New qualitative approaches in molecular biology

AACTGCTGCATGACTGCTAGCTGATCGAGTACAAACTGCTGC11101000111000101000110011001011101110100111010001110001010001100110010111011TTGACGACGTACTGACGATCGACTAGCTCATGTTTGACGACG00010111000111010111001100110100010001011000101110001110101110011001101000100

Ovidiu Radulescu

IRMAR (UMR 6625), IRISA

University of Rennes 1

AACTGCTGCATGACTGCTAGCTGATCGAGTACAAACTGCTGCATGACTGCTAGCTGATCG11101000111000101000110011001011101110100111010001110001010001100110010111011011TTGACGACGTACTGACGATCGACTAGCTCATGTTTGACGACGTACTGACGATCGACTAGC00010111000111010111001100110100010001011000101110001110101110011001101000100100

Integrate heterogeneous data collected in high-throughput experiments

Use qualitative analysis as unifying modeling framework

Algorithms for creating and for correcting detailed models

Use modeling to propose new experiments

Objectives and methodology

Static response of networks Qualitative analysis Qualitative equations and Galois field coding Comparison model/data Example 1: lactose operon Experiment design Example 2: E.coli transcriptional network

Summary

Static response

Lactose operon

Static response

Topology and response

Differential dynamics dX/dt= F(X,P)

Interaction graph (G,A,s) defined by the Jacobian

A GG, (i,j) A iff F j / xi 0

s:A{-1,1}, s(i,j)=sign( F j / xi )

Steady state F(X,P)=0

Steady state shift X = - ( F/ X) -1 ( F/ P) P

Propagation of interaction, graph boundary

Qualitative equations, sign algebra

Li=Le+LacY-LacZ

Polynomial coding of systems of qualitative equations

Implementation

Software: Gardon, GARMeN, Sigali Coherence between model and data

from interaction graph write qualitative equations Galois field coding substitute experimental values existence of at least one solution coherence

Corection most parcimonious use Hamming distance can be applied to arcs (model) or nodes (data)

Gardon: knowledge data base

GARMeN: modeling support

Experiment design

256 valuations, only 18 solutions of qualitative equationsmany valuations are inconsistent with the model use data to invalidate or validate model

Invalidate

Validation power

Any value of the triplet(Le,G,A) can be extended to a solution

These variables have no validation power

Validation power

Only 2 values (out of 8) of (LacI,A,LacZ), namely(+,, ) (, +,+) can be extended to a solution

Predictive powerGiven (X1,X2,…,Xr,P) a number H(X1,X2,…,Xr,P) of variables (hard components) can be predicted.PP(1,2,…,r)= max H(X1,X2,…,Xr,P) / Nsize of the sphere of influence

Transcriptional network of E.Coli

Without sigma-factors the network is incompatible

microarray data (Guttierez-Rios et al 2006) not compatible with model,it becomes compatible after 6 corrections {xthA,cfa,gor,cpxR,crp,glpR}

1258 nodes 2526 interactions

Conclusions

Tools for qualitative modeling of data

Model validation, model correction, experiment design

sequential reverse engineering Comparison1> Correction1>Comparison2 …

Include heterogeneous data

EWS/FLI1

Acknowledgements

Anne Siegel, Michel Le Borgne, Philippe Veber, projet Symbiose, IRISA Rennes

E.Coli example Carito Vargas

New qualitative approaches in molecular biology

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