Stochastic Ion Channel Gating in Dendritic Neurons: Morphology Dependence and Probabilistic Synaptic Activation of Dendritic Spikes
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{"title"=>"Stochastic ion channel gating in dendritic neurons: Morphology dependence and probabilistic synaptic activation of dendritic spikes", "type"=>"journal", "authors"=>[{"first_name"=>"Robert C.", "last_name"=>"Cannon", "scopus_author_id"=>"7201491609"}, {"first_name"=>"Cian", "last_name"=>"O'Donnell", "scopus_author_id"=>"8546475200"}, {"first_name"=>"Matthew F.", "last_name"=>"Nolan", "scopus_author_id"=>"35569304900"}], "year"=>2010, "source"=>"PLoS Computational Biology", "identifiers"=>{"isbn"=>"10.1371/journal.pcbi.1000886", "scopus"=>"2-s2.0-78049444153", "doi"=>"10.1371/journal.pcbi.1000886", "pui"=>"359882435", "issn"=>"1553734X", "pmid"=>"20711353", "sgr"=>"78049444153"}, "id"=>"8ae694b2-6ba5-3d1f-b0ea-2092acb5f9d5", "abstract"=>"Neuronal activity is mediated through changes in the probability of stochastic transitions between open and closed states of ion channels. While differences in morphology define neuronal cell types and may underlie neurological disorders, very little is known about influences of stochastic ion channel gating in neurons with complex morphology. We introduce and validate new computational tools that enable efficient generation and simulation of models containing stochastic ion channels distributed across dendritic and axonal membranes. Comparison of five morphologically distinct neuronal cell types reveals that when all simulated neurons contain identical densities of stochastic ion channels, the amplitude of stochastic membrane potential fluctuations differs between cell types and depends on sub-cellular location. For typical neurons, the amplitude of membrane potential fluctuations depends on channel kinetics as well as open probability. Using a detailed model of a hippocampal CA1 pyramidal neuron, we show that when intrinsic ion channels gate stochastically, the probability of initiation of dendritic or somatic spikes by dendritic synaptic input varies continuously between zero and one, whereas when ion channels gate deterministically, the probability is either zero or one. At physiological firing rates, stochastic gating of dendritic ion channels almost completely accounts for probabilistic somatic and dendritic spikes generated by the fully stochastic model. These results suggest that the consequences of stochastic ion channel gating differ globally between neuronal cell-types and locally between neuronal compartments. Whereas dendritic neurons are often assumed to behave deterministically, our simulations suggest that a direct consequence of stochastic gating of intrinsic ion channels is that spike output may instead be a probabilistic function of patterns of synaptic input to dendrites.", "link"=>"http://www.mendeley.com/research/stochastic-ion-channel-gating-dendritic-neurons-morphology-dependence-probabilistic-synaptic-activat", "reader_count"=>82, "reader_count_by_academic_status"=>{"Unspecified"=>1, "Professor > Associate Professor"=>4, "Researcher"=>21, "Student > Doctoral Student"=>1, "Student > Ph. D. Student"=>24, "Student > Postgraduate"=>4, "Other"=>6, "Student > Master"=>9, "Student > Bachelor"=>4, "Professor"=>8}, "reader_count_by_user_role"=>{"Unspecified"=>1, "Professor > Associate Professor"=>4, "Researcher"=>21, "Student > Doctoral Student"=>1, "Student > Ph. D. Student"=>24, "Student > Postgraduate"=>4, "Other"=>6, "Student > Master"=>9, "Student > Bachelor"=>4, "Professor"=>8}, "reader_count_by_subject_area"=>{"Unspecified"=>5, "Engineering"=>6, "Mathematics"=>2, "Agricultural and Biological Sciences"=>46, "Neuroscience"=>7, "Philosophy"=>1, "Pharmacology, Toxicology and Pharmaceutical Science"=>1, "Physics and Astronomy"=>3, "Psychology"=>1, "Computer Science"=>9, "Economics, Econometrics and Finance"=>1}, "reader_count_by_subdiscipline"=>{"Engineering"=>{"Engineering"=>6}, "Neuroscience"=>{"Neuroscience"=>7}, "Physics and Astronomy"=>{"Physics and Astronomy"=>3}, "Psychology"=>{"Psychology"=>1}, "Economics, Econometrics and Finance"=>{"Economics, Econometrics and Finance"=>1}, "Agricultural and Biological Sciences"=>{"Agricultural and Biological Sciences"=>46}, "Computer Science"=>{"Computer Science"=>9}, "Mathematics"=>{"Mathematics"=>2}, "Unspecified"=>{"Unspecified"=>5}, "Pharmacology, Toxicology and Pharmaceutical Science"=>{"Pharmacology, Toxicology and Pharmaceutical Science"=>1}, "Philosophy"=>{"Philosophy"=>1}}, "reader_count_by_country"=>{"Canada"=>1, "Netherlands"=>1, "Belgium"=>1, "United States"=>4, "Poland"=>1, "United Kingdom"=>7, "Israel"=>1, "France"=>1, "Portugal"=>1, "Germany"=>2, "India"=>2}, "group_count"=>3}

