Email updates

Keep up to date with the latest news and content from BMC Neuroscience and BioMed Central.

This article is part of the supplement: Seventeenth Annual Computational Neuroscience Meeting: CNS*2008

Open Access Poster presentation

Cost of linearization for different time constants

Danielle Morel1 and William B Levy2*

Author Affiliations

1 Department of Physics and Astronomy, James Madison University, Harrisonburg, VA 22807, USA

2 Department of Neurosurgery, University of Virginia, Charlottesville, VA 22908, USA

For all author emails, please log on.

BMC Neuroscience 2008, 9(Suppl 1):P52  doi:10.1186/1471-2202-9-S1-P52

The electronic version of this article is the complete one and can be found online at: http://www.biomedcentral.com/1471-2202/9/S1/P52


Published:11 July 2008

© 2008 Morel and Levy; licensee BioMed Central Ltd.

Poster presentation

Persistent sodium and A-type potassium conductances serve as linearizing mechanisms over limited and different voltage ranges. This research investigates the relationship between time constants and the metabolic cost (here total potassium current IK) of such linearization. This metabolic cost is a window into explaining the 40% energy use by postsynaptic elements of the brain [1].

We consider neurons under constant synaptic bombardment spending much of their time in a range of -62 to -58 mV with threshold around -55 to -52 mV. For this subthreshold voltage range, the A-type potassium (gA) [2] and the persistent sodium (gNaP) [3,4] are the most relevant linearizing conductances. Here 'linear' means that, within a certain voltage range, each additional active synapse makes the same depolarizing contribution, in contrast to the sublinear contributions occurring in purely passive dendrites.

Steady-state voltages and currents are evaluated for a single-compartment dendritic model under synaptic bombardment. There are three conductances in each analysis: the resting dendritic conductance gd with a reversal potential of -72 mV; the synaptic conductance gs with a reversal potential of 0 mV; and a voltage-dependent conductance, either gNaP or gA, with reversal potentials of +55 mV and -95 mV respectively. The assumed capacitance of this collapsed dendritic field is 1 nF.

Table 1 shows that, in the presence of an appropriate amount of active conductance (gA or gNaP), there is 1) a constant voltage range of linearization across time constants and 2) there exists a direct relationship between time constant and total cost. Indeed as the time constant speeds up, the metabolic cost in terms of coulombs/sec increases as dictated by higher total conductance. To conclude: 1) faster computing is linearly increasing in metabolic cost; 2) changing inhibitory tone appears to require dynamic control of the available linearizing conductance if threshold is unchanged.

Table 1. Sample results

References

  1. Attwell D, Laughlin SB: An energy budget for signalling in the grey matter of the brain.

    J Cereb Blood Flow Metab 2001, 21(10):1133-1145. PubMed Abstract | Publisher Full Text OpenURL

  2. Hoffman DA, Magee JC, Colbert CM, Johnston D: K+ channel regulation of signal propagation in dendrites of hippocampal pyramidal neurons.

    Nature 1997, 387(6636):869-875. PubMed Abstract | Publisher Full Text OpenURL

  3. Magistretti J, Alonso A: Biophysical properties and slow voltage-dependent inactivation of a sustained sodium Current in entorhinal cortex layer-II principal neurons.

    J Gen Physiol 1999, 114(4):491-509. PubMed Abstract | Publisher Full Text | PubMed Central Full Text OpenURL

  4. Agrawal N, Hamam BN, Magistretti J, Alonso A, Ragsdale DS: Persistent sodium channel activity mediates subthreshold membrane potential oscillations and low-threshold spikes in rat entorhinal cortex layer V neurons.

    Neuroscience 2001, 102(1):53-64. PubMed Abstract | Publisher Full Text OpenURL