Molecule as Computation Ehud Shapiro Weizmann Institute of Science Joint work with Aviv Regev and Bill Silverman In collaboration with Corrado Priami, Naama Barkai and Luca Cardelli

The talk has three parts: 1.Briefly introduce molecular biology 2.Computer-based consolidation of molecular biology 3.Our work on helping this happen

Part I Brief Introduction to Molecular Biology

4 Pentium II E. Coli

5  1 million macromolecules  1 million bytes of static genetic memory  1 million amino- acids per second  3 million transistors  1/4 million bytes of memory  80 million operations per second Comparison courtesy of Eric Winfree

6 Pentium II E. Coli

7 1 micron

8 Pentium II E. Coli 1 micron

9 Inside E. Coli

10 (1Mbyte) Inside E. Coli

11 Ribosomes in operation Ribosomes translate RNA to Proteins RNA Polymerase transcribes DNA to RNA

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

13 Ribosome operation

14 Ribosome operation

15 Ribosome operation

16 Ribosome operation

17 Seqeunces and String Transducers Ribosomes translate RNA to Proteins RNA Polymerase transcribes DNA to RNA

Molecular Biology in One Slide  Sequence: Sequence of DNA and Proteins

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Molecule as Computation Ehud Shapiro Weizmann Institute of Science Joint work with Aviv Regev and Bill Silverman In collaboration with Corrado Priami, Naama Barkai and Luca Cardelli

The talk has three parts: 1.Briefly introduce molecular biology 2.Computer-based consolidation of molecular biology 3.Our work on helping this happen

Part I Brief Introduction to Molecular Biology

24 Pentium II E. Coli

25 Pentium II E. Coli  1 million macromolecules  1 million bytes of static genetic memory  1 million amino- acids per second  3 million transistors  1/4 million bytes of memory  80 million operations per second Comparison courtesy of Eric Winfree

What about “The Rest” of biology: the function, activity and interaction of molecular systems in cells? ?

Part III An Abstraction for Molecular Systems

The “New Biology”  The cell as an information processing device  Cellular information processing and passing are carried out by networks of interacting molecules  Ultimate understanding of the cell requires an information processing model  Which?

29 “We have no real ‘algebra’ for describing regulatory circuits across different systems...” - T. F. Smith (TIG 14: , 1998) “The data are accumulating and the computers are humming, what we are lacking are the words, the grammar and the syntax of a new language…” - D. Bray (TIBS 22: , 1997)

30 Our Proposal: Molecule as Computational Process “Cellular Abstractions: Cells as Computation”, to appear in Nature, September 26th, 2002 A system of interacting molecular entities is described and modelled by a system of interacting computational entities.

31 Composition of two processes is a process, therefore :  Molecular ensembles as processes  Molecular networks as processes  Cells as processes (virtual cell)  Multi-cellular organisms as processes  Collections of organisms as processes

Towards “Molecule as Process” 1.Use the  - calculus process algebra as molecule description language

33 The  -calculus (Milner, Walker and Parrow 1989)  A program specifies a network of interacting processes  Processes are defined by their potential communication activities  Communication occurs on complementary channels, identified by names  Message content: Channel name

34  -calculus key constructs ParallelA | B ChoiceA ; B CommunicationX ! M or X ? Y Recursion, with state change P :- … P’…

35 Molecules as Processes MoleculeProcess Interaction capabilityChannel InteractionCommunication ModificationState change

36 Na + Cl <  Na+ + Cl- Na | Na | … | Na | Cl | Cl | … | Cl Na::= e ! [], Na_plus. Na_plus::= e ? [], Na. Cl::= e ? [], Cl_minus. Cl_minus::= e ! [], Cl. Processes, guarded communication, alternation between two states.

