Cellerator: A System for Simulating Biochemical Reaction Networks Bruce E Shapiro Jet Propulsion Laboratory California Institute of Technology

From: Kohn (1999) Molecular interaction map of the mammalian cell cycle control and DNA repair systems. Mol Biol Cell 10: Part of a Biochemical Network

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

Online network databases exist...

... but mathematical simulations of these networks are hopelessly naive...

Solver Output Canonical Form System of ODEs Input Canonical Form Biochemical Notation Concentrations vs. Time Activity (e.g., Cell Division) A B C

Caltech ERATO* Simulator Architecture A B C Application Text Transfer Protocol XML based protocol GUI and Modeling meta-language *Exploratory Research for Advanced Technology (Japan Science & Technology Corporation)

A simpler network for cell division Goldbeter, A (1991) A minimal cascade model for the mitotic oscillator involving cyclin and cdc2 kinase. PNAS 88: C=Cyclin: enzyme that gets things going M=MPF promoting factor. M>Threshold induces cell division X=Cyclin Protease: enzyme that breaks down C

Equations and prections of Goldbeter Mitotic Oscillator

Cellerator canonical form for input STN = {{reaction, rate-constants}, {reaction, rate-constants},…}; interpret[STN]; Simulation = predictTimeCourse[STN, options]; Reactions are input with a biochemical based notation Prints out ODES Returns tables of values as a function of time, with optional plots

Cellerator input/output for Goldbeter Mitotic Oscillator

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...

Translation of Biochemical Formula to ODE Law of Mass Action Two-way Reaction Complex reactions built from simple reactions is described by rate constant Concentrations is described by Similar ODE’s can be written for B and C

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 Rate constants Explicit Hidden Cellerator syntax for this set of reactions

Two-way catalytic reaction A second enzyme F catalyzes the reverse reaction Total of Six Elementary Reactions Write more compactly as Rate constants Explicit Hidden Cellerator syntax for this set of reactions

Canonical Forms for Translation: Chemical reactions Input Canonical Form for Chemical Reaction Output Canonical Form: Terms in an ODE

Cellerator Arrows: Law of Mass Action

Cellerator Arrows: Catalytic Reactions

Cellerator Arrows: Transcriptional Regulation

MAP Kinase Cascade INPUT OUTPUT

MAP Kinase in Scaffold

The combinatoric explosion

IP3 Calcium Receptor

IP3 Calcium Receptor (continued)

Repressilator

Object Oriented Implementation: “Domains” 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 –neighbors[g,n] returns a list of nodeDomains that are neighbors of node n n in graph g

Multicellular Organisms

Myogenesis: Collaboration with Laboratory Dr. Barbara Wold (Chris Hart), Caltech

Plant Growth: Collaboration with Laboratory Dr. Elliot Meyerowitz, Caltech

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 Hodgkin’s disease and non-Hodgkin’s lymphoma

JPL Collaborations using Cellerator Effects of microgravity during space flight on bone and muscle development (Caltech, JSC, and UCI) Development of childhood leukemias (Caltech, Children’s 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)

Acknowledgements Eric Mjolsness* - UC, Irivine Andre Levchenko* - Johns Hopkins University Barbara Wold - Caltech Elliot Meyerowitz - Caltech * Original Developers