Membrane Capacitive Memory Alters Spiking in Neurons Described by the Fractional-Order Hodgkin-Huxley Model
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{"title"=>"Membrane capacitive memory alters spiking in neurons described by the fractional-order Hodgkin-Huxley model", "type"=>"journal", "authors"=>[{"first_name"=>"Seth H.", "last_name"=>"Weinberg", "scopus_author_id"=>"35981171500"}], "year"=>2015, "source"=>"PLoS ONE", "identifiers"=>{"scopus"=>"2-s2.0-84929377761", "doi"=>"10.1371/journal.pone.0126629", "sgr"=>"84929377761", "pmid"=>"25970534", "issn"=>"19326203", "pui"=>"604377904"}, "id"=>"4b90470d-b554-3f43-8be0-3f53022ef872", "abstract"=>"Excitable cells and cell membranes are often modeled by the simple yet elegant parallel resistor-capacitor circuit. However, studies have shown that the passive properties of membranes may be more appropriately modeled with a non-ideal capacitor, in which the current-voltage relationship is given by a fractional-order derivative. Fractional-order membrane potential dynamics introduce capacitive memory effects, i.e., dynamics are influenced by a weighted sum of the membrane potential prior history. However, it is not clear to what extent fractional-order dynamics may alter the properties of active excitable cells. In this study, we investigate the spiking properties of the neuronal membrane patch, nerve axon, and neural networks described by the fractional-order Hodgkin-Huxley neuron model. We find that in the membrane patch model, as fractional-order decreases, i.e., a greater influence of membrane potential memory, peak sodium and potassium currents are altered, and spike frequency and amplitude are generally reduced. In the nerve axon, the velocity of spike propagation increases as fractional-order decreases, while in a neural network, electrical activity is more likely to cease for smaller fractional-order. Importantly, we demonstrate that the modulation of the peak ionic currents that occurs for reduced fractional-order alone fails to reproduce many of the key alterations in spiking properties, suggesting that membrane capacitive memory and fractional-order membrane potential dynamics are important and necessary to reproduce neuronal electrical activity.", "link"=>"http://www.mendeley.com/research/membrane-capacitive-memory-alters-spiking-neurons-described-fractionalorder-hodgkinhuxley-model", "reader_count"=>11, "reader_count_by_academic_status"=>{"Researcher"=>2, "Student > Ph. D. Student"=>6, "Student > Postgraduate"=>1, "Student > Bachelor"=>2}, "reader_count_by_user_role"=>{"Researcher"=>2, "Student > Ph. D. Student"=>6, "Student > Postgraduate"=>1, "Student > Bachelor"=>2}, "reader_count_by_subject_area"=>{"Engineering"=>2, "Biochemistry, Genetics and Molecular Biology"=>1, "Agricultural and Biological Sciences"=>2, "Medicine and Dentistry"=>2, "Philosophy"=>1, "Neuroscience"=>1, "Physics and Astronomy"=>1, "Unspecified"=>1}, "reader_count_by_subdiscipline"=>{"Engineering"=>{"Engineering"=>2}, "Medicine and Dentistry"=>{"Medicine and Dentistry"=>2}, "Neuroscience"=>{"Neuroscience"=>1}, "Physics and Astronomy"=>{"Physics and Astronomy"=>1}, "Agricultural and Biological Sciences"=>{"Agricultural and Biological Sciences"=>2}, "Biochemistry, Genetics and Molecular Biology"=>{"Biochemistry, Genetics and Molecular Biology"=>1}, "Unspecified"=>{"Unspecified"=>1}, "Philosophy"=>{"Philosophy"=>1}}, "reader_count_by_country"=>{"United States"=>2}, "group_count"=>0}

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Figshare

  • {"files"=>["https://ndownloader.figshare.com/files/2065875"], "description"=>"<p>(A) A space-time plot of the membrane potential <i>V</i><sub><i>m</i></sub>(<i>x</i>, <i>t</i>) is shown for different values of fractional-order <i>α</i>. (B) The peak sodium current <i>I</i><sub><i>Na</i></sub>, potassium current <i>I</i><sub><i>K</i></sub>, leak current <i>I</i><sub><i>L</i></sub>, and voltage memory trace <i>v</i><sub><i>mem</i></sub> magnitude are shown as a function of position along the cable <i>x</i>, for different values of <i>α</i>. (C) Spike propagation velocity is shown in the fractional-order Hodgkin-Huxley (fHH) nerve axon, as a function of <i>α</i>, for different values of longitudinal conductance <i>g</i> (solid lines). Velocity measurements are also shown (dashed lines) for simulations in which the sodium <i>g</i><sub><i>Na</i></sub> and potassium <i>g</i><sub><i>K</i></sub> conductances are scaled such that peak current measurements are equivalent to values for particular value of <i>α</i>. See text for more details. In A and B, axon conductance <i>g</i> = 7.06 <i>μ</i>S. Propagating spikes are elicited by a brief 0.1-ms duration, 500-<i>μ</i>A/cm<sup>2</sup> stimulus at <i>x</i> = 0.