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

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"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. ... "
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]
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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:
Simulation Environment: MATLAB;
Model Concept(s): Bifurcation; Activity Patterns; Parameter Fitting; Action Potential Initiation; Action Potentials; Parameter sensitivity;
Search NeuronDB for information about:  I Na,t; I A; I K; I Potassium;
%Arjun Balachandar 2016
%Bivariate Normal Distribution
%Function defining a bivariate normal distribution (BND) with set describing
%parameters, used by fit_bivariate and fit_bivariate_sigma

function [fun] = bivariable_gaussian(p,x0,y0,sigma_x,sigma_y)
    A = 1/(2*pi*sigma_x*sigma_y*(1-p^2)^0.5);

    a = 1/(sigma_x^2);
    b = p/(sigma_x*sigma_y);
    c = 1/(sigma_y^2);

    %BND equation:
    fun = @(x,y) A*exp( - (a*(x-x0).^2 - 2*b*(x-x0).*(y-y0) + c*(y-y0).^2)/(2*(1-p^2)) );