Lecture 2: Overview of Computer Simulation of Biological Pathways and Network Crosstalk Y.Z. Chen Department of Pharmacy National University of Singapore Tel: [phone]; Email: [e-mail] ; Web: http://bidd.nus.edu.sg

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Lecture 2 Overview of Computer Simulation of
Biological Pathways and Network Crosstalk Y.Z.
ChenDepartment of PharmacyNational University
of Singapore Tel [phone] Email
phacyz_at_nus.edu.sg Web http//bidd.nus.edu.sg

• Content
• Biological pathways and crosstalk
• Simulation model development
• Example Development of simulation model of RhoA
  crosstalk to EGFR-ERK pathways
• Future perspectives more pathways, more
  crosstalk, network level drug effects, signaling
  specificity, component sensitivity, TCM mechanism

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Generic Signaling Pathway
Signal Receptor (sensor) Transduction
Cascade Targets Response
Metabolic Enzyme
Cytoskeletal Protein
Gene Regulator
Altered Metabolism
Altered Gene Expression
Altered Cell Shape or Motility
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Integrated circuit of the cell
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EGFR-ERK/MAPK Signaling Pathways
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Crosstalk of Rho and Ras
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The Multiple Functions of Rho
Aznar Lacal Cancer Lett 165, 1 (2001) Hall
Biochem Society Transactions 33, 891 (2005)
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Actin Cytoskeleton Regulation Pathways
KEGG database
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Crosstalk between RhoA and EGFR-ERK/MAPK via
MEKK1 and PTEN

• RhoA promotes ERK activation by its interaction
  with Rho kinase, an effector of RhoA, which helps
  to delay EGF receptor endocytosis by
  phosphorylating endophilin A1 and to prevent Akt
  inhibition of Raf by activating phosphatase PTEN
  that hydrolyzes Akt second messenger PIP3.
• RhoA binds to MEKK1 and activate its kinase
  activity which subsequently phosphorylates and
  activates MEK1
• As activated MEK1 promotes ERK activation, it is
  of interest to examine to what extent RhoA can
  prolong ERK/MAPK activity via this MEKK1-mediated
  crosstalk between RhoA and EGFR-ERK signaling
  networks
• Gallagher et al. J Biol Chem 2004 279, 1872

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RhoA's crosstalk to EGFR-mediated Ras/MAPK
activation via MEKK1
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RhoA's crosstalk to EGFR-mediated Ras/MAPK
activation via PTEN
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Pathway Mathematical Model

• Biochemical kinetics based on mass action law
  (Guldberg and Waage 1864)

Fussenegger et al Nature Biotech 18, 768
(2000) Schoeberl et al Nature Biotech 20, 370
(2002) Sasagawa et al Nature Cell Biol 7, 365
(2005) Kiyatkin et al J Biol Chem 281, 19925
(2006)
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Pathway Mathematical Model

• Biochemical kinetics based on mass action law
  (Guldberg and Waage 1864)

Fussenegger et al Nature Biotech 18, 768
(2000) Schoeberl et al Nature Biotech 20, 370
(2002) Sasagawa et al Nature Cell Biol 7, 365
(2005) Kiyatkin et al J Biol Chem 281, 19925
(2006)
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Pathway Mathematical Model

• Michaelis-Menton Kinetics (Leonor Michaelis
  1875-1947 Maud Menton 1879-1960)
• The rate of the reaction is equal to the negative
  rate of decay of the substate as well as the rate
  of product formation
• Initial concentration of the substrate is much
  larger than the concentration of the enzyme
• Leading to

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Pathway Mathematical Model
Materi Wishart Drug Discov Today 12, 295 (2007)
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Pathway Mathematical Model
Alderidge et al. Nature Cell Biol 8, 1195
(2006)
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Pathway Mathematical Model
Alderidge et al. Nature Cell Biol 8, 1195
(2006)
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Pathway Mathematical Model
Alderidge et al. Nature Cell Biol 8, 1195
(2006)
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Solving the Pathway EquationsRunge-Kutta method

• Our task is to solve the differential equation
  dx/dt f(t, y), x(t0) x0
• Clearly, the most obvious scheme to solve the
  above equation is to replace the differentials by
  finite differences
• dt h
• dx x(th) - x(t)
• One can then apply the Euler method or
  first-order Runge-Kutta formula
• x(th) x(t) h f(t, x(t)) O(h2)
• The term first order refers to the fact that the
  equation is accurate to first order in the small
  step size h, thus the (local) truncation error is
  of order h2. The Euler method is not recommended
  for practical use, because it is less accurate in
  comparison to other methods and it is not very
  stable.