</p>", "links"=>[], "tags"=>["membrane capacitive memory", "dynamic", "membrane patch model", "spike propagation increases", "capacitive memory effects", "spiking properties", "Membrane Capacitive Memory Alters Spiking", "nerve axon"], "article_id"=>1413229, "categories"=>["Uncategorised"], "users"=>["Seth H. Weinberg"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0126629.g008", "stats"=>{"downloads"=>0, "page_views"=>7, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Spike_propagation_in_the_fractional_order_Hodgkin_Huxley_nerve_axon_following_a_brief_stimulus_pulse_/1413229", "title"=>"Spike propagation in the fractional-order Hodgkin-Huxley nerve axon following a brief stimulus pulse.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2015-05-13 03:10:15"}
  • {"files"=>["https://ndownloader.figshare.com/files/2065874"], "description"=>"<p>(A) The impulse response function <i>G</i>(<i>x</i>/<i>λ</i>, <i>t</i>/<i>τ</i>) is shown as a function of space <i>x</i>, normalized by space constant <i>λ</i>, at times <i>t</i> = 0.05<i>τ</i> and <i>t</i> = <i>τ</i>, where <i>τ</i> is the time constant, on a linear (top) and logarithmic (bottom) scale, for different values of fractional-order <i>α</i>. (B) <i>G</i>(<i>x</i>/<i>λ</i>, <i>t</i>/<i>τ</i>) is shown as a function of normalized time <i>t</i>/<i>τ</i> at location <i>x</i> = 0 (top) and <i>x</i> = <i>λ</i> (bottom). (C) The normalized voltage response to a current step input at the origin <i>x</i> = 0 is shown as a function of normalized time <i>t</i>/<i>τ</i> at locations <i>x</i> = 0 and <i>x</i> = <i>λ</i>. The voltage response in the membrane patch is shown for comparison (dashed lines, <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0126629#pone.0126629.g001\" target=\"_blank\">Fig 1C</a>). (D) The normalized position of stimulus propagation <i>x</i>/<i>λ</i> is shown as a function of normalized time <i>t</i>/<i>τ</i> (the time at which the normalized voltage response is 0.5) (E) The pseudo-velocity, given by the slope of the stimulus propagation, in units of <i>λ</i>/<i>τ</i>, is shown as a function of <i>α</i>.</p>", "links"=>[], "tags"=>["membrane capacitive memory", "dynamic", "membrane patch model", "spike propagation increases", "capacitive memory effects", "spiking properties", "Membrane Capacitive Memory Alters Spiking", "nerve axon"], "article_id"=>1413228, "categories"=>["Uncategorised"], "users"=>["Seth H. Weinberg"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0126629.g007", "stats"=>{"downloads"=>2, "page_views"=>3, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Sub_threshold_impulse_and_voltage_response_in_the_passive_fractional_order_cable_equation_/1413228", "title"=>"Sub-threshold impulse and voltage response in the passive fractional-order cable equation.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2015-05-13 03:10:15"}
  • {"files"=>["https://ndownloader.figshare.com/files/2065871"], "description"=>"<p>(A) The membrane potential <i>V</i><sub><i>m</i></sub>, sodium current <i>I</i><sub><i>Na</i></sub>, potassium current <i>I</i><sub><i>K</i></sub>, and voltage memory trace <i>v</i><sub><i>mem</i></sub> are shown as a function of time in response to a constant applied current, <i>I</i><sub><i>app</i></sub> = 20 (left), 100 (middle), and 140 (right) <i>μ</i>A/cm<sup>2</sup>, for different values of fractional-order <i>α</i>. (B) The instantaneous spike frequency is shown as a function of the interspike interval (ISI) number for different values of <i>α</i>.</p>", "links"=>[], "tags"=>["membrane capacitive memory", "dynamic", "membrane patch model", "spike propagation increases", "capacitive memory effects", "spiking properties", "Membrane Capacitive Memory Alters Spiking", "nerve axon"], "article_id"=>1413225, "categories"=>["Uncategorised"], "users"=>["Seth H. Weinberg"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0126629.g004", "stats"=>{"downloads"=>2, "page_views"=>2, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Repetitive_firing_in_the_fractional_order_Hodgkin_Huxley_model_/1413225", "title"=>"Repetitive firing in the fractional-order Hodgkin-Huxley model.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2015-05-13 03:10:15"}
