On the Firing Rate Dependency of the Phase Response Curve of Rat Purkinje Neurons In Vitro
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{"title"=>"On the Firing Rate Dependency of the Phase Response Curve of Rat Purkinje Neurons In Vitro", "type"=>"journal", "authors"=>[{"first_name"=>"João", "last_name"=>"Couto", "scopus_author_id"=>"55565780200"}, {"first_name"=>"Daniele", "last_name"=>"Linaro", "scopus_author_id"=>"24587496200"}, {"first_name"=>"E.", "last_name"=>"De Schutter", "scopus_author_id"=>"7007086441"}, {"first_name"=>"Michele", "last_name"=>"Giugliano", "scopus_author_id"=>"55242654700"}], "year"=>2015, "source"=>"PLoS Computational Biology", "identifiers"=>{"scopus"=>"2-s2.0-84926350492", "pui"=>"603513931", "pmid"=>"25775448", "issn"=>"15537358", "doi"=>"10.1371/journal.pcbi.1004112", "sgr"=>"84926350492"}, "id"=>"fce851d8-8178-37a7-89bd-64162771956f", "abstract"=>"Synchronous spiking during cerebellar tasks has been observed across Purkinje cells: however, little is known about the intrinsic cellular mechanisms responsible for its initiation, cessation and stability. The Phase Response Curve (PRC), a simple input-output characterization of single cells, can provide insights into individual and collective properties of neurons and networks, by quantifying the impact of an infinitesimal depolarizing current pulse on the time of occurrence of subsequent action potentials, while a neuron is firing tonically. Recently, the PRC theory applied to cerebellar Purkinje cells revealed that these behave as phase-independent integrators at low firing rates, and switch to a phase-dependent mode at high rates. Given the implications for computation and information processing in the cerebellum and the possible role of synchrony in the communication with its post-synaptic targets, we further explored the firing rate dependency of the PRC in Purkinje cells. We isolated key factors for the experimental estimation of the PRC and developed a closed-loop approach to reliably compute the PRC across diverse firing rates in the same cell. Our results show unambiguously that the PRC of individual Purkinje cells is firing rate dependent and that it smoothly transitions from phase independent integrator to a phase dependent mode. Using computational models we show that neither channel noise nor a realistic cell morphology are responsible for the rate dependent shift in the phase response curve.", "link"=>"http://www.mendeley.com/research/firing-rate-dependency-phase-response-curve-rat-purkinje-neurons-vitro-1", "reader_count"=>18, "reader_count_by_academic_status"=>{"Professor > Associate Professor"=>1, "Student > Doctoral Student"=>2, "Researcher"=>4, "Student > Ph. D. Student"=>7, "Student > Postgraduate"=>1, "Student > Master"=>3}, "reader_count_by_user_role"=>{"Professor > Associate Professor"=>1, "Student > Doctoral Student"=>2, "Researcher"=>4, "Student > Ph. D. Student"=>7, "Student > Postgraduate"=>1, "Student > Master"=>3}, "reader_count_by_subject_area"=>{"Engineering"=>1, "Unspecified"=>1, "Agricultural and Biological Sciences"=>11, "Neuroscience"=>3, "Chemical Engineering"=>1, "Computer Science"=>1}, "reader_count_by_subdiscipline"=>{"Engineering"=>{"Engineering"=>1}, "Neuroscience"=>{"Neuroscience"=>3}, "Agricultural and Biological Sciences"=>{"Agricultural and Biological Sciences"=>11}, "Computer Science"=>{"Computer Science"=>1}, "Unspecified"=>{"Unspecified"=>1}, "Chemical Engineering"=>{"Chemical Engineering"=>1}}, "reader_count_by_country"=>{"Sweden"=>1, "Belgium"=>1, "Germany"=>1}, "group_count"=>1}

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Figshare

