The Role of Extracellular Conductivity Profiles in Compartmental Models for Neurons: Particulars for Layer 5 Pyramidal Cells

With the rapid increase in the number of technologies aimed at observing electric activity inside the brain, scientists have felt the urge to create proper links between intracellular- and extracellular-based experimental approaches. Biophysical models at both physical scales have been formalized under assumptions that impede the creation of such links. In this work, we address this issue by proposing a multicompartment model that allows the introduction of complex extracellular and intracellular resistivity profiles. This model accounts for the geometrical and electrotonic properties of any type of neuron through the combination of four devices: the integrator, the propagator, the 3D connector, and the collector. In particular, we applied this framework to model the tufted pyramidal cells of layer 5 (PCL5) in the neocortex. Our model was able to reproduce the decay and delay curves of backpropagating action potentials (APs) in this type of cell with better agreement with experimental data. We used the voltage drops of the extracellular resistances at each compartment to approximate the local field potentials generated by a PCL5 located in close proximity to linear microelectrode arrays. Based on the voltage drops produced by backpropagating APs, we were able to estimate the current multipolar moments generated by a PCL5. By adding external current sources in parallel to the extracellular resistances, we were able to create a sensitivity profile of PCL5 to electric current injections from nearby microelectrodes. In our model for PCL5, the kinetics and spatial profile of each ionic current were determined based on a literature survey, and the geometrical properties of these cells were evaluated experimentally. We concluded that the inclusion of the extracellular space in the compartmental models of neurons as an extra electrotonic medium is crucial for the accurate simulation of both the propagation of the electric potentials along the neuronal dendrites and the neuronal reactivity to an electrical stimulation using external microelectrodes.

[1]  T. Sejnowski,et al.  Reduced compartmental models of neocortical pyramidal cells , 1993, Journal of Neuroscience Methods.

[2]  Benjamin H. Brinkmann,et al.  Large-scale electrophysiology: Acquisition, compression, encryption, and storage of big data , 2009, Journal of Neuroscience Methods.

[3]  C. Koch,et al.  On the origin of the extracellular action potential waveform: A modeling study. , 2006, Journal of neurophysiology.

[4]  A. Hodgkin,et al.  A quantitative description of membrane current and its application to conduction and excitation in nerve , 1990 .

[5]  Yu-Ming Chang,et al.  Diversity of Layer 5 Pyramidal Cells in the Prefrontal Cortex of the Rhesus Monkey : In Vitro Slice Studies , 2007 .

[6]  C Gabriel,et al.  The dielectric properties of biological tissues: I. Literature survey. , 1996, Physics in medicine and biology.

[7]  H. Swadlow,et al.  Dendritic Backpropagation and the State of the Awake Neocortex , 2007, The Journal of Neuroscience.

[8]  J. Csicsvari,et al.  Intracellular features predicted by extracellular recordings in the hippocampus in vivo. , 2000, Journal of neurophysiology.

[9]  W. Rall.  Electrophysiology of a dendritic neuron model. , 1962, Biophysical journal.

[10]  Klas H. Pettersen,et al.  Current-source density estimation based on inversion of electrostatic forward solution: Effects of finite extent of neuronal activity and conductivity discontinuities , 2006, Journal of Neuroscience Methods.

[11]  T. Sejnowski,et al.  A model of spike initiation in neocortical pyramidal neurons , 1995, Neuron.

[12]  Wilfrid Rall,et al.  Theoretical significance of dendritic trees for neuronal input-output relations , 1964 .

[13]  Horacio G Rotstein,et al.  Orthogonal arrangement of rhythm-generating microcircuits in the hippocampus. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[14]  Douglas B. Ehlenberger,et al.  Automated reconstruction of three-dimensional neuronal morphology from laser scanning microscopy images. , 2003, Methods.

[15]  R. W. Lau,et al.  The dielectric properties of biological tissues: II. Measurements in the frequency range 10 Hz to 20 GHz. , 1996, Physics in medicine and biology.

[16]  J. Pearce.  Emil Heinrich Du Bois-Reymond (1818–96) , 2001, Journal of neurology, neurosurgery, and psychiatry.

[17]  D. Pinault,et al.  The Juxtacellular Recording-Labeling Technique , 2011 .

[18]  A. Lehmenkühler,et al.  Extracellular space parameters in the rat neocortex and subcortical white matter during postnatal development determined by diffusion analysis , 1993, Neuroscience.

