Fit data to a hill equation using lsqnonlin

Hi guys,

I'm trying to fit some data to a hill equation. My X-Axis:

    Agonist = [0.1 0.5 1 5 10 19 50 100 114 500 1000 2000];

My Y-Axis:

    atRA = [0 0 7 15 30 50 58 80 83 87 90 90];

My function:

    function [F] = hill_fit(x,Emax,EC50)
    num = Emax*x;
    denom = EC50+x
    F = num./denom
    end

My fitting code:

    EMax = 90;
    EC50 = 19;
    x = lsqnonlin(@hill_fit,Agonist,Emax,EC50,atRA);

However this gives me a shed load of warmings so I don't think its doing what I want it to. In essence all I want to do is fit the data to the hill equation, can anybody help?

Thanks

Answer 1

[Star Strider]

I don’t recognise this particular Hill equation (there are several), but that aside, estimating your parameters and plotting them is relatively straightforward:

Agonist = [0.1 0.5 1 5 10 19 50 100 114 500 1000 2000];
atRA = [0 0 7 15 30 50 58 80 83 87 90 90];

% MAPPING: Emax = b(1),  EC50 = b(2)
hill_fit = @(b,x)  b(1).*x./(b(2)+x);

b0 = [90; 19];                                  % Initial Parameter Estimates

B = lsqcurvefit(hill_fit, b0, Agonist, atRA);

AgVct = linspace(min(Agonist), max(Agonist));   % Plot Finer Resolution

figure(1)
plot(Agonist, atRA, 'bp')
hold on
plot(AgVct, hill_fit(B,AgVct), '-r')
hold off
grid
xlabel('Agonist')
ylabel('atRA')
legend('Data', 'Hill Equation Fit', 'Location','SE')

If you’re doing curve-fitting, it’s easiest to use the lsqcurvefit function. It uses lsqnonlin but is specifically designed to make curve-fitting straightforward.