A Calcium-Dependent Plasticity Rule for HCN Channels Maintains Activity Homeostasis and Stable Synaptic Learning

Theoretical and computational frameworks for synaptic plasticity and learning have a long and cherished history, with few parallels within the well-established literature for plasticity of voltage-gated ion channels. In this study, we derive rules for plasticity in the hyperpolarization-activated cyclic nucleotide-gated (HCN) channels, and assess the synergy between synaptic and HCN channel plasticity in establishing stability during synaptic learning. To do this, we employ a conductance-based model for the hippocampal pyramidal neuron, and incorporate synaptic plasticity through the well-established Bienenstock-Cooper-Munro (BCM)-like rule for synaptic plasticity, wherein the direction and strength of the plasticity is dependent on the concentration of calcium influx. Under this framework, we derive a rule for HCN channel plasticity to establish homeostasis in synaptically-driven firing rate, and incorporate such plasticity into our model. In demonstrating that this rule for HCN channel plasticity helps maintain firing rate homeostasis after bidirectional synaptic plasticity, we observe a linear relationship between synaptic plasticity and HCN channel plasticity for maintaining firing rate homeostasis. Motivated by this linear relationship, we derive a calcium-dependent rule for HCN-channel plasticity, and demonstrate that firing rate homeostasis is maintained in the face of synaptic plasticity when moderate and high levels of cytosolic calcium influx induced depression and potentiation of the HCN-channel conductance, respectively. Additionally, we show that such synergy between synaptic and HCN-channel plasticity enhances the stability of synaptic learning through metaplasticity in the BCM-like synaptic plasticity profile. Finally, we demonstrate that the synergistic interaction between synaptic and HCN-channel plasticity preserves robustness of information transfer across the neuron under a rate-coding schema. Our results establish specific physiological roles for experimentally observed plasticity in HCN channels accompanying synaptic plasticity in hippocampal neurons, and uncover potential links between HCN-channel plasticity and calcium influx, dynamic gain control and stable synaptic learning.

[1]  Simon Haykin,et al.  Neural Networks and Learning Machines , 2010 .

[2]  W. Abraham.  Metaplasticity: tuning synapses and networks for plasticity , 2008, Nature Reviews Neuroscience.

[3]  D. Johnston,et al.  The h Channel Mediates Location Dependence and Plasticity of Intrinsic Phase Response in Rat Hippocampal Neurons , 2008, The Journal of Neuroscience.

[4]  M. Shah.  HCN1 Channels: A New Therapeutic Target for Depressive Disorders? , 2012, Science Signaling.

[5]  Michele Migliore,et al.  Role of an A-Type K+ Conductance in the Back-Propagation of Action Potentials in the Dendrites of Hippocampal Pyramidal Neurons , 1999, Journal of Computational Neuroscience.

[6]  Daniel Johnston,et al.  LTP is accompanied by an enhanced local excitability of pyramidal neuron dendrites , 2004, Nature Neuroscience.

[7]  Giorgio A. Ascoli,et al.  Local Control of Postinhibitory Rebound Spiking in CA1 Pyramidal Neuron Dendrites , 2010, The Journal of Neuroscience.

[8]  William Bialek,et al.  Spikes: Exploring the Neural Code , 1996 .

[9]  M. Quirk,et al.  Experience-Dependent Asymmetric Shape of Hippocampal Receptive Fields , 2000, Neuron.

[10]  D. Linden,et al.  Ubiquitous Plasticity and Memory Storage , 2007, Neuron.

[11]  Zhihong Man,et al.  Lyapunov-theory-based radial basis function networks for adaptive filtering , 2002 .

[12]  W. Wadman,et al.  Homeostatic scaling of neuronal excitability by synaptic modulation of somatic hyperpolarization-activated Ih channels. , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[13]  J. Storm,et al.  Two forms of electrical resonance at theta frequencies, generated by M‐current, h‐current and persistent Na+ current in rat hippocampal pyramidal cells , 2002, The Journal of physiology.

[14]  Christof Koch,et al.  How voltage-dependent conductances can adapt to maximize the information encoded by neuronal firing rate , 1999, Nature Neuroscience.

[15]  R. Luján,et al.  New sites of action for GIRK and SK channels , 2009, Nature Reviews Neuroscience.

[16]  J. Magee.  Dendritic Hyperpolarization-Activated Currents Modify the Integrative Properties of Hippocampal CA1 Pyramidal Neurons , 1998, The Journal of Neuroscience.

[17]  S. Hoffman,et al.  Funding for malaria genome sequencing , 1997, Nature.

[18]  Rishikesh Narayanan,et al.  Inactivating ion channels augment robustness of subthreshold intrinsic response dynamics to parametric variability in hippocampal model neurons , 2012, The Journal of physiology.

[19]  G. Ellis‐Davies,et al.  Structural basis of long-term potentiation in single dendritic spines , 2004, Nature.

[20]  L. Cooper,et al.  A unified model of NMDA receptor-dependent bidirectional synaptic plasticity , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[21]  Michel Vidal-Naquet,et al.  Visual features of intermediate complexity and their use in classification , 2002, Nature Neuroscience.

