1. PML: Toward a High-Level Formal Language for Biological Systems Bor-Yuh Evan Chang and Manu Sridharan July 24, 2003

2. 2 7/24/2003 Why Formal Models for Biology? Experiments have led to an enormous wealth of (detailed) knowledge but in a fragmented form –serve as a common language for sharing modular, compositional, varying levels of abstraction Much information described through prose or graph-like diagrams with loose semantics –make assumptions explicit

3. 3 7/24/2003 Why Formal Models for Biology? Mathematical abstraction convenient for reasoning and simulation –DNA ! string over the alphabet {A,C,G,T} enables the use of string comparison algorithms –Cellular Pathways ! ?

4. 4 7/24/2003 Previous Abstractions Chemical kinetic models –can derive differential equations –well-studied, with considerable theoretical basis –variables do not directly correspond with biological entities –may become difficult to see how multiple equations relate to each other

5. 5 7/24/2003 Previous Abstractions Pathway Databases (e.g., EcoCyc, KEGG) –store information in a symbolic form and provide ways to query the database –behavior of biological entities not directly described Petri nets –directed bipartite multigraph (P,T,E) of places, transitions, and edges; places contain tokens –place = molecular species, token = molecule, transition = reaction 2

6. 6 7/24/2003 Previous Abstractions Concurrent computational processes –each biological entity is a process that may carry some state and interacts with other processes –each process described by a “program” –prior proposals based on process algebras, such as the  -calculus [Regev et al. ’01] –we take this view

7. 7 7/24/2003 Computer Systems vs. Biological Processes Similarities –elementary pieces build-up components that in turn build-up large components and so forth to create highly complex systems –all systems seem to have similar cores but exhibit great diversity Differences! –theory of computation and computer systems are purely man-made (controlled-design) but biology is observational

8. 8 7/24/2003 Model of Concurrent Computation Must choose a machine model as a basis –The  -calculus [Milner ’90 and others] A formalism aimed at capturing the essence of concurrent computation. –focuses on communication by message passing System composed of processes Communication on channels –send: send message m on channel c –receive: receive message on channel c, call it x –Many variants—the stochastic  -calculus

9. 9 7/24/2003 The  -calculus Syntax Operational Semantics

10. 10 7/24/2003 The  -calculus Congruence

11. 11 7/24/2003 Modeling in the  -calculus The  -calculus is concise and compact, yet powerful –not clear if another machine model would be particularly better or worse However, it is far too low-level for direct modeling (ad-hoc structuring)

12. 12 7/24/2003 Informal Graphical Diagrams Protein Enzyme ProteinEnzyme Protein k k -1 k cat sites domains rules

13. 13 7/24/2003 PML: Enzyme Enzyme bind_substrate

14. 14 7/24/2003 PML: Protein Protein bind_substratebind_product

15. 15 7/24/2003 PML: A Simple System

16. 16 7/24/2003 Compartments Critical part of biological pathways –prevents interactions that would otherwise occur Description of the behavior of a molecule should not depend on the compartment Regev et al. use “private” channels in the  - calculus for both complexing and compartmentalization

17. 17 7/24/2003 PML: Simple Compartments Example MolA MolB bind_a

18. 18 7/24/2003 PML: Simple Compartments Example MolA MolB ERCytosol CytERBridge

19. 19 7/24/2003 PML: Simple Compartments Example MolB ERCytosol CytERBridge MolA

20. 20 7/24/2003 Semantics of PML Defined in terms of the  -calculus via two translations –from PML to CorePML “flattens” compartments, removes bridges, explicit rule names

21. 21 7/24/2003 Semantics of PML –from CorePML to the  -calculus

22. 22 7/24/2003 Larger Models Modeled a general description of ER cotranslational-translocation –unclearly or incompletely specified aspects became apparent e.g., can the signal sequence and translocon bind without SRP? Yes [Herskovits and Bibi ’00] Extended to model targeting ER membrane with minor modifications

23. 23 7/24/2003 Benefits of PML Easier to write and understand because of more consistent biological metaphor (binding sites) Block structure for controlling namespace and modularity Special syntax for compartments –separate complexing from compartmentalization

24. 24 7/24/2003 Future Work Naming? Proximity of molecules Integrating quantitative information (reaction rates, etc.) –start from work by Priami et al. Type systems Graphical and simulation tools

26. 26 7/24/2003 Example: Cotranslational Translocation Ribosome translates mRNA exposing a signal sequence Signal sequence attracts SRP stopping translation SRP receptor (on ER membrane) attracts SRP Signal sequence interacts with translocon, SRP disassociates resuming translation Signal peptidase cleaves the signal sequence in the ER lumen, Hsc70 chaperones aid in protein folding

27. 27 7/24/2003 Example: Cotranslational Translocation

28. 28 7/24/2003 Example: Cotranslational Translocation

29. 29 7/24/2003 Example: Cotranslational Translocation

30. 30 7/24/2003 Example: Cotranslational Translocation

31. 31 7/24/2003 Example: Cotranslational Translocation

32. 32 7/24/2003 Example: Cotranslational Translocation

33. 33 7/24/2003 Example: Cotranslational Translocation