Below is an example that does exactly what you are describing. Save it into a file and run it. First I just made some sample data, and then I fit your equations to it, getting both K1 and K2, as well as initial conditions on the data.
function fitdata
% True Values
[K1,K2,A0,B0,C0] = deal(3.5,4.2,1,2,3);
[T,Y0] = ode45(@(t,y)[-(K1+K2)*y(1); K1*y(1); K2*y(1)],[0:0.005:1],[A0;B0;C0]);
Ymeas = Y0 + 0.1*randn(size(Y0));
figure;
plot(T,Ymeas);
hold on;
h = plot(T,nan*Ymeas,'k','linewidth',2);
minERR = Inf;
opts = optimset('fminunc');
opts.LargeScale = 'off';
Xest = fminunc(@(X)objfun(X),[0;0;0;0;0],opts);
Xest = num2cell(Xest);
[K1,K2,A0,B0,C0] = deal(Xest{:}),
legend({'A','B','C'});
function ERR = objfun(X);
X = num2cell(X);
[K1,K2,A0,B0,C0] = deal(X{:});
[T,Yest] = ode45(@(t,y)[-(K1+K2)*y(1); K1*y(1); K2*y(1)],[0:0.005:1],[A0;B0;C0]);
ERR = sum((Ymeas(:) - Yest(:)).^2);
if ERR < minERR
minERR = ERR;
for n = 1:3; set(h(n),'Ydata',Yest(:,n)); end
drawnow;
end;
end;
end