[22]  D. Kullmann,et al.  Ih-mediated depolarization enhances the temporal precision of neuronal integration , 2011, Nature communications.

[23]  Jochen Triesch,et al.  Synergies Between Intrinsic and Synaptic Plasticity Mechanisms , 2007, Neural Computation.

[24]  Terrence J. Sejnowski,et al.  The “independent components” of natural scenes are edge filters , 1997, Vision Research.

[25]  D. Johnston,et al.  Characterization of single voltage‐gated Na+ and Ca2+ channels in apical dendrites of rat CA1 pyramidal neurons. , 1995, The Journal of physiology.

[26]  J. Kotaleski,et al.  Modelling the molecular mechanisms of synaptic plasticity using systems biology approaches , 2010, Nature Reviews Neuroscience.

[27]  Eve Marder,et al.  Modeling stability in neuron and network function: the role of activity in homeostasis. , 2002, BioEssays : news and reviews in molecular, cellular and developmental biology.

[28]  M. Mayer,et al.  Permeation and block of N‐methyl‐D‐aspartic acid receptor channels by divalent cations in mouse cultured central neurones. , 1987, The Journal of physiology.

[29]  J. Lisman,et al.  A mechanism for the Hebb and the anti-Hebb processes underlying learning and memory. , 1989, Proceedings of the National Academy of Sciences of the United States of America.

[30]  P. J. Sjöström,et al.  Dendritic excitability and synaptic plasticity. , 2008, Physiological reviews.

[31]  Kenneth D. Miller,et al.  The Role of Constraints in Hebbian Learning , 1994, Neural Computation.

[32]  A. Hodgkin,et al.  The effect of sodium ions on the electrical activity of the giant axon of the squid , 1949, The Journal of physiology.

[33]  Michael L. Hines,et al.  The NEURON Book , 2006 .

[34]  Terrence J. Sejnowski,et al.  Independent Component Analysis Using an Extended Infomax Algorithm for Mixed Subgaussian and Supergaussian Sources , 1999, Neural Computation.

[35]  Michael S. Lewicki,et al.  Efficient coding of natural sounds , 2002, Nature Neuroscience.

[36]  W. Gerstner,et al.  Generalized Bienenstock-Cooper-Munro rule for spiking neurons that maximizes information transmission. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[37]  N. Swindale.  The development of topography in the visual cortex: a review of models. , 1996, Network.

[38]  Nicolas Brunel,et al.  Mutual Information, Fisher Information, and Population Coding , 1998, Neural Computation.

[39]  D. Johnston,et al.  Ion channels in genetic and acquired forms of epilepsy , 2013, The Journal of physiology.

[40]  Jochen Triesch,et al.  Rules for information maximization in spiking neurons using intrinsic plasticity , 2009, 2009 International Joint Conference on Neural Networks.

[41]  Daniel Johnston,et al.  Plasticity of Intrinsic Excitability during Long-Term Depression Is Mediated through mGluR-Dependent Changes in Ih in Hippocampal CA1 Pyramidal Neurons , 2007, The Journal of Neuroscience.

[42]  Bartlett W. Mel,et al.  Arithmetic of Subthreshold Synaptic Summation in a Model CA1 Pyramidal Cell , 2003, Neuron.

[43]  T. H. Brown,et al.  Biophysical model of a Hebbian synapse. , 1990, Proceedings of the National Academy of Sciences of the United States of America.

[44]  R. Chitwood,et al.  Activity-dependent decrease of excitability in rat hippocampal neurons through increases in Ih , 2005, Nature Neuroscience.

[45]  D. Johnston,et al.  Enhancement of Dorsal Hippocampal Activity by Knockdown of HCN1 Channels Leads to Anxiolytic- and Antidepressant-like Behaviors , 2012, Neuron.

[46]  Jochen Triesch,et al.  Independent Component Analysis in Spiking Neurons , 2010, PLoS Comput. Biol..

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

[48]  Rishikesh Narayanan,et al.  Functional maps within a single neuron. , 2012, Journal of neurophysiology.

[49]  Kenneth D. Miller,et al.  Adaptive filtering enhances information transmission in visual cortex , 2006, Nature.

[50]  D. Johnston,et al.  K+ channel regulation of signal propagation in dendrites of hippocampal pyramidal neurons , 1997, Nature.

[51]  R. Dingledine,et al.  The glutamate receptor ion channels. , 1999, Pharmacological reviews.

[52]  W. Gerstner,et al.  Connectivity reflects coding: a model of voltage-based STDP with homeostasis , 2010, Nature Neuroscience.

[53]  Heinz Beck,et al.  Plasticity of intrinsic neuronal properties in CNS disorders , 2008, Nature Reviews Neuroscience.

[54]  Emilie Campanac,et al.  Downregulation of Dendritic Ih in CA1 Pyramidal Neurons after LTP , 2008, The Journal of Neuroscience.

[55]  Bruno A. Olshausen,et al.  Book Review , 2003, Journal of Cognitive Neuroscience.

