Entrainment of the Mammalian Cell Cycle by the Circadian Clock: Modeling Two Coupled Cellular Rhythms
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{"title"=>"Entrainment of the mammalian cell cycle by the circadian clock: Modeling two coupled cellular rhythms", "type"=>"journal", "authors"=>[{"first_name"=>"Claude", "last_name"=>"Gérard", "scopus_author_id"=>"35319811700"}, {"first_name"=>"Albert", "last_name"=>"Goldbeter", "scopus_author_id"=>"7004394703"}], "year"=>2012, "source"=>"PLoS Computational Biology", "identifiers"=>{"scopus"=>"2-s2.0-84863643126", "doi"=>"10.1371/journal.pcbi.1002516", "sgr"=>"84863643126", "isbn"=>"1553-7358", "pmid"=>"22693436", "issn"=>"1553734X", "pui"=>"365220675"}, "id"=>"ad4f6378-6c2b-3ea1-83db-df46636f3666", "abstract"=>"The cell division cycle and the circadian clock represent two major cellular rhythms. These two periodic processes are coupled in multiple ways, given that several molecular components of the cell cycle network are controlled in a circadian manner. For example, in the network of cyclin-dependent kinases (Cdks) that governs progression along the successive phases of the cell cycle, the synthesis of the kinase Wee1, which inhibits the G2/M transition, is enhanced by the complex CLOCK-BMAL1 that plays a central role in the circadian clock network. Another component of the latter network, REV-ERBα, inhibits the synthesis of the Cdk inhibitor p21. Moreover, the synthesis of the oncogene c-Myc, which promotes G1 cyclin synthesis, is repressed by CLOCK-BMAL1. Using detailed computational models for the two networks we investigate the conditions in which the mammalian cell cycle can be entrained by the circadian clock. We show that the cell cycle can be brought to oscillate at a period of 24 h or 48 h when its autonomous period prior to coupling is in an appropriate range. The model indicates that the combination of multiple modes of coupling does not necessarily facilitate entrainment of the cell cycle by the circadian clock. Entrainment can also occur as a result of circadian variations in the level of a growth factor controlling entry into G1. Outside the range of entrainment, the coupling to the circadian clock may lead to disconnected oscillations in the cell cycle and the circadian system, or to complex oscillatory dynamics of the cell cycle in the form of endoreplication, complex periodic oscillations or chaos. The model predicts that the transition from entrainment to 24 h or 48 h might occur when the strength of coupling to the circadian clock or the level of growth factor decrease below critical values.", "link"=>"http://www.mendeley.com/research/entrainment-mammalian-cell-cycle-circadian-clock-modeling-two-coupled-cellular-rhythms", "reader_count"=>88, "reader_count_by_academic_status"=>{"Unspecified"=>1, "Professor > Associate Professor"=>1, "Researcher"=>18, "Student > Doctoral Student"=>1, "Student > Ph. D. Student"=>28, "Student > Postgraduate"=>2, "Student > Master"=>17, "Other"=>3, "Student > Bachelor"=>10, "Lecturer"=>1, "Professor"=>6}, "reader_count_by_user_role"=>{"Unspecified"=>1, "Professor > Associate Professor"=>1, "Researcher"=>18, "Student > Doctoral Student"=>1, "Student > Ph. D. Student"=>28, "Student > Postgraduate"=>2, "Student > Master"=>17, "Other"=>3, "Student > Bachelor"=>10, "Lecturer"=>1, "Professor"=>6}, "reader_count_by_subject_area"=>{"Engineering"=>2, "Unspecified"=>2, "Biochemistry, Genetics and Molecular Biology"=>12, "Mathematics"=>7, "Agricultural and Biological Sciences"=>37, "Medicine and Dentistry"=>9, "Neuroscience"=>4, "Physics and Astronomy"=>7, "Chemical Engineering"=>1, "Chemistry"=>2, "Computer Science"=>4, "Linguistics"=>1}, "reader_count_by_subdiscipline"=>{"Engineering"=>{"Engineering"=>2}, "Medicine and Dentistry"=>{"Medicine and Dentistry"=>9}, "Neuroscience"=>{"Neuroscience"=>4}, "Chemistry"=>{"Chemistry"=>2}, "Physics and Astronomy"=>{"Physics and Astronomy"=>7}, "Agricultural and Biological Sciences"=>{"Agricultural and Biological Sciences"=>37}, "Computer Science"=>{"Computer Science"=>4}, "Linguistics"=>{"Linguistics"=>1}, "Biochemistry, Genetics and Molecular Biology"=>{"Biochemistry, Genetics and Molecular Biology"=>12}, "Mathematics"=>{"Mathematics"=>7}, "Unspecified"=>{"Unspecified"=>2}, "Chemical Engineering"=>{"Chemical Engineering"=>1}}, "reader_count_by_country"=>{"Sweden"=>1, "Netherlands"=>1, "Turkey"=>1, "United States"=>2, "Ireland"=>1, "United Kingdom"=>1, "Italy"=>1, "India"=>1}, "group_count"=>1}

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Figshare

