The Journal of Neurophysiology Vol. 79 No. 3 March 1998, pp. 1549-1566
Copyright ©1998 The American Physiological Society

Calcium Coding and Adaptive Temporal Computation in Cortical Pyramidal Neurons

Xiao-Jing Wang

Center for Complex Systems and Department of Physics, Brandeis University, Waltham, Massachusetts 02254

Wang, Xiao-Jing. Calcium coding and adaptive temporal computation in cortical pyramidal neurons. J. Neurophysiol. 79: 1549-1566, 1998. In this work, we present a quantitative theory of temporal spike-frequency adaptation in cortical pyramidal cells. Our model pyramidal neuron has two-compartments (a "soma" and a "dendrite") with a voltage-gated Ca²⁺ conductance (g_Ca) and a Ca²⁺-dependent K⁺ conductance (g_AHP) located at the dendrite or at both compartments. Its frequency-current relations are comparable with data from cortical pyramidal cells, and the properties of spike-evoked intracellular [Ca²⁺] transients are matched with recent dendritic [Ca²⁺] imaging measurements. Spike-frequency adaptation in response to a current pulse is characterized by an adaptation time constant _adap and percentage adaptation of spike frequency F_adap [% (peak  steady state)/peak]. We show how _adap and F_adap can be derived in terms of the biophysical parameters of the neural membrane and [Ca²⁺] dynamics. Two simple, experimentally testable, relations between _adap and F_adap are predicted. The dependence of _adap and F_adap on current pulse intensity, electrotonic coupling between the two compartments, g_AHP as well the [Ca²⁺] decay time constant _Ca, is assessed quantitatively. In addition, we demonstrate that the intracellular [Ca²⁺] signal can encode the instantaneous neuronal firing rate and that the conductance-based model can be reduced to a simple calcium-model of neuronal activity that faithfully predicts the neuronal firing output even when the input varies relatively rapidly in time (tens to hundreds of milliseconds). Extensive simulations have been carried out for the model neuron with random excitatory synaptic inputs mimicked by a Poisson process. Our findings include 1) the instantaneous firing frequency (averaged over trials) shows strong adaptation similar to the case with current pulses; 2) when the g_AHP is blocked, the dendritic g_Ca could produce a hysteresis phenomenon where the neuron is driven to switch randomly between a quiescent state and a repetitive firing state. The firing pattern is very irregular with a large coefficient of variation of the interspike intervals (ISI CV > 1). The ISI distribution shows a long tail but is not bimodal. 3) By contrast, in an intrinsically bursting regime (with different parameter values), the model neuron displays a random temporal mixture of single action potentials and brief bursts of spikes. Its ISI distribution is often bimodal and its power spectrum has a peak. 4) The spike-adapting current I_AHP, as delayed inhibition through intracellular Ca²⁺ accumulation, generates a "forward masking" effect, where a masking input dramatically reduces or completely suppresses the neuronal response to a subsequent test input. When two inputs are presented repetitively in time, this mechanism greatly enhances the ratio of the responses to the stronger and weaker inputs, fulfilling a cellular form of lateral inhibition in time. 5) The [Ca²⁺]-dependent I_AHP provides a mechanism by which the neuron unceasingly adapts to the stochastic synaptic inputs, even in the stationary state following the input onset. This creates strong negative correlations between output ISIs in a frequency-dependent manner, while the Poisson input is totally uncorrelated in time. Possible functional implications of these results are discussed.

This article has been cited by other articles:

				R. Krahe, J. Bastian, and M. J. Chacron Temporal Processing Across Multiple Topographic Maps in the Electrosensory System J Neurophysiol, August 1, 2008; 100(2): 852 - 867. [Abstract] [Full Text] [PDF]

				M. Teagarden, J. F. Atherton, M. D. Bevan, and C. J. Wilson Accumulation of cytoplasmic calcium, but not apamin-sensitive afterhyperpolarization current, during high frequency firing in rat subthalamic nucleus cells J. Physiol., February 1, 2008; 586(3): 817 - 833. [Abstract] [Full Text] [PDF]

				H. Y. Jeong and B. Gutkin Synchrony of neuronal oscillations controlled by GABAergic reversal potentials. Neural Comput., March 1, 2007; 19(3): 706 - 729. [Abstract] [Full Text] [PDF]

