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{"title"=>"Accurate Encoding and Decoding by Single Cells: Amplitude Versus Frequency Modulation", "type"=>"journal", "authors"=>[{"first_name"=>"Gabriele", "last_name"=>"Micali", "scopus_author_id"=>"56397811200"}, {"first_name"=>"Gerardo", "last_name"=>"Aquino", "scopus_author_id"=>"6603614279"}, {"first_name"=>"David M.", "last_name"=>"Richards", "scopus_author_id"=>"10241416400"}, {"first_name"=>"Robert G.", "last_name"=>"Endres", "scopus_author_id"=>"7004320444"}], "year"=>2015, "source"=>"PLoS Computational Biology", "identifiers"=>{"sgr"=>"84953233591", "doi"=>"10.1371/journal.pcbi.1004222", "pui"=>"607497666", "pmid"=>"26030820", "scopus"=>"2-s2.0-84953233591", "issn"=>"15537358", "isbn"=>"1553-7358 (Electronic)\\r1553-734X (Linking)", "arxiv"=>"1505.05410"}, "id"=>"5bd51430-fe69-350e-a03a-da2cbc3267dd", "abstract"=>"Cells sense external concentrations and, via biochemical signaling, respond by regulating the expression of target proteins. Both in signaling networks and gene regulation there are two main mechanisms by which the concentration can be encoded internally: amplitude modulation (AM), where the absolute concentration of an internal signaling molecule encodes the stimulus, and frequency modulation (FM), where the period between successive bursts represents the stimulus. Although both mechanisms have been observed in biological systems, the question of when it is beneficial for cells to use either AM or FM is largely unanswered. Here, we first consider a simple model for a single receptor (or ion channel), which can either signal continuously whenever a ligand is bound, or produce a burst in signaling molecule upon receptor binding. We find that bursty signaling is more accurate than continuous signaling only for sufficiently fast dynamics. This suggests that modulation based on bursts may be more common in signaling networks than in gene regulation. We then extend our model to multiple receptors, where continuous and bursty signaling are equivalent to AM and FM respectively, finding that AM is always more accurate. This implies that the reason some cells use FM is related to factors other than accuracy, such as the ability to coordinate expression of multiple genes or to implement threshold crossing mechanisms.", "link"=>"http://www.mendeley.com/research/accurate-encoding-decoding-single-cells-amplitude-versus-frequency-modulation", "reader_count"=>70, "reader_count_by_academic_status"=>{"Unspecified"=>1, "Professor > Associate Professor"=>7, "Researcher"=>18, "Student > Doctoral Student"=>2, "Student > Ph. D. Student"=>29, "Student > Postgraduate"=>2, "Other"=>1, "Student > Master"=>2, "Student > Bachelor"=>3, "Lecturer > Senior Lecturer"=>1, "Professor"=>4}, "reader_count_by_user_role"=>{"Unspecified"=>1, "Professor > Associate Professor"=>7, "Researcher"=>18, "Student > Doctoral Student"=>2, "Student > Ph. D. Student"=>29, "Student > Postgraduate"=>2, "Other"=>1, "Student > Master"=>2, "Student > Bachelor"=>3, "Lecturer > Senior Lecturer"=>1, "Professor"=>4}, "reader_count_by_subject_area"=>{"Engineering"=>7, "Unspecified"=>3, "Biochemistry, Genetics and Molecular Biology"=>11, "Mathematics"=>2, "Agricultural and Biological Sciences"=>30, "Medicine and Dentistry"=>2, "Neuroscience"=>3, "Physics and Astronomy"=>8, "Psychology"=>1, "Computer Science"=>2, "Immunology and Microbiology"=>1}, "reader_count_by_subdiscipline"=>{"Engineering"=>{"Engineering"=>7}, "Medicine and Dentistry"=>{"Medicine and Dentistry"=>2}, "Neuroscience"=>{"Neuroscience"=>3}, "Physics and Astronomy"=>{"Physics and Astronomy"=>8}, "Psychology"=>{"Psychology"=>1}, "Immunology and Microbiology"=>{"Immunology and Microbiology"=>1}, "Agricultural and Biological Sciences"=>{"Agricultural and Biological Sciences"=>30}, "Computer Science"=>{"Computer Science"=>2}, "Biochemistry, Genetics and Molecular Biology"=>{"Biochemistry, Genetics and Molecular Biology"=>11}, "Mathematics"=>{"Mathematics"=>2}, "Unspecified"=>{"Unspecified"=>3}}, "reader_count_by_country"=>{"Argentina"=>1, "United States"=>1, "United Kingdom"=>1, "Israel"=>1, "Portugal"=>1, "Germany"=>3, "Russia"=>1}, "group_count"=>3}

