Abstract
We investigate the effects of the stochastic nature of ion channels on the faithfulness, precision and reproducibility of electrical signal transmission in weakly active, dendritic membrane under in vitro conditions. The properties of forward and backpropagating action potentials (BPAPs) in the dendritic tree of pyramidal cells are the subject of intense empirical work and theoretical speculation (Larkum et al., 1999; Zhu, 2000; Larkum et al., 2001; Larkum and Zhu, 2002; Schaefer et al., 2003; Williams, 2004; Waters et al., 2005). We numerically simulate the effects of stochastic ion channels on the forward and backward propagation of dendritic spikes in Monte-Carlo simulations on a reconstructed layer 5 pyramidal neuron. We report that in most instances there is little variation in timing or amplitude for a single BPAP, while variable backpropagation can occur for trains of action potentials. Additionally, we find that the generation and forward propagation of dendritic Ca2+ spikes are susceptible to channel variability. This indicates limitations on computations that depend on the precise timing of Ca2+ spikes.
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Abbreviations
- BAC:
-
Backpropagation activated Ca2+ spike
- AP:
-
Action potential
- BPAP:
-
Backpropagating action potential
- ISI:
-
Interstimulus interval
- rp :
-
Reference point
References
Ariav G, Polsky A, Schiller J (2003) Submillisecond precision of the input-output transformation function mediated by fast sodium dendritic spikes in basal dendrites of CA1 pyramidal neurons. J. Neurosci. 23: 7750–7758.
Bernard C, Johnston D (2003) Distance-dependent modifiable threshold for action potential back-propagation in hippocampal dendrites. J. Neurophysiol. 90: 1807–1816.
Buzsaki G, Penttonen M, Nadasdy Z, Bragin A (1996) Pattern and inhibition-dependent invasion of pyramidal cell dendrites by fast spikes in the hippocampus in vivo. Proc. Natl. Acad. Sci. USA 93: 9921–9925.
Chow CC, White JA (1996) Spontaneous action potentials due to channel fluctuations. Biophys. J. 71: 3013–3021.
Colbert CM, Magee JC, Hoffman DA, Johnston D (1997) Slow recovery from inactivation of Na+ channels underlies the activity-dependent attenuation of dendritic action potentials in hippocampal CA1 pyramidal neurons. J. Neurosci. 17: 6512–6521.
Debanne D (2004) Information processing in the axon. Nat. Rev. Neurosci. 5: 304–316.
DeFelice LJ (1981) Introduction to Membrane Noise. Plenum Press, New York.
Destexhe A, Rudolph M, Pare D (2003) The high-conductance state of neocortical neurons in vivo. Nat. Rev. Neurosci. 4: 739–751.
Diba K, Lester HA, Koch C (2004) Intrinsic noise in cultured hippocampal neurons: experiment and modeling. J. Neurosci. 24: 9723–9733.
Faisal AA, Laughlin SB (2002) Channel noise limits the minimum diameter of axons. Journal of Physiology-London 543: 21P–21P.
Golding NL, Spruston N (1998) Dendritic sodium spikes are variable triggers of axonal action potentials in hippocampal CA1 pyramidal neurons. Neuron 21: 1189–1200.
Golding NL, Kath WL, Spruston N (2001) Dichotomy of action-potential backpropagation in CA1 pyramidal neuron dendrites. J. Neurophysiol. 86: 2998–3010.
Hille B (2001) Ion Channels of Excitable Membranes, 3rd edn. Sinauer, Sunderland, Mass.
Hines ML, Carnevale NT (1997) The NEURON simulation environment. Neural Comput. 9: 1179–1209.
Hodgkin AL, Huxley AF (1952) A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol. 117: 500–544.
Hoffman DA, Magee JC, Colbert CM, Johnston D (1997) K+ channel regulation of signal propagation in dendrites of hippocampal pyramidal neurons. Nature 387: 869–875.
Horikawa Y (1991) Noise effects on spike propagation in the stochastic Hodgkin-Huxley models. Biol. Cybern. 66: 19–25.
Horikawa Y (1993) Simulation study on effects of channel noise on differential conduction at an axon branch. Biophys. J. 65: 680–686.
Jacobson GA, Diba K, Yaron-Jakoubovitch A, Oz Y, Koch C, Segev I, Yarom Y (2005) Subthreshold voltage noise of rat neocortical pyramidal neurones. J. Physiol. 564: 145–160.
Johnston D, Wu SM-S (1995) Foundations of Cellular Neurophysiology. MIT Press, Cambridge, Mass.
Johnston D, Hoffman DA, Colbert CM, Magee JC (1999) Regulation of back-propagating action potentials in hippocampal neurons. Curr. Opin. Neurobiol. 9: 288–292.
Jones SW (2003) Calcium channels: unanswered questions. J. Bioenerg. Biomembr. 35: 461–475.
Jung HY, Mickus T, Spruston N (1997) Prolonged sodium channel inactivation contributes to dendritic action potential attenuation in hippocampal pyramidal neurons. J. Neurosci. 17: 6639–6646.
Kang J, Huguenard JR, Prince DA (1996) Development of BK channels in neocortical pyramidal neurons. J. Neurophysiol. 76: 188–198.
Kim HG, Connors BW (1993) Apical dendrites of the neocortex: correlation between sodium- and calcium-dependent spiking and pyramidal cell morphology. J. Neurosci. 13: 5301–5311.
Kuriscak E, Trojan S, Wunsch Z (2002) Model of spike propagation reliability along the myelinated axon corrupted by axonal intrinsic noise sources. Physiol. Res. 51: 205–215.
