The Influence of Synaptic Weight Distribution on Neuronal Population Dynamics
Publication Date
October 24, 2013
Journal
PLOS Computational Biology
Authors
Ramakrishnan Iyer, Vilas Menon, Michael Buice, Christof Koch, et al
Volume
9
Issue
10
Pages
e1003248
DOI
https://dx.plos.org/10.1371/journal.pcbi.1003248
Publisher URL
http://journals.plos.org/ploscompbiol/article?id=10.1371%2Fjournal.pcbi.1003248
PubMed
http://www.ncbi.nlm.nih.gov/pubmed/24204219
PubMed Central
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3808453
Europe PMC
http://europepmc.org/abstract/MED/24204219
Web of Science
000330355300011
Scopus
84887290826
Mendeley
http://www.mendeley.com/research/influence-synaptic-weight-distribution-neuronal-population-dynamics
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Mendeley | Further Information

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Scopus | Further Information

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Figshare

  • {"files"=>["https://ndownloader.figshare.com/files/1258095"], "description"=>"<p>Panels (a)–(e) show results for excitatory, low-frequency, large amplitude current-based synapses of constant weight. Topmost panels show time evolution of the probability distribution of membrane potentials in the neuronal population obtained with Poisson input for with synaptic weight (maximum EPSP) mV and input rate Hz from, a) simulations of 10,000 leaky integrate-and-fire (LIF) neurons (see <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003248#s4\" target=\"_blank\">Methods</a>: Population Simulations for parameters used in simulations) , b) the numerical solution to the DiPDE <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003248#pcbi.1003248.e029\" target=\"_blank\">equation (3)</a>, and c) the Fokker-Planck (FP) equation. Middle panels: d) Output firing rates as a function of time. e) The distribution of the sub-threshold steady-state membrane potential after 200 ms. These discrete synaptic jumps are evident in the voltage distributions just after synaptic input is switched on. Bottom panels: f) Expected 95% intervals for spike counts obtained from DiPDE for simulation data shown in panels (a)–(e). g) Output firing rates obtained from <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003248#pcbi.1003248.e345\" target=\"_blank\">equation (21)</a> for leaky integrate-and-fire (LIF) neurons and equivalent numerical simulations (see <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003248#s4\" target=\"_blank\">Methods</a>: Population Simulations for parameters used in simulations), for excitatory conductance-based synapses. Poisson input for with maximum depolarization achieved by a neuron starting from rest mV and input rate Hz. h) Output firing rates obtained from <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003248#pcbi.1003248.e345\" target=\"_blank\">equation (21)</a> for exponential integrate-and-fire (EIF) neurons and equivalent numerical simulations (see <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003248#s4\" target=\"_blank\">Methods</a>: Population Simulations for parameters used in simulations), for excitatory conductance-based synapses without adaptation. Poisson input for with maximum depolarization achieved by a neuron starting from rest mV and input rate Hz.</p>", "links"=>[], "tags"=>["simulations"], "article_id"=>832407, "categories"=>["Biological Sciences"], "users"=>["Ramakrishnan Iyer", "Vilas Menon", "Michael Buice", "Christof Koch", "Stefan Mihalas"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1003248.g001"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Comparisons_between_simulations_and_DiPDE_/832407", "title"=>"Comparisons between simulations and DiPDE.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-10-24 03:59:57"}
  • {"files"=>["https://ndownloader.figshare.com/files/1258096"], "description"=>"<p>Top panels: a) Two self-similar Gaussian synaptic weight distributions. b) The distribution of the sub-threshold, steady-state membrane potential when the two Gaussian synaptic inputs are activated with either a low (solid curves) or a high input firing rate (dashed curves) adjusted such that the mean input currents are equal. The low-amplitude distribution always has twice the input rate of the high amplitude one. In the absence of a threshold, these synaptic input would depolarize by 12 mV and 30 mV respectively. As we use a threshold of 20 mV, these inputs lead to distinct results, with the first being driven primarily by variations in input and the second by the mean input. c) Output firing rates as a function of time. In b) and c), green curves correspond to the Gaussian distribution with mean (3 mV) and standard deviation (SD) of (1 mV) and blue curves correspond to the Gaussian distribution with mean (6 mV) and SD (2 mV). For equal currents, stronger synapses produce a quicker response and a higher equilibrium firing rate. Bottom panels: d) Semi-log plot of -function (Delta), Gaussian (Gauss), exponential (Exp), lognormal (LogN), bi-modal (BiMod) and power-law (PL) synaptic weight distributions, matched for mean weight (1 mV) (see <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003248#s4\" target=\"_blank\">Methods</a>: Matched distributions for the exact forms used for these distributions). e) Steady-state, sub-threshold voltage distributions and f) output firing rates for an input rate of 1,000 Hz. Heavier-tailed distributions produce quicker transients.</p>", "links"=>[], "tags"=>["instantaneous", "excitatory", "synaptic", "weights"], "article_id"=>832408, "categories"=>["Biological Sciences"], "users"=>["Ramakrishnan Iyer", "Vilas Menon", "Michael Buice", "Christof Koch", "Stefan Mihalas"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1003248.g002"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Distributions_of_instantaneous_excitatory_synaptic_weights_with_same_mean_input_current_/832408", "title"=>"Distributions of instantaneous excitatory synaptic weights with same mean input current.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-10-24 03:59:57"}
