A Density-Dependent Switch Drives Stochastic Clustering and Polarization of Signaling Molecules
Publication Date
November 10, 2011
Journal
PLOS Computational Biology
Authors
Alexandra Jilkine, Sigurd B. Angenent, Lani F. Wu & Steven J. Altschuler
Volume
7
Issue
11
Pages
e1002271
DOI
https://dx.plos.org/10.1371/journal.pcbi.1002271
Publisher URL
http://journals.plos.org/ploscompbiol/article?id=10.1371%2Fjournal.pcbi.1002271
PubMed
http://www.ncbi.nlm.nih.gov/pubmed/22102805
PubMed Central
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3213192
Europe PMC
http://europepmc.org/abstract/MED/22102805
Web of Science
000297263700022
Scopus
81355133231
Mendeley
http://www.mendeley.com/research/densitydependent-switch-drives-stochastic-clustering-polarization-signaling-molecules
Events
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Mendeley | Further Information

{"title"=>"A Density-Dependent switch drives stochastic clustering and polarization of signaling molecules", "type"=>"journal", "authors"=>[{"first_name"=>"Alexandra", "last_name"=>"Jilkine", "scopus_author_id"=>"14060366900"}, {"first_name"=>"Sigurd B.", "last_name"=>"Angenent", "scopus_author_id"=>"6701419609"}, {"first_name"=>"Lani F.", "last_name"=>"Wu", "scopus_author_id"=>"8787374000"}, {"first_name"=>"Steven J.", "last_name"=>"Altschuler", "scopus_author_id"=>"7004905349"}], "year"=>2011, "source"=>"PLoS Computational Biology", "identifiers"=>{"scopus"=>"2-s2.0-81355133231", "doi"=>"10.1371/journal.pcbi.1002271", "sgr"=>"81355133231", "isbn"=>"1553-7358 (Electronic) 1553-734X (Linking)", "pmid"=>"22102805", "issn"=>"1553734X", "pui"=>"362947801"}, "id"=>"c3c07cac-784a-3837-a5b1-1ca0eb3ffb48", "abstract"=>"Positive feedback plays a key role in the ability of signaling molecules to form highly localized clusters in the membrane or cytosol of cells. Such clustering can occur in the absence of localizing mechanisms such as pre-existing spatial cues, diffusional barriers, or molecular cross-linking. What prevents positive feedback from amplifying inevitable biological noise when an un-clustered \"off\" state is desired? And, what limits the spread of clusters when an \"on\" state is desired? Here, we show that a minimal positive feedback circuit provides the general principle for both suppressing and amplifying noise: below a critical density of signaling molecules, clustering switches off; above this threshold, highly localized clusters are recurrently generated. Clustering occurs only in the stochastic regime, suggesting that finite sizes of molecular populations cannot be ignored in signal transduction networks. The emergence of a dominant cluster for finite numbers of molecules is partly a phenomenon of random sampling, analogous to the fixation or loss of neutral mutations in finite populations. We refer to our model as the \"neutral drift polarity model.\" Regulating the density of signaling molecules provides a simple mechanism for a positive feedback circuit to robustly switch between clustered and un-clustered states. The intrinsic ability of positive feedback both to create and suppress clustering is a general mechanism that could operate within diverse biological networks to create dynamic spatial organization.", "link"=>"http://www.mendeley.com/research/densitydependent-switch-drives-stochastic-clustering-polarization-signaling-molecules", "reader_count"=>87, "reader_count_by_academic_status"=>{"Professor > Associate Professor"=>8, "Librarian"=>1, "Researcher"=>32, "Student > Doctoral Student"=>2, "Student > Ph. D. Student"=>22, "Student > Postgraduate"=>1, "Student > Master"=>8, "Other"=>2, "Student > Bachelor"=>6, "Lecturer > Senior Lecturer"=>1, "Professor"=>4}, "reader_count_by_user_role"=>{"Professor > Associate Professor"=>8, "Librarian"=>1, "Researcher"=>32, "Student > Doctoral Student"=>2, "Student > Ph. D. Student"=>22, "Student > Postgraduate"=>1, "Student > Master"=>8, "Other"=>2, "Student > Bachelor"=>6, "Lecturer > Senior Lecturer"=>1, "Professor"=>4}, "reader_count_by_subject_area"=>{"Engineering"=>2, "Unspecified"=>1, "Biochemistry, Genetics and Molecular Biology"=>12, "Mathematics"=>6, "Agricultural and Biological Sciences"=>38, "Medicine and Dentistry"=>1, "Arts and Humanities"=>3, "Physics and Astronomy"=>13, "Chemistry"=>4, "Computer Science"=>5, "Immunology and Microbiology"=>2}, "reader_count_by_subdiscipline"=>{"Engineering"=>{"Engineering"=>2}, "Medicine and Dentistry"=>{"Medicine and Dentistry"=>1}, "Chemistry"=>{"Chemistry"=>4}, "Physics and Astronomy"=>{"Physics and Astronomy"=>13}, "Immunology and Microbiology"=>{"Immunology and Microbiology"=>2}, "Agricultural and Biological Sciences"=>{"Agricultural and Biological Sciences"=>38}, "Computer Science"=>{"Computer Science"=>5}, "Biochemistry, Genetics and Molecular Biology"=>{"Biochemistry, Genetics and Molecular Biology"=>12}, "Mathematics"=>{"Mathematics"=>6}, "Unspecified"=>{"Unspecified"=>1}, "Arts and Humanities"=>{"Arts and Humanities"=>3}}, "reader_count_by_country"=>{"Canada"=>1, "United States"=>5, "Japan"=>1, "Brazil"=>1, "Switzerland"=>3, "Portugal"=>2, "Germany"=>2}, "group_count"=>3}