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• http://doi.org/10.1007/s10955-015-1412-9
• http://doi.org/10.1016/j.devcel.2017.08.023
• http://doi.org/10.1371/journal.pcbi.1008011
• http://doi.org/10.1371/journal.pcbi.1005479
• http://doi.org/10.1142/S012918311650056X
• http://doi.org/10.1016/j.coisb.2017.03.003
• http://doi.org/10.1002/1873-3468.13012
• http://doi.org/10.3389/fncir.2017.00080
• http://doi.org/10.1038/s41598-018-21945-2
• http://doi.org/10.1371/journal.pcbi.1005101
• http://doi.org/10.1103/PhysRevE.93.052411
• http://doi.org/10.3389/fphys.2016.00525
• http://doi.org/10.1038/srep42128

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• {"files"=>["https://ndownloader.figshare.com/files/2091829"], "description"=>"<p>Output noise, <i>i.e</i>. relative variance of <i>x</i> (top) and <i>y</i> (bottom), as function of the non-dimensional ramp time <i>u</i>₁<i>t</i>/<i>u</i>₀ for <i>k</i>₊<i>c</i>₀ < <i>k</i>₋<i>i.e</i>. ⟨<i>τ</i>_<i>b</i>⟩ < ⟨<i>τ</i>_<i>u</i>⟩ (left) and <i>k</i>₊<i>c</i>₀ > <i>k</i>₋<i>i.e</i>. ⟨<i>τ</i>_<i>b</i>⟩ > ⟨<i>τ</i>_<i>u</i>⟩ (right). CM and BM are shown by blue and red lines respectively. (A,B) BM is more accurate than AM for <i>k</i>₊<i>c</i>₀ = 10⁷<i>s</i>⁻¹ and <i>k</i>₋ = 6.7 × 10⁷<i>s</i>⁻¹. (C,D) CM is more accurate then BM for <i>k</i>₊<i>c</i>₀ = 10⁷<i>s</i>⁻¹ and <i>k</i>₋ = 6.7 × 10⁶<i>s</i>⁻¹. Remaining parameters: <i>k</i>₊<i>c</i>₁ = 10⁵<i>s</i>⁻², <i>k</i>_<i>x</i> = 5<i>s</i>⁻¹ and <i>k</i>_<i>y</i> = 10<i>s</i>⁻¹.</p>", "links"=>[], "tags"=>["receptor", "Amplitude Versus Frequency Modulation Cells sense", "concentration", "mechanism", "cells use FM", "Gene regulation", "modulation", "molecule", "am", "stimulus", "bursty", "model", "expression"], "article_id"=>1433626, "categories"=>["Biological Sciences"], "users"=>["Gabriele Micali", "Gerardo Aquino", "David M. Richards", "Robert G. Endres"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1004222.g006", "stats"=>{"downloads"=>0, "page_views"=>8, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Two_regimes_in_incoherent_feedforward_loop_based_on_the_small_noise_approximation_/1433626", "title"=>"Two regimes in incoherent feedforward loop based on the small-noise approximation.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2015-06-01 05:13:12"}
• {"files"=>["https://ndownloader.figshare.com/files/2091824"], "description"=>"<p>(A-B) fast (<i>k</i>₊<i>c</i>₀ = 20<i>s</i>⁻¹, <i>k</i>₋ = 100<i>s</i>⁻¹, <i>γ</i> = 0.1<i>s</i>⁻¹, <i>α</i> = 100<i>s</i>⁻¹, <i>ζ</i> = 1) and (C-D) slow (<i>k</i>₊<i>c</i>₀ = 0.01<i>s</i>⁻¹, <i>k</i>₋ = 0.05<i>s</i>⁻¹, <i>γ</i> = 1<i>s</i>⁻¹, <i>α</i> = 25<i>s</i>⁻¹, <i>ζ</i> = 500) switching. (A,C) Protein number as a function of time from Gillespie simulations for CM (blue lines) and BM (red lines). (B) The probability distribution for <i>n</i> target proteins is unimodal for both AM (blue) and FM (red). (D) The probability distribution is bimodal for AM (blue) and remains unimodal for BM (red) but with a long tail in the slow switching regime.</p>", "links"=>[], "tags"=>["receptor", "Amplitude Versus Frequency Modulation Cells sense", "concentration", "mechanism", "cells use FM", "Gene regulation", "modulation", "molecule", "am", "stimulus", "bursty", "model", "expression"], "article_id"=>1433621, "categories"=>["Biological Sciences"], "users"=>["Gabriele Micali", "Gerardo Aquino", "David M. Richards", "Robert G. Endres"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1004222.g004", "stats"=>{"downloads"=>0, "page_views"=>10, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_The_two_regimes_in_the_linear_pathway_model_based_on_the_master_equation_/1433621", "title"=>"The two regimes in the linear pathway model based on the master equation.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2015-06-01 05:13:12"}