  • {"files"=>["https://ndownloader.figshare.com/files/1258098"], "description"=>"<p>Top row: Protocol used to investigate the response of the neuronal population with a given excitatory synaptic weight distribution to a sudden perturbation in its synaptic input. a) Input rate as a function of time. For the first 500 ms, the cumulative synaptic input rate is varied between 500 and 1,000 Hz, expressed as a fraction of the 1,000 Hz base input rate (see <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003248#s4\" target=\"_blank\">Methods</a>: Input-Output curves). The population evolves according to <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003248#pcbi.1003248.e029\" target=\"_blank\">equation (3)</a> for a -function distribution of synaptic weights. At 500 ms, the input firing rate instantaneously returns to the base rate of 1000 Hz. b) Output firing rate as a function of time for . The peak output rate attained provides a measure of how strongly the system responds to sudden changes in its input rate. c) Zooming in onto the transient response in (b). The smaller the difference in input rate, the quicker the response of the network, with less overshoot. Bottom row: Quantifying response to sudden changes in input rate. d) Peak output firing rate for different fractions of the base input rate as a function of base input rate for . e) Difference in the peak output firing rate normalized by the difference between input rates, when the input is instantaneously changed from 1/2 the base rate to the full base rate. Normalized differences in output rates for different synaptic weight distributions are plotted as a function of the full input base rate. Heavier-tailed distributions result in lesser overshoot. f) Semi-log plot of the steady state output firing rate as a function of the input firing rate, for different synaptic distributions with the inclusion of short-term synaptic depression. Onset of saturation for very high effective synaptic input rates is evident. Note the greater response of the heavier-tailed power-law and bimodal distributions for lower input firing rates, leading to higher dynamical range.</p>", "links"=>[], "tags"=>[], "article_id"=>832410, "categories"=>["Biological Sciences"], "users"=>["Ramakrishnan Iyer", "Vilas Menon", "Michael Buice", "Christof Koch", "Stefan Mihalas"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1003248.g003"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Input_output_characteristics_/832410", "title"=>"Input-output characteristics.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-10-24 03:59:57"}
  • {"files"=>["https://ndownloader.figshare.com/files/1258100"], "description"=>"<p>The graphs show the relative excitability as a function of the additional synaptic input per neuron in the population on average (so that is the mean number of inputs per neuron on average in a time ), a) without and b) with synaptic depression. The black square indicates the relative excitability for a population with a -function distribution of synaptic weights with additional synaptic inputs per neuron on average. The corresponding relative excitability with a bimodal distribution is . Heavy-tailed distributions lead to smaller changes in excitability due to fluctuations in synaptic input.</p>", "links"=>[], "tags"=>["fluctuations", "synaptic", "excitatory", "distributions", "equilibrium"], "article_id"=>832412, "categories"=>["Biological Sciences"], "users"=>["Ramakrishnan Iyer", "Vilas Menon", "Michael Buice", "Christof Koch", "Stefan Mihalas"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1003248.g004"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Effects_of_external_fluctuations_in_synaptic_input_due_to_different_excitatory_synaptic_weight_distributions_starting_from_the_equilibrium_of_Figure_2_obtained_with_an_input_rate_Hz_/832412", "title"=>"Effects of external fluctuations in synaptic input due to different excitatory synaptic weight distributions starting from the equilibrium of Figure (2) obtained with an input rate Hz.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-10-24 03:59:57"}
  • {"files"=>["https://ndownloader.figshare.com/files/1258101"], "description"=>"<p>Table shows the sum of squared residuals for best fit exponentials to (the times taken to reach of the equilibrium firing rate), for the first few moments of 1222 randomly generated synaptic weight distributions between 0 and . For both moments and tail weight numbers, the entries in bold in each column correspond to the lowest value of . Tail weight numbers provide a better fit to transient times than moments.</p>", "links"=>[], "tags"=>["transient", "times", "moments"], "article_id"=>832413, "categories"=>["Biological Sciences"], "users"=>["Ramakrishnan Iyer", "Vilas Menon", "Michael Buice", "Christof Koch", "Stefan Mihalas"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1003248.t002"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Explaining_transient_times_with_moments_and_tail_weight_numbers_/832413", "title"=>"Explaining transient times with moments and tail weight numbers.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2013-10-24 03:59:57"}