Scopus | Further Information

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Figshare

  • {"files"=>["https://ndownloader.figshare.com/files/713904"], "description"=>"<p>Positive feedback can recurrently generate a single, polarized cluster of signaling molecules.</p>", "links"=>[], "tags"=>["recurrently", "polarized", "signaling"], "article_id"=>384269, "categories"=>["Mathematics", "Genetics"], "users"=>["Alexandra Jilkine", "Sigurd B. Angenent", "Lani F. Wu", "Steven J. Altschuler"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002271.g004", "stats"=>{"downloads"=>0, "page_views"=>11, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Positive_feedback_can_recurrently_generate_a_single_polarized_cluster_of_signaling_molecules_/384269", "title"=>"Positive feedback can recurrently generate a single, polarized cluster of signaling molecules.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2011-11-10 01:11:09"}
  • {"files"=>["https://ndownloader.figshare.com/files/713673"], "description"=>"<p>(<b>A</b>) A simple 2-state model of positive feedback. Signaling molecules can either be in an active (red) or inactive (green) state. Molecules can transition between active and inactive states. Positive feedback occurs because active signaling molecules can recruit inactive molecules to change state. (<b>B</b>) Application of model to cell polarity. Here, active or inactive states correspond to signaling molecule localization on the membrane or cytosol, respectively. Signaling molecules may only be spontaneously activated (with rate ), or recruited (with rate ) if they are within the volumes or of the membrane, respectively. Active molecules can spontaneously transition to an inactive state (with rate ). (<b>C</b>) Signaling molecule flux between the membrane and the cytosol. The total number of molecules in the membrane and cytosol are denoted by and , respectively. The volume of the cell is denoted by .</p>", "links"=>[], "tags"=>["genetics and genomics", "mathematics"], "article_id"=>384030, "categories"=>["Mathematics", "Genetics"], "users"=>["Alexandra Jilkine", "Sigurd B. Angenent", "Lani F. Wu", "Steven J. Altschuler"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002271.g001", "stats"=>{"downloads"=>0, "page_views"=>2, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Conceptual_model_of_positive_feedback_/384030", "title"=>"Conceptual model of positive feedback.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2011-11-10 01:07:10"}
  • {"files"=>["https://ndownloader.figshare.com/files/713733"], "description"=>"<p>(<b>A</b>) Three regions of polarization behavior are shown: repression (blue bar); spontaneous emergence (cyan bar) and loss (red bar);. Black curve: averaged membrane fractions of molecules. Red curves: averaged probabilities of observing polarization; signaling molecules are considered clustered when more than 20 molecules are present on the membrane, and 50% of all molecules on the membrane are within a small region covering 15% (dotted curve), 20% (dashed curve), or 25% (solid curve) of the membrane. (*) indicates critical number of molecules . Results are averaged of 50 simulations, performed for each indicated value of . Changing the minimum cluster size to 10 molecules from 20 does not affect results (not shown). (<b>B</b>) Kymographs of simulations for values of chosen from the three regions shown in (A). (<b>C</b>) Positive feedback circuits give rise to switch-like behaviors in time and space. 0 min: the positive feedback circuit is initialized with molecules, 10% of which are randomly distributed on the membrane, and polarity is repressed (); 30 min (red triangle): 10% of the cytosolic molecules are reseeded to 10% of the membrane; 60 min: 200 particles are added to the cytosol, and polarity switches on (); 90 min: 200 particles are removed from the cytosol and polarity switches off. Bottom panel: kymograph of simulation is as in (B); top panel: total number of molecules on membrane (gray curve and left axis) and total number of molecules in cell (red curve and right axis). Simulations were performed on a 1-D circular membrane (see <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002271#pcbi-1002271-t003\" target=\"_blank\">Table 3</a> for model parameters).</p>", "links"=>[], "tags"=>["polarity", "concentrations", "signaling"], "article_id"=>384091, "categories"=>["Mathematics", "Genetics"], "users"=>["Alexandra Jilkine", "Sigurd B. Angenent", "Lani F. Wu", "Steven J. Altschuler"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002271.g002", "stats"=>{"downloads"=>1, "page_views"=>8, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Repression_emergence_and_loss_of_polarity_for_increasing_concentrations_of_signaling_molecules_/384091", "title"=>"Repression, emergence, and loss of polarity for increasing concentrations of signaling molecules.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2011-11-10 01:08:11"}
