets: isocitrate lyase and malate synthase
                               8                                                                                                                                                                                           enzyme analogous to                                                                  "Applications of whole cell and large pathway mathematical models in the pharmaceutical industry"
                                                                                                                                                                                                                           the IDH kinase/
                               4                 Flux_through_ICL (v2)                                                                                                                                                                                                                                          Metabolic Engineering in the Post-Genomic Era, Editors B. Kholodenko and H. Westerhoff, Horizon
                               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.
   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