  • {"files"=>["https://ndownloader.figshare.com/files/1949553", "https://ndownloader.figshare.com/files/1949554", "https://ndownloader.figshare.com/files/1949555", "https://ndownloader.figshare.com/files/1949556", "https://ndownloader.figshare.com/files/1949557"], "description"=>"<div><p>Synchronous spiking during cerebellar tasks has been observed across Purkinje cells: however, little is known about the intrinsic cellular mechanisms responsible for its initiation, cessation and stability. The Phase Response Curve (PRC), a simple input-output characterization of single cells, can provide insights into individual and collective properties of neurons and networks, by quantifying the impact of an infinitesimal depolarizing current pulse on the time of occurrence of subsequent action potentials, while a neuron is firing tonically. Recently, the PRC theory applied to cerebellar Purkinje cells revealed that these behave as phase-independent integrators at low firing rates, and switch to a phase-dependent mode at high rates. Given the implications for computation and information processing in the cerebellum and the possible role of synchrony in the communication with its post-synaptic targets, we further explored the firing rate dependency of the PRC in Purkinje cells. We isolated key factors for the experimental estimation of the PRC and developed a closed-loop approach to reliably compute the PRC across diverse firing rates in the same cell. Our results show unambiguously that the PRC of individual Purkinje cells is firing rate dependent and that it smoothly transitions from phase independent integrator to a phase dependent mode. Using computational models we show that neither channel noise nor a realistic cell morphology are responsible for the rate dependent shift in the phase response curve.</p></div>", "links"=>[], "tags"=>["Firing Rate Dependency", "prc", "phase response curve", "Vitro Synchronous spiking", "cerebellar Purkinje cells", "Rat Purkinje Neurons", "Purkinje cells"], "article_id"=>1336382, "categories"=>["Biological Sciences"], "users"=>["João Couto", "Daniele Linaro", "E De Schutter", "Michele Giugliano"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1004112.s001", "https://dx.doi.org/10.1371/journal.pcbi.1004112.s002", "https://dx.doi.org/10.1371/journal.pcbi.1004112.s003", "https://dx.doi.org/10.1371/journal.pcbi.1004112.s004", "https://dx.doi.org/10.1371/journal.pcbi.1004112.s005"], "stats"=>{"downloads"=>4, "page_views"=>6, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/On_the_Firing_Rate_Dependency_of_the_Phase_Response_Curve_of_Rat_Purkinje_Neurons_In_Vitro_/1336382", "title"=>"On the Firing Rate Dependency of the Phase Response Curve of Rat Purkinje Neurons <i>In Vitro</i>", "pos_in_sequence"=>0, "defined_type"=>4, "published_date"=>"2015-03-16 03:11:16"}
  • {"files"=>["https://ndownloader.figshare.com/files/1949536"], "description"=>"<p>The PRCs of the model incorporating channel noise (gray curves) are strikingly similar to those of the deterministic model (black curves). The variability of the spike trains does not affect the curves either at low (A and C) or high (B and D) firing rates (left and right columns, respectively). The membrane area of the model with channel noise was chosen to obtain the desired value of CV at low firing rate (around 10% for A, and 5% for C) and that same area was used for the simulations at high firing rate (panels B and D). Comparable values of CV were obtained in the deterministic model by changing the magnitude of the fluctuations of the injected current. For a given perturbation size, the model is less sensitive at high firing rates (B and D).</p>", "links"=>[], "tags"=>["Firing Rate Dependency", "prc", "phase response curve", "Vitro Synchronous spiking", "cerebellar Purkinje cells", "Rat Purkinje Neurons", "Purkinje cells"], "article_id"=>1336378, "categories"=>["Biological Sciences"], "users"=>["João Couto", "Daniele Linaro", "E De Schutter", "Michele Giugliano"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1004112.g006", "stats"=>{"downloads"=>0, "page_views"=>12, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Stochastic_channel_noise_is_not_responsible_for_the_firing_rate_dependency_of_the_PRC_/1336378", "title"=>"Stochastic channel noise is not responsible for the firing rate dependency of the PRC.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2015-03-16 03:11:16"}
