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MultiMovie.m
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MultiMovie.m
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% "Capturing the bursting dynamics of a two-cell inhibitory network
% using a one-dimensional map"
% Victor Matveev (1), Amitabha Bose (1), Farzan Nadim(1,2)
% (1) Dept Math Sci, NJIT (2) Dept Bio Sci, Rutgers-Newark
%
% Multistable bursting (Figs. 1, 10 and 11)
% February 3, 2007
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
global gbarsyn gtbar Vh;
% List of initial conditions for different bursting states
ICS(1,1:8) = [-23.1 -54.1 0.00104 0 0.0855 0.111 0.107 0 ];
ICS(2,1:8) = [-38.7 -56.9 0.00848 0 0.122 0.0774 0.303 0 ];
ICS(3,1:8) = [-58.3 -34.1 0 0.425 0.0951 0.126 0 0.647 ];
ICS(4,1:8) = [-56 5.9 0 0.58 0.161 0.0958 0 0.916 ];
ICS(5,1:8) = [-58.1 -18.6 0 0.591 0.137 0.121 0 0.78 ];
SN = 0;
while SN < 7 || SN > 11
SN = input('*** How many spikes per burst? (7, 8, 9, 10 or 11):_');
end;
IC = ICS(SN-6,:);
Period = 50;
twindow = Period * 1.2;
T = 2 *(Period + twindow);
figure(1); set(1, 'position', [250, 500, 640, 320]);
options = [];
options = odeset(options,'RelTol',1e-4);
Params = [1.1 1.38 -52 1 0.2 100 20 -3];
[t,y] = ode45(@burstODE, [0 T], IC, options, Params);
Vinterval = [-65:2:30];
Yw = 0.5*(1+tanh((Vinterval+8)/6));
i = find(t>twindow/2, 1);
while t(i) < T - twindow/2;
i = i + 6;
subplot('position',[0.1 0.15 0.45 0.78]);
hold off;
plot(Vinterval, Yw, 'b-', 'linewidth', 2);
xlabel('V','fontsize',14); ylabel('w','fontsize',14);
hold on;
plot([Vh Vh], [-0.1 0.8], 'r--', 'linewidth', 2);
V1 = y(i,1); w = y(i,3);
plot(V1, w,'om', 'linewidth', 2);
V2 = y(i,2); w = y(i,4);
plot(V2, w,'ok', 'linewidth', 2);
ix = y(i,5); s = y(i,8);
Y = Vnullcline(Vinterval, V1, ix, s);
plot(Vinterval, Y, '-m', 'linewidth', 2);
ix = y(i,6); s = y(i,7);
Y = Vnullcline(Vinterval, V2, ix,s);
plot(Vinterval, Y, '-k', 'linewidth', 2);
axis([-65 30 -0.1 0.7]);
title(['\bf Inhibitory network with T-currents: ', num2str(SN), '-spike burst']);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
subplot('position', [0.6 0.6 0.37 0.25]);
hold off;
tt = t - t(i) + twindow/2;
vmin = min(y(:,1))*1.1; vmax = max(y(:,1))*1.1;
plot([twindow/2 twindow/2], [vmin vmax], 'y-', 'linewidth', 2); hold on;
plot([0 twindow], [Vh Vh], 'b-', 'linewidth', 2);
plot(tt,y(:,1),'m-','linewidth',1);
plot(tt,y(:,2),'k-','linewidth',1);
axis([0 twindow vmin vmax]);
title('Voltage: V_1(t), V_2(t)','fontsize',12);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
hmax = max(y(:,5))*1.1;
subplot('position', [0.6 0.15 0.37 0.25]);
hold off;
tt = t - t(i) + twindow/2;
plot([twindow/2 twindow/2], [0 hmax], 'y-', 'linewidth', 2);
hold on;
plot(tt,y(:,5),'m-','linewidth',1);
plot(tt,y(:,6),'k-','linewidth',1);
axis([0 twindow 0 hmax]);
title('Inactivation: h_1(t), h_2(t)','fontsize',12);
xlabel('time (ms)', 'fontsize', 12);
drawnow;
end;