  • {"files"=>["https://ndownloader.figshare.com/files/2065868"], "description"=>"<p>The minimum time period between stimuli (top), the time to the spike peak (middle), and their difference (bottom) are shown as a function of fractional-order <i>α</i>. Spikes are elicited by a brief 0.1-ms duration, 1.5x threshold stimulus.</p>", "links"=>[], "tags"=>["membrane capacitive memory", "dynamic", "membrane patch model", "spike propagation increases", "capacitive memory effects", "spiking properties", "Membrane Capacitive Memory Alters Spiking", "nerve axon"], "article_id"=>1413222, "categories"=>["Uncategorised"], "users"=>["Seth H. Weinberg"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0126629.g003", "stats"=>{"downloads"=>0, "page_views"=>4, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Refractoriness_in_the_fractional_order_Hodgkin_Huxley_model_/1413222", "title"=>"Refractoriness in the fractional-order Hodgkin-Huxley model.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2015-05-13 03:10:15"}
  • {"files"=>["https://ndownloader.figshare.com/files/2065865"], "description"=>"<p>(A) Strength-duration curves, derived from the fractional passive membrane, are shown as a function of fractional-order <i>α</i> (<a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0126629#pone.0126629.e011\" target=\"_blank\">Eq 9</a>). (B) The magnitude (top) and phase (bottom) of the complex impedance of the fractional-order passive membrane are shown as a function of the normalized frequency <i>ωτ</i>, for different values of <i>α</i>. (C) The normalized membrane potential <i>V</i><sub><i>m</i></sub>/(<i>I</i><sub><i>m</i></sub><i>R</i><sub><i>m</i></sub>) response following a current step is shown as a function of normalized time <i>t</i>/<i>τ</i> on a linear (top) and logarithmic (bottom scale), for different values of <i>α</i>.</p>", "links"=>[], "tags"=>["membrane capacitive memory", "dynamic", "membrane patch model", "spike propagation increases", "capacitive memory effects", "spiking properties", "Membrane Capacitive Memory Alters Spiking", "nerve axon"], "article_id"=>1413219, "categories"=>["Uncategorised"], "users"=>["Seth H. Weinberg"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0126629.g001", "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Properties_of_the_fractional_order_passive_membrane_/1413219", "title"=>"Properties of the fractional-order passive membrane.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2015-05-13 03:10:15"}
  • {"files"=>["https://ndownloader.figshare.com/files/2065879", "https://ndownloader.figshare.com/files/2065880"], "description"=>"<div><p>Excitable cells and cell membranes are often modeled by the simple yet elegant parallel resistor-capacitor circuit. However, studies have shown that the passive properties of membranes may be more appropriately modeled with a non-ideal capacitor, in which the current-voltage relationship is given by a fractional-order derivative. Fractional-order membrane potential dynamics introduce capacitive memory effects, i.e., dynamics are influenced by a weighted sum of the membrane potential prior history. However, it is not clear to what extent fractional-order dynamics may alter the properties of active excitable cells. In this study, we investigate the spiking properties of the neuronal membrane patch, nerve axon, and neural networks described by the fractional-order Hodgkin-Huxley neuron model. We find that in the membrane patch model, as fractional-order decreases, i.e., a greater influence of membrane potential memory, peak sodium and potassium currents are altered, and spike frequency and amplitude are generally reduced. In the nerve axon, the velocity of spike propagation increases as fractional-order decreases, while in a neural network, electrical activity is more likely to cease for smaller fractional-order. Importantly, we demonstrate that the modulation of the peak ionic currents that occurs for reduced fractional-order alone fails to reproduce many of the key alterations in spiking properties, suggesting that membrane capacitive memory and fractional-order membrane potential dynamics are important and necessary to reproduce neuronal electrical activity.