Computation π-calculus and biological modeling

Lecture 3Concurrency and Biology

Luca Bortolussi1 Alberto Policriti2

1Dipartimento di Matematica ed InformaticaUniversità degli studi di TriesteVia Valerio 12/a, 34100 Trieste.

luca@dmi.units.it2Dipartimento di Matematica ed Informatica

Università degli studi di UdineVia delle Scienze 206, 33100 Udine.

policriti@dimi.uniud.it

SISSA, January 2007

Computation π-calculus and biological modeling

Computation and Biology

Cells as computational machines?A. Regev and E. Shapiro. Cells as computation. Nature vol. 419 (2002)

[...] We believe that computer science can provide the much-needed

abstraction for biomolecular systems. Advanced computer science concepts

are being used to investigate the “molecule-as-computation” abstraction, in

which a system of interacting molecular entities is described and modeled by

a system of interacting computational entities. Abstract computer languages,

such as Petri Nets, State Charts and the Pi-calculus, were developed for the

specification and study of systems of interacting computations, yet are now

being used to represent biomolecular systems, including regulatory,

metabolic and signalling pathways, as well as multicellular processes such as

immune responses. [...]

Computation π-calculus and biological modeling

Outline

1 Computation

2 π-calculus and biological modeling

Computation π-calculus and biological modeling

Outline

1 Computation

2 π-calculus and biological modeling

Computation π-calculus and biological modeling

What is Computation?

Analyzing Computation

Yesterday (sequential)(formal) analysis of the (informal) notion of computability

no hardware

Today (concurrent)(formal) evolution of the (informal) notion of informationpassing

different kinds of hardware

Computation π-calculus and biological modeling

History

Church“An Unsolvable Problem of Elementary Number Theory”

Turing“On Computable Numbers, with an application to theEntscheidungsproblem”

MilnerTuring, Computing and Communication

Computation π-calculus and biological modeling

Old and New computing

Computation π-calculus and biological modeling

Computation vs. Interaction

Computation π-calculus and biological modeling

Outline

1 Computation

2 π-calculus and biological modeling

Computation π-calculus and biological modeling

π-calculus: Computing by Exchanging Information

π-calculusThere are two basic entities: agents and names

Agents interacts by exchanging names throughcommunication channels (message-based computation).

Computation resides in the evolution of the status of theagents, by means of message passing (behavioralcomputation).

That’s all!

R. Milner, J. Parrow, D. Walker: A Calculus of Mobile Processes, I & II, Inf. Comput. , vol. 100, 1992

Computation π-calculus and biological modeling

π-calculus: Graphical Syntax

A. Phillips, L. Cardelli: A Graphical Representation for the Stochastic π-calculus, BioCONCUR05 , 2005.

Computation π-calculus and biological modeling

π-calculus: Formal Syntax

π ::= x〈n〉 Output| x(m) Input, x 6= m

Σ ::= 0 Null| π.P + Σ Action

P, Q ::= νxP Restriction| P ‖ Q Parallel Composition| Σ Summation| !π.P Repication

Computation π-calculus and biological modeling

Example: basics

Agent P sends 5 to agent R along channel a.

P ≡ a〈5〉.P ′ and R ≡ a(x).R′

νa(a〈5〉.P ′ ‖ a(x).R′) ⇒ νa(P ′ ‖ R′[5/x ])

Computation π-calculus and biological modeling

Example: basics

Agent P sends 5 to agent R along channel a.

P ≡ a〈5〉.P ′ and R ≡ a(x).R′

νa(a〈5〉.P ′ ‖ a(x).R′) ⇒ νa(P ′ ‖ R′[5/x ])

Computation π-calculus and biological modeling

Example: basics

Agent P sends 5 to agent R along channel a.

P ≡ a〈5〉.P ′ and R ≡ a(x).R′

νa(a〈5〉.P ′ ‖ a(x).R′) ⇒ νa(P ′ ‖ R′[5/x ])

Computation π-calculus and biological modeling

Example: flow in a network

Agent P sends a message to R through Q.

P ≡ a〈n〉.P ′ Q ≡ a(y).b〈y〉.Q′ R ≡ b(x).R′

νb νa(a〈n〉.P′ ‖ a(y).b〈y〉.Q′ ‖ b(x).R′)⇓

νb νa(P′ ‖ b〈n〉.Q′ ‖ b(x).R′)⇓

νb νa(P′ ‖〉.Q′ ‖ R′[n/x ])

Example: dynamic reconfiguration of networks

Computation π-calculus and biological modeling

Example: flow in a network

Agent P sends a message to R through Q.

P ≡ a〈n〉.P ′ Q ≡ a(y).b〈y〉.Q′ R ≡ b(x).R′

νb νa(a〈n〉.P′ ‖ a(y).b〈y〉.Q′ ‖ b(x).R′)⇓

νb νa(P′ ‖ b〈n〉.Q′ ‖ b(x).R′)⇓

νb νa(P′ ‖〉.Q′ ‖ R′[n/x ])

Example: dynamic reconfiguration of networks

Computation π-calculus and biological modeling

Example: flow in a network

Agent P sends a message to R through Q.