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Solving the Pathway EquationsRunge-Kutta method

• The accuracy of the approximation can be improved
  by evaluating the function f at two points, once
  at the starting point, and once at the midpoint.
  This lead to the second-order Runge-Kutta or
  midpoint method
• k1 h f(t, x(t))
• k2 h f(th/2, x(t)k1/2)
• x(t h) x(t) k2 O(h3)
• The most popular Runge-Kutta formula is the
  fourth-order one
• k1 h f(t, x(t))
• k2 h f(th/2, x(t)k1/2)
• k3 h f(th/2, x(t)k2/2)
• k4 h f(th, x(t)k3)
• x(t h) x(t) k1/6 k2/3 k3/3 k4/6
  O(h5)

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Solving the Pathway EquationsCash-Karp embedded
Runge-Kutta algorithm
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Mathematical Model of EGFR-ERK/MAPK Pathway

• Interaction equations and kinetic parameters

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Mathematical Model of EGFR-ERK/MAPK Pathway

• Interaction equations and kinetic parameters

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Mathematical Model of EGFR-ERK/MAPK Pathway

• Analysis of kinetic parameters

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Mathematical Model of EGFR-ERK/MAPK Pathway

• Analysis of kinetic parameters

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Mathematical Model of EGFR-ERK/MAPK Pathway

• Analysis of kinetic parameters

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Validation of RhoA EGFR-ERK/MAPK Crosstalk Model

• Time-dependent behavior of EGF activation of ERK
  in PC12 cells
• Our model predicted that ERK activation peaks at
  5 minutes and decays within 50 minutes, in good
  agreement with observation

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Validation of RhoA EGFR-ERK/MAPK Crosstalk Model

• EGF variation on duration of ERK activation in
  PC12 cells
• Our model predicted that further increase of EGF
  levels leads to sustained ERK activation, in good
  agreement with observation and previous
  simulation results

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Validation of RhoA EGFR-ERK/MAPK Crosstalk Model

• Time-dependent behavior of active RasGTP and
  their effects on ERK activation in PC12 cells
• Our model predicted that RasGTP peaks at 2.5
  minutes and quickly decays to its basal levels
  within 20 minutes, in good agreement with
  observation and previous simulation results

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Validation of RhoA EGFR-ERK/MAPK Crosstalk Model

• Time-dependent behavior of active RasGTP and
  their effects on ERK activation in PC12 cells
• Our model predicted that Ras over-expression
  prolongs ERK activation by delaying its decay
  rate without altering the time cause for reaching
  the peak of activation, in good agreement with
  observation and previous simulation results

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Validation of RhoA EGFR-ERK/MAPK Crosstalk Model

• Effect of scaffold protein MEKK1 on ERK
  activities
• Our model predicted that Increased MEKK1
  concentration helps to increase the level of
  active ERK, delay its peak time, and slightly
  prolong the duration of ERK activation, in good
  agreement with observation

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Validation of RhoA EGFR-ERK/MAPK Crosstalk Model

• Effects of Ras over-expression on RhoA and ERK
  activities
• Our model predicted that Ras over-expression
  increases the amount of active GTP-bound RhoA and
  prolongs the duration of its activation, leads to
  sustained ERK activation, in good agreement with
  observation and previous simulation results

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Effects of RhoA over-expression on ERK activation

• When Ras expression is at the normal level, RhoA
  over-expression was found to prolong ERK
  activation in a dose-dependent manner

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Effects of RhoA over-expression on ERK activation

• Effect of scaffold

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Effects of RhoA over-expression on ERK activation

• When Ras is over-expressed, RhoA over-expression
  significantly reduces the number of active ERK
  while further prolonging its activation

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Future Work Other Pathways
KEGG database
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Pathways and Disease

• Mapping normal and cancer cell signalling
  networks towards single-cell proteomics Nature
  Rev Cancer 6, 146, 2006

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P
Future Trend More crosstalk e.g. crosstalk of
EGFR-ERK pathway to others via RTK - PI3K AKT
pathways
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Future Trend Network level drug effects e.g.
drug combinations in RTK-ERK and RTK - PI3K AKT
pathways
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Annals Oncology 18, 421 (2007)
Drug metabolism pathway simulation published in
PloS Comput Biol 3, e55 (2007)
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Future Trend Knowledge learned and
information gained be used for studying TCM
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Project Assignment

• Project 1 Development of pathway simulation
  models
• You will be given a section of a biological
  pathway. You are required to try to generate a
  more detailed and precise pathway section, derive
  the corresponding pathway equations and
  parameters, and implement the equations in an ODE
  solver
• Project 2 Mechanism of biological crosstalks
• You will be given a few papers of crosstalks
  between different biological entities. You are
  required to probe the mechanism of each of these
  crosstalks based on their network relationships
  (generated by Pathway studio), expression
  profiles (generated by microarray analysis), and
  biochemical or regulatory profiles (from
  literature reports)