M ODELING IN S CCP O REGONATOR M ODELING BIOCHEMICAL REACTIONS k 1 - - PowerPoint PPT Presentation

▶
m odeling in s ccp
SMART_READER_LITE
LIVE PREVIEW

M ODELING IN S CCP O REGONATOR M ODELING BIOCHEMICAL REACTIONS k 1 - - PowerPoint PPT Presentation

Jan 13, 2024 251 likes •531 views

S CCP MIM S MIM S IN S CCP C ONSTRAINT - BASED SIMULATION OF BIOLOGICAL SYSTEMS DESCRIBED BY M OLECULAR I NTERACTION M APS Luca Bortolussi 1 Simone Fonda 4 Alberto Policriti 2 , 3 1 Dipartimento di Matematica ed Informatica Universit degli studi

slide-1
SLIDE 1

SCCP

MIMS MIMS IN SCCP

CONSTRAINT-BASED SIMULATION OF

BIOLOGICAL SYSTEMS DESCRIBED BY

MOLECULAR INTERACTION MAPS

Luca Bortolussi1 Simone Fonda4 Alberto Policriti2,3

1Dipartimento di Matematica ed Informatica

Università degli studi di Trieste luca@dmi.units.it

2Dipartimento di Matematica ed Informatica

Università degli studi di Udine

3Istituto di Genomica Applicata

Parco Scientifico Tecnologico, Udine.

4Dipartimento di Informatica

Università degli studi di Pisa.

BIBM 2007, Silicon Valley, 3th November 2007

slide-2
SLIDE 2

SCCP

MIMS MIMS IN SCCP

VIEWS OF COMPUTATIONAL SYSTEMS BIOLOGY

slide-3
SLIDE 3

SCCP

MIMS MIMS IN SCCP

OUTLINE

1 MIDDLE LEVEL LANGUAGE: STOCHASTIC CONCURRENT

CONSTRAINT PROGRAMMING

2 HIGHER LEVEL LANGUAGE: MOLECULAR INTERACTION

MAPS

3 ENCODING MIMS IN SCCP

slide-4
SLIDE 4

SCCP

MIMS MIMS IN SCCP

OUTLINE

1 MIDDLE LEVEL LANGUAGE: STOCHASTIC CONCURRENT

CONSTRAINT PROGRAMMING

2 HIGHER LEVEL LANGUAGE: MOLECULAR INTERACTION

MAPS

3 ENCODING MIMS IN SCCP

slide-5
SLIDE 5

SCCP

MIMS MIMS IN SCCP

STOCHASTIC CONCURRENT CONSTRAINT PROGRAMMING

CCP = CONSTRAINTS + AGENTS Constraints are formulae over an interpreted first order language (i.e. X = 10, Y > X − 3); they can be added to a "container", the constraint store, but can never be removed. Agents can perform two basic operations on this store (asynchronously): tell or ask a constraint. rw(X):- ask(X > 0). tell(X ′ = X − 1).rw(X) + tell(X ′ = X + 1).rw(X)

STOCHASTIC CCP

Each ask and tell instruction has a rate (function) attached to it: λ : C − → R+. The semantics of the language is given in terms of a Continuous Time Markov Chain.

  • L. Bortolussi, Stochastic Concurrent Constraint Programming, QAPL, 2006
slide-6
SLIDE 6

SCCP

MIMS MIMS IN SCCP

STOCHASTIC CONCURRENT CONSTRAINT PROGRAMMING

CCP = CONSTRAINTS + AGENTS Constraints are formulae over an interpreted first order language (i.e. X = 10, Y > X − 3); they can be added to a "container", the constraint store, but can never be removed. Agents can perform two basic operations on this store (asynchronously): tell or ask a constraint. rw(X):- askλ(X)(X > 0). tell∞(X ′ = X − 1).rw(X) + tellλ(X)(X ′ = X + 1).rw(X)

STOCHASTIC CCP

Each ask and tell instruction has a rate (function) attached to it: λ : C − → R+. The semantics of the language is given in terms of a Continuous Time Markov Chain.