37 The RTK-MAPK pathway  16 molecular species  24 domains; 15 sub-domains  Four cellular compartments  Binding, dimerization, phosphorylation, de-phosphorylation, conformational changes, translocation  ~100 literature articles  250 lines of code ERK1 RAF GRB2 RTK SHC SOS RAS GAP PP2A MKK1 GF MP1 MKP1 IEG IEP JF

38 Molecular systems with  -calculus  Can express, qualitatively, the behavior of many complex molecular systems  Cannot express quantitative aspects

Towards “Molecule as Process” 1.Use the  - calculus process algebra as molecule description language 2.Provide a biochemistry-oriented stochastic extension (with Corrado Priami)

40 Stochastic  -Calculus (Priami, 1995, Regev, Priami, Shapiro, Silverman 2000 )  Every channel x attached with a base rate r  A global (external) clock is maintained  The clock is advanced and a communication is selected according to a race condition  Rate calculation and race condition adapted for chemical reactions:  Rate(A+B  C) = BaseRate *[A]*[B]  [A] = number of A’s willing to communicate with B’s.  [B] = number of B’s willing to communicate with A’s.

41 BioSPI implementation:  -calculus + Gillespie’s algorithm  Gillespie (1977): Accurate stochastic simulation of chemical reactions  The BioSPI system:  Compiles (full)  calculus  Runtime incorporates Gillespie’s algorithm

42 global(e1(100),e2(10)). Na::= e1 ! [], Na_plus. Na_plus::= e2 ? [], Na. Cl::= e1 ? [], Cl_minus. Cl_minus::= e2 ! [], Cl. Na + Cl <  Na+ + Cl-

Programming Experience with Stochastic Pi Calculus  Taught semesterial M.Sc. Course (available online) with lots of examples, exercises and final projects  Textbook examples from chemistry, organic chemistry, enzymatic reactions, metabolic pathways, signal-transduction pathways…

44 Circadian Clocks J. Dunlap, Science (1998)

45 The circadian clock machinery (Barkai and Leibler, Nature 2000) PRPR UTR R R R R_GENE R_RNA transcription translation degradation PAPA UTR A A A A_GENE A_RNA transcription translation degradation Differential rates: Very fast, fast and slow

46 The machinery in  -calculus: “A” molecules A_GENE::= PROMOTED_A + BASAL_A PROMOTED_A::= pA ? {e}.ACTIVATED_TRANSCRIPTION_A(e) BASAL_A::= bA ? [].( A_GENE | A_RNA) ACTIVATED_TRANSCRIPTION_A::=  1. (ACTIVATED_TRANSCRIPTION_A | A_RNA) + e ? []. A_GENE RNA_A::= TRANSLATION_A + DEGRADATION_mA TRANSLATION_A::= utrA ? []. (A_RNA | A_PROTEIN) DEGRADATION_mA::= degmA ? []. 0 A_PROTEIN::= (new e1,e2,e3) PROMOTION_A-R + BINDING_R + DEGRADATION_A PROMOTION_A-R ::= pA!{e2}.e2![]. A_PROTEIN + pR!{e3}.e3![]. A_PRTOEIN BINDING_R ::= rbs ! {e1}. BOUND_A_PRTOEIN BOUND_A_PROTEIN::= e1 ? [].A_PROTEIN + degpA ? [].e1 ![].0 DEGRADATION_A::= degpA ? [].0 A_Gene A_RNA A_protein

47 The machinery in  -calculus: “R” molecules R_GENE::= PROMOTED_R + BASAL_R PROMOTED_R::= pR ? {e}.ACTIVATED_TRANSCRIPTION_R(e) BASAL_R::= bR ? [].( R_GENE | R_RNA) ACTIVATED_TRANSCRIPTION_R::=  2. (ACTIVATED_TRANSCRIPTION_R | R_RNA) + e ? []. R_GENE RNA_R::= TRANSLATION_R + DEGRADATION_mR TRANSLATION_R::= utrR ? []. (R_RNA | R_PROTEIN) DEGRADATION_mR::= degmR ? []. 0 R_PROTEIN::= BINDING_A + DEGRADATION_R BINDING_R ::= rbs ? {e}. BOUND_R_PRTOEIN BOUND_R_PROTEIN::= e1 ? []. A_PROTEIN + degpR ? [].e1 ![].0 DEGRADATION_R::= degpR ? [].0 R_Gene R_RNA R_protein

