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PML: Toward a High-Level Formal Language for Biological Systems. Bor-Yuh Evan Chang and Manu Sridharan July 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
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PML: Toward a High-Level Formal Language for Biological Systems Bor-Yuh Evan Chang and Manu Sridharan July 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
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 ! ?
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
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
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
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
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
The -calculus • Syntax • Operational Semantics
The -calculus • Congruence
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)
sites Informal Graphical Diagrams k-1 Protein Enzyme Protein Enzyme k kcat rules Protein Enzyme domains
Enzyme PML: Enzyme bind_substrate
Protein Protein PML: Protein bind_substrate bind_product
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
MolA PML: Simple Compartments Example MolB bind_a bind_a
CytERBridge PML: Simple Compartments Example ER Cytosol MolB MolA
MolA PML: Simple Compartments Example ER Cytosol CytERBridge MolB
Semantics of PML • Defined in terms of the -calculus via two translations • from PML to CorePML • “flattens” compartments, removes bridges, explicit rule names
Semantics of PML • from CorePML to the -calculus
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
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
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
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