• {"files"=>["https://ndownloader.figshare.com/files/2091819"], "description"=>"<p>AM may be less noisy than FM (A,B), but FM may allow coordinated expression of many genes (C,D) [<a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004222#pcbi.1004222.ref015\" target=\"_blank\">15</a>, <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004222#pcbi.1004222.ref019\" target=\"_blank\">19</a>]. (A) In AM, low/high stimuli result in low/high levels of transcription factor (TF) inside the nucleus. (B) In AM, different nuclear TF concentrations (blue and red curves) lead to gene expression of proteins A and B (see orange and green promoter functions respectively) with variable ratios (order of dot and square changes). (C) In FM, the stimulus strength only affects the frequency of bursts, not their amplitude. (Inset) Schematic of TF (purple dots) binding promoter <i>P</i>_<i>A</i> of gene <i>A</i> (orange) and promoter <i>P</i>_<i>B</i> of gene <i>B</i> (green) with different binding strengths. (D) In FM, the nuclear TF concentration is always the same during a burst, only the frequency of occurrence changes. As a consequence, the protein ratio stays constant.</p>", "links"=>[], "tags"=>["receptor", "Amplitude Versus Frequency Modulation Cells sense", "concentration", "mechanism", "cells use FM", "Gene regulation", "modulation", "molecule", "am", "stimulus", "bursty", "model", "expression"], "article_id"=>1433616, "categories"=>["Biological Sciences"], "users"=>["Gabriele Micali", "Gerardo Aquino", "David M. Richards", "Robert G. Endres"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1004222.g002", "stats"=>{"downloads"=>0, "page_views"=>8, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Advantages_and_disadvantages_of_amplitude_and_frequency_modulation_/1433616", "title"=>"Advantages and disadvantages of amplitude and frequency modulation.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2015-06-01 05:13:12"}
• {"files"=>["https://ndownloader.figshare.com/files/2091817"], "description"=>"<p>(A and B) Example data showing amplitude modulation from [<a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004222#pcbi.1004222.ref010\" target=\"_blank\">10</a>]. (A) Single-cell nuclear localization of Msn2 transcription factor in response to H₂O₂ stress as a function of time. The stimulus profile (input) is a step change applied at <i>t</i> = 0 (inset) which applies to all figure panels. (B) Average time trace for different concentrations of H₂O₂ stress. (C and D) Example data showing frequency modulation from [<a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004222#pcbi.1004222.ref015\" target=\"_blank\">15</a>]. (C) Single-cell nuclear localization of Crz1 in response to calcium stress as a function of time, showing bursts of Crz1. (D) The average frequency of bursts against calcium concentration, showing an increased frequency with increased concentration. (Inset) Burst duration distribution for low (blue bars) and high (red bars) concentration. Both histograms are well described by the Gamma distribution <math><mrow><mi>h</mi><mo stretchy=\"false\">(</mo><mi>t</mi><mo stretchy=\"false\">)</mo><mo>=</mo><mi>t</mi><mi>e</mi><mrow><mo>−</mo><mi>t</mi><mo>/</mo><msub><mi>τ</mi><mi>b</mi></msub></mrow></mrow></math>, with <i>τ</i>_<i>b</i> = 70s (black solid line), demonstrating that pulse duration is independent of calcium concentration. Experimental data in arbitrary units (AU) of fluorescence.