  When protein stability is measured by denaturant induced unfolding the linear
extrapolation method is usually used to analyse the data. This method is based
on the observation that the change in Gibbs free energy associated with
unfolding, $\Delta_rG$, is often found to be a linear function of the
denaturant concentration, $D$. The free energy change of unfolding in the
absence of denaturant, $\Delta_rG_0$, is estimated by extrapolation from this
linear relationship. Data analysis is generally done by nonlinear least-squares
regression to obtain estimates of the parameters as well as confidence
intervals. We have compared different methods for calculating confidence
intervals of the parameters and found that a simple method based on linear
theory gives as good, if not better, results than more advanced methods. We
have also compared three different parameterizations of the linear
extrapolation method and show that one of the forms, $\Delta_rG(D) =
\Delta_rG_0 - mD$, is problematic since the value of $\Delta_rG_0$ and that of
the $m$-value are correlated in the nonlinear least-squares analysis. Parameter
correlation can in some cases cause problems in the estimation of
confidence-intervals and -regions and should be avoided when possible. Two
alternative parameterizations, $\Delta_rG(D) = -m(D-D_{50})$ and $\Delta_rG(D)
= \Delta_rG_0(1-D/D_{50})$, where $D_{50}$ is the midpoint of the transition
region show much less correlation between parameters.