  • {"files"=>["https://ndownloader.figshare.com/files/629667"], "description"=>"<p>(A) Domains of entrainment of the cell cycle by the circadian clock at 24 h and 48 h. As in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002516#pcbi-1002516-g004\" target=\"_blank\">Fig. 4</a>, periods of the cell cycle smaller or larger than 24 h can be entrained at 24 h by the circadian clock, although the domain enlarges for periods less than 24 h. The two domains are close to each other when the autonomous period is in the range 30 h–40 h. (B) Time series showing the switch from entrainment of the cell cycle by the circadian clock at 48 h (t<240 h) to entrainment at 24 h (t>240 h) resulting from an increase of about 6.5% in coupling strength, when the autonomous period is equal to 34 h. The light-dark (LD) cycle is represented by a dashed line; the high and low portions of the square wave correspond to the L (16 h) and D (8 h) phases, respectively. In the presence of entrainment at 24 h, cyclin B/Cdk1 peaks at the end of the L phase, in agreement with experimental observations <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002516#pcbi.1002516-Bjarnason1\" target=\"_blank\">[23]</a>. Parameter values in eqs. [3] and [4] (see <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002516#s4\" target=\"_blank\">Methods</a>) are: <i>K</i><sub>ip21</sub> = 0.05 nM, <i>nmp21</i> = 1, <i>V</i><sub>dmp21</sub> = 0.5 µM h<sup>−1</sup>, <i>K</i><sub>dmp21</sub> = 0.5 µM, and <i>v</i><sub>s1p21</sub> = 50 h<sup>−1</sup>. Moreover, in (B), at t = 240 h parameter <i>v</i><sub>smp21</sub> measuring coupling strength increases from 0.46 µM h<sup>−1</sup> to 0.49 µM h<sup>−1</sup>. As in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002516#pcbi-1002516-g002\" target=\"_blank\">Fig. 2</a>, the values of the parameters in the model for the circadian clock are those corresponding to <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002516#pcbi-1002516-g008\" target=\"_blank\">Fig. 8</a> of the Supporting Information in Ref. <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002516#pcbi.1002516-Leloup1\" target=\"_blank\">[21]</a> with <i>K</i><sub>ib</sub> = 1 nM. While the shift in entrainment pattern in (B) follows from a permanent change in parameter value (here the coupling strength), a similar switch between the two modes of entrainment could also result from a transient perturbation, because in the region where the two domains of entrainment are close to each other in (A), numerical simulations indicate that the two stable modes of entrainment to 24 h and 48 h may sometimes coexist in the same conditions. This coexistence phenomenon corresponds to birhythmicity <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002516#pcbi.1002516-Goldbeter1\" target=\"_blank\">[1]</a>, <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002516#pcbi.1002516-Grard3\" target=\"_blank\">[36]</a>.</p>", "links"=>[], "tags"=>["cdk", "inhibitor", "p21", "induced", "circadian"], "article_id"=>300162, "categories"=>["Biological Sciences", "Genetics"], "users"=>["Claude Gérard", "Albert Goldbeter"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002516.g008", "stats"=>{"downloads"=>1, "page_views"=>8, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Entrainment_of_the_cell_cycle_through_the_Cdk_inhibitor_p21_induced_by_the_circadian_clock_protein_REV_ERB_945_/300162", "title"=>"Entrainment of the cell cycle through the Cdk inhibitor p21 induced by the circadian clock protein REV-ERBα.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-20 04:24:55"}
  • {"files"=>["https://ndownloader.figshare.com/files/629031"], "description"=>"<p>The time series show the evolution of cyclin B/Cdk1 (red), the kinase Wee1 (blue), and the circadian complex CLOCK-BMAL1 (green) in the absence (A, B) or presence (C, D) of coupling to the circadian clock. The autonomous period of the cell cycle is either smaller (left column) or larger (right column) than 24 h; prior to coupling (upper row), the oscillations in the cell cycle (reflected by Wee1 and cyclin B/Cdk1) have then a period distinct from that of the circadian clock (reflected by CLOCK-BMAL1). In both cases the coupling to the circadian clock via Wee1 (see <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002516#s4\" target=\"_blank\">Methods</a>) results in the entrainment of the cell cycle (lower row): the period then shifts from 20 h (A) to 24 h (C), and from 28 h (B) to 24 h (D), so that now Wee1, cyclin B/Cdk1 and CLOCK-BMAL1 all oscillate with a fixed phase relationship and with the same period equal to 24 h. The curves have been obtained by numerical integration of the kinetic equations [1]–[39] listed in the Supporting Information in Ref. 14, supplemented with eqs. [1]–[2] given in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002516#s4\" target=\"_blank\">Methods</a>. The latter equations include the variable CLOCK-BMAL1 whose time evolution is obtained by the concomitant numerical integration of eqs. [1]–[19] that govern the dynamics of the model for the mammalian circadian clock <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002516#pcbi.1002516-Leloup1\" target=\"_blank\">[21]</a>; these equations are listed together with parameter values in the Supporting Information in Ref. 21 (see <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002516#s4\" target=\"_blank\">Methods</a>). Parameter values for the Cdk network are those listed in Table S2 of <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002516#pcbi.1002516-Grard1\" target=\"_blank\">[14]</a>, with <i>v</i><sub>cb</sub> = 0.055 µM h<sup>−1</sup>. Moreover, <i>v</i><sub>sw</sub> = 0 for A and B, and 0.1 µM h<sup>−1</sup> for C and D; <i>K</i><sub>aw</sub> = 2 nM, <i>V</i><sub>dmw</sub> = 0.5 µM h<sup>−1</sup>, <i>K</i><sub>dmw</sub> = 0.5 µM, <i>nmw</i> = 4, and <i>k</i><sub>sw</sub> = 5 h<sup>−1</sup>.