  • {"files"=>["https://ndownloader.figshare.com/files/714000"], "description"=>"<p>(<b>A</b>) Modification of model shown in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002271#pcbi-1002271-g001\" target=\"_blank\">Figure 1B</a>, removing the assumptions that the active and inactive molecules are spatially segregated into different spatial compartments, and that the inactive form is spatially homogeneous (infinite rate of diffusion). Here, both the active (red) and inactive (green) molecules can occupy the same compartment and diffuse at finite speeds given by rates and , respectively. (<b>B</b>) Numerical implementation of the modified model shown in (A) for three different spatial geometries: (i) active molecules reside on the surface of sphere, while inactive molecules reside in the interior (polarity); (ii) both active and inactive molecules reside in a 3-D volume (cytosol); and (iii) both active and inactive molecules reside on a 2-D surface (membrane). For all geometries, we observe progression from buffered off state to localized clusters to homogeneous on state as the number of molecules is increased. (<b>C</b>) Phase plane diagram for the 2-D model as a function of molecule numbers and membrane area. Numerical simulations using the stochastic molecule simulator Smoldyn illustrate a density-dependent switch in clustering behavior. Inset: analytically computed phase plane diagram; “+” marks indicate locations of simulations; <i>V</i> in equations has dimensions of area (see labels at bottom (B)). All simulations in (B–C) were performed using the Smoldyn stochastic molecule simulator version 2.15 <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002271#pcbi.1002271-Andrews1\" target=\"_blank\">[51]</a>; . Shown are results from running the stochastic simulation for 100 time units (see <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002271#pcbi.1002271.s004\" target=\"_blank\">Protocol S1</a>, Appendix for code and parameter values).</p>", "links"=>[], "tags"=>["spatial", "clustering", "observed"], "article_id"=>384361, "categories"=>["Mathematics", "Genetics"], "users"=>["Alexandra Jilkine", "Sigurd B. Angenent", "Lani F. Wu", "Steven J. Altschuler"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002271.g005", "stats"=>{"downloads"=>0, "page_views"=>3, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Density_dependence_of_spatial_clustering_is_observed_for_different_spatial_geometries_/384361", "title"=>"Density-dependence of spatial clustering is observed for different spatial geometries.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2011-11-10 01:12:41"}
  • {"files"=>["https://ndownloader.figshare.com/files/714104"], "description"=>"<p>Examples of cluster formation in cell signaling systems with positive feedback.</p>", "links"=>[], "tags"=>["signaling", "systems"], "article_id"=>384469, "categories"=>["Mathematics", "Genetics"], "users"=>["Alexandra Jilkine", "Sigurd B. Angenent", "Lani F. Wu", "Steven J. Altschuler"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002271.t002", "stats"=>{"downloads"=>2, "page_views"=>4, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Examples_of_cluster_formation_in_cell_signaling_systems_with_positive_feedback_/384469", "title"=>"Examples of cluster formation in cell signaling systems with positive feedback.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2011-11-10 01:14:29"}
  • {"files"=>["https://ndownloader.figshare.com/files/714139"], "description"=>"<p>Summary of models for positive feedback driven switches and resulting behavior.</p>", "links"=>[], "tags"=>["models", "driven", "switches", "resulting"], "article_id"=>384500, "categories"=>["Mathematics", "Genetics"], "users"=>["Alexandra Jilkine", "Sigurd B. Angenent", "Lani F. Wu", "Steven J. Altschuler"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002271.t001", "stats"=>{"downloads"=>1, "page_views"=>6, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Summary_of_models_for_positive_feedback_driven_switches_and_resulting_behavior_/384500", "title"=>"Summary of models for positive feedback driven switches and resulting behavior.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2011-11-10 01:15:00"}
