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{"title"=>"Order and stochastic dynamics in drosophila planar cell polarity", "type"=>"journal", "authors"=>[{"first_name"=>"Yoram", "last_name"=>"Burak", "scopus_author_id"=>"14619138200"}, {"first_name"=>"Boris I.", "last_name"=>"Shraiman", "scopus_author_id"=>"7003677005"}], "year"=>2009, "source"=>"PLoS Computational Biology", "identifiers"=>{"isbn"=>"1553-7358 (Electronic)\\r1553-734X (Linking)", "sgr"=>"74549214364", "doi"=>"10.1371/journal.pcbi.1000628", "pui"=>"358137751", "scopus"=>"2-s2.0-74549214364", "issn"=>"1553734X", "pmid"=>"20041171"}, "id"=>"f015de2c-ee3c-3289-8c9f-3cbbf95d176e", "abstract"=>"Cells in the wing blade of Drosophila melanogaster exhibit an in-plane polarization causing distal orientation of hairs. Establishment of the Planar Cell Polarity (PCP) involves intercellular interactions as well as a global orienting signal. Many of the genetic and molecular components underlying this process have been experimentally identified and a recently advanced system-level model has suggested that the observed mutant phenotypes can be understood in terms of intercellular interactions involving asymmetric localization of membrane bound proteins. Among key open questions in understanding the emergence of ordered polarization is the effect of stochasticity and the role of the global orienting signal. These issues relate closely to our understanding of ferromagnetism in physical systems. Here we pursue this analogy to understand the emergence of PCP order. To this end we develop a semi-phenomenological representation of the underlying molecular processes and define a \"phase diagram\" of the model which provides a global view of the dependence of the phenotype on parameters. We show that the dynamics of PCP has two regimes: rapid growth in the amplitude of local polarization followed by a slower process of alignment which progresses from small to large scales. We discuss the response of the tissue to various types of orienting signals and show that global PCP order can be achieved with a weak orienting signal provided that it acts during the early phase of the process. Finally we define and discuss some of the experimental predictions of the model.", "link"=>"http://www.mendeley.com/research/order-stochastic-dynamics-drosophila-planar-cell-polarity", "reader_count"=>56, "reader_count_by_academic_status"=>{"Professor > Associate Professor"=>9, "Researcher"=>17, "Student > Doctoral Student"=>2, "Student > Ph. D. Student"=>11, "Student > Postgraduate"=>2, "Student > Master"=>11, "Other"=>1, "Student > Bachelor"=>1, "Professor"=>2}, "reader_count_by_user_role"=>{"Professor > Associate Professor"=>9, "Researcher"=>17, "Student > Doctoral Student"=>2, "Student > Ph. D. Student"=>11, "Student > Postgraduate"=>2, "Student > Master"=>11, "Other"=>1, "Student > Bachelor"=>1, "Professor"=>2}, "reader_count_by_subject_area"=>{"Engineering"=>3, "Unspecified"=>1, "Biochemistry, Genetics and Molecular Biology"=>3, "Mathematics"=>1, "Agricultural and Biological Sciences"=>27, "Arts and Humanities"=>1, "Business, Management and Accounting"=>1, "Physics and Astronomy"=>18, "Chemical Engineering"=>1}, "reader_count_by_subdiscipline"=>{"Engineering"=>{"Engineering"=>3}, "Physics and Astronomy"=>{"Physics and Astronomy"=>18}, "Agricultural and Biological Sciences"=>{"Agricultural and Biological Sciences"=>27}, "Business, Management and Accounting"=>{"Business, Management and Accounting"=>1}, "Biochemistry, Genetics and Molecular Biology"=>{"Biochemistry, Genetics and Molecular Biology"=>3}, "Mathematics"=>{"Mathematics"=>1}, "Unspecified"=>{"Unspecified"=>1}, "Chemical Engineering"=>{"Chemical Engineering"=>1}, "Arts and Humanities"=>{"Arts and Humanities"=>1}}, "reader_count_by_country"=>{"Netherlands"=>1, "United States"=>3, "Japan"=>1, "Germany"=>1}, "group_count"=>3}

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• http://doi.org/10.1016/j.cell.2010.07.042
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Figshare

• {"files"=>["https://ndownloader.figshare.com/files/870403"], "description"=>"<p>(A) Phase diagram in the deterministic limit, dissected in the - plane. The other parameters are , , and . Crosses designate the two loci, A and B, used in the numerical simulations shown in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000628#pcbi-1000628-g004\" target=\"_blank\">Figs. 4</a>,<a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000628#pcbi-1000628-g005\" target=\"_blank\">5</a>, and <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000628#pcbi-1000628-g006\" target=\"_blank\">6</a>. (B) Steady state in region S: polarity points towards a side. (C) Steady state in region V: polarity points towards a vertex. In region U protein distribution is unpolarized.</p>", "links"=>[], "tags"=>["diagram", "deterministic"], "article_id"=>540865, "categories"=>["Cell Biology", "Physics", "Developmental Biology", "Medicine", "Biophysics"], "users"=>["Yoram Burak", "Boris I. Shraiman"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1000628.g003", "stats"=>{"downloads"=>1, "page_views"=>6, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Phase_diagram_in_the_deterministic_limit_/540865", "title"=>"Phase diagram in the deterministic limit.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2009-12-24 00:14:25"}