				F. Gabbiani and H. G. Krapp Spike-Frequency Adaptation and Intrinsic Properties of an Identified, Looming-Sensitive Neuron J Neurophysiol, December 1, 2006; 96(6): 2951 - 2962. [Abstract] [Full Text] [PDF]

				G. Soto, N. Kopell, and K. Sen Network Architecture, Receptive Fields, and Neuromodulation: Computational and Functional Implications of Cholinergic Modulation in Primary Auditory Cortex J Neurophysiol, December 1, 2006; 96(6): 2972 - 2983. [Abstract] [Full Text] [PDF]

				N. S. Desai and E. C. Walcott Synaptic bombardment modulates muscarinic effects in forelimb motor cortex. J. Neurosci., February 22, 2006; 26(8): 2215 - 2226. [Abstract] [Full Text] [PDF]

				C. Geisler, N. Brunel, and X.-J. Wang Contributions of Intrinsic Membrane Dynamics to Fast Network Oscillations With Irregular Neuronal Discharges J Neurophysiol, December 1, 2005; 94(6): 4344 - 4361. [Abstract] [Full Text] [PDF]

				B. S. Gutkin, G. B. Ermentrout, and A. D. Reyes Phase-Response Curves Give the Responses of Neurons to Transient Inputs J Neurophysiol, August 1, 2005; 94(2): 1623 - 1635. [Abstract] [Full Text] [PDF]

				G. Gilboa, R. Chen, and N. Brenner History-Dependent Multiple-Time-Scale Dynamics in a Single-Neuron Model J. Neurosci., July 13, 2005; 25(28): 6479 - 6489. [Abstract] [Full Text] [PDF]

				J. Benda, A. Longtin, and L. Maler Spike-Frequency Adaptation Separates Transient Communication Signals from Background Oscillations J. Neurosci., March 2, 2005; 25(9): 2312 - 2321. [Abstract] [Full Text] [PDF]

				R. M. Glantz and J. P. Schroeter Analysis and Simulation of Gain Control and Precision in Crayfish Visual Interneurons J Neurophysiol, November 1, 2004; 92(5): 2747 - 2761. [Abstract] [Full Text] [PDF]

				G. La Camera, A. Rauch, H.-R. Luscher, W. Senn, and S. Fusi Minimal Models of Adapted Neuronal Response to In Vivo-Like Input Currents Neural Comput., October 1, 2004; 16(10): 2101 - 2124. [Abstract] [Full Text] [PDF]

				R. Jolivet, T. J. Lewis, and W. Gerstner Generalized Integrate-and-Fire Models of Neuronal Activity Approximate Spike Trains of a Detailed Model to a High Degree of Accuracy J Neurophysiol, August 1, 2004; 92(2): 959 - 976. [Abstract] [Full Text] [PDF]

				R. M. Glantz and J. P. Schroeter Encoder Adaptation Modulates the Visual Responses of Crayfish Interneurons J Neurophysiol, July 1, 2004; 92(1): 327 - 340. [Abstract] [Full Text] [PDF]

				C. J. Wilson, A. Weyrick, D. Terman, N. E. Hallworth, and M. D. Bevan A Model of Reverse Spike Frequency Adaptation and Repetitive Firing of Subthalamic Nucleus Neurons J Neurophysiol, May 1, 2004; 91(5): 1963 - 1980. [Abstract] [Full Text] [PDF]

				H. J. Abel, J.C.F. Lee, J. C. Callaway, and R. C. Foehring Relationships Between Intracellular Calcium and Afterhyperpolarizations in Neocortical Pyramidal Neurons J Neurophysiol, January 1, 2004; 91(1): 324 - 335. [Abstract] [Full Text]

				J. Benda and A. V. M. Herz A Universal Model for Spike-Frequency Adaptation Neural Comput., November 1, 2003; 15(11): 2523 - 2564. [Abstract] [Full Text] [PDF]

				A. Rauch, G. La Camera, H.-R. Luscher, W. Senn, and S. Fusi Neocortical Pyramidal Cells Respond as Integrate-and-Fire Neurons to In Vivo-Like Input Currents J Neurophysiol, September 1, 2003; 90(3): 1598 - 1612. [Abstract] [Full Text] [PDF]

