Canalization and Control in Automata Networks: Body Segmentation in Drosophila melanogaster
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{"title"=>"Canalization and Control in Automata Networks: Body Segmentation in Drosophila melanogaster", "type"=>"journal", "authors"=>[{"first_name"=>"Manuel", "last_name"=>"Marques-Pita", "scopus_author_id"=>"24832121800"}, {"first_name"=>"Luis M.", "last_name"=>"Rocha", "scopus_author_id"=>"7102199516"}], "year"=>2013, "source"=>"PLoS ONE", "identifiers"=>{"isbn"=>"1932-6203 (Electronic)\\r1932-6203 (Linking)", "pmid"=>"23520449", "doi"=>"10.1371/journal.pone.0055946", "pui"=>"368490119", "issn"=>"19326203", "arxiv"=>"1301.5831", "sgr"=>"84874767199", "scopus"=>"2-s2.0-84874767199"}, "id"=>"0deafd64-bb0e-3452-9886-485d19ca01d7", "abstract"=>"We present schema redescription as a methodology to characterize canalization in automata networks used to model biochemical regulation and signalling. In our formulation, canalization becomes synonymous with redundancy present in the logic of automata. This results in straightforward measures to quantify canalization in an automaton (micro-level), which is in turn integrated into a highly scalable framework to characterize the collective dynamics of large-scale automata networks (macro-level). This way, our approach provides a method to link micro- to macro-level dynamics -- a crux of complexity. Several new results ensue from this methodology: uncovering of dynamical modularity (modules in the dynamics rather than in the structure of networks), identification of minimal conditions and critical nodes to control the convergence to attractors, simulation of dynamical behaviour from incomplete information about initial conditions, and measures of macro-level canalization and robustness to perturbations. We exemplify our methodology with a well-known model of the intra- and inter cellular genetic regulation of body segmentation in Drosophila melanogaster. We use this model to show that our analysis does not contradict any previous findings. But we also obtain new knowledge about its behaviour: a better understanding of the size of its wild-type attractor basin (larger than previously thought), the identification of novel minimal conditions and critical nodes that control wild-type behaviour, and the resilience of these to stochastic interventions. Our methodology is applicable to any complex network that can be modelled using automata, but we focus on biochemical regulation and signalling, towards a better understanding of the (decentralized) control that orchestrates cellular activity -- with the ultimate goal of explaining how do cells and tissues 'compute'.", "link"=>"http://www.mendeley.com/research/canalization-control-automata-networks-body-segmentation-drosophila-melanogaster", "reader_count"=>33, "reader_count_by_academic_status"=>{"Professor > Associate Professor"=>2, "Librarian"=>1, "Researcher"=>10, "Student > Doctoral Student"=>4, "Student > Ph. D. Student"=>6, "Student > Postgraduate"=>1, "Other"=>2, "Student > Master"=>1, "Student > Bachelor"=>1, "Professor"=>5}, "reader_count_by_user_role"=>{"Professor > Associate Professor"=>2, "Librarian"=>1, "Researcher"=>10, "Student > Doctoral Student"=>4, "Student > Ph. D. Student"=>6, "Student > Postgraduate"=>1, "Other"=>2, "Student > Master"=>1, "Student > Bachelor"=>1, "Professor"=>5}, "reader_count_by_subject_area"=>{"Engineering"=>2, "Mathematics"=>1, "Agricultural and Biological Sciences"=>11, "Medicine and Dentistry"=>3, "Neuroscience"=>1, "Sports and Recreations"=>1, "Physics and Astronomy"=>4, "Psychology"=>1, "Social Sciences"=>1, "Computer Science"=>7, "Economics, Econometrics and Finance"=>1}, "reader_count_by_subdiscipline"=>{"Engineering"=>{"Engineering"=>2}, "Medicine and Dentistry"=>{"Medicine and Dentistry"=>3}, "Neuroscience"=>{"Neuroscience"=>1}, "Social Sciences"=>{"Social Sciences"=>1}, "Sports and Recreations"=>{"Sports and Recreations"=>1}, "Physics and Astronomy"=>{"Physics and Astronomy"=>4}, "Psychology"=>{"Psychology"=>1}, "Economics, Econometrics and Finance"=>{"Economics, Econometrics and Finance"=>1}, "Agricultural and Biological Sciences"=>{"Agricultural and Biological Sciences"=>11}, "Computer Science"=>{"Computer Science"=>7}, "Mathematics"=>{"Mathematics"=>1}}, "reader_count_by_country"=>{"United States"=>3, "Denmark"=>1, "Italy"=>1, "Portugal"=>2}, "group_count"=>6}

Scopus | Further Information

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Figshare