  • {"files"=>["https://ndownloader.figshare.com/files/1258102"], "description"=>"<p>Table shows the equilibrium output firing rates , transient times to 10% of and 95% confidence intervals for for matched synaptic weight distributions. 95% confidence intervals are calculated for neurons with bin-size  = 2 ms.</p>", "links"=>[], "tags"=>["rates", "transient"], "article_id"=>832414, "categories"=>["Biological Sciences"], "users"=>["Ramakrishnan Iyer", "Vilas Menon", "Michael Buice", "Christof Koch", "Stefan Mihalas"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1003248.t001"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Equilibrium_rates_and_transient_times_/832414", "title"=>"Equilibrium rates and transient times.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2013-10-24 03:59:57"}
  • {"files"=>["https://ndownloader.figshare.com/files/1258107", "https://ndownloader.figshare.com/files/1258108", "https://ndownloader.figshare.com/files/1258109", "https://ndownloader.figshare.com/files/1258110", "https://ndownloader.figshare.com/files/1258111", "https://ndownloader.figshare.com/files/1258112", "https://ndownloader.figshare.com/files/1258113", "https://ndownloader.figshare.com/files/1258114", "https://ndownloader.figshare.com/files/1258115", "https://ndownloader.figshare.com/files/1258116", "https://ndownloader.figshare.com/files/1258117", "https://ndownloader.figshare.com/files/1258118", "https://ndownloader.figshare.com/files/1258119", "https://ndownloader.figshare.com/files/1258120", "https://ndownloader.figshare.com/files/1258121", "https://ndownloader.figshare.com/files/1258122", "https://ndownloader.figshare.com/files/1258123", "https://ndownloader.figshare.com/files/1258124", "https://ndownloader.figshare.com/files/1258125", "https://ndownloader.figshare.com/files/1258126", "https://ndownloader.figshare.com/files/1258127", "https://ndownloader.figshare.com/files/1258128", "https://ndownloader.figshare.com/files/1258129"], "description"=>"<div><p>The manner in which different distributions of synaptic weights onto cortical neurons shape their spiking activity remains open. To characterize a homogeneous neuronal population, we use the master equation for generalized leaky integrate-and-fire neurons with shot-noise synapses. We develop fast semi-analytic numerical methods to solve this equation for either current or conductance synapses, with and without synaptic depression. We show that its solutions match simulations of equivalent neuronal networks better than those of the Fokker-Planck equation and we compute bounds on the network response to non-instantaneous synapses. We apply these methods to study different synaptic weight distributions in feed-forward networks. We characterize the synaptic amplitude distributions using a set of measures, called tail weight numbers, designed to quantify the preponderance of very strong synapses. Even if synaptic amplitude distributions are equated for both the total current and average synaptic weight, distributions with sparse but strong synapses produce higher responses for small inputs, leading to a larger operating range. Furthermore, despite their small number, such synapses enable the network to respond faster and with more stability in the face of external fluctuations.</p></div>", "links"=>[], "tags"=>["synaptic", "neuronal"], "article_id"=>832419, "categories"=>["Biological Sciences"], "users"=>["Ramakrishnan Iyer", "Vilas Menon", "Michael Buice", "Christof Koch", "Stefan Mihalas"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1003248.s001", "https://dx.doi.org/10.1371/journal.pcbi.1003248.s002", "https://dx.doi.org/10.1371/journal.pcbi.1003248.s003", "https://dx.doi.org/10.1371/journal.pcbi.1003248.s004", "https://dx.doi.org/10.1371/journal.pcbi.1003248.s005", "https://dx.doi.org/10.1371/journal.pcbi.1003248.s006", "https://dx.doi.org/10.1371/journal.pcbi.1003248.s007", "https://dx.doi.org/10.1371/journal.pcbi.1003248.s008", "https://dx.doi.org/10.1371/journal.pcbi.1003248.s009", "https://dx.doi.org/10.1371/journal.pcbi.1003248.s010", "https://dx.doi.org/10.1371/journal.pcbi.1003248.s011", "https://dx.doi.org/10.1371/journal.pcbi.1003248.s012", "https://dx.doi.org/10.1371/journal.pcbi.1003248.s013", "https://dx.doi.org/10.1371/journal.pcbi.1003248.s014", "https://dx.doi.org/10.1371/journal.pcbi.1003248.s015", "https://dx.doi.org/10.1371/journal.pcbi.1003248.s016", "https://dx.doi.org/10.1371/journal.pcbi.1003248.s017", "https://dx.doi.org/10.1371/journal.pcbi.1003248.s018", "https://dx.doi.org/10.1371/journal.pcbi.1003248.s019", "https://dx.doi.org/10.1371/journal.pcbi.1003248.s020", "https://dx.doi.org/10.1371/journal.pcbi.1003248.s021", "https://dx.doi.org/10.1371/journal.pcbi.1003248.s022", "https://dx.doi.org/10.1371/journal.pcbi.1003248.s023"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_The_Influence_of_Synaptic_Weight_Distribution_on_Neuronal_Population_Dynamics_/832419", "title"=>"The Influence of Synaptic Weight Distribution on Neuronal Population Dynamics", "pos_in_sequence"=>0, "defined_type"=>4, "published_date"=>"2013-10-24 03:59:57"}

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Relative Metric

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