</p>", "links"=>[], "tags"=>["circadian", "kinase"], "article_id"=>299524, "categories"=>["Biological Sciences", "Genetics"], "users"=>["Claude Gérard", "Albert Goldbeter"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002516.g002", "stats"=>{"downloads"=>0, "page_views"=>8, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Entrainment_of_the_cell_cycle_by_the_circadian_clock_through_the_kinase_Wee1_/299524", "title"=>"Entrainment of the cell cycle by the circadian clock through the kinase Wee1.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-20 04:21:23"}
  • {"files"=>["https://ndownloader.figshare.com/files/630376"], "description"=>"<p>The curves show the time evolution of cyclin B/Cdk1 (red curve) and Wee1 mRNA (blue curve) in the presence (t<120 h) or absence (t>120 h) of the clock protein Cry. For t<120 h, the cell cycle is entrained by the circadian clock via the kinase Wee1 to oscillate at 24 h (conditions correspond in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002516#pcbi-1002516-g004\" target=\"_blank\">Fig. 4A</a> to an autonomous period of the cell cycle of 18 h and a coupling strength <i>v</i><sub>sw</sub>, which is equal to 0.05 µM h<sup>−1</sup>). When Cry is deleted (t>120 h), the maximum level of Wee1 mRNA increases by about 35%, which fits with experimental observations (see <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002516#pcbi.1002516-Matsuo1\" target=\"_blank\">[10]</a>). The model also shows that in the absence of Cry, the circadian network ceases to oscillate while the cell cycle is slowed down; as a result of the increase in Wee1 the period of the cell cycle indeed passes from 24 h (its value upon entrainment) to nearly 40 h, which value is larger than its autonomous period in the absence of coupling, i.e. 18 h. Other parameter values are as in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002516#pcbi-1002516-g004\" target=\"_blank\">Fig. 4A</a>.</p>", "links"=>[], "tags"=>["cdk", "coupling", "circadian", "deletion"], "article_id"=>300869, "categories"=>["Biological Sciences", "Genetics"], "users"=>["Claude Gérard", "Albert Goldbeter"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002516.g015", "stats"=>{"downloads"=>1, "page_views"=>7, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Dynamical_behavior_of_the_Cdk_network_in_the_model_for_coupling_the_cell_cycle_to_the_circadian_clock_upon_deletion_of_the_circadian_clock_protein_Cry_/300869", "title"=>"Dynamical behavior of the Cdk network in the model for coupling the cell cycle to the circadian clock upon deletion of the circadian clock protein Cry.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-20 04:28:39"}
  • {"files"=>["https://ndownloader.figshare.com/files/629315"], "description"=>"<p>The cell cycle is coupled to the circadian clock through the kinase Wee1. Shown in each panel are the time series for cyclin B/Cdk1 (red), the kinase Wee1 (blue) and the circadian complex CLOCK-BMAL1 (green) before (t<120 h) or after (t>120 h) coupling to the circadian clock. Conditions A–C correspond, respectively, to points A–C in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002516#pcbi-1002516-g004\" target=\"_blank\">Fig. 4A</a>. (A) The cell cycle has an autonomous period of 16 h and is entrained to 24 h when the coupling strength, measured by parameter <i>v</i><sub>sw</sub> is sufficiently large. In t = 120 h, <i>v</i><sub>sw</sub> is raised from 0 to 0.02 µM h<sup>−1</sup>. (B) For the same coupling strength, i.e. for the same increase in <i>v</i><sub>sw</sub>, entrainment to 48 h occurs when the autonomous period prior to coupling is 38 h. One peak in Cdk1 occurs for every second peak in BMAL1. (C) When the autonomous period is 16 h as in (A), the cell cycle fails to be entrained by the circadian clock when the coupling strength is reduced; here <i>v</i><sub>sw</sub> increases from 0 to 0.0012 µM h<sup>−1</sup> in t = 120 h. Other parameters values are the same as in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002516#pcbi-1002516-g004\" target=\"_blank\">Fig. 4A</a>.</p>", "links"=>[], "tags"=>["24", "48"], "article_id"=>299815, "categories"=>["Biological Sciences", "Genetics"], "users"=>["Claude Gérard", "Albert Goldbeter"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002516.g005", "stats"=>{"downloads"=>1, "page_views"=>4, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Entrainment_of_the_cell_cycle_to_24_h_or_48_h_/299815", "title"=>"Entrainment of the cell cycle to 24 h or 48 h.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-20 04:22:58"}