  • {"files"=>["https://ndownloader.figshare.com/files/1006641"], "description"=>"<p>The table lists the relative canalization measures for every set of MCs reported in the main text. Canalization measures were obtained, for each MC set, from independent samples of configurations, thus . Values shown refer to the mean plus 95% confidence intervals for the 10 independent measurements.</p>", "links"=>[], "tags"=>["canalization", "wildcard", "mc", "sets", "converging", "wild-type"], "article_id"=>667264, "categories"=>["Biological Sciences", "Genetics", "Developmental Biology"], "users"=>["Manuel Marques-Pita", "Luis M. Rocha"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0055946.t004", "stats"=>{"downloads"=>3, "page_views"=>6, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Macro_level_canalization_in_the_wildcard_MC_sets_converging_to_wild_type_in_the_SPN_/667264", "title"=>"Macro-level canalization in the wildcard MC sets converging to wild-type in the SPN.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2013-03-08 02:01:04"}
  • {"files"=>["https://ndownloader.figshare.com/files/1006602"], "description"=>"<p>Connectivity rules in canalizing maps.</p>", "links"=>[], "tags"=>["rules", "canalizing"], "article_id"=>667232, "categories"=>["Biological Sciences", "Genetics", "Developmental Biology"], "users"=>["Manuel Marques-Pita", "Luis M. Rocha"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0055946.t002", "stats"=>{"downloads"=>6, "page_views"=>8, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Connectivity_rules_in_canalizing_maps_/667232", "title"=>"Connectivity rules in canalizing maps.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2013-03-08 02:00:32"}
  • {"files"=>["https://ndownloader.figshare.com/files/1006587"], "description"=>"<p>The table lists for every set of MCs reported in the main text: cardinality, minimum number of enputs, maximum number of enputs, estimated canalization. Canalization measures were obtained, for each MC set, from independent samples of configurations, thus . Values shown refer to the mean plus 95% confidence intervals for the 10 independent measurements.</p>", "links"=>[], "tags"=>["canalization", "wildcard", "mc", "sets", "converging", "wild-type"], "article_id"=>667209, "categories"=>["Biological Sciences", "Genetics", "Developmental Biology"], "users"=>["Manuel Marques-Pita", "Luis M. Rocha"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0055946.t003", "stats"=>{"downloads"=>1, "page_views"=>11, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Macro_level_canalization_in_the_wildcard_MC_sets_converging_to_wild_type_in_the_SPN_/667209", "title"=>"Macro-level canalization in the wildcard MC sets converging to wild-type in the SPN.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2013-03-08 02:00:09"}
  • {"files"=>["https://ndownloader.figshare.com/files/982629"], "description"=>"<p>\n <b> and (B) components of a single LUT entry.</b></p>", "links"=>[], "tags"=>["lut", "boolean", "automaton"], "article_id"=>648720, "categories"=>["Biological Sciences", "Genetics", "Developmental Biology"], "users"=>["Manuel Marques-Pita", "Luis M. Rocha"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0055946.g001", "stats"=>{"downloads"=>1, "page_views"=>17, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_A_LUT_for_Boolean_automaton_/648720", "title"=>"(A) LUT for Boolean automaton", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-03-09 12:14:17"}
  • {"files"=>["https://ndownloader.figshare.com/files/982630"], "description"=>"<p>The fifteen genes and proteins considered in the SPN model are represented (white nodes). The incoming edges to a node originate in the nodes that are used by to determine its transition. Shaded nodes represent the spatial signals (states of WG, HH and in neighbouring cells). Note that SLP – derived from an upstream intra-cellular signal – is an <i>input</i> node to this network. The self-connection it has represents the steady-state assumption: . Notice also that this graph represents the fully synchronous version of the model, where modifications concerning PH and SMO have been made (see main text for details).</p>", "links"=>[], "tags"=>["graph", "spn"], "article_id"=>648721, "categories"=>["Biological Sciences", "Genetics", "Developmental Biology"], "users"=>["Manuel Marques-Pita", "Luis M. Rocha"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0055946.g002", "stats"=>{"downloads"=>0, "page_views"=>19, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Connectivity_graph_of_the_SPN_model_/648721", "title"=>"Connectivity graph of the SPN model.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-03-09 12:14:20"}