[56]  Carmen C. Canavier,et al.  Sodium Dynamics Underlying Burst Firing and Putative Mechanisms for the Regulation of the Firing Pattern in Midbrain Dopamine Neurons: A Computational Approach , 2004, Journal of Computational Neuroscience.

[57]  D. Hoffman,et al.  Dendritic ion channel trafficking and plasticity , 2010, Trends in Neurosciences.

[58]  Erkki Oja,et al.  Independent component analysis: algorithms and applications , 2000, Neural Networks.

[59]  Wolfgang Maass,et al.  Branch-Specific Plasticity Enables Self-Organization of Nonlinear Computation in Single Neurons , 2011, The Journal of Neuroscience.

[60]  L. Abbott,et al.  Hyperpolarization-activated cation channels inhibit EPSPs by interactions with M-type K+ channels , 2009, Nature Neuroscience.

[61]  L F Abbott,et al.  Balancing homeostasis and learning in neural circuits. , 2003, Zoology.

[62]  E. Marder,et al.  Variability, compensation and homeostasis in neuron and network function , 2006, Nature Reviews Neuroscience.

[63]  Erkki Oja,et al.  Independent component analysis by general nonlinear Hebbian-like learning rules , 1998, Signal Process..

[64]  C. Wahl-Schott,et al.  Hyperpolarization-activated cation channels: from genes to function. , 2009, Physiological reviews.

[65]  E. Marder,et al.  Multiple models to capture the variability in biological neurons and networks , 2011, Nature Neuroscience.

[66]  Rishikesh Narayanan,et al.  Long-Term Potentiation in Rat Hippocampal Neurons Is Accompanied by Spatially Widespread Changes in Intrinsic Oscillatory Dynamics and Excitability , 2007, Neuron.

[67]  J. Byrne,et al.  More than synaptic plasticity: role of nonsynaptic plasticity in learning and memory , 2010, Trends in Neurosciences.

[68]  Eero P. Simoncelli,et al.  Natural image statistics and neural representation. , 2001, Annual review of neuroscience.

[69]  D. Johnston,et al.  Active dendrites, potassium channels and synaptic plasticity. , 2003, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[70]  Xiao-Jing Wang.  Neurophysiological and computational principles of cortical rhythms in cognition. , 2010, Physiological reviews.

[71]  L. Abbott,et al.  Competitive Hebbian learning through spike-timing-dependent synaptic plasticity , 2000, Nature Neuroscience.

[72]  G. Turrigiano.  Too many cooks? Intrinsic and synaptic homeostatic mechanisms in cortical circuit refinement. , 2011, Annual review of neuroscience.

[73]  D. Johnston,et al.  Pharmacological upregulation of h-channels reduces the excitability of pyramidal neuron dendrites , 2002, Nature Neuroscience.

[74]  W. Wildman,et al.  Theoretical Neuroscience , 2014 .

[75]  M. Bear,et al.  Homosynaptic long-term depression in area CA1 of hippocampus and effects of N-methyl-D-aspartate receptor blockade. , 1992, Proceedings of the National Academy of Sciences of the United States of America.

[76]  S. Siegelbaum,et al.  HCN1 Channels Constrain Synaptically Evoked Ca2+ Spikes in Distal Dendrites of CA1 Pyramidal Neurons , 2007, Neuron.

[77]  E. Bienenstock,et al.  Theory for the development of neuron selectivity: orientation specificity and binocular interaction in visual cortex , 1982, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[78]  Ahmad Banakar.  Lyapunov Stability Analysis of Gradient Descent-Learning Algorithm in Network Training , 2011 .

[79]  D. E. Goldman.  POTENTIAL, IMPEDANCE, AND RECTIFICATION IN MEMBRANES , 1943, The Journal of general physiology.

[80]  L. Cooper,et al.  A biophysical model of bidirectional synaptic plasticity: Dependence on AMPA and NMDA receptors , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[81]  Mark C. W. van Rossum,et al.  Stable Hebbian Learning from Spike Timing-Dependent Plasticity , 2000, The Journal of Neuroscience.

[82]  Idan Segev,et al.  Two opposing plasticity mechanisms pulling a single synapse , 2008, Trends in Neurosciences.

[83]  J E Lisman,et al.  Three Ca2+ levels affect plasticity differently: the LTP zone, the LTD zone and no man's land , 2001, The Journal of physiology.

[84]  C. Stevens,et al.  Voltage dependence of NMDA-activated macroscopic conductances predicted by single-channel kinetics , 1990, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[85]  D. Johnston,et al.  The h current is a candidate mechanism for regulating the sliding modification threshold in a BCM-like synaptic learning rule. , 2010, Journal of neurophysiology.

[86]  R. Morgan,et al.  Double Trouble? Potential for Hyperexcitability Following Both Channelopathic up- and Downregulation of Ih in Epilepsy , 2009, Front. Neurosci..

[87]  L. Cooper,et al.  Synaptic homeostasis and input selectivity follow from a calcium-dependent plasticity model. , 2004, Proceedings of the National Academy of Sciences of the United States of America.