</p>", "links"=>[], "tags"=>["receptor", "Amplitude Versus Frequency Modulation Cells sense", "concentration", "mechanism", "cells use FM", "Gene regulation", "modulation", "molecule", "am", "stimulus", "bursty", "model", "expression"], "article_id"=>1433614, "categories"=>["Biological Sciences"], "users"=>["Gabriele Micali", "Gerardo Aquino", "David M. Richards", "Robert G. Endres"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1004222.g001", "stats"=>{"downloads"=>0, "page_views"=>8, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Experimental_evidence_for_amplitude_and_frequency_modulation_/1433614", "title"=>"Experimental evidence for amplitude and frequency modulation.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2015-06-01 05:13:12"}
• {"files"=>["https://ndownloader.figshare.com/files/2091831", "https://ndownloader.figshare.com/files/2091832", "https://ndownloader.figshare.com/files/2091833", "https://ndownloader.figshare.com/files/2091834", "https://ndownloader.figshare.com/files/2091835", "https://ndownloader.figshare.com/files/2091836", "https://ndownloader.figshare.com/files/2091837"], "description"=>"<div><p>Cells sense external concentrations and, via biochemical signaling, respond by regulating the expression of target proteins. Both in signaling networks and gene regulation there are two main mechanisms by which the concentration can be encoded internally: amplitude modulation (AM), where the absolute concentration of an internal signaling molecule encodes the stimulus, and frequency modulation (FM), where the period between successive bursts represents the stimulus. Although both mechanisms have been observed in biological systems, the question of when it is beneficial for cells to use either AM or FM is largely unanswered. Here, we first consider a simple model for a single receptor (or ion channel), which can either signal continuously whenever a ligand is bound, or produce a burst in signaling molecule upon receptor binding. We find that bursty signaling is more accurate than continuous signaling only for sufficiently fast dynamics. This suggests that modulation based on bursts may be more common in signaling networks than in gene regulation. We then extend our model to multiple receptors, where continuous and bursty signaling are equivalent to AM and FM respectively, finding that AM is always more accurate. This implies that the reason some cells use FM is related to factors other than accuracy, such as the ability to coordinate expression of multiple genes or to implement threshold crossing mechanisms.</p></div>", "links"=>[], "tags"=>["receptor", "Amplitude Versus Frequency Modulation Cells sense", "concentration", "mechanism", "cells use FM", "Gene regulation", "modulation", "molecule", "am", "stimulus", "bursty", "model", "expression"], "article_id"=>1433628, "categories"=>["Biological Sciences"], "users"=>["Gabriele Micali", "Gerardo Aquino", "David M. Richards", "Robert G. Endres"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1004222.s001", "https://dx.doi.org/10.1371/journal.pcbi.1004222.s002", "https://dx.doi.org/10.1371/journal.pcbi.1004222.s003", "https://dx.doi.org/10.1371/journal.pcbi.1004222.s004", "https://dx.doi.org/10.1371/journal.pcbi.1004222.s005", "https://dx.doi.org/10.1371/journal.pcbi.1004222.s006", "https://dx.doi.org/10.1371/journal.pcbi.1004222.s007"], "stats"=>{"downloads"=>19, "page_views"=>12, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Accurate_Encoding_and_Decoding_by_Single_Cells_Amplitude_Versus_Frequency_Modulation_/1433628", "title"=>"Accurate Encoding and Decoding by Single Cells: Amplitude Versus Frequency Modulation", "pos_in_sequence"=>0, "defined_type"=>4, "published_date"=>"2015-06-01 05:13:12"}