  • {"files"=>["https://ndownloader.figshare.com/files/982631"], "description"=>"<p>Cells are represented horizontally, where the top (bottom) row is the most anterior (posterior) cell. Each column is a gene, protein or complex – a node in the context of the BN model. The specific pattern shown corresponds to the wild-type initial expression pattern observed at the onset of the segment polarity genes regulatory dynamics (); Black/on (white/off) squares represent expressed (not expressed) genes or proteins.</p>", "links"=>[], "tags"=>["parasegment", "spn"], "article_id"=>648722, "categories"=>["Biological Sciences", "Genetics", "Developmental Biology"], "users"=>["Manuel Marques-Pita", "Luis M. Rocha"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0055946.g003", "stats"=>{"downloads"=>0, "page_views"=>19, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_A_parasegment_in_the_SPN_model_/648722", "title"=>"A parasegment in the SPN model.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-03-09 12:14:21"}
  • {"files"=>["https://ndownloader.figshare.com/files/982633"], "description"=>"<p>These attractors are divided in four groups: wild-type, broad-stripe, no segmentation and ectopic. More specifically: (a) wild-type, (b) variant of (a), (c) wild-type with two stripes, (d) variant of (c), (e) broad-stripe, (f) no segmentation, (g) ectopic, (h) variant of (g), (i) ectopic with two stripes, and (j) variant of (i). The wild-type attractor (a) is referred to as in the results and discussion sections.</p>", "links"=>[], "tags"=>["attractors", "reached"], "article_id"=>648724, "categories"=>["Biological Sciences", "Genetics", "Developmental Biology"], "users"=>["Manuel Marques-Pita", "Luis M. Rocha"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0055946.g004", "stats"=>{"downloads"=>1, "page_views"=>20, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_The_ten_attractors_reached_by_the_SPN_/648724", "title"=>"The ten attractors reached by the SPN.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-03-09 12:14:27"}
  • {"files"=>["https://ndownloader.figshare.com/files/982635"], "description"=>"<p>(A) Subset of LUT entries of an example automaton that prescribe state transitions to <i>on</i> (1); white (black) states are 0 (1). (B) Wildcard schema redescription; wildcards denoted also by grey states. Schema is highlighted to identify the subset of LUT entries it redescribes. (C) Two-symbol schema redescription, using the additional position-free symbol; the entire set is compressed into a single two-symbol schema: . Any permutation of the inputs marked with the position-free symbol in results in a schema in . Note that redescribes the entire set of entries with transition to <i>on</i> and thus . Since there is only one set of marked inputs, the position-free symbol does not require an index. Although this figure depicts only the schemata obtained for the subset of LUT entries of that transition to <i>on</i>, entries that do not match any of these schemata transition to <i>off</i> (since is a Boolean automaton).</p>", "links"=>[], "tags"=>["genetics and genomics", "Computational biology", "developmental biology"], "article_id"=>648726, "categories"=>["Biological Sciences", "Genetics", "Developmental Biology"], "users"=>["Manuel Marques-Pita", "Luis M. Rocha"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0055946.g005", "stats"=>{"downloads"=>0, "page_views"=>17, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Schema_redescription_/648726", "title"=>"Schema redescription.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-03-09 12:14:32"}
  • {"files"=>["https://ndownloader.figshare.com/files/982636"], "description"=>"<p>The conjunction clauses in Expression (1) for the example automaton are directly mapped onto a standard McCulloch & Pitts network with two layers. On one layer the two literal enputs are accounted for by a threshold unit (at the top) with threshold . There is also a group-invariant enput with permutation subconstraints on both Boolean states. Two threshold units on the same layer are used to capture these. The threshold unit on the left accounts for the permutation subconstraint . It thus has as incoming s-units the inputs and threshold . In a similar way, the threshold unit on the right accounts for the subconstraint . When all the constraints (literal and group-invariant) are satisfied, the last threshold unit (second layer) ‘fires’ causing the transition to <i>on</i>.</p>", "links"=>[], "tags"=>["pitts"], "article_id"=>648727, "categories"=>["Biological Sciences", "Genetics", "Developmental Biology"], "users"=>["Manuel Marques-Pita", "Luis M. Rocha"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0055946.g006", "stats"=>{"downloads"=>0, "page_views"=>16, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_McCulloch_amp_Pitts_representation_of_Expression_1_/648727", "title"=>"McCulloch & Pitts representation of Expression (1).", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-03-09 12:14:35"}
