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An Introduction to Modeling Biochemical Signal Transduction Keynote Lecture 2012 CMACS Winter Workshop Lehman College

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Cell as Information Processor http://en.wikipedia.org/wiki/Cell_signaling

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The cellular brain http://www.biochemweb.org/fenteany/research/cell_migration/neutrophil.html Original film from David Rogers (Vanderbuilt University)

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Other examples of cellular decisions

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Evolution in understanding of cell signaling Linear pathwayBranched pathway / complexes EGF EGFR GRB2 SOS RAS RAF MAPK MYC Combinatorial complexityBlack box

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Organization of Signaling Networks Yarden & Sliwkowski, Nature Rev. Mol. Cell Biol. 02: 127-137 (2001).

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Figure 5.15 The Biology of Cancer ( Garland Science 2007) Initiating Events: Receptor Aggregation

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Figure 6.12 The Biology of Cancer ( Garland Science 2007) Initiating Events: Complex Formation Effector Activation

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Figure 6.9 The Biology of Cancer ( Garland Science 2007) Complexity of Membrane Complexes

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Figure 6.9 The Biology of Cancer ( Garland Science 2007) The curse of complexity Number of States 3 3 3 4 3 4 3 3,888 7,560,216 Monomers Dimers

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Figure 6.9 The Biology of Cancer ( Garland Science 2007) The curse of complexity Number of States 3 3 3 4 3 4 3 3,888 7,560,216 Monomers Dimers Number of States 3 4 3 6 6 3 5 19,440 188,966,520

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Ras at Multiple Scales The Biology of Cancer ( Garland Science 2007) >20% human tumors carry Ras point mutations. >90% in pancreatic cancer. >20% human tumors carry Ras point mutations. >90% in pancreatic cancer. Transformed

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Ras Structure to Model

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Ras pi3kral gn sosraf ~GDP ~GTP Sos Ras GAP Ras GAP Raf PI3K Ral

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Figure 6.10a The Biology of Cancer ( Garland Science 2007) Modularity of Signaling Proteins

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Figure 6.10b The Biology of Cancer ( Garland Science 2007) Diversity of Modular Elements

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Syk Lyn Fc RI Transmembrane Adaptors Wiring of Modules Produces More Complexity

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AIM: Model the biochemical machinery by which cells process information (and respond to it). RepresentationSimulation Modeling cell signaling

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Goals Knowledge representation Predictive understanding Different stimulation conditions Protein expression levels Manipulation of protein modules Site-specific inhibitors Mechanistic insights Why do signal proteins contain so many diverse elements? How do feedback loops affect signal processing? Drug development New targets Combination therapies

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Standard Chemical Kinetics Species Reactions

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Reaction Network Model of Signaling Kholodenko et al., J. Biol. Chem. 274, 30169 (1999) EGF EGFR GRB2 SOS EGF EGFR GRB2 SOS SHC

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Reaction Network Model of Signaling Kholodenko et al., J. Biol. Chem. 274, 30169 (1999) 22 species 25 reactions

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General formulation of chemical kinetics (continuum limit) x is vector of species concentrations S is the stoichiometry matrix, S ij = number of molecules of species i consumed by reaction j. v is the reaction flux vector, v j is the rate of reaction j. For an elementary reaction,

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Early events in Fc RI signaling

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Syk activation model Mol. Immunol.,2002 J. Immunol., 2003 Key variables ligand properties protein expression levels multiple Lyn-FceRI interactions transphosphorylation Key variables ligand properties protein expression levels multiple Lyn-FceRI interactions transphosphorylation

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Standard modeling protocol 1. Identify components and interactions. 2. Determine concentrations and rate constants 3. Write and solve model equations.

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Combinatorial complexity

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Addressing combinatorial complexity 354 species / 3680 reactions Standard approach writing equations by hand wont work! New approach Write model by describing interactions. Automatically generate the equations. Standard approach writing equations by hand wont work! New approach Write model by describing interactions. Automatically generate the equations.

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Rule-based modeling protocol 1. Define components as structured objects and interactions as rules. 2. Determine concentrations and rate constants 3. Generate and simulate the model.