</p></div>", "links"=>[], "tags"=>["membrane capacitive memory", "dynamic", "membrane patch model", "spike propagation increases", "capacitive memory effects", "spiking properties", "Membrane Capacitive Memory Alters Spiking", "nerve axon"], "article_id"=>1413233, "categories"=>["Uncategorised"], "users"=>["Seth H. Weinberg"], "doi"=>["https://dx.doi.org/10.1371/journal.pone.0126629.s001", "https://dx.doi.org/10.1371/journal.pone.0126629.s002"], "stats"=>{"downloads"=>7, "page_views"=>8, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Membrane_Capacitive_Memory_Alters_Spiking_in_Neurons_Described_by_the_Fractional_Order_Hodgkin_Huxley_Model_/1413233", "title"=>"Membrane Capacitive Memory Alters Spiking in Neurons Described by the Fractional-Order Hodgkin-Huxley Model", "pos_in_sequence"=>0, "defined_type"=>4, "published_date"=>"2015-05-13 03:10:15"}
  • {"files"=>["https://ndownloader.figshare.com/files/2065877"], "description"=>"<p>(A) Rastergram of spikes in the neural network for different values of fractional-order <i>α</i>. Synaptic connections and network architecture were identical in all simulations. (B) The pseudo-electroencephalogram (pEEG, <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0126629#pone.0126629.e053\" target=\"_blank\">Eq 25</a>) and (C) firing rate are shown as functions of time, for the simulations in A. Firing rate is measured in a sliding 50-ms window, with 10-ms steps. (D) Interspike interval (ISI) histograms are shown for each simulation. The gray bar denotes the 50-ms applied stimulus, during which a 40-<i>μ</i>A/cm<sup>2</sup> current was applied to 13 randomly chosen neurons. (E) The mean network activity duration ± standard error of the mean and (F) the fraction of sustained network activity are shown in the fractional-order Hodgkin-Huxley (fHH) neural network, as a function of <i>α</i> (solid lines). Network simulations in which the sodium, potassium, and leak conductances, <i>g</i><sub><i>Na</i></sub>, <i>g</i><sub><i>K</i></sub>, and <i>g</i><sub><i>L</i></sub>, respectively, are scaled such that peak current measurements are equivalent to values for particular value of <i>α</i>, as described in the text, are shown for comparison (dashed lines). Values in E and F are calculated for 12 network architectures.</p>", "links"=>[], "tags"=>["membrane capacitive memory", "dynamic", "membrane patch model", "spike propagation increases", "capacitive memory effects", "spiking properties", "Membrane Capacitive Memory Alters Spiking", "nerve axon"], "article_id"=>1413231, "categories"=>["Uncategorised"], "users"=>["Seth H. Weinberg"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0126629.g010", "stats"=>{"downloads"=>0, "page_views"=>5, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Electrical_activity_in_a_fractional_order_Hodgkin_Huxley_neural_network_/1413231", "title"=>"Electrical activity in a fractional-order Hodgkin-Huxley neural network.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2015-05-13 03:10:15"}
  • {"files"=>["https://ndownloader.figshare.com/files/2065878"], "description"=>"<p>(A) The excitatory and inhibitory synaptic currents, <i>I</i><sub><i>synE</i></sub> and <i>I</i><sub><i>synI</i></sub>, respectively, averaged over all network neurons, are shown as a function of time, for different values of fractional-order <i>α</i>, for the same network as shown in Fig <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0126629#pone.0126629.g010\" target=\"_blank\">10A</a>–<a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0126629#pone.0126629.g010\" target=\"_blank\">10D</a>. The gray bar denotes the 50-ms applied stimulus, during which a 40-<i>μ</i>A/cm<sup>2</sup> current was applied to 13 randomly chosen neurons. (B) The mean of excitatory and inhibitory current charge magnitude, <i>Q</i><sub><i>synE</i></sub> and <i>Q</i><sub><i>synI</i></sub>, respectively, ± standard error of the mean, are shown as a function of <i>α</i>, calculated for 12 network architectures (solid lines). Network simulations in which the sodium, potassium, and leak conductances, <i>g</i><sub><i>Na</i></sub>, <i>g</i><sub><i>K</i></sub>, and <i>g</i><sub><i>L</i></sub>, respectively, are scaled such that peak current measurements are equivalent to values for particular value of <i>α</i>, as described in the text, are shown for comparison (dashed lines).