Inverse stochastic resonance of cerebellar Purkinje cell (Buchin et al. 2016)

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Accession:206364
This code shows the simulations of the adaptive exponential integrate-and-fire model (http://www.scholarpedia.org/article/Adaptive_exponential_integrate-and-fire_model) at different stimulus conditions. The parameters of the model were tuned to the Purkinje cell of cerebellum to reproduce the inhibiion of these cells by noisy current injections. Similar experimental protocols were also applied to the detailed biophysical model of Purkinje cells, de Shutter & Bower (1994) model. The repository also includes the XPPaut version of the model with the corresponding bifurcation analysis.
Reference:
1 . Buchin A, Rieubland S, Häusser M, Gutkin BS, Roth A (2016) Inverse Stochastic Resonance in Cerebellar Purkinje Cells. PLoS Comput Biol 12:e1005000 [PubMed]
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Model Information (Click on a link to find other models with that property)
Model Type: Synapse; Neuron or other electrically excitable cell;
Brain Region(s)/Organism: Cerebellum;
Cell Type(s): Cerebellum Purkinje GABA cell; Abstract integrate-and-fire leaky neuron; Abstract integrate-and-fire adaptive exponential (AdEx) neuron;
Channel(s):
Gap Junctions:
Receptor(s): Gaba; Glutamate;
Gene(s):
Transmitter(s): Glutamate; Gaba;
Simulation Environment: MATLAB; NEURON; XPP;
Model Concept(s): Information transfer; Activity Patterns; Synaptic noise; Oscillations;
Implementer(s): Roth, Arnd ; Buchin, Anatoly [anat.buchin at gmail.com];
Search NeuronDB for information about:  Cerebellum Purkinje GABA cell; Glutamate; Gaba; Gaba; Glutamate;
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BuchinEtAl2016ISR
.git
deShutter-Bower
XPP
README.md
aeif.m
dendrite.m
dendritenodendrite.m
FI.m
hist_v.m
hist2.m
K.m *
matlabserver.m
newaEIF_parameters.xls
nodendrite.m
par.txt
parsave.m
psth.m
psthhold.m
psthprob.m
psthprobnew.m
psthsigma.m
ramp.m
ramp_test.m
ramp2 (rough method).m
ramp2.m
sevencells.m
sigma_opt.m
SNRprocessing.m
test_orn.m
test_orn_par.m
test_prob.m
test_prob_par.m
trajectory.m
trajectory_increase_noise.fig
trajectory_increase_noise.jpg
trajectory_increase_noise.m
trajectory_rand_noise.eps
trajectory_rand_noise.fig
trajectory_rand_noise.jpg
trajectory_rand_noise.m
trajectory_rand_noise.png
v1-v2.mw
                            
N=100; %ms

dt=0.01; %ms

cormax=2;

% cell 1
c=268; 
gl=8.47;
el=-51.31; 
vt=-53.23;
delta=0.85; 
vreset=-60.35;

a=37.79; tauw=20.76; b=441.12;


% dendritic filtering
tauc=0.7039;  % ms
taus=32.91;   % ms
c1=1;         % microF/cm^2
p=0.0759;     % somatic S / total S
gc=p*(p-1)*(c1/taus-c1/tauc)*1000; % 1000, cm^2
G=gl +gc/p/(1-p);       % total conductance: coupling conductance + leak conductance

vspike=0;
Ihold=-500;

% compensation for the dendrite
%Ihold=Ihold/( 1-(1-p)*c1*1000/G*(1/tauc-1/taus) );

sigma=0;
corr=cormax;
n_spike=0;
temp=0;


% start from spiking state
v(1)=-50;
w(1)=0;

vd(1)=-50;
V(1)=0;           % V is vs=vd, V=vs-vd
wd(1)=0;

vn(1)=-50;
wn(1)=0;

t(1)=0;
input(1)=Ihold;

INT(1)=0;        % dendrite filter
 
for i=2:1:round(N/dt)
     t(i)=(i-1)*dt;    
     
temp=temp-dt/corr*temp + sqrt(2*dt/corr)*random('normal',0,1,1,1);
input(i)=Ihold;
%+ temp*sigma;

 % dendrite diff equation
 vd(i)=dt/c*( -gl*(vd(i-1)-el) +gl*delta*exp((vd(i-1)-vt)/delta) -wd(i-1) + input(i) -gc/p*V(i-1) ) + vd(i-1);
 V(i)=dt/c*( -G*V(i-1) +input(i) ) + V(i-1);
 wd(i)=dt/tauw*(a*(vd(i-1)-el)-wd(i-1)) + wd(i-1);

 % dendrite integral
 %INT(i)=-gc/p*exp(-t(i)*G/c)*trapz(t,input.*exp(t*G/c))/c; % dendrite integral
 %v(i)=dt/c*(-gl*(v(i-1)-el)+gl*delta*exp((v(i-1)-vt)/delta)-w(i-1)+input(i)+INT(i)) + v(i-1);
 %w(i)=dt/tauw*(a*(v(i-1)-el)-w(i-1)) + w(i-1);
 
 % no dendrite *( 1-(1-p)*c1*1000/G*(1/tauc-1/taus) )
 vn(i)=dt/c*(-gl*(vn(i-1)-el)+gl*delta*exp((vn(i-1)-vt)/delta)-wn(i-1)+input(i)*( 1-(1-p)*c1*1000/G*(1/tauc-1/taus) )) + vn(i-1);
 wn(i)=dt/tauw*(a*(vn(i-1)-el)-wn(i-1)) + wn(i-1);
 
          %   if  v(i)>=vspike
          %       v(i-1)=0;            % add sticks to the previous step     
          %       v(i)=vreset;
          %       w(i)=w(i) + b;
          %   end

             if  vd(i)>=vspike
                 vd(i-1)=0;            % add sticks to the previous step     
                 vd(i)=vreset;
                 wd(i)=wd(i) + b;
             end

              if vn(i)>=vspike
                 vn(i-1)=0;            % add sticks to the previous step     
                 vn(i)=vreset;
                 wn(i)=wn(i) + b;
             end
             
end

plot(t,vd,t,vn);
legend('v','vd','vn');
xlabel('time, ms');
ylabel('V, mV');