Cable and Compartmental Models of Dendritic Trees
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Significance Historically, neurons were thought to collect synaptic currents from across their dendritic trees and passively conduct them to the soma where action potentials (APs) are generated. More recent studies have shown that dendrites can generate local spikes and thus may function as independent computational subunits. It remains unknown, however, how dendrites can maintain the integrity and separateness of their local computations, which depend on voltage, despite the repeated synchronization of dendritic potentials by back-propagating somatic APs. This modeling study identifies three biophysical specializations that allow dendrites to remain functionally independent in a firing neuron, one of which is the somatic spiking mechanism itself. Our results suggest that a major class of neurons has been optimized for subunitized computation.
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Event Abstract Back to Event Modelling the extracellular potentials from single neurons and cortical populations Klas H. Pettersen1* and Gaute T. Einevoll1 1 Norwegian University of Life Sciences, Norway Methods for extracellular recordings of activity from single neurons and neural populations are rapidly improving, and new computational tools for the quantitative interpretation of such data are needed. Here, both features seen in spike recordings from single cells and linear electrode recordings from neural populations are studied. The transmembrane currents act as sources for the potential, weighted according to their sign and distance from the recording electrode. In the present model studies, the neuronal transmembrane currents are calculated by using compartmental modelling, and these currents are then used as sources in electrostatic forward modelling of the field potential. In the first study the influence of neural morphology and passive electrical parameters on the width and amplitude of extracellular spikes (action potentials) is investigated by combined analytical and numerical investigations of idealized and anatomically reconstructed pyramidal and stellate neuron models. The main results are: (i) All models yield a lowpass filtering effect, that is, a spike-width increase with increasing distance from soma. (ii) A neuron's extracellular spike amplitude is seen to be approximately proportional to the sum of the dendritic cross-sectional areas of all dendritic branches connected to the soma. Thus, neurons with many, thick dendrites connected to soma will produce large amplitude spikes, and therefore have the largest radius of visibility. (iii) The spike shape and amplitude are found to depend on the membrane capacitance and axial resistivity, but not on the membrane resistivity. (iv) The spike-amplitude decay with distance r is found to depend on dendritic morphology, and is decaying as 1/rn with 12 far away [1]. The second model study investigates the validity of methods used to interpret linear (laminar) multielectrode recordings. In computer experiments extracellular potentials from a synaptically activated population of about 1000 pyramidal neurons are calculated. The somas of the pyramidal neurons are located in a 0.4 mm high and wide columnar cylinder, mimicking a stimulus-evoked layer-5 population in a neocortical column. Current-source density (CSD) analysis of the low-frequency part (<500Hz) of the calculated potentials (local field potentials, LFP) based on the 'inverse' CSD method [2] is, in contrast to the 'standard' CSD method, seen to give excellent estimates of the true underlying CSD. The high-frequency part (>750Hz) of the potentials (multi-unit activity, MUA) is found to scale approximately as the population firing rate to the power 3/4 and to give excellent estimates of the underlying population firing rate for trial-averaged data. The MUA signal is found to decay much sharper outside the columnar populations than the LFP [3]. References 1. KH Pettersen and GT Einevoll, Biophys J, 94, 784-802 (2008). 2. ] KH Pettersen, A Devor, I Ulbert, AM Dale, GT Einevoll, J Neurosci Meth, 154, 116-33 (2006). 3. KH Pettersen, E Hagen and GT Einevoll, J Comput Neurosci, 24, 291-313 (2008). Conference: Neuroinformatics 2008, Stockholm, Sweden, 7 Sep - 9 Sep, 2008. Presentation Type: Poster Presentation Topic: Computational Neuroscience Citation: Pettersen KH and Einevoll GT (2008). Modelling the extracellular potentials from single neurons and cortical populations. Front. Neuroinform. Conference Abstract: Neuroinformatics 2008. doi: 10.3389/conf.neuro.11.2008.01.036 Copyright: The abstracts in this collection have not been subject to any Frontiers peer review or checks, and are not endorsed by Frontiers. They are made available through the Frontiers publishing platform as a service to conference organizers and presenters. The copyright in the individual abstracts is owned by the author of each abstract or his/her employer unless otherwise stated. Each abstract, as well as the collection of abstracts, are published under a Creative Commons CC-BY 4.0 (attribution) licence (https://creativecommons.org/licenses/by/4.0/) and may thus be reproduced, translated, adapted and be the subject of derivative works provided the authors and Frontiers are attributed. For Frontiers’ terms and conditions please see https://www.frontiersin.org/legal/terms-and-conditions. Received: 28 Jul 2008; Published Online: 28 Jul 2008. * Correspondence: Klas H Pettersen, Norwegian University of Life Sciences, Aas, Norway, klas.pettersen@gmail.com Login Required This action requires you to be registered with Frontiers and logged in. To register or login click here. Abstract Info Abstract The Authors in Frontiers Klas H Pettersen Gaute T Einevoll Google Klas H Pettersen Gaute T Einevoll Google Scholar Klas H Pettersen Gaute T Einevoll PubMed Klas H Pettersen Gaute T Einevoll Related Article in Frontiers Google Scholar PubMed Abstract Close Back to top Javascript is disabled. Please enable Javascript in your browser settings in order to see all the content on this page.