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Figshare

  • {"files"=>["https://ndownloader.figshare.com/files/835651"], "description"=>"<p>(A–B) Examples of membrane currents (top), membrane potential (middle) and corresponding power spectra from 100 s of simulated activity (bottom), for models containing passive leak Na<sup>+</sup> and K<sup>+</sup> channels with slow (A) or fast (B) kinetics. The power spectra are shown for simulations with time steps of 10 µs (solid traces), 100 µs and 1000 µs (light traces). The voltage-clamp simulations are of a single isopotential compartment containing 201 Na<sup>+</sup> and 1407 K<sup>+</sup> leak channels. The current-clamp simulations are for a cable of length 1000 µm and radius 1 µm, containing 8050 channels distributed across 237 compartments. (C) The error in the mean and variance of a simulated current, mediated by 50 Na<sup>+</sup> channels clamped at −20 mV for 100 s of simulated time, is plotted as a function of the simulation time step. (D) Power spectra for the currents in (C). Long time steps fail to simulate high frequency current fluctuations and introduce aliasing effects at low frequencies. (E–F) The computation time per simulation time step, required by NEURON (closed symbols) or PSICS (open symbols) for simulations as in (C–D), is plotted as a function of the duration of the simulation time step (E), or as a function of the number of simulated channels when the time step is 20 µs (F). (G) The computation time per simulation time step, required by NEURON or PSICS for simulations as in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000886#pcbi-1000886-g003\" target=\"_blank\">Figure 3F</a>, is plotted as a function of the duration of the simulation time-step. Simulation times are for a cable divided into either 101 compartments (triangles) or 1001 compartments (circles).</p>", "links"=>[], "tags"=>["simulation"], "article_id"=>506028, "categories"=>["Neuroscience", "Medicine", "Biophysics"], "users"=>["Robert C. Cannon", "Cian O'Donnell", "Matthew F. Nolan"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1000886.g004", "stats"=>{"downloads"=>0, "page_views"=>5, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Relationships_between_channel_kinetics_simulation_configuration_accuracy_and_efficiency_/506028", "title"=>"Relationships between channel kinetics, simulation configuration, accuracy and efficiency.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2010-08-12 01:40:28"}
  • {"files"=>["https://ndownloader.figshare.com/files/835565"], "description"=>"<p>(A) Simulated uniform cable with recording and current injection sites. (B) Example membrane potential traces (left) from simulations using leak Na<sup>+</sup> and K<sup>+</sup> channels with the indicated single channel conductances. The membrane potential variance is plotted as a function of the single channel conductance (right). (C) Voltage responses to injection of a current step at one end of the cable. Simulated stochastic (Stoch) and deterministic (Det) responses are plotted along with the analytical solution (Ref). Insets show the voltage as the current responses approach their steady-state values. In each case the traces overlap. As a result the Ref and Det traces are obscured by the Stoch trace. (D) Simulated branched cable structure with recording and current injection sites. (E) Voltage responses to injection of a current step at the base of the tree. Insets show the voltage as the current responses approach their steady-state values. Labels are as in (C). Ref and Det traces are obscured by the Stoch trace. (F) Action potentials generated when Hodgkin-Huxley channels are inserted into the cable in A. The top panel compares results of deterministic simulations using NEURON or PSICS, with stochastic PSICS simulations using a single channel conductance of 0.01 pS. The lower panel shows the output of several stochastic PSICS simulations using a single channel conductance of 20 pS. Membrane potentials in (E) and (F) are labeled as in (C), except that the blue trace is data from a simulation using NEURON.