Non Linear Programming (NLP) Formulation for Quantitative Modeling of Protein Signal Transduction Pathways
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{"title"=>"Non Linear Programming (NLP) Formulation for Quantitative Modeling of Protein Signal Transduction Pathways", "type"=>"journal", "authors"=>[{"first_name"=>"Alexander", "last_name"=>"Mitsos", "scopus_author_id"=>"8979766700"}, {"first_name"=>"Ioannis N.", "last_name"=>"Melas", "scopus_author_id"=>"35491332700"}, {"first_name"=>"Melody K.", "last_name"=>"Morris", "scopus_author_id"=>"36464016600"}, {"first_name"=>"Julio", "last_name"=>"Saez-Rodriguez", "scopus_author_id"=>"24473386000"}, {"first_name"=>"Douglas A.", "last_name"=>"Lauffenburger", "scopus_author_id"=>"7101609910"}, {"first_name"=>"Leonidas G.", "last_name"=>"Alexopoulos", "scopus_author_id"=>"55889907300"}], "year"=>2012, "source"=>"PLoS ONE", "identifiers"=>{"doi"=>"10.1371/journal.pone.0050085", "sgr"=>"84870577280", "issn"=>"19326203", "pui"=>"366207264", "pmid"=>"23226239", "scopus"=>"2-s2.0-84870577280"}, "id"=>"a0b8da79-ae24-3d92-a0c3-88890df8d6a2", "abstract"=>"Modeling of signal transduction pathways plays a major role in understanding cells' function and predicting cellular response. Mathematical formalisms based on a logic formalism are relatively simple but can describe how signals propagate from one protein to the next and have led to the construction of models that simulate the cells response to environmental or other perturbations. Constrained fuzzy logic was recently introduced to train models to cell specific data to result in quantitative pathway models of the specific cellular behavior. There are two major issues in this pathway optimization: i) excessive CPU time requirements and ii) loosely constrained optimization problem due to lack of data with respect to large signaling pathways. Herein, we address both issues: the former by reformulating the pathway optimization as a regular nonlinear optimization problem; and the latter by enhanced algorithms to pre/post-process the signaling network to remove parts that cannot be identified given the experimental conditions. As a case study, we tackle the construction of cell type specific pathways in normal and transformed hepatocytes using medium and large-scale functional phosphoproteomic datasets. The proposed Non Linear Programming (NLP) formulation allows for fast optimization of signaling topologies by combining the versatile nature of logic modeling with state of the art optimization algorithms.", "link"=>"http://www.mendeley.com/research/non-linear-programming-nlp-formulation-quantitative-modeling-protein-signal-transduction-pathways-4", "reader_count"=>57, "reader_count_by_academic_status"=>{"Unspecified"=>1, "Researcher"=>20, "Student > Doctoral Student"=>4, "Student > Ph. D. Student"=>17, "Student > Master"=>10, "Other"=>3, "Student > Bachelor"=>2}, "reader_count_by_user_role"=>{"Unspecified"=>1, "Researcher"=>20, "Student > Doctoral Student"=>4, "Student > Ph. D. Student"=>17, "Student > Master"=>10, "Other"=>3, "Student > Bachelor"=>2}, "reader_count_by_subject_area"=>{"Engineering"=>10, "Unspecified"=>2, "Biochemistry, Genetics and Molecular Biology"=>7, "Agricultural and Biological Sciences"=>28, "Neuroscience"=>1, "Pharmacology, Toxicology and Pharmaceutical Science"=>1, "Physics and Astronomy"=>2, "Chemical Engineering"=>1, "Computer Science"=>5}, "reader_count_by_subdiscipline"=>{"Engineering"=>{"Engineering"=>10}, "Neuroscience"=>{"Neuroscience"=>1}, "Physics and Astronomy"=>{"Physics and Astronomy"=>2}, "Agricultural and Biological Sciences"=>{"Agricultural and Biological Sciences"=>28}, "Computer Science"=>{"Computer Science"=>5}, "Biochemistry, Genetics and Molecular Biology"=>{"Biochemistry, Genetics and Molecular Biology"=>7}, "Unspecified"=>{"Unspecified"=>2}, "Pharmacology, Toxicology and Pharmaceutical Science"=>{"Pharmacology, Toxicology and Pharmaceutical Science"=>1}, "Chemical Engineering"=>{"Chemical Engineering"=>1}}, "reader_count_by_country"=>{"Austria"=>1, "Iran"=>1, "United States"=>5, "Japan"=>1, "Denmark"=>1, "United Kingdom"=>1, "India"=>1}, "group_count"=>4}

