Modeling and Static Analysis of Complex Biological Systems

Débora Schuch da Rosa

University of Trento

Context

• 20th century: – century of gene - starting with the rediscovery of

Mendel's laws on inheritance, it ended with the sequencing of the human genome.

• 21st century: – century of information society– major challenge: novel computing paradigms for

improved processing of human and biological data

Modeling biological systems

• is a challenge for computer science.

• complexity exceeds that of computer systems by orders of magnitude.

• models of dynamics needed to organize the huge amount of data available in the post-genomic era.

• mapping structure to function

Problem: state space explosion• huge size of the representation • investigation of properties of interest grows

exponentially in the size of the program

Solution: static analysis• classical alternative to dynamic analysis

Collaborations and references• Magali Roux-Rouquié

CNRS,Université Marie Curie, Laboratoire d’Informatique de Paris 6

• Corrado Priami

Microsoft-Research-University of Trento Centre for Computational and Systems Biology

• F.&H.Nielson, DTU, Copenhagen

•Control flow analysis in BioAmbients, Proceedings BioConcur 2003

•Static analysis for systems biology, Proceedings WISICT 2004

•Ten top reasons for systems biology to get into model-driven engineering, Proceedings GaMMa2006

Outline1. Static Analysis and the Succinct Solver

2. Language Definition: Star Ambients

3. Methodology

4. Application in Systems Biology

5. Model-Driven Engineering

6. Automatic Translation: diagrams to formal language

1. Related work

2. Conclusions and Future work

1. Static analysis

• static extraction of complex information about the dynamic behavior of programs by:• systematic inspecting the program text

• instead of program execution/ simulation

• origin:

• compiler optimization, to handle large programs• validation of safety and security properties of

programs and system

Benefits & drawbacks

• The information extracted from a program is guaranteed to be a correct description of the behavior of the program.

• For most interesting properties it is impossible to obtain exact information

• thus static analysis is typically approximative.

Approximations

The exact word

Under-approximation

Over-approximation

Unacceptable situation

universe

exact answer static analysis result

Under-approximation

universe

exact answer

under-approx.

When we have an under-approximation to the exact behavior of a program

we can guarantee the certain events will indeed happen

– namely those included in the analysis result.

Over-approximation

universe

exact answer

static analysisresult

When we have an over-approximation to the exact behavior of a program

we can guarantee the certain events will never happen

– namely those not included in the analysis result.

Succinct Solver

• implemented in SML thus formally featured with modular structures, continuation and memoryzations.

• Control Flow Analysis – polynomial time

2. Star Ambients: motivation

• problems in static analysis in BioAmbients:• kill capability

• acid capability

• duplicate capability

• divide capability

• difficulties in creating a quantitative version of the calculus

• not present in Star Ambients.

Star ambients: characteristics

• free domain formal language for global computing

• messages are signals • ambients are processes,• ambients move using special movement capabilities

• operators easily capture dynamics

• coding methodology

• check properties of complex systems

• static analysis via succinct solver

Star Ambients: syntax

Closure conditions

Reduction rule

µ

Reduction rule:

[enter n.P | Q] | [accept n.R | S] [[P | Q] | R | S] ] Red In µ

)accept ,()enter ,(

),(

)accept ,()enter ,(

),(),(:,,

)enter (*,

'2'1

12

'2'1

2121

'

DD

I

II

II

I

µ1

| R | S

µ2

P | Q

µ1

µ2

enter n.P | Q

enter n.P | Q

enter µ’.P | Q accept µ’.R | S

Why approximative results?

• We have studied the two basic capabilities of the calculus – communication and movement

• We have detected when the Succinct Solver loses control of the flow of the information

Example Movement capability

3. Methodology

Mechanism for Safe Movement

Static Analysis (Star Ambients + mechanisms)

=

The exact world

The Universe

exact answers to the problem

over-approx.Over-approximation

over-approx. (inexact answers)

over-approx.

a) b)

c) d)

A language and a tool for diverse analysis

• Pathway and reachability » 6 mechanisms

• Heredity» 12 mechanisms

• Inverse heredity» 12 mechanisms

• Learning » 12 mechanisms

In total, we offered 50 mechanisms, that would be added automatically for the Star Ambients codes

4. Applications in Systems Biology

We covered a wide range of biomolecular mechanisms:

• covalent binding

• proteolytic cleavage

• stoichiometric conversion

• stimulation

• transcriptional activation

• transport

• state combination connectors

• degradation

• non-covalent binding

• inhibition

Covalent modification

Cleavage of covalent bound

Enzimatic stimulation of a reaction

Proteolitic cleavage

Stoichiometric conversion

General symbol for stimulation

Transcriptional activation

Transport

State-combination connectors

Degradation products (garbage collection!)

Non-covalent binding

Asymetric binding

Multimolecular complex

Homodimer formation

5. Model driven engineering

• conceptual convergence: – towards a system view– complexity of design– context awareness– star-abilities– modeling at the heart– computational evaluation– models integration– domain specific modeling language– biological systems as engineering systems

6. Automatic translation

• hide formal details to the designer

• extraction of process algebra specifications from UML diagrams

• step towards the current use of formal methods in the practice of software development.

Knowledge hierarchies • towards extraction of biological information

registered from public databases and their integration into SB-UML framework notably in terms of hierarchies.

• UML class hierarchies:• aggregation

• composition

• outputs of SB-UML automatic code generator as input for static analysis based on Star Ambients.

7. Related work: differences

Nielson & Nielson & Pillegard:• implementation of the

succinct solver, aims: • in order to get more

powerful analysis for BioAmbients codes,

• towards the precision in the analysis results.

Our work:• keep the use of the

simplest implementation of the succinct solver

• created a specific language for running on the succinct solver,

• aiming also to obtain precise analysis results.

Advantages of our approach

• Star Ambients, is a free-domain formal language

• delivers a methodology of programming

• precise analysis of models at minimal computational cost

6) first approach based on model-driven engineering using metamodeling in Systems Biology

7) automatic translation of class hierarchies in Star Ambients

This translation is XMI based, following the Object Management Group (OMG) standards

8) new programming paradigm - data and programs are not disjoined: data carrying executable codes

9) precision in the analysis results without increasing the time complexity of the tool created to this end.

8 Conlusion: inovative aspects

1) first approach: the use of static analysis and Systems Biology

2) Star Ambients formal language

3) methodology for programming in Star Ambients intrinsically related to static analysis outcomes

4) suggested implementations for discovering knowledge in an optimized way and for facilitating the sharing of static analysis results through the web

5) two Star Ambients mechanisms had their origin in the understanding of principals of modeling protein interaction

2) Improvement of the automatic translation: state diagrams to Star Ambients

3) Association of quantitative analysis to Star Ambients

4) Application of Star Ambients for other domain specific problems considered intractable

Future work:

1) Use of the metamodel-framework for confirming a method that:

• describes incrementally any biological system at different levels of abstraction,

• formalizes the experimental observations and knowledge, and

• transforms models into coded representation which will lead to model-based testing with formal tools.

• no adequate formalism for complex problems • such that functional compositional constructions

of systems• could be dynamically evaluated in polynomial

time.

Before Star Ambients

Thank you!Questions?