Introduction Modelling the Biological Problem GRN Inference Ongoing work Results Summary Inferring parameters in genetic regulatory networks Camilo La Rota 1 Fabien Tarissan 2 Leo Liberti 2 1 Complex Systems Institute (IXXI) Ecole Normale Superieure - CNRS, Lyon, France 2 LIX (Computer science laboratory) Ecole Polytechnique, Palaiseau, France ARS Workshop, LIX-Polytechnique, Palaiseau, October 31 2008 Camilo La Rota, Fabien Tarissan, Leo Liberti Inferring parameters in genetic regulatory networks
Introduction Modelling the Biological Problem GRN Inference Ongoing work Results Summary Outline 1 Introduction Inverse Problems in Biological Complex Systems Biological Context Modelling the Biological Problem 2 Gene Expression, regions and tissues Gene Interaction Network Gene Regulatory Network models GRN Inference 3 Modelling the inverse problem Defining the GRN Defining the inverse problem Mathematical Programming Formulation Definitions Objective Function and Constraints Objective Function and Constraints Reformulation and linearization Camilo La Rota, Fabien Tarissan, Leo Liberti Inferring parameters in genetic regulatory networks Ongoing work 4
Introduction Modelling the Biological Problem GRN Inference Inverse Problems in Biological Complex Systems Ongoing work Biological Context Results Summary Outline 1 Introduction Inverse Problems in Biological Complex Systems Biological Context Modelling the Biological Problem 2 Gene Expression, regions and tissues Gene Interaction Network Gene Regulatory Network models GRN Inference 3 Modelling the inverse problem Defining the GRN Defining the inverse problem Mathematical Programming Formulation Definitions Objective Function and Constraints Objective Function and Constraints Reformulation and linearization Camilo La Rota, Fabien Tarissan, Leo Liberti Inferring parameters in genetic regulatory networks Ongoing work 4
Introduction Modelling the Biological Problem GRN Inference Inverse Problems in Biological Complex Systems Ongoing work Biological Context Results Summary European Morphex Project Biological Problem Complex Systems: Simulation Platform: Solving: Meta-model and Generic pre and post Gene regulatory networks associated simulation tools and and cell interactions in concepts for generic protocols. morphogenesis. designing tools Models and protocols for and protocols. parameter inference. Camilo La Rota, Fabien Tarissan, Leo Liberti Inferring parameters in genetic regulatory networks
Introduction Modelling the Biological Problem GRN Inference Inverse Problems in Biological Complex Systems Ongoing work Biological Context Results Summary Outline 1 Introduction Inverse Problems in Biological Complex Systems Biological Context Modelling the Biological Problem 2 Gene Expression, regions and tissues Gene Interaction Network Gene Regulatory Network models GRN Inference 3 Modelling the inverse problem Defining the GRN Defining the inverse problem Mathematical Programming Formulation Definitions Objective Function and Constraints Objective Function and Constraints Reformulation and linearization Camilo La Rota, Fabien Tarissan, Leo Liberti Inferring parameters in genetic regulatory networks Ongoing work 4
Introduction Modelling the Biological Problem GRN Inference Inverse Problems in Biological Complex Systems Ongoing work Biological Context Results Summary Genetic regulatory networks (GRN) and morphogenesis Developmental stages of Arabidopsis Thaliana Arabidopsis Flower Development GRN dynamics + other factors : morphogenesis, structure, tissue diversity Continuous development Discrete stages Genetic Control of Morphogenesis Camilo La Rota, Fabien Tarissan, Leo Liberti Inferring parameters in genetic regulatory networks
Introduction Modelling the Biological Problem GRN Inference Inverse Problems in Biological Complex Systems Ongoing work Biological Context Results Summary GRN Subnetworks’ Stability Mutants stable states ∼ Unstable states at wild-type stages. Camilo La Rota, Fabien Tarissan, Leo Liberti Inferring parameters in genetic regulatory networks