  • {"files"=>["https://ndownloader.figshare.com/files/713826"], "description"=>"<p>(<b>A</b>) Illustration shows stability of equilibrium values for cytosolic densities, and , for varying when . Red: stable root; black unstable root. (<b>B</b>) Shown is equilibrium membrane fraction of signaling molecules on the membrane for various cell densities and different values of . Cytosolic buffering occurs when is nearly zero. (<b>C</b>) The probability, , that the: cytosol contains exactly molecules is shown for different total molecule numbers, , scanned between 0 and . Steady state probabilities of molecule numbers in the cytosol are computed from stochastic master equation (Protocol S1). Inset: zoom-in of transition region showing bimodality of probability distribution.</p>", "links"=>[], "tags"=>["repressed", "signaling"], "article_id"=>384188, "categories"=>["Mathematics", "Genetics"], "users"=>["Alexandra Jilkine", "Sigurd B. Angenent", "Lani F. Wu", "Steven J. Altschuler"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002271.g003", "stats"=>{"downloads"=>0, "page_views"=>3, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Polarity_is_repressed_below_a_critical_total_density_of_signaling_molecules_/384188", "title"=>"Polarity is repressed below a critical total density of signaling molecules.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2011-11-10 01:09:48"}
  • {"files"=>["https://ndownloader.figshare.com/files/361773", "https://ndownloader.figshare.com/files/361822", "https://ndownloader.figshare.com/files/361871", "https://ndownloader.figshare.com/files/361908", "https://ndownloader.figshare.com/files/362030", "https://ndownloader.figshare.com/files/362094"], "description"=>"<div><p>Positive feedback plays a key role in the ability of signaling molecules to form highly localized clusters in the membrane or cytosol of cells. Such clustering can occur in the absence of localizing mechanisms such as pre-existing spatial cues, diffusional barriers, or molecular cross-linking. What prevents positive feedback from amplifying inevitable biological noise when an un-clustered “off” state is desired? And, what limits the spread of clusters when an “on” state is desired? Here, we show that a minimal positive feedback circuit provides the general principle for both suppressing and amplifying noise: below a critical density of signaling molecules, clustering switches off; above this threshold, highly localized clusters are recurrently generated. Clustering occurs only in the stochastic regime, suggesting that finite sizes of molecular populations cannot be ignored in signal transduction networks. The emergence of a dominant cluster for finite numbers of molecules is partly a phenomenon of random sampling, analogous to the fixation or loss of neutral mutations in finite populations. We refer to our model as the “neutral drift polarity model.” Regulating the density of signaling molecules provides a simple mechanism for a positive feedback circuit to robustly switch between clustered and un-clustered states. The intrinsic ability of positive feedback both to create and suppress clustering is a general mechanism that could operate within diverse biological networks to create dynamic spatial organization.</p> </div>", "links"=>[], "tags"=>["density-dependent", "drives", "stochastic", "clustering", "polarization", "signaling", "molecules"], "article_id"=>131516, "categories"=>["Mathematics", "Genetics"], "users"=>["Alexandra Jilkine", "Sigurd B. Angenent", "Lani F. Wu", "Steven J. Altschuler"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1002271.s001", "https://dx.doi.org/10.1371/journal.pcbi.1002271.s002", "https://dx.doi.org/10.1371/journal.pcbi.1002271.s003", "https://dx.doi.org/10.1371/journal.pcbi.1002271.s004", "https://dx.doi.org/10.1371/journal.pcbi.1002271.s005", "https://dx.doi.org/10.1371/journal.pcbi.1002271.s006"], "stats"=>{"downloads"=>17, "page_views"=>13, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/A_Density_Dependent_Switch_Drives_Stochastic_Clustering_and_Polarization_of_Signaling_Molecules/131516", "title"=>"A Density-Dependent Switch Drives Stochastic Clustering and Polarization of Signaling Molecules", "pos_in_sequence"=>0, "defined_type"=>4, "published_date"=>"2011-11-10 00:25:16"}
  • {"files"=>["https://ndownloader.figshare.com/files/714082"], "description"=>"<p>Parameters used for simulations in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002271#pcbi-1002271-g002\" target=\"_blank\">Figure 2</a>.</p>", "links"=>[], "tags"=>["simulations"], "article_id"=>384447, "categories"=>["Mathematics", "Genetics"], "users"=>["Alexandra Jilkine", "Sigurd B. Angenent", "Lani F. Wu", "Steven J. Altschuler"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002271.t003", "stats"=>{"downloads"=>0, "page_views"=>4, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Parameters_used_for_simulations_in_Figure_2_/384447", "title"=>"Parameters used for simulations in Figure 2.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2011-11-10 01:14:07"}

PMC Usage Stats | Further Information

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Relative Metric

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