  • L. Bortolussi, Stochastic Concurrent Constraint Programming, QAPL, 2006
slide-7
SLIDE 7

SCCP

MIMS MIMS IN SCCP

MODELING IN SCCP

MODELING BIOCHEMICAL REACTIONS R1 + . . . + Rn →f(R,X;k) P1 + . . . + Pm f-reaction(R, X, P, k) :- tellf(R,X;k)(R′ = R − 1 ∧ P′ = P + 1). f-reaction(R, X, P, k) ANALYSIS TOOLS Stochastic simulation (Gillespie algorithm) Stochastic model checking and CTMC analysis Approximation with ODE’s and Hybrid Automata OREGONATOR B →k1 A A + B →k2 ∅ A →k3 2A + C 2A →k4 ∅ C →k5 B

  • L. Bortolussi, A. Policriti. Modeling Biological

systems in sCCP , Constraints, in print.

slide-8
SLIDE 8

SCCP

MIMS MIMS IN SCCP

OUTLINE

1 MIDDLE LEVEL LANGUAGE: STOCHASTIC CONCURRENT

CONSTRAINT PROGRAMMING

2 HIGHER LEVEL LANGUAGE: MOLECULAR INTERACTION

MAPS

3 ENCODING MIMS IN SCCP

slide-9
SLIDE 9

SCCP

MIMS MIMS IN SCCP

MAPS

EXPLICIT A:B B:C pB COMBINATORIAL pB A:B B:C A:B:C A:pB pB:C A:pB:C

  • K. W. Kohn et alt. MIM of bioregulatory networks: A general rubric for systems biology. Mol. Bio. of the Cell, 2006.
slide-10
SLIDE 10

SCCP

MIMS MIMS IN SCCP

MAPS AND THEIR INTERPRETATION

EXPLICIT A:B B:C pB COMBINATORIAL pB A:B B:C A:B:C A:pB pB:C A:pB:C

  • K. W. Kohn et alt. MIM of bioregulatory networks: A general rubric for systems biology. Mol. Bio. of the Cell, 2006.
slide-11
SLIDE 11

SCCP

MIMS MIMS IN SCCP

COMBINATORIAL EXPLOSION

EXPLICIT 1 REACTION A + B → A:B COMBINATORIAL 4 REACTIONS A + B → A:B A + pB → A:pB A + B:C → A:B:C A + pB:C → A:pB:C

slide-12
SLIDE 12

SCCP

MIMS MIMS IN SCCP

CONTINGENCIES

EXPLICIT pB B:C A:pB COMBINATORIAL pB B:C A:pB Interpretation = formal semantic

slide-13
SLIDE 13

SCCP

MIMS MIMS IN SCCP

CONTINGENCIES

EXPLICIT pB B:C A:pB COMBINATORIAL pB B:C A:pB Interpretation = formal semantic

slide-14
SLIDE 14

SCCP

MIMS MIMS IN SCCP

OUTLINE

1 MIDDLE LEVEL LANGUAGE: STOCHASTIC CONCURRENT

CONSTRAINT PROGRAMMING

2 HIGHER LEVEL LANGUAGE: MOLECULAR INTERACTION

MAPS

3 ENCODING MIMS IN SCCP

slide-15
SLIDE 15

SCCP

MIMS MIMS IN SCCP

OVERVIEW

GENERAL IDEAS Proteins and complexes are represented as graphs, suitably encoded by predicates of the constraint store. Complexes are manipulated by predicates acting on their representations in the store. Contingencies are represented as list of logical rules. Reactions and interactions are associated to different sCCP-agents. KEY ISSUE In the encoding, complexes are created at run-time. Hence the simulation is implicit.

