Democracy-Independence Trade-Off in Oscillating Dendrites and Its Implications for Grid Cells

Summary Dendritic democracy and independence have been characterized for near-instantaneous processing of synaptic inputs. However, a wide class of neuronal computations requires input integration on long timescales. As a paradigmatic example, entorhinal grid fields have been thought to be generated by the democratic summation of independent dendritic oscillations performing direction-selective path integration. We analyzed how multiple dendritic oscillators embedded in the same neuron integrate inputs separately and determine somatic membrane voltage jointly. We found that the interaction of dendritic oscillations leads to phase locking, which sets an upper limit on the timescale for independent input integration. Factors that increase this timescale also decrease the influence that the dendritic oscillations exert on somatic voltage. In entorhinal stellate cells, interdendritic coupling dominates and causes these cells to act as single oscillators. Our results suggest a fundamental trade-off between local and global processing in dendritic trees integrating ongoing signals.

[1]  Bartlett W. Mel,et al.  Computational subunits in thin dendrites of pyramidal cells , 2004, Nature Neuroscience.

[2]  R. Llinás,et al.  Subthreshold Na+-dependent theta-like rhythmicity in stellate cells of entorhinal cortex layer II , 1989, Nature.

[3]  Eugene M. Izhikevich,et al.  Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting , 2006 .

[4]  F ROSENBLATT,et al.  The perceptron: a probabilistic model for information storage and organization in the brain. , 1958, Psychological review.

[5]  J Rinzel,et al.  Transient response in a dendritic neuron model for current injected at one branch. , 1974, Biophysical journal.

[6]  Torkel Hafting,et al.  Conjunctive Representation of Position, Direction, and Velocity in Entorhinal Cortex , 2006, Science.

[7]  A. Polsky,et al.  Properties of basal dendrites of layer 5 pyramidal neurons: a direct patch-clamp recording study , 2007, Nature Neuroscience.

[8]  J. Magee,et al.  Integrative Properties of Radial Oblique Dendrites in Hippocampal CA1 Pyramidal Neurons , 2006, Neuron.

[9]  Charles J. Wilson,et al.  Response properties and synchronization of rhythmically firing dendritic neurons. , 2007, Journal of neurophysiology.

[10]  T. Hafting,et al.  Hippocampus-independent phase precession in entorhinal grid cells , 2008, Nature.

[11]  R. S. Jones,et al.  A comparison of spontaneous EPSCs in layer II and layer IV-V neurons of the rat entorhinal cortex in vitro. , 1996, Journal of neurophysiology.

[12]  J. White,et al.  A bifurcation analysis of neuronal subthreshold oscillations. , 1995, Biophysical journal.

[13]  J. O’Keefe,et al.  Dual phase and rate coding in hippocampal place cells: Theoretical significance and relationship to entorhinal grid cells , 2005, Hippocampus.

[14]  M. Häusser,et al.  Synaptic function: Dendritic democracy , 2001, Current Biology.

[15]  C. Y. Yim,et al.  Intrinsic membrane potential oscillations in hippocampal neurons in vitro , 1991, Brain Research.

[16]  Nace L. Golding,et al.  Posthearing Developmental Refinement of Temporal Processing in Principal Neurons of the Medial Superior Olive , 2005, The Journal of Neuroscience.

[17]  J. Kao,et al.  Compartmentalized and Binary Behavior of Terminal Dendrites in Hippocampal Pyramidal Neurons , 2001, Science.

[18]  B. Kampa,et al.  Action potential generation requires a high sodium channel density in the axon initial segment , 2008, Nature Neuroscience.

[19]  A. Alonso,et al.  Biophysical Properties and Slow Voltage-Dependent Inactivation of a Sustained Sodium Current in Entorhinal Cortex Layer-II Principal Neurons , 1999, The Journal of general physiology.

[20]  F. Netter,et al.  Supplemental References , 2002, We Came Naked and Barefoot.

[21]  Bartlett W. Mel,et al.  Pyramidal Neuron as Two-Layer Neural Network , 2003, Neuron.

[22]  Nicholas T. Carnevale,et al.  The NEURON Simulation Environment , 1997, Neural Computation.

[23]  Mark C. Fuhs,et al.  A Spin Glass Model of Path Integration in Rat Medial Entorhinal Cortex , 2006, The Journal of Neuroscience.

[24]  Idan Segev,et al.  Subthreshold oscillations and resonant frequency in guinea‐pig cortical neurons: physiology and modelling. , 1995, The Journal of physiology.

[25]  Idan Segev,et al.  Synaptic scaling in vitro and in vivo , 2001, Nature Neuroscience.

[26]  James L. McClelland,et al.  Parallel distributed processing: explorations in the microstructure of cognition, vol. 1: foundations , 1986 .

[27]  M. Hasselmo Arc length coding by interference of theta frequency oscillations may underlie context-dependent hippocampal unit data and episodic memory function. , 2007, Learning & memory.

[28]  Máté Lengyel,et al.  Theta oscillation‐coupled dendritic spiking integrates inputs on a long time scale , 2005, Hippocampus.

[29]  N T Carnevale,et al.  Electrophysiological characterization of remote chemical synapses. , 1982, Journal of neurophysiology.

