Dynamic Properties of Network Motifs Contribute to Biological Network Organization
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{"title"=>"Dynamic properties of network motifs contribute to biological network organization", "type"=>"journal", "authors"=>[{"first_name"=>"Robert J.", "last_name"=>"Prill", "scopus_author_id"=>"36916876700"}, {"first_name"=>"Pablo A.", "last_name"=>"Iglesias", "scopus_author_id"=>"26643366900"}, {"first_name"=>"Andre", "last_name"=>"Levchenko", "scopus_author_id"=>"55789505518"}], "year"=>2005, "source"=>"PLoS Biology", "identifiers"=>{"issn"=>"15449173", "scopus"=>"2-s2.0-27844551326", "pui"=>"41652440", "doi"=>"10.1371/journal.pbio.0030343", "isbn"=>"1545-7885 (Linking)", "sgr"=>"27844551326", "pmid"=>"16187794"}, "id"=>"3138cf81-1e83-38e8-933a-744975d8fd06", "abstract"=>"Biological networks, such as those describing gene regulation, signal transduction, and neural synapses, are representations of large-scale dynamic systems. Discovery of organizing principles of biological networks can be enhanced by embracing the notion that there is a deep interplay between network structure and system dynamics. Recently, many structural characteristics of these non-random networks have been identified, but dynamical implications of the features have not been explored comprehensively. We demonstrate by exhaustive computational analysis that a dynamical property--stability or robustness to small perturbations--is highly correlated with the relative abundance of small subnetworks (network motifs) in several previously determined biological networks. We propose that robust dynamical stability is an influential property that can determine the non-random structure of biological networks.", "link"=>"http://www.mendeley.com/research/dynamic-properties-network-motifs-contribute-biological-network-organization-5", "reader_count"=>327, "reader_count_by_academic_status"=>{"Unspecified"=>7, "Professor > Associate Professor"=>29, "Librarian"=>1, "Researcher"=>90, "Student > Doctoral Student"=>8, "Student > Ph. D. Student"=>100, "Student > Postgraduate"=>10, "Other"=>10, "Student > Master"=>36, "Student > Bachelor"=>17, "Lecturer"=>2, "Lecturer > Senior Lecturer"=>1, "Professor"=>16}, "reader_count_by_user_role"=>{"Unspecified"=>7, "Professor > Associate Professor"=>29, "Librarian"=>1, "Researcher"=>90, "Student > Doctoral Student"=>8, "Student > Ph. D. Student"=>100, "Student > Postgraduate"=>10, "Other"=>10, "Student > Master"=>36, "Student > Bachelor"=>17, "Lecturer"=>2, "Lecturer > Senior Lecturer"=>1, "Professor"=>16}, "reader_count_by_subject_area"=>{"Unspecified"=>13, "Agricultural and Biological Sciences"=>161, "Philosophy"=>1, "Business, Management and Accounting"=>2, "Chemical Engineering"=>1, "Chemistry"=>6, "Computer Science"=>37, "Earth and Planetary Sciences"=>1, "Economics, Econometrics and Finance"=>1, "Engineering"=>22, "Environmental Science"=>6, "Biochemistry, Genetics and Molecular Biology"=>11, "Materials Science"=>1, "Mathematics"=>11, "Medicine and Dentistry"=>16, "Neuroscience"=>12, "Physics and Astronomy"=>21, "Psychology"=>3, "Social Sciences"=>1}, "reader_count_by_subdiscipline"=>{"Materials Science"=>{"Materials Science"=>1}, "Medicine and Dentistry"=>{"Medicine and Dentistry"=>16}, "Social Sciences"=>{"Social Sciences"=>1}, "Physics and Astronomy"=>{"Physics and Astronomy"=>21}, "Psychology"=>{"Psychology"=>3}, "Mathematics"=>{"Mathematics"=>11}, "Unspecified"=>{"Unspecified"=>13}, "Environmental Science"=>{"Environmental Science"=>6}, "Chemical Engineering"=>{"Chemical Engineering"=>1}, "Engineering"=>{"Engineering"=>22}, "Chemistry"=>{"Chemistry"=>6}, "Neuroscience"=>{"Neuroscience"=>12}, "Earth and Planetary Sciences"=>{"Earth and Planetary Sciences"=>1}, "Economics, Econometrics and Finance"=>{"Economics, Econometrics and Finance"=>1}, "Agricultural and Biological Sciences"=>{"Agricultural and Biological Sciences"=>161}, "Computer Science"=>{"Computer Science"=>37}, "Business, Management and Accounting"=>{"Business, Management and Accounting"=>2}, "Biochemistry, Genetics and Molecular Biology"=>{"Biochemistry, Genetics and Molecular Biology"=>11}, "Philosophy"=>{"Philosophy"=>1}}, "reader_count_by_country"=>{"Republic of Singapore"=>1, "United States"=>13, "Netherlands"=>2, "Latvia"=>1, "Austria"=>1, "Sweden"=>1, "Ireland"=>1, "China"=>2, "Brazil"=>3, "Serbia and Montenegro"=>1, "France"=>2, "Colombia"=>1, "Argentina"=>1, "Japan"=>5, "United Kingdom"=>9, "Belarus"=>1, "Switzerland"=>2, "Spain"=>3, "India"=>1, "New Zealand"=>1, "Canada"=>3, "Turkey"=>1, "Norway"=>1, "Denmark"=>1, "Mexico"=>1, "Australia"=>1, "Germany"=>4}, "group_count"=>17}