</p>", "links"=>[], "tags"=>["membrane", "polarization", "spike", "propagation", "structures", "containing", "stochastic", "ion"], "article_id"=>505926, "categories"=>["Neuroscience", "Medicine", "Biophysics"], "users"=>["Robert C. Cannon", "Cian O'Donnell", "Matthew F. Nolan"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1000886.g003", "stats"=>{"downloads"=>0, "page_views"=>8, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Simulation_of_membrane_polarization_and_spike_propagation_in_cable_structures_containing_stochastic_ion_channels_/505926", "title"=>"Simulation of membrane polarization and spike propagation in cable structures containing stochastic ion channels.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2010-08-12 01:38:46"}
  • {"files"=>["https://ndownloader.figshare.com/files/836003"], "description"=>"<p>(A) Morphology of the simulated CA1 pyrmidal neurons (described in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000886#pcbi.1000886-Jarsky1\" target=\"_blank\">[44]</a>), illustrating positions of recording electrodes placed on the soma (grey), apical (blue) and basal (red) dendrites. (B) Examples of membrane potential responses of the deterministic (red trace) and stochastic (black traces) versions of the model to distributed synaptic input. The summed synaptic current is shown in yellow. Letters and grey bars indicate times of action potentials highlighted in subsequent panels. (C) Spike rasters (top) for responses of the determinisitc model (red) and for 50 consecutive trials of the stochastic model (black) to the synaptic input pattern used in (B). Plotted below is the probability of somatic spike firing in 10 ms duration bins for the deterministic (red) and stochastic (black) versions of the model. (D–G) Examples of determinisitc responses (top row) and representative stochastic respones (lower two rows), illustrating “extra” somatic action potentials triggered by an “extra” actively propagating dendritic spike (D), “dropped” somatic action potentials resulting from failed dendritic depolarization (E–F), and an “extra” somatic action potental resulting from additional dendritic depolarizing potentials.</p>", "links"=>[], "tags"=>["ion", "channels", "synaptically", "driven", "spike", "ca1", "pyramidal"], "article_id"=>506371, "categories"=>["Neuroscience", "Medicine", "Biophysics"], "users"=>["Robert C. Cannon", "Cian O'Donnell", "Matthew F. Nolan"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1000886.g008", "stats"=>{"downloads"=>3, "page_views"=>9, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Stochastic_ion_channels_modify_synaptically_driven_spike_output_from_a_CA1_pyramidal_neuron_/506371", "title"=>"Stochastic ion channels modify synaptically driven spike output from a CA1 pyramidal neuron.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2010-08-12 01:46:11"}
  • {"files"=>["https://ndownloader.figshare.com/files/835794"], "description"=>"<p>(A–F) Recordings of resting membrane potential at proximal (grey traces) and distal (black traces) locations on a multi-compartmental model of a cylinder of length 320 µm and diameter 16 µm (A–C) or a hypothetical branched dendrite (D–F). The cylinder in (A–C) is electrically ‘equivalent’ to the dendrite in (D–F), which has a branching organization that follows Rall's 3/2 power law. The distal recordings are from location ‘10’ and the proximal recordings are from location ‘0’. In each panel the membrane potential when the leak channels have fast kinetics (upper traces) is compared to the membrane potential when the leak channels have slower kinetics (lower traces). Membrane potential when the models have a membrane time constant on the order of 0.1 ms (B,E) is compared to models with a membrane time constant on the order of 10 ms (C,F). The scale bars apply to all traces. (G–H) The standard deviation of the resting membrane potential of the models in (A–F) is plotted as a function of recording location. Each point is the average of data from 5 simulations of 1s of neuronal activity. The same data were used for statistical analysis (ANOVA). Black and grey symbols correspond to distal and proximal recording locations as in (A–F) above.