Inhibitory plasticity balances excitation and inhibition (Vogels et al. 2011)

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"Cortical neurons receive balanced excitatory and inhibitory synaptic currents. Such a balance could be established and maintained in an experience-dependent manner by synaptic plasticity at inhibitory synapses. We show that this mechanism provides an explanation for the sparse firing patterns observed in response to natural stimuli and fits well with a recently observed interaction of excitatory and inhibitory receptive field plasticity. ... Our results suggest an essential role of inhibitory plasticity in the formation and maintenance of functional cortical circuitry."
1 . Vogels TP, Sprekeler H, Zenke F, Clopath C, Gerstner W (2011) Inhibitory plasticity balances excitation and inhibition in sensory pathways and memory networks. Science 334:1569-73 [PubMed]
Model Information (Click on a link to find other models with that property)
Model Type: Neuron or other electrically excitable cell;
Brain Region(s)/Organism: Neocortex;
Cell Type(s):
Gap Junctions:
Simulation Environment: MATLAB; Brian; Python;
Model Concept(s): Synaptic Plasticity; STDP;
Implementer(s): Zenke, Friedemann [friedemann.zenke at]; Vogels, Tim [tim.vogels at];
clear all
close all

%% Figure dimensions

    set(gcf,'PaperUnits','centimeters') %Setting the units of the figure on paper to centimeters.
    xSize = 13; 
    ySize = 13; 
    %Size of the figure 

    xLeft = (21-xSize)/2;
    yTop = (30-ySize)/2; 
    %Coordinates to center the figure on A4-paper
    set(gcf,'PaperPosition',[xLeft yTop xSize ySize])
    %This command sets the position and size of the figure on the paper to the desired values. 
    set(gcf,'Position',[0.5 0.5 xSize*50 ySize*50]) 
    set(gcf, 'Color', 'w');

%% Parameter Initialization:

duration=5000;  % duration in ms
dt=0.1;         % simulation time step.
tau=50;         % Filter time for the input. 
tRef=5;         % Refractory period for the spike trains. 
nn=100;         % Number of spiketrains we seek to create later. 
spikebin=5;     % Number of ms per PSTH bin.

Timevector=(0.1:dt:duration);               % A vector of time in ms, in steps of dt.
WhiteNoise=rand(1,length(Timevector))-0.5;  % uniform white noise drawn from +/- 0.5 as long as the time vector.
FilteredWhiteNoise=WhiteNoise.*0;           % an empty vector which we will use to create the time-filtered input.
SpikeTrains=zeros(nn,length(Timevector));   %A Matrix that will hold all spiketrains.
PloTrains=SpikeTrains;                      % This is just a plotting variable to oercome a screen resolution problem in matlab.

avetrain=0;     % A counter to calculate the average firing rate.
tslt=0;         % (== t(ime)s(ince)l(ast)(t)oggle (this serves as a Boolean for the sparsification of the input signal.

tsls=zeros(nn,1);                               % (== t(ime)s(ince)l(ast)(s)pike (to keep track of the refractory period of each spike train)
BinnedSpikeTrains=zeros(1,duration/spikebin);   % a vector to create a PSTH with binwidth ?spikebin? from the spike trains.

%% Making the time-filtered white noise signal:

for t=2:duration/dt FilteredWhiteNoise(t) = WhiteNoise (t) - ...
            (WhiteNoise (t) - FilteredWhiteNoise(t-1))*exp(-dt/tau);

%% This routine changes the signal trace ?FilteredWhiteNoise? by a ?exp(-dt/tau)? fraction of the difference between the signal and a random number.

%Normalize to a maximum value of 1.

%% Plotting:

plot(Timevector, FilteredWhiteNoise) 
axis([0 duration -1 1]) 
x=sprintf('Time Filtered White Noise (FWN)'); 
title (x)

%% Normalize and Rectify:

FilteredWhiteNoise=FilteredWhiteNoise.*(500*dt/1000); % Normalizes the trace to a peak value of 500Hz*dt (=0.05).
FilteredWhiteNoise(FilteredWhiteNoise<0)=0; %Sets all negative values of ?FilteredWhiteNoise? to 0.

%% Plotting:

    hold on
    plot(Timevector,FilteredWhiteNoise, 'b', 'LineWidth', 1.1)

%% Sparsifieing the Input Signals:

% This routine goes through the signal trace and deletes entire ?activity bumps? if certain conditions are fullfilled: 
toggle = 0; 

for d=1:duration/dt-1
    % Routine becomes active (sets toggle == 1) if the signal is ==0, and the toggle is off (==0) and has been off for at least 1 ms:
    if(FilteredWhiteNoise(d)==0 && toggle==0 && (d-tslt>10))
        toggle=1; % toggle set 
        tslt=d; % ?refractory? for toggle is set
    % If routine active, every signal value is set to zero:
    if (toggle==1)
        FilteredWhiteNoise(d) = 0; % If routine has been active for longer than 0.5 ms, and the signal is 0, routine becomes inactive:    
        if (FilteredWhiteNoise(d+1)==0 && (d-tslt>5)) 

%% Plotting:
    hold on 
    plot(Timevector, FilteredWhiteNoise, 'r')
    axis([0 duration -0.005 0.05]) 
    title ('Rectified & callibrated (blue) and sparsened (red) FWN')

%% Adding background firing rate:


% This is adjusted so that without any FilteredWhiteNoise the firing rate is 5 Hz*dt (0.0005).

%% Creating 100 spike trains:
for i=1:nn 
    for t=1:duration/dt
        if (tsls (i) <= 0) % Allows potential spike if refractory period has subsided
                SpikeTrains (i,t) = 1;%Firesifrandomvariable<?FilteredWhiteNoise?. 
                tsls (i) = tRef;% Sets the absolute refractory period.
                avetrain=avetrain+1;% Counts the total number of spikes.
                if(duration/dt-t>25)% This is just a plotting routine. 
                    PloTrains (i,t:t+25)=1;%(Spike is elongated for plotting.)
            tsls (i)=tsls (i) -dt;% subtracts dt from refractory counter if it is still >0
avetrain=avetrain/(nn*duration/1000); %Calculates the average firing rate in Hz.

%% Plotting:
    title ('100 Spiketrains')

%% Recording a PSTH / Binned Input rate:

% This bins the spikes into bins and calculates the instantaneous firing rate in Hz.
for i=1:(duration/spikebin)-1 

BinnedSpikeTrains= (BinnedSpikeTrains*(1000/spikebin))/nn;

%% Plotting:
    x=sprintf('Average input rate for 1 excitatory channel, \%3.2f Hz, peak \%3.2f Hz', avetrain, max(BinnedSpikeTrains));
    title (x)

%%End of code.

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