[19]  G. Stuart,et al.  Action Potential Initiation and Propagation in Layer 5 Pyramidal Neurons of the Rat Prefrontal Cortex: Absence of Dopamine Modulation , 2003, The Journal of Neuroscience.

[20]  M. Hawken,et al.  Loose-patch–juxtacellular recording in vivo—A method for functional characterization and labeling of neurons in macaque V1 , 2006, Journal of Neuroscience Methods.

[21]  A. Evans,et al.  Pitfalls in the dipolar model for the neocortical EEG sources. , 2012, Journal of neurophysiology.

[22]  E. Neher.  Two Fast Transient Current Components during Voltage Clamp on Snail Neurons , 1971, The Journal of general physiology.

[23]  Gaute T. Einevoll,et al.  Intrinsic dendritic filtering gives low-pass power spectra of local field potentials , 2010, Journal of Computational Neuroscience.

[24]  R Kawashima,et al.  Nonlinear local electrovascular coupling. II: From data to neuronal masses , 2007, Human brain mapping.

[25]  C. Gabriel,et al.  Electrical conductivity of tissue at frequencies , 2009 .

[26]  W. Rall.  Membrane time constant of motoneurons. , 1957, Science.

[27]  R. Kawashima,et al.  An evaluation of the conductivity profile in the somatosensory barrel cortex of Wistar rats. , 2010, Journal of neurophysiology.

[28]  W. Rall.  Branching dendritic trees and motoneuron membrane resistivity. , 1959, Experimental neurology.

[29]  J. C. Jimenez,et al.  Nonlinear local electrovascular coupling. I: A theoretical model , 2006, Human brain mapping.

[30]  Michael London,et al.  Local and Global Effects of Ih Distribution in Dendrites of Mammalian Neurons , 2007, The Journal of Neuroscience.

[31]  B. Roth.  The Electrical Conductivity of Tissues , 1999 .

[32]  Noam Peled,et al.  Constraining compartmental models using multiple voltage recordings and genetic algorithms. , 2005, Journal of neurophysiology.

[33]  Paul A. Rhodes,et al.  The Properties and Implications of NMDA Spikes in Neocortical Pyramidal Cells , 2006, The Journal of Neuroscience.

[34]  H. Markram,et al.  Morphological Development of Thick-Tufted Layer V Pyramidal Cells in the Rat Somatosensory Cortex , 2011, Front. Neuroanat..

[35]  W. Rall.  Membrane potential transients and membrane time constant of motoneurons. , 1960, Experimental neurology.

[36]  Prof. Dr. Dr. Valentino Braitenberg,et al.  Cortex: Statistics and Geometry of Neuronal Connectivity , 1998, Springer Berlin Heidelberg.

[37]  B Sakmann,et al.  Patch clamp techniques for studying ionic channels in excitable membranes. , 1984, Annual review of physiology.

[38]  Fiona E. N. LeBeau,et al.  Single-column thalamocortical network model exhibiting gamma oscillations, sleep spindles, and epileptogenic bursts. , 2005, Journal of neurophysiology.

[39]  Donald A Wilson,et al.  Single-Unit Activity in Piriform Cortex during Slow-Wave State Is Shaped by Recent Odor Experience , 2010, The Journal of Neuroscience.

[40]  D. Johnston,et al.  Foundations of Cellular Neurophysiology , 1994 .

[41]  B. Sakmann,et al.  Amplification of EPSPs by axosomatic sodium channels in neocortical pyramidal neurons , 1995, Neuron.

[42]  G. Buzsáki.  Rhythms of the brain , 2006 .

[43]  W. Bryan Wilent,et al.  Mapping of microstimulation evoked responses and unit activity patterns in the lateral hypothalamic area recorded in awake humans. Technical note. , 2011, Journal of neurosurgery.

[44]  A. Berrebi,et al.  Connections of the Superior Paraolivary Nucleus of the Rat: II. Reciprocal Connections with the Tectal Longitudinal Column , 2010, Front. Neuroanat..

[45]  M. de Curtis,et al.  Fast activity at seizure onset is mediated by inhibitory circuits in the entorhinal cortex in vitro , 2008, Annals of neurology.

[46]  L. Garey.  Cortex: Statistics and Geometry of Neuronal Connectivity, 2nd edn. By V. BRAITENBERG and A. SCHÜZ. (Pp. xiii+249; 90 figures; ISBN 3 540 63816 4). Berlin: Springer. 1998. , 1999 .

