The Impact of Phenotypic Switching on Glioblastoma Growth and Invasion
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{"title"=>"The impact of phenotypic switching on glioblastoma growth and invasion", "type"=>"journal", "authors"=>[{"first_name"=>"Philip", "last_name"=>"Gerlee", "scopus_author_id"=>"25121071600"}, {"first_name"=>"Sven", "last_name"=>"Nelander", "scopus_author_id"=>"24329614700"}], "year"=>2012, "source"=>"PLoS Computational Biology", "identifiers"=>{"issn"=>"1553734X", "sgr"=>"84864044363", "scopus"=>"2-s2.0-84864044363", "isbn"=>"9783319037585", "doi"=>"10.1371/journal.pcbi.1002556", "pmid"=>"22719241", "pui"=>"365284180"}, "id"=>"628c3999-d866-346c-9c2e-4e71d19a033d", "abstract"=>"The brain tumour glioblastoma is characterised by diffuse and infiltrative growth into surrounding brain tissue. At the macroscopic level, the progression speed of a glioblastoma tumour is determined by two key factors: the cell proliferation rate and the cell migration speed. At the microscopic level, however, proliferation and migration appear to be mutually exclusive phenotypes, as indicated by recent in vivo imaging data. Here, we develop a mathematical model to analyse how the phenotypic switching between proliferative and migratory states of individual cells affects the macroscopic growth of the tumour. For this, we propose an individual-based stochastic model in which glioblastoma cells are either in a proliferative state, where they are stationary and divide, or in motile state in which they are subject to random motion. From the model we derive a continuum approximation in the form of two coupled reaction-diffusion equations, which exhibit travelling wave solutions whose speed of invasion depends on the model parameters. We propose a simple analytical method to predict progression rate from the cell-specific parameters and demonstrate that optimal glioblastoma growth depends on a non-trivial trade-off between the phenotypic switching rates. By linking cellular properties to an in vivo outcome, the model should be applicable to designing relevant cell screens for glioblastoma and cytometry-based patient prognostics.", "link"=>"http://www.mendeley.com/research/impact-phenotypic-switching-glioblastoma-growth-invasion", "reader_count"=>46, "reader_count_by_academic_status"=>{"Professor > Associate Professor"=>4, "Researcher"=>17, "Student > Doctoral Student"=>1, "Student > Ph. D. Student"=>15, "Student > Postgraduate"=>1, "Student > Master"=>3, "Student > Bachelor"=>3, "Professor"=>2}, "reader_count_by_user_role"=>{"Professor > Associate Professor"=>4, "Researcher"=>17, "Student > Doctoral Student"=>1, "Student > Ph. D. Student"=>15, "Student > Postgraduate"=>1, "Student > Master"=>3, "Student > Bachelor"=>3, "Professor"=>2}, "reader_count_by_subject_area"=>{"Unspecified"=>1, "Engineering"=>1, "Biochemistry, Genetics and Molecular Biology"=>4, "Materials Science"=>1, "Mathematics"=>5, "Agricultural and Biological Sciences"=>14, "Medicine and Dentistry"=>12, "Neuroscience"=>2, "Physics and Astronomy"=>4, "Computer Science"=>2}, "reader_count_by_subdiscipline"=>{"Engineering"=>{"Engineering"=>1}, "Materials Science"=>{"Materials Science"=>1}, "Medicine and Dentistry"=>{"Medicine and Dentistry"=>12}, "Neuroscience"=>{"Neuroscience"=>2}, "Physics and Astronomy"=>{"Physics and Astronomy"=>4}, "Agricultural and Biological Sciences"=>{"Agricultural and Biological Sciences"=>14}, "Computer Science"=>{"Computer Science"=>2}, "Biochemistry, Genetics and Molecular Biology"=>{"Biochemistry, Genetics and Molecular Biology"=>4}, "Mathematics"=>{"Mathematics"=>5}, "Unspecified"=>{"Unspecified"=>1}}, "reader_count_by_country"=>{"Sweden"=>1, "United States"=>1, "Brazil"=>1, "Germany"=>2}, "group_count"=>0}