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Figshare

  • {"files"=>["https://ndownloader.figshare.com/files/961742"], "description"=>"<p>Density groups consisting of four, five, and six-edge network motifs contain at least one motif in each stability class. Box and whisker plots indicate a difference in the average Z score between stability classes (I, II, and III correspond to SSS = 1, SSS ≈ 0.4, and SSS < 0.2, respectively). The networks examined here are the transcriptional networks of (A) <i>E. coli,</i> (B) <i>S. cerevisiae,</i> (C) STKE network, (D) <i>D. melanogaster</i> developmental transcriptional network, and (E) <i>C. elegans</i> neuronal network. A box and whisker plot is interpreted as follows: The box indicates the inner quartile range. The median Z score is indicated by a horizontal red line within the box. The whiskers extend to cover the upper and lower quartiles up to a distance of 1.5 times the inner quartile range. Red crosses indicate extreme scores (beyond the whisker length). <i>P</i>-values attached to each plot express the probability that the observed difference in Z scores between stability classes is expected by chance.</p>", "links"=>[], "tags"=>["scores", "four-node", "classified"], "article_id"=>631731, "categories"=>["Biotechnology", "Biochemistry", "Biophysics", "Biological Sciences", "Medicine", "Evolutionary Biology"], "users"=>["Robert J Prill", "Pablo A Iglesias", "Andre Levchenko"], "doi"=>"https://dx.doi.org/10.1371/journal.pbio.0030343.g005", "stats"=>{"downloads"=>1, "page_views"=>11, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Z_Scores_of_Four_Node_Network_Motifs_Classified_by_Stability_/631731", "title"=>"Z Scores of Four-Node Network Motifs, Classified by Stability", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-22 08:59:24"}
  • {"files"=>["https://ndownloader.figshare.com/files/961466"], "description"=>"<p>The number of instances of all three-node (left) and four-node (right) motifs in biological networks (log scale), and SSS (black dashed line). The motifs are sorted on the <i>x</i>-axis from high to low SSS.</p>", "links"=>[], "tags"=>["motif", "correlated"], "article_id"=>631460, "categories"=>["Biotechnology", "Biochemistry", "Biophysics", "Biological Sciences", "Medicine", "Evolutionary Biology"], "users"=>["Robert J Prill", "Pablo A Iglesias", "Andre Levchenko"], "doi"=>"https://dx.doi.org/10.1371/journal.pbio.0030343.g002", "stats"=>{"downloads"=>1, "page_views"=>4, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Abundance_of_a_Motif_Is_Correlated_with_Its_SSS_/631460", "title"=>"Abundance of a Motif Is Correlated with Its SSS", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-22 08:57:30"}
  • {"files"=>["https://ndownloader.figshare.com/files/961406"], "description"=>"<div><p>(Top) Schematic of a simple feedback circuit with the nodes and edges labeled.</p>\n <p>(Middle) We illustrate the dependence of stability on the values of <i>a</i><sub>12</sub> and <i>a</i><sub>21</sub> as they are varied from −1 to 1, with constant self-degradation terms <i>a</i><sub>11</sub> = −0.3 and <i>a</i><sub>22</sub> = −0.7. The system can be stable (green), oscillatory (blue), or unstable (red). These regions are determined by gain k = <i>a</i><sub>12</sub><i>a</i><sub>21</sub>. Shown in white are contours of constant gain k. The quadrants labeled (+) correspond to positive feedback (<i>a</i><sub>12</sub> and <i>a</i><sub>11</sub> have the same sign), while the quadrants labeled (−) correspond to negative feedback (<i>a</i><sub>11</sub> and <i>a</i><sub>21</sub> have opposite signs).</p>\n <p>(Bottom) The stability regions vary as the values of self-degradation terms <i>a</i><sub>11</sub> and <i>a</i><sub>12</sub> change. The more stable the open-loop nodes (more negative <i>a</i><sub>11</sub> and <i>a</i><sub>22</sub>), the greater the regions of closed-loop stability. However, if <i>a</i><sub>11</sub> and <i>a</i><sub>22</sub> are close in sign and magnitude, the size of the oscillatory regions increases.</p></div>", "links"=>[], "tags"=>["behaviors", "two-node", "perturbation"], "article_id"=>631397, "categories"=>["Biotechnology", "Biochemistry", "Biophysics", "Biological Sciences", "Medicine", "Evolutionary Biology"], "users"=>["Robert J Prill", "Pablo A Iglesias", "Andre Levchenko"], "doi"=>"https://dx.doi.org/10.1371/journal.pbio.0030343.g001", "stats"=>{"downloads"=>1, "page_views"=>4, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Dynamic_Behaviors_of_a_Two_Node_Feedback_Loop_in_Response_to_a_Small_Perturbation_from_Steady_State_/631397", "title"=>"Dynamic Behaviors of a Two-Node Feedback Loop in Response to a Small Perturbation from Steady-State", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-22 08:57:01"}