[30]  G. Kane Parallel Distributed Processing: Explorations in the Microstructure of Cognition, vol 1: Foundations, vol 2: Psychological and Biological Models , 1994 .

[31]  N. H. Sabah,et al.  Subthreshold oscillatory responses of the Hodgkin-Huxley cable model for the squid giant axon. , 1969, Biophysical journal.

[32]  T. Hafting,et al.  Microstructure of a spatial map in the entorhinal cortex , 2005, Nature.

[33]  Alessandro Treves,et al.  The emergence of grid cells: Intelligent design or just adaptation? , 2008, Hippocampus.

[34]  C. Chapman,et al.  Intrinsic theta-frequency membrane potential oscillations in hippocampal CA1 interneurons of stratum lacunosum-moleculare. , 1999, Journal of neurophysiology.

[35]  M. Hasselmo,et al.  Properties and role of I(h) in the pacing of subthreshold oscillations in entorhinal cortex layer II neurons. , 2000, Journal of neurophysiology.

[36]  J Rinzel,et al.  Branch input resistance and steady attenuation for input to one branch of a dendritic neuron model. , 1973, Biophysical journal.

[37]  A. Treves,et al.  Hippocampal remapping and grid realignment in entorhinal cortex , 2007, Nature.

[38]  J. C. Anderson,et al.  Map of the synapses formed with the dendrites of spiny stellate neurons of cat visual cortex , 1994, The Journal of comparative neurology.

[39]  A. Polsky,et al.  Synaptic Integration in Tuft Dendrites of Layer 5 Pyramidal Neurons: A New Unifying Principle , 2009, Science.

[40]  E. Schuman,et al.  Dendrites , 1978, Journal of the Geological Society.

[41]  Lisa M. Giocomo,et al.  Grid cell firing may arise from interference of theta frequency membrane potential oscillations in single neurons , 2007, Hippocampus.

[42]  Horacio G. Rotstein,et al.  The dynamic structure underlying subthreshold oscillatory activity and the onset of spikes in a model of medial entorhinal cortex stellate cells , 2006, Journal of Computational Neuroscience.

[43]  J. DeFelipe,et al.  The pyramidal neuron of the cerebral cortex: Morphological and chemical characteristics of the synaptic inputs , 1992, Progress in Neurobiology.

[44]  D. Paré,et al.  Two types of intrinsic oscillations in neurons of the lateral and basolateral nuclei of the amygdala. , 1998, Journal of neurophysiology.

[45]  Bruce L. McNaughton,et al.  Path integration and the neural basis of the 'cognitive map' , 2006, Nature Reviews Neuroscience.

[46]  Nace L. Golding,et al.  Dendritic Sodium Spikes Are Variable Triggers of Axonal Action Potentials in Hippocampal CA1 Pyramidal Neurons , 1998, Neuron.

[47]  C. Koch,et al.  Synaptic Background Activity Influences Spatiotemporal Integration in Single Pyramidal Cells. , 1991, The Biological bulletin.

[48]  Boris S. Gutkin,et al.  The Role of Ongoing Dendritic Oscillations in Single-Neuron Dynamics , 2009, PLoS Comput. Biol..

[49]  J. Bacigalupo,et al.  Intrinsic subthreshold oscillations of the membrane potential in pyramidal neurons of the olfactory amygdala , 2005, The European journal of neuroscience.

[50]  Michael Rudolph,et al.  A Fast-Conducting, Stochastic Integrative Mode for Neocortical Neurons InVivo , 2003, The Journal of Neuroscience.

[51]  J. Magee,et al.  On the Initiation and Propagation of Dendritic Spikes in CA1 Pyramidal Neurons , 2004, The Journal of Neuroscience.

[52]  Christof Koch,et al.  Cable theory in neurons with active, linearized membranes , 2004, Biological Cybernetics.

[53]  J J Hopfield,et al.  Neural networks and physical systems with emergent collective computational abilities. , 1982, Proceedings of the National Academy of Sciences of the United States of America.

[54]  A. Alonso,et al.  Differential electroresponsiveness of stellate and pyramidal-like cells of medial entorhinal cortex layer II. , 1993, Journal of neurophysiology.

[55]  J. O’Keefe,et al.  An oscillatory interference model of grid cell firing , 2007, Hippocampus.

[56]  M. Lengyel,et al.  Dynamically detuned oscillations account for the coupled rate and temporal code of place cell firing , 2003, Hippocampus.

[57]  A. Alonso,et al.  Morphological characteristics of layer II projection neurons in the rat medial entorhinal cortex , 1997, Hippocampus.

[58]  W S McCulloch,et al.  A logical calculus of the ideas immanent in nervous activity , 1990, The Philosophy of Artificial Intelligence.

[59]  Michael E Hasselmo,et al.  Ionic mechanisms in the generation of subthreshold oscillations and action potential clustering in entorhinal layer II stellate neurons , 2004, Hippocampus.

[60]  Lisa M. Giocomo,et al.  Temporal Frequency of Subthreshold Oscillations Scales with Entorhinal Grid Cell Field Spacing , 2007, Science.