Modeling hebbian and homeostatic plasticity (Toyoizumi et al. 2014)

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Accession:180791
"... We propose a model in which synaptic strength is the product of a synapse-specific Hebbian factor and a postsynaptic- cell-specific homeostatic factor, with each factor separately arriving at a stable inactive state. This model captures ODP dynamics and has plausible biophysical substrates. We confirm model predictions experimentally that plasticity is inactive at stable states and that synaptic strength overshoots during recovery from visual deprivation. ..."
Reference:
1 . Toyoizumi T, Kaneko M, Stryker MP, Miller KD (2014) Modeling the dynamic interaction of Hebbian and homeostatic plasticity. Neuron 84:497-510 [PubMed]
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Model Information (Click on a link to find other models with that property)
Model Type: Realistic Network;
Brain Region(s)/Organism:
Cell Type(s): Neocortex V1 L2/6 pyramidal intratelencephalic GLU cell;
Channel(s):
Gap Junctions:
Receptor(s):
Gene(s):
Transmitter(s):
Simulation Environment: MATLAB;
Model Concept(s): Development; Homeostasis; Hebbian plasticity;
Implementer(s):
Search NeuronDB for information about:  Neocortex V1 L2/6 pyramidal intratelencephalic GLU cell;
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Toyoizumi_etal_2014
readme.html
screenshot.png
twofm.m
                            
function twofm()
% function twofm()
% A code used to simulate the two-factor model of OD plasticity 
% March 2015 by Taro Toyoizumi
%
% Reference:
% Toyoizumi T, Kaneko M, Stryker MP, Miller KD (2014)
% Modeling the dynamic interaction of hebbian and homeostatic plasticity.
% Neuron 84:497-510

%%% Parameters %%%
rcontra=.62; %ratio of contra-eye neurons
P.N.total=500; %total #neurons 
P.N.contra=round(rcontra*P.N.total); %#contra-eye neurons 
P.N.ipsi=P.N.total-P.N.contra; %#ipsi-eye neurons 
P.Input.mu=1.; %baseline firing rate
P.Input.BE=.5; %between-eye correlation
P.Input.MD=.5; %MD factor
P.Input.L=.2; %input correlation width
P.th.corr=.6; %constant threshold
P.y0=1.; %homeostatic setpoint
P.rhom=.7; %minimum value of Hebbian factor
P.rhoM=1.; %maximum value of Hebbian factor
P.tau.rho=.2; %Hebbian time-constant (day) 
P.tau.Hh=4.; %homeostatic hidden averaging time (day) 
P.T.wu=50; %warm-up (day)  
P.T.baseline=1; %warm-up (day)  
P.T.MD=7; %MD period (day)  
P.T.recovery=3; %recovery period (day)  
P.Hfun = @(x) max(1,x); 
P.Hhfun = @(x) (1+tanh(x-1)).*(x>1.05);
flag_trk=1;
flag_tnf=1;
flag_nmda=1;

%%% Simulation %%%
stages=fieldnames(P.T);
[Mu,Q,S]=InputStat(P.N,P.Input,0);

Init.time=-P.T.wu;
Init.rho=P.rhom+(P.rhoM-P.rhom)*[abs((1:P.N.contra)'-.5*P.N.contra)<.25*P.N.contra; abs((1:P.N.ipsi)'-.5*P.N.ipsi)<.25*P.N.ipsi];
Init.Hh=0;
Init.H=1;
    
Flags(1)=struct('MD',0,'Trk',1,'TNF',1,'NMDA',1);
Flags(2)=struct('MD',0,'Trk',1,'TNF',flag_tnf,'NMDA',1);
Flags(3)=struct('MD',1,'Trk',flag_trk,'TNF',flag_tnf,'NMDA',flag_nmda);
Flags(4)=struct('MD',0,'Trk',flag_trk,'TNF',flag_tnf,'NMDA',1);
    
Out0=PlastSim(Init,S,Flags(1),P,stages{1}); %warm-up
Hist=FinalValues(Out0);
for i=2:length(stages)
    disp(stages{i});
    Out=PlastSim(FinalValues(Hist),S,Flags(i),P,stages{i});
    Hist=AppendStruct(Hist,Out);
end

%%% Plotting %%%
FS=15;
Hist.time=Hist.time-P.T.baseline;
[Time,Ind]=meshgrid(Hist.time,1:P.N.total);
figure(1); clf;

% panel 1
subplot(2,3,1); 
pcolor(Time,Ind,Hist.w); cb=colorbar; shading flat;
set(gca,'fontsize',FS,'xtick',[0,P.T.MD,P.T.MD+P.T.recovery],'ytick',[1,round(.5*P.N.contra),P.N.contra,P.N.contra+round(.5*P.N.ipsi),P.N.total],'yticklabel',{'-','C','-','I','-'});
title(cb,'w'); xlabel('time (day) '); ylabel('index');

% panel 2
subplot(2,3,2); 
pcolor(Time,Ind,Hist.rho); shading flat; cb=colorbar; 
set(gca,'fontsize',FS,'xtick',[0,P.T.MD,P.T.MD+P.T.recovery],'ytick',[1,round(.5*P.N.contra),P.N.contra,P.N.contra+round(.5*P.N.ipsi),P.N.total],'yticklabel',{'-','C','-','I','-'});
title(cb,'r'); xlabel('time (day) '); ylabel('index');

% panel 3
subplot(2,3,3); 
plot(Hist.time,Hist.ODI,'k-','linewidth',2);
set(gca,'fontsize',FS,'xtick',[0,3,P.T.MD,P.T.MD+P.T.recovery]); xlim([-P.T.baseline,P.T.MD+P.T.recovery]); grid on;
xlabel('time (day) '); ylabel('ODI'); ylim([0 .4]);