• {"files"=>["https://ndownloader.figshare.com/files/2091826"], "description"=>"<p>Averages (A,B), variance (C,D), and skewness (E,F) as a function of the frequency of binding events, <i>f</i> = <i>k</i>₊<i>c</i>₀/(1+<i>k</i>₊<i>c</i>₀/<i>k</i>₋). (Insets) Magnification of small-noise approximation region (fast switching). Analytical results for CM (blue) and numerical results for BM (red) as function of the frequency of binding events (logarithmic scale). Two regimes are shown: <i>k</i>₋ = 10 <i>k</i>₊<i>c</i>₀ (<i>α</i> = 100<i>s</i>⁻¹, <i>γ</i> = 1<i>s</i>⁻¹, <i>ζ</i> from 1000 to 1) (left column) and <i>k</i>₋ = 0.1 <i>k</i>₊<i>c</i>₀ (<i>α</i> = 10<i>s</i>⁻¹, <i>γ</i> = 1<i>s</i>⁻¹, <i>ζ</i> from 1000 to 1) (right column). Averages from CM and BM are constrained to be equal, <i>i.e</i>. <math><mrow><mi>ζ</mi><mo>=</mo><mi>α</mi><msubsup><mi>k</mi><mo>−</mo><mrow><mo>−</mo><mn>1</mn></mrow></msubsup></mrow></math>. Variances of CM and BM exhibit two different regimes for fast switching: for <i>k</i>₊<i>c</i>₀ < <i>k</i>₋ BM is more accurate than CM (inset in C), while for <i>k</i>₊<i>c</i>₀ > <i>k</i>₋ CM is generally more accurate (inset in D), except for <i>ζ</i> = 1. Third moments show that, for large noise, the probability distributions become asymmetric.</p>", "links"=>[], "tags"=>["receptor", "Amplitude Versus Frequency Modulation Cells sense", "concentration", "mechanism", "cells use FM", "Gene regulation", "modulation", "molecule", "am", "stimulus", "bursty", "model", "expression"], "article_id"=>1433623, "categories"=>["Biological Sciences"], "users"=>["Gabriele Micali", "Gerardo Aquino", "David M. Richards", "Robert G. Endres"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1004222.g005", "stats"=>{"downloads"=>0, "page_views"=>2, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_First_three_moments_of_the_protein_distribution_in_concentration_sensing_from_the_master_equation_/1433623", "title"=>"First three moments of the protein distribution in concentration sensing from the master equation.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2015-06-01 05:13:12"}
• {"files"=>["https://ndownloader.figshare.com/files/2091822"], "description"=>"<p>(A) Cartoon of <i>S. cerevisiae</i> in presence of extracellular calcium, considered a paradigm of bursty frequency modulation. Calcium enters through plasma-membrane ion channels and can be stored (released) in (from) vacuoles. Intracellular calcium activates calcineurin, which dephosphorylates Crz1p. Once dephosphorylated, Crz1 binds inporting Nmd5p and enters the nucleus. Exportin Msn5p subsequently removes Crz1 from the nucleus. Cytoplasmic calcium pulses may correspond to Crz1 bursts in the nucleus [<a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004222#pcbi.1004222.ref015\" target=\"_blank\">15</a>]. Red arrows indicate movement while blue arrows stand for chemical signaling. (B) Single receptor/ion channel activity, <i>r</i>(<i>t</i>) (blue line), depends on the concentration of extra-cellular stimulus <i>c</i>. The signaling rate <i>u</i> differs between continuous (CM) and bursty modulation (BM). In CM, <i>u</i> is constant rate <i>α</i> during bound intervals, with <i>p</i>_<i>b</i> the probability of being bound. In BM, <i>ζ</i> molecules are realized at the time of binding with <i>τ</i>_bursts the duration between consecutive bursts (binding events). (C) Different regulatory networks. Linear pathway used for concentration sensing. Incoherent feedforward loop and integral feedback control allow chemical ramps to be sensed.</p>", "links"=>[], "tags"=>["receptor", "Amplitude Versus Frequency Modulation Cells sense", "concentration", "mechanism", "cells use FM", "Gene regulation", "modulation", "molecule", "am", "stimulus", "bursty", "model", "expression"], "article_id"=>1433619, "categories"=>["Biological Sciences"], "users"=>["Gabriele Micali", "Gerardo Aquino", "David M. Richards", "Robert G. Endres"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1004222.g003", "stats"=>{"downloads"=>0, "page_views"=>7, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Schematic_view_of_signaling_and_gene_regulation_/1433619", "title"=>"Schematic view of signaling and gene regulation.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2015-06-01 05:13:12"}

