Biophysical Basis for Three Distinct Dynamical Mechanisms of Action Potential Initiation

Transduction of graded synaptic input into trains of all-or-none action potentials (spikes) is a crucial step in neural coding. Hodgkin identified three classes of neurons with qualitatively different analog-to-digital transduction properties. Despite widespread use of this classification scheme, a generalizable explanation of its biophysical basis has not been described. We recorded from spinal sensory neurons representing each class and reproduced their transduction properties in a minimal model. With phase plane and bifurcation analysis, each class of excitability was shown to derive from distinct spike initiating dynamics. Excitability could be converted between all three classes by varying single parameters; moreover, several parameters, when varied one at a time, had functionally equivalent effects on excitability. From this, we conclude that the spike-initiating dynamics associated with each of Hodgkin's classes represent different outcomes in a nonlinear competition between oppositely directed, kinetically mismatched currents. Class 1 excitability occurs through a saddle node on invariant circle bifurcation when net current at perithreshold potentials is inward (depolarizing) at steady state. Class 2 excitability occurs through a Hopf bifurcation when, despite net current being outward (hyperpolarizing) at steady state, spike initiation occurs because inward current activates faster than outward current. Class 3 excitability occurs through a quasi-separatrix crossing when fast-activating inward current overpowers slow-activating outward current during a stimulus transient, although slow-activating outward current dominates during constant stimulation. Experiments confirmed that different classes of spinal lamina I neurons express the subthreshold currents predicted by our simulations and, further, that those currents are necessary for the excitability in each cell class. Thus, our results demonstrate that all three classes of excitability arise from a continuum in the direction and magnitude of subthreshold currents. Through detailed analysis of the spike-initiating process, we have explained a fundamental link between biophysical properties and qualitative differences in how neurons encode sensory input.

[1]  G. Uhlenbeck,et al.  On the Theory of the Brownian Motion , 1930 .

[2]  E. Adrian The Mechanism of Nervous Action: Electrical Studies of the Neurone , 1932 .

[3]  H. Schwan,et al.  Biological Engineering , 1941, Science.

[4]  A. Hodgkin The local electric changes associated with repetitive action in a non‐medullated axon , 1948, The Journal of physiology.

[5]  A. Hodgkin,et al.  A quantitative description of membrane current and its application to conduction and excitation in nerve , 1952, The Journal of physiology.

[6]  P. Mazur On the theory of brownian motion , 1959 .

[7]  R. FitzHugh Impulses and Physiological States in Theoretical Models of Nerve Membrane. , 1961, Biophysical journal.

[8]  R. Mazo On the theory of brownian motion , 1973 .

[9]  C. Nicholson Electric current flow in excitable cells J. J. B. Jack, D. Noble &R. W. Tsien Clarendon Press, Oxford (1975). 502 pp., £18.00 , 1976, Neuroscience.

[10]  C. Morris,et al.  Voltage oscillations in the barnacle giant muscle fiber. , 1981, Biophysical journal.

[11]  R. Llinás The intrinsic electrophysiological properties of mammalian neurons: insights into central nervous system function. , 1988, Science.

[12]  G. Ermentrout,et al.  Analysis of neural excitability and oscillations , 1989 .

[13]  J. Hindmarsh,et al.  The assembly of ionic currents in a thalamic neuron I. The three-dimensional model , 1989, Proceedings of the Royal Society of London. B. Biological Sciences.

[14]  A. Thomson,et al.  Membrane Characteristics and Synaptic Responsiveness of Superficial Dorsal Horn Neurons in a Slice Preparation of Adult Rat Spinal Cord , 1989, The European journal of neuroscience.

[15]  B. Connors,et al.  Intrinsic firing patterns of diverse neocortical neurons , 1990, Trends in Neurosciences.

[16]  W. R. Foster,et al.  Characteristic firing behavior of cell types in the cardiorespiratory region of the nucleus tractus solitarii of the rat , 1993, Brain Research.

[17]  Steven H. Strogatz,et al.  Nonlinear Dynamics and Chaos , 2024 .

[18]  J. Lopez-Garcia,et al.  Membrane Properties of Physiologically Classified Rat Dorsal Horn Neurons In Vitro: Correlation with Cutaneous Sensory Afferent Input , 1994, The European journal of neuroscience.

[19]  S. H. Chandler,et al.  Electrophysiological properties of guinea pig trigeminal motoneurons recorded in vitro. , 1994, Journal of neurophysiology.

[20]  P. H. Smith,et al.  Structural and functional differences distinguish principal from nonprincipal cells in the guinea pig MSO slice. , 1995, Journal of neurophysiology.

[21]  I. Forsythe,et al.  Two voltage-dependent K+ conductances with complementary functions in postsynaptic integration at a central auditory synapse , 1995, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[22]  Bard Ermentrout,et al.  Type I Membranes, Phase Resetting Curves, and Synchrony , 1996, Neural Computation.

[23]  E. Ağar,,et al.  MEMBRANE PROPERTIES OF MOUSE ANTEROVENTRAL COCHLEAR NUCLEUS NEURONS IN VITRO , 1996, Journal of basic and clinical physiology and pharmacology.

[24]  S. Bisti,et al.  Functional development of intrinsic properties in ganglion cells of the mammalian retina. , 1997, Journal of neurophysiology.

[25]  L. Trussell,et al.  Characterization of outward currents in neurons of the avian nucleus magnocellularis. , 1998, Journal of neurophysiology.