  • {"files"=>["https://ndownloader.figshare.com/files/1949526"], "description"=>"<p>(A) A direct estimate of the PRC, obtained for the same PC, is plotted after data smoothing (see <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004112#sec002\" target=\"_blank\">Methods</a>) while altering the cell’s firing rate in the range 20 − 160 Hz): a strong dependency on the firing rate is apparent. The transition from an approximately flat to a phase-dependent PRC profile does not occur abruptly, but smoothly: in each subplot, the horizontal gray dashed lines represent <i>Z</i>(<i>φ</i>) = 0, while the continuous black thick traces are the PRCs, estimated at distinct firing rates (<a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004112#pcbi.1004112.g001\" target=\"_blank\">Fig. 1</a>). Black circles indicate the location of the extrema for each of the two halves of the curves (i.e., in <i>φ</i> ∈ [0; 0.5] or [0.5; 1], emphasized by the vertical thin black line), used to concisely characterize the PRC shape according to its peak-to-baseline ratio (see <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004112#sec002\" target=\"_blank\">Methods</a>). The graded PRC shape dependency on the firing rate is confirmed in three other PCs (B, markers) and quantified by their peak-to-baseline ratio. The black curve represents the function (1 + <i>e</i><sup>−(<i>F</i>−<i>a</i>)/<i>b</i></sup>)<sup>−1</sup>, with best-fit parameters <i>a</i> = 44.1, <i>b</i> = 20.5. The inset further displays the location of the PRC peak, relative to the time of the AP following the stimulus (i.e., <i>τ</i><sub><i>peak</i></sub> = (<i>τ</i><sub><i>peak</i></sub> − 1) ⋅ ⟨<i>ISI</i>⟩), for the same five cells.</p>", "links"=>[], "tags"=>["Firing Rate Dependency", "prc", "phase response curve", "Vitro Synchronous spiking", "cerebellar Purkinje cells", "Rat Purkinje Neurons", "Purkinje cells"], "article_id"=>1336368, "categories"=>["Biological Sciences"], "users"=>["João Couto", "Daniele Linaro", "E De Schutter", "Michele Giugliano"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1004112.g002", "stats"=>{"downloads"=>0, "page_views"=>27, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Direct_method_for_the_estimation_of_the_PRC_/1336368", "title"=>"Direct method for the estimation of the PRC.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2015-03-16 03:11:16"}
  • {"files"=>["https://ndownloader.figshare.com/files/1949525"], "description"=>"<p>(A) A real-time closed-loop in vitro set-up for experimentally estimating the PRC at a fixed firing rate, based on a Proportional-Integral-Derivative (PID) controller and on a reactive-clamp paradigm, was employed to rapidly and optimally explore the dependency of the PRC of PCs on the cell’s firing rate. To this aim, a brief external current-pulse (B-D at different scales) was repeatedly delivered at different phases <i>φ</i> of the cell cycle (E), and the resulting impact on the time of the next AP was quantified as a phase delay or of advance Δ<i>φ</i> (E).</p>", "links"=>[], "tags"=>["Firing Rate Dependency", "prc", "phase response curve", "Vitro Synchronous spiking", "cerebellar Purkinje cells", "Rat Purkinje Neurons", "Purkinje cells"], "article_id"=>1336366, "categories"=>["Biological Sciences"], "users"=>["João Couto", "Daniele Linaro", "E De Schutter", "Michele Giugliano"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1004112.g001", "stats"=>{"downloads"=>5, "page_views"=>10, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Experimental_set_up_/1336366", "title"=>"Experimental set-up.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2015-03-16 03:11:16"}