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In hippocampal CA1 pyramidal neurons, action potentials are typically initiated in the axon and backpropagate into the dendrites, shaping the integration of synaptic activity and influencing the induction of synaptic plasticity. Despite previous reports describing action-potential propagation in the proximal apical dendrites, the extent to which action potentials invade the distal dendrites of CA1 pyramidal neurons remains controversial. Using paired somatic and dendritic whole cell recordings, we find that in the dendrites proximal to 280 μm from the soma, single backpropagating action potentials exhibit <50% attenuation from their amplitude in the soma. However, in dendritic recordings distal to 300 μm from the soma, action potentials in most cells backpropagated either strongly (26–42% attenuation; n = 9/20) or weakly (71–87% attenuation; n = 10/20) with only one cell exhibiting an intermediate value (45% attenuation). In experiments combining dual somatic and dendritic whole cell recordings with calcium imaging, the amount of calcium influx triggered by backpropagating action potentials was correlated with the extent of action-potential invasion of the distal dendrites. Quantitative morphometric analyses revealed that the dichotomy in action-potential backpropagation occurred in the presence of only subtle differences in either the diameter of the primary apical dendrite or branching pattern. In addition, action-potential backpropagation was not dependent on a number of electrophysiological parameters (input resistance, resting potential, voltage sensitivity of dendritic spike amplitude). There was, however, a striking correlation of the shape of the action potential at the soma with its amplitude in the dendrite; larger, faster-rising, and narrower somatic action potentials exhibited more attenuation in the distal dendrites (300–410 μm from the soma). Simple compartmental models of CA1 pyramidal neurons revealed that a dichotomy in action-potential backpropagation could be generated in response to subtle manipulations of the distribution of either sodium or potassium channels in the dendrites. Backpropagation efficacy could also be influenced by local alterations in dendritic side branches, but these effects were highly sensitive to model parameters. Based on these findings, we hypothesize that the observed dichotomy in dendritic action-potential amplitude is conferred primarily by differences in the distribution, density, or modulatory state of voltage-gated channels along the somatodendritic axis.
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Action potentials generated near the soma propagate not only into the axonal nerve connecting to the adjacent neurons but also into the dendrites interacting with a diversity of synaptic inputs as well as voltage gated ion channels. Measuring voltage attenuation factors between the soma and all single points of the dendrites in the anatomically reconstructed primary neurons with the same cable properties, we report the signal propagation data showing how the alternating current (AC) signal such as action potentials back-propagates over the dendrites among different types of primary neurons. Fitting equations and their parameter values for the data are also presented to quantitatively capture the spatial profile of AC signal propagation from the soma to the dendrites in primary neurons. Our data is supplemental to our original study for the dependency of dendritic signal propagation and excitability, and their relationship on the cell type-specific structure in primary neurons (DOI: 10.1016/j.neulet.2015.10.017 [1]).