  • {"files"=>["https://ndownloader.figshare.com/files/629409"], "description"=>"<p>As in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002516#pcbi-1002516-g002\" target=\"_blank\">Figs. 2</a>–<a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002516#pcbi-1002516-g003\" target=\"_blank\"></a><a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002516#pcbi-1002516-g004\" target=\"_blank\"></a><a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002516#pcbi-1002516-g005\" target=\"_blank\">5</a> and <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002516#pcbi-1002516-g007\" target=\"_blank\">7</a>, coupling is achieved through the kinase Wee1. Shown is the time evolution of cyclin E/Cdk2 (blue) and cyclin B/Cdk1 (red) in the absence (t<120 h) or presence (t>120 h) of coupling to the circadian clock. Conditions A–D correspond, respectively, to the points D–G surrounding the domain of entrainment to 24 h in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002516#pcbi-1002516-g004\" target=\"_blank\">Fig. 4A</a>. (A) Complex periodic oscillations. The autonomous period of the cell cycle is equal to 4 h and the coupling strength, measured by the rate constant for the synthesis of Wee1 mRNA, <i>v</i><sub>sw</sub>, is equal to 0.05 µM h<sup>−1</sup>; the period of the cell cycle is too short to be well entrained by the circadian clock, and two peaks of cyclin B/Cdk1 appear every 24 h, together with a small and a large peak in cyclin E/Cdk2. (B) The autonomous period of the cell cycle is equal to 30 h and <i>v</i><sub>sw</sub> is still equal to 0.05 µM h<sup>−1</sup>. In this case, two peaks of cyclin E/Cdk2 appear for each peak of cyclin B/Cdk1. Such complex periodic oscillations would correspond to tetraploidy. (C) The autonomous period of the cell cycle is equal to 16 h and <i>v</i><sub>sw</sub> is equal to 0.01 µM h<sup>−1</sup>. Coupling is not strong enough to allow correct entrainment of the cell cycle by the circadian clock, resulting in irregular, chaotic oscillatory behavior (cyclin E/Cdk2 is not shown, for the sake of clarity). The chaotic nature of the oscillations was characterized by means of Poincaré sections, as described in Fig. 9 of <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002516#pcbi.1002516-Grard2\" target=\"_blank\">[25]</a>. (D) The autonomous period of the cell cycle is equal to 16 h and <i>v</i><sub>sw</sub> is equal to 0.3 µM h<sup>−1</sup>. Here, the coupling is so strong that it induces a high level of Wee1, which continuously inhibits the kinase Cdk1 while oscillations of Cdk2 persist. This simple periodic behavior would correspond to endoreplication. Other parameter values are as in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002516#pcbi-1002516-g004\" target=\"_blank\">Fig. 4A</a>.</p>", "links"=>[], "tags"=>["oscillatory", "induced", "coupling", "circadian"], "article_id"=>299901, "categories"=>["Biological Sciences", "Genetics"], "users"=>["Claude Gérard", "Albert Goldbeter"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002516.g006", "stats"=>{"downloads"=>1, "page_views"=>3, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Complex_oscillatory_behavior_of_the_cell_cycle_induced_by_coupling_to_the_circadian_clock_/299901", "title"=>"Complex oscillatory behavior of the cell cycle induced by coupling to the circadian clock.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-20 04:23:30"}
  • {"files"=>["https://ndownloader.figshare.com/files/630184"], "description"=>"<p>(A) In the continuous presence of GF at a constant value (GF = 1 µM), for t<120 h and t>280 h, cells proliferate with an autonomous period of 16 h. For 120 h[14]. Parameter values are listed in Table S2 of Ref. 14.</p>", "links"=>[], "tags"=>["circadian"], "article_id"=>300688, "categories"=>["Biological Sciences", "Genetics"], "users"=>["Claude Gérard", "Albert Goldbeter"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002516.g013", "stats"=>{"downloads"=>1, "page_views"=>7, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Entrainment_of_the_cell_cycle_by_a_circadian_variation_of_growth_factor_GF_/300688", "title"=>"Entrainment of the cell cycle by a circadian variation of growth factor (GF).", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-20 04:27:41"}
