Cellerator: A System for Simulating Biochemical Reaction Networks

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Cellerator A System for Simulating Biochemical
Reaction Networks

• Bruce E Shapiro

Jet Propulsion Laboratory California Institute of
Technology
bshapiro_at_jpl.nasa.gov
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Part of a Biochemical Network
From Kohn (1999) Molecular interaction map of
the mammalian cell cycle control and DNA repair
systems. Mol Biol Cell 102703-2734
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Biochemical Networks Are...

• Complex
• Mutually interacting
• Large
• Number of reactions grows exponentially with
  number of states
• Best understood pictorially
• Best described quantitatively by a large system
  of differential equations (ODEs)

Need to translate pictures to ODEs
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Online network databases exist ...
http//www.genome.ad.jp/kegg/
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... but mathematical simulations of these
networks are hopelessly naive...
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A
B
C
Input Canonical Form Biochemical Notation
Output Canonical Form System of ODEs
Activity (e.g., Cell Division)
Solver
Concentrations vs. Time
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Caltech ERATO Simulator Architecture
A
GUI and Modeling meta-language
B
C
Text Transfer Protocol
XML based protocol
Application
Application
Application
Application
Exploratory Research for Advanced Technology
(Japan Science Technology Corporation)
http//www.systems-biology.org
Application
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A simpler network for cell division
CCyclin enzyme that gets things going MMPF
promoting factor. MgtThreshold induces cell
division XCyclin Protease enzyme that breaks
down C
Goldbeter, A (1991) A minimal cascade model for
the mitotic oscillator involving cyclin and cdc2
kinase. PNAS 889107-9111
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Equations and prections of Goldbeter Mitotic
Oscillator
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Cellerator canonical form for input
Reactions are input with a biochemical based
notation
Prints out ODES
STN reaction, rate-constants, reaction,
rate-constants, interpretSTN Simulation
predictTimeCourseSTN, options
Returns tables of values as a function of time,
with optional plots
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Cellerator input/output for Goldbeter Mitotic
Oscillator
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(No Transcript)
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The Basis of Cellerator Chemical Reactions

• Simple
• Cooperative
• Conversion
• Creation, Degradation
• Enzymatic
• Reversible Enzymatic

• Transcription (Gene ? RNA)
• Post-transcriptional Processing
• Translation (RNA ? Protein)
• Diffusion
• and more ...

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Translation of Biochemical Formula to ODE
rate constant
Concentrations

• Law of Mass Action
• Two-way Reaction
• Complex reactions built from simple reactions

is described by
Similar ODEs can be written for B and C
is described by
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Enzyme Kinetic (Catalytic) Reaction

• Enzyme E catalyzes the production of product P
  from substrate (source) S
• Write more compactly as

3 Reactions written two different ways
Explicit
Hidden
Cellerator syntax for this set of reactions
Rate constants
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Two-way catalytic reaction

• A second enzyme F catalyzes the reverse reaction
• Total of Six Elementary Reactions
• Write more compactly as

Explicit
Rate constants
Hidden
Cellerator syntax for this set of reactions
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Canonical Forms for Translation Chemical
reactions

• Input Canonical Form for Chemical Reaction
• Output Canonical Form Terms in an ODE

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Cellerator Arrows Law of Mass Action
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Cellerator Arrows Catalytic Reactions
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Cellerator Arrows Transcriptional Regulation
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INPUT
OUTPUT
MAP Kinase Cascade
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MAP Kinase in Scaffold
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The combinatoric explosion
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(No Transcript)
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IP3 Calcium Receptor
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IP3 Calcium Receptor (continued)
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Repressilator
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Repressilator
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Object Oriented ImplementationDomains and
Fields

• Domain object
• Field function that maps domains to R
• Field of Domains maps domain elements to domains
• Example
• graphDomain represents tissue
• node Domains cells
• neighborsg,n returns a list of nodeDomains that
  are neighbors of node n n in graph g

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Multicellular Organisms
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Myogenesis Collaboration with Laboratory Dr.
Barbara Wold (Chris Hart), Caltech
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Plant Growth Collaboration with Laboratory Dr.
Elliot Meyerowitz, Caltech
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Secondary Leukemia Collaboration with City of
Hope National Medical Center (NASA/BSRP)
Focus Pathogenesis of myelodysplasia acute
myeloid leukemia following high-dose
chemo/radiotherapy and autologous peripheral
blood stem cell transplantation for treatment of
Hodgkins disease and non-Hodgkins lymphoma
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JPL Collaborations using Cellerator

• Effects of microgravity during space flight on
  bone and muscle development (Caltech, JSC, and
  UCI)
• Development of childhood leukemias (Caltech,
  Childrens Hospital of LA, and UC, Irvine)
• Description of core signal transduction units
  (Johns Hopikins)
• Improving algorithms for micro-array data
  analysis (Caltech, Harvey Mudd)
• Systems Biology Workbench (Caltech, JST/Erato)

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Acknowledgements

• Eric Mjolsness - UC, Irivine
• Andre Levchenko - Johns Hopkins University
• Barbara Wold - Caltech
• Elliot Meyerowitz - Caltech

Original Developers