Two Qualitative Dynamics Semantics for SBGN Process Description Maps

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Two Qualitative Dynamics Semantics for SBGN Process Description Maps

Adrien Rougny, Christine Froidevaux, Loïc Paulevé

To cite this version:

Adrien Rougny, Christine Froidevaux, Loïc Paulevé. Two Qualitative Dynamics Semantics for SBGN Process Description Maps. CMSB’15, Sep 2015, Nantes, France. 2015. �hal-01258943�

Two Qualitative Dynamics Semantics for SBGN Process Description Maps

Adrien Rougny, Christine Froidevaux and Lo¨ıc Paulev´e

Laboratoire de Recherche en Informatique, Orsay, FRANCE UMR8623 Universit´e Paris-Sud - CNRS

Contact: [email protected]

Context

Larger and larger reaction networks modelling various biological processes (from databases, automatic inference)

Standards to represent reaction networks: e.g. Systems Biology Graphical Notation Process Description language (SBGN-PD)

Analysis of the dynamics to understand and control these processes

Motivations

Qualitative semantics allows to capture important dynamical features (e.g. attractors, reachability) without numerical parameters

Model SBGN-PD maps under qualitative semantics

We propose two semantics formalized by asynchronous automata networks: the general semantics, together with a refinement called process conflicts , and the stories semantics

Asynchronous Automata Networks

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State transition graph:

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General Semantics

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`_a

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`p = {m₁, a₁, b₁}

`c = `_d = {p₁}

`_p = {c₁, d₁}

`<sub>a</sub> = `_b = {p₁, c₁, d₁}

Each chemical entity is modelled by one automaton

Refinement 1: Process Conflicts

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`<sub>a1</sub>, `_a2 `_p

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`p = {a₁, q₀}

`_q = {a₁, p₀}

`_b = {q₁}

`c = {p₁}

`_p = {c₁}

`_q = {b₁}

`_a1 = {p₁, c₁}

`_a2 = {q₁, b₁}

Processes p and q cannot occur at the same time

Refinement 2: Stories Semantics

Story:

accounts for successive transformations of a chemical entity

a set of entities that cannot be present at the same time, i.e. that are mutually exclusive

Identification of stories:

automatic computation

relevance determined by expert knowledge The stories semantics is a refinement of the general semantics driven by expert knowledge

Set of non-singleton stories { a, aP } , { a, c } ,

{ b, c } , { a, aP, c }

Maximal sets of compatible stories

{ a, c } ,

{ a, aP, c } ,

{ a, aP } , { b, c }

s

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`_c = {q₁}

`_adp = {p₁}

`_atp = {p₁,s_aP}

`_b = {q₁,s_c}

`_p = {s_aP, adp₁}

`_q = {s_c}

Stories reduce the dimension of the dynamics

Example: the AT _1A R-induced network

HR

A B C D E F G

SBGN-PD map adapted from: D. Heitzler et al., Competing G protein-coupled receptor kinases balance G protein and b-arrestin signaling, MSB, 2012.

semantics general general stories

with conflicts

No. of automata 41 41 30

No. of reachable states ' 10¹¹ ' 10¹⁰ ' 10⁵

Conclusion and Prospects

Main features of SBGN-PD are supported

The stories semantics is a refinement of the general semantics that:

– models several chemical species with a unique variable

– reduces the state space, increasing the scalability of the exhaustive computation of the dynamics

The dynamics of SBGN-PD maps modelled under both semantics can be analyzed with state-of-the art tools (PRISM, NuSMV . . . )

Ongoing work and prospects:

Application to a large network, the E2F/RB pathway:

– 153 out of 208 molecules in 28 stories

– No. of automata reduced from 367 to 242

Explore the relationship between the stories semantics and

Boolean semantics applied to SBGN-AF maps