Ephaptic interactions in olfactory nerve (Bokil et al 2001)

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Bokil, H., Laaris, N., Blinder, K., Ennis, M., and Keller, A. (2001) Ephaptic interactions in the mammalian olfactory system. J. Neurosci. 21:RC173(1-5)
1 . Bokil H, Laaris N, Blinder K, Ennis M, Keller A (2001) Ephaptic interactions in the mammalian olfactory system. J Neurosci 21:RC173 [PubMed]
Model Information (Click on a link to find other models with that property)
Model Type: Axon; Extracellular;
Brain Region(s)/Organism:
Cell Type(s): Olfactory receptor GLU cell;
Gap Junctions:
Simulation Environment: NEURON;
Model Concept(s): Axonal Action Potentials; Extracellular Fields; Ephaptic coupling; Olfaction;
Implementer(s): Hines, Michael [Michael.Hines at Yale.edu];
Search NeuronDB for information about:  Olfactory receptor GLU cell;
// Automatically display figure 2B and provide a
// Grapher for generating curves for figure 2A.
Graph[1].exec_menu("Keep Lines")
Graph[1].exec_menu("Keep Lines")
{N=19 extcelnet()}

// This simulation seems to produce different quantitative (but same
// qualitative) results
// from those shown in Fig 2B with regard to height at x=1000 and relative minima
// of unstimulated axon (x=~1100).
// The simulation output has been verified to be a linear superposition
// of two exponentials with lambda1 and lambda2 given in the paper.
// The simulation output for N=2 is best fit by
// stimulated a1*exp(-($1-1000)/l1)+ a2*exp(-($1-1000)/l2)
// unstimulated a1*exp(-($1-1000)/l1) - a2*exp(-($1-1000)/l2)
//  "a1", 0.818485
//  "a2", 0.181507
//  "l1", 28.359
//  "l2", 129.129
This is consistent with a private communication from
Hemant Bokil <bokil@postbox.div111.lucent.com>
I checked my notes for the anaytical calculations and the complete
formulae are 
V_A(x)=0.5*(1-f)*sqrt(r_i * r_m)*exp(-x/l2)+0.5*f*sqrt(r_i*r_m)

where l1 and l2 are as listed in the paper. For plotting 2b, i divided
both these expressions by V_A(0) and this leads to amplitudes of 0.8207
and -0.1791, for V_B(x) (with f=0.5; 2 neurons), very close to your
answers (perhaps a rounding error ?).

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