Larkum ME, Zhu JJ (2002) Signaling of layer 1 and whisker-evoked Ca2+ and Na+ action potentials in distal and terminal dendrites of rat neocortical pyramidal neurons in vitro and in vivo. J. Neurosci. 22: 6991–7005.
Larkum ME, Zhu JJ, Sakmann B (1999) A new cellular mechanism for coupling inputs arriving at different cortical layers. Nature 398: 338–341.
Larkum ME, Zhu JJ, Sakmann B (2001) Dendritic mechanisms underlying the coupling of the dendritic with the axonal action potential initiation zone of adult rat layer 5 pyramidal neurons. J. Physiol. 533: 447–466.
Luscher C, Streit J, Lipp P, Luscher HR (1994) Action potential propagation through embryonic dorsal root ganglion cells in culture. II. Decrease of conduction reliability during repetitive stimulation. J. Neurophysiol. 72: 634–643.
Mainen ZF, Sejnowski TJ (1995) Reliability of spike timing in neocortical neurons. Science 268: 1503–1506.
Mainen ZF, Sejnowski TJ (1996) Influence of dendritic structure on firing pattern in model neocortical neurons. Nature 382: 363–366.
Mainen ZF, Sejnowski TJ (1998) Modeling active dendritic processes in pyramidal neurons. In: Koch C, Segev I, eds. Methods in Neuronal Modeling: From Ions to Networks, 2nd ed. MIT Press, Cambridge, MA, pp. 171–210.
Manwani A, Koch C (1999) Detecting and estimating signals in noisy cable structures, II: information theoretical analysis. Neural Comput. 11: 1831–1873.
Migliore M, Hoffman DA, Magee JC, Johnston D (1999) Role of an A-type K+ conductance in the back-propagation of action potentials in the dendrites of hippocampal pyramidal neurons. J. Comput. Neurosci. 7: 5–15.
Press WH (1992) Numerical recipes in C: The art of scientific computing. Cambridge University Press, New York.
Rudolph M, Destexhe A (2003) A fast-conducting, stochastic integrative mode for neocortical neurons in vivo. J. Neurosci. 23: 2466–2476.
Schaefer AT, Larkum ME, Sakmann B, Roth A (2003) Coincidence detection in pyramidal neurons is tuned by their dendritic branching pattern. J. Neurophysiol. 89: 3143–3154.
Schneidman E, Freedman B, Segev I (1998) Ion channel stochasticity may be critical in determining the reliability and precision of spike timing. Neural Comput. 10: 1679–1703.
Skaugen E, Walloe L (1979) Firing behaviour in a stochastic nerve membrane model based upon the Hodgkin-Huxley equations. Acta Physiol. Scand 107: 343–363.
Spruston N, Schiller Y, Stuart G, Sakmann B (1995) Activity-dependent action potential invasion and calcium influx into hippocampal CA1 dendrites. Science 268: 297–300.
Steinmetz PN, Manwani A, Koch C, London M, Segev I (2000) Subthreshold voltage noise due to channel fluctuations in active neuronal membranes. J. Comput. Neurosci, 9: 133–148.
Steriade M, Nunez A, Amzica F (1993) A novel slow (<1 Hz) oscillation of neocortical neurons in vivo: depolarizing and hyperpolarizing components. J. Neurosci. 13: 3252–3265.
Stuart G, Spruston N, Sakmann B, Hausser M (1997) Action potential initiation and backpropagation in neurons of the mammalian CNS. Trends Neurosci 20: 125–131.
van Rossum MC, O’Brien BJ, Smith RG (2003) Effects of noise on the spike timing precision of retinal ganglion cells. J. Neurophysiol. 89: 2406–2419.
Vetter P, Roth A, Hausser M (2001) Propagation of action potentials in dendrites depends on dendritic morphology. J. Neurophysiol. 85: 926–937.
Waters J, Helmchen F (2004) Boosting of action potential backpropagation by neocortical network activity in vivo. J. Neurosci. 24: 11127–11136.
Waters J, Schaefer A, Sakmann B (2005) Backpropagating action potentials in neurones: measurement, mechanisms and potential functions. Prog. Biophys. Mol. Biol. 87: 145–170.
Waters J, Larkum M, Sakmann B, Helmchen F (2003) Supralinear Ca2+ influx into dendritic tufts of layer 2/3 neocortical pyramidal neurons in vitro and in vivo. J. Neurosci. 23: 8558–8567.
White JA, Rubinstein JT, Kay AR (2000) Channel noise in neurons. Trends Neurosci. 23: 131–137.
White JA, Klink R, Alonso A, Kay AR (1998) Noise from voltage-gated ion channels may influence neuronal dynamics in the entorhinal cortex. J. Neurophysiol. 80: 262–269.
Williams SR (2004) Spatial compartmentalization and functional impact of conductance in pyramidal neurons. Nat. Neurosci. 7: 961–967.
Zhu JJ (2000) Maturation of layer 5 neocortical pyramidal neurons: amplifying salient layer 1 and layer 4 inputs by Ca2+ action potentials in adult rat tuft dendrites. J. Physiol. 526 Pt3: 571–587.
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Diba, K., Koch, C. & Segev, I. Spike propagation in dendrites with stochastic ion channels. J Comput Neurosci 20, 77–84 (2006). https://doi.org/10.1007/s10870-006-4770-0
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DOI: https://doi.org/10.1007/s10870-006-4770-0