PML: Toward a High-Level Formal Language for Biological

SystemsBor-Yuh Evan Chang and Manu Sridharan

Computer Science DivisionUniversity of California, Berkeley

BioConcur, MarseilleSeptember 6, 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

• Mathematical abstraction convenient for reasoning and simulation

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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– place = particular state of a molecular

specie, token = molecule, transition = reaction

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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 biological entity 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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Modeling in the -calculus• The -calculus is concise and compact,

yet powerful [Milner ’90]– take this as the underlying machine

model– not looking for another machine model

• 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

parameterized

declared in outer scope

interactions within the complex

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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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PML: Summary• Domains

– set of mutually dependent binding sites– defines at the lowest-level the reactions a

biological entity can undergo• Groups

– static structure for controlling namespace– may represent a large biological entity

• large complex, a system, etc.• Compartments

– special groups that define boundaries

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Semantics of PML• Defined in terms of the -calculus via

two translations– from PML to CorePML

• “flattens” compartments, removes bridges

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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 a more direct biological metaphor

• 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.

• Compartment fusion and fission• Type checking PML specifications• Exceptional / higher-level specifications• Graphical and simulation tools

Syntax of PML

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Syntax of PML

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Syntax of PML

The -calculus

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The -calculus• Syntax

• Operational Semantics

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The -calculus• Congruence

Example: Cotranslational Translocation

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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

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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