% panel 4
subplot(2,3,4); 
indC=round(.5*P.N.contra);
indI=P.N.contra+round(.5*P.N.ipsi);
plot(Hist.time,Hist.resp(1,:)./Hist.resp(1,1),'r-',Hist.time,Hist.resp(2,:)./Hist.resp(2,1),'b-','linewidth',2); grid on;
set(gca,'fontsize',FS,'xtick',[0,3,P.T.MD,P.T.MD+P.T.recovery]); xlim([-P.T.baseline,P.T.MD+P.T.recovery]); 
ylim([.6,1.4]);
xlabel('time (day) '); ylabel('response ');

% panel 5
subplot(2,3,5); 
plot(Hist.time,Hist.Hh,'g-',Hist.time,Hist.H,'k-','linewidth',2); xlim([-P.T.baseline,P.T.MD+P.T.recovery]); 
set(gca,'fontsize',FS,'xtick',[0,3,P.T.MD,P.T.MD+P.T.recovery]); grid on;
xlabel('time (day) '); ylabel('H, h'); ylim([-.02,1.5]); 
    
% panel 6
subplot(2,3,6);
plot(Hist.time,Hist.y,'k-','linewidth',2);
set(gca,'fontsize',FS,'xtick',[0,3,P.T.MD,P.T.MD+P.T.recovery]); xlim([-P.T.baseline,P.T.MD+P.T.recovery]); grid on;
xlabel('time (day) '); ylabel('y'); ylim([.5,1.5]);

%%% Functions %%%
function CopyStruct(In)
% copy fileds of a structure array to local variables
flds=fieldnames(In);
for i=1:length(flds)
    assignin('caller', flds{i}, In.(flds{i}));
end

function Out=FinalValues(In)
% extract the final part of structure
flds=fieldnames(In);
for i=1:length(flds)
    Out.(flds{i})=In.(flds{i})(:,end);
end

function Out=AppendStruct(In1,In2)
% append In2 to In1
flds=fieldnames(In1);
for i=1:length(flds)
    Out.(flds{i})=[In1.(flds{i}), In2.(flds{i})];
end

function Out=OutSub(In1,In2)
% outer product of the subtraction of two vectors 
if size(In1,1)<size(In1,2); In1=In1'; end;
if size(In2,1)<size(In2,2); In2=In2'; end;
Out=In1*ones(size(In2'))-ones(size(In1))*In2';

function [Mu,Q,S]=InputStat(N,Input,MDflag)
% generate input mean vector and covariance matrix
CopyStruct(Input);
F=@(x) 1./(1+exp(3*(x-1)));
muC=mu*(MD*(MDflag==1)+1*(MDflag~=1));
muI=mu*(MD*(MDflag==2)+1*(MDflag~=2));
axC=transpose(linspace(0,1,N.contra));
axI=transpose(linspace(0,1,N.ipsi));
Mu=[muC*ones(size(axC)); muI*(ones(size(axI)))];
QCC=muC^2*exp(-.5*OutSub(axC,axC).^2/L^2)/sqrt(2*pi*L^2);
QII=muI^2*exp(-.5*OutSub(axI,axI).^2/L^2)/sqrt(2*pi*L^2);
QCI=BE*muC*muI*exp(-.5*OutSub(axC,axI).^2/L^2)/sqrt(2*pi*L^2);
Q=[QCC,QCI; QCI',QII];
S=F([(axC-.5).^2; (axI-.5).^2]./L^2);
S=S./sum(S);
Nz=randn(N.total,N.total); 
Q=Q+(Nz+Nz'); 

function Hist=PlastSim(V,S,Flags,P,stage)
% simulation the two-factor rule of plasticity
TL=@(x) x.*(x>0);
N=P.N.total;
X0=[V.rho; V.Hh]; %initialization
[Mu,Q]=InputStat(P.N,P.Input,Flags.MD); %acquire input statistics
[T,X]=ode45(@(t,X) PlastRule(t,X,Flags,P,Mu,Q,S),V.time(end)+[0,P.T.(stage)],X0);
X=transpose(X);

Hist.time=transpose(T(2:end));
Hist.rho=X(1:N,2:end); 
Hist.Hh=X(end,2:end);
Hist.H=P.Hfun(X(end,2:end));
if Flags.TNF==0; Hist.H=ones(size(X(end,2:end))); end;
Hist.w=Hist.rho.*(ones(N,1)*Hist.H).*(S*ones(size(Hist.time)));
Hist.y=Mu'*Hist.w;
Hist.resp=[sum(Hist.w(1:P.N.contra,:)); sum(Hist.w(P.N.contra+1:P.N.total,:))];
Hist.ODI=(Hist.resp(1,:)-Hist.resp(2,:))./(Hist.resp(1,:)+Hist.resp(2,:));

function dX=PlastRule(t,X,Flags,P,Mu,Q,S)
% dynamical equations used in PlastSim
TL = @(x) x.*(x>0); %threshold-linear function
N=P.N.total;
rho=X(1:N);
Hh=X(end);
H=P.Hfun(Hh);
if Flags.TNF==0; H=1; end;
w=H*rho.*S;
y=Mu'*w;
Corr=Q*w-P.th.corr;

HON=(Flags.NMDA)||(t<4);
dX=zeros(N+1,1);
dX(1:N)=HON*(Flags.Trk*TL(P.rhoM-rho).*TL(Corr)-TL(rho-P.rhom./sqrt(H)).*TL(-Corr))/P.tau.rho;
dX(end)=(-Hh+P.Hhfun(H*P.y0/y))/P.tau.Hh;