  • {"files"=>["https://ndownloader.figshare.com/files/475022", "https://ndownloader.figshare.com/files/475037", "https://ndownloader.figshare.com/files/475051", "https://ndownloader.figshare.com/files/475065", "https://ndownloader.figshare.com/files/475080", "https://ndownloader.figshare.com/files/475102", "https://ndownloader.figshare.com/files/475131"], "description"=>"<div><p>Biological networks, such as those describing gene regulation, signal transduction, and neural synapses, are representations of large-scale dynamic systems. Discovery of organizing principles of biological networks can be enhanced by embracing the notion that there is a deep interplay between network structure and system dynamics. Recently, many structural characteristics of these non-random networks have been identified, but dynamical implications of the features have not been explored comprehensively. We demonstrate by exhaustive computational analysis that a dynamical property—stability or robustness to small perturbations—is highly correlated with the relative abundance of small subnetworks (network motifs) in several previously determined biological networks. We propose that robust dynamical stability is an influential property that can determine the non-random structure of biological networks.</p> </div>", "links"=>[], "tags"=>["properties", "motifs"], "article_id"=>153606, "categories"=>["Biotechnology", "Biochemistry", "Biophysics", "Biological Sciences", "Medicine", "Evolutionary Biology"], "users"=>["Robert J Prill", "Pablo A Iglesias", "Andre Levchenko"], "doi"=>["https://dx.doi.org/10.1371/journal.pbio.0030343.sg001", "https://dx.doi.org/10.1371/journal.pbio.0030343.sg002", "https://dx.doi.org/10.1371/journal.pbio.0030343.sg003", "https://dx.doi.org/10.1371/journal.pbio.0030343.sg004", "https://dx.doi.org/10.1371/journal.pbio.0030343.sg005", "https://dx.doi.org/10.1371/journal.pbio.0030343.sd001", "https://dx.doi.org/10.1371/journal.pbio.0030343.sd002"], "stats"=>{"downloads"=>15, "page_views"=>9, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/Dynamic_Properties_of_Network_Motifs_Contribute_to_Biological_Network_Organization/153606", "title"=>"Dynamic Properties of Network Motifs Contribute to Biological Network Organization", "pos_in_sequence"=>0, "defined_type"=>4, "published_date"=>"2013-01-20 13:39:22"}
  • {"files"=>["https://ndownloader.figshare.com/files/961811"], "description"=>"<div><p>(I) An example network motif (10) depicted with nodes and edges labeled. The sign and weight of an edge from node <i>j</i> to node <i>i</i> is denoted <i>a<sub>ij</sub></i> (solid line) consistent with the notation in the rest of the figure. Additionally, we assume that every node may have a self-interaction <i>a<sub>ii</sub></i> (dotted line).</p>\n <p>(II) A motif is a graphical depiction of a dynamical system that can be modeled using (possibly nonlinear) ordinary differential equations, which are functions of the state of the nodes in the motif.</p>\n <p>(III) Assuming that the motif can achieve steady-state dynamics, the stability of the equilibrium may be analyzed by making a linear approximation of the (possibly nonlinear) functions. Linearization involves computation of the Jacobian, a matrix of partial derivatives of the functional dependencies expressed in the equations with respect to the variables. The linearized system is evaluated at the equilibrium point(s), resulting in specific values of <i>a<sub>ij</sub></i>.</p>\n <p>(IV) The general form of the Jacobian matrix corresponding to this motif contains zero entries wherever one node exerts no influence on another node and non-zero elements wherever it does. An instance of a Jacobian consistent with the corresponding motif is created by sampling the non-zero terms from some distribution. Eigenvalues of the Jacobian indicate the local stability properties of the equilibrium point. Sampling many instances of structurally equivalent Jacobians allows computation of the <i>probability</i> of stability of an equilibrium point.