# Neural Networks B, SS06 1

UA Dr. Robert Legenstein, WiMAus Prashant Joshi, M.S.

Institute for Theoretical Computer Science
Technische Universität Graz
A-8010 Graz, Austria
{legi, joshi}@igi.tugraz.at

 NACHNAME Vorname Matrikelnmr Teammitglieder

# Exercise 7: The HH Model

NOTE: You can download this exercise in pdf or postscript(ps) format here.

In this task you have to analyze the action-potential generation mechanism of the Hodgkin-Huxley(HH) model neuron for various current injections.

The Matlab program hh_model.m simulates a HH neuron.

• Find the minimum current (by only varying the variable ) that is required to generate a single action potential.
• Change so that the neuron starts to fire repetitively throughout the simulation. We will call this current as . What is the minimum value for ? Is this transition a sharp one?
• Inject a negative current into the model(onset time 5ms, onset amplitude -100nA, duration 5ms). What happens?
• The gain function of a neuron is defined as the plot between the mean-firing rate(y-axis) and the input current (x-axis). Plot the gain function for a HH neuron, and an Integrate and fire neuron 2 in the range and compare them.

# Matlab Code

% hh_neuron implements a HH-Model with current injection Iext
clear all;
csim('destroy');

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% parameters
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

dtSim = 1e-5;             % integration time constant for simulation
dtRec = 1e-4;             % intervals for recording traces
Tsim  = 1.0;              % simulation time

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% define the input Iext
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

T1 = 5e-3;               % onset of stimulus [sec]
I0 = 1;                  % DC current injection [nA]

% make the current with a resolution of dtSim
Iext = [zeros(1,ceil(T1/dtSim)) I0*1e-9*ones(1,ceil((Tsim-T1)/dtSim)+1)];

% the time base for the input Iext and the simulation
t=[1:length(Iext)]*dtSim;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% set up the model
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% create the HHNeuron
hhn = csim('create','HHNeuron');

syn=csim('create','StaticAnalogSynapse');

% connect the input neuron to the HH-Neuron
csim('connect',hhn,ain,syn);

% record some values during the simulation
rec=csim('create','MexRecorder');
csim('set',rec,'dt',dtRec);

% tell the recorder to record Vm and the spikes
csim('connect',rec,hhn,'Vm');
csim('connect',rec,hhn,'spikes');

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% simulate model with Iext as input
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% set parameters regarding the simulation control
csim('set','dt',dtSim);              % the integration time constant

% define an input signal (Iext) for the simulator
input(1).spiking = 0;
input(1).dt      = dtSim;
input(1).idx     = ain;
input(1).data    = Iext;

% set the integration time constant
csim('set','dt',dtSim);

% set time to 0.0
csim('reset');

% run simulation for Tsim seconds
csim('simulate',Tsim,input);

% get the relevant traces
output=csim('get',rec,'traces');
Vm      = output.channel(1).data;
spikes  = output.channel(2).data;
nSpikes = length(spikes);

% time base for recorded traces
trec    = [dtRec:dtRec:Tsim];

% print number of spikes
fprintf('%i spikes / %g sec n',nSpikes,Tsim);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% plot the results
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

figure(1); clf reset;

% plot input current
subplot(3,1,1);
plot(t,Iext);
xlabel('time [sec]');
ylabel('Iext [nA]');
title('injected current','Fontweight','bold');
set(gca,'Xlim',[0 Tsim]);

% plot membrane voltage
subplot(3,1,2);
plot(trec,Vm,'r'); hold on;
xlabel('time [sec]');
ylabel('Vm [V]');
title('membrane Voltage','Fontweight','bold');
axis tight

% plot the spikes
subplot(3,1,3);
line([spikes;spikes],[0.03; 0.00]*ones(1,length(spikes)),...
'Color','k','Linewidth',1.5);
hold on;
xlabel('time [sec]');
ylabel('Spikes');
axis([0 1 0 0.1]) ;

Neural Networks B, SS06 1

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