function Popt=findparam
clear,
close all
%Parameters
Tmax=100; %Time
of the simulation
Npoints=40; %Number
of points available. We assume for the tests that they are regularly distant.
x=1:Tmax/Npoints:Tmax;%Definition of the
inducer vector.
%The
following function provides a Hill function, given a X vector and
%some
parameter that characterizes it.
function y= Hill(x,K,Vmax,n)
l=length(x);
for i=1:l
if K<0
s(i)=K; else s(i)=x(i); end
y(i)=(Vmax*(s(i)^n))/((x(i)^n)+(K^n));
end
end
%Then, we want to introduce some noise in the
data obtained, in order to
%simulate biological results.
function y = NoisyHill(x,K,Vmax,n)
y=Hill(x,K,Vmax,n);
for i=1:length(x)
y(i)=random('normal',y(i),Vmax/20);
end
end
%Finally, we create a 'noisy Hill' vector that
will be considered as
%biological data.
function set = genset
K=30;
Vmax=2;
n=3;
set=NoisyHill([1:Tmax/Npoints:Tmax],K,Vmax,n);
end
set=genset();
%The
heart of the problem is to minimize the distance between a
%deterministic Hill function
and the noisy one obtained. 'Toopt' is
%just the
criteria to minimize.
function y = toopt(x,P)
y=Hill(x,10*P(1),P(2),P(3))-set;
end
%These lines use a Matlab function to carry out
the optimization process
options=optimset('LevenbergMarquardt','on','TolX',1e-10,'MaxFunEvals',1e7,'TolFun',1e-5);
Popt=lsqnonlin(@(P)toopt(x,P),[0.1,1,1],[0,0,0],[5,10,10],options);
Popt=Popt(:);
%In order to see the results, we plot both the noisy curve and the
%estimated one.
plot(set)
hold on
plot(Hill(x,10*Popt(1),Popt(2),Popt(3)
),'r');
legend('Experimental
Hill function','Estimation of the experimental hill function');
gtext('NPoints=40,
Standard Deviation=1/10');
xlabel('Concentration of X');
ylabel('Rate of Y
production');
end
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