Exponential integrate and fire model from LIF model

Hello!

How can I create a simple synapse model between 2 neurons? So far I have the code of the LIF model, and I'm supposed to connect two of these neurons to create a synapse and have a version of facilitation and one of depression (short-term plasticity).

I really have no idea how to start from there. I'm supposed to used the equations in here 3.1 Synapses | Neuronal Dynamics online book (epfl.ch) part 3.1.3 to obtain the graphs of fig. 3.3. I'm getting really frustraded cause I'm not very good at matlab and don't even know where to start. The LIF model itself took me a whole bunch of time. Any help would be very appreciated.

My code of the LIF model is as follows:

%Parameters

Cm = 200; % [nF] membrane capacitance

Rm = 10*1e-3; % [MOhm] resistance

tau = Cm * Rm; %[ms] time constant

Erest = - 70; % [mV] resting potential

current = 3*1e3; %[nA] injected current

time_len = 10; % [ms] time duration for plotting

dt = 0.001; % [ms] time step

timevec = 0:dt:time_len; % time vector with original time step

Istim = zeros(1,length(timevec)); % Istim vector with 1ms time step

Istim(1:end) = current;

Vth = -50; %[mV]

%% stimulating

Vm = Erest;

vecVm = zeros(1,length(timevec)+1); % vector of membrane potential

vecVm(1) = Erest;

i = 1;

for t = 1:(length(timevec)-1) % loop through time vector

dVm = (1/Cm * Istim(t) + 1/tau * (Erest-Vm))*dt;

% calculate derivative of each time

% step

Vm = Vm + dVm; % adding differential to update Vm

if Vm >= Vth % elicite spikes

Vm = Erest;

tsp(i) = t;

i = i+1;

end

vecVm(t+1) = Vm;

end

Plot Vm(t):

%% plotting

num_sp = length(tsp);

figure

plot(timevec,vecVm(1:end-1),'k','linewidth',1.4)

hold on

for k = 1:num_sp

xline(tsp(k)*dt,'k','linewidth',1.4)

end

title('simulated membrane voltage','fontsize',16)

ylabel('membrane voltage [mV]')

xlabel('time [ms]')

set(gca,'ylim',[-70 0])