• {"files"=>["https://ndownloader.figshare.com/files/870284"], "description"=>"<p>(A) Bistability on an interface. (B) Notation used for − complex binding and unbinding, Eqs. (1)–(2). (C) Nullclines for and (red and black lines), exhibiting an unstable fixed point with and two symmetry-breaking stable fixed points. (D)–(E) Possible mechanisms for the generation of a non-local field, based on the modification of a diffusible protein: (D) A cytoplasmic messenger protein is modified when it meets the side of an − complex. It then continues to diffuse and, when it meets the side of a complex it promotes its unbinding. (E) Instead of modifying a separate messenger protein, the protein is directly modified by binding a cytoplasmic protein; complexes locally affect the fraction of modified proteins and this, in turn, affects their affinity for forming complexes with -s on the opposite side of the interface.</p>", "links"=>[], "tags"=>["biophysics/theory and simulation", "cell biology/developmental molecular mechanisms", "cell biology/morphogenesis and cell biology", "computational biology/systems biology", "developmental biology/morphogenesis and cell biology", "physics"], "article_id"=>540738, "categories"=>["Cell Biology", "Physics", "Developmental Biology", "Medicine", "Biophysics"], "users"=>["Yoram Burak", "Boris I. Shraiman"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1000628.g002", "stats"=>{"downloads"=>1, "page_views"=>15, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Key_model_ingredients_/540738", "title"=>"Key model ingredients.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2009-12-24 00:12:18"}
• {"files"=>["https://ndownloader.figshare.com/files/870564"], "description"=>"<p>Results from a stochastic simulation in locus A of <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000628#pcbi-1000628-g003\" target=\"_blank\">Fig. 3A</a> with and with no orienting signal, starting from the uniform steady state. The lattice contains 1840 hexagonal cells tiling a square region with periodic boundary conditions. (A) Pattern of polarity orientation shortly after amplitude saturation, at . Arrows point in the direction of the dipole moment. Inset: Close-up. Green and red represent and concentration, respectively. (B) Average square amplitude of polarity as a function of time. Arrow marks the time shown in panel A. Dashed line: Eq. (5). (C) Measure of the correlation length as a function of time, where is the radial correlation function .</p>", "links"=>[], "tags"=>["orienting"], "article_id"=>541025, "categories"=>["Cell Biology", "Physics", "Developmental Biology", "Medicine", "Biophysics"], "users"=>["Yoram Burak", "Boris I. Shraiman"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1000628.g005", "stats"=>{"downloads"=>0, "page_views"=>4, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Stochastic_dynamics_in_the_absence_of_an_orienting_signal_/541025", "title"=>"Stochastic dynamics in the absence of an orienting signal.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2009-12-24 00:17:05"}
• {"files"=>["https://ndownloader.figshare.com/files/433008", "https://ndownloader.figshare.com/files/433057", "https://ndownloader.figshare.com/files/433103", "https://ndownloader.figshare.com/files/433133"], "description"=>"<div><p>Cells in the wing blade of <em>Drosophila melanogaster</em> exhibit an in-plane polarization causing distal orientation of hairs. Establishment of the Planar Cell Polarity (PCP) involves intercellular interactions as well as a global orienting signal. Many of the genetic and molecular components underlying this process have been experimentally identified and a recently advanced system-level model has suggested that the observed mutant phenotypes can be understood in terms of intercellular interactions involving asymmetric localization of membrane bound proteins. Among key open questions in understanding the emergence of ordered polarization is the effect of stochasticity and the role of the global orienting signal. These issues relate closely to our understanding of ferromagnetism in physical systems. Here we pursue this analogy to understand the emergence of PCP order. To this end we develop a semi-phenomenological representation of the underlying molecular processes and define a “phase diagram” of the model which provides a global view of the dependence of the phenotype on parameters. We show that the dynamics of PCP has two regimes: rapid growth in the amplitude of local polarization followed by a slower process of alignment which progresses from small to large scales. We discuss the response of the tissue to various types of orienting signals and show that global PCP order can be achieved with a weak orienting signal provided that it acts during the early phase of the process. Finally we define and discuss some of the experimental predictions of the model.