Computation of Induction Current in a Set of Dendrites

In this paper, the cable model of dendrites have been considered. The dendrites are cylindrical cables of various segments having variable length and reducing radius from start point at synapse and end points. For a particular event signal being received by a neuron in response only some dendrite are active at a particular instance. Initial current signals with different current flows in dendrite are assumed. Due to overlapping and coupling of active dendrite, they induce currents in the dendrite segments of each other at a particular instance. But how these currents are induced in the various segments of active dendrites due to coupling between these dendrites, It is not presented in the literature. Here the paper presents a model for induced currents in active dendrite segments due to mutual coupling at the starting instance of an activity in dendrite. The model is as discussed further.

Authors:

• Sudhakar Tripathi
• R. B. Mishra

Keywords:

• Currents
• dendrites
• induction
• simulation.

References:

[1] W. Rall, Exp. Neurol. 1, 491 (1959).
[2] Koch, C., and A. Zador. "The function of dendritic spines: devices
subserving biochemical rather than electrical computation." Journal of
Neuroscience 13 (1993): 413-413.
[3] Rall, Wilfrid. "Theoretical significance of dendritic trees for neuronal
input-output relations." Neural theory and modeling (1964): 73-97.
[4] Segev, I., J. Rinzel, G. M. Shepherd, and A. Borst. "The theoretical
foundation of dendritic function." Trends in Neurosciences 18, no. 11
(1995): 512-512.
[5] B. I. Henry and T. A. M. Langlands, “Fractional Cable Models for Spiny
Neuronal Dendrites”, Physical Review Letters, PRL 100, 128103 (2008)
The American Physical Society DOI: 10.1103/PhysRevLett.100.128103.
[6] Robert Costalat And Gilbert Chauvet, “Basic Properties Of Electrical
Field Coupling Between Neurons: An Analytical Approach”
Journal: Journal of Integrative Neuroscience, 2008, Volume 07, Number
02, Page 225DOI: 10.1142/S0219635208001836.
[7] Kathryn R. Hedrick and Steven J. Cox, “Structure-preserving model
reduction of passive and quasi-active neurons”, Journal: Journal of
Computational Neuroscience, 2013, Volume 34, Number 1, Page1
DOI: 10.1007/s10827-012-0403-y.
[8] Anthony R. Kellems, Derrick Roos, Nan Xiao and Steven J. Cox, “Lowdimensional,
morphologically accurate models of subthreshold
membrane potential”, Journal: Journal of Computational Neuroscience,
2009, Volume 27, Number 2, Page 161 DOI: 10.1007/s10827-008-0134-
2.
[9] Roman R. Poznanski, “A generalized tapering equivalent cable model
for dendritic neurons”, Bulletin of Mathematical Biology1991, Volume
53, Issue 3, pp 457-467. [10] Rall, Wilfred, and Iden Segev. "Functional possibilities for synapses on
dendrites and on dendritic spines." Synaptic function (1987): 605-636.