</p>", "links"=>[], "tags"=>["membrane capacitive memory", "dynamic", "membrane patch model", "spike propagation increases", "capacitive memory effects", "spiking properties", "Membrane Capacitive Memory Alters Spiking", "nerve axon"], "article_id"=>1413232, "categories"=>["Uncategorised"], "users"=>["Seth H. Weinberg"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0126629.g011", "stats"=>{"downloads"=>0, "page_views"=>2, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Synaptic_activity_in_a_fractional_order_Hodgkin_Huxley_neural_network_/1413232", "title"=>"Synaptic activity in a fractional-order Hodgkin-Huxley neural network.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2015-05-13 03:10:15"}
  • {"files"=>["https://ndownloader.figshare.com/files/2065876"], "description"=>"<p>(A) Spike propagation velocity (top) and the change in velocity, as a percentage of the final velocity (bottom), are shown as functions of spike number, for different values of fractional-order <i>α</i> and applied current amplitude <i>I</i><sub><i>app</i></sub>. (B) Velocity measurements are shown for simulations in which the sodium, potassium, and leak conductances, <i>g</i><sub><i>Na</i></sub>, <i>g</i><sub><i>K</i></sub>, and <i>g</i><sub><i>L</i></sub>, respectively, are scaled such that peak current measurements are equivalent to values for particular value of <i>α</i> and location <i>x</i>, as described in the text. Axon conductance <i>g</i> = 7.06 <i>μ</i>S. Propagating spikes are elicited by a constant stimulus at <i>x</i> = 0.</p>", "links"=>[], "tags"=>["membrane capacitive memory", "dynamic", "membrane patch model", "spike propagation increases", "capacitive memory effects", "spiking properties", "Membrane Capacitive Memory Alters Spiking", "nerve axon"], "article_id"=>1413230, "categories"=>["Uncategorised"], "users"=>["Seth H. Weinberg"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0126629.g009", "stats"=>{"downloads"=>0, "page_views"=>7, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Spike_propagation_in_the_fractional_order_Hodgkin_Huxley_nerve_axon_during_a_constant_stimulus_/1413230", "title"=>"Spike propagation in the fractional-order Hodgkin-Huxley nerve axon during a constant stimulus.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2015-05-13 03:10:15"}
  • {"files"=>["https://ndownloader.figshare.com/files/2065873"], "description"=>"<p>(A) Bifurcation diagram of <i>V</i><sub><i>m</i></sub>, sodium current <i>I</i><sub><i>Na</i></sub>, and potassium current <i>I</i><sub><i>K</i></sub>, showing steady-state values and limit cycle maximum and minimum, as a function of the applied current <i>I</i><sub><i>app</i></sub>, for different values of <i>α</i>. (B) The critical values denoting <i>I</i><sub><i>app</i></sub> lower and upper limits for spiking (Hopf bifurcations), <i>I</i><sub>1</sub> and <i>I</i><sub>2</sub>, respectively, are indicated (fractional-order Hodgkin-Huxley model (fHH), solid lines). (C) The spike frequency (top) and amplitude (bottom) are shown as a function of <i>I</i><sub><i>app</i></sub> and <i>α</i>. In B and C, values for <i>I</i><sub>1</sub>, <i>I</i><sub>2</sub>, and spike frequency and amplitude are shown for the first-order model with scaled conductances for comparison (dashed lines, see <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0126629#pone.0126629.g005\" target=\"_blank\">Fig 5</a> and main text for more details). In the bottom panel of C, the solid and dashed lines are nearly identical.</p>", "links"=>[], "tags"=>["membrane capacitive memory", "dynamic", "membrane patch model", "spike propagation increases", "capacitive memory effects", "spiking properties", "Membrane Capacitive Memory Alters Spiking", "nerve axon"], "article_id"=>1413227, "categories"=>["Uncategorised"], "users"=>["Seth H. Weinberg"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0126629.g006", "stats"=>{"downloads"=>0, "page_views"=>3, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Spike_properties_in_the_fractional_order_Hodgkin_Huxley_model_/1413227", "title"=>"Spike properties in the fractional-order Hodgkin-Huxley model.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2015-05-13 03:10:15"}