				N. E. Hallworth, C. J. Wilson, and M. D. Bevan Apamin-Sensitive Small Conductance Calcium-Activated Potassium Channels, through their Selective Coupling to Voltage-Gated Calcium Channels, Are Critical Determinants of the Precision, Pace, and Pattern of Action Potential Generation in Rat Subthalamic Nucleus Neurons In Vitro J. Neurosci., August 20, 2003; 23(20): 7525 - 7542. [Abstract] [Full Text] [PDF]

				X.-J. Wang, Y. Liu, M. V. Sanchez-Vives, and D. A. McCormick Adaptation and Temporal Decorrelation by Single Neurons in the Primary Visual Cortex J Neurophysiol, June 1, 2003; 89(6): 3279 - 3293. [Abstract] [Full Text] [PDF]

				M.C.W. van Rossum, B. J. O'Brien, and R. G. Smith Effects of Noise on the Spike Timing Precision of Retinal Ganglion Cells J Neurophysiol, May 1, 2003; 89(5): 2406 - 2419. [Abstract] [Full Text] [PDF]

				A. Compte, M. V. Sanchez-Vives, D. A. McCormick, and X.-J. Wang Cellular and Network Mechanisms of Slow Oscillatory Activity (<1 Hz) and Wave Propagations in a Cortical Network Model J Neurophysiol, May 1, 2003; 89(5): 2707 - 2725. [Abstract] [Full Text] [PDF]

				A. Kepecs, X.-J. Wang, and J. Lisman Bursting Neurons Signal Input Slope J. Neurosci., October 15, 2002; 22(20): 9053 - 9062. [Abstract] [Full Text] [PDF]

				J. Feng and G. Li Impact of Geometrical Structures on the Output of Neuronal Models: A Theoretical and Numerical Analysis Neural Comput., March 1, 2002; 14(3): 621 - 640. [Abstract] [Full Text]

				X.-J. Wang Pacemaker Neurons for the Theta Rhythm and Their Synchronization in the Septohippocampal Reciprocal Loop J Neurophysiol, February 1, 2002; 87(2): 889 - 900. [Abstract] [Full Text] [PDF]

				V. Booth and A. Bose Neural Mechanisms for Generating Rate and Temporal Codes in Model CA3 Pyramidal Cells J Neurophysiol, June 1, 2001; 85(6): 2432 - 2445. [Abstract] [Full Text] [PDF]

				B. Ermentrout, M. Pascal, and B. Gutkin The Effects of Spike Frequency Adaptation and Negative Feedback on the Synchronization of Neural Oscillators Neural Comput., June 1, 2001; 13(6): 1285 - 1310. [Abstract] [Full Text] [PDF]

				A. E. Stewart and R. C. Foehring Effects of Spike Parameters and Neuromodulators on Action Potential Waveform-Induced Calcium Entry Into Pyramidal Neurons J Neurophysiol, April 1, 2001; 85(4): 1412 - 1423. [Abstract] [Full Text] [PDF]

				C. J. Wilson and J. C. Callaway Coupled Oscillator Model of the Dopaminergic Neuron of the Substantia Nigra J Neurophysiol, May 1, 2000; 83(5): 3084 - 3100. [Abstract] [Full Text] [PDF]

				G. D. Smith, C. L. Cox, S. M. Sherman, and J. Rinzel Fourier Analysis of Sinusoidally Driven Thalamocortical Relay Neurons and a Minimal Integrate-and-Fire-or-Burst Model J Neurophysiol, January 1, 2000; 83(1): 588 - 610. [Abstract] [Full Text] [PDF]

				X.-J. Wang Synaptic Basis of Cortical Persistent Activity: the Importance of NMDA Receptors to Working Memory J. Neurosci., November 1, 1999; 19(21): 9587 - 9603. [Abstract] [Full Text] [PDF]

				J. J. Eggermont The Magnitude and Phase of Temporal Modulation Transfer Functions in Cat Auditory Cortex J. Neurosci., April 1, 1999; 19(7): 2780 - 2788. [Abstract] [Full Text] [PDF]

				S. G. Lisberger and J. A. Movshon Visual Motion Analysis for Pursuit Eye Movements in Area MT of Macaque Monkeys J. Neurosci., March 15, 1999; 19(6): 2224 - 2246. [Abstract] [Full Text] [PDF]