  • {"files"=>["https://ndownloader.figshare.com/files/1949534"], "description"=>"<p>(A) Population summary obtained over distinct firing rates, obtained averaging across 95 PRCs, binned for similar firing rates and obtained from 16 PCs. As in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004112#pcbi.1004112.g003\" target=\"_blank\">Fig. 3D</a>, the average PRCs are equivalently represented (B) as a function of time (i.e., <i>τ</i> = (<i>φ</i> − 1) ⋅ ⟨<i>ISI</i>⟩) for the 20 ms preceding the perturbed AP. (C) The peak-to-baseline ratio once more confirms the observations obtained in Figs. <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004112#pcbi.1004112.g002\" target=\"_blank\">2</a>, <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004112#pcbi.1004112.g004\" target=\"_blank\">4</a> and <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004112#pcbi.1004112.g003\" target=\"_blank\">3</a> (individual cells, <i>n</i> = 16: gray markers; averages from A: red markers). The black curve represents the function (1 + <i>e</i><sup>−(<i>F</i>−<i>a</i>)/<i>b</i></sup>)<sup>−1</sup>, with best-fit parameters <i>a</i> = 105.6, <i>b</i> = 55.8 optimized over the set of individual PCs. The inset displays the location of the PRC peak, relative to the time of the AP following the stimulus (i.e., <i>τ</i><sub><i>peak</i></sub> = (<i>φ</i><sub><i>peak</i></sub> − 1) ⋅ ⟨<i>ISI</i>⟩), for the same cells, as in Figs. <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004112#pcbi.1004112.g002\" target=\"_blank\">2B</a> and <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004112#pcbi.1004112.g003\" target=\"_blank\">3C</a>.</p>", "links"=>[], "tags"=>["Firing Rate Dependency", "prc", "phase response curve", "Vitro Synchronous spiking", "cerebellar Purkinje cells", "Rat Purkinje Neurons", "Purkinje cells"], "article_id"=>1336377, "categories"=>["Biological Sciences"], "users"=>["João Couto", "Daniele Linaro", "E De Schutter", "Michele Giugliano"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1004112.g005", "stats"=>{"downloads"=>1, "page_views"=>10, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Population_summary_using_the_WSTA_indirect_method_/1336377", "title"=>"Population summary using the WSTA (indirect) method.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2015-03-16 03:11:16"}
  • {"files"=>["https://ndownloader.figshare.com/files/1949529"], "description"=>"<p>PRCs were smoothed and normalized by the total charge of the injected pulse <i>Q</i> = <i>I</i><sub><i>pulse</i></sub> ⋅ <i>T</i><sub><i>pulse</i></sub>. Increasing the amplitude <i>I</i><sub><i>pulse</i></sub> increased the estimates confidence (A-B), reducing the standard deviation of the PRC raw data points, especially as PCs fire at low firing rates. The plots display the PRC estimates obtained without the PID controller for <i>I</i><sub><i>pulse</i></sub> = 50 and 100 pA, in the same PC over a comparable number of stimulation trials (i.e., 1911 and 1338 at high firing rates, and 3361 and 3350 at low firing rates, respectively). The smoothed PRCs and their 68% confidence intervals (C-D) are plotted, as a function of time (i.e., <i>τ</i> = (<i>φ</i> − 1) ⋅ ⟨<i>ISI</i>⟩) by the lines and shaded areas (i.e., dashed/gray for 50 pA and continuous/white for 100 pA).</p>", "links"=>[], "tags"=>["Firing Rate Dependency", "prc", "phase response curve", "Vitro Synchronous spiking", "cerebellar Purkinje cells", "Rat Purkinje Neurons", "Purkinje cells"], "article_id"=>1336371, "categories"=>["Biological Sciences"], "users"=>["João Couto", "Daniele Linaro", "E De Schutter", "Michele Giugliano"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1004112.g004", "stats"=>{"downloads"=>0, "page_views"=>22, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Signal_to_noise_ratio_in_PRC_estimates_/1336371", "title"=>"Signal to noise ratio in PRC estimates.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2015-03-16 03:11:16"}