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Rule-based modeling protocol 1. Define components as structured objects and interactions as rules. 2. Determine concentrations and rate constants 3. Generate and simulate the model. Objects and rules B IO N ET G EN Reaction Network ODE Solver Stochastic Simulator (Gillespie) Output http://bionetgen.org Faeder, Blinov, and Hlavacek, Methods Mol. Biol. (2009)

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Defining Molecules IgE(a,a) FceRI(a,b~U~P,g2~U~P) Lyn(U,SH2) Syk(tSH2,lY~U~P,aY~U~P) B IO N ET G EN Language

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Defining Interaction Rules IgE(a,a)+ FceRI(a) IgE(a,a!1).FceRI(a!1) B IO N ET G EN Language binding and dissociation Transphosphorylation component state change Lyn(U!1).FceRI(b!1).FceRI(b~U)-> \ Lyn(U!1).FceRI(b!1).FceRI(b~P)

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BioNetGen A b Y1 B A(b,Y1) B(a) Molecules are structured objects (hierarchical graphs) a BNGL: Faeder et al., In Methods in Molecular Biology: Systems Biology, Ed. I.V. Maly (2009)

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BioNetGen A b Y1 B A(b,Y1) B(a) Molecules are structured objects (hierarchical graphs) Rules define interactions (graph rewriting rules) A B + k +1 k -1 A B A(b) + B(a) A(b!1).B(a!1) kp1,km1 a bond between two components a Faeder et al., In Methods in Molecular Biology: Systems Biology, Ed. I.V. Maly (2009) BNGL:

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Rules generate events A B + k +1 A B Rule1 A b Y1 B a + Reaction1 12

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Rules generate events A B + k +1 A B Rule1 A b Y1 B a + Reaction1 12

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Rules generate events A B + k +1 A B Rule1 A b Y1 B a A b B a k +1 + Reaction1 123

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Rules may specify contextual requirements A b Y1 Rule2 p1p1 A b Y1 P context not changed by rule must be bound A b Y1 B a 3 Reaction2 A(b!+,Y1~U) -> A(b!+,Y1~P) p1 BNGL: context

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Rules may specify contextual requirements A b Y1 Rule2 p1p1 A b Y1 P context not changed by rule must be bound A b Y1 B a 3 Reaction2 A(b!+,Y1~U) -> A(b!+,Y1~P) p1 BNGL: context

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Rules may specify contextual requirements A b Y1 Rule2 p1p1 A b Y1 P context not changed by rule must be bound A b Y1 B a 3 Reaction2 p1p1 A b Y1 B a 4 P A(b!+,Y1~U) -> A(b!+,Y1~P) p1 BNGL: context

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Rules may generate multiple events Second reaction generated by Rule 1 A B + k +1 A B Rule1 A b Y1 B a A b B a k +1 + Reaction3 425 P absence of context P

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More complex rules Lyn Fc RI 22 P SH2 p* L P P Lyn Fc RI Transphosphorylation of 2 by SH2-bound Lyn Generates 36 reactions (dimer model) with same rate constant Lyn Fc RI 22 P SH2 p* L Lyn Fc RI 22 P SH2 P example

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Automatic Network Generation Seed Species (4) Reaction Rules (19) New Reactions & Species FcRI Model Network FcRI (IgE) 2 Lyn Syk Network

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Automatic Network Generation Seed Species (4) Reaction Rules (19) FcRI Model FcRI (IgE) 2 Lyn Syk 354 Species 3680 Reactions 354 Species 3680 Reactions

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Automatic Network Generation Seed Species (4) Reaction Rules (19) FcRI Model FcRI (IgE) 2 Lyn Syk 354 Species 3680 Reactions 354 Species 3680 Reactions

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AIM: Model the biochemical machinery by which cells process information (and respond to it). RepresentationSimulation Modeling cell signaling B IO N ET G EN Language kappa etc. ODE, PDE Stochastic Simulation Algorithm Kinetic Monte Carlo Brownian dynamics

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Advantages of Formal Representations Precise interaction-based language for biochemistry knowledge representation Concise representation of combinatorially complex systems Documentation and model readability Modularity and reusability Accuracy and rigor Hlavacek et al. (2006) Sci. STKE, 2006, re6.

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Related Work StochSim Moleculizer Simmune -calculus / -factory little b Stochastic Simulation Compiler meredys

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Systems Modeled IgE Receptor (Fc RI) Faeder et al. J. Immunol. (2003) Goldstein et al. Nat. Rev. Immunol. (2004) Torigoe et al., J. Immunol. (2007) Nag et al., Biophys. J., (2009) [LAT] Receptor aggregation Yang et al., Phys. Rev. E (2008) Growth Factor Receptors, other Blinov et al. Biosyst. (2006) [EGFR] Barua et al. Biophys. J. (2006) [Shp2] Barua et al. J. Biol. Chem. (2008) [PI3K] Barua et al., PLoS Comp. Biol (2009). [GH / SH2B] Carbon Fate Maps Mu et al., Bioinformatics (2007) TCR ( Lipniacki, J. Theor. Biol., 2008 ) TLR4 (An & Faeder, Math. Biosci., 2009) See http://bionetgen.org for complete list.http://bionetgen.org