slide-16
SLIDE 16

SCCP

MIMS MIMS IN SCCP

ENCODING — ENTITIES IN THE STORE

interaction sites = ports (boolean state); molecules = collection of ports; complexes = graphs:

vertices are molecules; edges connect two ports;

molecular_type(molecular_type_id, port_list,contingency_list) node(molecular_type_id, mol_id) edge([mol_id1, port_id1], [mol_id2, port_id2]) complex_type(complex_id, node_list, edge_list,contingency_list) complex_number(complex_type_id, Num) port_number(port_id, Num)

slide-17
SLIDE 17

SCCP

MIMS MIMS IN SCCP

ENCODING — ENTITIES IN THE STORE

interaction sites = ports (boolean state); molecules = collection of ports; complexes = graphs:

vertices are molecules; edges connect two ports;

molecular_type(molecular_type_id, port_list,contingency_list) node(molecular_type_id, mol_id) edge([mol_id1, port_id1], [mol_id2, port_id2]) complex_type(complex_id, node_list, edge_list,contingency_list) complex_number(complex_type_id, Num) port_number(port_id, Num)

slide-18
SLIDE 18

SCCP

MIMS MIMS IN SCCP

ENCODING — CONTINGENCIES

CONTINGENCIES ARE LOGICAL RULES IF (there are some edges) THEN (inhibit or allow some other ports of edges) IF (there is y) THEN (inhibit z) IF (there is y) THEN (allow x)

slide-19
SLIDE 19

SCCP

MIMS MIMS IN SCCP

SIMULATION IN SCCP (IMPLICIT)

1

choose reaction

Interaction agents compete stochastically to determine next reaction reactions act on port (types)

2

choose actual complexes involved

Each port type has a port manager agent doing this

3

build product and apply enabled contingencies

slide-20
SLIDE 20

SCCP

MIMS MIMS IN SCCP

SIMULATION IN SCCP (IMPLICIT)

1

choose reaction

Interaction agents compete stochastically to determine next reaction reactions act on port (types)

2

choose actual complexes involved

Each port type has a port manager agent doing this

3

build product and apply enabled contingencies

slide-21
SLIDE 21

SCCP

MIMS MIMS IN SCCP

SIMULATION IN SCCP (IMPLICIT)

1

choose reaction

Interaction agents compete stochastically to determine next reaction reactions act on port (types)

2

choose actual complexes involved

Each port type has a port manager agent doing this

3

build product and apply enabled contingencies

slide-22
SLIDE 22

SCCP

MIMS MIMS IN SCCP

SIMULATION IN SCCP (IMPLICIT)

1

choose reaction

Interaction agents compete stochastically to determine next reaction reactions act on port (types)

2

choose actual complexes involved

Each port type has a port manager agent doing this

3

build product and apply enabled contingencies

slide-23
SLIDE 23

SCCP

MIMS MIMS IN SCCP

SIMULATION IN SCCP (IMPLICIT)

1

choose reaction

Interaction agents compete stochastically to determine next reaction reactions act on port (types)

2

choose actual complexes involved

Each port type has a port manager agent doing this

3

build product and apply enabled contingencies

slide-24
SLIDE 24

SCCP

MIMS MIMS IN SCCP

SIMULATION IN SCCP (IMPLICIT)

1

choose reaction

Interaction agents compete stochastically to determine next reaction reactions act on port (types)

2

choose actual complexes involved

Each port type has a port manager agent doing this

3

build product and apply enabled contingencies

slide-25
SLIDE 25

SCCP

MIMS MIMS IN SCCP

A SIMPLE EXAMPLE

Mammalian G1/S cell cycle phase transition

slide-26
SLIDE 26

SCCP

MIMS MIMS IN SCCP

A SIMPLE EXAMPLE

slide-27
SLIDE 27

SCCP

MIMS MIMS IN SCCP

CONCLUSIONS

sCCP allows an implicit simulation of MIMs The key ingredient is the use of the constraint store to represent and manage graph-based representation of complexes. The encoding is compositional and linear in the size of

  • MIMs. This is possible only due to the implicit encoding:

expliciting reactions causes an exponential increase the description. The stochastic simulation is a natural consequence of the semantics of sCCP . Future work: a more efficient implementation and an automatic compiler from MIMs.