Criticality Is an Emergent Property of Genetic Networks that Exhibit Evolvability
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{"title"=>"Criticality Is an Emergent Property of Genetic Networks that Exhibit Evolvability", "type"=>"journal", "authors"=>[{"first_name"=>"Christian", "last_name"=>"Torres-Sosa", "scopus_author_id"=>"55370433100"}, {"first_name"=>"Sui", "last_name"=>"Huang", "scopus_author_id"=>"55553736375"}, {"first_name"=>"Maximino", "last_name"=>"Aldana", "scopus_author_id"=>"8418916400"}], "year"=>2012, "source"=>"PLoS Computational Biology", "identifiers"=>{"sgr"=>"84866931077", "doi"=>"10.1371/journal.pcbi.1002669", "pui"=>"365755962", "pmid"=>"22969419", "scopus"=>"2-s2.0-84866931077", "issn"=>"1553734X", "isbn"=>"1553-7358"}, "id"=>"d750fc8b-e1c0-3112-8661-67b2e300e21f", "abstract"=>"Accumulating experimental evidence suggests that the gene regulatory networks of living organisms operate in the critical phase, namely, at the transition between ordered and chaotic dynamics. Such critical dynamics of the network permits the coexistence of robustness and flexibility which are necessary to ensure homeostatic stability (of a given phenotype) while allowing for switching between multiple phenotypes (network states) as occurs in development and in response to environmental change. However, the mechanisms through which genetic networks evolve such critical behavior have remained elusive. Here we present an evolutionary model in which criticality naturally emerges from the need to balance between the two essential components of evolvability: phenotype conservation and phenotype innovation under mutations. We simulated the Darwinian evolution of random Boolean networks that mutate gene regulatory interactions and grow by gene duplication. The mutating networks were subjected to selection for networks that both (i) preserve all the already acquired phenotypes (dynamical attractor states) and (ii) generate new ones. Our results show that this interplay between extending the phenotypic landscape (innovation) while conserving the existing phenotypes (conservation) suffices to cause the evolution of all the networks in a population towards criticality. Furthermore, the networks produced by this evolutionary process exhibit structures with hubs (global regulators) similar to the observed topology of real gene regulatory networks. Thus, dynamical criticality and certain elementary topological properties of gene regulatory networks can emerge as a byproduct of the evolvability of the phenotypic landscape.", "link"=>"http://www.mendeley.com/research/criticality-emergent-property-genetic-networks-exhibit-evolvability", "reader_count"=>152, "reader_count_by_academic_status"=>{"Unspecified"=>1, "Professor > Associate Professor"=>6, "Researcher"=>54, "Student > Doctoral Student"=>7, "Student > Ph. D. Student"=>26, "Student > Postgraduate"=>9, "Student > Master"=>18, "Other"=>5, "Student > Bachelor"=>11, "Lecturer > Senior Lecturer"=>1, "Professor"=>13}, "reader_count_by_user_role"=>{"Unspecified"=>1, "Professor > Associate Professor"=>6, "Researcher"=>54, "Student > Doctoral Student"=>7, "Student > Ph. D. Student"=>26, "Student > Postgraduate"=>9, "Student > Master"=>18, "Other"=>5, "Student > Bachelor"=>11, "Lecturer > Senior Lecturer"=>1, "Professor"=>13}, "reader_count_by_subject_area"=>{"Unspecified"=>3, "Agricultural and Biological Sciences"=>79, "Philosophy"=>1, "Computer Science"=>9, "Economics, Econometrics and Finance"=>2, "Engineering"=>6, "Environmental Science"=>3, "Biochemistry, Genetics and Molecular Biology"=>10, "Mathematics"=>1, "Medicine and Dentistry"=>3, "Neuroscience"=>4, "Sports and Recreations"=>1, "Physics and Astronomy"=>26, "Psychology"=>1, "Social Sciences"=>2}, "reader_count_by_subdiscipline"=>{"Medicine and Dentistry"=>{"Medicine and Dentistry"=>3}, "Social Sciences"=>{"Social Sciences"=>2}, "Sports and Recreations"=>{"Sports and Recreations"=>1}, "Physics and Astronomy"=>{"Physics and Astronomy"=>26}, "Psychology"=>{"Psychology"=>1}, "Mathematics"=>{"Mathematics"=>1}, "Unspecified"=>{"Unspecified"=>3}, "Environmental Science"=>{"Environmental Science"=>3}, "Engineering"=>{"Engineering"=>6}, "Neuroscience"=>{"Neuroscience"=>4}, "Economics, Econometrics and Finance"=>{"Economics, Econometrics and Finance"=>2}, "Agricultural and Biological Sciences"=>{"Agricultural and Biological Sciences"=>79}, "Computer Science"=>{"Computer Science"=>9}, "Biochemistry, Genetics and Molecular Biology"=>{"Biochemistry, Genetics and Molecular Biology"=>10}, "Philosophy"=>{"Philosophy"=>1}}, "reader_count_by_country"=>{"Colombia"=>1, "United States"=>14, "Japan"=>1, "United Kingdom"=>1, "Spain"=>1, "Canada"=>1, "Netherlands"=>1, "Iran"=>1, "Norway"=>2, "Poland"=>1, "Serbia and Montenegro"=>1, "Italy"=>1, "Mexico"=>2, "Israel"=>1, "Australia"=>1, "France"=>1}, "group_count"=>7}