P ≡ a〈n〉.P ′ Q ≡ a(y).b〈y〉.Q′ R ≡ b(x).R′

νb νa(a〈n〉.P′ ‖ a(y).b〈y〉.Q′ ‖ b(x).R′)⇓

νb νa(P′ ‖ b〈n〉.Q′ ‖ b(x).R′)⇓

νb νa(P′ ‖〉.Q′ ‖ R′[n/x ])

Example: dynamic reconfiguration of networks

Computation π-calculus and biological modeling

Example: flow in a network

Agent P sends a message to R through Q.

P ≡ a〈n〉.P ′ Q ≡ a(y).b〈y〉.Q′ R ≡ b(x).R′

νb νa(a〈n〉.P′ ‖ a(y).b〈y〉.Q′ ‖ b(x).R′)⇓

νb νa(P′ ‖ b〈n〉.Q′ ‖ b(x).R′)⇓

νb νa(P′ ‖〉.Q′ ‖ R′[n/x ])

Example: dynamic reconfiguration of networks

Computation π-calculus and biological modeling

Abstract Machines of Systems Biology (L. Cardelli)

Computation π-calculus and biological modeling

π-calculus for biology

Can we use π-calculus for (biological) simulation?

Molecule ProcessInteraction capability Channel

Interaction CommunicationModification State change

(of cellular components) (state transition systems)

A. Regev and E. Shapiro Cellular Abstractions: Cells as Computation. Nature , vol. 429 (2002)

Quantitative aspects must enter the picture: interaction “rates”assigned to channels.

C.Priami. The stochastic pi-calculus. The Computer Journal 38: 578-589, 1995.

Computation π-calculus and biological modeling

Example: Na + Cl

Simulate!

Computation π-calculus and biological modeling

Example: H + Cl

A. Phillips - Feb. 2005

Simulate!

Computation π-calculus and biological modeling

Example: a genetic network with feedback

Computation π-calculus and biological modeling

Example: π-encoding

Simulate!

Computation π-calculus and biological modeling

Implementing the Stochastic π-calculus

A Correct Abstract Machine for the Stochastic Pi-calculusA. Phillips and L. Cardelli

Abstract . This paper presents an abstract machine for avariant of the stochastic pi-calculus, in order to correctly modelthe stochastic simulation of biological processes. The abstractmachine is proved sound and complete with respect to thecalculus, and then used as the basis for implementing astochastic simulator. The correctness of the machine helpsensure that the simulator is correctly implemented, givinggreater confidence in the simulation results. A graphicalrepresentation for the pi-calculus is also presented, as apotential front-end to the simulator.

http://research.microsoft.com/~aphillip/spim/

Computation π-calculus and biological modeling

The logic of interaction

R. Milner. Turing, computing and communication, 1997.

My message is that we must develop this logical theory [thelogic of interaction]; partly because otherwise the interactivesystems which we build, or which just happen, will escape ourunderstanding and the consequences may be serious, andpartly because it is a new scientific challenge. Besides, it hasall the charm of inventing the science of navigation whilealready on board ship.

Other π examples

Outline

3 Other π examples

Other π examples

Example: modifying connectivity

Modeling a client accessing a printer through a server:

Return

Other π examples

Example: channels sent over channels

Agent S gives access to agent C to to printer P.

S ≡ b〈a〉.S′ C ≡ b(y).y〈m〉.0 P ≡ a(x).P ′

νb νa(b〈a〉.S′ ‖ b(y).y〈m〉.0 ‖ a(x).P′) ⇒ νb νa(S′ ‖ a〈m〉.0 ‖ a(x).P′)

Return

Other π examples

Example: channels sent over channels

Agent S gives access to agent C to to printer P.

S ≡ b〈a〉.S′ C ≡ b(y).y〈m〉.0 P ≡ a(x).P ′

νb νa(b〈a〉.S′ ‖ b(y).y〈m〉.0 ‖ a(x).P′) ⇒ νb νa(S′ ‖ a〈m〉.0 ‖ a(x).P′)

Return

Other π examples

Example: channels sent over channels

Agent S gives access to agent C to to printer P.

S ≡ b〈a〉.S′ C ≡ b(y).y〈m〉.0 P ≡ a(x).P ′

νb νa(b〈a〉.S′ ‖ b(y).y〈m〉.0 ‖ a(x).P′) ⇒ νb νa(S′ ‖ a〈m〉.0 ‖ a(x).P′)

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Other π examples

Example: Na + Cl - continued

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Other π examples

Example: Na + Cl - continued

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Other π examples

Example: Na + Cl - continued

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Other π examples

Example: Na + Cl - continued

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Other π examples

Example: Na + Cl - continued

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Other π examples

Example: H + Cl - continued

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Other π examples

Example: H + Cl - continued

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Other π examples

Example: H + Cl - continued

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Other π examples

Example: H + Cl - continued

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Other π examples

Example: H + Cl - continued

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Other π examples

Example: genetic network simulation

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Other π examples

Example: genetic network simulation

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Other π examples

Example: genetic network simulation

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Other π examples

Example: genetic network simulation

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Other π examples

Example: genetic network simulation

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Other π examples

Example: genetic network simulation

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Other π examples

Example: genetic network simulation

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Other π examples

Example: genetic network simulation

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Other π examples

Example: genetic network simulation

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Other π examples

Example: genetic network simulation

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Other π examples

Example: genetic network simulation

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Other π examples

Example: genetic network simulation

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Other π examples

Example: genetic network simulation

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Other π examples

Example: genetic network simulation

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