</p></div>", "links"=>[], "tags"=>["stochastic", "drosophila", "planar", "polarity"], "article_id"=>145451, "categories"=>["Cell Biology", "Physics", "Developmental Biology", "Medicine", "Biophysics"], "users"=>["Yoram Burak", "Boris I. Shraiman"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1000628.s001", "https://dx.doi.org/10.1371/journal.pcbi.1000628.s002", "https://dx.doi.org/10.1371/journal.pcbi.1000628.s003", "https://dx.doi.org/10.1371/journal.pcbi.1000628.s004"], "stats"=>{"downloads"=>5, "page_views"=>12, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/Order_and_Stochastic_Dynamics_in_Drosophila_Planar_Cell_Polarity/145451", "title"=>"Order and Stochastic Dynamics in Drosophila Planar Cell Polarity", "pos_in_sequence"=>0, "defined_type"=>4, "published_date"=>"2009-12-24 01:30:51"}
• {"files"=>["https://ndownloader.figshare.com/files/870787"], "description"=>"<p>Response of PCP orientation to a noisy orienting signal present in each cell. The direction of the signal (yellow arrows in panel A) is uncorrelated in different cells and is biased towards the direction designated by the red vertical line in panel (B) (roughly the distal direction), but is widely distributed in the range (A) The PCP response (white arrows) is shown from a stochastic simulation in locus A of the phase diagram (<a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000628#pcbi-1000628-g003\" target=\"_blank\">Fig. 3A</a>) with , at . (B) Distribution of PCP orientation at (gray bars) compared to the distribution of orientation of the orienting signal (yellow bars).</p>", "links"=>[], "tags"=>["noisy", "orienting"], "article_id"=>541250, "categories"=>["Cell Biology", "Physics", "Developmental Biology", "Medicine", "Biophysics"], "users"=>["Yoram Burak", "Boris I. Shraiman"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1000628.g007", "stats"=>{"downloads"=>1, "page_views"=>4, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Smoothing_of_a_noisy_orienting_signal_/541250", "title"=>"Smoothing of a noisy orienting signal.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2009-12-24 00:20:50"}
• {"files"=>["https://ndownloader.figshare.com/files/870665"], "description"=>"<p>Position of the front during a stochastic simulation. The front location is defined as the most distal position such that all cells proximal to this position have their PCP dipole pointing distally (<i>i.e.</i>, the dipole has a positive projection in the proximal-distal direction) and is shown in units of , the distance between neighboring cells. Simulations were run on a honeycomb lattice with rectangular boundaries, extending 200 cells sizes () in the direction of front propagation (the proximal-distal axis), and in the perpendicular direction. (A) Locus A in the phase diagram of <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000628#pcbi-1000628-g003\" target=\"_blank\">Fig. 3A</a>, far from the phase transition. The red trace corresponds to a realistic number of molecules per cell, , and to stochastic noise . The other two traces correspond to higher, non-realistic values of (gray) and (black). Dashed lines show the prediction of Eqs. (S49)–(S50), where in all traces was estimated from the polarity amplitude near the boundary in the beginning of the simulation, and the numbers next to each trace represent . The arrows designate the time of amplitude saturation in the bulk, estimated from Eq. (S44) of the supporting analysis (<a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000628#pcbi.1000628.s004\" target=\"_blank\">Text S1</a>). Note that after saturation front propagation is slowed down considerably. (B) Similar plots obtained from locus B in the phase diagram. Proximity to the phase transition increases the range of front propagation [as seen from comparison with (A)], but even here an unrealistically small amount of noise is required to reach a propagation range comparable to the wing size. This is due to the weak, logarithmic dependence on (through the value of ) in Eq. (S50).</p>", "links"=>[], "tags"=>["orienting"], "article_id"=>541135, "categories"=>["Cell Biology", "Physics", "Developmental Biology", "Medicine", "Biophysics"], "users"=>["Yoram Burak", "Boris I. Shraiman"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1000628.g006", "stats"=>{"downloads"=>4, "page_views"=>4, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Response_to_an_orienting_signal_at_a_boundary_/541135", "title"=>"Response to an orienting signal at a boundary.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2009-12-24 00:18:55"}
