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

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

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

4. Other examples of cellular decisions

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

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

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

8. Figure 6.12 The Biology of Cancer (© Garland Science 2007) Initiating Events: Complex Formation  “Effector” Activation

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

10. 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

11. 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

12. 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

13. Ras Structure to Model

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

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

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

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

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

19. 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

20. Standard Chemical Kinetics Species Reactions

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

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

23. 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,

24. Early events in Fc  RI signaling

25. 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

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

27. Combinatorial complexity

29. Addressing combinatorial complexity 354 species / 3680 reactions Standard approach – writing equations by hand – won’t work! New approach  Write model by describing interactions.  Automatically generate the equations. Standard approach – writing equations by hand – won’t work! New approach  Write model by describing interactions.  Automatically generate the equations.

30. 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.

31. 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)

32. 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

33. 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)

34. 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)

35. 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:

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

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

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

39. 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

40. 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

41. 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

42. 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

43. More complex rules Lyn Fc  RI 22  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 22 P SH2 p* L  Lyn Fc  RI 22 P SH2 P example

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

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

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

47. 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

48. 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.

49. Related Work StochSim Moleculizer Simmune  -calculus /  -factory little b Stochastic Simulation Compiler meredys …

50. 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

51. 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

52. 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

53. 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

54. 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 …

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

56. 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

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

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

59. 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

60. Large number of reaction events required for Syk activation

61. Small number of reaction events required for receptor phosphorylation

62. 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

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

64. 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)

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

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

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

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

69. 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)

70. 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.

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

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

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

74. Complexity in Chemotaxis Signaling Receptor aggregation makes simulation difficult

75. NFsim NFsim can be embedded into other higher level agents

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

77. 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.