What you mean by y(1)? That you have data only for the first variable y1? Your equations seem to be coupled, so if you optimize all the parameters for y1, the other yX will also have a reasonable result based on your data. What you can do then is to have all parameters as optimization variables and define a cost function equals to the difference between the integration and your experimental data. A general code for this problem would be something like this:
function cost = opt(x,yexperimental)
par1=x(1);
par2=x(2);
...
% Integrate system
[t,y] = ode45(@(t,y)YourOdeFunction(t,y,par1,par2,par3,par4),tspan,y0)
...
% Calculate error
cost = rms(y-yexperimental)
end
%% Run optimizer
...
f = @(x)opt(x,yexperimental);
[par,fval] = fminsearch(f,x0)