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Figshare

  • {"files"=>["https://ndownloader.figshare.com/files/580093"], "description"=>"<p>The top-left network shows the structure of the giant component of the transcription factor interaction network of <i>E. coli</i> according to the RegulonDB <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002669#pcbi.1002669-GamaCastro1\" target=\"_blank\">[3]</a>. This network has <i>N</i> = 101 nodes and average connectivity <i>K</i> = 2.46. The structure on the top-right corresponds to the typical network that results from our evolutionary algorithm, which in this particular case has <i>N</i> = 100 nodes and average connectivity <i>K</i> = 1.85. Note the existence of global regulators, i.e. nodes with a great number of output connections. The bottom panel presents in a log-log plot the out-degree distribution of these two networks to illustrate their remarkable similarity.</p>", "links"=>[], "tags"=>["generated", "evolutionary"], "article_id"=>250587, "categories"=>["Biological Sciences", "Genetics"], "users"=>["Christian Torres-Sosa", "Sui Huang", "Maximino Aldana"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002669.g006", "stats"=>{"downloads"=>0, "page_views"=>45, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Network_structure_generated_by_the_evolutionary_process_/250587", "title"=>"Network structure generated by the evolutionary process.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2012-09-06 00:09:47"}
  • {"files"=>["https://ndownloader.figshare.com/files/579817"], "description"=>"<p>This parameter, which measures whether the genes are frozen in one state, either 0 or 1, or if they more or less switch back and forth between these two states, can be computed in two distinct ways. The first way (horizontal variability ) is to measure along each attractor state, as shown in A, and then average over all the attractor states and over all the attractors in the attractor landscape. The second way (variability ) shown in B, is to measure the variability for each gene throughout time along the attractor cycle, then average over all the genes in the network and over all the attractors. This is illustrated by the particular example for the same attractor where , whereas .</p>", "links"=>[], "tags"=>["variability"], "article_id"=>250315, "categories"=>["Biological Sciences", "Genetics"], "users"=>["Christian Torres-Sosa", "Sui Huang", "Maximino Aldana"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002669.g002", "stats"=>{"downloads"=>0, "page_views"=>1, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Gene_expression_variability_945_/250315", "title"=>"Gene expression variability <i>α</i>.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2012-09-06 00:05:15"}
  • {"files"=>["https://ndownloader.figshare.com/files/580468"], "description"=>"<p>Plots of the probability that a percentage <i>q</i> of the network attractors is conserved after a gene the knockout of one gene for critical networks constructed <i>de novo</i> (A) and the critical networks that result from the evolutionary process (B). The differently colored distributions in B correspond to populations that started in different dynamical regimes (as in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002669#pcbi-1002669-g001\" target=\"_blank\">Fig. 1</a>). Note the high probability for the <i>de novo</i> networks to lose all their attractors by a gene knockout () which does not happen for the evolved networks ( in all cases). Conversely the probability to conserve all attractors is considerably larger for the latter than for the former ( and, respectively). These data were computed from populations of 1000 networks and 500 attractors per network.</p>", "links"=>[], "tags"=>["attractor"], "article_id"=>250971, "categories"=>["Biological Sciences", "Genetics"], "users"=>["Christian Torres-Sosa", "Sui Huang", "Maximino Aldana"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002669.g010", "stats"=>{"downloads"=>1, "page_views"=>3, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Robustness_of_the_attractor_landscape_/250971", "title"=>"Robustness of the attractor landscape.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2012-09-06 00:16:11"}
