Abstract Processes Go Live: Representing Biomolecular Process Networks with Process Algebra Ehud Shapiro Joint work with Aviv Regev, Bill Silverman, Naama Barkai

2 The Cell

3

4 DNA, RNA, and Ribosomes creating Proteins Ribosomes translate RNA to Proteins RNA Polymerase transcribes DNA to RNA

5 Computationally: A stateless string transducer from the RNA alphabet of nucleic acids to the Protein alphabet of amino acids (= protein) Ribosomes in operation 25 nm

6 Biochemical Pathways

7 Types of biological knowledge Sequence: Sequence of the genome ( long sequences of 4 nucleic acids) and identity of its protein products ( long sequences of 22 amino acids) Structure: 3D structure of biomolecules Molecular interactions: Inter-molecular interaction capabilities Network behavior: Behavior of biomolecular networks

8 Computer representation and generation of biological knowledge

9 Formal representation languages for biological knowledge Sequence: Strings Structure: 3D modelling language Molecular interaction: ? Network behavior: ? Computer use is key driver of explosive growth in sequence and structure branches of biology

10 Our goal: Formal language for representing biomolecular networks

11 Formal language for representing biomolecular process networks Enables objective repository  Deposited knowledge can be easily shared and critically evaluated. Enables computer manipulation  Analysis and discovery Distant goal (10-25yrs): Full simulations of virtual cells and of virtual organisms, derived from such knowledge repositories

12 Our approach: Represent biomolecular networks as computational process networks

13 The molecule as a computational process Example: The enzyme ERK1 Ser/Thr kinase Detect: Binds proteins with Ser and Thr amino acids Modify: Adds phosphate group to these amino acids Be Modified: Can be bound and phosphorylated by other proteins and eznymes

14 The molecule as a computational process Binding MP1 molecules Regulatory T-loop: Change conformation Kinase site: Phosphorylate Ser/Thr residues (PXT/SP motifs) ATP binding site: Bind ATP, and use it for phsophorylation Binding to substrates COOH Nt lobe Catalytic core Ct lobe NH 2 StructureFunction p-Y p-T

15 The correspondence between molecular and computational processes

16 Our approach, specifically: Represent biomolecular networks as Stochastic  -Calculus programs

17 Process algebras (calculi) Research direction began in the late 70’s Guarded commands (Dijkstra), CSP, Occam (Hoare), CCS (Milner) Culminated in the  -Calculus in the late 80’s Except for Occam, no viable implementations (viewed as mathematical tools, not “real” programming languages)

18 The  -calculus A program specifies a network of interacting processes Processes are defined by their potential communication activities Communication occurs via channels, defined by names Communication content: Channel names (mobility, reconfiguration) (Milner, Walker and Parrow, 1989)

19 Syntax: Channels All communication events, input or output, occur on channels

20 Syntax: Processes Processes are composed of communication events and of other processes

21 The  -calculus: Reduction rules COMM: z replaces y in P Actions consumed; Alternative choices discarded Ready to send z on x ( … + x ! z. Q ) | (… + x ? y. P)  Q | P {z/y} Ready to receive y on x

22 Principles for mapping molecules to  - calculus Domain = Process SYSTEM ::= R_GENE | A_GENE | R | R | A |... A ::= ( new internal_channels) (BINDING_DOMAIN |CATALYTIC_DOMAIN) A Residue stretches = Global (free) channel names and co-names BINDING_DOMAIN (rbs )::= rbs ? {e}. BOUND_DOMAIN (e ) A R R_GENE

23 Principles for mapping molecules to  - calculus Molecular integrity (molecule) = Local channels as unique identifiers A ::= ( new e) (BINDING_DOMAIN |CATALYTIC_DOMAIN) Molecule binding = Exporting local channels rbs ! {e}. e ! { … } | rbs ? {cross_e}. cross_e ? {…} A A R

24 Principles for mapping molecules to  - calculus Molecular interaction and modification = Communication and change of channel names tyr ! p-tyr. CATALYTIC_DOMAIN | … + tyr ? tyr’. BINDING_DOMAIN  CATALYTIC_DOMAIN | BINDING_DOMAIN {p-tyr / tyr } Y Y

25 Quantitative aspects ~10 9 protein molecules within the cell Packed tightly in space Important proteins in only small amounts (100’s,1000’s) Stochastic effects on molecular interaction

26 Stochastic  -calculus (Priami, 1995) Every channel x or internal communication  attached with a delay parameter d Delay for each communication is chosen from an exponential distribution with d At each time step all enabled communications occur

27 A simple example of stochastic molecular processes sP R R R R_GENE Synthesis machinery Degradation machinery Fast synthesis of protein R from single gene R Slow degradation of each protein R Result: Steady state level of protein R

28 A simple example of stochastic molecular processes:  -calculus code TEST::= R_GENE | SYNTHESIS | DEGRADATION R_GENE::= spR(1,0) ? []. ( R_GENE | R ) R::= degR(100,0) ? []. 0 SYNTHESIS::= spR(1,0) ! []. SYNTHESIS DEGRADATION::= degpR(100,0) ! []. DEGRADATION sP R R R R_GENE Synthesis machinery Degradation machinery