[26]  J. Rinzel,et al.  The role of dendrites in auditory coincidence detection , 1998, Nature.

[27]  C. Koch,et al.  Methods in Neuronal Modeling: From Ions to Networks , 1998 .

[28]  H. Wilson Simplified dynamics of human and mammalian neocortical neurons. , 1999, Journal of theoretical biology.

[29]  A. Erisir,et al.  Function of specific K(+) channels in sustained high-frequency firing of fast-spiking neocortical interneurons. , 1999, Journal of neurophysiology.

[30]  Xiao Hong Yu,et al.  Visualization of lamina I of the dorsal horn in live adult rat spinal cord slices , 2000, Journal of Neuroscience Methods.

[31]  W. C. Groat,et al.  Electrophysiological properties of lumbosacral preganglionic neurons in the neonatal rat spinal cord , 2000, Brain Research.

[32]  P. Sah,et al.  Morphological and electrophysiological properties of principal neurons in the rat lateral amygdala in vitro. , 2001, Journal of neurophysiology.

[33]  J. Sandkühler,et al.  Lamina‐specific membrane and discharge properties of rat spinal dorsal horn neurones in vitro , 2002, The Journal of physiology.

[34]  E. Perl,et al.  Correlations between neuronal morphology and electrophysiological features in the rodent superficial dorsal horn , 2002, The Journal of physiology.

[35]  P. Glazebrook,et al.  Potassium channels Kv1.1, Kv1.2 and Kv1.6 influence excitability of rat visceral sensory neurons , 2002, The Journal of physiology.

[36]  M. Ferragamo,et al.  Octopus cells of the mammalian ventral cochlear nucleus sense the rate of depolarization. , 2002, Journal of neurophysiology.

[37]  Bard Ermentrout,et al.  Simulating, analyzing, and animating dynamical systems - a guide to XPPAUT for researchers and students , 2002, Software, environments, tools.

[38]  Y. Koninck,et al.  Four cell types with distinctive membrane properties and morphologies in lamina I of the spinal dorsal horn of the adult rat , 2002, The Journal of physiology.

[39]  J. Rinzel,et al.  Sodium along with low-threshold potassium currents enhance coincidence detection of subthreshold noisy signals in MSO neurons. , 2004, Journal of neurophysiology.

[40]  H. Robinson,et al.  Threshold firing frequency-current relationships of neurons in rat somatosensory cortex: type 1 and type 2 dynamics. , 2004, Journal of neurophysiology.

[41]  Boris S. Gutkin,et al.  Spike Generating Dynamics and the Conditions for Spike-Time Precision in Cortical Neurons , 2003, Journal of Computational Neuroscience.

[42]  Eve Marder,et al.  Reduction of conductance-based neuron models , 1992, Biological Cybernetics.

[43]  H. Markram,et al.  Correlation maps allow neuronal electrical properties to be predicted from single-cell gene expression profiles in rat neocortex. , 2004, Cerebral cortex.

[44]  André Longtin,et al.  Comparison of Coding Capabilities of Type I and Type II Neurons , 2004, Journal of Computational Neuroscience.

[45]  Alla Borisyuk,et al.  UNDERSTANDING NEURONAL DYNAMICS BY GEOMETRICAL DISSECTION OF MINIMAL MODELS , 2005 .

[46]  D. Oertel,et al.  Temperature affects voltage-sensitive conductances differentially in octopus cells of the mammalian cochlear nucleus. , 2005, Journal of neurophysiology.

[47]  S. Prescott,et al.  Integration Time in a Subset of Spinal Lamina I Neurons Is Lengthened by Sodium and Calcium Currents Acting Synergistically to Prolong Subthreshold Depolarization , 2005, The Journal of Neuroscience.

[48]  H. Robinson,et al.  Rate coding and spike-time variability in cortical neurons with two types of threshold dynamics. , 2006, Journal of neurophysiology.

[49]  Peter A. Smith,et al.  Sciatic chronic constriction injury produces cell-type-specific changes in the electrophysiological properties of rat substantia gelatinosa neurons. , 2006, Journal of neurophysiology.

[50]  H. Robinson,et al.  Phase resetting curves and oscillatory stability in interneurons of rat somatosensory cortex. , 2007, Biophysical journal.

[51]  David Golomb,et al.  Mechanisms of Firing Patterns in Fast-Spiking Cortical Interneurons , 2007, PLoS Comput. Biol..

[52]  D. McCormick,et al.  Selective control of cortical axonal spikes by a slowly inactivating K+ current , 2007, Proceedings of the National Academy of Sciences.

[53]  Adrienne L. Fairhall,et al.  Single Neuron Computation: From Dynamical System to Feature Detector , 2006, Neural Computation.

[54]  W. C. Groat,et al.  Neurokinins enhance excitability in capsaicin-responsive DRG neurons , 2007, Experimental Neurology.

[55]  M. Häusser,et al.  High-fidelity transmission of sensory information by single cerebellar mossy fibre boutons , 2007, Nature.

[56]  Adrienne L. Fairhall,et al.  Two Computational Regimes of a Single-Compartment Neuron Separated by a Planar Boundary in Conductance Space , 2007, Neural Computation.

[57]  T. Sejnowski,et al.  Pyramidal neurons switch from integrators in vitro to resonators under in vivo-like conditions. , 2008, Journal of neurophysiology.