  • {"files"=>["https://ndownloader.figshare.com/files/306124", "https://ndownloader.figshare.com/files/306162", "https://ndownloader.figshare.com/files/306210", "https://ndownloader.figshare.com/files/306271", "https://ndownloader.figshare.com/files/306303"], "description"=>"<div><p>Accumulating experimental evidence suggests that the gene regulatory networks of living organisms operate in the critical phase, namely, at the transition between ordered and chaotic dynamics. Such critical dynamics of the network permits the coexistence of robustness and flexibility which are necessary to ensure homeostatic stability (of a given phenotype) while allowing for switching between multiple phenotypes (network states) as occurs in development and in response to environmental change. However, the mechanisms through which genetic networks evolve such critical behavior have remained elusive. Here we present an evolutionary model in which criticality naturally emerges from the need to balance between the two essential components of evolvability: phenotype conservation and phenotype innovation under mutations. We simulated the Darwinian evolution of random Boolean networks that mutate gene regulatory interactions and grow by gene duplication. The mutating networks were subjected to selection for networks that both (i) preserve all the already acquired phenotypes (dynamical attractor states) and (ii) generate new ones. Our results show that this interplay between extending the phenotypic landscape (innovation) while conserving the existing phenotypes (conservation) suffices to cause the evolution of all the networks in a population towards criticality. Furthermore, the networks produced by this evolutionary process exhibit structures with hubs (global regulators) similar to the observed topology of real gene regulatory networks. Thus, dynamical criticality and certain elementary topological properties of gene regulatory networks can emerge as a byproduct of the evolvability of the phenotypic landscape.</p> </div>", "links"=>[], "tags"=>["criticality", "emergent", "networks", "evolvability"], "article_id"=>120396, "categories"=>["Biological Sciences", "Genetics"], "users"=>["Christian Torres-Sosa", "Sui Huang", "Maximino Aldana"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1002669.s001", "https://dx.doi.org/10.1371/journal.pcbi.1002669.s002", "https://dx.doi.org/10.1371/journal.pcbi.1002669.s003", "https://dx.doi.org/10.1371/journal.pcbi.1002669.s004", "https://dx.doi.org/10.1371/journal.pcbi.1002669.s005"], "stats"=>{"downloads"=>8, "page_views"=>30, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/Criticality_Is_an_Emergent_Property_of_Genetic_Networks_that_Exhibit_Evolvability/120396", "title"=>"Criticality Is an Emergent Property of Genetic Networks that Exhibit Evolvability", "pos_in_sequence"=>0, "defined_type"=>4, "published_date"=>"2012-09-06 00:06:36"}
  • {"files"=>["https://ndownloader.figshare.com/files/580598"], "description"=>"<p>This second type of mutation affects the way in which a given gene regulates its targets. (A) If is one of the regulators of a target gene . Then mutation in the coding region of may afford gene the capacity to bind to a new site in the regulatory region of the same target gene (B), or abrogate the capacity to bind to an existing binding site of that target gene (C). Conversely a change in the coding region of gene may provide new binding capacity for a site in the regulatory region of a new target, as it is shown in (D) and (E).</p>", "links"=>[], "tags"=>["genetics and genomics", "Computational biology"], "article_id"=>251098, "categories"=>["Biological Sciences", "Genetics"], "users"=>["Christian Torres-Sosa", "Sui Huang", "Maximino Aldana"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002669.g012", "stats"=>{"downloads"=>1, "page_views"=>3, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Mutations_in_the_regulatory_region_of_a_gene_/251098", "title"=>"Mutations in the regulatory region of a gene.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2012-09-06 00:18:18"}