  • {"files"=>["https://ndownloader.figshare.com/files/982637"], "description"=>"<p>Every s-unit is a circle, labelled according the automaton's input it represents and coloured according to its state: black is <i>on</i> and white is <i>off</i> (here we use light-blue for a generic state). The t-unit (schema) is represented using a larger circle. One of its halves is coloured, and the other labelled with the t-unit's threshold . Fibres can be single, or branched. In this example there are branching fibres only, where fibre fusions represent all possible combinations of two out of the three s-units.</p>", "links"=>[], "tags"=>["canalizing"], "article_id"=>648728, "categories"=>["Biological Sciences", "Genetics", "Developmental Biology"], "users"=>["Manuel Marques-Pita", "Luis M. Rocha"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0055946.g007", "stats"=>{"downloads"=>1, "page_views"=>20, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Elements_of_a_Canalizing_Map_/648728", "title"=>"Elements of a Canalizing Map.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-03-09 12:14:38"}
  • {"files"=>["https://ndownloader.figshare.com/files/982638"], "description"=>"<p>(A) Since (shown on top) has , the corresponding s-units for literal enputs are directly linked to the t-unit for with single fibres; . (B) Adding the subconstraint of the group-invariant enput . In this case, , so there is only one subset and thus a single branch from each s-unit in the group-invariant, fused into a single ending. The threshold becomes . (C) Finally, we add the second subconstraint of the group-invariant enput , which has the same properties as the subconstraint integrated in (B). The final threshold of the t-unit is given by (9), therefore . Notice that only the input-combinations that satisfy the constraints of Expression (1) for can lead to the firing of the t-unit; in other words, the canalizing map is equivalent to schema .</p>", "links"=>[], "tags"=>["automaton"], "article_id"=>648729, "categories"=>["Biological Sciences", "Genetics", "Developmental Biology"], "users"=>["Manuel Marques-Pita", "Luis M. Rocha"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0055946.g008", "stats"=>{"downloads"=>1, "page_views"=>19, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Canalizing_map_of_example_automaton_characterized_by_a_single_schema_/648729", "title"=>"Canalizing map of example automaton characterized by a single schema.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-03-09 12:14:42"}
  • {"files"=>["https://ndownloader.figshare.com/files/982640"], "description"=>"<p>(A) subconstraint defined by , where . The first step is to consider the s-units (in state 0) for the four input variables in the group invariant enput . Next we identify all the subsets of these s-units containing s-units: (shown with dotted arrows). From every s-unit in each such subset , we take an outgoing fibre to be joined together into a single fibre ending as input to the t-unit. Finally, we increase the threshold of the t-unit by the total number of subsets, that is . (B) An example of the same procedure but for and : .</p>", "links"=>[], "tags"=>["obtaining", "canalizing", "group-invariant"], "article_id"=>648731, "categories"=>["Biological Sciences", "Genetics", "Developmental Biology"], "users"=>["Manuel Marques-Pita", "Luis M. Rocha"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0055946.g009", "stats"=>{"downloads"=>2, "page_views"=>21, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Procedure_for_obtaining_the_canalizing_map_of_a_group_invariant_subconstraint_/648731", "title"=>"Procedure for obtaining the canalizing map of a group-invariant subconstraint.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-03-09 12:14:45"}
  • {"files"=>["https://ndownloader.figshare.com/files/982641"], "description"=>"<p>x<b>.</b> (A) complete set of schemata for , including the transitions to <i>on</i> shown in <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0055946#pone-0055946-g005\" target=\"_blank\">Figure 5</a> and the transitions of <i>off</i> (the negation of the first).(B) canalizing map; t-units for schemata and were merged into a single t-unit with threshold (see main text). (C) effective connectivity, input symmetry and input redundancy of .</p>", "links"=>[], "tags"=>["genetics and genomics", "Computational biology", "developmental biology"], "article_id"=>648732, "categories"=>["Biological Sciences", "Genetics", "Developmental Biology"], "users"=>["Manuel Marques-Pita", "Luis M. Rocha"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0055946.g010", "stats"=>{"downloads"=>0, "page_views"=>20, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Canalizing_Map_of_automaton_/648732", "title"=>"Canalizing Map of automaton", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-03-09 12:14:48"}
