Modelling of Protein Networks

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					Modelling of Protein Networks


             Workshop
   Computational Life Sciences 2005
      Innsbruck – 2005-10-14

          Marc Breit, M.Sc.

  Institute for Biomedical Engineering
      UMIT - Hall in Tyrol - Austria
        Healthcare & Life Sciences

                 Early diagnosis of
                     diseases



Drugs without side effects
                                  Improved
                                  Healthcare


                                         Reliable
                                        diagnosis

     Tracing of
   drug treatments
                              Targeted therapeutic
                                   treatment
                                                                       www.gradschool.purdue.edu/CLS/


           Computational Life Sciences
•The development and                                                    •The research,
    application of data-                                         development or application
      analytical and                                               of computational tools
  theoretical methods,                                                and approaches for
mathematical modeling                                               expanding the use of
    and computational                                                 biological, medical,
simulation techniques to                                          behavioral or health data,
 the study of biological,                                        including those to acquire,
  behavioral, and social                                          store, organize, archive,
         systems.                                                analyze, or visualize such
                                                                             data.




                      •The development of quantitative, mechanistic
                      based models of the whole cell, collections
                          of cells or large pieces of the cellular
                           machinery, where the objective is an
                         integrated picture that compliments the
                        reductionist viewpoint of molecular biology.
   Research fields                             Data Mining



       Metabolomics

                                    Genomics




                         Bioinformatics



                                               Proteomics
Evolution              Systems biology


  Phylogeny

Biological diversity
                                                            www.systemsbiology.org


         Systems biology

Introduction                            History

•   Systematic analysis of biological   •   Systems-theory in biology
    systems
                                             – 1948: Wiener N – Cybernetics
                                             – 1970: Metabolic Control Theory
•   Integrating the „–omics“
     –   Genomics
     –   Transcriptomics                •   Former problems
     –   Proteomics                          – Appropriate data & experiments
     –   Metabolomics                        – Quantitative biology

•   Understanding of systems            •   Cell biology
     –   Structure                           – 1838: Cell Theory
     –   Dynamics – Analysis & models        – 2000: Human genome project
     –   Control-Methods
     –   Design-Methods
                                        •   Improvements
•   Multidisciplinarity                      – Accuracy of measuring
                                               methods
                                             – Quantitative experiments
         Clinical question
         Inflammatory diseases – Morbus Crohn
•   Tumor Necrosis Factor α (TNFα)

•   Plays an important role in various
    diseases
     – Cancer, sepsis, diabetes
     – Osteoporosis, Multiple sclerosis
     – Morbus Crohn

•   Drugs
     – e.g. Infliximab

•   Mode of operation
     – Patient-dependent
     – Non-specific impact

•   Problems
     –   Blocking of the receptor
     –   Various complications
     –   Immune-suppression
     –   Generation of antibodies
      Tumor Necrosis Factor α (TNFα)

Idea                             Biological Cartoon
• Examination of the TNFα        • Abstract representation
   signalling cascade            • Compartments
                                 • Interactions
TNFα signalling cascade
• Apoptosis, Cell growth
• Proteins controlled through
  signalling cascade
• Activation of gene-
  transcription
• Generation of proteins
• Controls level of expression

Objective
• Specific inhibition             Cho KH et al. Simulation. 2003 Dec;79(12):726-39.
              Modelling and simulation of biological
              systems

                                                        • Literature, Databases


                                                        • Cartoons
                                                              –   abstract
                                                              –   Proteins
                                                              –   Interactions
                                                              –   not: time

     Dhar P. pawan_sysbio_lect11.pdf.



                                                        • Problem                  Biocarta: EGF MAPK Kaskade
                                                              – Reaction equations
                                                              – Estimation
                                                                   • Kinetic parameters
                                                                   • Initial conditions

Wolkenhauer O. Briefings in Bioinformatics. 2001;2:258-270.
     Modelling and simulation of biological
     systems

                               • Graphical representation




• Simulation
                                 Schoeberl B et al. Nat Biotechnol. 2002 Apr;20(4):370-5.


                               • Mathematical model
• Hypothesis and predictions     dm1/dt = -k1*m1*m2 + k2*m3
         Model for the kinetics of enzyme-catalysed
         reactions

• Michaelis Menten 1913                                    E

                                                               k2
       k 2
        
   ES      ES k 3 E  P
                                                                  ES        P
                                                                      k3
        k1                                                 S   k1




• Set of differential equations
   dE(t )
            k1  E (t )  S (t )  (k2  k3 )  ES(t )
    dt
   dS (t )
            k1  E (t )  S (t )  k2  ES(t )
    dt
   dES(t )
            k1  E (t )  S (t )  (k2  k3 )  ES(t )
     dt
   dP(t )
           k3  ES(t )
    dt


• Fundamental assumptions
    – Slowly time-varying system
    – Steady-state
                  State of Research