  • {"files"=>["https://ndownloader.figshare.com/files/629203"], "description"=>"<p>The domains are determined as a function of the autonomous period of the cell cycle prior to coupling and of the strength of coupling (see text and <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002516#s4\" target=\"_blank\">Methods</a>). We consider that the cell cycle is entrained when Cdk2 and Cdk1 both exhibit one large-amplitude peak per 24 h or 48 h. Entrainment of the cell cycle to 24 h occurs for autonomous periods smaller or larger than 24 h. The domains of entrainment are determined in the presence (A) or absence (B) of a basal rate of synthesis, <i>v</i><sub>swee1</sub>, of the kinase Wee1, which is equal to 0.06 µM h<sup>−1</sup> or 0, respectively. The size of the domains of entrainment of the cell cycle by the circadian clock increases as the basal rate of synthesis of Wee1 diminishes. Points A–I refer to situations illustrated in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002516#pcbi-1002516-g005\" target=\"_blank\">Figs. 5</a>–<a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002516#pcbi-1002516-g006\" target=\"_blank\"></a><a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002516#pcbi-1002516-g007\" target=\"_blank\">7</a>. The results are obtained as described in the legend to <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002516#pcbi-1002516-g002\" target=\"_blank\">Fig. 2</a>, for <i>v</i><sub>cb</sub> = 0.05 µM h<sup>−1</sup>. Other parameters values are the same as in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002516#pcbi-1002516-g002\" target=\"_blank\">Fig. 2</a>.</p>", "links"=>[], "tags"=>["entrainment", "circadian", "kinase"], "article_id"=>299697, "categories"=>["Biological Sciences", "Genetics"], "users"=>["Claude Gérard", "Albert Goldbeter"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002516.g004", "stats"=>{"downloads"=>1, "page_views"=>3, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Domains_of_entrainment_of_the_cell_cycle_by_the_circadian_clock_via_circadian_control_of_the_kinase_Wee1_/299697", "title"=>"Domains of entrainment of the cell cycle by the circadian clock via circadian control of the kinase Wee1.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-20 04:22:21"}
  • {"files"=>["https://ndownloader.figshare.com/files/630313"], "description"=>"<p>The curves show the time evolution of cyclin A/Cdk2 (green) and cyclin B/Cdk1 (red), as well as the LD cycle (dashed line). The Cdk network is coupled to the circadian clock through Wee1 and cyclin E, for μ = 0.028 —for this value of the coupling strength the domains of entrainment to 24 h or 48 h are very close to each other in the diagram of <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002516#pcbi-1002516-g009\" target=\"_blank\">Fig. 9D</a>. In these conditions a decrease in the level of the growth factor GF in t = 240 h (arrow) from 1 µM to 0.3 µM lengthens the autonomous period of the cell cycle from 21.6 h to 23.0 h. The rise in period associated with the decrease in GF results in shifting the period of the entrained cell cycle from 24 h to 48 h. Parameter values are as in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002516#pcbi-1002516-g009\" target=\"_blank\">Fig. 9D</a>. The scaling parameter <i>eps</i> is equal to 15 (see <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002516#s4\" target=\"_blank\">Methods</a>).</p>", "links"=>[], "tags"=>["entrainment", "circadian"], "article_id"=>300821, "categories"=>["Biological Sciences", "Genetics"], "users"=>["Claude Gérard", "Albert Goldbeter"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002516.g014", "stats"=>{"downloads"=>0, "page_views"=>2, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Growth_factor_induced_switch_in_the_pattern_of_entrainment_of_the_cell_cycle_by_the_circadian_clock_/300821", "title"=>"Growth-factor-induced switch in the pattern of entrainment of the cell cycle by the circadian clock.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-20 04:28:21"}
  • {"files"=>["https://ndownloader.figshare.com/files/629912"], "description"=>"<p>Conditions correspond to the black dot in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002516#pcbi-1002516-g009\" target=\"_blank\">Fig. 9F</a>: the cell cycle period changes from 18 h to 24 h upon coupling (vertical arrow). Shown is the time evolution of cyclin A/Cdk2 (green) and cyclin B/Cdk1 (red) in the absence (t<240 h) or presence (t>240 h) of multiple coupling to the circadian clock. The dashed line represents the LD cycle, as explained in the legend to <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002516#pcbi-1002516-g003\" target=\"_blank\">Figs. 3</a> and <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002516#pcbi-1002516-g008\" target=\"_blank\">8</a>. Parameter μ, which measures the coupling strength (see <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002516#s4\" target=\"_blank\">Methods</a>), is equal to 0 for t<240 h and 0.01 for t>240 h.</p>", "links"=>[], "tags"=>["circadian", "modes", "coupling", "cyclin"], "article_id"=>300406, "categories"=>["Biological Sciences", "Genetics"], "users"=>["Claude Gérard", "Albert Goldbeter"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002516.g010", "stats"=>{"downloads"=>1, "page_views"=>16, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Entrainment_of_the_cell_cycle_by_the_circadian_clock_in_the_presence_of_multiple_modes_of_coupling_through_Wee1_p21_and_cyclin_E_/300406", "title"=>"Entrainment of the cell cycle by the circadian clock in the presence of multiple modes of coupling through Wee1, p21, and cyclin E.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-20 04:26:18"}