</p>", "links"=>[], "tags"=>["morphology", "determines", "stochastic", "membrane"], "article_id"=>506164, "categories"=>["Neuroscience", "Medicine", "Biophysics"], "users"=>["Robert C. Cannon", "Cian O'Donnell", "Matthew F. Nolan"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1000886.g005", "stats"=>{"downloads"=>0, "page_views"=>3, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Dendrite_morphology_determines_the_influence_of_stochastic_channel_opening_on_membrane_potential_/506164", "title"=>"Dendrite morphology determines the influence of stochastic channel opening on membrane potential.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2010-08-12 01:42:44"}
  • {"files"=>["https://ndownloader.figshare.com/files/835336"], "description"=>"<p>In PSICS individual ion channels have unique locations that can be viewed along with the compartmentalization chosen for a particular simulation using additional software called ICING. (A) Screen shot of ICING. (B) Detailed view of the compartmentalization of part of the model neuron in (A). (C) Low magnification 3 dimensional detail of dendritic branches from (B). (D) High magnification 3 dimensional detail of dendritic branches in (C) illustrating the location of individual ion channels.</p>", "links"=>[], "tags"=>["visualization", "ion"], "article_id"=>505711, "categories"=>["Neuroscience", "Medicine", "Biophysics"], "users"=>["Robert C. Cannon", "Cian O'Donnell", "Matthew F. Nolan"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1000886.g001", "stats"=>{"downloads"=>0, "page_views"=>2, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Specification_and_visualization_of_ion_channel_location_/505711", "title"=>"Specification and visualization of ion channel location.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2010-08-12 01:35:11"}
  • {"files"=>["https://ndownloader.figshare.com/files/416362", "https://ndownloader.figshare.com/files/416394", "https://ndownloader.figshare.com/files/416423", "https://ndownloader.figshare.com/files/416449", "https://ndownloader.figshare.com/files/416476"], "description"=>"<div><p>Neuronal activity is mediated through changes in the probability of stochastic transitions between open and closed states of ion channels. While differences in morphology define neuronal cell types and may underlie neurological disorders, very little is known about influences of stochastic ion channel gating in neurons with complex morphology. We introduce and validate new computational tools that enable efficient generation and simulation of models containing stochastic ion channels distributed across dendritic and axonal membranes. Comparison of five morphologically distinct neuronal cell types reveals that when all simulated neurons contain identical densities of stochastic ion channels, the amplitude of stochastic membrane potential fluctuations differs between cell types and depends on sub-cellular location. For typical neurons, the amplitude of membrane potential fluctuations depends on channel kinetics as well as open probability. Using a detailed model of a hippocampal CA1 pyramidal neuron, we show that when intrinsic ion channels gate stochastically, the probability of initiation of dendritic or somatic spikes by dendritic synaptic input varies continuously between zero and one, whereas when ion channels gate deterministically, the probability is either zero or one. At physiological firing rates, stochastic gating of dendritic ion channels almost completely accounts for probabilistic somatic and dendritic spikes generated by the fully stochastic model. These results suggest that the consequences of stochastic ion channel gating differ globally between neuronal cell-types and locally between neuronal compartments. Whereas dendritic neurons are often assumed to behave deterministically, our simulations suggest that a direct consequence of stochastic gating of intrinsic ion channels is that spike output may instead be a probabilistic function of patterns of synaptic input to dendrites.