Sparsity as Cellular Objective to Infer Directed Metabolic Networks from Steady-State Metabolome Data: A Theoretical Analysis
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{"title"=>"Sparsity as cellular objective to infer directed metabolic networks from steady-state metabolome data: A theoretical analysis", "type"=>"journal", "authors"=>[{"first_name"=>"Melik", "last_name"=>"Öksüz", "scopus_author_id"=>"55892581300"}, {"first_name"=>"Hasan", "last_name"=>"Sadikoǧlu", "scopus_author_id"=>"6603014474"}, {"first_name"=>"Tunahan", "last_name"=>"Çakir", "scopus_author_id"=>"55893508000"}], "year"=>2013, "source"=>"PLoS ONE", "identifiers"=>{"issn"=>"19326203", "pui"=>"372403256", "doi"=>"10.1371/journal.pone.0084505", "sgr"=>"84896721750", "scopus"=>"2-s2.0-84896721750", "isbn"=>"1932-6203 (Electronic)\\r1932-6203 (Linking)", "pmid"=>"24391961"}, "id"=>"3f9acc65-6324-3af5-ba89-7f959501cf7c", "abstract"=>"Since metabolome data are derived from the underlying metabolic network, reverse engineering of such data to recover the network topology is of wide interest. Lyapunov equation puts a constraint to the link between data and network by coupling the covariance of data with the strength of interactions (Jacobian matrix). This equation, when expressed as a linear set of equations at steady state, constitutes a basis to infer the network structure given the covariance matrix of data. The sparse structure of metabolic networks points to reactions which are active based on minimal enzyme production, hinting at sparsity as a cellular objective. Therefore, for a given covariance matrix, we solved Lyapunov equation to calculate Jacobian matrix by a simultaneous use of minimization of Euclidean norm of residuals and maximization of sparsity (the number of zeros in Jacobian matrix) as objective functions to infer directed small-scale networks from three kingdoms of life (bacteria, fungi, mammalian). The inference performance of the approach was found to be promising, with zero False Positive Rate, and almost one True positive Rate. The effect of missing data on results was additionally analyzed, revealing superiority over similarity-based approaches which infer undirected networks. Our findings suggest that the covariance of metabolome data implies an underlying network with sparsest pattern. The theoretical analysis forms a framework for further investigation of sparsity-based inference of metabolic networks from real metabolome data.", "link"=>"http://www.mendeley.com/research/sparsity-cellular-objective-infer-directed-metabolic-networks-steadystate-metabolome-data-theoretica", "reader_count"=>11, "reader_count_by_academic_status"=>{"Professor > Associate Professor"=>1, "Researcher"=>6, "Student > Ph. D. Student"=>2, "Student > Master"=>1, "Student > Doctoral Student"=>1}, "reader_count_by_user_role"=>{"Professor > Associate Professor"=>1, "Researcher"=>6, "Student > Ph. D. Student"=>2, "Student > Master"=>1, "Student > Doctoral Student"=>1}, "reader_count_by_subject_area"=>{"Biochemistry, Genetics and Molecular Biology"=>3, "Mathematics"=>1, "Agricultural and Biological Sciences"=>5, "Chemistry"=>1, "Chemical Engineering"=>1}, "reader_count_by_subdiscipline"=>{"Chemistry"=>{"Chemistry"=>1}, "Agricultural and Biological Sciences"=>{"Agricultural and Biological Sciences"=>5}, "Biochemistry, Genetics and Molecular Biology"=>{"Biochemistry, Genetics and Molecular Biology"=>3}, "Mathematics"=>{"Mathematics"=>1}, "Chemical Engineering"=>{"Chemical Engineering"=>1}}, "group_count"=>1}