         Analysis und Modelling                •   2001 Astaghiri
         • Examination of structure and             –   MAPK
            dynamics of cellular function           –   Matlab ode23s
[Kitano;
Tyson; •    Necessity of mathematical models   •   2002 Schoeberl
Astaghiri]                                          –   MAPK EGF
         Examples for signalling cascades           –   94 Variable
                                                    –   95 Parameter
         • 1996 Huang
              –   MAPK
                                               •   2003 Cho
              –   18 rate equations                 –   RKIP ERK
                                                    –   ODEs
         •   1997 Ferrell
              –   MAPK
                                               •   2003 Cho
              –   Mathematica                       –   TNFα NF-κB
                                                    –   18 ODEs
         •   1999 Bhalla
                                                    –   Initial Values
              –   Networks
              –   Michaelis-Menten
                                               •   2003 Cho
                                                    –   TNFα NF-κB
         •   2001 Schoeberl
                                                    –   31 ODEs
              –   TNFα
                                                    –   MPSA
              –   280 ODEs
              –   110 Parameter
                                               •   2004 Babu
                                                    –   EGFR
                                                    –   29 molecules
        The TNFα - NF-κB signalling cascade
        A quantitative mathematical model

• Graphical representation                           • Set of differential equations




 Cho KH et al. Simulation. 2003 Dec;79(12):726-39.
     The TNFα - NF-κB signalling cascade
     A quantitative mathematical model

• Kinetic parameters   • Initial concentrations
               Ordinary differential equations

• In the model                                                          • Corresponds with the form
     dm1/dt = -k1*m1*m2 + k2*m3                                           M (t )m'  f (t , m, k )


• Variation of kinetic                                                  • Matlab Routine sens_ind
  parameters
                                                                         [t,m,dmdk] =
 k   (i )
             k   i ei  k   i (0,  , 1,..., 0) , i  1,..., p
                                             
                                                     t
                                                                         sens_ind(odefile,tspan,m0,options,k)
                                             i


 dm m(i )  m                                                                 – 3-dimensional array
                                                                             – gradient
 dki   i
                                                                              – time-dependent
 k2                                                                       m         t:
                      αi

                       k(1)

                                      k1                                                     k
                                  E

Parametric sensitivity analysis       k2


                                           ES        P
                                                k3
                                  S   k1



           m4


                         m4




           m4


                         k1




           m4


                         k3
      Matlab Software tool
                                                       sensitivityGui.m


• Mathematical model                                   sensitivityMain.m

    – Dataimport                       kinetics.m                          importData.m



• Sensitivity analysis
                                     parameters.m      sensAnalysis.m


    – Calculation of concentration   initialValues.m   paramVariation.m    saveResults.m

    – Calculation of gradient
    – Analysis of the 3-
      dimensional array

• Parameter-Variation
    – Calculation of the solutions
      depending from the actual
      value

• Saving the results
    – Matlab Workspace .mat-file
              Validation through sensitivity analysis

•   Parameters
     –   with highest values of gradients
     –   involved with various components,
     –   supposed to be the most sensitives

•   Identified parameters
     –   TNFα/TNFR1 association (k1),
     –   TNFα/TNFR1/TRADD association
         (k3),
     –   TNFα/TNFR1/TRADD/RIP1
         association (k5),
     –   TNFα/TNFR1/TRADD/TRAF2
         association (k7),
     –   RIP1/Caspase-8 association (k17),
     –   NF-κB→c-IAP (k19),
     –   TNFα/TNFR1/TRADD/FADD
         association (k20)
     –   caspase-8/Effector association (k25)
     –   k1, k3, k5, k7, k17, k19, k20, k25


•   Parameter with effect on small
    number of components
     –   RIP1/Caspase-8→RIP1c+RIP1n
         (k18)
       Variation of parameter k7
• TRAF2 and
  TNFα/TNFR1/TRADD
  complex (k7)
• Nominal value
  – 0.185 μM-1s-1
• Range
  – from 0.037 μM-1s-1
  – to 0.925 μM-1s-1,
  – Number of values 50
       Variation of parameter k20
• FADD and
  TNFα/TNFR1/TRADD
  complex (k20)
• Nominal value
  – 0.185 μM-1s-1
• Range
  – from 0.037 μM-1s-1
  – to 0.925 μM-1s-1,
  – Number of values 50
        Variation of parameter k18
• RIP1/Caspase-8 →
  RIP1c+RIP1n (k18)
• Nominal value
   – 0.37 s-1
• Range
   – from 0.074 s-1
   – to 1.85 s-1
   – Number of values 50
        Validation of the approach of sensitivity
        analysis
                                                     k1
• Literature
   – Known sensitive kinetic
                                                     k3
     parameters
                                   k20                    k7
   – k1, k3, k7, k17, k19, k20
                                                     k5


                                         k17

• With our research
   – Eight parameters identified
   – k1, k3, k5, k7, k17, k19,
     k20, k25
                                   k25



• Primary key positions

• Parameter k18                                k19

   – Border area of the model
      Development of a framework

Software platform              Further activities

• Systematic analysis          • Tool for visualisation of
                                 dynamical behaviour
• Examination of any pathway
  possible                     • Enhancement of the TNFα
    – Databases, eg DOQCS        signalling cascade
                                   – Application and analysis
• Pathway-Interactions
                               • Development of a database
Extensions                       for biological knowledge
                                   – Interfacing and connection

• Examination of initial
  concentrations
      Acknowledgement

•   Christian Baumgartner
•   Bernhard Pfeifer
•   Mahesh Visvanathan
•   Bernhard Tilg
•   Robert Modre




            Institute for Biomedical Engineering
                UMIT - Hall in Tyrol - Austria
Thank you for your attention

				
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