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T. W. McKeithan, PNAS, 92, 5042-5046 (1995). k p k on k off k k k k B 2 B 1 B N-1 B N B 0 k p k p k p k p... receptor + ligand Modifications Ligand dissociation rate can determine ligand efficacy Kinetic Proofreading in Receptor Signaling Signal See also Chapter 9 of Alon, Introduction to Systems Biology

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T. W. McKeithan, PNAS, 92, 5042-5046 (1995). k p k on k off k k k k B 2 B 1 B N-1 B N B 0 k p k p k p k p... receptor + ligand Modifications Ligand dissociation rate can determine ligand efficacy Kinetic Proofreading in Receptor Signaling Signal

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T. W. McKeithan, PNAS, 92, 5042-5046 (1995). k p k on k off k k k k B 2 B 1 B N-1 B N B 0 k p k p k p k p... receptor + ligand Modifications Ligand dissociation rate can determine ligand efficacy Kinetic Proofreading in Receptor Signaling Signal Enhancement ratio

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Kinetic Proofreading in Sports Malcolm Gladwell, Outliers. Many sports (and education systems) have cutoff dates to establish eligibility Having a birthdate close to the cutoff date confers a small but tangible advantage 12345NYear Probability to make the cut (p I /p IV ) N

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Kinetic Proofreading in Sports Malcolm Gladwell, Outliers. Born Jan-Mar Born Oct-Dec 2.5-4 fold!

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T. W. McKeithan, PNAS, 92, 5042-5046 (1995). k p k on k off k k k k B 2 B 1 B N-1 B N B 0 k p k p k p k p... receptor + ligand Modifications Ligand dissociation rate can determine ligand efficacy Kinetic Proofreading in Receptor Signaling Signal Output state of Syk activation model

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Evidence for Kinetic Proofreading in Mast Cell Responses to Two Ligands Torigoe, Inman & Metzger, Science, 281, 568 (1998) Input

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Evidence for Kinetic Proofreading in Mast Cell Responses to Two Ligands Torigoe, Inman & Metzger, Science, 281, 568 (1998) Input Outputs

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Evidence for Kinetic Proofreading in Mast Cell Responses to Two Ligands Ligand with shorter dwell time gives low Syk phosphorylation Torigoe, Inman & Metzger, Science, 281, 568 (1998) Input Outputs

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Large number of reaction events required for Syk activation

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Small number of reaction events required for receptor phosphorylation

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Rapid fall in efficiency of Syk phosphorylation Goldstein et al. (2004) Nat. Rev. Immunol. 4, 445-456. Kinetic proofreading of Syk activation but not receptor phosphorylation Ligand dissociation rate (off rate) Fraction of aggregated receptors

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Bimodal dose-response curves B. Goldstein, in Theoretical Immunology, Part One, Ed. A. S. Perelson

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Bimodal dose-response curves B. Goldstein, in Theoretical Immunology, Part One, Ed. A. S. Perelson Syk expression is highly variable in human basophils (5,000-60,000 copies per cell) MacGlashan (2007) Syk expression is highly variable in human basophils (5,000-60,000 copies per cell) MacGlashan (2007)

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Dose-response curves for reversibly binding ligand high Syk low Syk

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The multivalent scaffold effect *Syk and scaffold concentrations are equal *

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Bimodal response occurs when Syk concentration below maximal number of aggregated receptors R agg = Syk tot

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Limits of the network generation approach Extending model to include Lyn regulation results in >20,000 states.

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Limits of the network generation approach Extending model to include Lyn regulation results in >20,000 states. LAT may form large oligomers under physiological conditions. Houtman et al., Nat. Struct. Mol. Biol. (2006) Nag et al., Biophys. J. (2009)

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Limits of the network generation approach Extending model to include Lyn regulation results in >20,000 states. LAT may form large oligomers under physiological conditions. Many more components are still missing.

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Network-free: A kinetic Monte Carlo approach to simulating rule-based models Michael Sneddon Yang et al., Phys. Rev E (2008)

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NFsim: General implementation of Network-free algorithm Sneddon, Faeder, and Emonet, in preparation.

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Cell and Population Level Behavior Molecular Level Interactions Goal: Multiscale Agent-based, simulation of biological systems, building up from the stochastic molecular level

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Complexity in Chemotaxis Signaling Receptor aggregation makes simulation difficult

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NFsim NFsim can be embedded into other higher level agents

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Digital Chemotaxis Experiments 200 E. coli Cells 2mm from Capillary 10mM Attractant 40 min simulation

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Conclusions Kinetics and stoichiometry of complex formation can have a profound effect in signal transduction. Modeling these effects requires a new approach to modeling that addresses the issue of combinatorial complexity. Rule-based (or interaction-based) modeling is such an approach. Network-free simulation is a powerful technique that circumvents combinatorial complexity.