29 A simple example of stochastic molecular processes: spiFCP simulation sP R R R R_GENE Synthesis machinery Degradation machinery

30 The spiFCP simulation system Based on the Logix system (Flat Concurrent Prolog) Supports synchronous interaction Appropriate insulated surface syntax (PiFCP) Compiler: Generate FCP computational processes from input  -calculus (in PiFCP syntax) code  Each channel to an FCP message stream  Each process to an FCP process

31 The spiFCP simulation system Regular version  Step-by-step execution and tracing, at process and channel level Stochastic version  A Scheduler mechanism ensures behavior  Monitoring time evolution of quantities of process instances

32 Circadian Clocks: Implementations J. Dunlap, Science (1998)

33 AR mA PAPA mR PRPR Hysteretic Oscillator A R fast Induced Repressed The circadian clock machinery (Barkai and Leibler, Nature 2000)

34 The circadian clock machinery (Barkai and Leibler, Nature 2000) PAPA PRPR UTR A UTR R RA AR A_GENE A_RNA R_GENE R_RNA transcription translation transcription translation degradation Figure 1

35 The circadian clock machinery: Stochastic aspects (Barkai and Leibler, Nature 2000) Appropriate behavior requires different rates Basal transcription A >>> R Promoted transcription A > R Degradation A > R degradation R binding to A (repression) >> A binding to pA or pR (promotion)

36 The machinery in  -calculus: “A” molecules A gene_a ::= PROMOTED_A + BASAL_A PROMOTED_A::= pA ? {e}. ACTIVATED_TRANSCRIPTION_A(e) BASAL_A::= bA ? []. ( A gene_a | A mRNA_a ) ACTIVATED_TRANSCRIPTION_A::=  1. (ACTIVATED_TRANSCRIPTION_A | A mRNA_a ) + e ? []. A gene_a A mRNA_a ::= TRANSLATION_A + DEGRADATION_mA TRANSLATION_A::= utrA ? []. (A mRNA_a | A prot_A ) DEGRADATION_mA::= degmA ? []. 0 A prot_A ::= (new e1,e2,e3) PROMOTION_A-R + BINDING_R + DEGRADATION_A PROMOTION_A-R ::= pA ! {e2}. e2 ! []. A prot_A + pR ! {e3}. e3 ! []. A prot_A BINDING_R ::= rbs ! {e1}. BOUND_A prot_A BOUND_A prot_A ::= e1 ! []. A prot_A + degpA ? []. e1 ! []. 0 DEGRADATION_A::= degpA ? []. 0

37 The machinery in  -calculus: “R” molecules R gene_r ::= PROMOTED_R + BASAL_R PROMOTED_R::= pR ? {e}. ACTIVATED_TRANSCRIPTION_R(e) BASAL_R::= bR ? []. ( R gene_r | R mRNA_r ) ACTIVATED_TRANSCRIPTION_R::=  2. (ACTIVATED_TRANSCRIPTION_R | R mRNA_r ) + e ? []. R gene_r R mRNA_r ::= TRANSLATION_R + DEGRADATION_mR TRANSLATION_R::= utrR ? []. (R mRNA_r | R prot_R ) DEGRADATION_mR::= degmR ? []. 0 R prot_R ::= BINDING_R + DEGRADATION_A BINDING_A ::= rbs ? {e}. BOUND_R prot_R BOUND_R prot_R ::= e1 ! []. R prot_R DEGRADATION_R::= degpR ? []. 0

38 spiFCP simulation Free A protein A mRNA Free R protein R mRNA A-R complex

39 Utilizing Concurrency Theory to assign function to biomolecular ensembles Semantic concept: Two processes are equivalent if can be exchanged within a context without changing system behavior Build two representations in the  -calculus  molecular level (implementation)  functional module level (specification) Show the equivalence of both representations  by computer simulation  by formal verification

40 The circadian clock specification: Hysteresis module (Barkai and Leibler, Nature 2000) A R ON OFF Fast

41 Hysteresis module “R” processes remain intact All “A” processes replaced by a single process, the H-MODULE H-MODULE::= (new e1, e2, e3) ON_H-MODULE(C A )

42 Hysteresis module (ON) ON_H-MODULE(C A )::= {C A T1}. (rbs ! {e1}. ON_DECREASE + e1 ! []. ON_H_MODULE + pR ! {e2}. (e2 ! [].0 | ON_H_MODULE) +  1. ON_INCREASE ) ON_INCREASE::= {C A ++}. ON_H-MODULE ON_DECREASE::= {C A --}. ON_H-MODULE

43 Hysteresis module (OFF) OFF_H-MODULE(C A )::= {C A >T2}. ON_H-MODULE(C A ) + {C A <=T2}. (rbs ! {e1}. OFF_DECREASE + e1 ! []. OFF_H_MODULE +  2. OFF_INCREASE ) OFF_INCREASE::= {C A ++}. OFF_H-MODULE OFF_DECREASE::= {C A --}. OFF_H-MODULE