Origin of heterogeneous spiking patterns in spinal dorsal horn neurons (Balachandar & Prescott 2018)

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Accession:256628
"Neurons are often classified by spiking pattern. Yet, some neurons exhibit distinct patterns under subtly different test conditions, which suggests that they operate near an abrupt transition, or bifurcation. A set of such neurons may exhibit heterogeneous spiking patterns not because of qualitative differences in which ion channels they express, but rather because quantitative differences in expression levels cause neurons to operate on opposite sides of a bifurcation. Neurons in the spinal dorsal horn, for example, respond to somatic current injection with patterns that include tonic, single, gap, delayed and reluctant spiking. It is unclear whether these patterns reflect five cell populations (defined by distinct ion channel expression patterns), heterogeneity within a single population, or some combination thereof. We reproduced all five spiking patterns in a computational model by varying the densities of a low-threshold (KV1-type) potassium conductance and an inactivating (A-type) potassium conductance and found that single, gap, delayed and reluctant spiking arise when the joint probability distribution of those channel densities spans two intersecting bifurcations that divide the parameter space into quadrants, each associated with a different spiking pattern. ... "
Reference:
1 . Balachandar A, Prescott SA (2018) Origin of heterogeneous spiking patterns from continuously distributed ion channel densities: a computational study in spinal dorsal horn neurons. J Physiol 596:1681-1697 [PubMed]
Model Information (Click on a link to find other models with that property)
Model Type:
Brain Region(s)/Organism:
Cell Type(s): Abstract Morris-Lecar neuron; Dorsal Root Ganglion (DRG) cell;
Channel(s): I Na,t; I K; I A; I Potassium;
Gap Junctions:
Receptor(s):
Gene(s):
Transmitter(s):
Simulation Environment: MATLAB;
Model Concept(s): Bifurcation; Activity Patterns; Parameter Fitting; Action Potential Initiation; Action Potentials; Parameter sensitivity;
Implementer(s):
Search NeuronDB for information about:  I Na,t; I A; I K; I Potassium;
TITLE transient potassium (A-) current

COMMENT Equations from
   Huguenard JR, McCormick DA (1992) Simulation of the currents involved
   in rhythmic oscillations in thalamic relay neurons. J Neurophys 68(4):
   1373-1383.

>< Temperature adjusts time constants measured at 23.5 degC.
>< Written by Arthur Houweling for MyFirstNEURON.
ENDCOMMENT

NEURON {
	SUFFIX iA
	USEION k READ ek WRITE ik 
        RANGE gk, minf, mtau, hinf, htau, ik
}

UNITS {
	(mA) = (milliamp)
	(mV) = (millivolt)
}

PARAMETER {
	v		(mV)
	celsius		(degC)
	ek		(mV)
	gk= 3.45e-3	(mho/cm2)
}

STATE { m h }

ASSIGNED {
	ik	(mA/cm2)
	mtau	(ms)
	htau	(ms)
	minf
	hinf
	tadj
}

BREAKPOINT { 
	SOLVE states METHOD cnexp
 	ik= gk* m^4* h* (v- ek)
}

DERIVATIVE states { 
	rates()

	m'= (minf- m)/ mtau
	h'= (hinf- h)/ htau
}

INITIAL { UNITSOFF
	tadj= 3^ ((celsius- 23.5)/ 10)
	rates()
	m= minf
        h= hinf
}

PROCEDURE rates() { 
	minf= 1/ (1+exp(-(v+60)/8.5))
	hinf= 1/ (1+ exp((v+ 78)/ 6))
	mtau= (1/ (exp((v+ 35.82)/ 19.69)+ exp(-(v+ 79.69)/ 12.7))+ 0.37)/ tadj
	if (v< -63) { htau= 1/ (( exp((v+ 46.05)/ 5)+ exp(-(v+ 238.4)/ 37.45)))/ tadj }
	else { htau= 19/ tadj }
} 

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