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• {"unique-ip"=>"22", "full-text"=>"20", "pdf"=>"2", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"1", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2018", "month"=>"9"}
• {"unique-ip"=>"37", "full-text"=>"38", "pdf"=>"6", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"6", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2018", "month"=>"10"}
• {"unique-ip"=>"46", "full-text"=>"51", "pdf"=>"3", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"2", "cited-by"=>"3", "year"=>"2018", "month"=>"11"}
• {"unique-ip"=>"25", "full-text"=>"30", "pdf"=>"1", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"1", "year"=>"2018", "month"=>"12"}
• {"unique-ip"=>"25", "full-text"=>"27", "pdf"=>"1", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"1", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2019", "month"=>"2"}
• {"unique-ip"=>"22", "full-text"=>"23", "pdf"=>"3", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"2", "cited-by"=>"0", "year"=>"2019", "month"=>"3"}
• {"unique-ip"=>"25", "full-text"=>"29", "pdf"=>"2", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2019", "month"=>"4"}
• {"unique-ip"=>"14", "full-text"=>"14", "pdf"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2019", "month"=>"5"}
• {"unique-ip"=>"15", "full-text"=>"17", "pdf"=>"2", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2019", "month"=>"8"}
• {"unique-ip"=>"26", "full-text"=>"26", "pdf"=>"3", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2019", "month"=>"9"}
• {"unique-ip"=>"45", "full-text"=>"47", "pdf"=>"3", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2019", "month"=>"10"}
• {"unique-ip"=>"23", "full-text"=>"25", "pdf"=>"2", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"3", "supp-data"=>"0", "cited-by"=>"1", "year"=>"2019", "month"=>"12"}
• {"unique-ip"=>"25", "full-text"=>"23", "pdf"=>"3", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"2", "year"=>"2020", "month"=>"2"}
• {"unique-ip"=>"18", "full-text"=>"19", "pdf"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"2", "supp-data"=>"2", "cited-by"=>"0", "year"=>"2020", "month"=>"3"}
• {"unique-ip"=>"35", "full-text"=>"39", "pdf"=>"2", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2020", "month"=>"4"}
• {"unique-ip"=>"41", "full-text"=>"51", "pdf"=>"5", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"1", "cited-by"=>"0", "year"=>"2020", "month"=>"5"}
• {"unique-ip"=>"14", "full-text"=>"30", "pdf"=>"1", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"1", "cited-by"=>"0", "year"=>"2020", "month"=>"6"}
• {"unique-ip"=>"19", "full-text"=>"21", "pdf"=>"4", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2020", "month"=>"7"}
• {"unique-ip"=>"15", "full-text"=>"15", "pdf"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2020", "month"=>"8"}
• {"unique-ip"=>"17", "full-text"=>"45", "pdf"=>"1", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2020", "month"=>"9"}
• {"unique-ip"=>"25", "full-text"=>"39", "pdf"=>"2", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2020", "month"=>"10"}
• {"unique-ip"=>"31", "full-text"=>"35", "pdf"=>"5", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2020", "month"=>"11"}
• {"unique-ip"=>"13", "full-text"=>"14", "pdf"=>"5", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2020", "month"=>"12"}
• {"unique-ip"=>"20", "full-text"=>"23", "pdf"=>"2", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2021", "month"=>"1"}
• {"unique-ip"=>"21", "full-text"=>"28", "pdf"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2021", "month"=>"2"}

Relative Metric

{"start_date"=>"2015-01-01T00:00:00Z", "end_date"=>"2015-12-31T00:00:00Z", "subject_areas"=>[]}

F1000Prime