</p></div>", "links"=>[], "tags"=>["modeling"], "article_id"=>631799, "categories"=>["Biotechnology", "Biochemistry", "Biophysics", "Biological Sciences", "Medicine", "Evolutionary Biology"], "users"=>["Robert J Prill", "Pablo A Iglesias", "Andre Levchenko"], "doi"=>"https://dx.doi.org/10.1371/journal.pbio.0030343.g006", "stats"=>{"downloads"=>1, "page_views"=>11, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Scheme_for_Modeling_the_Local_Stability_of_a_Network_Motif_/631799", "title"=>"Scheme for Modeling the Local Stability of a Network Motif", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-22 08:59:53"}
  • {"files"=>["https://ndownloader.figshare.com/files/961651"], "description"=>"<div><p>(Top panel) All 199 motifs are sorted on the <i>x</i>-axis first, according to increasing number of edges (solid red line). For a given number of edges, they are then sorted from high to low SSS (black bars).</p>\n <p>(Bottom five panels) Normalized Z scores (green bars) for all 199 network motifs of the indicated biological networks, shown with outlines of the SSS from the top panel (dotted black outline provided as a guide to the eye). Each vertical red line indicates a change in the number of motif edges, indicating boundaries of density groups. The composition of the four-node density groups is specified in <a href=\"http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.0030343#sd002\" target=\"_blank\">Protocol S1</a>.</p></div>", "links"=>[], "tags"=>["normalized", "scores", "four-node"], "article_id"=>631640, "categories"=>["Biotechnology", "Biochemistry", "Biophysics", "Biological Sciences", "Medicine", "Evolutionary Biology"], "users"=>["Robert J Prill", "Pablo A Iglesias", "Andre Levchenko"], "doi"=>"https://dx.doi.org/10.1371/journal.pbio.0030343.g004", "stats"=>{"downloads"=>1, "page_views"=>3, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Distribution_of_Normalized_Z_Scores_of_Four_Node_Network_Motifs_/631640", "title"=>"Distribution of Normalized Z Scores of Four-Node Network Motifs", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-22 08:58:46"}
  • {"files"=>["https://ndownloader.figshare.com/files/961561"], "description"=>"<div><p>(Top panel, left) All 13 network motifs are sorted on the <i>x</i>-axis first, according to increasing number of edges (solid red line). For a given number of edges, they are then sorted from high to low SSS (black bars).</p>\n <p>(Bottom five panels, left) Normalized Z scores (green bars) for all 13 motifs of the transcriptional networks of <i>E. coli</i> and <i>S. cerevisiae</i>, STKE network, <i>D. melanogaster</i> developmental transcriptional network, and <i>C. elegans</i> neuronal network, shown with outlines of the SSS from the top panel (dotted black outline provided as a guide to the eye). Each vertical red line indicates a change in the number of motif edges, indicating boundaries of density groups.</p>\n <p>(Right) Z scores of network motifs in the three-edge and four-edge density groups are plotted in columns labeled I, II, and III, corresponding to the three stability classes, SSS = 1, SSS ≈ 0.4, and SSS < 0.2, respectively. Note that the four-edge density group does not contain any motifs with SSS = 1 since four edges among three nodes dictates at least one feedback loop.</p></div>", "links"=>[], "tags"=>["normalized", "scores", "three-node", "motifs", "classified", "groups"], "article_id"=>631545, "categories"=>["Biotechnology", "Biochemistry", "Biophysics", "Biological Sciences", "Medicine", "Evolutionary Biology"], "users"=>["Robert J Prill", "Pablo A Iglesias", "Andre Levchenko"], "doi"=>"https://dx.doi.org/10.1371/journal.pbio.0030343.g003", "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Distribution_of_Normalized_Z_Scores_of_Three_Node_Network_Motifs_Left_and_Z_Scores_Classified_by_Stability_within_Specific_Density_Groups_Right_/631545", "title"=>"Distribution of Normalized Z Scores of Three-Node Network Motifs (Left), and Z Scores Classified by Stability within Specific Density Groups (Right)", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-22 08:58:04"}

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Relative Metric

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