The activity phase of postsynaptic neurons (Bose et al 2004)

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Accession:45513
We show, in a simplified network consisting of an oscillator inhibiting a follower neuron, how the interaction between synaptic depression and a transient potassium current in the follower neuron determines the activity phase of this neuron. We derive a mathematical expression to determine at what phase of the oscillation the follower neuron becomes active. This expression can be used to understand which parameters determine the phase of activity of the follower as the frequency of the oscillator is changed. See paper for more.
Reference:
1 . Bose A, Manor Y, Nadim F (2004) The activity phase of postsynaptic neurons in a simplified rhythmic network. J Comput Neurosci 17:245-61 [PubMed]
Model Information (Click on a link to find other models with that property)
Model Type: Realistic Network;
Brain Region(s)/Organism: Stomatogastric ganglion;
Cell Type(s): Abstract Morris-Lecar neuron;
Channel(s): I A;
Gap Junctions:
Receptor(s):
Gene(s):
Transmitter(s):
Simulation Environment: XPP; MATLAB;
Model Concept(s): Activity Patterns; Bursting; Temporal Pattern Generation; Oscillations; Simplified Models;
Implementer(s): Nadim, Farzan [Farzan at andromeda.Rutgers.edu]; Bose, Amitabha [bose at njit.edu]; Lewis, Timothy [tlewis at cns.nyu.edu];
Search NeuronDB for information about:  I A;
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activityphase
readme.txt
DBdep+A.ode
DBdep+A.ode.set
DBjcns1.m
DBjcns2.m
DBjcns3.m
                            
%%  THIS IS FOR TA CONSTANT WITH A-CURRENT
clear;

global x1 y gsyn ta tb c1 c2 c3 tk tw tmed tlo c4 ga c5
global r1 r2 r3 
global z2

xmin=10.0;
xmax=1000.0;
dx=5.0;
x=[xmin:dx:xmax];
k=length(x);

% parameters
c1=4.0;
c2=4.6;
c3=3.0;
ta=400.0;
tb=5.0;
tk=125.0;
tw=15.0;
gsyn=4.0;
y=5.0;
tmed=1200.0;
tlo=465.0;
c4=1.0;
ga=3.5;
c5=1.0;
r1=5.0;
r2=0.1;
r3=5.0;

% initial guess
z2=2.0;
z4=5.0;

% find tf for different x
for i=1:k
   x1=x(i);
   z2=fzero('DBjcns2',z2);
   tf(i)=z2;
%   delt(i)=tmed*log((1-exp(-z2/tlo))/c4);
    z3=ga*(1.0-exp(-z2/tlo))/c4;
%   z3=(1.0-exp(-z2/tlo))/c4;
%   z4=ga*((1-exp(-z2/tlo))/c4);
    z4=fzero('DBjcns3',z4); 
    delt(i)=0.0;
%   if (z3 > 1.0) delt(i)=tmed*log(z4);
    if (z3 > 1.0) delt(i)=z4;
    end;
%      else {delt(i)=0.0};

%  delt(i)=tmed*log(z3);

% % checks solutions graphically ...    
%     t=[0:0.01:1000.0];
%     do=(1-exp(-x1/ta))/(1-exp(-x1/ta)*exp(-y/tb));
%	  	 gpeak=gsyn*do;
%		 tfo=(gpeak*c1*exp(-t/tk)+c2*exp(-t/tw)-c3);
%		 clf;
%     plot(t,tfo);
%     hold on
%     plot([0,1000.0],[0,0]);
%     z2
%     pause(0.1);
end;

% plot phase vs period
period=x+y;
%phase=(tf+delt)./(y+x);
phase=(tf+delt)./period;
figure(1)
%clf;
plot(period,phase,'linewidth',2);
xlabel('period','fontsize',14);
ylabel('phase','fontsize',14);

% plot gpeak vs period
%do=(1-exp(-x./ta))./(1-exp(-x./ta)*exp(-y/tb));
%gpeak=gsyn*do;
%figure(2)
%clf;
%plot(period,gpeak,'linewidth',2);
%xlabel('period','fontsize',14);
%ylabel('gpeak','fontsize',14);

% plot ta vs period
%figure(3)
%clf;
%plot(period,delt,'linewidth',2);
%xlabel('period','fontsize',14);
%ylabel('tf','fontsize',14);

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