  • {"files"=>["https://ndownloader.figshare.com/files/580028"], "description"=>"<p>(<b>A</b>) Plot of the network labels (strains) that are present in the population at a given generation. Each horizontal line indicates the survival time of a particular strain. The vertical lines indicate the fixation events in which all the networks in the population are relabeled after only one strain was left in the entire population. (B) Distribution of survival times computed during generations (black curve). This distribution was computed using logarithmic bins. Only data for are presented because we checked the existence of strains every 20 generations. The red dashed line is the best fit which corresponds to the power-law . The inset shows the corresponding cumulative distribution , which better reveals the goodness of the power-law fit. The fact that has a more or less power-law behavior implies that almost all the strains disappear from the population very quickly, whereas only very few networks are able to survive the Darwinian selection mechanism given by the ACC, the AIC and the <i>α</i>-fitness criterion.</p>", "links"=>[], "tags"=>["times", "strains"], "article_id"=>250523, "categories"=>["Biological Sciences", "Genetics"], "users"=>["Christian Torres-Sosa", "Sui Huang", "Maximino Aldana"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002669.g005", "stats"=>{"downloads"=>1, "page_views"=>5, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Survival_times_of_the_different_strains_in_the_population_/250523", "title"=>"Survival times of the different strains in the population.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2012-09-06 00:08:43"}
  • {"files"=>["https://ndownloader.figshare.com/files/579722"], "description"=>"<p>(A) Schematic representation of the network, showing that each node (circles) “contains” one gene (little bars inside the circles). The arrows represent the regulatory interactions between the genes. (B) Each gene is composed of a regulatory region and a coding region. The regulatory region contains binding sites which can be added to, or removed from, the regulatory region with the same probability. (C) The binding sites in the regulatory region determine the regulators of (its input connections). There can be more than one binding site per regulator (as the regulator on the very left), although at the beginning of the evolutionary process the initial networks have only one binding site per regulator. The regulatory region of determines which other genes it regulates.</p>", "links"=>[], "tags"=>["genetics and genomics", "Computational biology"], "article_id"=>250223, "categories"=>["Biological Sciences", "Genetics"], "users"=>["Christian Torres-Sosa", "Sui Huang", "Maximino Aldana"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002669.g001", "stats"=>{"downloads"=>0, "page_views"=>5, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Gene_structure_/250223", "title"=>"Gene structure.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2012-09-06 00:03:43"}
  • {"files"=>["https://ndownloader.figshare.com/files/580528"], "description"=>"<p>This type of mutation affects how the regulators of a given target gene (inputs to node ) jointly control its output. (A) Gene has acquired a new binding site, represented by the leftmost square in green. (B) The new binding site is occupied by one of the already existing regulators of . (C) The new binding site is occupied by a completely different gene (green circle) that thus becomes a new regulator of . (D) Another mutation in the regulatory region is the deletion of existing binding sites. Here, the deleted site belongs to a regulator for which there are alternative binding sites left which thus remains a regulator. (E) Conversely, the removal of the binding site can completely break the regulatory interaction between and the respective regulator. Deletion of binding sites that can leave a given gene with no regulators at all are not allowed.</p>", "links"=>[], "tags"=>["coding"], "article_id"=>251024, "categories"=>["Biological Sciences", "Genetics"], "users"=>["Christian Torres-Sosa", "Sui Huang", "Maximino Aldana"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002669.g011", "stats"=>{"downloads"=>0, "page_views"=>1, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Mutations_in_the_coding_region_of_a_gene_/251024", "title"=>"Mutations in the coding region of a gene.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2012-09-06 00:17:04"}