• {"files"=>["https://ndownloader.figshare.com/files/870206"], "description"=>"<p>(A) Protein localization pattern in wild-type wing: Fz (green) localizes on the distal membrane, together with Dsh, while Vang (red) localizes on the proximal membrane, together with Pk. (B) Key PCP proteins localize apically in the adherens junction area, within a strip of about from the top <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000628#pcbi.1000628-Strutt1\" target=\"_blank\">[7]</a>,<a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000628#pcbi.1000628-Shimada1\" target=\"_blank\">[11]</a>,<a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000628#pcbi.1000628-Bastock1\" target=\"_blank\">[12]</a>,<a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000628#pcbi.1000628-Usui1\" target=\"_blank\">[39]</a>. (C,D) Mutant <i>fz</i> (C) and <i>Vang</i> (D) clones influence the polarity of wild-type cells bordering the clone such that it points towards the clone (<i>fz</i>, C) or away from it (<i>Vang</i>, D). This effect is propagated to a large patch of wild-type cells that are distal to the clone (<i>fz</i>) or proximal to it (<i>Vang</i>) <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000628#pcbi.1000628-Adler3\" target=\"_blank\">[40]</a>. Over-expression of <i>fz</i> causes an effect similar to that of <i>Vang</i> mutant clones, and over-expression of <i>Vang</i> causes an effect similar to <i>fz</i> mutants.</p>", "links"=>[], "tags"=>["biophysics/theory and simulation", "cell biology/developmental molecular mechanisms", "cell biology/morphogenesis and cell biology", "computational biology/systems biology", "developmental biology/morphogenesis and cell biology", "physics"], "article_id"=>540656, "categories"=>["Cell Biology", "Physics", "Developmental Biology", "Medicine", "Biophysics"], "users"=>["Yoram Burak", "Boris I. Shraiman"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1000628.g001", "stats"=>{"downloads"=>0, "page_views"=>2, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Summary_of_experimental_observations_/540656", "title"=>"Summary of experimental observations.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2009-12-24 00:10:56"}
• {"files"=>["https://ndownloader.figshare.com/files/870489"], "description"=>"<p>Ordered and disordered states under stochastic dynamics. A lattice containing 1840 cells (as in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000628#pcbi-1000628-g005\" target=\"_blank\">Fig. 5</a>) is initiated with all dipoles pointing in the downwards direction. Stochastic dynamics are then followed to assess whether long range order in the cell array is maintained, and this is done for several different values of , the average number of molecules per interface. While long range order is maintained for and 500 (left and center panels), long range order is destroyed by the stochastic fluctuations for (right panels), as quantified by the center panels which track the dynamics of the polarization averaged over all cells (Center panels, amplitude: ; Bottom panels, orientation). The top panels show a snapshot of a subset of cells at the end of the simulation.</p>", "links"=>[], "tags"=>["ordered", "disordered"], "article_id"=>540954, "categories"=>["Cell Biology", "Physics", "Developmental Biology", "Medicine", "Biophysics"], "users"=>["Yoram Burak", "Boris I. Shraiman"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1000628.g004", "stats"=>{"downloads"=>0, "page_views"=>3, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Stochasticity_ordered_and_disordered_states_/540954", "title"=>"Stochasticity: ordered and disordered states.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2009-12-24 00:15:54"}
• {"files"=>["https://ndownloader.figshare.com/files/870825"], "description"=>"*<p> is the concentration of complexes in the unstable uniform steady state.</p>†<p> and are defined in the supporting analysis.</p>", "links"=>[], "tags"=>["parameters", "properties"], "article_id"=>541295, "categories"=>["Cell Biology", "Physics", "Developmental Biology", "Medicine", "Biophysics"], "users"=>["Yoram Burak", "Boris I. Shraiman"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1000628.t001", "stats"=>{"downloads"=>4, "page_views"=>4, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Model_parameters_and_properties_of_the_uniform_steady_state_/541295", "title"=>"Model parameters and properties of the uniform steady state.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2009-12-24 00:21:35"}

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• {"unique-ip"=>"6", "full-text"=>"3", "pdf"=>"2", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"3", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2019", "month"=>"8"}
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• {"unique-ip"=>"4", "full-text"=>"1", "pdf"=>"3", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2019", "month"=>"12"}
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Relative Metric

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F1000Prime