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Figshare

  • {"files"=>["https://ndownloader.figshare.com/files/623805"], "description"=>"<p>The wave speed of the propagating tumour margin as a function of (a) , (b) and (c) . The phenotypic switching rates were fixed at . The dashed line in the inset of (c) has slope 1/2 and shows that .</p>", "links"=>[], "tags"=>["Computational biology", "oncology", "mathematics"], "article_id"=>294296, "categories"=>["Cancer", "Mathematics", "Biological Sciences"], "users"=>["Philip Gerlee", "Sven Nelander"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002556.g007", "stats"=>{"downloads"=>0, "page_views"=>12, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Impact_of_model_parameters_/294296", "title"=>"Impact of model parameters.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-20 03:53:37"}
  • {"files"=>["https://ndownloader.figshare.com/files/623457"], "description"=>"<p>Simulation results for and . (a) The result of a single realisation where P-cells are coloured blue and M-cells are coloured red. (b) The occupancy probability of finding a cell at location obtained by averaging over a large number of simulations. (c) A slice through the function in panel (b) at .</p>", "links"=>[], "tags"=>["individual-based"], "article_id"=>293955, "categories"=>["Cancer", "Mathematics", "Biological Sciences"], "users"=>["Philip Gerlee", "Sven Nelander"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002556.g002", "stats"=>{"downloads"=>0, "page_views"=>3, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Simulating_the_individual_based_model_/293955", "title"=>"Simulating the individual-based model.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-20 03:51:43"}
  • {"files"=>["https://ndownloader.figshare.com/files/623738"], "description"=>"<p>The wave speed of the propagating tumour margin determined from both the individual-based model (dashed line) and phase space analysis of the continuum approximation (solid line). In (a) the switch rate to proliferation is fixed at , while in (b) we have fixed .</p>", "links"=>[], "tags"=>["ib-model", "analytical"], "article_id"=>294229, "categories"=>["Cancer", "Mathematics", "Biological Sciences"], "users"=>["Philip Gerlee", "Sven Nelander"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002556.g006", "stats"=>{"downloads"=>0, "page_views"=>8, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Comparison_between_IB_model_and_analytical_result_/294229", "title"=>"Comparison between IB-model and analytical result.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-20 03:53:16"}
  • {"files"=>["https://ndownloader.figshare.com/files/623382"], "description"=>"<p>A living glioma cell can be in either of two states, proliferating (P) or migrating (M), and transitions between the states with rates and respectively. A P-cell divides at rate while an M-cell moves with rate . Both cell types go into apoptosis and die with a constant rate .</p>", "links"=>[], "tags"=>["describing", "markov"], "article_id"=>293879, "categories"=>["Cancer", "Mathematics", "Biological Sciences"], "users"=>["Philip Gerlee", "Sven Nelander"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002556.g001", "stats"=>{"downloads"=>1, "page_views"=>11, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Schematic_describing_the_continuous_time_Markov_process_each_cell_is_subject_to_/293879", "title"=>"Schematic describing the continuous time Markov process each cell is subject to.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-20 03:51:17"}
  • {"files"=>["https://ndownloader.figshare.com/files/623605"], "description"=>"<p>Solutions of the 1-dimensional continuum model (equation (3) and (4)) for three different values of the switching rates at (black) and (red). The initial condition was set to , and . In (a) , (b) and in (c) . All solutions exhibit similar characteristics with an invading front of cancer cells stretching into the healthy tissue, similar to the solutions of the Fisher equation (1). The similarity between the solutions at the two different time points clearly shows that our system exhibits travelling wave solutions.</p>", "links"=>[], "tags"=>["solutions", "continuum"], "article_id"=>294104, "categories"=>["Cancer", "Mathematics", "Biological Sciences"], "users"=>["Philip Gerlee", "Sven Nelander"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002556.g004", "stats"=>{"downloads"=>0, "page_views"=>12, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Numerical_solutions_of_the_continuum_model_/294104", "title"=>"Numerical solutions of the continuum model.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-20 03:52:33"}
  • {"files"=>["https://ndownloader.figshare.com/files/623536"], "description"=>"<p>(a) The tumour mass at for the 2-dimensional model as a function of the phenotypic switching rates (the rate at which cells become proliferative) and (the rate at which they become motile). (b) The tumour mass at for the 3-dimensional as a function of and . The results in 2 and 3 dimensions are similar, although a larger variability seems to exists in the 3-dimensional case.</p>", "links"=>[], "tags"=>["phenotypic", "switching", "rates", "tumour"], "article_id"=>294027, "categories"=>["Cancer", "Mathematics", "Biological Sciences"], "users"=>["Philip Gerlee", "Sven Nelander"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002556.g003", "stats"=>{"downloads"=>0, "page_views"=>11, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_The_impact_of_phenotypic_switching_rates_on_tumour_mass_/294027", "title"=>"The impact of phenotypic switching rates on tumour mass.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-20 03:52:08"}
  • {"files"=>["https://ndownloader.figshare.com/files/623685"], "description"=>"<p>The wave speed of the propagating tumour margin determined from both phase space analysis (solid line) and numerical simulation (dashed line). In (a) the switch rate to proliferation is fixed at , while in (b) we have fixed .</p>", "links"=>[], "tags"=>["continuum", "analytical"], "article_id"=>294172, "categories"=>["Cancer", "Mathematics", "Biological Sciences"], "users"=>["Philip Gerlee", "Sven Nelander"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002556.g005", "stats"=>{"downloads"=>2, "page_views"=>35, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Comparison_between_continuum_model_and_analytical_result_/294172", "title"=>"Comparison between continuum model and analytical result.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-20 03:52:57"}

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Relative Metric

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