I don’t know what function you used to fit your data, but I would generate the fit (or use only the data) for a range of x between about 250 and 500, and then use interp1 but with the arguments reversed from the usual:
yq = [0.1, 0.3, 0.5, 0.8];
xq = interp1(ydata, xdata, yq);
The reason for restricting the data to that range is due to the interp1 requirement that the data be monotonically increasing (in ‘ydata’ here), and it is not over the entire range. So you must restrict it to that range of x if you want it to work with interp1.