Introduction Modelling the Biological Problem Gene Expression, regions and tissues GRN Inference Gene Interaction Network Ongoing work Gene Regulatory Network models Results Summary Outline 1 Introduction Inverse Problems in Biological Complex Systems Biological Context Modelling the Biological Problem 2 Gene Expression, regions and tissues Gene Interaction Network Gene Regulatory Network models GRN Inference 3 Modelling the inverse problem Defining the GRN Defining the inverse problem Mathematical Programming Formulation Definitions Objective Function and Constraints Objective Function and Constraints Reformulation and linearization Camilo La Rota, Fabien Tarissan, Leo Liberti Inferring parameters in genetic regulatory networks Ongoing work 4
Introduction Modelling the Biological Problem Gene Expression, regions and tissues GRN Inference Gene Interaction Network Ongoing work Gene Regulatory Network models Results Summary Gene Expression, regions and tissues Expression data mRNA spatiotemporal distribution Qualitative Imprecise Time-discrete Exploiting the data Superposition of expression patterns reveals regions. Data is difficult to analyze, multiple interpretations are possible. Tentative subdivisions in homogeneous regions are proposed. Camilo La Rota, Fabien Tarissan, Leo Liberti Inferring parameters in genetic regulatory networks
Introduction Modelling the Biological Problem Gene Expression, regions and tissues GRN Inference Gene Interaction Network Ongoing work Gene Regulatory Network models Results Summary Cell or tissue lineage Camilo La Rota, Fabien Tarissan, Leo Liberti Inferring parameters in genetic regulatory networks
Introduction Modelling the Biological Problem Gene Expression, regions and tissues GRN Inference Gene Interaction Network Ongoing work Gene Regulatory Network models Results Summary Outline 1 Introduction Inverse Problems in Biological Complex Systems Biological Context Modelling the Biological Problem 2 Gene Expression, regions and tissues Gene Interaction Network Gene Regulatory Network models GRN Inference 3 Modelling the inverse problem Defining the GRN Defining the inverse problem Mathematical Programming Formulation Definitions Objective Function and Constraints Objective Function and Constraints Reformulation and linearization Camilo La Rota, Fabien Tarissan, Leo Liberti Inferring parameters in genetic regulatory networks Ongoing work 4
Introduction Modelling the Biological Problem Gene Expression, regions and tissues GRN Inference Gene Interaction Network Ongoing work Gene Regulatory Network models Results Summary Gene Interaction Network Interaction data Molecular evidence Genetic evidence Exploiting the Data Uncertain Conflicting interpretations Error prone Prior Interaction Network Camilo La Rota, Fabien Tarissan, Leo Liberti Inferring parameters in genetic regulatory networks
Introduction Modelling the Biological Problem Gene Expression, regions and tissues GRN Inference Gene Interaction Network Ongoing work Gene Regulatory Network models Results Summary Outline 1 Introduction Inverse Problems in Biological Complex Systems Biological Context Modelling the Biological Problem 2 Gene Expression, regions and tissues Gene Interaction Network Gene Regulatory Network models GRN Inference 3 Modelling the inverse problem Defining the GRN Defining the inverse problem Mathematical Programming Formulation Definitions Objective Function and Constraints Objective Function and Constraints Reformulation and linearization Camilo La Rota, Fabien Tarissan, Leo Liberti Inferring parameters in genetic regulatory networks Ongoing work 4
Introduction Modelling the Biological Problem Gene Expression, regions and tissues GRN Inference Gene Interaction Network Ongoing work Gene Regulatory Network models Results Summary Gene Regulatory Network models Gene transcription mechanisms, mass action kinetics: the Shea-Ackers model Quantitative activity of gene i d ([ x i ]( t )) = f i ([ P ] , [ x 1 ] ,..., [ x m ]) − λ i [ x i ] dt f i ([ P ] , [ x 1 ] ,..., [ x m ]) = ∑ ν ( s ) P ( s i = s ) s ∈ S i K B ( s )[ P ] α s [ x 1 ] α 1 s ... [ x m ] α m s P ( s i = s ) = K B ( z )[ P ] α z [ x 1 ] α 1 z ... [ x m ] α m 1 + ∑ z z ∈ Si Exemples of regulatory phenomena Activation f i ([ P ] , [ x a ]) = [ P ]( ν p K p + ν ap K ap [ x a ]) 1 + K p [ P ]+ K a [ x a ]+ K ap [ x a ][ P ] Camilo La Rota, Fabien Tarissan, Leo Liberti Inferring parameters in genetic regulatory networks
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