Cell signaling/ion channel variability effects on neuronal response (Anderson, Makadia, et al. 2015)

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" ... We evaluated the impact of molecular variability in the expression of cell signaling components and ion channels on electrophysiological excitability and neuromodulation. We employed a computational approach that integrated neuropeptide receptor-mediated signaling with electrophysiology. We simulated a population of neurons in which expression levels of a neuropeptide receptor and multiple ion channels were simultaneously varied within a physiological range. We analyzed the effects of variation on the electrophysiological response to a neuropeptide stimulus. ..."
1 . Anderson WD, Makadia HK, Vadigepalli R (2016) Molecular variability elicits a tunable switch with discrete neuromodulatory response phenotypes. J Comput Neurosci 40:65-82 [PubMed]
Model Information (Click on a link to find other models with that property)
Model Type: Neuron or other electrically excitable cell; Channel/Receptor; Molecular Network;
Brain Region(s)/Organism:
Cell Type(s): Brainstem neuron;
Channel(s): I L high threshold; I A; I K,Ca; I Sodium; I Potassium; Na/Ca exchanger; I_Na,Ca; I_KD;
Gap Junctions:
Receptor(s): AT1R;
Transmitter(s): Angiotensin;
Simulation Environment: MATLAB;
Model Concept(s): Activity Patterns; Action Potentials; Signaling pathways; Spike Frequency Adaptation; Parameter sensitivity; Depolarization block; G-protein coupled; Conductance distributions; Bifurcation; Synaptic noise; Neuromodulation;
Implementer(s): Makadia, Hirenkumar K [hiren.makadia at gmail.com]; Anderson, Warren D [warren.anderson at jefferson.edu]; Vadigepalli, Rajanikanth [Rajanikanth.Vadigepalli at jefferson.edu];
Search NeuronDB for information about:  AT1R; I L high threshold; I A; I K,Ca; I Sodium; I Potassium; Na/Ca exchanger; I_Na,Ca; I_KD; Angiotensin;
function [firing_rate] = runModel(g)
% this function will simulate the signaling-electrophysiology model
% the ode's for the model are in the file odemodel.m
%%%% input: g, a vector of 6 values weighting the reference levels of AT1R
%%%%%%% and five channels: gNa, gKdr, gKa, gKahp, gCaL
%%%%%%% code to run reference simulation:
%%%%%%% [firing_rate] = runModel([1,1,1,1,1,1]); 
%%%% output: firing rate (firing_rate)

options = odeset( 'RelTol', 1e-9, 'AbsTol', 1e-9 );

% simulation time parameters
ti      = -1;               % initial simulation time (s)
dt      = 0.5*10^(-3);      % time step (0.0005 s)
tf      = 300;              % final simulation time (s)
tspan   = ti:dt:tf;         % simulation time span (s)

% load initial conditons
y0      = LoadInitialConditions;

% modify AT1R level according to input g(1)
% these parameters are part of the AT1R complex
y0(94)  = y0(94)*g(1);
y0(116) = y0(116)*g(1);
y0(117) = y0(117)*g(1);
y0(118) = y0(118)*g(1);
y0      = abs(y0);

% load model parameters
% input g is supplied to LoadParameters so that conductances are modified
params  = LoadParameters(g);

% AngII stimulus, applied continuously starting at t = 0
AngII100 = [ti:0.01:(tf+1); ti:0.01:(tf+1)]';
AngII100(AngII100(:,1)<0,2) = 0;
AngII100(AngII100(:,1)>0,2) = 0.1;

% run simuations
[t, y] = ode15s(@odemodel, tspan, y0, options, params, AngII100);

% determine firing rate
[tp_fr fr index]    = freq(t,y(:,179));
firing_rate         = interp1(tp_fr, fr,tspan);

%%%%% error checking %%%%%
% replace firing rate output with zeros simulation errors occur

%%% check the length of the firing rate vector
%%% if too short, replace with zeros
if (length(firing_rate) < length(tspan))
    firing_rate = zeros(length(tspan),1);

%%% check for nan's and replace with zeros
indNAN = find(isnan(firing_rate));
if (isempty(indNAN)>0)
    firing_rate(indNAN) = 0;

xlabel('time (s)');
ylabel('firing rate (Hz)')


function [tp, f, index] = freq(t,x)
% Function to calculate firing frequency
%  inputs: t - time vector
%          x - oscillating function (indices should match t)
%  outputs: tp - time points 
%           f  - corresponding frequency (at that time point)
%           index - indices of the time vector

for i=1:length(t)-1
    if (x(i)<-0&x(i+1)>-0), 
        index = i;    

    f=[f, f(end)];
     tp=[t(1) t(end)];
     f=[0, 0];


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