  • {"files"=>["https://ndownloader.figshare.com/files/982643"], "description"=>"<p>Schemata for inhibition (transitions to off) and expression (transitions to on) are shown for each node (genes or proteins) in model. In-degree (), input redundancy (), effective connectivity (), and input symmetry () are also shown.</p>", "links"=>[], "tags"=>["canalization", "automata", "spn"], "article_id"=>648734, "categories"=>["Biological Sciences", "Genetics", "Developmental Biology"], "users"=>["Manuel Marques-Pita", "Luis M. Rocha"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0055946.g011", "stats"=>{"downloads"=>1, "page_views"=>24, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Micro_level_canalization_for_the_Automata_in_the_SPN_model_/648734", "title"=>"Micro-level canalization for the Automata in the SPN model.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-03-09 12:15:03"}
  • {"files"=>["https://ndownloader.figshare.com/files/982645"], "description"=>"<p>Relative input redundancy is measured in the horizontal axis () and relative input symmetry is measured in the vertical axis (). Most automata in the SPN fall in the class II quadrant, showing that most canalization is of the input redundancy kind, though nodes such as CIR and display strong input symmetry too.</p>", "links"=>[], "tags"=>["canalization", "spn"], "article_id"=>648736, "categories"=>["Biological Sciences", "Genetics", "Developmental Biology"], "users"=>["Manuel Marques-Pita", "Luis M. Rocha"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0055946.g012", "stats"=>{"downloads"=>1, "page_views"=>21, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Quantification_of_canalization_in_the_SPN_automata_/648736", "title"=>"Quantification of canalization in the SPN automata.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-03-09 12:15:05"}
  • {"files"=>["https://ndownloader.figshare.com/files/982646"], "description"=>"<p>The set of schemata for each automaton is converted into two CMs: one representing the minimal control logic for its inhibition, and another for its expression. Note that denotes the state of node in both neighbour cells: and , where is one of the spatial-signals , HH, or WG (see text).</p>", "links"=>[], "tags"=>["maps", "nodes", "spn"], "article_id"=>648737, "categories"=>["Biological Sciences", "Genetics", "Developmental Biology"], "users"=>["Manuel Marques-Pita", "Luis M. Rocha"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0055946.g013", "stats"=>{"downloads"=>0, "page_views"=>17, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Canalizing_Maps_of_individual_nodes_in_the_SPN_model_part_1_/648737", "title"=>"Canalizing Maps of individual nodes in the SPN model (part 1).", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-03-09 12:15:10"}
  • {"files"=>["https://ndownloader.figshare.com/files/982647"], "description"=>"<p>The set of schemata for each automaton is converted into two CMs: one representing the minimal control logic for its inhibition, and another for its expression. Note that denotes the state of node in both neighbour cells: and , where is one of the spatial-signals , HH, or WG (see text).</p>", "links"=>[], "tags"=>["maps", "nodes", "spn"], "article_id"=>648738, "categories"=>["Biological Sciences", "Genetics", "Developmental Biology"], "users"=>["Manuel Marques-Pita", "Luis M. Rocha"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0055946.g014", "stats"=>{"downloads"=>1, "page_views"=>18, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Canalizing_Maps_of_individual_nodes_in_the_SPN_model_cont_/648738", "title"=>"Canalizing Maps of individual nodes in the SPN model (cont).", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-03-09 12:15:16"}
  • {"files"=>["https://ndownloader.figshare.com/files/982648"], "description"=>"<p>Also depicted are pathway modules (pink) and (blue), whose initial conditions depend exclusively on the expression and inhibition of input node SLP and of WG in neighbouring cells (the nWG spatial-signals). , (see details in text).</p>", "links"=>[], "tags"=>["canalization", "spn"], "article_id"=>648739, "categories"=>["Biological Sciences", "Genetics", "Developmental Biology"], "users"=>["Manuel Marques-Pita", "Luis M. Rocha"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0055946.g015", "stats"=>{"downloads"=>1, "page_views"=>22, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Dynamics_Canalization_Map_for_a_single_cell_of_the_SPN_Model_/648739", "title"=>"Dynamics Canalization Map for a single cell of the SPN Model.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-03-09 12:15:22"}