  • {"files"=>["https://ndownloader.figshare.com/files/629788"], "description"=>"<p>(A) Domains of entrainment through the kinase Wee1 in the presence of a basal rate of synthesis of the protein, <i>v</i><sub>swee1</sub> = 0.06 µM h<sup>−1</sup>. (B) Entrainment through the Cdk inhibitor p21. (C) Entrainment through the circadian regulation of the synthesis of cyclin E. (D) Entrainment of the cell cycle by the circadian clock through Wee1 and cyclin E. (E) Entrainment through Wee1 and p21. (F) Entrainment through Wee1, p21, and cyclin E. The black dot in (F) refers to the conditions in which entrainment through multiple modes of coupling occurs in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002516#pcbi-1002516-g010\" target=\"_blank\">Fig. 10</a>. In (C), (D) and (F), parameter values in eqs. [5] and [6] (see <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002516#s4\" target=\"_blank\">Methods</a>) are: <i>K</i><sub>ice</sub> = 1 nM, <i>V</i><sub>dmce</sub> = 0.5 µM h<sup>−1</sup>, <i>K</i><sub>dmce</sub> = 0.5 µM, <i>nce</i> = 4, <i>k</i><sub>ce2</sub> = 5 h<sup>−1</sup>. The strength of coupling through cyclin E is measured by the rate of synthesis of cyclin E mRNA depending on CLOCK-BMAL1, <i>v</i><sub>sce</sub>. When multiple modes of coupling operate simultaneously, we multiply the rate of synthesis of <i>Mw</i>, <i>Mp21</i>, or <i>Mce</i> in eqs. [1]–[6] by the parameter μ, and put the value of <i>v</i><sub>sw</sub>, <i>v</i><sub>smp21</sub>, or <i>v</i><sub>sce</sub> equal to 1 µM h<sup>−1</sup>; μ then measures the strength of coupling to the circadian clock (see <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002516#s4\" target=\"_blank\">Methods</a> where the various modes of coupling are detailed). The diagrams in (A) and (B) are the same as those of <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002516#pcbi-1002516-g004\" target=\"_blank\">Fig. 4A</a> and <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002516#pcbi-1002516-g008\" target=\"_blank\">8A</a>, respectively; they are reproduced here to facilitate comparison with the other modes of entrainment.</p>", "links"=>[], "tags"=>["24", "48", "circadian", "modes"], "article_id"=>300280, "categories"=>["Biological Sciences", "Genetics"], "users"=>["Claude Gérard", "Albert Goldbeter"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002516.g009", "stats"=>{"downloads"=>4, "page_views"=>7, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Entrainment_of_the_cell_cycle_at_24_h_or_48_h_by_the_circadian_clock_through_multiple_modes_of_coupling_/300280", "title"=>"Entrainment of the cell cycle at 24 h or 48 h by the circadian clock through multiple modes of coupling.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-20 04:25:36"}
  • {"files"=>["https://ndownloader.figshare.com/files/630070"], "description"=>"<p>(A) Upon raising the rate of pRB synthesis, <i>v</i><sub>spRB</sub>, above a critical value, and in the absence of coupling to the circadian clock (0[14]. Coupling to the circadian clock through Wee1 is achieved by raising the rate of synthesis of Wee1 mRNA, <i>v</i><sub>sw</sub>, from 0 to 0.1 µM h<sup>−1</sup> in t = 120 h (vertical arrow); this results in the entrainment of the Cdk network, reflected by the circadian variation of cyclin B/Cdk1 (red). (B) Further increase in the rate of synthesis of pRB still yields a stable steady state, but entrainment by the circadian clock fails to occur, as only tiny variations in the level of cyclin B/Cdk1 are observed. (C) Instead of increasing pRB, we increase the level of the phosphatase Cdc25 acting on Cdk1. The Cdk network then reaches a stable steady state characterized by a high level of cyclin B/Cdk1 <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002516#pcbi.1002516-Grard1\" target=\"_blank\">[14]</a>. Circadian entrainment of Cdk1 through the circadian variation in Wee1 (blue) is also obtained in such conditions. Parameter <i>v</i><sub>spRB</sub>, which is equal to 0.8 µM h<sup>−1</sup> in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002516#pcbi-1002516-g002\" target=\"_blank\">Figs. 2</a>–<a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002516#pcbi-1002516-g003\" target=\"_blank\"></a><a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002516#pcbi-1002516-g004\" target=\"_blank\"></a><a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002516#pcbi-1002516-g005\" target=\"_blank\"></a><a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002516#pcbi-1002516-g006\" target=\"_blank\"></a><a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002516#pcbi-1002516-g007\" target=\"_blank\"></a><a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002516#pcbi-1002516-g008\" target=\"_blank\"></a><a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002516#pcbi-1002516-g009\" target=\"_blank\"></a><a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002516#pcbi-1002516-g010\" target=\"_blank\"></a><a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002516#pcbi-1002516-g011\" target=\"_blank\">11</a>, is