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 Università degli studi di Trieste luca@dmi.units.it 2 Dipartimento di Matematica ed Informatica Università degli studi di Udine 3 Istituto di Genomica Applicata Parco Scientifico Tecnologico, Udine. 4 Dipartimento di Informatica Università degli studi di Pisa. BIBM 2007, Silicon Valley, 3 th November 2007
S CCP MIM S MIM S IN S CCP V IEWS OF C OMPUTATIONAL S YSTEMS B IOLOGY
S CCP MIM S MIM S IN S CCP O UTLINE 1 M IDDLE L EVEL L ANGUAGE : S TOCHASTIC C ONCURRENT C ONSTRAINT P ROGRAMMING 2 H IGHER L EVEL L ANGUAGE : M OLECULAR I NTERACTION M APS 3 E NCODING MIM S IN S CCP
S CCP MIM S MIM S IN S CCP O UTLINE 1 M IDDLE L EVEL L ANGUAGE : S TOCHASTIC C ONCURRENT C ONSTRAINT P ROGRAMMING 2 H IGHER L EVEL L ANGUAGE : M OLECULAR I NTERACTION M APS 3 E NCODING MIM S IN S CCP
S CCP MIM S MIM S IN S CCP S TOCHASTIC C ONCURRENT C ONSTRAINT P ROGRAMMING CCP = C ONSTRAINTS + A GENTS 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. STOCHASTIC CCP Each ask and tell instruction has a rw ( X ) :- ask ( X > 0 ) . rate (function) attached to it: tell ( X ′ = X − 1 ) . rw ( X ) → R + . λ : C − + tell ( X ′ = X + 1 ) . rw ( X ) The semantics of the language is given in terms of a Continuous Time Markov Chain. L. Bortolussi, Stochastic Concurrent Constraint Programming , QAPL, 2006
S CCP MIM S MIM S IN S CCP S TOCHASTIC C ONCURRENT C ONSTRAINT P ROGRAMMING CCP = C ONSTRAINTS + A GENTS 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. STOCHASTIC CCP Each ask and tell instruction has a rw ( X ) :- ask λ ( X ) ( X > 0 ) . rate (function) attached to it: tell ∞ ( X ′ = X − 1 ) . rw ( X ) → R + . λ : C − + tell λ ( X ) ( X ′ = X + 1 ) . rw ( X ) The semantics of the language is given in terms of a Continuous Time Markov Chain. L. Bortolussi, Stochastic Concurrent Constraint Programming , QAPL, 2006
S CCP MIM S MIM S IN S CCP M ODELING IN S CCP O REGONATOR M ODELING BIOCHEMICAL REACTIONS → k 1 B A R 1 + . . . + R n → f ( R , X ; k ) P 1 + . . . + P m → k 2 ∅ A + B → k 3 A 2 A + C f -reaction ( R , X , P , k ) :- → k 4 ∅ 2 A tell f ( R , X ; k ) ( R ′ = R − 1 ∧ P ′ = P + 1 ) . → k 5 C B f -reaction ( R , X , P , k ) A NALYSIS TOOLS Stochastic simulation (Gillespie algorithm) Stochastic model checking and CTMC analysis Approximation with ODE’s and Hybrid Automata L. Bortolussi, A. Policriti. Modeling Biological systems in sCCP , Constraints , in print.
S CCP MIM S MIM S IN S CCP O UTLINE 1 M IDDLE L EVEL L ANGUAGE : S TOCHASTIC C ONCURRENT C ONSTRAINT P ROGRAMMING 2 H IGHER L EVEL L ANGUAGE : M OLECULAR I NTERACTION M APS 3 E NCODING MIM S IN S CCP
S CCP MIM S MIM S IN S CCP M APS E XPLICIT A:B B:C pB C OMBINATORIAL 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.
S CCP MIM S MIM S IN S CCP M APS AND THEIR I NTERPRETATION E XPLICIT A:B B:C pB C OMBINATORIAL 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.
S CCP MIM S MIM S IN S CCP C OMBINATORIAL EXPLOSION E XPLICIT 1 REACTION A + B → A:B C OMBINATORIAL 4 REACTIONS A + B → A:B A + pB → A:pB A + B:C → A:B:C A + pB:C → A:pB:C
S CCP MIM S MIM S IN S CCP C ONTINGENCIES E XPLICIT pB B:C A:pB C OMBINATORIAL pB B:C A:pB Interpretation � = formal semantic
S CCP MIM S MIM S IN S CCP C ONTINGENCIES E XPLICIT pB B:C A:pB C OMBINATORIAL pB B:C A:pB Interpretation � = formal semantic
S CCP MIM S MIM S IN S CCP O UTLINE 1 M IDDLE L EVEL L ANGUAGE : S TOCHASTIC C ONCURRENT C ONSTRAINT P ROGRAMMING 2 H IGHER L EVEL L ANGUAGE : M OLECULAR I NTERACTION M APS 3 E NCODING MIM S IN S CCP
S CCP MIM S MIM S IN S CCP O VERVIEW G ENERAL I DEAS 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. K EY I SSUE In the encoding, complexes are created at run-time. Hence the simulation is implicit.
S CCP MIM S MIM S IN S CCP E NCODING — 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)
S CCP MIM S MIM S IN S CCP E NCODING — 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)
S CCP MIM S MIM S IN S CCP E NCODING — CONTINGENCIES C ONTINGENCIES 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 )
S CCP MIM S MIM S IN S CCP S IMULATION IN S CCP (IMPLICIT) choose reaction 1 Interaction agents compete stochastically to determine next reaction reactions act on port (types) choose actual complexes involved 2 Each port type has a port manager agent doing this build product and apply enabled contingencies 3
S CCP MIM S MIM S IN S CCP S IMULATION IN S CCP (IMPLICIT) choose reaction 1 Interaction agents compete stochastically to determine next reaction reactions act on port (types) choose actual complexes involved 2 Each port type has a port manager agent doing this build product and apply enabled contingencies 3
S CCP MIM S MIM S IN S CCP S IMULATION IN S CCP (IMPLICIT) choose reaction 1 Interaction agents compete stochastically to determine next reaction reactions act on port (types) choose actual complexes involved 2 Each port type has a port manager agent doing this build product and apply enabled contingencies 3
S CCP MIM S MIM S IN S CCP S IMULATION IN S CCP (IMPLICIT) choose reaction 1 Interaction agents compete stochastically to determine next reaction reactions act on port (types) choose actual complexes involved 2 Each port type has a port manager agent doing this build product and apply enabled contingencies 3
S CCP MIM S MIM S IN S CCP S IMULATION IN S CCP (IMPLICIT) choose reaction 1 Interaction agents compete stochastically to determine next reaction reactions act on port (types) choose actual complexes involved 2 Each port type has a port manager agent doing this build product and apply enabled contingencies 3
S CCP MIM S MIM S IN S CCP S IMULATION IN S CCP (IMPLICIT) choose reaction 1 Interaction agents compete stochastically to determine next reaction reactions act on port (types) choose actual complexes involved 2 Each port type has a port manager agent doing this build product and apply enabled contingencies 3
S CCP MIM S MIM S IN S CCP A SIMPLE EXAMPLE Mammalian G1/S cell cycle phase transition
S CCP MIM S MIM S IN S CCP A SIMPLE EXAMPLE
S CCP MIM S MIM S IN S CCP C ONCLUSIONS 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.
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