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

Poster presentation

Cost of linearization for different time constants

Danielle Morel¹ and William B Levy²

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

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

author email corresponding author email

from Seventeenth Annual Computational Neuroscience Meeting: CNS*2008
Portland, OR, USA. 19–24 July 2008

BMC Neuroscience 2008, 9(Suppl 1):P52doi:10.1186/1471-2202-9-S1-P52

The electronic version of this abstract 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 I_K) 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 (g_A) [2] and the persistent sodium (g_NaP) [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 g_d with a reversal potential of -72 mV; the synaptic conductance g_s with a reversal potential of 0 mV; and a voltage-dependent conductance, either g_NaP or g_A, 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 (g_A or g_NaP), 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.

References

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

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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

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.

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