  • {"files"=>["https://ndownloader.figshare.com/files/580409"], "description"=>"<p>(A) Typical example of the attractors obtained when the evolution of the population is carried out without implementing the -fitness criterion. In this particular case, instead of the -fitness we used the <i>S</i>-fitness which assigns a higher replication rate to the networks whose sensitivity is closer to 1. The final attractor landscape consisted of 91 attractors, and only 4 are partially shown here (only the first 45 digits in each attractor state are shown; the remaining 55 digits are all 0's). Note that only the first 10 digits in each attractor state show some activity. There are the 10 genes in the networks of the original population. (B) Plot of the average sensitivity of the population throughout generations, showing that the sensitivity very quickly approaches 1 and remains very close to 1. This is expected since we are explicitly selecting for networks with sensitivities . (C) Histogram of sensitivities in the final population (generation <i>g</i> = 200000), showing that most networks in the final population have become critical. The inset shows the structure of a typical network in the final population. Note that this network exhibits a more homogeneous random topology with no hubs. This is always the case when -fitness is not used as selection criterion.</p>", "links"=>[], "tags"=>["variability"], "article_id"=>250909, "categories"=>["Biological Sciences", "Genetics"], "users"=>["Christian Torres-Sosa", "Sui Huang", "Maximino Aldana"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002669.g009", "stats"=>{"downloads"=>0, "page_views"=>5, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Importance_of_the_gene_expression_variability_as_a_fitness_criterion_/250909", "title"=>"Importance of the gene expression variability as a fitness criterion.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2012-09-06 00:15:09"}
  • {"files"=>["https://ndownloader.figshare.com/files/580169"], "description"=>"<p>Although all networks in the final population have the same attractor landscape, they are structurally not completely identical to each other. Here we show three networks randomly chosen from the final population (A, B and C). The image in D is a superposition of all the networks in that population. The <i>link persistence</i> is defined as , where is the number of networks in the final population in which the nodes and were connected. The links in D have been colored according to their persistence (white for and red for ). It is apparent that the highly persistent links mostly belong to the global regulators (hubs). This strongly suggests that the global regulators play an important role in determining the phenotypic landscape of the population.</p>", "links"=>[], "tags"=>["variability"], "article_id"=>250667, "categories"=>["Biological Sciences", "Genetics"], "users"=>["Christian Torres-Sosa", "Sui Huang", "Maximino Aldana"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002669.g007", "stats"=>{"downloads"=>0, "page_views"=>6, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Structural_variability_within_the_population_/250667", "title"=>"Structural variability within the population.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2012-09-06 00:11:07"}
  • {"files"=>["https://ndownloader.figshare.com/files/580343"], "description"=>"<p>(A) The common ancestor network has 10 nodes and one of them (node number 9) is a global regulator that regulates 8 other nodes. (B) Diagram of strain survival times showing the first fixation event at generation <i>g</i> = 6411 (indicated by the red arrow). The common ancestor network is the one that gives rise to the population of the first fixation event. (C) Structure of a randomly chosen network in the final population (generation <i>g</i> = 250000). The initial hub (node number 9) is the one marked with the red circle. Note that at the end this is not a hub anymore, but just another ordinary node of the network. (D) Distribution of the link persistence for the 10 connections of the common ancestor. The black and red histograms represent the populations at the first fixation event and at the end of the simulation, respectively. Even after the first fixation event, the links , and almost disappear from the population. Furthermore, in the final population none of the links of the initial hub occur at significant frequency. By contrast, link is present in all the networks of the final population because node 2 became a hub throughout the evolutionary processes. Link is indicated with the blue bold arrow in (A).</p>", "links"=>[], "tags"=>["genetics and genomics", "Computational biology"], "article_id"=>250839, "categories"=>["Biological Sciences", "Genetics"], "users"=>["Christian Torres-Sosa", "Sui Huang", "Maximino Aldana"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002669.g008", "stats"=>{"downloads"=>1, "page_views"=>5, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Evolution_of_the_network_topology_/250839", "title"=>"Evolution of the network topology.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2012-09-06 00:13:59"}