raised up to 1 µM h<sup>−1</sup> in (A) and 2 µM h<sup>−1</sup> in (B). In (C), the rate of synthesis of Cdc25, <i>v</i><sub>spbi</sub>, which is equal to 0.12 µM h<sup>−1</sup> in all other figures, is raised to 0.3 µM h<sup>−1</sup>, with <i>v</i><sub>spRB</sub> = 0.8 µM h<sup>−1</sup>. Other parameters are in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002516#pcbi-1002516-g004\" target=\"_blank\">Fig. 4A</a>.</p>", "links"=>[], "tags"=>["entrainment", "quiescent"], "article_id"=>300570, "categories"=>["Biological Sciences", "Genetics"], "users"=>["Claude Gérard", "Albert Goldbeter"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002516.g012", "stats"=>{"downloads"=>0, "page_views"=>6, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Circadian_entrainment_of_a_quiescent_cell_/300570", "title"=>"Circadian entrainment of a quiescent cell.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-20 04:27:05"}
  • {"files"=>["https://ndownloader.figshare.com/files/629119"], "description"=>"<p>The time series show the time evolution of cyclin B/Cdk1 and of Wee1 mRNA in the absence (<i>v</i><sub>sw</sub> = 0 for t<120 h) or presence (<i>v</i><sub>sw</sub> = 0.1 µM h<sup>−1</sup> for t>120 h) of coupling to the circadian clock, when the autonomous period of the cell cycle, prior to coupling via Wee1, is smaller (20 h, A) or larger (28 h, B) than 24 h. In both cases, cyclin B/Cdk1 peaks at the end of the L phase upon entrainment, in agreement with experimental observations <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002516#pcbi.1002516-Bjarnason1\" target=\"_blank\">[23]</a>. The square wave (dashed line) represents the 24-h LD cycle; it corresponds to the increase above a basal value in the rate of synthesis, <i>v</i><sub>sP</sub>, of <i>Per</i> mRNA during the L phase. This increment goes from zero in the D phase to 0.3 nM h<sup>−1</sup> in the L phase. In all figures the durations of the L and D phases are equal to 16 h and 8 h, respectively. The values of the parameters in the model for the circadian clock are those corresponding to <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002516#pcbi-1002516-g008\" target=\"_blank\">Fig. 8</a> of the Supporting Information in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002516#pcbi.1002516-Leloup1\" target=\"_blank\">[21]</a>, with <i>K</i><sub>ib</sub> = 1 nM. The desired autonomous period of the cell cycle is achieved by adjusting the scaling parameter <i>eps</i> (see <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002516#pcbi.1002516-Grard1\" target=\"_blank\">[14]</a> and <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002516#s4\" target=\"_blank\">Methods</a>), with <i>eps</i> = 21.58 in A, and 15.37 in B. Parameter values are the same as in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002516#pcbi-1002516-g002\" target=\"_blank\">Fig. 2</a>.</p>", "links"=>[], "tags"=>["light-dark", "entrainment", "circadian", "kinase"], "article_id"=>299615, "categories"=>["Biological Sciences", "Genetics"], "users"=>["Claude Gérard", "Albert Goldbeter"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002516.g003", "stats"=>{"downloads"=>3, "page_views"=>6, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Phase_of_the_cell_cycle_in_the_light_dark_LD_cycle_upon_entrainment_by_the_circadian_clock_through_the_kinase_Wee1_/299615", "title"=>"Phase of the cell cycle in the light-dark (LD) cycle upon entrainment by the circadian clock through the kinase Wee1.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-20 04:21:52"}
  • {"files"=>["https://ndownloader.figshare.com/files/629974"], "description"=>"<p>The curves illustrate the effect of an activation of the ATR/Chk1 DNA replication checkpoint in the presence of coupling to the circadian clock through the kinase Wee1. Shown is the time evolution of cyclin E/Cdk2 (blue) and cyclin B/Cdk1 (red) in the absence (t<120 h) or presence (t>120 h) of coupling. For t>240 h, the DNA replication checkpoint is activated (second vertical arrow) by increasing the rate of synthesis of the kinase ATR, <i>k</i><sub>aatr</sub>, which passes from 0 to 0.025 µM<sup>−1</sup> h<sup>−1</sup> (weak activation) in (A) or from 0 to 0.075 µM<sup>−1</sup> h<sup>−1</sup> (strong activation) in (B). The autonomous period of the cell cycle prior to coupling is equal to 28 h; similar results are obtained for the case where the cell cycle autonomous period is equal to 20 h. Numerical simulations show that weak activation of the checkpoint will not perturb circadian entrainment (A), while stronger activation leads to tetraploidy where two peaks of cyclin E/Cdk2 are present per peak of cyclin B/Cdk1 (B). In these simulations, the basal rate of synthesis of kinase Wee1, <i>v</i><sub>swee1</sub>, is set equal to 0. Coupling to the circadian clock is achieved by raising the rate of synthesis of Wee1 mRNA, <i>v</i><sub>sw</sub>, from 0 to 0.1 µM h<sup>−1</sup> in t = 120 h (first vertical arrow). Other parameter values are as in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002516#pcbi-1002516-g004\" target=\"_blank\">Fig. 4</a>.