Modeling Signal Transduction With Process Algebra Aviv Regev, Department of Cell Research and Immunology, Faculty of Life Sciences, Tel Aviv University, Tel Aviv, 69978, Israel. E-mail: aviv 5@netvision. net. il The complexity of ST networks The problem: Although molecular information on signal transduction (ST) systems is rapidly accumulating, it is difficult to analyze it, since it is diverse, disparate and fraught with molecular details. A formalism for ST Why ? From receptors on the cell membrane Our solution: A novel unifying view of ST as a mobile communication system that can be formally represented analyzed by process algebras, such as the p calculus. G protein receptors Cytokine receptors DNA damage, stress sensors RTK Gb Ga Gg SHCGRB 2 SOS RAB Rho. A GCK Ca+2 C-ABL RAC/Cdc 42 Multiple connections HPK PAK RAS Results: A model for ST that is mathematically welldefined and biologically visible, which represents both dynamic behavior of the system (biochemical signaling, feedback, cross-talk) and the structural molecular implementation (residues, domains) underlying it. We employ this approach to: 1. Model the RTK-MAPK cascade ST pathway 2. Perform simulated or formal mutational analysis 3. Formally study the homology of processes GAP PYK 2 • Unified view of disparate data • Experiment in silico (simulation, verification) • Comparative studies • Scalability to higher levels of organization Previous approaches ? PKA Modular at domain, component and pathway level RAF MOS TLP 2 MKK 1/2 MKK 4/7 ASK 1 MKK 3/6 PP 2 A ERK 1/2 Conclusions: A novel theory and formal approach to biological communication systems is established that allows us to model, simulate, analyze and compare ST pathways. The approach can be reified and applied to communication systems at higher levels of organization. MLK/DLK MEKK 1, 2, 3, 4 MAPKKK 5 Rsk, MAPKAP’s P 38 a/b/g/d JNK 1/2/3 TFs, cytoskeletal proteins Kinases, TFs How ? Inflammation, Apoptosis Mitosis, Meiosis, Differentiation, Development Model ST as a mobile communication system in a process algebra: Combine molecular structure with dynamics To intracellular (functional) end-points ST as a mobile communication system The p-calculus: highlights • • The functional domain = process A community of interacting processes Processes are defined by their potential communication activities Communication occurs via channels Communication content: change of channel names (mobility) The language x, y Communication step Input y on x The component residues = channels Ready to send z on x x<y> Output y on x (nx) RECEPTORi: : =EXTRACELLi|TRANSMEMBRANALi|INTRACELLi Before: Channel names x(y) SYSTEM: : =RECEPTOR 1|…|RECEPTORn|LIGAND 1|. . . |LIGANDm|… Ready to receive y on x …+ x<z>. P Create a new channel name x SERINE_PHOSPHORYLATION_SITEi(Ser 298 l): : = Ser 298 l. SERINE _PHOSPHORYLATION_SITEi(Ser 298 l) + mkk_kinasel(Ser 298 l’). SERINE _PHOSPHORYLATION_SITEi(Ser 298 l’) | x(y). Q +… Condition: same channel x processes 0 After: z replaces y in Q Empty process p. P P|Q parallel composition P p is either input or output p 1. P+p 2. Q mutual exclusive choice | Q { z/ y } +kinase<p-tyrosine>. ACTIVE_KINASE_DOMAIN|kinase(tyrosine). PHOSPHORYLATION_SITE+. . . … Communication is consumed Alternative choices are discarded Mutational analysis of the RTK-MAPK pathway Deletion of domains / residues Conversion of residues Insertion of domains Molecular interaction and modification = communication and change of channel names ® ACTIVE_KINASE_DOMAIN | PHOSPHORYLATION_SITE{p-tyrosine/tyrosine} Homology of processes Parameters: Remove processes / channels Change prefixes Add processes RAF wildtype: LIGAND: : = n (ligand) (RECEPTOR_BD | RECEPTOR_BD) Remove one RECEPTOR_BD process in the LIGAND Difference in domain structure (residues) Extra or missing domains or molecules Identical pathway in different organisms Dominant negative mutant MOS TLP 2 MEKK 1, 2, 3, 4 MAPKKK 5 MKK 1/2 MKK 4/7 ERK 1/2 GF GF Conclusions and prospects JNK 1/2/3 MLK/DLK ASK 1 MKK 3/6 mutant: LIGAND: : = n ligand (RECEPTOR_BD) P 38 a/b/g/d Our p-calculus formalism for ST supports: 3 Visible Molecular structure 3 Full dynamic behavior 3 Mutational analysis and simulated evolution 3 Combined homology measure for structural and dynamic comparison RTK Identical, additional, or missing interactions SHC GRB 2 SOS RAS Method: GAP Constitutive mutant RAF wildtype: SER 218(Ser 218): : = Ser 218. SER 218(Ser 218) + cross_enzyme(Ser 218’). SER 218(Ser 218’) Change Ser to p. Ser MKK 1/2 mutant: SER 218(p. Ser 218): : = p. SER 218(p. Ser 218) PP 2 A ERK 1/2 MKP 1/2/3 • The p-calculus model includes both structure and dynamics • Two models can be formally compared to determine the degree of mutual similarity of their behavior (bisimulation) • We determine a single homology measure of ST pathways based on such bisimilarity Further developments include: 3 A stochastic version using Sp-calculus 3 Computerized “lab” for mutational analysis 3 Standard numerical homology measure, combined with sequence homology 3 Scaling to additional molecular and non-molecular mobile biological systems
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