Scopus | Further Information

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Figshare

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  • {"files"=>["https://ndownloader.figshare.com/files/531709"], "description"=>"<p>The transfer functions supported by the proposed constrained fuzzy logic (cFL) formulation are illustrated. (A) “single reactant – single product” activation. (B) AND gate with two reacting species. (C) OR gate with two signaling species., (D) “single reactant – single product” inhibition. In all instances, function <i>f(x)</i> refers to the normalized hill function, with <i>p = 0.5, a = 1.0</i> and <i>n = 4</i>.</p>", "links"=>[], "tags"=>["modules", "signaling", "pathways", "constrained", "fuzzy"], "article_id"=>202194, "categories"=>["Information And Computing Sciences", "Biological Sciences", "Genetics"], "users"=>["Alexander Mitsos", "Ioannis N. Melas", "Melody K. Morris", "Julio Saez-Rodriguez", "Douglas A. Lauffenburger", "Leonidas G. Alexopoulos"], "doi"=>["https://dx.doi.org/10.1371/journal.pone.0050085.g001"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Connectivity_modules_of_signaling_pathways_in_the_proposed_constrained_fuzzy_logic_formulation_/202194", "title"=>"Connectivity modules of signaling pathways in the proposed constrained fuzzy logic formulation.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2012-11-30 00:36:34"}
  • {"files"=>["https://ndownloader.figshare.com/files/531849"], "description"=>"<p>(A) Generic pathway is represented as a signed directed graph, also refers as PKN. Green nodes refer to different cytokines (ligands) where the signaling process initiates; Red nodes refer to inhibitors present in the in-silico dataset; Grey nodes refer to measured proteins; White nodes refer to latent species, i.e. proteins whose activation state is not measured. (B) In-silico signaling data under combinatorial treatment with stimuli (TGFα, TNFα, no-treatment) and inhibitors (mek12i, pi3ki, no-inhibitor). Each subplot shows the average activation level within 30 minutes upon stimulation <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0050085#pone.0050085-Alexopoulos1\" target=\"_blank\">[37]</a>. Red background refers to model-prediction mismatches (C) Optimized pathway, grey arrows refer to reactions with limited activity (<i>z<sub>i</sub><sup>k</sup></i>) (caused by <i>a</i> parameters being close to 0). The opacity of each edge corresponds to the activity (<i>z<sub>i</sub><sup>k</sup></i>) of the corresponding reaction. (D) In silico signaling dataset and fitness error after the optimization procedure. Decrease in the red background color shows the optimized model is in accordance to the signaling dataset. (E) Optimized transfer functions presented in C.</p>", "links"=>[], "tags"=>["signaling"], "article_id"=>202345, "categories"=>["Information And Computing Sciences", "Biological Sciences", "Genetics"], "users"=>["Alexander Mitsos", "Ioannis N. Melas", "Melody K. Morris", "Julio Saez-Rodriguez", "Douglas A. Lauffenburger", "Leonidas G. Alexopoulos"], "doi"=>["https://dx.doi.org/10.1371/journal.pone.0050085.g002"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Optimization_of_a_toy_model_to_signaling_data_/202345", "title"=>"Optimization of a toy model to signaling data.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2012-11-30 00:39:05"}
  • {"files"=>["https://ndownloader.figshare.com/files/531974"], "description"=>"<p>(A) Initial topology as presented in <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0050085#pone.0050085-Morris2\" target=\"_blank\">[33]</a>. (B) Signaling data under combinatorial treatments of 6 stimuli (green nodes) and 7 inhibitors (red nodes) reporting 15 signals (grey nodes). The red background represents the measurement – prediction mismatch of the initial topology (46%) (mean fitness error). To generate model predictions, the initial guesses of all model parameters were used (<i>a = 1.0, p = 0.5</i>). (C) Optimized pathway. Bold lines refer to the optimized pathway after removing redundant/conflicting reactions. Dashed lines refer to reactions present in the family of solutions that although being redundant are reported since they may bare biological significance. The opacity of each edge corresponds to the activity (<i>z<sub>i</sub><sup>k</sup></i>) of the corresponding reaction. (D) Signaling dataset and remaining fitness error (8%) (mean fitness error). The red background refers to the fitness error of the solution. Decrease in the red background compared to (B) implies the optimized model successfully fits the signaling dataset (mean fitness error went from 46% to 8%). A and C were generated using graphviz package (<a href=\"http://www.graphviz.org/\" target=\"_blank\">http://www.graphviz.org/</a>). B and D were generated using Datarail toolbox <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0050085#pone.0050085-SaezRodriguez2\" target=\"_blank\">[52]</a>.</p>", "links"=>[], "tags"=>["medium-scale", "signaling"], "article_id"=>202468, "categories"=>["Information And Computing Sciences", "Biological Sciences", "Genetics"], "users"=>["Alexander Mitsos", "Ioannis N. Melas", "Melody K. Morris", "Julio Saez-Rodriguez", "Douglas A. Lauffenburger", "Leonidas G. Alexopoulos"], "doi"=>["https://dx.doi.org/10.1371/journal.pone.0050085.g003"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Optimization_of_a_medium_scale_model_to_signaling_data_/202468", "title"=>"Optimization of a medium-scale model to signaling data.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2012-11-30 00:41:08"}