  • {"files"=>["https://ndownloader.figshare.com/files/1949528"], "description"=>"<p>(A) Population summary obtained over distinct firing rates, by averaging PRCs across individual cells. (B) Individual responses are plotted in gray and pooled according to the corresponding firing rate. Cell numbers are further indicated in parentheses. This summary, quantified by the peak-to-baseline ratio as in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004112#pcbi.1004112.g002\" target=\"_blank\">Fig. 2C</a> (individual cells, n = 42: gray markers; averages from A: red markers), confirms (C) our observations in single PCs (<a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004112#pcbi.1004112.g002\" target=\"_blank\">Fig. 2</a>). The black curve represents the function (1 + <i>e</i><sup>−(<i>F</i>−<i>a</i>)/<i>b</i></sup>)<sup>−1</sup>, with best-fit parameters <i>a</i> = 47.6, <i>b</i> = 21.7 optimized over the set of 42 PCs. The inset further displays the location of the summary PRCs peak, relative to the time of the AP following the stimulus (i.e., <i>τ</i><sub><i>peak</i></sub> = (<i>φ</i><sub><i>peak</i></sub> − 1) ⋅ ⟨<i>ISI</i>⟩), as in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004112#pcbi.1004112.g002\" target=\"_blank\">Fig. 2B</a>. (D) The average PRCs are equivalently represented as a function of time (i.e., <i>τ</i> = (<i>φ</i> − 1) ⋅ ⟨<i>ISI</i>⟩) for the 20 ms preceding the perturbed AP.</p>", "links"=>[], "tags"=>["Firing Rate Dependency", "prc", "phase response curve", "Vitro Synchronous spiking", "cerebellar Purkinje cells", "Rat Purkinje Neurons", "Purkinje cells"], "article_id"=>1336370, "categories"=>["Biological Sciences"], "users"=>["João Couto", "Daniele Linaro", "E De Schutter", "Michele Giugliano"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1004112.g003", "stats"=>{"downloads"=>0, "page_views"=>13, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Population_summary_using_the_direct_method_/1336370", "title"=>"Population summary using the direct method.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2015-03-16 03:11:16"}

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  • {"unique-ip"=>"10", "full-text"=>"7", "pdf"=>"2", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"3", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2019", "month"=>"5"}
  • {"unique-ip"=>"3", "full-text"=>"2", "pdf"=>"1", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2019", "month"=>"8"}
  • {"unique-ip"=>"5", "full-text"=>"2", "pdf"=>"3", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2019", "month"=>"9"}
  • {"unique-ip"=>"5", "full-text"=>"5", "pdf"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"1", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2019", "month"=>"10"}
  • {"unique-ip"=>"8", "full-text"=>"2", "pdf"=>"6", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"1", "cited-by"=>"0", "year"=>"2019", "month"=>"12"}
  • {"unique-ip"=>"2", "full-text"=>"1", "pdf"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"2", "year"=>"2020", "month"=>"2"}
  • {"unique-ip"=>"3", "full-text"=>"3", "pdf"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2020", "month"=>"3"}
  • {"unique-ip"=>"3", "full-text"=>"2", "pdf"=>"2", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2020", "month"=>"4"}
  • {"unique-ip"=>"5", "full-text"=>"31", "pdf"=>"2", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"35", "supp-data"=>"5", "cited-by"=>"4", "year"=>"2020", "month"=>"5"}
  • {"unique-ip"=>"2", "full-text"=>"1", "pdf"=>"1", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2020", "month"=>"6"}
  • {"unique-ip"=>"4", "full-text"=>"2", "pdf"=>"1", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"4", "cited-by"=>"0", "year"=>"2020", "month"=>"7"}
  • {"unique-ip"=>"2", "full-text"=>"1", "pdf"=>"1", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2020", "month"=>"8"}
  • {"unique-ip"=>"2", "full-text"=>"2", "pdf"=>"1", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2020", "month"=>"9"}

Relative Metric

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