  • {"files"=>["https://ndownloader.figshare.com/files/982651"], "description"=>"<p>The eight initial partial configurations tested correspond to the combinations of the steady-states of intra- and inter-cellular inputs SLP, WG and (and where HH and are merged into a single node, ). The specific state-combinations of these three variables is depicted on the middle (white) tab of each dynamical unfolding plot. Initial patterns that reach the same target pattern are grouped together in five groups to (identified in the top tab of each plot). The six input configurations in groups G1, G2, and G3 depict the dynamics where pathway module is involved (nodes involved in this module are highlighted in pink.) The two input configurations in G4 and G5 depict the dynamics where pathway module is involved (nodes involved in this module are highlighted in blue.) Three of the eight combinations are in because they reach the same final configuration which, although partial, can only match the attractor . There are five possible attractor patterns of the SPN model for a single cell, shown in bottom right inset: to (see background). Attractors reached by each group are identified in the bottom tab of each plot. Groups and both unfold to an ambiguous target pattern that can end in or for , and or for . Finally, the initial partial configurations in groups and are sufficient to resolve the states of every node in the network.</p>", "links"=>[], "tags"=>["unfolding", "spn"], "article_id"=>648742, "categories"=>["Biological Sciences", "Genetics", "Developmental Biology"], "users"=>["Manuel Marques-Pita", "Luis M. Rocha"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0055946.g016", "stats"=>{"downloads"=>1, "page_views"=>19, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Dynamical_unfolding_of_the_single_cell_SPN_with_partial_input_configurations_/648742", "title"=>"Dynamical unfolding of the (single-cell) SPN with partial input configurations.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-03-09 12:15:29"}
  • {"files"=>["https://ndownloader.figshare.com/files/982652"], "description"=>"<p><b><i>X<sub>wt</sub></i></b><b>.</b> The pair were the two-symbol schemata obtained in our stochastic search; both include 4 pairs of symmetric node-pairs, each denoted by a circle and a numerical index.</p>", "links"=>[], "tags"=>["schemata", "largest", "position-free", "redescription"], "article_id"=>648743, "categories"=>["Biological Sciences", "Genetics", "Developmental Biology"], "users"=>["Manuel Marques-Pita", "Luis M. Rocha"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0055946.g017", "stats"=>{"downloads"=>1, "page_views"=>21, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Two_Symbol_schemata_with_largest_number_of_position_free_symbols_obtained_from_redescription_of_/648743", "title"=>"Two-Symbol schemata with largest number of position-free symbols, obtained from redescription of", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-03-09 12:15:33"}
  • {"files"=>["https://ndownloader.figshare.com/files/982654"], "description"=>"<p>Enput power is shown for each of the four sets of MCs considered in our analysis: (A) , (B) , (C) and (D) . A parasegment is represented by four rounded rectangles, one for each cell, where the anterior cell is at the top, and posterior at the bottom. Since enput power is computed for every node in each of its two possible states, every cell rectangle has two rows of circles. The bottom row (marked on the sides with a white circle on the outside) corresponds to enput power of the nodes when <i>off</i>, while the top row is the enput power when the same nodes are <i>on</i> (marked on the sides with a dark circle). Each circle inside a cell's rectangle corresponds to the power of a given enput in the corresponding subset of MCs identified by the letters A to D. Full power is highlighted in red, other values in blue and scaled, while null power is depicted using small grey circles. Full power occurs only for enputs that are present in every MC (and configurations) of the respective set, whereas null power identifies nodes that are never enputs in any MC – always irrelevant for the respective dynamical behaviour.</p>", "links"=>[], "tags"=>["wild-type", "basin", "spatial", "spn"], "article_id"=>648745, "categories"=>["Biological Sciences", "Genetics", "Developmental Biology"], "users"=>["Manuel Marques-Pita", "Luis M. Rocha"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0055946.g018", "stats"=>{"downloads"=>1, "page_views"=>50, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Enput_power_in_the_wild_type_basin_of_attraction_of_the_spatial_SPN_model_/648745", "title"=>"Enput power in the wild-type basin of attraction of the spatial SPN model.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-03-09 12:15:40"}