48 BioSPI simulation Robust to random perturbations AR

49 The A hysteresis module  The entire population of A molecules (gene, RNA, and protein) behaves as one bi-stable module A R ON OFF Fast A R

50 Hysteresis module 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 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 ON OFF

51 Modular cell biology  Build two representations in the  -calculus  Implementation (how?): molecular level  Specification (what?): functional module level

52 The circadian specification R (gene, RNA, protein) processes are unchanged (modular;compositional) PRPR UTR R R R R_GENE R_RNA transcription translation degradation ONOFF Counter_A

53 BioSPI simulation Module, R protein and R RNAR (module vs. molecules)

54 Modular cell biology  Build two representations in the  -calculus  Implementation (how?): molecular level  Specification (what?): functional module level  Ascribing a function to a biomolecular system ~ equivalence between specification and implementation

55 Limitation of stochastic  - calculus: Lack of location information  Membranes: Cells and cellular compartments, “inside” and “outside”  Molecular proximity: The identity of complexes and single molecules  Limited solution: programming tricks

Towards “Molecule as Process” 1.Use the  - calculus process algebra as molecule description language 2.Provide a biochemistry-oriented stochastic extension (with Corrado Priami) 3.Provide an Ambient Calculus extension (with Luca Cardelli)

57 Mobile compartments CompartmentCompartment mobility Process mobility CellsCell movementTrans-membranal molecules (receptors, channels, transporters); Molecule entry and exit Organelles and vesicles Merging, budding, bursting Multi- molecular complexes Form and breakBind and unbind to molecular scaffolds

58 The ambient calculus (Cardelli and Gordon)  An ambient is a bounded place where computation happens AmbientProcesses

59 The ambient calculus (Cardelli and Gordon)  The ambient’s boundary restricts process interactions across it AmbientProcesses

60 The ambient calculus (Cardelli and Gordon)  Processes can move in and out of ambients AmbientProcesses Ambient are mobile processes, too !

61 Compartments as ambients Cells, vesicles, compartments ~ Ambients Cell Nucleus P Q R R cell [ P | Q | R | nuc [R] ]

62 Synchronized ambient movement enter/accept exit/expel merge+/merge- vesicle[merge- c. P|Q] | lysozome [merge+ c. R|S]  lysozome [P|Q|R|S] Lysozome vesicle Enter, exit, merge ~ Budding-in or -out, endo- or exo-cytosis merge enter exit merge

63 Molecules and complexes Merge, enter, exit (with private channels) ~ Complex formation and breakage, molecule re-localization Complex Mol1 PQ Mol2 RS PQRS Mol1 [P|merge+ c.Q] Mol2[merge- c. R|S] |  Complex [P|Q|R|S] enter/accept exit/expel merge+/merge-

64 Vesicle merging Vesicle Cell

65 Single substrate reactions: Enzyme and substrate as ambients Enzyme SXP enter exit

66 Bi-substrate reactions: Inter-ambient communication Enzyme S1XP1 enter exit S2YP2 enter exit s2s

Example: Multi-cellular system (hypothalamic body weight control system)

IRS-1 IR tub 1 st order ARC VMN PVN 2 nd order PVN PFA LHA Uterine function Efferent signal Fat cell mass Leptin expression Insulin expression Insulin resistanceGlucose utilization in adipocytes POMC*/CART* POMC CART  MSH expression cleavage NPY*/AgRP* NPY/AgRP expression Orexin PFA MCH LHA TRH*CRH*OXY PVN Thyroid axis Hypothalamic Pituitary Adrenal axis Energy expenditure Food intake Afferent signal Weight gain / Weight loss Controlled system 2  MSH MC4 Gs cAMP,PKA Gi NPY NPYR AgRP IRS-1tub IRLR JAK STAT LR JAK STAT Input

69 Conclusions  The most advanced tools for computer process description seem to be also the best tools for the description of biomolecular systems  This intellectual economy validates the decades-long study of concurrency in computer science  An essential foundation for the forthcoming “Virtual Cell Project”