</p>", "links"=>[], "tags"=>["circadian"], "article_id"=>300477, "categories"=>["Biological Sciences", "Genetics"], "users"=>["Claude Gérard", "Albert Goldbeter"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002516.g011", "stats"=>{"downloads"=>1, "page_views"=>6, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Entrainment_by_the_circadian_clock_in_the_presence_of_a_cell_cycle_checkpoint_/300477", "title"=>"Entrainment by the circadian clock in the presence of a cell cycle checkpoint.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-20 04:26:38"}
  • {"files"=>["https://ndownloader.figshare.com/files/628922"], "description"=>"<p>The Cdk network contains four modules. Each of these modules is centered around one cyclin/Cdk complex: cyclin D/Cdk4–6 and cyclin E/Cdk2 promote progression in G1 and elicit the G1/S transition; cyclin A/Cdk2 ensures progression in S and the S/G2 transition, while cyclin B/Cdk1 brings about the G2/M transition. The growth factor (GF) promotes the G0/G1 transition by activating the synthesis of cyclin D. The model for the Cdk network also incorporates regulation by the Cdk inhibitor p21 (or p27) as well as the antagonistic effects of the transcription factor E2F and the tumor suppressor pRB; E2F promotes cell cycle progression by activating the synthesis of cyclins, which is repressed by pRB (see Ref. 14 for further details). The cell cycle network is coupled to the circadian clock through circadian variations in the levels of Wee1, p21 and cyclin E. The level of Wee1 is controlled by the circadian variation of the complex CLOCK-BMAL1, generated by the circadian clock; this complex also controls the levels of cyclin E (via c-Myc) and of REV-ERBα, which in turn controls the level of p21.</p>", "links"=>[], "tags"=>["cdk", "mammalian"], "article_id"=>299422, "categories"=>["Biological Sciences", "Genetics"], "users"=>["Claude Gérard", "Albert Goldbeter"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002516.g001", "stats"=>{"downloads"=>1, "page_views"=>17, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Scheme_of_the_model_for_the_Cdk_network_driving_the_mammalian_cell_cycle_/299422", "title"=>"Scheme of the model for the Cdk network driving the mammalian cell cycle.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-20 04:20:45"}
  • {"files"=>["https://ndownloader.figshare.com/files/629556"], "description"=>"<p>The curves show the time course of cyclin B/Cdk1 (red), CLOCK-BMAL1 (green), and the LD cycle (dashed line) when the autonomous period of the cell cycle prior to coupling is equal to 4 h, as in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002516#pcbi-1002516-g006\" target=\"_blank\">Fig. 6A</a>, the coupling strength, <i>v</i><sub>sw</sub>, is equal to 0.025 µM h<sup>−1</sup> (A) or 0.005 µM h<sup>−1</sup> (B). Panels (A) and (B) correspond, respectively, to points H and I in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002516#pcbi-1002516-g004\" target=\"_blank\">Fig. 4A</a>. Whereas two peaks in cyclin B/Cdk1 occur in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002516#pcbi-1002516-g006\" target=\"_blank\">Fig. 6A</a> at a higher coupling strength for the same autonomous period corresponding to point D in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002516#pcbi-1002516-g004\" target=\"_blank\">Fig. 4A</a>, three or four peaks of cyclin B/Cdk1 occur during the L phase of the LD cycle when the coupling strength is progressively decreased. This is due to the accompanying decrease in the peak of the Cdk inhibitor Wee1 associated with the circadian peak in CLOCK-BMAL1 during the L phase. Other parameters values are the same as in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002516#pcbi-1002516-g004\" target=\"_blank\">Fig. 4A</a>.</p>", "links"=>[], "tags"=>["inhibition", "cycles", "coupling"], "article_id"=>300053, "categories"=>["Biological Sciences", "Genetics"], "users"=>["Claude Gérard", "Albert Goldbeter"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002516.g007", "stats"=>{"downloads"=>1, "page_views"=>15, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Circadian_inhibition_of_rapid_cell_cycles_due_to_coupling_through_Wee1_/300053", "title"=>"Circadian inhibition of rapid cell cycles due to coupling through Wee1.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-20 04:24:20"}

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Relative Metric

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