  • {"files"=>["https://ndownloader.figshare.com/files/982655"], "description"=>"<p>When proteins are allowed to be expressed initially, the second necessary condition, reported in <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0055946#pone.0055946-Chaves1\" target=\"_blank\">[38]</a>, ceases to be a necessary condition, as discussed in the main text; in the MC shown, and can be in any state and the network still converges to the wild-type attractor.</p>", "links"=>[], "tags"=>["mc", "requiring", "wild-type", "attractor"], "article_id"=>648746, "categories"=>["Biological Sciences", "Genetics", "Developmental Biology"], "users"=>["Manuel Marques-Pita", "Luis M. Rocha"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0055946.g019", "stats"=>{"downloads"=>1, "page_views"=>17, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_A_MC_not_requiring_in_wild_type_attractor_basin_/648746", "title"=>"A MC not requiring in wild-type attractor basin.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-03-09 12:15:42"}
  • {"files"=>["https://ndownloader.figshare.com/files/982657"], "description"=>"<p>(A) A configuration with the minimal number of nodes expressed that converges to wild-type, and its corresponding MC: 32 nodes are irrelevant, 24 must be unexpressed (<i>off</i>), and only 4 must be expressed (<i>on</i>). (B) The opposite extreme condition where 16 genes and proteins are unexpressed and all other 44 are expressed.</p>", "links"=>[], "tags"=>["configurations", "converging", "wild-type", "spn"], "article_id"=>648748, "categories"=>["Biological Sciences", "Genetics", "Developmental Biology"], "users"=>["Manuel Marques-Pita", "Luis M. Rocha"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0055946.g020", "stats"=>{"downloads"=>1, "page_views"=>5, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_8216_Extreme_8217_configurations_converging_to_wild_type_in_the_SPN_model_/648748", "title"=>"‘Extreme’ configurations converging to wild-type in the SPN model.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-03-09 12:15:49"}
  • {"files"=>["https://ndownloader.figshare.com/files/982659"], "description"=>"<p>Each coordinate in a given diagram (each corresponding to a tested enput) contains a circle, depicting the proportion of trials that converged to attractor when noise level was used. Red circles mean that all trajectories tested converged to .</p>", "links"=>[], "tags"=>["enput", "disruption", "spn"], "article_id"=>648750, "categories"=>["Biological Sciences", "Genetics", "Developmental Biology"], "users"=>["Manuel Marques-Pita", "Luis M. Rocha"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0055946.g021", "stats"=>{"downloads"=>1, "page_views"=>9, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Wild_type_enput_disruption_in_the_SPN_model_/648750", "title"=>"Wild-type enput disruption in the SPN model.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-03-09 12:16:02"}
  • {"files"=>["https://ndownloader.figshare.com/files/1006619"], "description"=>"<p>The subscript represents the cell index; the superscript represents time. Note that every node has a numerical index assigned to it, which we use for easy referral throughout the present work. The extra-cellular nodes, and in adjacent cells are indexed as follows: 16 to 21 denote , , , , and in this order.</p>", "links"=>[], "tags"=>["formulae", "state-transition", "functions", "node", "spn"], "article_id"=>667248, "categories"=>["Biological Sciences", "Genetics", "Developmental Biology"], "users"=>["Manuel Marques-Pita", "Luis M. Rocha"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0055946.t001", "stats"=>{"downloads"=>1, "page_views"=>8, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Boolean_logic_formulae_representing_the_state_transition_functions_for_each_node_in_the_SPN_four_cell_parasegment_model_/667248", "title"=>"Boolean logic formulae representing the state-transition functions for each node in the SPN (four-cell parasegment) model.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2013-03-08 02:00:48"}
  • {"files"=>["https://ndownloader.figshare.com/files/982663", "https://ndownloader.figshare.com/files/982664", "https://ndownloader.figshare.com/files/982666", "https://ndownloader.figshare.com/files/982667", "https://ndownloader.figshare.com/files/982668", "https://ndownloader.figshare.com/files/982669", "https://ndownloader.figshare.com/files/982670", "https://ndownloader.figshare.com/files/982671", "https://ndownloader.figshare.com/files/982672", "https://ndownloader.figshare.com/files/982673", "https://ndownloader.figshare.com/files/982674", "https://ndownloader.figshare.com/files/982675", "https://ndownloader.figshare.com/files/982676", "https://ndownloader.figshare.com/files/982677"], "description"=>"<div><p>We present schema redescription as a methodology to characterize