1. Needs to be described: Objects – Have multiple states – Consist of other objects, that may have multiple states – May be connected with each other via different bonds – Located in multiple compartments, with two objects within the third can be in three different compartments. Rules: – Select sets of objects with common properties – Transform sets of objects into another sets of objects, generating reactions – Add kinetic laws to reactions Representational issues (compatible with SBGN) Rules application: – Stochastic application – Rules priority, score, confidence – Restrictions on the number of applications

2. Two approaches to define SBML Graph-based approach with the fixed hierarchy (BNG, Simmune, StochSim, Moleculizer, MIM) Graph-based approach with an arbitrary level of hierarchy (A Finney) Start with the simplest

3. Main features of the proposal 1.Species are constructed of molecules, molecules – of components. 2.Component = binding site = state variable 3.Attributes, variables, stoichiometry = properties of a component 4.Species configuration space is defined by rules later on, not during molecules declarations. 5.Concentrations (all numerics!) are declared separately from species declaration.

4. Molecular Entities and Chemical Species graphs A Chemical Species Graph C is a fully defined molecular entity or a set of molecular entities. – Any and all variable attributes taking specific values.

5. Reaction is a graph rewriting consistent with chemistry Mapping ρ: R ρ -> P ρ preserves, adds and removes molecular entity graphs as units.

6. Pattern graphs and chemical species selected by patterns

7. Graph transformation on patterns Find reactant chemical species C matched by RP Replace image of RP in C by PP via f. Preserve edges, vertices and attributes of vertices in C not specified in RP. Remove dangling edges.

8. General XML/SBML structure SBML L1-L2 Units Compartments Parameters Species Reactions Reactants speciesReference Products speciesReference KineticLaw SBML L3-RBM Species + components + physicalEntities + bonds Reactions Reactants + speciesTemplate Products +? speciesTemplate +? ReactionTemplate Graph XML Graph Nodes Edges NodeReferences Transformation RHS GraphReference LHS GraphReference Map NodeToNode EgdeToEdge

9. Introduction to BioNetGen Language (BNGL) A b Y B A(b) B(a,Y~U~P,location~Cyt~Nuc) a A(b) + B(a) -> A(b!1).B(a!1) p B(Y~P) -> B(Y~U) d a bond between two components B_tot B() B_unbound B(a) B_bound B(a!+) B_phospho_all B(Y~P!?) B_phospho_unbound B(Y~P) B_phospho_bound B(Y~P!+) A_B_complex A().B() Molecules Patterns Reaction rules

10. Components and physical entities R(a,b~u~p,g~u~p)

11. Species R(a!1,b~p!2,g~u).L(Fc!1,Fc).Lyn(SH2!2) …..

12. speciesTemplate R(a!1).L(Fc!1,Fc) R(a,g~p!?) …. …. …

14. Reactions and reaction rules Option 1: Option 2: ……

15. ReactionRule specification: graph-based approach …… …… …… ….. R(a) + L(Fc,Fc) -> R(a!1).L(Fc!1,Fc)

16. ReactionRule specification: chemistry-based approach … …

17. A a B a How to select A as reactant and transform into B while preserving states of component a? Easy to do operationally, but harder to define using standard semantics of chemical semantics. Need notion of mapping. Challenge: L3M should encompass.

18. Reaction or ReactionRule R(a) + L(Fc,Fc) -> R(a!1).L(Fc!1,Fc) ……

19. Logic and Range (BioPAX) ……

20. Arbitrary level of hierarchy Why not specify components and physicalEntities as speciesTypes? Advantage: generality Problem: does not allowed by current SBML standard Cost: complexity of connectivity

21. speciesType speciesTypeIncluded <speciesTypeState value="p" name="phosphorylated"/

22. speciesType id : SId name : string {use="optional"} class: string {"component", "physicalEntity", …} {use="optional"} speciesTypeState: string [0..*] {use="optional"} speciesTypeIncluded: speciesTypeIncluded[0..*] compartment: Sid {use="optional"} <speciesTypeState value="p" name="phosphorylated"/

23. speciesTypeIncluded Id: SId name : string {use="optional"} multiplicity: int { minInclusive="0" use="optional" default="1"} maxExternalBonds: int { minInclusive="0" use="optional" default="1"} maxInternalBonds: int { minInclusive="0" use="optional" default="0"} compartment: Sid {use="optional"}

24. Bonds

25. id : SId {use="optional"} name : string {use="optional"} speciesTypeInstance: speciesType[0..*] compartment: Sid {use="optional"} speciesTypeInstance id : SId speciesTypeValue: speciesTypeValue {use="optional"} name : string {use="optional"} multiplicity: int { minInclusive="0" use="optional" default="1"} extBonds: int { minInclusive="0" maxInclusive="maxExtBonds" use="optional"} intBonds: int { minInclusive="0" maxInclusive="maxIntBonds" use="optional"} speciesTemplate