PML: Toward a High-Level Formal Language for Biological Systems
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Transcript of PML: Toward a High-Level Formal Language for Biological Systems
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PML: Toward a High-Level Formal Language for Biological
Systems
Bor-Yuh Evan Chang and Manu Sridharan
July 24, 2003
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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
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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 ! ?
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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
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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 = reaction2
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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
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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
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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
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The -calculus• Syntax
• Operational Semantics
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The -calculus• Congruence
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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)
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Informal Graphical Diagrams
Protein
Enzyme Protein Enzyme
Enzyme
Proteink
k-1
kcatsites
domains
rules
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PML: EnzymeEnzymebind_substrate
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PML: ProteinProtein Proteinbind_substrate bind_product
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PML: A Simple System
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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
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PML: Simple Compartments Example
MolAMolB
bind_a bind_a
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PML: Simple Compartments Example
MolAMolB
ER Cytosol
CytERBridge
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PML: Simple Compartments Example
MolB
ER Cytosol
CytERBridge MolA
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Semantics of PML• Defined in terms of the -calculus via
two translations– from PML to CorePML
• “flattens” compartments, removes bridges, explicit rule names
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Semantics of PML– from CorePML to the -calculus
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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
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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
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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
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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
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Example: Cotranslational Translocation
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Example: Cotranslational Translocation
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Example: Cotranslational Translocation
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Example: Cotranslational Translocation
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Example: Cotranslational Translocation
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Example: Cotranslational Translocation
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Example: Cotranslational Translocation