canalization in automata networks used to model biochemical regulation and signalling. In our formulation, canalization becomes synonymous with redundancy present in the logic of automata. This results in straightforward measures to quantify canalization in an automaton (micro-level), which is in turn integrated into a highly scalable framework to characterize the collective dynamics of large-scale automata networks (macro-level). This way, our approach provides a method to link micro- to macro-level dynamics – a crux of complexity. Several new results ensue from this methodology: uncovering of dynamical modularity (modules in the dynamics rather than in the structure of networks), identification of minimal conditions and critical nodes to control the convergence to attractors, simulation of dynamical behaviour from incomplete information about initial conditions, and measures of macro-level canalization and robustness to perturbations. We exemplify our methodology with a well-known model of the intra- and inter cellular genetic regulation of body segmentation in <i>Drosophila melanogaster</i>. We use this model to show that our analysis does not contradict any previous findings. But we also obtain new knowledge about its behaviour: a better understanding of the size of its wild-type attractor basin (larger than previously thought), the identification of novel minimal conditions and critical nodes that control wild-type behaviour, and the resilience of these to stochastic interventions. Our methodology is applicable to any complex network that can be modelled using automata, but we focus on biochemical regulation and signalling, towards a better understanding of the (decentralized) control that orchestrates cellular activity – with the ultimate goal of explaining how do cells and tissues ‘compute’.</p> </div>", "links"=>[], "tags"=>["canalization", "automata", "segmentation"], "article_id"=>648754, "categories"=>["Biological Sciences", "Genetics", "Developmental Biology"], "users"=>["Manuel Marques-Pita", "Luis M. Rocha"], "doi"=>["https://dx.doi.org/10.1371/journal.pone.0055946.s001", "https://dx.doi.org/10.1371/journal.pone.0055946.s002", "https://dx.doi.org/10.1371/journal.pone.0055946.s003", "https://dx.doi.org/10.1371/journal.pone.0055946.s004", "https://dx.doi.org/10.1371/journal.pone.0055946.s005", "https://dx.doi.org/10.1371/journal.pone.0055946.s006", "https://dx.doi.org/10.1371/journal.pone.0055946.s007", "https://dx.doi.org/10.1371/journal.pone.0055946.s008", "https://dx.doi.org/10.1371/journal.pone.0055946.s009", "https://dx.doi.org/10.1371/journal.pone.0055946.s010", "https://dx.doi.org/10.1371/journal.pone.0055946.s011", "https://dx.doi.org/10.1371/journal.pone.0055946.s012", "https://dx.doi.org/10.1371/journal.pone.0055946.s013", "https://dx.doi.org/10.1371/journal.pone.0055946.s014"], "stats"=>{"downloads"=>20, "page_views"=>16, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/Canalization_and_Control_in_Automata_Networks_Body_Segmentation_in_Drosophila_melanogaster__/648754", "title"=>"Canalization and Control in Automata Networks: Body Segmentation in <em>Drosophila melanogaster</em>", "pos_in_sequence"=>0, "defined_type"=>4, "published_date"=>"2013-03-09 12:16:52"}

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  • {"unique-ip"=>"11", "full-text"=>"3", "pdf"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"7", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2019", "month"=>"2"}
  • {"unique-ip"=>"5", "full-text"=>"1", "pdf"=>"1", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"2", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2019", "month"=>"3"}
  • {"unique-ip"=>"3", "full-text"=>"3", "pdf"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"1", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2019", "month"=>"4"}
  • {"unique-ip"=>"5", "full-text"=>"5", "pdf"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"1", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2019", "month"=>"5"}
  • {"unique-ip"=>"10", "full-text"=>"4", "pdf"=>"1", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"4", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2019", "month"=>"8"}
  • {"unique-ip"=>"5", "full-text"=>"3", "pdf"=>"2", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2019", "month"=>"9"}

Relative Metric

{"start_date"=>"2013-01-01T00:00:00Z", "end_date"=>"2013-12-31T00:00:00Z", "subject_areas"=>[{"subject_area"=>"/Biology and life sciences/Cell biology", "average_usage"=>[272, 472, 600, 713, 815, 911, 1004, 1094, 1185, 1273, 1358, 1441]}, {"subject_area"=>"/Physical sciences/Mathematics", "average_usage"=>[259, 431, 541, 639, 727, 816, 898, 980, 1061, 1136, 1214, 1294, 1356]}]}
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