</p></div>", "links"=>[], "tags"=>["stochastic", "ion", "gating", "dendritic", "morphology", "dependence", "probabilistic", "synaptic", "activation", "spikes"], "article_id"=>142192, "categories"=>["Neuroscience", "Medicine", "Biophysics"], "users"=>["Robert C. Cannon", "Cian O'Donnell", "Matthew F. Nolan"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1000886.s001", "https://dx.doi.org/10.1371/journal.pcbi.1000886.s002", "https://dx.doi.org/10.1371/journal.pcbi.1000886.s003", "https://dx.doi.org/10.1371/journal.pcbi.1000886.s004", "https://dx.doi.org/10.1371/journal.pcbi.1000886.s005"], "stats"=>{"downloads"=>9, "page_views"=>20, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/Stochastic_Ion_Channel_Gating_in_Dendritic_Neurons_Morphology_Dependence_and_Probabilistic_Synaptic_Activation_of_Dendritic_Spikes/142192", "title"=>"Stochastic Ion Channel Gating in Dendritic Neurons: Morphology Dependence and Probabilistic Synaptic Activation of Dendritic Spikes", "pos_in_sequence"=>0, "defined_type"=>4, "published_date"=>"2010-08-12 00:36:32"}
  • {"files"=>["https://ndownloader.figshare.com/files/835418"], "description"=>"<p>(A) Examples of simulated stochastic (black traces) and deterministic (red traces) currents in a membrane patch containing 50 stochastic Na<sup>+</sup> channels with single channel conductance of 20 pS. The membrane potential is clamped at −20 mV. The expanded trace (right) shows the first 5 ms of the compressed trace (left). (B–C) Cumulative estimate of the mean (B) and variance (C) of stochastic currents measured as in (A) are plotted as a function of time. Examples from 5 separate simulations of duration 100 s are shown. Values between 100 and 1000 s are from concatenation of separate 100 s simulations. (D) Examples of 10 simulated current responses (black traces, lower plot), of the membrane patch simulated in (A–C), to a step change in membrane potential from −80 mV to +30 mV (upper plot). The mean (red trace) and variance (blue trace) are calculated from 1000 stochastic current responses. (E–F) Plot of membrane the membrane current variance as a function of the mean membrane current for the rapid activation phase (E) and slower inactivation phase (F) of the 1000 simulated current responses used to obtain the data for (D). The time window for the activation phase is 0–0.3 ms after the onset of the voltage step, whereas the time window for the deactivation phase is 0.3–10 ms after the onset of the voltage step. The number of single channels (N) and the single channel current (I) are estimated from the fit to the simulation data. The red parabola is the variance-mean relationship predicted from I and N of the model and the blue parabola is the fit to the simulation data. (G–H) Estimates for the number of channels (G) and single channel current (H), obtained by variance mean analysis of the inactivation phase of the current responses analyzed as in (D), plotted as a function of the number of simulated responses used for the analysis. Each dot corresponds to a set of data used for analysis. The continuous lines show convergence of the estimates as additional simulations are analyzed up to a maximum of 10<sup>4</sup> simulated responses. (I) The RMS error, calculated from the difference between the variance mean fit and the expected variance mean relationship, is plotted as a function of the number of simulated responses. The solid lines indicate progressive convergence up to a maximum of 10<sup>4</sup> simulated responses. For all examples the simulation time step was 10 µS.</p>", "links"=>[], "tags"=>["stochastic", "ion"], "article_id"=>505789, "categories"=>["Neuroscience", "Medicine", "Biophysics"], "users"=>["Robert C. Cannon", "Cian O'Donnell", "Matthew F. Nolan"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1000886.g002", "stats"=>{"downloads"=>1, "page_views"=>8, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Accurate_stochastic_ion_channel_simulation_/505789", "title"=>"Accurate stochastic ion channel simulation.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2010-08-12 01:36:29"}