[47]  D. B. Heppner,et al.  Considerations of quasi-stationarity in electrophysiological systems. , 1967, The Bulletin of mathematical biophysics.

[48]  Christof Koch,et al.  Using extracellular action potential recordings to constrain compartmental models , 2007, Journal of Computational Neuroscience.

[49]  Eran Stark,et al.  Predicting Movement from Multiunit Activity , 2007, The Journal of Neuroscience.

[50]  Y. Okada,et al.  Contributions of principal neocortical neurons to magnetoencephalography and electroencephalography signals , 2006, The Journal of physiology.

[51]  H. Swadlow,et al.  Activation of a Cortical Column by a Thalamocortical Impulse , 2002, The Journal of Neuroscience.

[52]  T. Sejnowski,et al.  Simulations of cortical pyramidal neurons synchronized by inhibitory interneurons. , 1991, Journal of neurophysiology.

[53]  J. Csicsvari,et al.  Accuracy of tetrode spike separation as determined by simultaneous intracellular and extracellular measurements. , 2000, Journal of neurophysiology.

[54]  Christof Koch,et al.  Dynamic Moment Analysis of the Extracellular Electric Field of a Biologically Realistic Spiking Neuron , 2007, Neural Computation.

[55]  Henry C. Tuckwell,et al.  Introduction to theoretical neurobiology , 1988 .

[56]  Nuno Maçarico da Costa,et al.  How Thalamus Connects to Spiny Stellate Cells in the Cat's Visual Cortex , 2011, The Journal of Neuroscience.

[57]  Claude Bédard,et al.  Evidence for frequency-dependent extracellular impedance from the transfer function between extracellular and intracellular potentials , 2009, Journal of Computational Neuroscience.

[58]  S. Moran,et al.  On the Origin , 2012 .

[59]  Z. Somogyvári,et al.  Model-based source localization of extracellular action potentials , 2005, Journal of Neuroscience Methods.

[60]  Alon Korngreen,et al.  Dendritic voltage‐gated K+ conductance gradient in pyramidal neurones of neocortical layer 5B from rats , 2007, The Journal of physiology.

[61]  G. Major,et al.  The modelling of pyramidal neurones in the visual cortex , 1989 .

[62]  B. Sakmann,et al.  Active propagation of somatic action potentials into neocortical pyramidal cell dendrites , 1994, Nature.

[63]  C. Gabriel,et al.  Electrical conductivity of tissue at frequencies below 1 MHz , 2009, Physics in medicine and biology.

[64]  James P. Evans.  The Origin , 2009, Genetics in Medicine.

[65]  R. W. Lau,et al.  The dielectric properties of biological tissues: III. Parametric models for the dielectric spectrum of tissues. , 1996, Physics in medicine and biology.

[66]  A. Larkman.  Dendritic morphology of pyramidal neurones of the visual cortex of the rat: I. Branching patterns , 1991, The Journal of comparative neurology.

[67]  Beat Lutz,et al.  Synaptic Integration in Tuft Dendrites of Layer 5 Pyramidal Neurons : A New Unifying Principle , 2009 .

[68]  Alon Korngreen,et al.  Dendritic excitability during increased synaptic activity in rat neocortical L5 pyramidal neurons , 2008, The European journal of neuroscience.

[69]  C. Bédard,et al.  Macroscopic models of local field potentials and the apparent 1/f noise in brain activity. , 2008, Biophysical journal.

[70]  G. Stuart,et al.  Single Ih Channels in Pyramidal Neuron Dendrites: Properties, Distribution, and Impact on Action Potential Output , 2006, The Journal of Neuroscience.

[71]  G. Einevoll.  Modeling of extracellular potentials recorded with multicontact microelectrodes , 2010 .

[72]  B. Sakmann,et al.  Voltage‐gated K+ channels in layer 5 neocortical pyramidal neurones from young rats: subtypes and gradients , 2000, The Journal of physiology.

[73]  C. Nicholson,et al.  Diffusion in brain extracellular space. , 2008, Physiological reviews.

[74]  A. Larkman,et al.  Dendritic morphology of pyramidal neurones of the visual cortex of the rat: II. Parameter correlations , 1991, The Journal of comparative neurology.

[75]  Alain Destexhe,et al.  Simplified models of neocortical pyramidal cells preserving somatodendritic voltage attenuation , 2001, Neurocomputing.