SBML2Murphi: a Translator from a Biology Markup Language to Murphy

Andrea RomeiCiclo di Seminari su Model

CheckingDipartimento di Informatica

Università di PisaPisa, April 2009

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Targets of this talk

Provide a quick look to Murphi descriptive language

Show how a biological system can be modelled as a Murhpi Finite State System in an (semi-)automatic way.

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Outline

I. IntroductionII. The Murphi LanguageIII. The “sort” ExampleIV. The Systems Biology Markup

LanguageV. SBML2Murphi TranslatorVI. An example of applicationVII. Final remarks

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Introduction

Model checking is the process of checking whether a given structure is a model of a given logical formula.

Murphi is a formal verifier based on explicit state enumeration. Originally developed at Stanford, now

maintained at University of Utah. It works on various versions of Unix/Linux.

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Murphi in brief

Murphi takes a Finite State System S and checks that a given invariant property for S is satisfied

An execution is a finite sequence of states s0,s1,…: s0 is one of the start states si+1 is obtained by applying one transition rule whose

condition is true in si and whose action transforms si in si+1

The invariants are applied whenever a state is explored

si can satisfy several conditions, the verifier must cover all the possibilities

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The Murphi Program

A Murphi program has the following structure constant, type, and variable declarations procedure and function declarations rules, start states, and invariants

A Murphi program implicitly determines a state graph (i.e. an assignment of a value to each global variable)

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Constants, types and variables

Murphi supports the specification of constants, variables and types The simple types are boolean,

enumerations, finite sub-ranges of integers

The compound types are arrays or records of compound or simple types

Sub-ranges and enumerations are important to avoid memory consumption

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Constants, types and variables

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Functions and procedures

Functions and procedures can have side effects Formal parameters declared “var” are

passed by reference. Formals that are not declared “var” are

passed by reference, but the function or procedure is not allowed to modify them.

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Rule

A rule determines a transition from one state of the finite automaton to another It consists of a body and a

condition A program must have at

least one rule

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Start State

A start state is a special type of rule It is only executed at the beginning of an

execution A start state must assign a value to every

global variable

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Invariant

An invariant is a boolean expression that references the defined variables

Its value doesn’t change during the program execution

An invariant is a special rule

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Example: sorting by swapping

Array of integers 0..N-1 and pointers for swapping

Swaps the positions “i” and “j” of the array

Increases the input pointer mod N

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Example: sorting by swapping

Increments the “i” pointer

Increments the “j” pointer

Swaps the elements pointed by “i” and “j” if they are not in the right order

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Example: sorting by swapping

The program violates invariant when the data is sorted

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Example: sorting by swapping

Murphi usage: Write sort.m Run the Murphi compiler over it by typing

“./mu sort.m”; this yields a file “sort.C” Run the C++ compiler over “sort.C”

together with the verifier code Run “sort.exe –ta”

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Example: sorting by swapping

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SBML (from wikipedia)

The Systems Biology Markup Language (SBML) is a machine-readable language for representing models of biochemical reaction networks It is based on the XML technology

SBML can represent metabolic networks, cell-signaling, pathways, regulatory networks and other kinds of systems studied in systems biology

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SBML purposes

SBML has three main purposes enabling the use of multiple software tools

without rewriting models for each tool enabling models to be shared and published ensuring the survival of models beyond the

lifetime of the software used to create them

SBML serves as a “lingua franca”

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SBML Hierarchy

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Species and Reactions

A specie is a substance or entity that takes part in a reaction (e.g. the glucose molecule)

A reaction is a statement describing some transformation that can change the amount of one or more species It describes how certain entities (reactants) are

transformed into certain other entities (products) It has associated a kinetic rate expression

describing how quickly it takes place

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SBML Example

The reactions of human CO hemoglobin An equation used in enzyme

characterizations formulated by A. Hill in 1910 to describe the sigmoidal binding curve of hemoglobin

Five species: S0 , S1 , S2 , S3 , S4

Four reactions:

Hill-l2.xml

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Why an SBML2Murphi translator?

Reactions are driven by empirical laws Species in a model change their values

along the time The target may be to verify some basic

properties of a biological model E.g. verify the consistency of the model

when the initial concentrations of the species varies in a computed range

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The Law of Mass Action

It states that the rate of a chemical reaction is proportional to the probability that the reacting molecules will be found together in a small volume Produces a differential equation for each

distinct specie belonging to a reaction The system of differential equations can be

solved to determine how species change values against the time

The Law of Mass Action: Example

Reactants

Products

Kinetic Rate

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The law of Mass Action: Example

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Reactions in SBML

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The Role of the Translator

Murphi SBML How

Variables &Constants

Species Directly by parsing the SBML model

State transitions

Reactions

Computed by means of a procedure that implements the computation of the law of mass action

Start states ? ?

Invariants ? ?

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The “Hill” model in Murphi

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The “Hill” model in Murphi

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The “Hill” model in Murphi

The start states in the Hill model indicate what happens when the initial concentrations vary. I used about 500 assignments to S1, S2

and S3 by varying three parameters. I got about 500 starting states each of

them corresponds to a different experiment (i.e. an initial concentration).

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The “Hill” model in Murphi

The invariant is used to test the consistency of the model by varying the initial concentrations

I assigned to “Hill.m” ranges in which the species must fall into during the experiment 0 <= S1 < 16 0 <= S2 < 0.5 0 <= S3 < 0.5

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Conclusion

Murphi SBML How

Variables &Constants

Species Directly by parsing the SBML model

State transitions

Reactions

Computed by means of a procedure that implements the computation of the law of mass action

Start states - Empirical assignments

Invariants - Ranges in which the species fall into

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References

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References