  • {"files"=>["https://ndownloader.figshare.com/files/835853"], "description"=>"<p>(A) Examples of membrane potential (right) and corresponding morphology (left) from a simulated dentate gyrus granule cell (top), dopaminergic nigral cell (middle) and cortical layer V pyramidal cell (bottom). All models contained identical ion channel distributions. (B) Average membrane potential standard deviation for model neurons of each morphological type plotted as a function of increasing distance along the dendrite from the soma. The membrane potential standard deviation at a particular location corresponds to the right most end of the bar indicated by the corresponding color. The standard deviation increases with distance from the soma.</p>", "links"=>[], "tags"=>["stochastic", "ion", "gating", "morphologically", "neuronal"], "article_id"=>506218, "categories"=>["Neuroscience", "Medicine", "Biophysics"], "users"=>["Robert C. Cannon", "Cian O'Donnell", "Matthew F. Nolan"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1000886.g006", "stats"=>{"downloads"=>0, "page_views"=>2, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Consequences_of_stochastic_ion_channel_gating_differ_between_morphologically_distinct_neuronal_cell_types_/506218", "title"=>"Consequences of stochastic ion channel gating differ between morphologically distinct neuronal cell types.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2010-08-12 01:43:38"}
  • {"files"=>["https://ndownloader.figshare.com/files/836180"], "description"=>"<p>(A–B) Rasters for first 20 trials of responses of the CA1 pyramidal neuron simulated as in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000886#pcbi-1000886-g008\" target=\"_blank\">Figure 8</a>, but with stochastic axonal and deterministic dendritic ion channels (A) or stochastic denritic and deterministic axonal ion channels (B). (C) as for (A–B), but only channels mediating <i>I</i><sub>h</sub> are stochastic. Shown are rasters (left), examples of membrane potential responses of the fully deterministic model (red) and first six sweeps recorded from the stochastic model (black), and examples of membrane potential waveforms corresponding to an “extra” action potential triggered by an additional dendritic depolarization. (D) Number of “dropped” and “extra” axonal spikes (top) and dendritic spikes (bottom) during 1s of simulated time for each experimental condition tested. Because of their all or nothing nature, large dendritic depolariations are classified as spikes. ANOVA indicated a significant (p<<1e-9) effect of model configuration on “dropped” and “extra” axonal and dendritic spikes. Key post-hoc comparisons are referred to in the main text. (E) Jitter in the timing of axonal (top) and dendritic (bottom) action potentials for each experimental condition.</p>", "links"=>[], "tags"=>["ion", "types"], "article_id"=>506552, "categories"=>["Neuroscience", "Medicine", "Biophysics"], "users"=>["Robert C. Cannon", "Cian O'Donnell", "Matthew F. Nolan"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1000886.g009", "stats"=>{"downloads"=>1, "page_views"=>8, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Differential_impact_of_distinct_ion_channel_types_and_locations_/506552", "title"=>"Differential impact of distinct ion channel types and locations.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2010-08-12 01:49:12"}
  • {"files"=>["https://ndownloader.figshare.com/files/835922"], "description"=>"<p>(A–B) Simulated membrane potential of a model layer V pyramidal neuron (A) and a dentate gyrus granule cell (B) containing either a deterministic leak conductance, fast gating stochastic leak channels or slow gating stochastic leak channels. (C–D) Mean variance of membrane potential fluctuations, recorded from simulated layer V pyramidal neurons (C) and simulated dentate gyrus granule cells (D), plotted as a function of distance from the cell body.</p>", "links"=>[], "tags"=>["kinetics", "stochastic"], "article_id"=>506294, "categories"=>["Neuroscience", "Medicine", "Biophysics"], "users"=>["Robert C. Cannon", "Cian O'Donnell", "Matthew F. Nolan"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1000886.g007", "stats"=>{"downloads"=>1, "page_views"=>8, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Channel_kinetics_determine_the_functional_impact_of_stochastic_gating_/506294", "title"=>"Channel kinetics determine the functional impact of stochastic gating.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2010-08-12 01:44:54"}

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