  • {"files"=>["https://ndownloader.figshare.com/files/2065872"], "description"=>"<p>The membrane potential <i>V</i><sub><i>m</i></sub> is shown as a function of time in response to a constant applied current, <i>I</i><sub><i>app</i></sub> = 20 (left), 100 (middle), and 140 (right) <i>μ</i>A/cm<sup>2</sup>, for different values of fractional-order <i>α</i>. Sodium, potassium, and leak conductances, <i>g</i><sub><i>Na</i></sub>, <i>g</i><sub><i>K</i></sub>, and <i>g</i><sub><i>L</i></sub>, respectively, are scaled, individually (A-C) and combined (D, top), such that peak current measurements are equivalent to values for particular value of <i>α</i>, as described in the text. (D, bottom) The instantaneous spike frequency is shown as a function of the interspike interval (ISI) number for different values of <i>α</i>.</p>", "links"=>[], "tags"=>["membrane capacitive memory", "dynamic", "membrane patch model", "spike propagation increases", "capacitive memory effects", "spiking properties", "Membrane Capacitive Memory Alters Spiking", "nerve axon"], "article_id"=>1413226, "categories"=>["Uncategorised"], "users"=>["Seth H. Weinberg"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0126629.g005", "stats"=>{"downloads"=>0, "page_views"=>1, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Repetitive_firing_in_the_first_order_Hodgkin_Huxley_model_with_scaled_ionic_current_conductances_/1413226", "title"=>"Repetitive firing in the first-order Hodgkin-Huxley model with scaled ionic current conductances.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2015-05-13 03:10:15"}
  • {"files"=>["https://ndownloader.figshare.com/files/2065867"], "description"=>"<p>(A) The membrane potential <i>V</i><sub><i>m</i></sub>, sodium current <i>I</i><sub><i>Na</i></sub>, potassium current <i>I</i><sub><i>K</i></sub>, and voltage memory trace <i>v</i><sub><i>mem</i></sub> are shown as a function of time, for different values of fractional-order <i>α</i>. (B). <i>V</i><sub><i>m</i></sub> maximum and minimum (left), <i>I</i><sub><i>Na</i></sub> and <i>I</i><sub><i>K</i></sub> peak current magnitude, and <i>h</i><sub><i>peak</i></sub> (the sodium inactivation gating variable at the time of peak <i>I</i><sub><i>Na</i></sub> current) are shown as a function of <i>α</i>. Spikes are elicited by a brief 0.1-ms duration, 1.5x threshold stimulus.</p>", "links"=>[], "tags"=>["membrane capacitive memory", "dynamic", "membrane patch model", "spike propagation increases", "capacitive memory effects", "spiking properties", "Membrane Capacitive Memory Alters Spiking", "nerve axon"], "article_id"=>1413221, "categories"=>["Uncategorised"], "users"=>["Seth H. Weinberg"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0126629.g002", "stats"=>{"downloads"=>0, "page_views"=>6, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Properties_of_the_fractional_order_Hodgkin_Huxley_spike_/1413221", "title"=>"Properties of the fractional-order Hodgkin-Huxley spike.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2015-05-13 03:10:15"}

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  • {"unique-ip"=>"9", "full-text"=>"9", "pdf"=>"2", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"2", "cited-by"=>"0", "year"=>"2020", "month"=>"6"}
  • {"unique-ip"=>"10", "full-text"=>"7", "pdf"=>"2", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"2", "cited-by"=>"0", "year"=>"2020", "month"=>"7"}
  • {"unique-ip"=>"4", "full-text"=>"5", "pdf"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"4", "cited-by"=>"0", "year"=>"2020", "month"=>"8"}
  • {"unique-ip"=>"6", "full-text"=>"5", "pdf"=>"1", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2020", "month"=>"9"}
  • {"unique-ip"=>"11", "full-text"=>"10", "pdf"=>"2", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2020", "month"=>"10"}

Relative Metric

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