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This article is part of the supplement: Twenty First Annual Computational Neuroscience Meeting: CNS*2012

Open Access Poster presentation

Modeling and prediction of conduction delay in an unmyelinated axon

Yang Zhang1*, Dirk Bucher2 and Farzan Nadim1

Author Affiliations

1 Dept Math Sci and Dept Biol Sci, New Jersey Institute of Technology, Newark, NJ, 07102, USA

2 The Whitney Lab for Marine Bioscience and Dept of Neuroscience, University of Florida, St. Augustine, FL, 32080, USA

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BMC Neuroscience 2012, 13(Suppl 1):P81  doi:10.1186/1471-2202-13-S1-P81

The electronic version of this article is the complete one and can be found online at: http://www.biomedcentral.com/1471-2202/13/S1/P81


Published:16 July 2012

© 2012 Zhang et al; licensee BioMed Central Ltd.

This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Poster presentation

Conduction delay in axons is a function of the axon morphology, passive membrane properties and voltage-gated ionic currents. Although conduction delay is usually assumed to be constant, indicating perfect temporal fidelity, recent work has shown that the delay of each action potential depends on the prior short- and long-term history of activity in the axon [1]. Violation of temporal fidelity leads to substantial variations in inter-spike intervals which has potential impact on temporal neural activity.

In experiments using the motor axon of the pyloric dilator (PD) neuron of the lobster, H. americanus, we measured conduction delay using Poisson random stimuli applied at different mean rates [2]. These measurements showed that the mean value and the variance of conduction delay increases as a function of stimulus time until these values reach a steady state at about 5 minutes post-stimulation. Even at steady state, conduction delay showed a non-monotonic relationship with stimulus frequency (finst): it was higher at small or large values of finst but has a minimum at finst~45 Hz. Moreover, bath application of dopamine drastically improved the temporal fidelity of conduction delay.

We have constructed a conductance-based model of the PD axon to examine the role of different ionic currents in shaping the history dependence of conduction delay. In addition to the standard Hodgkin-Huxley currents, this model includes a transient potassium current IA and a hyperpolarization activated inward current Ih, both of which have been characterized in this axon. The main effect of dopamine in the biological axon is an increase of Ih which counteracts the activity-dependent hyperpolarization [3], mimicked by adding a Na+/K+ pump in the model.

We find that the Na+/K+ pump enables the model to reproduce the long-term history dependence observed in the biological PD axon. A pump current with a slow time constant (τ=90 sec) results in a slow increase of the mean and CV of conduction delay with stimulus time (Fig. 1A), and a non-monotonic relationship between conduction delay and finst (Fig. 1B), as observed experimentally [2]. Additionally, as in the experiments, temporal fidelity is improved as Ih is increased.

thumbnailFigure 1. Changes in action potential delay in the model axon in response to 5 mins of Poisson stimulation (mean rate 10 Hz). Compare with experimental data [2]. A. Both mean and CV of conduction delay increase slowly in response to activity. B. Delay (fifth minute) shows a non-monotonic relationship with stimulus frequency.

Action potential conduction velocity can be approximated by (d=axon diam, R*=total memb resistance/unit area at peak, Ra=axial resistivity, Cm=capacitance/unit area [4]. Although this equation accurately predicts the conduction velocity of a single action potential in our model, it fails to the variations in conduction velocity in the presence of the history-dependent effects. This discrepancy is partly due to non-uniform conduction velocity along the axon when active at high rates. We revise the formula to predict the relationship between the conduction delay and total membrane resistance at the action potential peak.

Acknowledgements

Supported by NIH MH60605 and NS58825

References

  1. Ballo AW, Bucher D: Complex intrinsic membrane properties and dopamine shape spiking activity in a motor axon.

    J Neurosci 2009, 29(16):5062-5074. PubMed Abstract | Publisher Full Text | PubMed Central Full Text OpenURL

  2. Ballo AW, Nadim F, Bucher D: Dopamine modulation of Ih improves the temporal fidelity of spike propagation in an unmyelinated axon.

    J Neurosci 2012, 32(15):5106-5119. PubMed Abstract | Publisher Full Text OpenURL

  3. Ballo AW, Keene JC, Troy PF, Goeritz ML, Nadim F, Bucher D: Dopamine modulates Ih in a motor axon.

    J Neurosci 2010, 30:8425-8434. PubMed Abstract | Publisher Full Text | PubMed Central Full Text OpenURL

  4. Matsumoto G, Tasaki I: A study of conduction velocity in nonmyelinated nerve fibers.

    Biophys J 1977, 20:1-13. PubMed Abstract | Publisher Full Text | PubMed Central Full Text OpenURL