% daspnet.m: Spiking network with DA-modulated STDP. Based on spnet.m
% Created by Eugene M.Izhikevich. November 3, 2004
%
% This program reproduces the experiment in Fig.1 in
% Izhikevich E.M. (2007) Solving the Distal Reward Problem through Linkage
% of STDP and Dopamine Signaling. Cerebral Cortex, 10.1093/cercor/bhl152
%
% n1 - the presynaptic neuron. syn is the synapse to be reinforced.
% Plot: top - spike raster. Bottom left - synaptic strength (blue), the
% eligibility trace (green), and the rewards (red x). Bottom right - the
% distribution of synaptic weights with the chosen synapse marked by red dot.
M=100; % number of synapses per neuron
D=1; % maximal conduction delay
% excitatory neurons % inhibitory neurons % total number
Ne=800; Ni=200; N=Ne+Ni;
a=[0.02*ones(Ne,1); 0.1*ones(Ni,1)];
d=[ 8*ones(Ne,1); 2*ones(Ni,1)];
sm=4; % maximal synaptic strength
post=ceil([N*rand(Ne,M);Ne*rand(Ni,M)]);
s=[ones(Ne,M);-ones(Ni,M)]; % synaptic weights
sd=zeros(N,M); % their derivatives
for i=1:N
if i<=Ne
for j=1:D
delays{i,j}=M/D*(j-1)+(1:M/D);
end;
else
delays{i,1}=1:M;
end;
pre{i}=find(post==i&s>0); % pre excitatory neurons
aux{i}=N*(D-1-ceil(ceil(pre{i}/N)/(M/D)))+1+mod(pre{i}-1,N);
end;
STDP = zeros(N,1001+D);
v = -65*ones(N,1); % initial values
u = 0.2.*v; % initial values
firings=[-D 0]; % spike timings
%---------------
% new stuff related to DA-STDP
T=3600; % the duration of experiment
DA=0; % level of dopamine above the baseline
rew=[];
n1=1; % presynaptic neuron
syn=1; % the synapse number to the postsynaptic neuron
n2=post(n1,syn) % postsynaptic neuron
s(n1,syn)=0; % start with 0 value
interval = 20; % the coincidence interval for n1 and n2
n1f=-100; % the last spike of n1
n2f=[]; % the last spike of n2
shist=zeros(1000*T,2);
%--------------
for sec=1:T % simulation of 1 day
for t=1:1000 % simulation of 1 sec
I=13*(rand(N,1)-0.5); % random thalamic input
fired = find(v>=30); % indices of fired neurons
v(fired)=-65;
u(fired)=u(fired)+d(fired);
STDP(fired,t+D)=0.1;
for k=1:length(fired)
sd(pre{fired(k)})=sd(pre{fired(k)})+STDP(N*t+aux{fired(k)});
end;
firings=[firings;t*ones(length(fired),1),fired];
k=size(firings,1);
while firings(k,1)>t-D
del=delays{firings(k,2),t-firings(k,1)+1};
ind = post(firings(k,2),del);
I(ind)=I(ind)+s(firings(k,2), del)';
sd(firings(k,2),del)=sd(firings(k,2),del)-1.5*STDP(ind,t+D)';
k=k-1;
end;
v=v+0.5*((0.04*v+5).*v+140-u+I); % for numerical
v=v+0.5*((0.04*v+5).*v+140-u+I); % stability time
u=u+a.*(0.2*v-u); % step is 0.5 ms
STDP(:,t+D+1)=0.95*STDP(:,t+D); % tau = 20 ms
DA=DA*0.995;
if (mod(t,10)==0)
s(1:Ne,:)=max(0,min(sm,s(1:Ne,:)+(0.002+DA)*sd(1:Ne,:)));
sd=0.99*sd;
end;
if any(fired==n1)
n1f=[n1f,sec*1000+t];
end
if any(fired==n2)
n2f=[n2f,sec*1000+t];
if (sec*1000+t-n1f(end)<interval) & (n2f(end)>n1f(end))
rew=[rew,sec*1000+t+1000+ceil(2000*rand)];
end;
end
if any(rew==sec*1000+t)
DA=DA+0.5;
end;
shist(sec*1000+t,:)=[s(n1,syn),sd(n1,syn)];
end;
% ---- plot -------
subplot(2,1,1)
plot(firings(:,1),firings(:,2),'.');
axis([0 1000 0 N]);
subplot(2,2,3);
plot(0.001*(1:(sec*1000+t)),shist(1:sec*1000+t,:), 0.001*rew,0*rew,'rx');
subplot(2,2,4);
hist(s(find(s>0)),sm*(0.01:0.01:1)); % only excitatory synapses
hold on; plot(s(n1,syn),0,'r.'); hold off;
drawnow;
% ---- end plot ------
STDP(:,1:D+1)=STDP(:,1001:1001+D);
ind = find(firings(:,1) > 1001-D);
firings=[-D 0;firings(ind,1)-1000,firings(ind,2)];
end;