  • {"files"=>["https://ndownloader.figshare.com/files/579969"], "description"=>"<p>(A) Histogram of the vertical genetic variability in the attractors of the evolved networks. Note that most of the genetic variability is concentrated around , which indicates that most of the genes in the attractors of the evolved networks switch back and forth between 0 and 1 throughout time. There are almost no frozen genes in these attractors ( is relatively small). (B) Histogram of the vertical variability in the attractors of <i>de novo</i> critical networks that were constructed to be critical by design and did not go through the evolutionary process. Note that in this case most of the genes are frozen in time, as the largest peak at indicates.</p>", "links"=>[], "tags"=>["variability"], "article_id"=>250468, "categories"=>["Biological Sciences", "Genetics"], "users"=>["Christian Torres-Sosa", "Sui Huang", "Maximino Aldana"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002669.g004", "stats"=>{"downloads"=>0, "page_views"=>6, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Genetic_variability_in_the_attractors_/250468", "title"=>"Genetic variability in the attractors.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2012-09-06 00:07:48"}
  • {"files"=>["https://ndownloader.figshare.com/files/579868"], "description"=>"<p>(A) Evolution of the average network sensitivity for four different populations, each initially composed of networks in one of the three dynamical regimes: ordered (, black), critical (, red), and chaotic (, green; and , blue). Under the Darwinian selection given by the ACC and AIC, all the populations quickly become critical (), regardless of their initial dynamical regime. The inset shows that convergence towards criticality occurs during the first 10000 generation steps. The control curves (in light gray) were obtained by evolving populations without selection, and show that the mutagenic method alone drives the networks into the chaotic regime (). (B) Distribution of sensitivities at two different generations for the population that started with chaotic networks. In early generations is quite broad (dashed line), reflecting a great diversity of networks. However, through evolution all the surviving networks approach criticality and the distribution narrows down (solid line). The distribution shown here at generation has .</p>", "links"=>[], "tags"=>["genetics and genomics", "Computational biology"], "article_id"=>250369, "categories"=>["Biological Sciences", "Genetics"], "users"=>["Christian Torres-Sosa", "Sui Huang", "Maximino Aldana"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002669.g003", "stats"=>{"downloads"=>1, "page_views"=>6, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Evolution_towards_criticality_/250369", "title"=>"Evolution towards criticality.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2012-09-06 00:06:09"}

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Relative Metric

{"start_date"=>"2012-01-01T00:00:00Z", "end_date"=>"2012-12-31T00:00:00Z", "subject_areas"=>[{"subject_area"=>"/Biology and life sciences/Genetics", "average_usage"=>[333, 576, 707, 814, 908, 1004, 1104, 1197, 1280, 1370, 1449, 1531, 1603, 1673, 1742, 1817, 1886, 1954, 2025, 2098, 2171, 2234, 2304, 2365, 2431]}, {"subject_area"=>"/Computer and information sciences", "average_usage"=>[352, 587, 696, 809, 901, 989, 1072, 1156, 1257, 1334, 1422, 1486, 1555, 1647, 1714, 1780, 1844, 1919, 1997, 2051, 2138, 2198, 2267, 2324, 2391]}, {"subject_area"=>"/Computer and information sciences/Network analysis", "average_usage"=>[388, 661, 797, 921, 1016, 1101, 1200, 1314, 1391, 1476, 1588, 1693, 1772, 1858, 1918, 2003, 2085, 2158, 2232, 2309, 2385, 2448, 2517, 2595, 2658]}]}
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