  • {"files"=>["https://ndownloader.figshare.com/files/532086"], "description"=>"<p>Blue line represents the fitness error corresponding to all measured data (total fitness error); red line corresponds to the fitness error of the predicted (excluded) data. Total fitness error initiates at ∼8% (mean fitness error) and stays relatively stable for excluded portions of the dataset smaller than 40% of the total. Implying that the proposed approach handles efficiently missing data. Even when no data is excluded (0% point in the plot) the total fitness error is at 8% (mean fitness error) because of conflicts in the data or poor prior knowledge of protein connectivity in the PKN. The fitness error corresponding to the excluded data (red line) initiates at 0% since the removal of random portions of the dataset may leave out of the training process datapoints that are easily inferred from the remaining data. E.g. measurement of MEK1/2 under TGFα and IKKi is easily inferred from TGFα and no-inhib experiment. As increasing portions of the data are left out of the training process (excluded data >40%) the fitness error increases significantly. For excluded portions greater than 80% the fitness error quickly reaches that of the null solution.</p>", "links"=>[], "tags"=>["validation", "nlp", "algorithm"], "article_id"=>202581, "categories"=>["Information And Computing Sciences", "Biological Sciences", "Genetics"], "users"=>["Alexander Mitsos", "Ioannis N. Melas", "Melody K. Morris", "Julio Saez-Rodriguez", "Douglas A. Lauffenburger", "Leonidas G. Alexopoulos"], "doi"=>["https://dx.doi.org/10.1371/journal.pone.0050085.g004"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Cross_validation_of_the_NLP_algorithm_medium_scale_pathway_/202581", "title"=>"Cross validation of the NLP algorithm (medium-scale pathway).", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2012-11-30 00:43:01"}
  • {"files"=>["https://ndownloader.figshare.com/files/532222"], "description"=>"<p>(A) optimized pathway upon compartmentalization based on the equivalent classes concept (right panel). The proposed compartmentalization scheme groups together nodes that share identical in-silico responses under all experimental conditions, thus decreasing the parameters space. (B) Signaling dataset, consisting of 15 cytokines in combinations of two, and 3 inhibitors (including the no-inhibitor treatment), total of 120 experimental treatments (see <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0050085#pone.0050085-Melas2\" target=\"_blank\">[48]</a>). The red background color corresponds to the measurement prediction mismatch of the solution.To generate model predictions the optimized values of all model parameters were used (i.e., parameter values obtained from the optimization procedure)</p>", "links"=>[], "tags"=>["large-scale", "transduction"], "article_id"=>202716, "categories"=>["Information And Computing Sciences", "Biological Sciences", "Genetics"], "users"=>["Alexander Mitsos", "Ioannis N. Melas", "Melody K. Morris", "Julio Saez-Rodriguez", "Douglas A. Lauffenburger", "Leonidas G. Alexopoulos"], "doi"=>["https://dx.doi.org/10.1371/journal.pone.0050085.g005"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Optimization_of_a_large_scale_signal_transduction_pathway_/202716", "title"=>"Optimization of a large-scale signal transduction pathway.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2012-11-30 00:45:16"}
  • {"files"=>["https://ndownloader.figshare.com/files/532377"], "description"=>"<p>Mapping of the optimization results to the PKN by removing the compartmentalized components. Reactions within the same compartment are plotted in blue and were not included in the optimization procedure. Reactions in black are the ones whose parameters were interrogated. Their opacity corresponds to their activity in the optimized model, with reactions that propagate more signal downstream being more opaque than the rest.</p>", "links"=>[], "tags"=>["optimized"], "article_id"=>202879, "categories"=>["Information And Computing Sciences", "Biological Sciences", "Genetics"], "users"=>["Alexander Mitsos", "Ioannis N. Melas", "Melody K. Morris", "Julio Saez-Rodriguez", "Douglas A. Lauffenburger", "Leonidas G. Alexopoulos"], "doi"=>["https://dx.doi.org/10.1371/journal.pone.0050085.g006"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Mapping_of_the_optimized_model_to_the_PKN_/202879", "title"=>"Mapping of the optimized model to the PKN.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2012-11-30 00:47:59"}

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Relative Metric

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