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Event Abstract Back to Event Evaluating dendritic impact using complex and reduced models of medium spiny neurons Robert Lindroos1, Jan Pieczkowski1, 2*, Kai Du3 and Jeanette Hellgren Kotaleski1, 3 1 KTH - Royal Institute of Technology, School of Computer Science and Communication, Sweden 2 University of Edinburgh, School of Informatics, United Kingdom 3 Karolinska Institute, Department of Neuroscience, Sweden Current advances in both experimental and theoretical fields have found that synaptic signals are not simply relayed passively to the soma or the axon; instead, dendrites, the main structure to receive synaptic inputs, can act as "computing units", performing arithmetic operations by themselves. However, to model neurons with active dendrites will lead to dramatically increased computing costs. In contrast, simple point-like artificial neuron models do not capture the full dynamics of individual neurons as they do not take into account dendritic computation. This lost accuracy, on the other hand, might play an important role in the overall dynamics of neural networks. To bridge this gap between the point-neuron models and very complex neuron models and to better understand how dendritic computation might affect signal integration at more macroscopic levels, we recently developed a biophysically detailed model of medium spiny neuron (MSN) in dorsal striatum with 634 compartments. An early version of this model has been confirmed to reproduce experimental findings [Evans et al. (2012)]. We derived a series of simplified versions of the model with a reduced number of compartments but conserved 3-dimensional morphology. With the complex model and its reduced offsprings, we explore the importance of dendritic morphology and synaptic topology on the input-output relationship of MSNs. For this purpose, we adopt a novel method by [Chen et al. (2011)], which combines metric space analysis and multidimensional scaling analysis, to quantify the impact of the dendrites. We also apply this method, as well as select techniques from information theory to verify the reduced models' behaviour. References 1. Evans, R.C.; Morera-Herreras, T.; Cui, Y.; Du, K.; Sheehan, T.; Hellgren Kotaleski, J.; Venance, L.; Blackwell, K.T. (2012). The effects of NMDA subunit composition on calcium influx and spike timing-dependent plasticity in striatal medium spiny neurons. PLoS Computational Biology 8(4) 2. Chen, J.-Y. (2010). A Simulation Study Investigating the Impact of Dendritic Morphology and Synaptic Topology on Neuronal Firing Patterns. Neural Computation 22 Keywords: Dendrite, Information Theory, compartmental models, Medium Spiny Neuron, spike train analysis, metric space, multidimensional scaling Conference: Neuroinformatics 2013, Stockholm, Sweden, 27 Aug - 29 Aug, 2013. Presentation Type: Poster Topic: Computational neuroscience Citation: Lindroos R, Pieczkowski J, Du K and Hellgren Kotaleski J (2013). Evaluating dendritic impact using complex and reduced models of medium spiny neurons. Front. Neuroinform. Conference Abstract: Neuroinformatics 2013. doi: 10.3389/conf.fninf.2013.09.00118 Copyright: The abstracts in this collection have not been subject to any Frontiers peer review or checks, and are not endorsed by Frontiers. They are made available through the Frontiers publishing platform as a service to conference organizers and presenters. The copyright in the individual abstracts is owned by the author of each abstract or his/her employer unless otherwise stated. Each abstract, as well as the collection of abstracts, are published under a Creative Commons CC-BY 4.0 (attribution) licence (https://creativecommons.org/licenses/by/4.0/) and may thus be reproduced, translated, adapted and be the subject of derivative works provided the authors and Frontiers are attributed. For Frontiers’ terms and conditions please see https://www.frontiersin.org/legal/terms-and-conditions. Received: 08 Apr 2013; Published Online: 11 Jul 2013. * Correspondence: Mr. Jan Pieczkowski, KTH - Royal Institute of Technology, School of Computer Science and Communication, Stockholm, Sweden, janpi@kth.se Login Required This action requires you to be registered with Frontiers and logged in. To register or login click here. Abstract Info Abstract The Authors in Frontiers Robert Lindroos Jan Pieczkowski Kai Du Jeanette Hellgren Kotaleski Google Robert Lindroos Jan Pieczkowski Kai Du Jeanette Hellgren Kotaleski Google Scholar Robert Lindroos Jan Pieczkowski Kai Du Jeanette Hellgren Kotaleski PubMed Robert Lindroos Jan Pieczkowski Kai Du Jeanette Hellgren Kotaleski Related Article in Frontiers Google Scholar PubMed Abstract Close Back to top Javascript is disabled. Please enable Javascript in your browser settings in order to see all the content on this page.
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