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: Enzyme

Enzymebind_substrate

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PML: Protein

Protein 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