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Figshare

  • {"files"=>["https://ndownloader.figshare.com/files/1335498"], "description"=>"<p>Our approach generates networks with very high TPR and no FPRs. Also, there is full correlation between the interaction strengths of real networks and inferred networks.</p>", "links"=>[], "tags"=>["Biochemistry", "metabolism", "Computational biology", "Biochemical simulations", "Metabolic networks", "systems biology", "signal processing", "data mining", "Applied mathematics", "algorithms", "metabolic"], "article_id"=>891736, "categories"=>["Biological Sciences", "Mathematics", "Engineering"], "users"=>["Melik Öksüz", "Hasan Sadıkoğlu", "Tunahan Çakır"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0084505.t001", "stats"=>{"downloads"=>1, "page_views"=>11, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Inference_results_for_three_metabolic_systems_/891736", "title"=>"Inference results for three metabolic systems.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2013-12-31 05:49:19"}
  • {"files"=>["https://ndownloader.figshare.com/files/1335501"], "description"=>"<div><p>Since metabolome data are derived from the underlying metabolic network, reverse engineering of such data to recover the network topology is of wide interest. Lyapunov equation puts a constraint to the link between data and network by coupling the covariance of data with the strength of interactions (Jacobian matrix). This equation, when expressed as a linear set of equations at steady state, constitutes a basis to infer the network structure given the covariance matrix of data. The sparse structure of metabolic networks points to reactions which are active based on minimal enzyme production, hinting at sparsity as a cellular objective. Therefore, for a given covariance matrix, we solved Lyapunov equation to calculate Jacobian matrix by a simultaneous use of minimization of Euclidean norm of residuals and maximization of sparsity (the number of zeros in Jacobian matrix) as objective functions to infer directed small-scale networks from three kingdoms of life (bacteria, fungi, mammalian). The inference performance of the approach was found to be promising, with zero False Positive Rate, and almost one True positive Rate. The effect of missing data on results was additionally analyzed, revealing superiority over similarity-based approaches which infer undirected networks. Our findings suggest that the covariance of metabolome data implies an underlying network with sparsest pattern. The theoretical analysis forms a framework for further investigation of sparsity-based inference of metabolic networks from real metabolome data.</p></div>", "links"=>[], "tags"=>["Biochemistry", "metabolism", "Computational biology", "Biochemical simulations", "Metabolic networks", "systems biology", "signal processing", "data mining", "Applied mathematics", "algorithms", "cellular", "infer", "directed", "metabolic", "networks", "steady-state", "metabolome"], "article_id"=>891739, "categories"=>["Biological Sciences", "Mathematics", "Engineering"], "users"=>["Melik Öksüz", "Hasan Sadıkoğlu", "Tunahan Çakır"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0084505", "stats"=>{"downloads"=>1, "page_views"=>12, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Sparsity_as_Cellular_Objective_to_Infer_Directed_Metabolic_Networks_from_Steady_State_Metabolome_Data_A_Theoretical_Analysis_/891739", "title"=>"Sparsity as Cellular Objective to Infer Directed Metabolic Networks from Steady-State Metabolome Data: A Theoretical Analysis", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2013-12-31 05:49:19"}
  • {"files"=>["https://ndownloader.figshare.com/files/1335499"], "description"=>"<p>Note that reported TPRs and FPRs are for directed network inference in our case whereas they are for undirected network inference for GGM method.</p><p>In <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0084505#pone.0084505-akir1\" target=\"_blank\">[6]</a>, two types of in silico steady-state data were generated. For details, check the related reference.</p>", "links"=>[], "tags"=>["Biochemistry", "metabolism", "Computational biology", "Biochemical simulations", "Metabolic networks", "systems biology", "signal processing", "data mining", "Applied mathematics", "algorithms", "similarity-based", "ggm"], "article_id"=>891737, "categories"=>["Biological Sciences", "Mathematics", "Engineering"], "users"=>["Melik Öksüz", "Hasan Sadıkoğlu", "Tunahan Çakır"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0084505.t002", "stats"=>{"downloads"=>1, "page_views"=>6, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Comparison_of_performance_of_our_approach_with_similarity_based_GGM_method_/891737", "title"=>"Comparison of performance of our approach with similarity-based GGM method.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2013-12-31 05:49:19"}
  • {"files"=>["https://ndownloader.figshare.com/files/1335500"], "description"=>"<p>Results are average of 10 noise-incorporated repetitions. Note that reported TPRs, FPRs and Spearman Correlations (R<sub>sp</sub>) are for directed network inference in our case whereas they are for undirected network inference for GGM method.</p><p>Value becomes 0.76 when interaction direction is not considered.</p><p>Value becomes 0.69 when interaction direction is not considered.</p>", "links"=>[], "tags"=>["Biochemistry", "metabolism", "Computational biology", "Biochemical simulations", "Metabolic networks", "systems biology", "signal processing", "data mining", "Applied mathematics", "algorithms", "inference", "directed", "undirected", "similarity-based", "ggm"], "article_id"=>891738, "categories"=>["Biological Sciences", "Mathematics", "Engineering"], "users"=>["Melik Öksüz", "Hasan Sadıkoğlu", "Tunahan Çakır"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0084505.t003", "stats"=>{"downloads"=>2, "page_views"=>10, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Effect_of_noise_on_the_inference_of_S_cerevisiae_network_for_our_directed_approach_and_for_undirected_similarity_based_GGM_approach_/891738", "title"=>"Effect of noise on the inference of <i>S. cerevisiae</i> network for our directed approach and for undirected similarity-based GGM approach.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2013-12-31 05:49:19"}
  • {"files"=>["https://ndownloader.figshare.com/files/1335497"], "description"=>"<p>The gene network is from <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0084505#pone.0084505-Kubat1\" target=\"_blank\">[24]</a>. The genetic-algorithm-coded approach uses covariance matrix as an input to predict interaction strengths (Jacobian matrix) based on a mathematical dual objective of maximal number of zeros and minimal Euclidean norm of the residuals. See also the algorithm presented in Supporting <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0084505#pone.0084505.s001\" target=\"_blank\">Information S1</a>.</p>", "links"=>[], "tags"=>["Biochemistry", "metabolism", "Computational biology", "Biochemical simulations", "Metabolic networks", "systems biology", "signal processing", "data mining", "Applied mathematics", "algorithms", "lyapunov-equation", "sparsity", "cellular"], "article_id"=>891735, "categories"=>["Biological Sciences", "Mathematics", "Engineering"], "users"=>["Melik Öksüz", "Hasan Sadıkoğlu", "Tunahan Çakır"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0084505.g001", "stats"=>{"downloads"=>0, "page_views"=>21, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Illustrating_Lyapunov_equation_based_approach_to_use_sparsity_as_cellular_objective_to_predict_underlying_network_structure_/891735", "title"=>"Illustrating Lyapunov-equation based approach to use sparsity as cellular objective to predict underlying network structure.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-12-31 05:49:19"}

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Relative Metric

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